LMFDB - Embedded newform 3549.2.a.bb.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$28.3389076774$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 9x^{6} + 14x^{5} + 25x^{4} - 24x^{3} - 16x^{2} + 8x + 1 $ x^8 - 2x^7 - 9x^6 + 14x^5 + 25x^4 - 24x^3 - 16x^2 + 8*x + 1
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			1.7
Root			$-1.77930$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.77930 q^{2} +1.00000 q^{3} +1.16591 q^{4} -0.681820 q^{5} +1.77930 q^{6} -1.00000 q^{7} -1.48409 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.77930 q^{2} +1.00000 q^{3} +1.16591 q^{4} -0.681820 q^{5} +1.77930 q^{6} -1.00000 q^{7} -1.48409 q^{8} +1.00000 q^{9} -1.21316 q^{10} -0.590249 q^{11} +1.16591 q^{12} -1.77930 q^{14} -0.681820 q^{15} -4.97247 q^{16} -6.29031 q^{17} +1.77930 q^{18} +3.58649 q^{19} -0.794942 q^{20} -1.00000 q^{21} -1.05023 q^{22} +3.68560 q^{23} -1.48409 q^{24} -4.53512 q^{25} +1.00000 q^{27} -1.16591 q^{28} -6.45218 q^{29} -1.21316 q^{30} -4.30692 q^{31} -5.87934 q^{32} -0.590249 q^{33} -11.1924 q^{34} +0.681820 q^{35} +1.16591 q^{36} -10.5343 q^{37} +6.38145 q^{38} +1.01188 q^{40} -0.157443 q^{41} -1.77930 q^{42} +4.72277 q^{43} -0.688179 q^{44} -0.681820 q^{45} +6.55779 q^{46} -11.2638 q^{47} -4.97247 q^{48} +1.00000 q^{49} -8.06935 q^{50} -6.29031 q^{51} +12.2243 q^{53} +1.77930 q^{54} +0.402444 q^{55} +1.48409 q^{56} +3.58649 q^{57} -11.4804 q^{58} +2.82660 q^{59} -0.794942 q^{60} +2.91142 q^{61} -7.66332 q^{62} -1.00000 q^{63} -0.516173 q^{64} -1.05023 q^{66} -7.48440 q^{67} -7.33395 q^{68} +3.68560 q^{69} +1.21316 q^{70} +6.99122 q^{71} -1.48409 q^{72} -7.30193 q^{73} -18.7437 q^{74} -4.53512 q^{75} +4.18154 q^{76} +0.590249 q^{77} -3.33737 q^{79} +3.39033 q^{80} +1.00000 q^{81} -0.280138 q^{82} +13.6469 q^{83} -1.16591 q^{84} +4.28886 q^{85} +8.40323 q^{86} -6.45218 q^{87} +0.875984 q^{88} -12.2481 q^{89} -1.21316 q^{90} +4.29709 q^{92} -4.30692 q^{93} -20.0416 q^{94} -2.44534 q^{95} -5.87934 q^{96} -10.6079 q^{97} +1.77930 q^{98} -0.590249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 8 q^{3} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 8 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 8 * q^3 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 8 * q^7 - 12 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} + 8 q^{3} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 8 q^{7} - 12 q^{8} + 8 q^{9} - 4 q^{10} - 8 q^{11} + 6 q^{12} + 2 q^{14} - 2 q^{15} + 10 q^{16} + 10 q^{17} - 2 q^{18} - 18 q^{19} - 2 q^{20} - 8 q^{21} + 2 q^{22} - 2 q^{23} - 12 q^{24} - 6 q^{25} + 8 q^{27} - 6 q^{28} - 12 q^{29} - 4 q^{30} - 16 q^{31} - 26 q^{32} - 8 q^{33} - 24 q^{34} + 2 q^{35} + 6 q^{36} - 24 q^{37} + 16 q^{38} - 30 q^{40} + 4 q^{41} + 2 q^{42} - 10 q^{43} + 20 q^{44} - 2 q^{45} - 12 q^{46} - 10 q^{47} + 10 q^{48} + 8 q^{49} + 16 q^{50} + 10 q^{51} + 6 q^{53} - 2 q^{54} - 10 q^{55} + 12 q^{56} - 18 q^{57} - 16 q^{58} - 6 q^{59} - 2 q^{60} + 6 q^{61} + 16 q^{62} - 8 q^{63} - 8 q^{64} + 2 q^{66} - 24 q^{67} + 20 q^{68} - 2 q^{69} + 4 q^{70} - 42 q^{71} - 12 q^{72} - 32 q^{73} - 18 q^{74} - 6 q^{75} - 28 q^{76} + 8 q^{77} - 2 q^{79} + 40 q^{80} + 8 q^{81} - 18 q^{82} + 2 q^{83} - 6 q^{84} - 4 q^{85} - 26 q^{86} - 12 q^{87} - 2 q^{88} - 12 q^{89} - 4 q^{90} - 10 q^{92} - 16 q^{93} - 16 q^{94} - 4 q^{95} - 26 q^{96} - 64 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 8 * q^3 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 8 * q^7 - 12 * q^8 + 8 * q^9 - 4 * q^10 - 8 * q^11 + 6 * q^12 + 2 * q^14 - 2 * q^15 + 10 * q^16 + 10 * q^17 - 2 * q^18 - 18 * q^19 - 2 * q^20 - 8 * q^21 + 2 * q^22 - 2 * q^23 - 12 * q^24 - 6 * q^25 + 8 * q^27 - 6 * q^28 - 12 * q^29 - 4 * q^30 - 16 * q^31 - 26 * q^32 - 8 * q^33 - 24 * q^34 + 2 * q^35 + 6 * q^36 - 24 * q^37 + 16 * q^38 - 30 * q^40 + 4 * q^41 + 2 * q^42 - 10 * q^43 + 20 * q^44 - 2 * q^45 - 12 * q^46 - 10 * q^47 + 10 * q^48 + 8 * q^49 + 16 * q^50 + 10 * q^51 + 6 * q^53 - 2 * q^54 - 10 * q^55 + 12 * q^56 - 18 * q^57 - 16 * q^58 - 6 * q^59 - 2 * q^60 + 6 * q^61 + 16 * q^62 - 8 * q^63 - 8 * q^64 + 2 * q^66 - 24 * q^67 + 20 * q^68 - 2 * q^69 + 4 * q^70 - 42 * q^71 - 12 * q^72 - 32 * q^73 - 18 * q^74 - 6 * q^75 - 28 * q^76 + 8 * q^77 - 2 * q^79 + 40 * q^80 + 8 * q^81 - 18 * q^82 + 2 * q^83 - 6 * q^84 - 4 * q^85 - 26 * q^86 - 12 * q^87 - 2 * q^88 - 12 * q^89 - 4 * q^90 - 10 * q^92 - 16 * q^93 - 16 * q^94 - 4 * q^95 - 26 * q^96 - 64 * q^97 - 2 * q^98 - 8 * 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 $

$2$	1.77930	1.25816	0.629078	−	0.777342i	$-0.283433\pi$
$2$	1.77930	1.25816	0.629078	+	0.777342i	$0.283433\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.16591	0.582956
$5$	−0.681820	−0.304919	−0.152460	−	0.988310i	$-0.548719\pi$
$5$	−0.681820	−0.304919	−0.152460	+	0.988310i	$0.548719\pi$
$6$	1.77930	0.726397
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.48409	−0.524706
$9$	1.00000	0.333333
$10$	−1.21316	−0.383636
$11$	−0.590249	−0.177967	−0.0889834	−	0.996033i	$-0.528362\pi$
$11$	−0.590249	−0.177967	−0.0889834	+	0.996033i	$0.528362\pi$
$12$	1.16591	0.336570
$13$	0	0
$13$	0	0
$14$	−1.77930	−0.475538
$15$	−0.681820	−0.176045
$16$	−4.97247	−1.24312
$17$	−6.29031	−1.52562	−0.762812	−	0.646620i	$-0.776182\pi$
$17$	−6.29031	−1.52562	−0.762812	+	0.646620i	$0.776182\pi$
$18$	1.77930	0.419385
$19$	3.58649	0.822798	0.411399	−	0.911455i	$-0.365040\pi$
$19$	3.58649	0.822798	0.411399	+	0.911455i	$0.365040\pi$
$20$	−0.794942	−0.177755
$21$	−1.00000	−0.218218
$22$	−1.05023	−0.223910
$23$	3.68560	0.768500	0.384250	−	0.923229i	$-0.374460\pi$
$23$	3.68560	0.768500	0.384250	+	0.923229i	$0.374460\pi$
$24$	−1.48409	−0.302939
$25$	−4.53512	−0.907024
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.16591	−0.220337
$29$	−6.45218	−1.19814	−0.599070	−	0.800697i	$-0.704463\pi$
$29$	−6.45218	−1.19814	−0.599070	+	0.800697i	$0.704463\pi$
$30$	−1.21316	−0.221492
$31$	−4.30692	−0.773546	−0.386773	−	0.922175i	$-0.626410\pi$
$31$	−4.30692	−0.773546	−0.386773	+	0.922175i	$0.626410\pi$
$32$	−5.87934	−1.03933
$33$	−0.590249	−0.102749
$34$	−11.1924	−1.91947
$35$	0.681820	0.115249
$36$	1.16591	0.194319
$37$	−10.5343	−1.73183	−0.865913	−	0.500195i	$-0.833262\pi$
$37$	−10.5343	−1.73183	−0.865913	+	0.500195i	$0.833262\pi$
$38$	6.38145	1.03521
$39$	0	0
$40$	1.01188	0.159993
$41$	−0.157443	−0.0245885	−0.0122942	−	0.999924i	$-0.503913\pi$
$41$	−0.157443	−0.0245885	−0.0122942	+	0.999924i	$0.503913\pi$
$42$	−1.77930	−0.274552
$43$	4.72277	0.720215	0.360108	−	0.932911i	$-0.382740\pi$
$43$	4.72277	0.720215	0.360108	+	0.932911i	$0.382740\pi$
$44$	−0.688179	−0.103747
$45$	−0.681820	−0.101640
$46$	6.55779	0.966893
$47$	−11.2638	−1.64299	−0.821494	−	0.570217i	$-0.806859\pi$
$47$	−11.2638	−1.64299	−0.821494	+	0.570217i	$0.806859\pi$
$48$	−4.97247	−0.717715
$49$	1.00000	0.142857
$50$	−8.06935	−1.14118
$51$	−6.29031	−0.880820
$52$	0	0
$53$	12.2243	1.67914	0.839571	−	0.543249i	$-0.182806\pi$
$53$	12.2243	1.67914	0.839571	+	0.543249i	$0.182806\pi$
$54$	1.77930	0.242132
$55$	0.402444	0.0542655
$56$	1.48409	0.198320
$57$	3.58649	0.475042
$58$	−11.4804	−1.50745
$59$	2.82660	0.367992	0.183996	−	0.982927i	$-0.441097\pi$
$59$	2.82660	0.367992	0.183996	+	0.982927i	$0.441097\pi$
$60$	−0.794942	−0.102627
$61$	2.91142	0.372769	0.186385	−	0.982477i	$-0.440323\pi$
$61$	2.91142	0.372769	0.186385	+	0.982477i	$0.440323\pi$
$62$	−7.66332	−0.973242
$63$	−1.00000	−0.125988
$64$	−0.516173	−0.0645217
$65$	0	0
$66$	−1.05023	−0.129274
$67$	−7.48440	−0.914365	−0.457182	−	0.889373i	$-0.651141\pi$
$67$	−7.48440	−0.914365	−0.457182	+	0.889373i	$0.651141\pi$
$68$	−7.33395	−0.889373
$69$	3.68560	0.443694
$70$	1.21316	0.145001
$71$	6.99122	0.829705	0.414852	−	0.909889i	$-0.363833\pi$
$71$	6.99122	0.829705	0.414852	+	0.909889i	$0.363833\pi$
$72$	−1.48409	−0.174902
$73$	−7.30193	−0.854626	−0.427313	−	0.904104i	$-0.640540\pi$
$73$	−7.30193	−0.854626	−0.427313	+	0.904104i	$0.640540\pi$
$74$	−18.7437	−2.17891
$75$	−4.53512	−0.523671
$76$	4.18154	0.479655
$77$	0.590249	0.0672651
$78$	0	0
$79$	−3.33737	−0.375484	−0.187742	−	0.982218i	$-0.560117\pi$
$79$	−3.33737	−0.375484	−0.187742	+	0.982218i	$0.560117\pi$
$80$	3.39033	0.379051
$81$	1.00000	0.111111
$82$	−0.280138	−0.0309361
$83$	13.6469	1.49794	0.748969	−	0.662605i	$-0.230549\pi$
$83$	13.6469	1.49794	0.748969	+	0.662605i	$0.230549\pi$
$84$	−1.16591	−0.127211
$85$	4.28886	0.465192
$86$	8.40323	0.906143
$87$	−6.45218	−0.691746
$88$	0.875984	0.0933802
$89$	−12.2481	−1.29830	−0.649148	−	0.760662i	$-0.724875\pi$
$89$	−12.2481	−1.29830	−0.649148	+	0.760662i	$0.724875\pi$
$90$	−1.21316	−0.127879
$91$	0	0
$92$	4.29709	0.448002
$93$	−4.30692	−0.446607
$94$	−20.0416	−2.06713
$95$	−2.44534	−0.250887
$96$	−5.87934	−0.600058
$97$	−10.6079	−1.07707	−0.538533	−	0.842604i	$-0.681021\pi$
$97$	−10.6079	−1.07707	−0.538533	+	0.842604i	$0.681021\pi$
$98$	1.77930	0.179737
$99$	−0.590249	−0.0593223
$100$	−5.28756	−0.528756
$101$	−4.26905	−0.424787	−0.212393	−	0.977184i	$-0.568126\pi$
$101$	−4.26905	−0.424787	−0.212393	+	0.977184i	$0.568126\pi$
$102$	−11.1924	−1.10821
$103$	6.67783	0.657987	0.328993	−	0.944332i	$-0.393291\pi$
$103$	6.67783	0.657987	0.328993	+	0.944332i	$0.393291\pi$
$104$	0	0
$105$	0.681820	0.0665388
$106$	21.7508	2.11262
$107$	−5.02359	−0.485649	−0.242824	−	0.970070i	$-0.578074\pi$
$107$	−5.02359	−0.485649	−0.242824	+	0.970070i	$0.578074\pi$
$108$	1.16591	0.112190
$109$	−15.0818	−1.44458	−0.722289	−	0.691591i	$-0.756910\pi$
$109$	−15.0818	−1.44458	−0.722289	+	0.691591i	$0.756910\pi$
$110$	0.716068	0.0682744
$111$	−10.5343	−0.999870
$112$	4.97247	0.469855
$113$	−2.34233	−0.220348	−0.110174	−	0.993912i	$-0.535141\pi$
$113$	−2.34233	−0.220348	−0.110174	+	0.993912i	$0.535141\pi$
$114$	6.38145	0.597677
$115$	−2.51291	−0.234330
$116$	−7.52268	−0.698463
$117$	0	0
$118$	5.02938	0.462992
$119$	6.29031	0.576632
$120$	1.01188	0.0923719
$121$	−10.6516	−0.968328
$122$	5.18030	0.469002
$123$	−0.157443	−0.0141962
$124$	−5.02150	−0.450944
$125$	6.50124	0.581488
$126$	−1.77930	−0.158513
$127$	−2.33606	−0.207292	−0.103646	−	0.994614i	$-0.533051\pi$
$127$	−2.33606	−0.207292	−0.103646	+	0.994614i	$0.533051\pi$
$128$	10.8403	0.958152
$129$	4.72277	0.415817
$130$	0	0
$131$	7.64336	0.667803	0.333902	−	0.942608i	$-0.391635\pi$
$131$	7.64336	0.667803	0.333902	+	0.942608i	$0.391635\pi$
$132$	−0.688179	−0.0598983
$133$	−3.58649	−0.310988
$134$	−13.3170	−1.15041
$135$	−0.681820	−0.0586817
$136$	9.33541	0.800504
$137$	−7.41962	−0.633901	−0.316951	−	0.948442i	$-0.602659\pi$
$137$	−7.41962	−0.633901	−0.316951	+	0.948442i	$0.602659\pi$
$138$	6.55779	0.558236
$139$	3.62613	0.307564	0.153782	−	0.988105i	$-0.450855\pi$
$139$	3.62613	0.307564	0.153782	+	0.988105i	$0.450855\pi$
$140$	0.794942	0.0671849
$141$	−11.2638	−0.948579
$142$	12.4395	1.04390
$143$	0	0
$144$	−4.97247	−0.414373
$145$	4.39922	0.365336
$146$	−12.9923	−1.07525
$147$	1.00000	0.0824786
$148$	−12.2821	−1.00958
$149$	−3.61075	−0.295805	−0.147902	−	0.989002i	$-0.547252\pi$
$149$	−3.61075	−0.295805	−0.147902	+	0.989002i	$0.547252\pi$
$150$	−8.06935	−0.658859
$151$	−9.51624	−0.774421	−0.387210	−	0.921991i	$-0.626561\pi$
$151$	−9.51624	−0.774421	−0.387210	+	0.921991i	$0.626561\pi$
$152$	−5.32269	−0.431727
$153$	−6.29031	−0.508542
$154$	1.05023	0.0846300
$155$	2.93655	0.235869
$156$	0	0
$157$	16.0302	1.27935	0.639675	−	0.768645i	$-0.279069\pi$
$157$	16.0302	1.27935	0.639675	+	0.768645i	$0.279069\pi$
$158$	−5.93819	−0.472417
$159$	12.2243	0.969454
$160$	4.00865	0.316912
$161$	−3.68560	−0.290466
$162$	1.77930	0.139795
$163$	17.0893	1.33854	0.669268	−	0.743021i	$-0.266608\pi$
$163$	17.0893	1.33854	0.669268	+	0.743021i	$0.266608\pi$
$164$	−0.183565	−0.0143340
$165$	0.402444	0.0313302
$166$	24.2819	1.88464
$167$	3.60779	0.279179	0.139589	−	0.990209i	$-0.455422\pi$
$167$	3.60779	0.279179	0.139589	+	0.990209i	$0.455422\pi$
$168$	1.48409	0.114500
$169$	0	0
$170$	7.63117	0.585284
$171$	3.58649	0.274266
$172$	5.50634	0.419854
$173$	9.85489	0.749254	0.374627	−	0.927176i	$-0.377771\pi$
$173$	9.85489	0.749254	0.374627	+	0.927176i	$0.377771\pi$
$174$	−11.4804	−0.870325
$175$	4.53512	0.342823
$176$	2.93500	0.221234
$177$	2.82660	0.212460
$178$	−21.7931	−1.63346
$179$	10.6600	0.796766	0.398383	−	0.917219i	$-0.369571\pi$
$179$	10.6600	0.796766	0.398383	+	0.917219i	$0.369571\pi$
$180$	−0.794942	−0.0592515
$181$	24.9606	1.85530	0.927652	−	0.373447i	$-0.121824\pi$
$181$	24.9606	1.85530	0.927652	+	0.373447i	$0.121824\pi$
$182$	0	0
$183$	2.91142	0.215219
$184$	−5.46977	−0.403237
$185$	7.18249	0.528067
$186$	−7.66332	−0.561902
$187$	3.71285	0.271511
$188$	−13.1326	−0.957790
$189$	−1.00000	−0.0727393
$190$	−4.35100	−0.315655
$191$	−15.8283	−1.14530	−0.572649	−	0.819800i	$-0.694084\pi$
$191$	−15.8283	−1.14530	−0.572649	+	0.819800i	$0.694084\pi$
$192$	−0.516173	−0.0372516
$193$	−18.8468	−1.35662	−0.678312	−	0.734774i	$-0.737288\pi$
$193$	−18.8468	−1.35662	−0.678312	+	0.734774i	$0.737288\pi$
$194$	−18.8746	−1.35512
$195$	0	0
$196$	1.16591	0.0832795
$197$	13.3136	0.948556	0.474278	−	0.880375i	$-0.342709\pi$
$197$	13.3136	0.948556	0.474278	+	0.880375i	$0.342709\pi$
$198$	−1.05023	−0.0746367
$199$	20.6093	1.46095	0.730476	−	0.682938i	$-0.239298\pi$
$199$	20.6093	1.46095	0.730476	+	0.682938i	$0.239298\pi$
$200$	6.73054	0.475921
$201$	−7.48440	−0.527909
$202$	−7.59593	−0.534448
$203$	6.45218	0.452854
$204$	−7.33395	−0.513479
$205$	0.107348	0.00749749
$206$	11.8819	0.827850
$207$	3.68560	0.256167
$208$	0	0
$209$	−2.11692	−0.146431
$210$	1.21316	0.0837162
$211$	−18.5174	−1.27479	−0.637394	−	0.770538i	$-0.719988\pi$
$211$	−18.5174	−1.27479	−0.637394	+	0.770538i	$0.719988\pi$
$212$	14.2525	0.978867
$213$	6.99122	0.479030
$214$	−8.93848	−0.611022
$215$	−3.22008	−0.219607
$216$	−1.48409	−0.100980
$217$	4.30692	0.292373
$218$	−26.8351	−1.81750
$219$	−7.30193	−0.493419
$220$	0.469214	0.0316344
$221$	0	0
$222$	−18.7437	−1.25799
$223$	−14.8049	−0.991409	−0.495704	−	0.868491i	$-0.665090\pi$
$223$	−14.8049	−0.991409	−0.495704	+	0.868491i	$0.665090\pi$
$224$	5.87934	0.392830
$225$	−4.53512	−0.302341
$226$	−4.16770	−0.277232
$227$	0.155323	0.0103092	0.00515458	−	0.999987i	$-0.498359\pi$
$227$	0.155323	0.0103092	0.00515458	+	0.999987i	$0.498359\pi$
$228$	4.18154	0.276929
$229$	−24.8216	−1.64026	−0.820129	−	0.572179i	$-0.806098\pi$
$229$	−24.8216	−1.64026	−0.820129	+	0.572179i	$0.806098\pi$
$230$	−4.47123	−0.294824
$231$	0.590249	0.0388355
$232$	9.57563	0.628671
$233$	−9.79706	−0.641826	−0.320913	−	0.947109i	$-0.603990\pi$
$233$	−9.79706	−0.641826	−0.320913	+	0.947109i	$0.603990\pi$
$234$	0	0
$235$	7.67985	0.500978
$236$	3.29557	0.214523
$237$	−3.33737	−0.216786
$238$	11.1924	0.725493
$239$	17.2503	1.11583	0.557914	−	0.829899i	$-0.311602\pi$
$239$	17.2503	1.11583	0.557914	+	0.829899i	$0.311602\pi$
$240$	3.39033	0.218845
$241$	0.836707	0.0538971	0.0269485	−	0.999637i	$-0.491421\pi$
$241$	0.836707	0.0538971	0.0269485	+	0.999637i	$0.491421\pi$
$242$	−18.9524	−1.21831
$243$	1.00000	0.0641500
$244$	3.39446	0.217308
$245$	−0.681820	−0.0435599
$246$	−0.280138	−0.0178610
$247$	0	0
$248$	6.39188	0.405884
$249$	13.6469	0.864835
$250$	11.5677	0.731603
$251$	−14.6092	−0.922122	−0.461061	−	0.887368i	$-0.652531\pi$
$251$	−14.6092	−0.922122	−0.461061	+	0.887368i	$0.652531\pi$
$252$	−1.16591	−0.0734456
$253$	−2.17542	−0.136768
$254$	−4.15655	−0.260805
$255$	4.28886	0.268579
$256$	20.3204	1.27003
$257$	−12.5301	−0.781607	−0.390804	−	0.920474i	$-0.627803\pi$
$257$	−12.5301	−0.781607	−0.390804	+	0.920474i	$0.627803\pi$
$258$	8.40323	0.523162
$259$	10.5343	0.654569
$260$	0	0
$261$	−6.45218	−0.399380
$262$	13.5998	0.840200
$263$	19.2485	1.18692	0.593458	−	0.804865i	$-0.297762\pi$
$263$	19.2485	1.18692	0.593458	+	0.804865i	$0.297762\pi$
$264$	0.875984	0.0539131
$265$	−8.33480	−0.512003
$266$	−6.38145	−0.391272
$267$	−12.2481	−0.749572
$268$	−8.72615	−0.533035
$269$	6.72792	0.410209	0.205104	−	0.978740i	$-0.434247\pi$
$269$	6.72792	0.410209	0.205104	+	0.978740i	$0.434247\pi$
$270$	−1.21316	−0.0738307
$271$	16.0265	0.973539	0.486769	−	0.873531i	$-0.338175\pi$
$271$	16.0265	0.973539	0.486769	+	0.873531i	$0.338175\pi$
$272$	31.2784	1.89653
$273$	0	0
$274$	−13.2017	−0.797546
$275$	2.67685	0.161420
$276$	4.29709	0.258654
$277$	−4.02854	−0.242052	−0.121026	−	0.992649i	$-0.538618\pi$
$277$	−4.02854	−0.242052	−0.121026	+	0.992649i	$0.538618\pi$
$278$	6.45198	0.386964
$279$	−4.30692	−0.257849
$280$	−1.01188	−0.0604716
$281$	13.1699	0.785649	0.392824	−	0.919614i	$-0.371498\pi$
$281$	13.1699	0.785649	0.392824	+	0.919614i	$0.371498\pi$
$282$	−20.0416	−1.19346
$283$	−6.32082	−0.375734	−0.187867	−	0.982195i	$-0.560157\pi$
$283$	−6.32082	−0.375734	−0.187867	+	0.982195i	$0.560157\pi$
$284$	8.15115	0.483682
$285$	−2.44534	−0.144850
$286$	0	0
$287$	0.157443	0.00929356
$288$	−5.87934	−0.346444
$289$	22.5680	1.32753
$290$	7.82755	0.459649
$291$	−10.6079	−0.621845
$292$	−8.51341	−0.498210
$293$	−21.0321	−1.22871	−0.614354	−	0.789031i	$-0.710583\pi$
$293$	−21.0321	−1.22871	−0.614354	+	0.789031i	$0.710583\pi$
$294$	1.77930	0.103771
$295$	−1.92723	−0.112208
$296$	15.6339	0.908699
$297$	−0.590249	−0.0342497
$298$	−6.42462	−0.372168
$299$	0	0
$300$	−5.28756	−0.305277
$301$	−4.72277	−0.272216
$302$	−16.9323	−0.974342
$303$	−4.26905	−0.245251
$304$	−17.8337	−1.02283
$305$	−1.98507	−0.113665
$306$	−11.1924	−0.639825
$307$	28.5122	1.62728	0.813638	−	0.581372i	$-0.197484\pi$
$307$	28.5122	1.62728	0.813638	+	0.581372i	$0.197484\pi$
$308$	0.688179	0.0392126
$309$	6.67783	0.379889
$310$	5.22500	0.296760
$311$	23.5329	1.33443	0.667213	−	0.744867i	$-0.267487\pi$
$311$	23.5329	1.33443	0.667213	+	0.744867i	$0.267487\pi$
$312$	0	0
$313$	−16.4524	−0.929942	−0.464971	−	0.885326i	$-0.653935\pi$
$313$	−16.4524	−0.929942	−0.464971	+	0.885326i	$0.653935\pi$
$314$	28.5226	1.60962
$315$	0.681820	0.0384162
$316$	−3.89109	−0.218891
$317$	15.7235	0.883119	0.441560	−	0.897232i	$-0.354425\pi$
$317$	15.7235	0.883119	0.441560	+	0.897232i	$0.354425\pi$
$318$	21.7508	1.21972
$319$	3.80839	0.213229
$320$	0.351937	0.0196739
$321$	−5.02359	−0.280390
$322$	−6.55779	−0.365451
$323$	−22.5602	−1.25528
$324$	1.16591	0.0647729
$325$	0	0
$326$	30.4070	1.68409
$327$	−15.0818	−0.834028
$328$	0.233660	0.0129017
$329$	11.2638	0.620991
$330$	0.716068	0.0394183
$331$	−4.43382	−0.243705	−0.121852	−	0.992548i	$-0.538883\pi$
$331$	−4.43382	−0.243705	−0.121852	+	0.992548i	$0.538883\pi$
$332$	15.9110	0.873232
$333$	−10.5343	−0.577275
$334$	6.41934	0.351250
$335$	5.10301	0.278807
$336$	4.97247	0.271271
$337$	−4.04766	−0.220490	−0.110245	−	0.993904i	$-0.535164\pi$
$337$	−4.04766	−0.220490	−0.110245	+	0.993904i	$0.535164\pi$
$338$	0	0
$339$	−2.34233	−0.127218
$340$	5.00044	0.271187
$341$	2.54216	0.137666
$342$	6.38145	0.345069
$343$	−1.00000	−0.0539949
$344$	−7.00903	−0.377901
$345$	−2.51291	−0.135291
$346$	17.5348	0.942678
$347$	24.9519	1.33949	0.669743	−	0.742593i	$-0.266404\pi$
$347$	24.9519	1.33949	0.669743	+	0.742593i	$0.266404\pi$
$348$	−7.52268	−0.403258
$349$	25.2777	1.35308	0.676541	−	0.736405i	$-0.263478\pi$
$349$	25.2777	1.35308	0.676541	+	0.736405i	$0.263478\pi$
$350$	8.06935	0.431325
$351$	0	0
$352$	3.47028	0.184966
$353$	21.0434	1.12003	0.560014	−	0.828483i	$-0.310796\pi$
$353$	21.0434	1.12003	0.560014	+	0.828483i	$0.310796\pi$
$354$	5.02938	0.267308
$355$	−4.76675	−0.252993
$356$	−14.2802	−0.756850
$357$	6.29031	0.332919
$358$	18.9674	1.00246
$359$	4.11834	0.217358	0.108679	−	0.994077i	$-0.465338\pi$
$359$	4.11834	0.217358	0.108679	+	0.994077i	$0.465338\pi$
$360$	1.01188	0.0533310
$361$	−6.13708	−0.323004
$362$	44.4123	2.33426
$363$	−10.6516	−0.559064
$364$	0	0
$365$	4.97860	0.260592
$366$	5.18030	0.270778
$367$	13.5033	0.704865	0.352433	−	0.935837i	$-0.385355\pi$
$367$	13.5033	0.704865	0.352433	+	0.935837i	$0.385355\pi$
$368$	−18.3265	−0.955337
$369$	−0.157443	−0.00819615
$370$	12.7798	0.664390
$371$	−12.2243	−0.634656
$372$	−5.02150	−0.260353
$373$	24.8181	1.28503	0.642517	−	0.766271i	$-0.277890\pi$
$373$	24.8181	1.28503	0.642517	+	0.766271i	$0.277890\pi$
$374$	6.60628	0.341603
$375$	6.50124	0.335722
$376$	16.7165	0.862086
$377$	0	0
$378$	−1.77930	−0.0915174
$379$	−36.0626	−1.85241	−0.926205	−	0.377021i	$-0.876948\pi$
$379$	−36.0626	−1.85241	−0.926205	+	0.377021i	$0.876948\pi$
$380$	−2.85105	−0.146256
$381$	−2.33606	−0.119680
$382$	−28.1634	−1.44096
$383$	−24.5207	−1.25295	−0.626474	−	0.779442i	$-0.715503\pi$
$383$	−24.5207	−1.25295	−0.626474	+	0.779442i	$0.715503\pi$
$384$	10.8403	0.553189
$385$	−0.402444	−0.0205104
$386$	−33.5342	−1.70685
$387$	4.72277	0.240072
$388$	−12.3679	−0.627883
$389$	−38.3037	−1.94208	−0.971038	−	0.238925i	$-0.923205\pi$
$389$	−38.3037	−1.94208	−0.971038	+	0.238925i	$0.923205\pi$
$390$	0	0
$391$	−23.1836	−1.17244
$392$	−1.48409	−0.0749580
$393$	7.64336	0.385556
$394$	23.6889	1.19343
$395$	2.27549	0.114492
$396$	−0.688179	−0.0345823
$397$	15.6502	0.785459	0.392729	−	0.919654i	$-0.371531\pi$
$397$	15.6502	0.785459	0.392729	+	0.919654i	$0.371531\pi$
$398$	36.6701	1.83811
$399$	−3.58649	−0.179549
$400$	22.5508	1.12754
$401$	30.5364	1.52492	0.762458	−	0.647038i	$-0.223992\pi$
$401$	30.5364	1.52492	0.762458	+	0.647038i	$0.223992\pi$
$402$	−13.3170	−0.664191
$403$	0	0
$404$	−4.97734	−0.247632
$405$	−0.681820	−0.0338799
$406$	11.4804	0.569761
$407$	6.21785	0.308208
$408$	9.33541	0.462171
$409$	−9.16639	−0.453249	−0.226625	−	0.973982i	$-0.572769\pi$
$409$	−9.16639	−0.453249	−0.226625	+	0.973982i	$0.572769\pi$
$410$	0.191004	0.00943301
$411$	−7.41962	−0.365983
$412$	7.78577	0.383577
$413$	−2.82660	−0.139088
$414$	6.55779	0.322298
$415$	−9.30470	−0.456750
$416$	0	0
$417$	3.62613	0.177572
$418$	−3.76664	−0.184233
$419$	26.2380	1.28181	0.640904	−	0.767621i	$-0.278560\pi$
$419$	26.2380	1.28181	0.640904	+	0.767621i	$0.278560\pi$
$420$	0.794942	0.0387892
$421$	8.78689	0.428247	0.214123	−	0.976807i	$-0.431311\pi$
$421$	8.78689	0.428247	0.214123	+	0.976807i	$0.431311\pi$
$422$	−32.9480	−1.60388
$423$	−11.2638	−0.547663
$424$	−18.1421	−0.881056
$425$	28.5273	1.38378
$426$	12.4395	0.602695
$427$	−2.91142	−0.140894
$428$	−5.85707	−0.283112
$429$	0	0
$430$	−5.72949	−0.276300
$431$	−38.0126	−1.83100	−0.915502	−	0.402313i	$-0.868206\pi$
$431$	−38.0126	−1.83100	−0.915502	+	0.402313i	$0.868206\pi$
$432$	−4.97247	−0.239238
$433$	−2.12832	−0.102281	−0.0511403	−	0.998691i	$-0.516286\pi$
$433$	−2.12832	−0.102281	−0.0511403	+	0.998691i	$0.516286\pi$
$434$	7.66332	0.367851
$435$	4.39922	0.210927
$436$	−17.5841	−0.842126
$437$	13.2184	0.632320
$438$	−12.9923	−0.620798
$439$	20.6388	0.985036	0.492518	−	0.870302i	$-0.336077\pi$
$439$	20.6388	0.985036	0.492518	+	0.870302i	$0.336077\pi$
$440$	−0.597264	−0.0284734
$441$	1.00000	0.0476190
$442$	0	0
$443$	−14.0681	−0.668395	−0.334197	−	0.942503i	$-0.608465\pi$
$443$	−14.0681	−0.668395	−0.334197	+	0.942503i	$0.608465\pi$
$444$	−12.2821	−0.582881
$445$	8.35100	0.395876
$446$	−26.3424	−1.24735
$447$	−3.61075	−0.170783
$448$	0.516173	0.0243869
$449$	6.25258	0.295078	0.147539	−	0.989056i	$-0.452865\pi$
$449$	6.25258	0.295078	0.147539	+	0.989056i	$0.452865\pi$
$450$	−8.06935	−0.380393
$451$	0.0929306	0.00437593
$452$	−2.73095	−0.128453
$453$	−9.51624	−0.447112
$454$	0.276367	0.0129705
$455$	0	0
$456$	−5.32269	−0.249258
$457$	−33.9909	−1.59003	−0.795014	−	0.606592i	$-0.792536\pi$
$457$	−33.9909	−1.59003	−0.795014	+	0.606592i	$0.792536\pi$
$458$	−44.1651	−2.06370
$459$	−6.29031	−0.293607
$460$	−2.92984	−0.136604
$461$	−11.8929	−0.553909	−0.276955	−	0.960883i	$-0.589325\pi$
$461$	−11.8929	−0.553909	−0.276955	+	0.960883i	$0.589325\pi$
$462$	1.05023	0.0488612
$463$	−13.4263	−0.623972	−0.311986	−	0.950087i	$-0.600994\pi$
$463$	−13.4263	−0.623972	−0.311986	+	0.950087i	$0.600994\pi$
$464$	32.0833	1.48943
$465$	2.93655	0.136179
$466$	−17.4319	−0.807518
$467$	−39.4492	−1.82549	−0.912745	−	0.408530i	$-0.866042\pi$
$467$	−39.4492	−1.82549	−0.912745	+	0.408530i	$0.866042\pi$
$468$	0	0
$469$	7.48440	0.345597
$470$	13.6648	0.630309
$471$	16.0302	0.738633
$472$	−4.19494	−0.193088
$473$	−2.78761	−0.128174
$474$	−5.93819	−0.272750
$475$	−16.2652	−0.746297
$476$	7.33395	0.336151
$477$	12.2243	0.559714
$478$	30.6935	1.40389
$479$	−33.6443	−1.53725	−0.768624	−	0.639701i	$-0.779058\pi$
$479$	−33.6443	−1.53725	−0.768624	+	0.639701i	$0.779058\pi$
$480$	4.00865	0.182969
$481$	0	0
$482$	1.48875	0.0678109
$483$	−3.68560	−0.167701
$484$	−12.4188	−0.564493
$485$	7.23266	0.328418
$486$	1.77930	0.0807107
$487$	−18.5443	−0.840321	−0.420161	−	0.907450i	$-0.638026\pi$
$487$	−18.5443	−0.840321	−0.420161	+	0.907450i	$0.638026\pi$
$488$	−4.32082	−0.195594
$489$	17.0893	0.772805
$490$	−1.21316	−0.0548051
$491$	−28.1815	−1.27181	−0.635906	−	0.771767i	$-0.719373\pi$
$491$	−28.1815	−1.27181	−0.635906	+	0.771767i	$0.719373\pi$
$492$	−0.183565	−0.00827574
$493$	40.5862	1.82791
$494$	0	0
$495$	0.402444	0.0180885
$496$	21.4161	0.961610
$497$	−6.99122	−0.313599
$498$	24.2819	1.08810
$499$	−14.1038	−0.631373	−0.315686	−	0.948864i	$-0.602235\pi$
$499$	−14.1038	−0.631373	−0.315686	+	0.948864i	$0.602235\pi$
$500$	7.57987	0.338982
$501$	3.60779	0.161184
$502$	−25.9941	−1.16017
$503$	22.2708	0.993004	0.496502	−	0.868036i	$-0.334617\pi$
$503$	22.2708	0.993004	0.496502	+	0.868036i	$0.334617\pi$
$504$	1.48409	0.0661067
$505$	2.91073	0.129526
$506$	−3.87073	−0.172075
$507$	0	0
$508$	−2.72364	−0.120842
$509$	6.93189	0.307251	0.153625	−	0.988129i	$-0.450905\pi$
$509$	6.93189	0.307251	0.153625	+	0.988129i	$0.450905\pi$
$510$	7.63117	0.337914
$511$	7.30193	0.323018
$512$	14.4756	0.639739
$513$	3.58649	0.158347
$514$	−22.2949	−0.983384
$515$	−4.55308	−0.200633
$516$	5.50634	0.242403
$517$	6.64842	0.292397
$518$	18.7437	0.823549
$519$	9.85489	0.432582
$520$	0	0
$521$	18.8949	0.827801	0.413900	−	0.910322i	$-0.364166\pi$
$521$	18.8949	0.827801	0.413900	+	0.910322i	$0.364166\pi$
$522$	−11.4804	−0.502482
$523$	12.5596	0.549194	0.274597	−	0.961559i	$-0.411456\pi$
$523$	12.5596	0.549194	0.274597	+	0.961559i	$0.411456\pi$
$524$	8.91148	0.389300
$525$	4.53512	0.197929
$526$	34.2490	1.49333
$527$	27.0919	1.18014
$528$	2.93500	0.127729
$529$	−9.41636	−0.409407
$530$	−14.8301	−0.644179
$531$	2.82660	0.122664
$532$	−4.18154	−0.181293
$533$	0	0
$534$	−21.7931	−0.943079
$535$	3.42518	0.148084
$536$	11.1075	0.479773
$537$	10.6600	0.460013
$538$	11.9710	0.516106
$539$	−0.590249	−0.0254238
$540$	−0.794942	−0.0342089
$541$	19.5342	0.839840	0.419920	−	0.907561i	$-0.362058\pi$
$541$	19.5342	0.839840	0.419920	+	0.907561i	$0.362058\pi$
$542$	28.5159	1.22486
$543$	24.9606	1.07116
$544$	36.9829	1.58563
$545$	10.2831	0.440479
$546$	0	0
$547$	23.0987	0.987630	0.493815	−	0.869567i	$-0.335602\pi$
$547$	23.0987	0.987630	0.493815	+	0.869567i	$0.335602\pi$
$548$	−8.65063	−0.369537
$549$	2.91142	0.124256
$550$	4.76292	0.203092
$551$	−23.1407	−0.985827
$552$	−5.46977	−0.232809
$553$	3.33737	0.141920
$554$	−7.16799	−0.304539
$555$	7.18249	0.304880
$556$	4.22775	0.179297
$557$	−13.4995	−0.571993	−0.285997	−	0.958231i	$-0.592325\pi$
$557$	−13.4995	−0.571993	−0.285997	+	0.958231i	$0.592325\pi$
$558$	−7.66332	−0.324414
$559$	0	0
$560$	−3.39033	−0.143268
$561$	3.71285	0.156757
$562$	23.4332	0.988468
$563$	−0.135042	−0.00569134	−0.00284567	−	0.999996i	$-0.500906\pi$
$563$	−0.135042	−0.00569134	−0.00284567	+	0.999996i	$0.500906\pi$
$564$	−13.1326	−0.552980
$565$	1.59705	0.0671882
$566$	−11.2466	−0.472732
$567$	−1.00000	−0.0419961
$568$	−10.3756	−0.435351
$569$	−10.4694	−0.438902	−0.219451	−	0.975624i	$-0.570427\pi$
$569$	−10.4694	−0.438902	−0.219451	+	0.975624i	$0.570427\pi$
$570$	−4.35100	−0.182243
$571$	−38.7700	−1.62247	−0.811237	−	0.584718i	$-0.801205\pi$
$571$	−38.7700	−1.62247	−0.811237	+	0.584718i	$0.801205\pi$
$572$	0	0
$573$	−15.8283	−0.661239
$574$	0.280138	0.0116928
$575$	−16.7146	−0.697049
$576$	−0.516173	−0.0215072
$577$	25.0470	1.04272	0.521359	−	0.853337i	$-0.325425\pi$
$577$	25.0470	1.04272	0.521359	+	0.853337i	$0.325425\pi$
$578$	40.1553	1.67024
$579$	−18.8468	−0.783248
$580$	5.12911	0.212975
$581$	−13.6469	−0.566167
$582$	−18.8746	−0.782378
$583$	−7.21541	−0.298832
$584$	10.8367	0.448428
$585$	0	0
$586$	−37.4224	−1.54591
$587$	−13.2480	−0.546802	−0.273401	−	0.961900i	$-0.588149\pi$
$587$	−13.2480	−0.546802	−0.273401	+	0.961900i	$0.588149\pi$
$588$	1.16591	0.0480814
$589$	−15.4467	−0.636472
$590$	−3.42913	−0.141175
$591$	13.3136	0.547649
$592$	52.3815	2.15286
$593$	12.0199	0.493597	0.246798	−	0.969067i	$-0.420621\pi$
$593$	12.0199	0.493597	0.246798	+	0.969067i	$0.420621\pi$
$594$	−1.05023	−0.0430915
$595$	−4.28886	−0.175826
$596$	−4.20982	−0.172441
$597$	20.6093	0.843481
$598$	0	0
$599$	−20.5324	−0.838931	−0.419465	−	0.907771i	$-0.637782\pi$
$599$	−20.5324	−0.838931	−0.419465	+	0.907771i	$0.637782\pi$
$600$	6.73054	0.274773
$601$	−35.1795	−1.43500	−0.717500	−	0.696558i	$-0.754714\pi$
$601$	−35.1795	−1.43500	−0.717500	+	0.696558i	$0.754714\pi$
$602$	−8.40323	−0.342490
$603$	−7.48440	−0.304788
$604$	−11.0951	−0.451453
$605$	7.26248	0.295262
$606$	−7.59593	−0.308564
$607$	−29.5744	−1.20039	−0.600194	−	0.799855i	$-0.704910\pi$
$607$	−29.5744	−1.20039	−0.600194	+	0.799855i	$0.704910\pi$
$608$	−21.0862	−0.855159
$609$	6.45218	0.261456
$610$	−3.53203	−0.143008
$611$	0	0
$612$	−7.33395	−0.296458
$613$	−35.3768	−1.42886	−0.714428	−	0.699709i	$-0.753313\pi$
$613$	−35.3768	−1.42886	−0.714428	+	0.699709i	$0.753313\pi$
$614$	50.7318	2.04737
$615$	0.107348	0.00432868
$616$	−0.875984	−0.0352944
$617$	10.8490	0.436765	0.218383	−	0.975863i	$-0.429922\pi$
$617$	10.8490	0.436765	0.218383	+	0.975863i	$0.429922\pi$
$618$	11.8819	0.477959
$619$	21.5126	0.864665	0.432332	−	0.901714i	$-0.357691\pi$
$619$	21.5126	0.864665	0.432332	+	0.901714i	$0.357691\pi$
$620$	3.42376	0.137501
$621$	3.68560	0.147898
$622$	41.8721	1.67892
$623$	12.2481	0.490710
$624$	0	0
$625$	18.2429	0.729717
$626$	−29.2737	−1.17001
$627$	−2.11692	−0.0845418
$628$	18.6898	0.745805
$629$	66.2639	2.64212
$630$	1.21316	0.0483336
$631$	−0.494169	−0.0196726	−0.00983628	−	0.999952i	$-0.503131\pi$
$631$	−0.494169	−0.0196726	−0.00983628	+	0.999952i	$0.503131\pi$
$632$	4.95297	0.197019
$633$	−18.5174	−0.736000
$634$	27.9768	1.11110
$635$	1.59277	0.0632072
$636$	14.2525	0.565149
$637$	0	0
$638$	6.77628	0.268275
$639$	6.99122	0.276568
$640$	−7.39110	−0.292159
$641$	10.0633	0.397477	0.198738	−	0.980053i	$-0.436316\pi$
$641$	10.0633	0.397477	0.198738	+	0.980053i	$0.436316\pi$
$642$	−8.93848	−0.352774
$643$	30.3453	1.19670	0.598351	−	0.801234i	$-0.295823\pi$
$643$	30.3453	1.19670	0.598351	+	0.801234i	$0.295823\pi$
$644$	−4.29709	−0.169329
$645$	−3.22008	−0.126790
$646$	−40.1413	−1.57934
$647$	−32.5345	−1.27906	−0.639531	−	0.768765i	$-0.720871\pi$
$647$	−32.5345	−1.27906	−0.639531	+	0.768765i	$0.720871\pi$
$648$	−1.48409	−0.0583007
$649$	−1.66840	−0.0654904
$650$	0	0
$651$	4.30692	0.168802
$652$	19.9246	0.780308
$653$	25.0183	0.979042	0.489521	−	0.871992i	$-0.337172\pi$
$653$	25.0183	0.979042	0.489521	+	0.871992i	$0.337172\pi$
$654$	−26.8351	−1.04934
$655$	−5.21139	−0.203626
$656$	0.782881	0.0305664
$657$	−7.30193	−0.284875
$658$	20.0416	0.781303
$659$	25.3216	0.986391	0.493195	−	0.869919i	$-0.335829\pi$
$659$	25.3216	0.986391	0.493195	+	0.869919i	$0.335829\pi$
$660$	0.469214	0.0182641
$661$	−7.38049	−0.287068	−0.143534	−	0.989645i	$-0.545847\pi$
$661$	−7.38049	−0.287068	−0.143534	+	0.989645i	$0.545847\pi$
$662$	−7.88910	−0.306619
$663$	0	0
$664$	−20.2532	−0.785977
$665$	2.44534	0.0948263
$666$	−18.7437	−0.726302
$667$	−23.7801	−0.920771
$668$	4.20636	0.162749
$669$	−14.8049	−0.572390
$670$	9.07979	0.350783
$671$	−1.71846	−0.0663406
$672$	5.87934	0.226801
$673$	−29.0732	−1.12069	−0.560344	−	0.828260i	$-0.689331\pi$
$673$	−29.0732	−1.12069	−0.560344	+	0.828260i	$0.689331\pi$
$674$	−7.20201	−0.277411
$675$	−4.53512	−0.174557
$676$	0	0
$677$	33.7362	1.29659	0.648293	−	0.761391i	$-0.275483\pi$
$677$	33.7362	1.29659	0.648293	+	0.761391i	$0.275483\pi$
$678$	−4.16770	−0.160060
$679$	10.6079	0.407093
$680$	−6.36507	−0.244089
$681$	0.155323	0.00595200
$682$	4.52327	0.173205
$683$	31.1764	1.19293	0.596465	−	0.802639i	$-0.296571\pi$
$683$	31.1764	1.19293	0.596465	+	0.802639i	$0.296571\pi$
$684$	4.18154	0.159885
$685$	5.05885	0.193289
$686$	−1.77930	−0.0679340
$687$	−24.8216	−0.947003
$688$	−23.4838	−0.895313
$689$	0	0
$690$	−4.47123	−0.170217
$691$	12.4412	0.473284	0.236642	−	0.971597i	$-0.423953\pi$
$691$	12.4412	0.473284	0.236642	+	0.971597i	$0.423953\pi$
$692$	11.4899	0.436782
$693$	0.590249	0.0224217
$694$	44.3969	1.68528
$695$	−2.47237	−0.0937822
$696$	9.57563	0.362963
$697$	0.990365	0.0375128
$698$	44.9766	1.70239
$699$	−9.79706	−0.370559
$700$	5.28756	0.199851
$701$	−37.9806	−1.43451	−0.717253	−	0.696813i	$-0.754601\pi$
$701$	−37.9806	−1.43451	−0.717253	+	0.696813i	$0.754601\pi$
$702$	0	0
$703$	−37.7811	−1.42494
$704$	0.304671	0.0114827
$705$	7.67985	0.289240
$706$	37.4426	1.40917
$707$	4.26905	0.160554
$708$	3.29557	0.123855
$709$	−51.1119	−1.91955	−0.959774	−	0.280775i	$-0.909409\pi$
$709$	−51.1119	−1.91955	−0.959774	+	0.280775i	$0.909409\pi$
$710$	−8.48148	−0.318304
$711$	−3.33737	−0.125161
$712$	18.1773	0.681224
$713$	−15.8736	−0.594471
$714$	11.1924	0.418864
$715$	0	0
$716$	12.4286	0.464480
$717$	17.2503	0.644224
$718$	7.32777	0.273470
$719$	42.4987	1.58493	0.792467	−	0.609915i	$-0.208796\pi$
$719$	42.4987	1.58493	0.792467	+	0.609915i	$0.208796\pi$
$720$	3.39033	0.126350
$721$	−6.67783	−0.248696
$722$	−10.9197	−0.406389
$723$	0.836707	0.0311175
$724$	29.1018	1.08156
$725$	29.2614	1.08674
$726$	−18.9524	−0.703390
$727$	10.7589	0.399024	0.199512	−	0.979895i	$-0.436064\pi$
$727$	10.7589	0.399024	0.199512	+	0.979895i	$0.436064\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	8.85843	0.327865
$731$	−29.7077	−1.09878
$732$	3.39446	0.125463
$733$	−18.9597	−0.700291	−0.350145	−	0.936695i	$-0.613868\pi$
$733$	−18.9597	−0.700291	−0.350145	+	0.936695i	$0.613868\pi$
$734$	24.0264	0.886830
$735$	−0.681820	−0.0251493
$736$	−21.6689	−0.798726
$737$	4.41766	0.162727
$738$	−0.280138	−0.0103120
$739$	−40.9577	−1.50665	−0.753327	−	0.657646i	$-0.771552\pi$
$739$	−40.9577	−1.50665	−0.753327	+	0.657646i	$0.771552\pi$
$740$	8.37415	0.307840
$741$	0	0
$742$	−21.7508	−0.798497
$743$	−1.66722	−0.0611643	−0.0305821	−	0.999532i	$-0.509736\pi$
$743$	−1.66722	−0.0611643	−0.0305821	+	0.999532i	$0.509736\pi$
$744$	6.39188	0.234338
$745$	2.46188	0.0901965
$746$	44.1589	1.61677
$747$	13.6469	0.499313
$748$	4.32886	0.158279
$749$	5.02359	0.183558
$750$	11.5677	0.422391
$751$	−45.3037	−1.65316	−0.826578	−	0.562823i	$-0.809715\pi$
$751$	−45.3037	−1.65316	−0.826578	+	0.562823i	$0.809715\pi$
$752$	56.0087	2.04243
$753$	−14.6092	−0.532388
$754$	0	0
$755$	6.48836	0.236136
$756$	−1.16591	−0.0424038
$757$	−35.3247	−1.28390	−0.641950	−	0.766747i	$-0.721874\pi$
$757$	−35.3247	−1.28390	−0.641950	+	0.766747i	$0.721874\pi$
$758$	−64.1662	−2.33062
$759$	−2.17542	−0.0789628
$760$	3.62911	0.131642
$761$	−6.80679	−0.246746	−0.123373	−	0.992360i	$-0.539371\pi$
$761$	−6.80679	−0.246746	−0.123373	+	0.992360i	$0.539371\pi$
$762$	−4.15655	−0.150576
$763$	15.0818	0.545999
$764$	−18.4545	−0.667659
$765$	4.28886	0.155064
$766$	−43.6297	−1.57640
$767$	0	0
$768$	20.3204	0.733250
$769$	−0.487660	−0.0175855	−0.00879273	−	0.999961i	$-0.502799\pi$
$769$	−0.487660	−0.0175855	−0.00879273	+	0.999961i	$0.502799\pi$
$770$	−0.716068	−0.0258053
$771$	−12.5301	−0.451261
$772$	−21.9738	−0.790853
$773$	36.4445	1.31082	0.655409	−	0.755274i	$-0.272496\pi$
$773$	36.4445	1.31082	0.655409	+	0.755274i	$0.272496\pi$
$774$	8.40323	0.302048
$775$	19.5324	0.701625
$776$	15.7431	0.565143
$777$	10.5343	0.377915
$778$	−68.1539	−2.44343
$779$	−0.564668	−0.0202313
$780$	0	0
$781$	−4.12656	−0.147660
$782$	−41.2505	−1.47512
$783$	−6.45218	−0.230582
$784$	−4.97247	−0.177588
$785$	−10.9297	−0.390098
$786$	13.5998	0.485090
$787$	−6.23840	−0.222375	−0.111187	−	0.993799i	$-0.535465\pi$
$787$	−6.23840	−0.222375	−0.111187	+	0.993799i	$0.535465\pi$
$788$	15.5225	0.552967
$789$	19.2485	0.685266
$790$	4.04878	0.144049
$791$	2.34233	0.0832836
$792$	0.875984	0.0311267
$793$	0	0
$794$	27.8463	0.988230
$795$	−8.33480	−0.295605
$796$	24.0286	0.851671
$797$	37.8613	1.34112	0.670559	−	0.741856i	$-0.266054\pi$
$797$	37.8613	1.34112	0.670559	+	0.741856i	$0.266054\pi$
$798$	−6.38145	−0.225901
$799$	70.8525	2.50658
$800$	26.6635	0.942698
$801$	−12.2481	−0.432766
$802$	54.3335	1.91858
$803$	4.30996	0.152095
$804$	−8.72615	−0.307748
$805$	2.51291	0.0885686
$806$	0	0
$807$	6.72792	0.236834
$808$	6.33567	0.222888
$809$	−39.8858	−1.40231	−0.701155	−	0.713009i	$-0.747332\pi$
$809$	−39.8858	−1.40231	−0.701155	+	0.713009i	$0.747332\pi$
$810$	−1.21316	−0.0426262
$811$	−35.7239	−1.25444	−0.627218	−	0.778843i	$-0.715807\pi$
$811$	−35.7239	−1.25444	−0.627218	+	0.778843i	$0.715807\pi$
$812$	7.52268	0.263994
$813$	16.0265	0.562073
$814$	11.0634	0.387773
$815$	−11.6518	−0.408145
$816$	31.2784	1.09496
$817$	16.9382	0.592592
$818$	−16.3098	−0.570258
$819$	0	0
$820$	0.125158	0.00437071
$821$	−29.8337	−1.04120	−0.520601	−	0.853800i	$-0.674292\pi$
$821$	−29.8337	−1.04120	−0.520601	+	0.853800i	$0.674292\pi$
$822$	−13.2017	−0.460464
$823$	−13.0573	−0.455149	−0.227575	−	0.973761i	$-0.573080\pi$
$823$	−13.0573	−0.455149	−0.227575	+	0.973761i	$0.573080\pi$
$824$	−9.91052	−0.345249
$825$	2.67685	0.0931960
$826$	−5.02938	−0.174994
$827$	14.8338	0.515821	0.257910	−	0.966169i	$-0.416966\pi$
$827$	14.8338	0.515821	0.257910	+	0.966169i	$0.416966\pi$
$828$	4.29709	0.149334
$829$	−45.3612	−1.57546	−0.787730	−	0.616020i	$-0.788744\pi$
$829$	−45.3612	−1.57546	−0.787730	+	0.616020i	$0.788744\pi$
$830$	−16.5559	−0.574662
$831$	−4.02854	−0.139749
$832$	0	0
$833$	−6.29031	−0.217946
$834$	6.45198	0.223414
$835$	−2.45986	−0.0851270
$836$	−2.46815	−0.0853627
$837$	−4.30692	−0.148869
$838$	46.6852	1.61271
$839$	−0.305908	−0.0105611	−0.00528056	−	0.999986i	$-0.501681\pi$
$839$	−0.305908	−0.0105611	−0.00528056	+	0.999986i	$0.501681\pi$
$840$	−1.01188	−0.0349133
$841$	12.6306	0.435539
$842$	15.6345	0.538801
$843$	13.1699	0.453594
$844$	−21.5896	−0.743146
$845$	0	0
$846$	−20.0416	−0.689045
$847$	10.6516	0.365994
$848$	−60.7852	−2.08737
$849$	−6.32082	−0.216930
$850$	50.7587	1.74101
$851$	−38.8251	−1.33091
$852$	8.15115	0.279254
$853$	25.1314	0.860484	0.430242	−	0.902714i	$-0.358428\pi$
$853$	25.1314	0.860484	0.430242	+	0.902714i	$0.358428\pi$
$854$	−5.18030	−0.177266
$855$	−2.44534	−0.0836289
$856$	7.45548	0.254823
$857$	−4.33277	−0.148005	−0.0740023	−	0.997258i	$-0.523577\pi$
$857$	−4.33277	−0.148005	−0.0740023	+	0.997258i	$0.523577\pi$
$858$	0	0
$859$	8.79868	0.300207	0.150104	−	0.988670i	$-0.452039\pi$
$859$	8.79868	0.300207	0.150104	+	0.988670i	$0.452039\pi$
$860$	−3.75433	−0.128022
$861$	0.157443	0.00536564
$862$	−67.6359	−2.30369
$863$	−21.2452	−0.723194	−0.361597	−	0.932334i	$-0.617768\pi$
$863$	−21.2452	−0.723194	−0.361597	+	0.932334i	$0.617768\pi$
$864$	−5.87934	−0.200019
$865$	−6.71926	−0.228462
$866$	−3.78692	−0.128685
$867$	22.5680	0.766450
$868$	5.02150	0.170441
$869$	1.96988	0.0668237
$870$	7.82755	0.265379
$871$	0	0
$872$	22.3828	0.757979
$873$	−10.6079	−0.359022
$874$	23.5195	0.795558
$875$	−6.50124	−0.219782
$876$	−8.51341	−0.287642
$877$	0.397425	0.0134201	0.00671004	−	0.999977i	$-0.497864\pi$
$877$	0.397425	0.0134201	0.00671004	+	0.999977i	$0.497864\pi$
$878$	36.7226	1.23933
$879$	−21.0321	−0.709394
$880$	−2.00114	−0.0674584
$881$	−28.2382	−0.951370	−0.475685	−	0.879616i	$-0.657800\pi$
$881$	−28.2382	−0.951370	−0.475685	+	0.879616i	$0.657800\pi$
$882$	1.77930	0.0599122
$883$	47.5408	1.59988	0.799938	−	0.600083i	$-0.204866\pi$
$883$	47.5408	1.59988	0.799938	+	0.600083i	$0.204866\pi$
$884$	0	0
$885$	−1.92723	−0.0647832
$886$	−25.0313	−0.840944
$887$	−3.73901	−0.125544	−0.0627719	−	0.998028i	$-0.519994\pi$
$887$	−3.73901	−0.125544	−0.0627719	+	0.998028i	$0.519994\pi$
$888$	15.6339	0.524638
$889$	2.33606	0.0783489
$890$	14.8590	0.498073
$891$	−0.590249	−0.0197741
$892$	−17.2612	−0.577948
$893$	−40.3974	−1.35185
$894$	−6.42462	−0.214871
$895$	−7.26820	−0.242949
$896$	−10.8403	−0.362148
$897$	0	0
$898$	11.1252	0.371254
$899$	27.7891	0.926817
$900$	−5.28756	−0.176252
$901$	−76.8949	−2.56174
$902$	0.165351	0.00550560
$903$	−4.72277	−0.157164
$904$	3.47623	0.115618
$905$	−17.0186	−0.565717
$906$	−16.9323	−0.562537
$907$	−30.1761	−1.00198	−0.500990	−	0.865453i	$-0.667031\pi$
$907$	−30.1761	−1.00198	−0.500990	+	0.865453i	$0.667031\pi$
$908$	0.181093	0.00600979
$909$	−4.26905	−0.141596
$910$	0	0
$911$	−39.3976	−1.30530	−0.652651	−	0.757659i	$-0.726343\pi$
$911$	−39.3976	−1.30530	−0.652651	+	0.757659i	$0.726343\pi$
$912$	−17.8337	−0.590534
$913$	−8.05505	−0.266583
$914$	−60.4801	−2.00050
$915$	−1.98507	−0.0656242
$916$	−28.9398	−0.956199
$917$	−7.64336	−0.252406
$918$	−11.1924	−0.369403
$919$	52.8073	1.74195	0.870976	−	0.491326i	$-0.163488\pi$
$919$	52.8073	1.74195	0.870976	+	0.491326i	$0.163488\pi$
$920$	3.72940	0.122955
$921$	28.5122	0.939508
$922$	−21.1611	−0.696904
$923$	0	0
$924$	0.688179	0.0226394
$925$	47.7743	1.57081
$926$	−23.8894	−0.785054
$927$	6.67783	0.219329
$928$	37.9346	1.24526
$929$	−43.9885	−1.44322	−0.721608	−	0.692302i	$-0.756596\pi$
$929$	−43.9885	−1.44322	−0.721608	+	0.692302i	$0.756596\pi$
$930$	5.22500	0.171335
$931$	3.58649	0.117543
$932$	−11.4225	−0.374157
$933$	23.5329	0.770432
$934$	−70.1920	−2.29675
$935$	−2.53150	−0.0827888
$936$	0	0
$937$	−24.1351	−0.788460	−0.394230	−	0.919012i	$-0.628989\pi$
$937$	−24.1351	−0.788460	−0.394230	+	0.919012i	$0.628989\pi$
$938$	13.3170	0.434815
$939$	−16.4524	−0.536902
$940$	8.95404	0.292049
$941$	37.7726	1.23135	0.615677	−	0.787999i	$-0.288883\pi$
$941$	37.7726	1.23135	0.615677	+	0.787999i	$0.288883\pi$
$942$	28.5226	0.929316
$943$	−0.580272	−0.0188962
$944$	−14.0552	−0.457458
$945$	0.681820	0.0221796
$946$	−4.96000	−0.161263
$947$	13.0607	0.424415	0.212207	−	0.977225i	$-0.431935\pi$
$947$	13.0607	0.424415	0.212207	+	0.977225i	$0.431935\pi$
$948$	−3.89109	−0.126377
$949$	0	0
$950$	−28.9406	−0.938959
$951$	15.7235	0.509869
$952$	−9.33541	−0.302562
$953$	−2.00320	−0.0648901	−0.0324450	−	0.999474i	$-0.510329\pi$
$953$	−2.00320	−0.0648901	−0.0324450	+	0.999474i	$0.510329\pi$
$954$	21.7508	0.704208
$955$	10.7921	0.349224
$956$	20.1123	0.650479
$957$	3.80839	0.123108
$958$	−59.8633	−1.93410
$959$	7.41962	0.239592
$960$	0.351937	0.0113587
$961$	−12.4504	−0.401626
$962$	0	0
$963$	−5.02359	−0.161883
$964$	0.975528	0.0314196
$965$	12.8501	0.413661
$966$	−6.55779	−0.210993
$967$	4.28316	0.137737	0.0688685	−	0.997626i	$-0.478061\pi$
$967$	4.28316	0.137737	0.0688685	+	0.997626i	$0.478061\pi$
$968$	15.8080	0.508087
$969$	−22.5602	−0.724736
$970$	12.8691	0.413201
$971$	16.0101	0.513788	0.256894	−	0.966440i	$-0.417301\pi$
$971$	16.0101	0.513788	0.256894	+	0.966440i	$0.417301\pi$
$972$	1.16591	0.0373967
$973$	−3.62613	−0.116248
$974$	−32.9958	−1.05725
$975$	0	0
$976$	−14.4770	−0.463396
$977$	52.1870	1.66961	0.834805	−	0.550546i	$-0.185581\pi$
$977$	52.1870	1.66961	0.834805	+	0.550546i	$0.185581\pi$
$978$	30.4070	0.972309
$979$	7.22944	0.231054
$980$	−0.794942	−0.0253935
$981$	−15.0818	−0.481526
$982$	−50.1433	−1.60014
$983$	−10.4204	−0.332358	−0.166179	−	0.986096i	$-0.553143\pi$
$983$	−10.4204	−0.332358	−0.166179	+	0.986096i	$0.553143\pi$
$984$	0.233660	0.00744881
$985$	−9.07749	−0.289233
$986$	72.2151	2.29980
$987$	11.2638	0.358529
$988$	0	0
$989$	17.4062	0.553486
$990$	0.716068	0.0227581
$991$	31.9327	1.01438	0.507188	−	0.861836i	$-0.330685\pi$
$991$	31.9327	1.01438	0.507188	+	0.861836i	$0.330685\pi$
$992$	25.3219	0.803971
$993$	−4.43382	−0.140703
$994$	−12.4395	−0.394556
$995$	−14.0518	−0.445472
$996$	15.9110	0.504161
$997$	−57.9514	−1.83534	−0.917670	−	0.397344i	$-0.869932\pi$
$997$	−57.9514	−1.83534	−0.917670	+	0.397344i	$0.869932\pi$
$998$	−25.0949	−0.794365
$999$	−10.5343	−0.333290

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bb.1.7		8
13.6	odd	12		273.2.bd.a.127.2	yes	16
13.11	odd	12		273.2.bd.a.43.2	✓	16
13.12	even	2		3549.2.a.bd.1.2		8
39.11	even	12		819.2.ct.b.316.7		16
39.32	even	12		819.2.ct.b.127.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.a.43.2	✓	16	13.11	odd	12
273.2.bd.a.127.2	yes	16	13.6	odd	12
819.2.ct.b.127.7		16	39.32	even	12
819.2.ct.b.316.7		16	39.11	even	12
3549.2.a.bb.1.7		8	1.1	even	1	trivial
3549.2.a.bd.1.2		8	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.77930 q^{2} +1.00000 q^{3} +1.16591 q^{4} -0.681820 q^{5} +1.77930 q^{6} -1.00000 q^{7} -1.48409 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.77930 q^{2} +1.00000 q^{3} +1.16591 q^{4} -0.681820 q^{5} +1.77930 q^{6} -1.00000 q^{7} -1.48409 q^{8} +1.00000 q^{9} -1.21316 q^{10} -0.590249 q^{11} +1.16591 q^{12} -1.77930 q^{14} -0.681820 q^{15} -4.97247 q^{16} -6.29031 q^{17} +1.77930 q^{18} +3.58649 q^{19} -0.794942 q^{20} -1.00000 q^{21} -1.05023 q^{22} +3.68560 q^{23} -1.48409 q^{24} -4.53512 q^{25} +1.00000 q^{27} -1.16591 q^{28} -6.45218 q^{29} -1.21316 q^{30} -4.30692 q^{31} -5.87934 q^{32} -0.590249 q^{33} -11.1924 q^{34} +0.681820 q^{35} +1.16591 q^{36} -10.5343 q^{37} +6.38145 q^{38} +1.01188 q^{40} -0.157443 q^{41} -1.77930 q^{42} +4.72277 q^{43} -0.688179 q^{44} -0.681820 q^{45} +6.55779 q^{46} -11.2638 q^{47} -4.97247 q^{48} +1.00000 q^{49} -8.06935 q^{50} -6.29031 q^{51} +12.2243 q^{53} +1.77930 q^{54} +0.402444 q^{55} +1.48409 q^{56} +3.58649 q^{57} -11.4804 q^{58} +2.82660 q^{59} -0.794942 q^{60} +2.91142 q^{61} -7.66332 q^{62} -1.00000 q^{63} -0.516173 q^{64} -1.05023 q^{66} -7.48440 q^{67} -7.33395 q^{68} +3.68560 q^{69} +1.21316 q^{70} +6.99122 q^{71} -1.48409 q^{72} -7.30193 q^{73} -18.7437 q^{74} -4.53512 q^{75} +4.18154 q^{76} +0.590249 q^{77} -3.33737 q^{79} +3.39033 q^{80} +1.00000 q^{81} -0.280138 q^{82} +13.6469 q^{83} -1.16591 q^{84} +4.28886 q^{85} +8.40323 q^{86} -6.45218 q^{87} +0.875984 q^{88} -12.2481 q^{89} -1.21316 q^{90} +4.29709 q^{92} -4.30692 q^{93} -20.0416 q^{94} -2.44534 q^{95} -5.87934 q^{96} -10.6079 q^{97} +1.77930 q^{98} -0.590249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 8 q^{3} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 8 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 8 * q^3 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 8 * q^7 - 12 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} + 8 q^{3} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 8 q^{7} - 12 q^{8} + 8 q^{9} - 4 q^{10} - 8 q^{11} + 6 q^{12} + 2 q^{14} - 2 q^{15} + 10 q^{16} + 10 q^{17} - 2 q^{18} - 18 q^{19} - 2 q^{20} - 8 q^{21} + 2 q^{22} - 2 q^{23} - 12 q^{24} - 6 q^{25} + 8 q^{27} - 6 q^{28} - 12 q^{29} - 4 q^{30} - 16 q^{31} - 26 q^{32} - 8 q^{33} - 24 q^{34} + 2 q^{35} + 6 q^{36} - 24 q^{37} + 16 q^{38} - 30 q^{40} + 4 q^{41} + 2 q^{42} - 10 q^{43} + 20 q^{44} - 2 q^{45} - 12 q^{46} - 10 q^{47} + 10 q^{48} + 8 q^{49} + 16 q^{50} + 10 q^{51} + 6 q^{53} - 2 q^{54} - 10 q^{55} + 12 q^{56} - 18 q^{57} - 16 q^{58} - 6 q^{59} - 2 q^{60} + 6 q^{61} + 16 q^{62} - 8 q^{63} - 8 q^{64} + 2 q^{66} - 24 q^{67} + 20 q^{68} - 2 q^{69} + 4 q^{70} - 42 q^{71} - 12 q^{72} - 32 q^{73} - 18 q^{74} - 6 q^{75} - 28 q^{76} + 8 q^{77} - 2 q^{79} + 40 q^{80} + 8 q^{81} - 18 q^{82} + 2 q^{83} - 6 q^{84} - 4 q^{85} - 26 q^{86} - 12 q^{87} - 2 q^{88} - 12 q^{89} - 4 q^{90} - 10 q^{92} - 16 q^{93} - 16 q^{94} - 4 q^{95} - 26 q^{96} - 64 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 8 * q^3 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 8 * q^7 - 12 * q^8 + 8 * q^9 - 4 * q^10 - 8 * q^11 + 6 * q^12 + 2 * q^14 - 2 * q^15 + 10 * q^16 + 10 * q^17 - 2 * q^18 - 18 * q^19 - 2 * q^20 - 8 * q^21 + 2 * q^22 - 2 * q^23 - 12 * q^24 - 6 * q^25 + 8 * q^27 - 6 * q^28 - 12 * q^29 - 4 * q^30 - 16 * q^31 - 26 * q^32 - 8 * q^33 - 24 * q^34 + 2 * q^35 + 6 * q^36 - 24 * q^37 + 16 * q^38 - 30 * q^40 + 4 * q^41 + 2 * q^42 - 10 * q^43 + 20 * q^44 - 2 * q^45 - 12 * q^46 - 10 * q^47 + 10 * q^48 + 8 * q^49 + 16 * q^50 + 10 * q^51 + 6 * q^53 - 2 * q^54 - 10 * q^55 + 12 * q^56 - 18 * q^57 - 16 * q^58 - 6 * q^59 - 2 * q^60 + 6 * q^61 + 16 * q^62 - 8 * q^63 - 8 * q^64 + 2 * q^66 - 24 * q^67 + 20 * q^68 - 2 * q^69 + 4 * q^70 - 42 * q^71 - 12 * q^72 - 32 * q^73 - 18 * q^74 - 6 * q^75 - 28 * q^76 + 8 * q^77 - 2 * q^79 + 40 * q^80 + 8 * q^81 - 18 * q^82 + 2 * q^83 - 6 * q^84 - 4 * q^85 - 26 * q^86 - 12 * q^87 - 2 * q^88 - 12 * q^89 - 4 * q^90 - 10 * q^92 - 16 * q^93 - 16 * q^94 - 4 * q^95 - 26 * q^96 - 64 * q^97 - 2 * q^98 - 8 * q^99

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