LMFDB - Embedded newform 3549.2.a.t.1.3

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:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.81361$ 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)

$f(q)$	$=$	$q+2.81361 q^{2} -1.00000 q^{3} +5.91638 q^{4} +1.28917 q^{5} -2.81361 q^{6} +1.00000 q^{7} +11.0192 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.81361 q^{2} -1.00000 q^{3} +5.91638 q^{4} +1.28917 q^{5} -2.81361 q^{6} +1.00000 q^{7} +11.0192 q^{8} +1.00000 q^{9} +3.62721 q^{10} -4.20555 q^{11} -5.91638 q^{12} +2.81361 q^{14} -1.28917 q^{15} +19.1708 q^{16} +1.62721 q^{17} +2.81361 q^{18} +6.33804 q^{19} +7.62721 q^{20} -1.00000 q^{21} -11.8328 q^{22} -2.71083 q^{23} -11.0192 q^{24} -3.33804 q^{25} -1.00000 q^{27} +5.91638 q^{28} -4.33804 q^{29} -3.62721 q^{30} +7.49472 q^{31} +31.9008 q^{32} +4.20555 q^{33} +4.57834 q^{34} +1.28917 q^{35} +5.91638 q^{36} -3.42166 q^{37} +17.8328 q^{38} +14.2056 q^{40} +7.62721 q^{41} -2.81361 q^{42} -4.91638 q^{43} -24.8816 q^{44} +1.28917 q^{45} -7.62721 q^{46} +1.08362 q^{47} -19.1708 q^{48} +1.00000 q^{49} -9.39194 q^{50} -1.62721 q^{51} +1.75971 q^{53} -2.81361 q^{54} -5.42166 q^{55} +11.0192 q^{56} -6.33804 q^{57} -12.2056 q^{58} +4.57834 q^{59} -7.62721 q^{60} -5.25443 q^{61} +21.0872 q^{62} +1.00000 q^{63} +51.4147 q^{64} +11.8328 q^{66} -8.67609 q^{67} +9.62721 q^{68} +2.71083 q^{69} +3.62721 q^{70} +6.78389 q^{71} +11.0192 q^{72} -4.07306 q^{73} -9.62721 q^{74} +3.33804 q^{75} +37.4983 q^{76} -4.20555 q^{77} -8.91638 q^{79} +24.7144 q^{80} +1.00000 q^{81} +21.4600 q^{82} +4.33804 q^{83} -5.91638 q^{84} +2.09775 q^{85} -13.8328 q^{86} +4.33804 q^{87} -46.3416 q^{88} -4.54359 q^{89} +3.62721 q^{90} -16.0383 q^{92} -7.49472 q^{93} +3.04888 q^{94} +8.17081 q^{95} -31.9008 q^{96} -11.3275 q^{97} +2.81361 q^{98} -4.20555 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} - 3 q^{3} + 4 q^{4} + 3 q^{5} - 2 q^{6} + 3 q^{7} + 12 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 - 3 * q^3 + 4 * q^4 + 3 * q^5 - 2 * q^6 + 3 * q^7 + 12 * q^8 + 3 * q^9	\( 3 q + 2 q^{2} - 3 q^{3} + 4 q^{4} + 3 q^{5} - 2 q^{6} + 3 q^{7} + 12 q^{8} + 3 q^{9} - 2 q^{10} + 2 q^{11} - 4 q^{12} + 2 q^{14} - 3 q^{15} + 18 q^{16} - 8 q^{17} + 2 q^{18} + 7 q^{19} + 10 q^{20} - 3 q^{21} - 8 q^{22} - 9 q^{23} - 12 q^{24} + 2 q^{25} - 3 q^{27} + 4 q^{28} - q^{29} + 2 q^{30} + 7 q^{31} + 36 q^{32} - 2 q^{33} + 12 q^{34} + 3 q^{35} + 4 q^{36} - 12 q^{37} + 26 q^{38} + 28 q^{40} + 10 q^{41} - 2 q^{42} - q^{43} - 36 q^{44} + 3 q^{45} - 10 q^{46} + 17 q^{47} - 18 q^{48} + 3 q^{49} - 20 q^{50} + 8 q^{51} - 5 q^{53} - 2 q^{54} - 18 q^{55} + 12 q^{56} - 7 q^{57} - 22 q^{58} + 12 q^{59} - 10 q^{60} + 10 q^{61} + 10 q^{62} + 3 q^{63} + 58 q^{64} + 8 q^{66} - 2 q^{67} + 16 q^{68} + 9 q^{69} - 2 q^{70} + 4 q^{71} + 12 q^{72} + 5 q^{73} - 16 q^{74} - 2 q^{75} + 30 q^{76} + 2 q^{77} - 13 q^{79} + 8 q^{80} + 3 q^{81} + 24 q^{82} + q^{83} - 4 q^{84} - 16 q^{85} - 14 q^{86} + q^{87} - 60 q^{88} + 13 q^{89} - 2 q^{90} - 6 q^{92} - 7 q^{93} - 2 q^{94} - 15 q^{95} - 36 q^{96} + 9 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 3 * q^3 + 4 * q^4 + 3 * q^5 - 2 * q^6 + 3 * q^7 + 12 * q^8 + 3 * q^9 - 2 * q^10 + 2 * q^11 - 4 * q^12 + 2 * q^14 - 3 * q^15 + 18 * q^16 - 8 * q^17 + 2 * q^18 + 7 * q^19 + 10 * q^20 - 3 * q^21 - 8 * q^22 - 9 * q^23 - 12 * q^24 + 2 * q^25 - 3 * q^27 + 4 * q^28 - q^29 + 2 * q^30 + 7 * q^31 + 36 * q^32 - 2 * q^33 + 12 * q^34 + 3 * q^35 + 4 * q^36 - 12 * q^37 + 26 * q^38 + 28 * q^40 + 10 * q^41 - 2 * q^42 - q^43 - 36 * q^44 + 3 * q^45 - 10 * q^46 + 17 * q^47 - 18 * q^48 + 3 * q^49 - 20 * q^50 + 8 * q^51 - 5 * q^53 - 2 * q^54 - 18 * q^55 + 12 * q^56 - 7 * q^57 - 22 * q^58 + 12 * q^59 - 10 * q^60 + 10 * q^61 + 10 * q^62 + 3 * q^63 + 58 * q^64 + 8 * q^66 - 2 * q^67 + 16 * q^68 + 9 * q^69 - 2 * q^70 + 4 * q^71 + 12 * q^72 + 5 * q^73 - 16 * q^74 - 2 * q^75 + 30 * q^76 + 2 * q^77 - 13 * q^79 + 8 * q^80 + 3 * q^81 + 24 * q^82 + q^83 - 4 * q^84 - 16 * q^85 - 14 * q^86 + q^87 - 60 * q^88 + 13 * q^89 - 2 * q^90 - 6 * q^92 - 7 * q^93 - 2 * q^94 - 15 * q^95 - 36 * q^96 + 9 * q^97 + 2 * q^98 + 2 * 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 $

$2$	2.81361	1.98952	0.994760	−	0.102237i	$-0.0325999\pi$
$2$	2.81361	1.98952	0.994760	+	0.102237i	$0.0325999\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.91638	2.95819
$5$	1.28917	0.576534	0.288267	−	0.957550i	$-0.406921\pi$
$5$	1.28917	0.576534	0.288267	+	0.957550i	$0.406921\pi$
$6$	−2.81361	−1.14865
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	11.0192	3.89586
$9$	1.00000	0.333333
$10$	3.62721	1.14703
$11$	−4.20555	−1.26802	−0.634011	−	0.773324i	$-0.718592\pi$
$11$	−4.20555	−1.26802	−0.634011	+	0.773324i	$0.718592\pi$
$12$	−5.91638	−1.70791
$13$	0	0
$13$	0	0
$14$	2.81361	0.751968
$15$	−1.28917	−0.332862
$16$	19.1708	4.79270
$17$	1.62721	0.394657	0.197329	−	0.980337i	$-0.436773\pi$
$17$	1.62721	0.394657	0.197329	+	0.980337i	$0.436773\pi$
$18$	2.81361	0.663173
$19$	6.33804	1.45405	0.727024	−	0.686613i	$-0.240903\pi$
$19$	6.33804	1.45405	0.727024	+	0.686613i	$0.240903\pi$
$20$	7.62721	1.70550
$21$	−1.00000	−0.218218
$22$	−11.8328	−2.52275
$23$	−2.71083	−0.565247	−0.282624	−	0.959231i	$-0.591205\pi$
$23$	−2.71083	−0.565247	−0.282624	+	0.959231i	$0.591205\pi$
$24$	−11.0192	−2.24928
$25$	−3.33804	−0.667609
$26$	0	0
$27$	−1.00000	−0.192450
$28$	5.91638	1.11809
$29$	−4.33804	−0.805555	−0.402777	−	0.915298i	$-0.631955\pi$
$29$	−4.33804	−0.805555	−0.402777	+	0.915298i	$0.631955\pi$
$30$	−3.62721	−0.662235
$31$	7.49472	1.34609	0.673046	−	0.739601i	$-0.264986\pi$
$31$	7.49472	1.34609	0.673046	+	0.739601i	$0.264986\pi$
$32$	31.9008	5.63932
$33$	4.20555	0.732092
$34$	4.57834	0.785178
$35$	1.28917	0.217909
$36$	5.91638	0.986064
$37$	−3.42166	−0.562518	−0.281259	−	0.959632i	$-0.590752\pi$
$37$	−3.42166	−0.562518	−0.281259	+	0.959632i	$0.590752\pi$
$38$	17.8328	2.89286
$39$	0	0
$40$	14.2056	2.24609
$41$	7.62721	1.19117	0.595585	−	0.803292i	$-0.296920\pi$
$41$	7.62721	1.19117	0.595585	+	0.803292i	$0.296920\pi$
$42$	−2.81361	−0.434149
$43$	−4.91638	−0.749741	−0.374871	−	0.927077i	$-0.622313\pi$
$43$	−4.91638	−0.749741	−0.374871	+	0.927077i	$0.622313\pi$
$44$	−24.8816	−3.75105
$45$	1.28917	0.192178
$46$	−7.62721	−1.12457
$47$	1.08362	0.158062	0.0790310	−	0.996872i	$-0.474817\pi$
$47$	1.08362	0.158062	0.0790310	+	0.996872i	$0.474817\pi$
$48$	−19.1708	−2.76707
$49$	1.00000	0.142857
$50$	−9.39194	−1.32822
$51$	−1.62721	−0.227855
$52$	0	0
$53$	1.75971	0.241714	0.120857	−	0.992670i	$-0.461436\pi$
$53$	1.75971	0.241714	0.120857	+	0.992670i	$0.461436\pi$
$54$	−2.81361	−0.382883
$55$	−5.42166	−0.731057
$56$	11.0192	1.47250
$57$	−6.33804	−0.839494
$58$	−12.2056	−1.60267
$59$	4.57834	0.596049	0.298024	−	0.954558i	$-0.403672\pi$
$59$	4.57834	0.596049	0.298024	+	0.954558i	$0.403672\pi$
$60$	−7.62721	−0.984669
$61$	−5.25443	−0.672760	−0.336380	−	0.941726i	$-0.609203\pi$
$61$	−5.25443	−0.672760	−0.336380	+	0.941726i	$0.609203\pi$
$62$	21.0872	2.67808
$63$	1.00000	0.125988
$64$	51.4147	6.42683
$65$	0	0
$66$	11.8328	1.45651
$67$	−8.67609	−1.05995	−0.529976	−	0.848012i	$-0.677799\pi$
$67$	−8.67609	−1.05995	−0.529976	+	0.848012i	$0.677799\pi$
$68$	9.62721	1.16747
$69$	2.71083	0.326346
$70$	3.62721	0.433535
$71$	6.78389	0.805099	0.402550	−	0.915398i	$-0.368124\pi$
$71$	6.78389	0.805099	0.402550	+	0.915398i	$0.368124\pi$
$72$	11.0192	1.29862
$73$	−4.07306	−0.476715	−0.238358	−	0.971177i	$-0.576609\pi$
$73$	−4.07306	−0.476715	−0.238358	+	0.971177i	$0.576609\pi$
$74$	−9.62721	−1.11914
$75$	3.33804	0.385444
$76$	37.4983	4.30135
$77$	−4.20555	−0.479267
$78$	0	0
$79$	−8.91638	−1.00317	−0.501586	−	0.865108i	$-0.667250\pi$
$79$	−8.91638	−1.00317	−0.501586	+	0.865108i	$0.667250\pi$
$80$	24.7144	2.76315
$81$	1.00000	0.111111
$82$	21.4600	2.36986
$83$	4.33804	0.476162	0.238081	−	0.971245i	$-0.423482\pi$
$83$	4.33804	0.476162	0.238081	+	0.971245i	$0.423482\pi$
$84$	−5.91638	−0.645530
$85$	2.09775	0.227533
$86$	−13.8328	−1.49163
$87$	4.33804	0.465087
$88$	−46.3416	−4.94003
$89$	−4.54359	−0.481620	−0.240810	−	0.970572i	$-0.577413\pi$
$89$	−4.54359	−0.481620	−0.240810	+	0.970572i	$0.577413\pi$
$90$	3.62721	0.382342
$91$	0	0
$92$	−16.0383	−1.67211
$93$	−7.49472	−0.777166
$94$	3.04888	0.314468
$95$	8.17081	0.838307
$96$	−31.9008	−3.25586
$97$	−11.3275	−1.15013	−0.575066	−	0.818107i	$-0.695024\pi$
$97$	−11.3275	−1.15013	−0.575066	+	0.818107i	$0.695024\pi$
$98$	2.81361	0.284217
$99$	−4.20555	−0.422674
$100$	−19.7491	−1.97491
$101$	14.3033	1.42323	0.711616	−	0.702569i	$-0.247964\pi$
$101$	14.3033	1.42323	0.711616	+	0.702569i	$0.247964\pi$
$102$	−4.57834	−0.453323
$103$	−19.6655	−1.93770	−0.968851	−	0.247645i	$-0.920343\pi$
$103$	−19.6655	−1.93770	−0.968851	+	0.247645i	$0.920343\pi$
$104$	0	0
$105$	−1.28917	−0.125810
$106$	4.95112	0.480896
$107$	2.20555	0.213219	0.106609	−	0.994301i	$-0.466001\pi$
$107$	2.20555	0.213219	0.106609	+	0.994301i	$0.466001\pi$
$108$	−5.91638	−0.569304
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	−15.2544	−1.45445
$111$	3.42166	0.324770
$112$	19.1708	1.81147
$113$	−2.17081	−0.204212	−0.102106	−	0.994774i	$-0.532558\pi$
$113$	−2.17081	−0.204212	−0.102106	+	0.994774i	$0.532558\pi$
$114$	−17.8328	−1.67019
$115$	−3.49472	−0.325884
$116$	−25.6655	−2.38298
$117$	0	0
$118$	12.8816	1.18585
$119$	1.62721	0.149166
$120$	−14.2056	−1.29678
$121$	6.68665	0.607877
$122$	−14.7839	−1.33847
$123$	−7.62721	−0.687723
$124$	44.3416	3.98199
$125$	−10.7491	−0.961433
$126$	2.81361	0.250656
$127$	−0.745574	−0.0661590	−0.0330795	−	0.999453i	$-0.510531\pi$
$127$	−0.745574	−0.0661590	−0.0330795	+	0.999453i	$0.510531\pi$
$128$	80.8591	7.14700
$129$	4.91638	0.432863
$130$	0	0
$131$	−14.5089	−1.26764	−0.633822	−	0.773479i	$-0.718515\pi$
$131$	−14.5089	−1.26764	−0.633822	+	0.773479i	$0.718515\pi$
$132$	24.8816	2.16567
$133$	6.33804	0.549578
$134$	−24.4111	−2.10880
$135$	−1.28917	−0.110954
$136$	17.9305	1.53753
$137$	−4.41110	−0.376866	−0.188433	−	0.982086i	$-0.560341\pi$
$137$	−4.41110	−0.376866	−0.188433	+	0.982086i	$0.560341\pi$
$138$	7.62721	0.649271
$139$	18.9894	1.61066	0.805332	−	0.592825i	$-0.201987\pi$
$139$	18.9894	1.61066	0.805332	+	0.592825i	$0.201987\pi$
$140$	7.62721	0.644617
$141$	−1.08362	−0.0912571
$142$	19.0872	1.60176
$143$	0	0
$144$	19.1708	1.59757
$145$	−5.59247	−0.464429
$146$	−11.4600	−0.948434
$147$	−1.00000	−0.0824786
$148$	−20.2439	−1.66404
$149$	9.42166	0.771853	0.385926	−	0.922530i	$-0.373882\pi$
$149$	9.42166	0.771853	0.385926	+	0.922530i	$0.373882\pi$
$150$	9.39194	0.766849
$151$	16.4111	1.33552	0.667758	−	0.744378i	$-0.267254\pi$
$151$	16.4111	1.33552	0.667758	+	0.744378i	$0.267254\pi$
$152$	69.8399	5.66476
$153$	1.62721	0.131552
$154$	−11.8328	−0.953511
$155$	9.66196	0.776067
$156$	0	0
$157$	−9.51941	−0.759732	−0.379866	−	0.925042i	$-0.624030\pi$
$157$	−9.51941	−0.759732	−0.379866	+	0.925042i	$0.624030\pi$
$158$	−25.0872	−1.99583
$159$	−1.75971	−0.139554
$160$	41.1255	3.25126
$161$	−2.71083	−0.213643
$162$	2.81361	0.221058
$163$	0.745574	0.0583979	0.0291989	−	0.999574i	$-0.490704\pi$
$163$	0.745574	0.0583979	0.0291989	+	0.999574i	$0.490704\pi$
$164$	45.1255	3.52371
$165$	5.42166	0.422076
$166$	12.2056	0.947334
$167$	−3.59247	−0.277994	−0.138997	−	0.990293i	$-0.544388\pi$
$167$	−3.59247	−0.277994	−0.138997	+	0.990293i	$0.544388\pi$
$168$	−11.0192	−0.850146
$169$	0	0
$170$	5.90225	0.452682
$171$	6.33804	0.484682
$172$	−29.0872	−2.21788
$173$	−15.7250	−1.19555	−0.597773	−	0.801665i	$-0.703948\pi$
$173$	−15.7250	−1.19555	−0.597773	+	0.801665i	$0.703948\pi$
$174$	12.2056	0.925300
$175$	−3.33804	−0.252332
$176$	−80.6238	−6.07725
$177$	−4.57834	−0.344129
$178$	−12.7839	−0.958193
$179$	24.9547	1.86520	0.932601	−	0.360910i	$-0.117534\pi$
$179$	24.9547	1.86520	0.932601	+	0.360910i	$0.117534\pi$
$180$	7.62721	0.568499
$181$	10.9411	0.813244	0.406622	−	0.913597i	$-0.366707\pi$
$181$	10.9411	0.813244	0.406622	+	0.913597i	$0.366707\pi$
$182$	0	0
$183$	5.25443	0.388418
$184$	−29.8711	−2.20212
$185$	−4.41110	−0.324311
$186$	−21.0872	−1.54619
$187$	−6.84333	−0.500434
$188$	6.41110	0.467578
$189$	−1.00000	−0.0727393
$190$	22.9894	1.66783
$191$	5.04888	0.365324	0.182662	−	0.983176i	$-0.441529\pi$
$191$	5.04888	0.365324	0.182662	+	0.983176i	$0.441529\pi$
$192$	−51.4147	−3.71053
$193$	−2.74557	−0.197631	−0.0988154	−	0.995106i	$-0.531505\pi$
$193$	−2.74557	−0.197631	−0.0988154	+	0.995106i	$0.531505\pi$
$194$	−31.8711	−2.28821
$195$	0	0
$196$	5.91638	0.422599
$197$	−5.42166	−0.386277	−0.193139	−	0.981171i	$-0.561867\pi$
$197$	−5.42166	−0.386277	−0.193139	+	0.981171i	$0.561867\pi$
$198$	−11.8328	−0.840918
$199$	−20.4111	−1.44690	−0.723452	−	0.690374i	$-0.757446\pi$
$199$	−20.4111	−1.44690	−0.723452	+	0.690374i	$0.757446\pi$
$200$	−36.7824	−2.60091
$201$	8.67609	0.611964
$202$	40.2439	2.83155
$203$	−4.33804	−0.304471
$204$	−9.62721	−0.674040
$205$	9.83276	0.686750
$206$	−55.3311	−3.85510
$207$	−2.71083	−0.188416
$208$	0	0
$209$	−26.6550	−1.84376
$210$	−3.62721	−0.250301
$211$	−14.4842	−0.997130	−0.498565	−	0.866852i	$-0.666140\pi$
$211$	−14.4842	−0.997130	−0.498565	+	0.866852i	$0.666140\pi$
$212$	10.4111	0.715037
$213$	−6.78389	−0.464824
$214$	6.20555	0.424203
$215$	−6.33804	−0.432251
$216$	−11.0192	−0.749759
$217$	7.49472	0.508775
$218$	−28.1361	−1.90561
$219$	4.07306	0.275232
$220$	−32.0766	−2.16261
$221$	0	0
$222$	9.62721	0.646136
$223$	−16.8469	−1.12815	−0.564076	−	0.825723i	$-0.690767\pi$
$223$	−16.8469	−1.12815	−0.564076	+	0.825723i	$0.690767\pi$
$224$	31.9008	2.13146
$225$	−3.33804	−0.222536
$226$	−6.10780	−0.406285
$227$	21.9305	1.45558	0.727790	−	0.685800i	$-0.240548\pi$
$227$	21.9305	1.45558	0.727790	+	0.685800i	$0.240548\pi$
$228$	−37.4983	−2.48338
$229$	5.25443	0.347222	0.173611	−	0.984814i	$-0.444456\pi$
$229$	5.25443	0.347222	0.173611	+	0.984814i	$0.444456\pi$
$230$	−9.83276	−0.648353
$231$	4.20555	0.276705
$232$	−47.8016	−3.13833
$233$	4.07306	0.266835	0.133417	−	0.991060i	$-0.457405\pi$
$233$	4.07306	0.266835	0.133417	+	0.991060i	$0.457405\pi$
$234$	0	0
$235$	1.39697	0.0911281
$236$	27.0872	1.76323
$237$	8.91638	0.579181
$238$	4.57834	0.296770
$239$	2.37279	0.153483	0.0767414	−	0.997051i	$-0.475548\pi$
$239$	2.37279	0.153483	0.0767414	+	0.997051i	$0.475548\pi$
$240$	−24.7144	−1.59531
$241$	−14.9164	−0.960849	−0.480424	−	0.877036i	$-0.659517\pi$
$241$	−14.9164	−0.960849	−0.480424	+	0.877036i	$0.659517\pi$
$242$	18.8136	1.20938
$243$	−1.00000	−0.0641500
$244$	−31.0872	−1.99015
$245$	1.28917	0.0823620
$246$	−21.4600	−1.36824
$247$	0	0
$248$	82.5855	5.24418
$249$	−4.33804	−0.274912
$250$	−30.2439	−1.91279
$251$	−1.08719	−0.0686228	−0.0343114	−	0.999411i	$-0.510924\pi$
$251$	−1.08719	−0.0686228	−0.0343114	+	0.999411i	$0.510924\pi$
$252$	5.91638	0.372697
$253$	11.4005	0.716746
$254$	−2.09775	−0.131625
$255$	−2.09775	−0.131366
$256$	124.676	7.79226
$257$	−16.6167	−1.03652	−0.518259	−	0.855224i	$-0.673420\pi$
$257$	−16.6167	−1.03652	−0.518259	+	0.855224i	$0.673420\pi$
$258$	13.8328	0.861190
$259$	−3.42166	−0.212612
$260$	0	0
$261$	−4.33804	−0.268518
$262$	−40.8222	−2.52200
$263$	−27.0524	−1.66813	−0.834063	−	0.551670i	$-0.813991\pi$
$263$	−27.0524	−1.66813	−0.834063	+	0.551670i	$0.813991\pi$
$264$	46.3416	2.85213
$265$	2.26856	0.139356
$266$	17.8328	1.09340
$267$	4.54359	0.278063
$268$	−51.3311	−3.13554
$269$	7.52946	0.459079	0.229540	−	0.973299i	$-0.426278\pi$
$269$	7.52946	0.459079	0.229540	+	0.973299i	$0.426278\pi$
$270$	−3.62721	−0.220745
$271$	−16.8222	−1.02188	−0.510938	−	0.859618i	$-0.670702\pi$
$271$	−16.8222	−1.02188	−0.510938	+	0.859618i	$0.670702\pi$
$272$	31.1950	1.89147
$273$	0	0
$274$	−12.4111	−0.749782
$275$	14.0383	0.846542
$276$	16.0383	0.965393
$277$	17.4947	1.05116	0.525578	−	0.850745i	$-0.323849\pi$
$277$	17.4947	1.05116	0.525578	+	0.850745i	$0.323849\pi$
$278$	53.4288	3.20445
$279$	7.49472	0.448697
$280$	14.2056	0.848944
$281$	−27.4005	−1.63458	−0.817290	−	0.576227i	$-0.804524\pi$
$281$	−27.4005	−1.63458	−0.817290	+	0.576227i	$0.804524\pi$
$282$	−3.04888	−0.181558
$283$	20.0766	1.19343	0.596716	−	0.802453i	$-0.296472\pi$
$283$	20.0766	1.19343	0.596716	+	0.802453i	$0.296472\pi$
$284$	40.1361	2.38164
$285$	−8.17081	−0.483997
$286$	0	0
$287$	7.62721	0.450220
$288$	31.9008	1.87977
$289$	−14.3522	−0.844246
$290$	−15.7350	−0.923992
$291$	11.3275	0.664029
$292$	−24.0978	−1.41021
$293$	27.0524	1.58042	0.790210	−	0.612836i	$-0.209971\pi$
$293$	27.0524	1.58042	0.790210	+	0.612836i	$0.209971\pi$
$294$	−2.81361	−0.164093
$295$	5.90225	0.343642
$296$	−37.7038	−2.19149
$297$	4.20555	0.244031
$298$	26.5089	1.53562
$299$	0	0
$300$	19.7491	1.14022
$301$	−4.91638	−0.283376
$302$	46.1744	2.65704
$303$	−14.3033	−0.821703
$304$	121.505	6.96881
$305$	−6.77384	−0.387869
$306$	4.57834	0.261726
$307$	20.1708	1.15121	0.575604	−	0.817728i	$-0.304767\pi$
$307$	20.1708	1.15121	0.575604	+	0.817728i	$0.304767\pi$
$308$	−24.8816	−1.41776
$309$	19.6655	1.11873
$310$	27.1849	1.54400
$311$	−6.57834	−0.373023	−0.186512	−	0.982453i	$-0.559718\pi$
$311$	−6.57834	−0.373023	−0.186512	+	0.982453i	$0.559718\pi$
$312$	0	0
$313$	−10.7456	−0.607376	−0.303688	−	0.952772i	$-0.598218\pi$
$313$	−10.7456	−0.607376	−0.303688	+	0.952772i	$0.598218\pi$
$314$	−26.7839	−1.51150
$315$	1.28917	0.0726364
$316$	−52.7527	−2.96757
$317$	−24.6066	−1.38204	−0.691022	−	0.722833i	$-0.742839\pi$
$317$	−24.6066	−1.38204	−0.691022	+	0.722833i	$0.742839\pi$
$318$	−4.95112	−0.277645
$319$	18.2439	1.02146
$320$	66.2822	3.70529
$321$	−2.20555	−0.123102
$322$	−7.62721	−0.425048
$323$	10.3133	0.573850
$324$	5.91638	0.328688
$325$	0	0
$326$	2.09775	0.116184
$327$	10.0000	0.553001
$328$	84.0455	4.64063
$329$	1.08362	0.0597418
$330$	15.2544	0.839729
$331$	−30.6550	−1.68495	−0.842475	−	0.538736i	$-0.818902\pi$
$331$	−30.6550	−1.68495	−0.842475	+	0.538736i	$0.818902\pi$
$332$	25.6655	1.40858
$333$	−3.42166	−0.187506
$334$	−10.1078	−0.553074
$335$	−11.1849	−0.611099
$336$	−19.1708	−1.04585
$337$	−6.50528	−0.354365	−0.177183	−	0.984178i	$-0.556698\pi$
$337$	−6.50528	−0.354365	−0.177183	+	0.984178i	$0.556698\pi$
$338$	0	0
$339$	2.17081	0.117902
$340$	12.4111	0.673086
$341$	−31.5194	−1.70687
$342$	17.8328	0.964285
$343$	1.00000	0.0539949
$344$	−54.1744	−2.92089
$345$	3.49472	0.188149
$346$	−44.2439	−2.37856
$347$	24.3033	1.30467	0.652335	−	0.757931i	$-0.273790\pi$
$347$	24.3033	1.30467	0.652335	+	0.757931i	$0.273790\pi$
$348$	25.6655	1.37582
$349$	−17.7597	−0.950655	−0.475328	−	0.879809i	$-0.657670\pi$
$349$	−17.7597	−0.950655	−0.475328	+	0.879809i	$0.657670\pi$
$350$	−9.39194	−0.502021
$351$	0	0
$352$	−134.160	−7.15077
$353$	−1.94056	−0.103286	−0.0516428	−	0.998666i	$-0.516446\pi$
$353$	−1.94056	−0.103286	−0.0516428	+	0.998666i	$0.516446\pi$
$354$	−12.8816	−0.684651
$355$	8.74557	0.464167
$356$	−26.8816	−1.42472
$357$	−1.62721	−0.0861212
$358$	70.2127	3.71086
$359$	33.6272	1.77478	0.887388	−	0.461023i	$-0.152517\pi$
$359$	33.6272	1.77478	0.887388	+	0.461023i	$0.152517\pi$
$360$	14.2056	0.748698
$361$	21.1708	1.11425
$362$	30.7839	1.61797
$363$	−6.68665	−0.350958
$364$	0	0
$365$	−5.25086	−0.274842
$366$	14.7839	0.772766
$367$	−10.5783	−0.552185	−0.276092	−	0.961131i	$-0.589040\pi$
$367$	−10.5783	−0.552185	−0.276092	+	0.961131i	$0.589040\pi$
$368$	−51.9688	−2.70906
$369$	7.62721	0.397057
$370$	−12.4111	−0.645222
$371$	1.75971	0.0913595
$372$	−44.3416	−2.29901
$373$	−5.47002	−0.283227	−0.141614	−	0.989922i	$-0.545229\pi$
$373$	−5.47002	−0.283227	−0.141614	+	0.989922i	$0.545229\pi$
$374$	−19.2544	−0.995623
$375$	10.7491	0.555083
$376$	11.9406	0.615787
$377$	0	0
$378$	−2.81361	−0.144716
$379$	5.42166	0.278492	0.139246	−	0.990258i	$-0.455532\pi$
$379$	5.42166	0.278492	0.139246	+	0.990258i	$0.455532\pi$
$380$	48.3416	2.47987
$381$	0.745574	0.0381969
$382$	14.2056	0.726819
$383$	−14.1461	−0.722833	−0.361416	−	0.932405i	$-0.617707\pi$
$383$	−14.1461	−0.722833	−0.361416	+	0.932405i	$0.617707\pi$
$384$	−80.8591	−4.12632
$385$	−5.42166	−0.276314
$386$	−7.72496	−0.393190
$387$	−4.91638	−0.249914
$388$	−67.0177	−3.40231
$389$	0.313348	0.0158874	0.00794370	−	0.999968i	$-0.497471\pi$
$389$	0.313348	0.0158874	0.00794370	+	0.999968i	$0.497471\pi$
$390$	0	0
$391$	−4.41110	−0.223079
$392$	11.0192	0.556551
$393$	14.5089	0.731875
$394$	−15.2544	−0.768507
$395$	−11.4947	−0.578362
$396$	−24.8816	−1.25035
$397$	−20.6797	−1.03788	−0.518941	−	0.854810i	$-0.673674\pi$
$397$	−20.6797	−1.03788	−0.518941	+	0.854810i	$0.673674\pi$
$398$	−57.4288	−2.87865
$399$	−6.33804	−0.317299
$400$	−63.9930	−3.19965
$401$	12.7456	0.636484	0.318242	−	0.948010i	$-0.396908\pi$
$401$	12.7456	0.636484	0.318242	+	0.948010i	$0.396908\pi$
$402$	24.4111	1.21752
$403$	0	0
$404$	84.6238	4.21019
$405$	1.28917	0.0640593
$406$	−12.2056	−0.605751
$407$	14.3900	0.713285
$408$	−17.9305	−0.887693
$409$	18.6514	0.922252	0.461126	−	0.887335i	$-0.347446\pi$
$409$	18.6514	0.922252	0.461126	+	0.887335i	$0.347446\pi$
$410$	27.6655	1.36630
$411$	4.41110	0.217584
$412$	−116.349	−5.73209
$413$	4.57834	0.225285
$414$	−7.62721	−0.374857
$415$	5.59247	0.274524
$416$	0	0
$417$	−18.9894	−0.929917
$418$	−74.9966	−3.66820
$419$	3.10831	0.151851	0.0759256	−	0.997113i	$-0.475809\pi$
$419$	3.10831	0.151851	0.0759256	+	0.997113i	$0.475809\pi$
$420$	−7.62721	−0.372170
$421$	−13.4005	−0.653102	−0.326551	−	0.945180i	$-0.605887\pi$
$421$	−13.4005	−0.653102	−0.326551	+	0.945180i	$0.605887\pi$
$422$	−40.7527	−1.98381
$423$	1.08362	0.0526873
$424$	19.3905	0.941685
$425$	−5.43171	−0.263477
$426$	−19.0872	−0.924777
$427$	−5.25443	−0.254279
$428$	13.0489	0.630741
$429$	0	0
$430$	−17.8328	−0.859972
$431$	−9.89220	−0.476491	−0.238245	−	0.971205i	$-0.576572\pi$
$431$	−9.89220	−0.476491	−0.238245	+	0.971205i	$0.576572\pi$
$432$	−19.1708	−0.922356
$433$	0.578337	0.0277931	0.0138966	−	0.999903i	$-0.495576\pi$
$433$	0.578337	0.0277931	0.0138966	+	0.999903i	$0.495576\pi$
$434$	21.0872	1.01222
$435$	5.59247	0.268138
$436$	−59.1638	−2.83343
$437$	−17.1814	−0.821896
$438$	11.4600	0.547579
$439$	23.7350	1.13281	0.566405	−	0.824127i	$-0.308334\pi$
$439$	23.7350	1.13281	0.566405	+	0.824127i	$0.308334\pi$
$440$	−59.7422	−2.84810
$441$	1.00000	0.0476190
$442$	0	0
$443$	−3.86751	−0.183751	−0.0918754	−	0.995771i	$-0.529286\pi$
$443$	−3.86751	−0.183751	−0.0918754	+	0.995771i	$0.529286\pi$
$444$	20.2439	0.960731
$445$	−5.85746	−0.277670
$446$	−47.4005	−2.24448
$447$	−9.42166	−0.445629
$448$	51.4147	2.42911
$449$	−1.68665	−0.0795980	−0.0397990	−	0.999208i	$-0.512672\pi$
$449$	−1.68665	−0.0795980	−0.0397990	+	0.999208i	$0.512672\pi$
$450$	−9.39194	−0.442740
$451$	−32.0766	−1.51043
$452$	−12.8433	−0.604099
$453$	−16.4111	−0.771061
$454$	61.7038	2.89590
$455$	0	0
$456$	−69.8399	−3.27055
$457$	3.83276	0.179289	0.0896445	−	0.995974i	$-0.471427\pi$
$457$	3.83276	0.179289	0.0896445	+	0.995974i	$0.471427\pi$
$458$	14.7839	0.690806
$459$	−1.62721	−0.0759518
$460$	−20.6761	−0.964028
$461$	11.2161	0.522386	0.261193	−	0.965287i	$-0.415884\pi$
$461$	11.2161	0.522386	0.261193	+	0.965287i	$0.415884\pi$
$462$	11.8328	0.550510
$463$	25.8328	1.20055	0.600275	−	0.799794i	$-0.295058\pi$
$463$	25.8328	1.20055	0.600275	+	0.799794i	$0.295058\pi$
$464$	−83.1638	−3.86078
$465$	−9.66196	−0.448062
$466$	11.4600	0.530873
$467$	41.0872	1.90129	0.950644	−	0.310283i	$-0.100424\pi$
$467$	41.0872	1.90129	0.950644	+	0.310283i	$0.100424\pi$
$468$	0	0
$469$	−8.67609	−0.400625
$470$	3.93051	0.181301
$471$	9.51941	0.438631
$472$	50.4494	2.32212
$473$	20.6761	0.950688
$474$	25.0872	1.15229
$475$	−21.1567	−0.970735
$476$	9.62721	0.441263
$477$	1.75971	0.0805715
$478$	6.67609	0.305357
$479$	−2.43580	−0.111294	−0.0556472	−	0.998450i	$-0.517722\pi$
$479$	−2.43580	−0.111294	−0.0556472	+	0.998450i	$0.517722\pi$
$480$	−41.1255	−1.87711
$481$	0	0
$482$	−41.9688	−1.91163
$483$	2.71083	0.123347
$484$	39.5608	1.79822
$485$	−14.6030	−0.663090
$486$	−2.81361	−0.127628
$487$	6.57834	0.298093	0.149046	−	0.988830i	$-0.452380\pi$
$487$	6.57834	0.298093	0.149046	+	0.988830i	$0.452380\pi$
$488$	−57.8993	−2.62098
$489$	−0.745574	−0.0337160
$490$	3.62721	0.163861
$491$	28.3033	1.27731	0.638655	−	0.769493i	$-0.279491\pi$
$491$	28.3033	1.27731	0.638655	+	0.769493i	$0.279491\pi$
$492$	−45.1255	−2.03441
$493$	−7.05892	−0.317918
$494$	0	0
$495$	−5.42166	−0.243686
$496$	143.680	6.45141
$497$	6.78389	0.304299
$498$	−12.2056	−0.546944
$499$	−28.8222	−1.29026	−0.645129	−	0.764073i	$-0.723197\pi$
$499$	−28.8222	−1.29026	−0.645129	+	0.764073i	$0.723197\pi$
$500$	−63.5960	−2.84410
$501$	3.59247	0.160500
$502$	−3.05892	−0.136526
$503$	8.67609	0.386848	0.193424	−	0.981115i	$-0.438041\pi$
$503$	8.67609	0.386848	0.193424	+	0.981115i	$0.438041\pi$
$504$	11.0192	0.490832
$505$	18.4394	0.820541
$506$	32.0766	1.42598
$507$	0	0
$508$	−4.41110	−0.195711
$509$	9.28917	0.411735	0.205868	−	0.978580i	$-0.433998\pi$
$509$	9.28917	0.411735	0.205868	+	0.978580i	$0.433998\pi$
$510$	−5.90225	−0.261356
$511$	−4.07306	−0.180181
$512$	189.072	8.35587
$513$	−6.33804	−0.279831
$514$	−46.7527	−2.06217
$515$	−25.3522	−1.11715
$516$	29.0872	1.28049
$517$	−4.55721	−0.200426
$518$	−9.62721	−0.422995
$519$	15.7250	0.690249
$520$	0	0
$521$	−11.7250	−0.513680	−0.256840	−	0.966454i	$-0.582681\pi$
$521$	−11.7250	−0.513680	−0.256840	+	0.966454i	$0.582681\pi$
$522$	−12.2056	−0.534222
$523$	0.676089	0.0295633	0.0147817	−	0.999891i	$-0.495295\pi$
$523$	0.676089	0.0295633	0.0147817	+	0.999891i	$0.495295\pi$
$524$	−85.8399	−3.74993
$525$	3.33804	0.145684
$526$	−76.1149	−3.31877
$527$	12.1955	0.531244
$528$	80.6238	3.50870
$529$	−15.6514	−0.680495
$530$	6.38283	0.277253
$531$	4.57834	0.198683
$532$	37.4983	1.62576
$533$	0	0
$534$	12.7839	0.553213
$535$	2.84333	0.122928
$536$	−95.6032	−4.12943
$537$	−24.9547	−1.07687
$538$	21.1849	0.913348
$539$	−4.20555	−0.181146
$540$	−7.62721	−0.328223
$541$	0.578337	0.0248647	0.0124323	−	0.999923i	$-0.496043\pi$
$541$	0.578337	0.0248647	0.0124323	+	0.999923i	$0.496043\pi$
$542$	−47.3311	−2.03304
$543$	−10.9411	−0.469527
$544$	51.9094	2.22560
$545$	−12.8917	−0.552219
$546$	0	0
$547$	−0.985867	−0.0421526	−0.0210763	−	0.999778i	$-0.506709\pi$
$547$	−0.985867	−0.0421526	−0.0210763	+	0.999778i	$0.506709\pi$
$548$	−26.0978	−1.11484
$549$	−5.25443	−0.224253
$550$	39.4983	1.68421
$551$	−27.4947	−1.17131
$552$	29.8711	1.27140
$553$	−8.91638	−0.379163
$554$	49.2233	2.09130
$555$	4.41110	0.187241
$556$	112.349	4.76465
$557$	−41.2333	−1.74711	−0.873556	−	0.486725i	$-0.838192\pi$
$557$	−41.2333	−1.74711	−0.873556	+	0.486725i	$0.838192\pi$
$558$	21.0872	0.892692
$559$	0	0
$560$	24.7144	1.04437
$561$	6.84333	0.288925
$562$	−77.0943	−3.25203
$563$	6.91995	0.291641	0.145821	−	0.989311i	$-0.453418\pi$
$563$	6.91995	0.291641	0.145821	+	0.989311i	$0.453418\pi$
$564$	−6.41110	−0.269956
$565$	−2.79854	−0.117735
$566$	56.4877	2.37436
$567$	1.00000	0.0419961
$568$	74.7527	3.13655
$569$	−29.5713	−1.23970	−0.619848	−	0.784722i	$-0.712806\pi$
$569$	−29.5713	−1.23970	−0.619848	+	0.784722i	$0.712806\pi$
$570$	−22.9894	−0.962922
$571$	−19.4252	−0.812921	−0.406460	−	0.913668i	$-0.633237\pi$
$571$	−19.4252	−0.812921	−0.406460	+	0.913668i	$0.633237\pi$
$572$	0	0
$573$	−5.04888	−0.210920
$574$	21.4600	0.895722
$575$	9.04888	0.377364
$576$	51.4147	2.14228
$577$	38.8222	1.61619	0.808095	−	0.589053i	$-0.200499\pi$
$577$	38.8222	1.61619	0.808095	+	0.589053i	$0.200499\pi$
$578$	−40.3814	−1.67964
$579$	2.74557	0.114102
$580$	−33.0872	−1.37387
$581$	4.33804	0.179972
$582$	31.8711	1.32110
$583$	−7.40054	−0.306499
$584$	−44.8816	−1.85722
$585$	0	0
$586$	76.1149	3.14428
$587$	−24.0731	−0.993601	−0.496801	−	0.867865i	$-0.665492\pi$
$587$	−24.0731	−0.993601	−0.496801	+	0.867865i	$0.665492\pi$
$588$	−5.91638	−0.243987
$589$	47.5019	1.95728
$590$	16.6066	0.683683
$591$	5.42166	0.223017
$592$	−65.5960	−2.69598
$593$	−40.4741	−1.66207	−0.831036	−	0.556218i	$-0.812252\pi$
$593$	−40.4741	−1.66207	−0.831036	+	0.556218i	$0.812252\pi$
$594$	11.8328	0.485504
$595$	2.09775	0.0859994
$596$	55.7422	2.28329
$597$	20.4111	0.835371
$598$	0	0
$599$	−2.49523	−0.101953	−0.0509763	−	0.998700i	$-0.516233\pi$
$599$	−2.49523	−0.101953	−0.0509763	+	0.998700i	$0.516233\pi$
$600$	36.7824	1.50164
$601$	35.2333	1.43720	0.718598	−	0.695426i	$-0.244784\pi$
$601$	35.2333	1.43720	0.718598	+	0.695426i	$0.244784\pi$
$602$	−13.8328	−0.563781
$603$	−8.67609	−0.353318
$604$	97.0943	3.95071
$605$	8.62022	0.350462
$606$	−40.2439	−1.63480
$607$	4.89169	0.198547	0.0992737	−	0.995060i	$-0.468348\pi$
$607$	4.89169	0.198547	0.0992737	+	0.995060i	$0.468348\pi$
$608$	202.189	8.19983
$609$	4.33804	0.175786
$610$	−19.0589	−0.771673
$611$	0	0
$612$	9.62721	0.389157
$613$	−7.83276	−0.316362	−0.158181	−	0.987410i	$-0.550563\pi$
$613$	−7.83276	−0.316362	−0.158181	+	0.987410i	$0.550563\pi$
$614$	56.7527	2.29035
$615$	−9.83276	−0.396495
$616$	−46.3416	−1.86716
$617$	−15.7350	−0.633468	−0.316734	−	0.948514i	$-0.602586\pi$
$617$	−15.7350	−0.633468	−0.316734	+	0.948514i	$0.602586\pi$
$618$	55.3311	2.22574
$619$	41.0177	1.64864	0.824320	−	0.566124i	$-0.191558\pi$
$619$	41.0177	1.64864	0.824320	+	0.566124i	$0.191558\pi$
$620$	57.1638	2.29575
$621$	2.71083	0.108782
$622$	−18.5089	−0.742137
$623$	−4.54359	−0.182035
$624$	0	0
$625$	2.83276	0.113311
$626$	−30.2338	−1.20839
$627$	26.6550	1.06450
$628$	−56.3205	−2.24743
$629$	−5.56777	−0.222002
$630$	3.62721	0.144512
$631$	19.5960	0.780106	0.390053	−	0.920792i	$-0.372457\pi$
$631$	19.5960	0.780106	0.390053	+	0.920792i	$0.372457\pi$
$632$	−98.2510	−3.90822
$633$	14.4842	0.575694
$634$	−69.2333	−2.74961
$635$	−0.961171	−0.0381429
$636$	−10.4111	−0.412827
$637$	0	0
$638$	51.3311	2.03222
$639$	6.78389	0.268366
$640$	104.241	4.12049
$641$	−20.8953	−0.825313	−0.412656	−	0.910887i	$-0.635399\pi$
$641$	−20.8953	−0.825313	−0.412656	+	0.910887i	$0.635399\pi$
$642$	−6.20555	−0.244914
$643$	9.15667	0.361104	0.180552	−	0.983565i	$-0.442212\pi$
$643$	9.15667	0.361104	0.180552	+	0.983565i	$0.442212\pi$
$644$	−16.0383	−0.631998
$645$	6.33804	0.249560
$646$	29.0177	1.14169
$647$	−6.24386	−0.245472	−0.122736	−	0.992439i	$-0.539167\pi$
$647$	−6.24386	−0.245472	−0.122736	+	0.992439i	$0.539167\pi$
$648$	11.0192	0.432873
$649$	−19.2544	−0.755802
$650$	0	0
$651$	−7.49472	−0.293741
$652$	4.41110	0.172752
$653$	−38.8222	−1.51923	−0.759615	−	0.650373i	$-0.774613\pi$
$653$	−38.8222	−1.51923	−0.759615	+	0.650373i	$0.774613\pi$
$654$	28.1361	1.10021
$655$	−18.7044	−0.730840
$656$	146.220	5.70893
$657$	−4.07306	−0.158905
$658$	3.04888	0.118858
$659$	−0.954695	−0.0371896	−0.0185948	−	0.999827i	$-0.505919\pi$
$659$	−0.954695	−0.0371896	−0.0185948	+	0.999827i	$0.505919\pi$
$660$	32.0766	1.24858
$661$	−2.28968	−0.0890584	−0.0445292	−	0.999008i	$-0.514179\pi$
$661$	−2.28968	−0.0890584	−0.0445292	+	0.999008i	$0.514179\pi$
$662$	−86.2510	−3.35224
$663$	0	0
$664$	47.8016	1.85506
$665$	8.17081	0.316850
$666$	−9.62721	−0.373047
$667$	11.7597	0.455338
$668$	−21.2544	−0.822358
$669$	16.8469	0.651339
$670$	−31.4700	−1.21579
$671$	22.0978	0.853074
$672$	−31.9008	−1.23060
$673$	−44.6797	−1.72227	−0.861137	−	0.508373i	$-0.830247\pi$
$673$	−44.6797	−1.72227	−0.861137	+	0.508373i	$0.830247\pi$
$674$	−18.3033	−0.705017
$675$	3.33804	0.128481
$676$	0	0
$677$	−37.0278	−1.42309	−0.711546	−	0.702639i	$-0.752005\pi$
$677$	−37.0278	−1.42309	−0.711546	+	0.702639i	$0.752005\pi$
$678$	6.10780	0.234569
$679$	−11.3275	−0.434709
$680$	23.1155	0.886437
$681$	−21.9305	−0.840379
$682$	−88.6832	−3.39586
$683$	26.8605	1.02779	0.513894	−	0.857853i	$-0.328202\pi$
$683$	26.8605	1.02779	0.513894	+	0.857853i	$0.328202\pi$
$684$	37.4983	1.43378
$685$	−5.68665	−0.217276
$686$	2.81361	0.107424
$687$	−5.25443	−0.200469
$688$	−94.2510	−3.59329
$689$	0	0
$690$	9.83276	0.374327
$691$	−2.86802	−0.109105	−0.0545523	−	0.998511i	$-0.517373\pi$
$691$	−2.86802	−0.109105	−0.0545523	+	0.998511i	$0.517373\pi$
$692$	−93.0349	−3.53666
$693$	−4.20555	−0.159756
$694$	68.3799	2.59567
$695$	24.4806	0.928602
$696$	47.8016	1.81191
$697$	12.4111	0.470104
$698$	−49.9688	−1.89135
$699$	−4.07306	−0.154057
$700$	−19.7491	−0.746448
$701$	−42.9930	−1.62382	−0.811912	−	0.583780i	$-0.801573\pi$
$701$	−42.9930	−1.62382	−0.811912	+	0.583780i	$0.801573\pi$
$702$	0	0
$703$	−21.6867	−0.817928
$704$	−216.227	−8.14936
$705$	−1.39697	−0.0526128
$706$	−5.45998	−0.205489
$707$	14.3033	0.537931
$708$	−27.0872	−1.01800
$709$	−3.49115	−0.131113	−0.0655564	−	0.997849i	$-0.520882\pi$
$709$	−3.49115	−0.131113	−0.0655564	+	0.997849i	$0.520882\pi$
$710$	24.6066	0.923469
$711$	−8.91638	−0.334390
$712$	−50.0666	−1.87632
$713$	−20.3169	−0.760875
$714$	−4.57834	−0.171340
$715$	0	0
$716$	147.641	5.51762
$717$	−2.37279	−0.0886134
$718$	94.6137	3.53095
$719$	27.5194	1.02630	0.513150	−	0.858299i	$-0.328478\pi$
$719$	27.5194	1.02630	0.513150	+	0.858299i	$0.328478\pi$
$720$	24.7144	0.921051
$721$	−19.6655	−0.732382
$722$	59.5663	2.21683
$723$	14.9164	0.554746
$724$	64.7316	2.40573
$725$	14.4806	0.537795
$726$	−18.8136	−0.698238
$727$	13.4983	0.500624	0.250312	−	0.968165i	$-0.419467\pi$
$727$	13.4983	0.500624	0.250312	+	0.968165i	$0.419467\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−14.7738	−0.546804
$731$	−8.00000	−0.295891
$732$	31.0872	1.14902
$733$	5.08362	0.187768	0.0938839	−	0.995583i	$-0.470072\pi$
$733$	5.08362	0.187768	0.0938839	+	0.995583i	$0.470072\pi$
$734$	−29.7633	−1.09858
$735$	−1.28917	−0.0475517
$736$	−86.4777	−3.18761
$737$	36.4877	1.34404
$738$	21.4600	0.789953
$739$	53.1638	1.95566	0.977831	−	0.209394i	$-0.0671492\pi$
$739$	53.1638	1.95566	0.977831	+	0.209394i	$0.0671492\pi$
$740$	−26.0978	−0.959372
$741$	0	0
$742$	4.95112	0.181761
$743$	46.1149	1.69179	0.845897	−	0.533347i	$-0.179066\pi$
$743$	46.1149	1.69179	0.845897	+	0.533347i	$0.179066\pi$
$744$	−82.5855	−3.02773
$745$	12.1461	0.444999
$746$	−15.3905	−0.563486
$747$	4.33804	0.158721
$748$	−40.4877	−1.48038
$749$	2.20555	0.0805890
$750$	30.2439	1.10435
$751$	−32.7774	−1.19606	−0.598032	−	0.801472i	$-0.704051\pi$
$751$	−32.7774	−1.19606	−0.598032	+	0.801472i	$0.704051\pi$
$752$	20.7738	0.757544
$753$	1.08719	0.0396194
$754$	0	0
$755$	21.1567	0.769970
$756$	−5.91638	−0.215177
$757$	−30.1708	−1.09658	−0.548288	−	0.836289i	$-0.684720\pi$
$757$	−30.1708	−1.09658	−0.548288	+	0.836289i	$0.684720\pi$
$758$	15.2544	0.554066
$759$	−11.4005	−0.413813
$760$	90.0354	3.26593
$761$	1.81915	0.0659440	0.0329720	−	0.999456i	$-0.489503\pi$
$761$	1.81915	0.0659440	0.0329720	+	0.999456i	$0.489503\pi$
$762$	2.09775	0.0759935
$763$	−10.0000	−0.362024
$764$	29.8711	1.08070
$765$	2.09775	0.0758444
$766$	−39.8016	−1.43809
$767$	0	0
$768$	−124.676	−4.49887
$769$	0.937507	0.0338074	0.0169037	−	0.999857i	$-0.494619\pi$
$769$	0.937507	0.0338074	0.0169037	+	0.999857i	$0.494619\pi$
$770$	−15.2544	−0.549731
$771$	16.6167	0.598434
$772$	−16.2439	−0.584629
$773$	8.03831	0.289118	0.144559	−	0.989496i	$-0.453824\pi$
$773$	8.03831	0.289118	0.144559	+	0.989496i	$0.453824\pi$
$774$	−13.8328	−0.497208
$775$	−25.0177	−0.898662
$776$	−124.819	−4.48075
$777$	3.42166	0.122751
$778$	0.881639	0.0316083
$779$	48.3416	1.73202
$780$	0	0
$781$	−28.5300	−1.02088
$782$	−12.4111	−0.443820
$783$	4.33804	0.155029
$784$	19.1708	0.684672
$785$	−12.2721	−0.438011
$786$	40.8222	1.45608
$787$	−25.3275	−0.902827	−0.451414	−	0.892315i	$-0.649080\pi$
$787$	−25.3275	−0.902827	−0.451414	+	0.892315i	$0.649080\pi$
$788$	−32.0766	−1.14268
$789$	27.0524	0.963093
$790$	−32.3416	−1.15066
$791$	−2.17081	−0.0771850
$792$	−46.3416	−1.64668
$793$	0	0
$794$	−58.1844	−2.06489
$795$	−2.26856	−0.0804575
$796$	−120.760	−4.28022
$797$	40.8122	1.44564	0.722820	−	0.691036i	$-0.242845\pi$
$797$	40.8122	1.44564	0.722820	+	0.691036i	$0.242845\pi$
$798$	−17.8328	−0.631273
$799$	1.76328	0.0623803
$800$	−106.486	−3.76486
$801$	−4.54359	−0.160540
$802$	35.8610	1.26630
$803$	17.1294	0.604485
$804$	51.3311	1.81031
$805$	−3.49472	−0.123173
$806$	0	0
$807$	−7.52946	−0.265050
$808$	157.610	5.54471
$809$	25.4947	0.896347	0.448173	−	0.893947i	$-0.352075\pi$
$809$	25.4947	0.896347	0.448173	+	0.893947i	$0.352075\pi$
$810$	3.62721	0.127447
$811$	13.1567	0.461993	0.230997	−	0.972955i	$-0.425801\pi$
$811$	13.1567	0.461993	0.230997	+	0.972955i	$0.425801\pi$
$812$	−25.6655	−0.900683
$813$	16.8222	0.589980
$814$	40.4877	1.41909
$815$	0.961171	0.0336683
$816$	−31.1950	−1.09204
$817$	−31.1602	−1.09016
$818$	52.4777	1.83484
$819$	0	0
$820$	58.1744	2.03154
$821$	23.1083	0.806486	0.403243	−	0.915093i	$-0.367883\pi$
$821$	23.1083	0.806486	0.403243	+	0.915093i	$0.367883\pi$
$822$	12.4111	0.432887
$823$	−17.4911	−0.609703	−0.304852	−	0.952400i	$-0.598607\pi$
$823$	−17.4911	−0.609703	−0.304852	+	0.952400i	$0.598607\pi$
$824$	−216.698	−7.54902
$825$	−14.0383	−0.488751
$826$	12.8816	0.448210
$827$	−39.3905	−1.36974	−0.684871	−	0.728665i	$-0.740141\pi$
$827$	−39.3905	−1.36974	−0.684871	+	0.728665i	$0.740141\pi$
$828$	−16.0383	−0.557370
$829$	10.8222	0.375871	0.187935	−	0.982181i	$-0.439820\pi$
$829$	10.8222	0.375871	0.187935	+	0.982181i	$0.439820\pi$
$830$	15.7350	0.546170
$831$	−17.4947	−0.606885
$832$	0	0
$833$	1.62721	0.0563796
$834$	−53.4288	−1.85009
$835$	−4.63130	−0.160273
$836$	−157.701	−5.45420
$837$	−7.49472	−0.259055
$838$	8.74557	0.302111
$839$	−4.57834	−0.158062	−0.0790309	−	0.996872i	$-0.525183\pi$
$839$	−4.57834	−0.158062	−0.0790309	+	0.996872i	$0.525183\pi$
$840$	−14.2056	−0.490138
$841$	−10.1814	−0.351082
$842$	−37.7038	−1.29936
$843$	27.4005	0.943725
$844$	−85.6938	−2.94970
$845$	0	0
$846$	3.04888	0.104823
$847$	6.68665	0.229756
$848$	33.7350	1.15847
$849$	−20.0766	−0.689028
$850$	−15.2827	−0.524192
$851$	9.27555	0.317962
$852$	−40.1361	−1.37504
$853$	54.6585	1.87147	0.935736	−	0.352700i	$-0.114737\pi$
$853$	54.6585	1.87147	0.935736	+	0.352700i	$0.114737\pi$
$854$	−14.7839	−0.505894
$855$	8.17081	0.279436
$856$	24.3033	0.830670
$857$	8.20555	0.280296	0.140148	−	0.990131i	$-0.455242\pi$
$857$	8.20555	0.280296	0.140148	+	0.990131i	$0.455242\pi$
$858$	0	0
$859$	−3.20503	−0.109354	−0.0546772	−	0.998504i	$-0.517413\pi$
$859$	−3.20503	−0.109354	−0.0546772	+	0.998504i	$0.517413\pi$
$860$	−37.4983	−1.27868
$861$	−7.62721	−0.259935
$862$	−27.8328	−0.947988
$863$	21.7038	0.738807	0.369404	−	0.929269i	$-0.379562\pi$
$863$	21.7038	0.738807	0.369404	+	0.929269i	$0.379562\pi$
$864$	−31.9008	−1.08529
$865$	−20.2721	−0.689273
$866$	1.62721	0.0552949
$867$	14.3522	0.487426
$868$	44.3416	1.50505
$869$	37.4983	1.27204
$870$	15.7350	0.533467
$871$	0	0
$872$	−110.192	−3.73156
$873$	−11.3275	−0.383377
$874$	−48.3416	−1.63518
$875$	−10.7491	−0.363387
$876$	24.0978	0.814188
$877$	38.5371	1.30131	0.650653	−	0.759375i	$-0.274495\pi$
$877$	38.5371	1.30131	0.650653	+	0.759375i	$0.274495\pi$
$878$	66.7810	2.25375
$879$	−27.0524	−0.912456
$880$	−103.938	−3.50374
$881$	−20.2056	−0.680742	−0.340371	−	0.940291i	$-0.610553\pi$
$881$	−20.2056	−0.680742	−0.340371	+	0.940291i	$0.610553\pi$
$882$	2.81361	0.0947391
$883$	5.49115	0.184792	0.0923959	−	0.995722i	$-0.470547\pi$
$883$	5.49115	0.184792	0.0923959	+	0.995722i	$0.470547\pi$
$884$	0	0
$885$	−5.90225	−0.198402
$886$	−10.8816	−0.365576
$887$	45.7633	1.53658	0.768290	−	0.640102i	$-0.221108\pi$
$887$	45.7633	1.53658	0.768290	+	0.640102i	$0.221108\pi$
$888$	37.7038	1.26526
$889$	−0.745574	−0.0250057
$890$	−16.4806	−0.552430
$891$	−4.20555	−0.140891
$892$	−99.6727	−3.33729
$893$	6.86802	0.229830
$894$	−26.5089	−0.886589
$895$	32.1708	1.07535
$896$	80.8591	2.70131
$897$	0	0
$898$	−4.74557	−0.158362
$899$	−32.5124	−1.08435
$900$	−19.7491	−0.658305
$901$	2.86342	0.0953943
$902$	−90.2510	−3.00503
$903$	4.91638	0.163607
$904$	−23.9205	−0.795583
$905$	14.1049	0.468863
$906$	−46.1744	−1.53404
$907$	6.67252	0.221557	0.110779	−	0.993845i	$-0.464666\pi$
$907$	6.67252	0.221557	0.110779	+	0.993845i	$0.464666\pi$
$908$	129.749	4.30588
$909$	14.3033	0.474411
$910$	0	0
$911$	23.5330	0.779684	0.389842	−	0.920882i	$-0.372530\pi$
$911$	23.5330	0.779684	0.389842	+	0.920882i	$0.372530\pi$
$912$	−121.505	−4.02345
$913$	−18.2439	−0.603784
$914$	10.7839	0.356699
$915$	6.77384	0.223936
$916$	31.0872	1.02715
$917$	−14.5089	−0.479125
$918$	−4.57834	−0.151108
$919$	−28.1955	−0.930084	−0.465042	−	0.885289i	$-0.653961\pi$
$919$	−28.1955	−0.930084	−0.465042	+	0.885289i	$0.653961\pi$
$920$	−38.5089	−1.26960
$921$	−20.1708	−0.664651
$922$	31.5577	1.03930
$923$	0	0
$924$	24.8816	0.818546
$925$	11.4217	0.375542
$926$	72.6832	2.38852
$927$	−19.6655	−0.645901
$928$	−138.387	−4.54278
$929$	6.97582	0.228869	0.114435	−	0.993431i	$-0.463494\pi$
$929$	6.97582	0.228869	0.114435	+	0.993431i	$0.463494\pi$
$930$	−27.1849	−0.891429
$931$	6.33804	0.207721
$932$	24.0978	0.789348
$933$	6.57834	0.215365
$934$	115.603	3.78265
$935$	−8.82220	−0.288517
$936$	0	0
$937$	45.5960	1.48956	0.744779	−	0.667311i	$-0.232555\pi$
$937$	45.5960	1.48956	0.744779	+	0.667311i	$0.232555\pi$
$938$	−24.4111	−0.797051
$939$	10.7456	0.350669
$940$	8.26499	0.269574
$941$	52.8086	1.72151	0.860755	−	0.509019i	$-0.169992\pi$
$941$	52.8086	1.72151	0.860755	+	0.509019i	$0.169992\pi$
$942$	26.7839	0.872666
$943$	−20.6761	−0.673306
$944$	87.7704	2.85668
$945$	−1.28917	−0.0419367
$946$	58.1744	1.89141
$947$	−8.73553	−0.283867	−0.141933	−	0.989876i	$-0.545332\pi$
$947$	−8.73553	−0.283867	−0.141933	+	0.989876i	$0.545332\pi$
$948$	52.7527	1.71333
$949$	0	0
$950$	−59.5266	−1.93130
$951$	24.6066	0.797924
$952$	17.9305	0.581131
$953$	56.0036	1.81413	0.907067	−	0.420987i	$-0.138316\pi$
$953$	56.0036	1.81413	0.907067	+	0.420987i	$0.138316\pi$
$954$	4.95112	0.160299
$955$	6.50885	0.210622
$956$	14.0383	0.454031
$957$	−18.2439	−0.589740
$958$	−6.85337	−0.221422
$959$	−4.41110	−0.142442
$960$	−66.2822	−2.13925
$961$	25.1708	0.811962
$962$	0	0
$963$	2.20555	0.0710729
$964$	−88.2510	−2.84237
$965$	−3.53951	−0.113941
$966$	7.62721	0.245402
$967$	−29.9094	−0.961821	−0.480911	−	0.876770i	$-0.659694\pi$
$967$	−29.9094	−0.961821	−0.480911	+	0.876770i	$0.659694\pi$
$968$	73.6813	2.36821
$969$	−10.3133	−0.331312
$970$	−41.0872	−1.31923
$971$	11.5194	0.369676	0.184838	−	0.982769i	$-0.440824\pi$
$971$	11.5194	0.369676	0.184838	+	0.982769i	$0.440824\pi$
$972$	−5.91638	−0.189768
$973$	18.9894	0.608773
$974$	18.5089	0.593062
$975$	0	0
$976$	−100.732	−3.22434
$977$	36.4182	1.16512	0.582561	−	0.812787i	$-0.302051\pi$
$977$	36.4182	1.16512	0.582561	+	0.812787i	$0.302051\pi$
$978$	−2.09775	−0.0670787
$979$	19.1083	0.610704
$980$	7.62721	0.243642
$981$	−10.0000	−0.319275
$982$	79.6344	2.54123
$983$	−17.6902	−0.564230	−0.282115	−	0.959381i	$-0.591036\pi$
$983$	−17.6902	−0.564230	−0.282115	+	0.959381i	$0.591036\pi$
$984$	−84.0455	−2.67927
$985$	−6.98944	−0.222702
$986$	−19.8610	−0.632504
$987$	−1.08362	−0.0344920
$988$	0	0
$989$	13.3275	0.423789
$990$	−15.2544	−0.484817
$991$	−11.0589	−0.351298	−0.175649	−	0.984453i	$-0.556202\pi$
$991$	−11.0589	−0.351298	−0.175649	+	0.984453i	$0.556202\pi$
$992$	239.087	7.59104
$993$	30.6550	0.972806
$994$	19.0872	0.605409
$995$	−26.3133	−0.834189
$996$	−25.6655	−0.813243
$997$	−49.6727	−1.57315	−0.786575	−	0.617495i	$-0.788147\pi$
$997$	−49.6727	−1.57315	−0.786575	+	0.617495i	$0.788147\pi$
$998$	−81.0943	−2.56700
$999$	3.42166	0.108257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.t.1.3		3
13.12	even	2		273.2.a.d.1.1	✓	3
39.38	odd	2		819.2.a.j.1.3		3
52.51	odd	2		4368.2.a.bq.1.2		3
65.64	even	2		6825.2.a.bd.1.3		3
91.90	odd	2		1911.2.a.n.1.1		3
273.272	even	2		5733.2.a.bc.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.a.d.1.1	✓	3	13.12	even	2
819.2.a.j.1.3		3	39.38	odd	2
1911.2.a.n.1.1		3	91.90	odd	2
3549.2.a.t.1.3		3	1.1	even	1	trivial
4368.2.a.bq.1.2		3	52.51	odd	2
5733.2.a.bc.1.3		3	273.272	even	2
6825.2.a.bd.1.3		3	65.64	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)

\(f(q)\)	\(=\)	\(q+2.81361 q^{2} -1.00000 q^{3} +5.91638 q^{4} +1.28917 q^{5} -2.81361 q^{6} +1.00000 q^{7} +11.0192 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.81361 q^{2} -1.00000 q^{3} +5.91638 q^{4} +1.28917 q^{5} -2.81361 q^{6} +1.00000 q^{7} +11.0192 q^{8} +1.00000 q^{9} +3.62721 q^{10} -4.20555 q^{11} -5.91638 q^{12} +2.81361 q^{14} -1.28917 q^{15} +19.1708 q^{16} +1.62721 q^{17} +2.81361 q^{18} +6.33804 q^{19} +7.62721 q^{20} -1.00000 q^{21} -11.8328 q^{22} -2.71083 q^{23} -11.0192 q^{24} -3.33804 q^{25} -1.00000 q^{27} +5.91638 q^{28} -4.33804 q^{29} -3.62721 q^{30} +7.49472 q^{31} +31.9008 q^{32} +4.20555 q^{33} +4.57834 q^{34} +1.28917 q^{35} +5.91638 q^{36} -3.42166 q^{37} +17.8328 q^{38} +14.2056 q^{40} +7.62721 q^{41} -2.81361 q^{42} -4.91638 q^{43} -24.8816 q^{44} +1.28917 q^{45} -7.62721 q^{46} +1.08362 q^{47} -19.1708 q^{48} +1.00000 q^{49} -9.39194 q^{50} -1.62721 q^{51} +1.75971 q^{53} -2.81361 q^{54} -5.42166 q^{55} +11.0192 q^{56} -6.33804 q^{57} -12.2056 q^{58} +4.57834 q^{59} -7.62721 q^{60} -5.25443 q^{61} +21.0872 q^{62} +1.00000 q^{63} +51.4147 q^{64} +11.8328 q^{66} -8.67609 q^{67} +9.62721 q^{68} +2.71083 q^{69} +3.62721 q^{70} +6.78389 q^{71} +11.0192 q^{72} -4.07306 q^{73} -9.62721 q^{74} +3.33804 q^{75} +37.4983 q^{76} -4.20555 q^{77} -8.91638 q^{79} +24.7144 q^{80} +1.00000 q^{81} +21.4600 q^{82} +4.33804 q^{83} -5.91638 q^{84} +2.09775 q^{85} -13.8328 q^{86} +4.33804 q^{87} -46.3416 q^{88} -4.54359 q^{89} +3.62721 q^{90} -16.0383 q^{92} -7.49472 q^{93} +3.04888 q^{94} +8.17081 q^{95} -31.9008 q^{96} -11.3275 q^{97} +2.81361 q^{98} -4.20555 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} - 3 q^{3} + 4 q^{4} + 3 q^{5} - 2 q^{6} + 3 q^{7} + 12 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 - 3 * q^3 + 4 * q^4 + 3 * q^5 - 2 * q^6 + 3 * q^7 + 12 * q^8 + 3 * q^9	\( 3 q + 2 q^{2} - 3 q^{3} + 4 q^{4} + 3 q^{5} - 2 q^{6} + 3 q^{7} + 12 q^{8} + 3 q^{9} - 2 q^{10} + 2 q^{11} - 4 q^{12} + 2 q^{14} - 3 q^{15} + 18 q^{16} - 8 q^{17} + 2 q^{18} + 7 q^{19} + 10 q^{20} - 3 q^{21} - 8 q^{22} - 9 q^{23} - 12 q^{24} + 2 q^{25} - 3 q^{27} + 4 q^{28} - q^{29} + 2 q^{30} + 7 q^{31} + 36 q^{32} - 2 q^{33} + 12 q^{34} + 3 q^{35} + 4 q^{36} - 12 q^{37} + 26 q^{38} + 28 q^{40} + 10 q^{41} - 2 q^{42} - q^{43} - 36 q^{44} + 3 q^{45} - 10 q^{46} + 17 q^{47} - 18 q^{48} + 3 q^{49} - 20 q^{50} + 8 q^{51} - 5 q^{53} - 2 q^{54} - 18 q^{55} + 12 q^{56} - 7 q^{57} - 22 q^{58} + 12 q^{59} - 10 q^{60} + 10 q^{61} + 10 q^{62} + 3 q^{63} + 58 q^{64} + 8 q^{66} - 2 q^{67} + 16 q^{68} + 9 q^{69} - 2 q^{70} + 4 q^{71} + 12 q^{72} + 5 q^{73} - 16 q^{74} - 2 q^{75} + 30 q^{76} + 2 q^{77} - 13 q^{79} + 8 q^{80} + 3 q^{81} + 24 q^{82} + q^{83} - 4 q^{84} - 16 q^{85} - 14 q^{86} + q^{87} - 60 q^{88} + 13 q^{89} - 2 q^{90} - 6 q^{92} - 7 q^{93} - 2 q^{94} - 15 q^{95} - 36 q^{96} + 9 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 3 * q^3 + 4 * q^4 + 3 * q^5 - 2 * q^6 + 3 * q^7 + 12 * q^8 + 3 * q^9 - 2 * q^10 + 2 * q^11 - 4 * q^12 + 2 * q^14 - 3 * q^15 + 18 * q^16 - 8 * q^17 + 2 * q^18 + 7 * q^19 + 10 * q^20 - 3 * q^21 - 8 * q^22 - 9 * q^23 - 12 * q^24 + 2 * q^25 - 3 * q^27 + 4 * q^28 - q^29 + 2 * q^30 + 7 * q^31 + 36 * q^32 - 2 * q^33 + 12 * q^34 + 3 * q^35 + 4 * q^36 - 12 * q^37 + 26 * q^38 + 28 * q^40 + 10 * q^41 - 2 * q^42 - q^43 - 36 * q^44 + 3 * q^45 - 10 * q^46 + 17 * q^47 - 18 * q^48 + 3 * q^49 - 20 * q^50 + 8 * q^51 - 5 * q^53 - 2 * q^54 - 18 * q^55 + 12 * q^56 - 7 * q^57 - 22 * q^58 + 12 * q^59 - 10 * q^60 + 10 * q^61 + 10 * q^62 + 3 * q^63 + 58 * q^64 + 8 * q^66 - 2 * q^67 + 16 * q^68 + 9 * q^69 - 2 * q^70 + 4 * q^71 + 12 * q^72 + 5 * q^73 - 16 * q^74 - 2 * q^75 + 30 * q^76 + 2 * q^77 - 13 * q^79 + 8 * q^80 + 3 * q^81 + 24 * q^82 + q^83 - 4 * q^84 - 16 * q^85 - 14 * q^86 + q^87 - 60 * q^88 + 13 * q^89 - 2 * q^90 - 6 * q^92 - 7 * q^93 - 2 * q^94 - 15 * q^95 - 36 * q^96 + 9 * q^97 + 2 * q^98 + 2 * q^99

Introduction

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