LMFDB - Embedded newform 6041.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49510 q^{2} -2.54767 q^{3} +4.22552 q^{4} +0.711578 q^{5} +6.35668 q^{6} +1.00000 q^{7} -5.55291 q^{8} +3.49060 q^{9} +O(q^{10})$	\(q-2.49510 q^{2} -2.54767 q^{3} +4.22552 q^{4} +0.711578 q^{5} +6.35668 q^{6} +1.00000 q^{7} -5.55291 q^{8} +3.49060 q^{9} -1.77546 q^{10} -0.691942 q^{11} -10.7652 q^{12} -1.98418 q^{13} -2.49510 q^{14} -1.81286 q^{15} +5.40401 q^{16} -0.422664 q^{17} -8.70939 q^{18} -3.67376 q^{19} +3.00679 q^{20} -2.54767 q^{21} +1.72647 q^{22} +2.80691 q^{23} +14.1469 q^{24} -4.49366 q^{25} +4.95073 q^{26} -1.24988 q^{27} +4.22552 q^{28} -3.27897 q^{29} +4.52327 q^{30} +8.26482 q^{31} -2.37773 q^{32} +1.76284 q^{33} +1.05459 q^{34} +0.711578 q^{35} +14.7496 q^{36} -3.41334 q^{37} +9.16641 q^{38} +5.05503 q^{39} -3.95133 q^{40} -2.42563 q^{41} +6.35668 q^{42} +8.63345 q^{43} -2.92382 q^{44} +2.48383 q^{45} -7.00352 q^{46} +5.50347 q^{47} -13.7676 q^{48} +1.00000 q^{49} +11.2121 q^{50} +1.07681 q^{51} -8.38421 q^{52} +10.9406 q^{53} +3.11858 q^{54} -0.492371 q^{55} -5.55291 q^{56} +9.35952 q^{57} +8.18135 q^{58} -7.08243 q^{59} -7.66030 q^{60} -4.92764 q^{61} -20.6216 q^{62} +3.49060 q^{63} -4.87534 q^{64} -1.41190 q^{65} -4.39846 q^{66} -1.26973 q^{67} -1.78598 q^{68} -7.15106 q^{69} -1.77546 q^{70} -5.24862 q^{71} -19.3830 q^{72} -5.97129 q^{73} +8.51663 q^{74} +11.4483 q^{75} -15.5236 q^{76} -0.691942 q^{77} -12.6128 q^{78} -12.6365 q^{79} +3.84537 q^{80} -7.28752 q^{81} +6.05220 q^{82} -3.85662 q^{83} -10.7652 q^{84} -0.300759 q^{85} -21.5413 q^{86} +8.35371 q^{87} +3.84229 q^{88} +15.5354 q^{89} -6.19741 q^{90} -1.98418 q^{91} +11.8607 q^{92} -21.0560 q^{93} -13.7317 q^{94} -2.61417 q^{95} +6.05766 q^{96} -3.93257 q^{97} -2.49510 q^{98} -2.41529 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) $ 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * 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 $

$2$	−2.49510	−1.76430	−0.882151	−	0.470966i	$-0.843905\pi$
$2$	−2.49510	−1.76430	−0.882151	+	0.470966i	$0.843905\pi$
$3$	−2.54767	−1.47090	−0.735448	−	0.677582i	$-0.763028\pi$
$3$	−2.54767	−1.47090	−0.735448	+	0.677582i	$0.763028\pi$
$4$	4.22552	2.11276
$5$	0.711578	0.318227	0.159114	−	0.987260i	$-0.449136\pi$
$5$	0.711578	0.318227	0.159114	+	0.987260i	$0.449136\pi$
$6$	6.35668	2.59510
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−5.55291	−1.96325
$9$	3.49060	1.16353
$10$	−1.77546	−0.561449
$11$	−0.691942	−0.208628	−0.104314	−	0.994544i	$-0.533265\pi$
$11$	−0.691942	−0.208628	−0.104314	+	0.994544i	$0.533265\pi$
$12$	−10.7652	−3.10765
$13$	−1.98418	−0.550313	−0.275157	−	0.961399i	$-0.588730\pi$
$13$	−1.98418	−0.550313	−0.275157	+	0.961399i	$0.588730\pi$
$14$	−2.49510	−0.666844
$15$	−1.81286	−0.468079
$16$	5.40401	1.35100
$17$	−0.422664	−0.102511	−0.0512556	−	0.998686i	$-0.516322\pi$
$17$	−0.422664	−0.102511	−0.0512556	+	0.998686i	$0.516322\pi$
$18$	−8.70939	−2.05282
$19$	−3.67376	−0.842819	−0.421409	−	0.906870i	$-0.638464\pi$
$19$	−3.67376	−0.842819	−0.421409	+	0.906870i	$0.638464\pi$
$20$	3.00679	0.672339
$21$	−2.54767	−0.555946
$22$	1.72647	0.368084
$23$	2.80691	0.585281	0.292640	−	0.956223i	$-0.405466\pi$
$23$	2.80691	0.585281	0.292640	+	0.956223i	$0.405466\pi$
$24$	14.1469	2.88773
$25$	−4.49366	−0.898731
$26$	4.95073	0.970919
$27$	−1.24988	−0.240540
$28$	4.22552	0.798549
$29$	−3.27897	−0.608889	−0.304444	−	0.952530i	$-0.598471\pi$
$29$	−3.27897	−0.608889	−0.304444	+	0.952530i	$0.598471\pi$
$30$	4.52327	0.825833
$31$	8.26482	1.48441	0.742203	−	0.670175i	$-0.233781\pi$
$31$	8.26482	1.48441	0.742203	+	0.670175i	$0.233781\pi$
$32$	−2.37773	−0.420327
$33$	1.76284	0.306871
$34$	1.05459	0.180861
$35$	0.711578	0.120279
$36$	14.7496	2.45827
$37$	−3.41334	−0.561150	−0.280575	−	0.959832i	$-0.590525\pi$
$37$	−3.41334	−0.561150	−0.280575	+	0.959832i	$0.590525\pi$
$38$	9.16641	1.48699
$39$	5.05503	0.809453
$40$	−3.95133	−0.624760
$41$	−2.42563	−0.378820	−0.189410	−	0.981898i	$-0.560658\pi$
$41$	−2.42563	−0.378820	−0.189410	+	0.981898i	$0.560658\pi$
$42$	6.35668	0.980857
$43$	8.63345	1.31659	0.658295	−	0.752760i	$-0.271278\pi$
$43$	8.63345	1.31659	0.658295	+	0.752760i	$0.271278\pi$
$44$	−2.92382	−0.440782
$45$	2.48383	0.370268
$46$	−7.00352	−1.03261
$47$	5.50347	0.802763	0.401382	−	0.915911i	$-0.368530\pi$
$47$	5.50347	0.802763	0.401382	+	0.915911i	$0.368530\pi$
$48$	−13.7676	−1.98718
$49$	1.00000	0.142857
$50$	11.2121	1.58563
$51$	1.07681	0.150783
$52$	−8.38421	−1.16268
$53$	10.9406	1.50280	0.751402	−	0.659845i	$-0.229378\pi$
$53$	10.9406	1.50280	0.751402	+	0.659845i	$0.229378\pi$
$54$	3.11858	0.424385
$55$	−0.492371	−0.0663913
$56$	−5.55291	−0.742038
$57$	9.35952	1.23970
$58$	8.18135	1.07426
$59$	−7.08243	−0.922054	−0.461027	−	0.887386i	$-0.652519\pi$
$59$	−7.08243	−0.922054	−0.461027	+	0.887386i	$0.652519\pi$
$60$	−7.66030	−0.988940
$61$	−4.92764	−0.630920	−0.315460	−	0.948939i	$-0.602159\pi$
$61$	−4.92764	−0.630920	−0.315460	+	0.948939i	$0.602159\pi$
$62$	−20.6216	−2.61894
$63$	3.49060	0.439774
$64$	−4.87534	−0.609418
$65$	−1.41190	−0.175125
$66$	−4.39846	−0.541412
$67$	−1.26973	−0.155122	−0.0775611	−	0.996988i	$-0.524713\pi$
$67$	−1.26973	−0.155122	−0.0775611	+	0.996988i	$0.524713\pi$
$68$	−1.78598	−0.216582
$69$	−7.15106	−0.860887
$70$	−1.77546	−0.212208
$71$	−5.24862	−0.622897	−0.311448	−	0.950263i	$-0.600814\pi$
$71$	−5.24862	−0.622897	−0.311448	+	0.950263i	$0.600814\pi$
$72$	−19.3830	−2.28430
$73$	−5.97129	−0.698887	−0.349443	−	0.936958i	$-0.613629\pi$
$73$	−5.97129	−0.698887	−0.349443	+	0.936958i	$0.613629\pi$
$74$	8.51663	0.990038
$75$	11.4483	1.32194
$76$	−15.5236	−1.78068
$77$	−0.691942	−0.0788541
$78$	−12.6128	−1.42812
$79$	−12.6365	−1.42171	−0.710856	−	0.703337i	$-0.751692\pi$
$79$	−12.6365	−1.42171	−0.710856	+	0.703337i	$0.751692\pi$
$80$	3.84537	0.429926
$81$	−7.28752	−0.809724
$82$	6.05220	0.668353
$83$	−3.85662	−0.423319	−0.211659	−	0.977344i	$-0.567887\pi$
$83$	−3.85662	−0.423319	−0.211659	+	0.977344i	$0.567887\pi$
$84$	−10.7652	−1.17458
$85$	−0.300759	−0.0326219
$86$	−21.5413	−2.32286
$87$	8.35371	0.895612
$88$	3.84229	0.409590
$89$	15.5354	1.64675	0.823373	−	0.567501i	$-0.192090\pi$
$89$	15.5354	1.64675	0.823373	+	0.567501i	$0.192090\pi$
$90$	−6.19741	−0.653265
$91$	−1.98418	−0.207999
$92$	11.8607	1.23656
$93$	−21.0560	−2.18341
$94$	−13.7317	−1.41632
$95$	−2.61417	−0.268208
$96$	6.05766	0.618257
$97$	−3.93257	−0.399292	−0.199646	−	0.979868i	$-0.563979\pi$
$97$	−3.93257	−0.399292	−0.199646	+	0.979868i	$0.563979\pi$
$98$	−2.49510	−0.252043
$99$	−2.41529	−0.242746
$100$	−18.9881	−1.89881
$101$	11.2605	1.12047	0.560233	−	0.828335i	$-0.310712\pi$
$101$	11.2605	1.12047	0.560233	+	0.828335i	$0.310712\pi$
$102$	−2.68674	−0.266027
$103$	15.1535	1.49312	0.746560	−	0.665318i	$-0.231704\pi$
$103$	15.1535	1.49312	0.746560	+	0.665318i	$0.231704\pi$
$104$	11.0180	1.08040
$105$	−1.81286	−0.176917
$106$	−27.2978	−2.65140
$107$	5.10493	0.493512	0.246756	−	0.969078i	$-0.420635\pi$
$107$	5.10493	0.493512	0.246756	+	0.969078i	$0.420635\pi$
$108$	−5.28141	−0.508204
$109$	12.1842	1.16703	0.583517	−	0.812101i	$-0.301676\pi$
$109$	12.1842	1.16703	0.583517	+	0.812101i	$0.301676\pi$
$110$	1.22851	0.117134
$111$	8.69605	0.825393
$112$	5.40401	0.510631
$113$	−1.43401	−0.134901	−0.0674503	−	0.997723i	$-0.521486\pi$
$113$	−1.43401	−0.134901	−0.0674503	+	0.997723i	$0.521486\pi$
$114$	−23.3529	−2.18720
$115$	1.99733	0.186252
$116$	−13.8554	−1.28644
$117$	−6.92599	−0.640308
$118$	17.6714	1.62678
$119$	−0.422664	−0.0387456
$120$	10.0667	0.918956
$121$	−10.5212	−0.956474
$122$	12.2950	1.11313
$123$	6.17970	0.557205
$124$	34.9232	3.13620
$125$	−6.75548	−0.604228
$126$	−8.70939	−0.775894
$127$	−1.56474	−0.138848	−0.0694240	−	0.997587i	$-0.522116\pi$
$127$	−1.56474	−0.138848	−0.0694240	+	0.997587i	$0.522116\pi$
$128$	16.9199	1.49552
$129$	−21.9952	−1.93656
$130$	3.52283	0.308973
$131$	−8.86660	−0.774678	−0.387339	−	0.921937i	$-0.626606\pi$
$131$	−8.86660	−0.774678	−0.387339	+	0.921937i	$0.626606\pi$
$132$	7.44891	0.648345
$133$	−3.67376	−0.318556
$134$	3.16810	0.273683
$135$	−0.889388	−0.0765464
$136$	2.34702	0.201255
$137$	−11.0050	−0.940217	−0.470109	−	0.882609i	$-0.655785\pi$
$137$	−11.0050	−0.940217	−0.470109	+	0.882609i	$0.655785\pi$
$138$	17.8426	1.51886
$139$	1.17198	0.0994063	0.0497032	−	0.998764i	$-0.484172\pi$
$139$	1.17198	0.0994063	0.0497032	+	0.998764i	$0.484172\pi$
$140$	3.00679	0.254120
$141$	−14.0210	−1.18078
$142$	13.0958	1.09898
$143$	1.37294	0.114811
$144$	18.8632	1.57194
$145$	−2.33324	−0.193765
$146$	14.8990	1.23305
$147$	−2.54767	−0.210128
$148$	−14.4232	−1.18558
$149$	7.47613	0.612468	0.306234	−	0.951956i	$-0.400931\pi$
$149$	7.47613	0.612468	0.306234	+	0.951956i	$0.400931\pi$
$150$	−28.5647	−2.33230
$151$	−9.59299	−0.780666	−0.390333	−	0.920674i	$-0.627640\pi$
$151$	−9.59299	−0.780666	−0.390333	+	0.920674i	$0.627640\pi$
$152$	20.4001	1.65466
$153$	−1.47535	−0.119275
$154$	1.72647	0.139123
$155$	5.88107	0.472379
$156$	21.3602	1.71018
$157$	1.43004	0.114130	0.0570649	−	0.998370i	$-0.481826\pi$
$157$	1.43004	0.114130	0.0570649	+	0.998370i	$0.481826\pi$
$158$	31.5292	2.50833
$159$	−27.8729	−2.21047
$160$	−1.69194	−0.133760
$161$	2.80691	0.221215
$162$	18.1831	1.42860
$163$	−18.5662	−1.45422	−0.727108	−	0.686523i	$-0.759136\pi$
$163$	−18.5662	−1.45422	−0.727108	+	0.686523i	$0.759136\pi$
$164$	−10.2496	−0.800357
$165$	1.25440	0.0976546
$166$	9.62264	0.746862
$167$	−5.69352	−0.440578	−0.220289	−	0.975435i	$-0.570700\pi$
$167$	−5.69352	−0.440578	−0.220289	+	0.975435i	$0.570700\pi$
$168$	14.1469	1.09146
$169$	−9.06302	−0.697155
$170$	0.750423	0.0575548
$171$	−12.8236	−0.980648
$172$	36.4809	2.78164
$173$	6.48783	0.493260	0.246630	−	0.969110i	$-0.420677\pi$
$173$	6.48783	0.493260	0.246630	+	0.969110i	$0.420677\pi$
$174$	−20.8433	−1.58013
$175$	−4.49366	−0.339689
$176$	−3.73926	−0.281857
$177$	18.0437	1.35624
$178$	−38.7623	−2.90536
$179$	6.65024	0.497062	0.248531	−	0.968624i	$-0.420052\pi$
$179$	6.65024	0.497062	0.248531	+	0.968624i	$0.420052\pi$
$180$	10.4955	0.782288
$181$	−8.20989	−0.610237	−0.305118	−	0.952314i	$-0.598696\pi$
$181$	−8.20989	−0.610237	−0.305118	+	0.952314i	$0.598696\pi$
$182$	4.95073	0.366973
$183$	12.5540	0.928017
$184$	−15.5865	−1.14905
$185$	−2.42886	−0.178573
$186$	52.5368	3.85219
$187$	0.292459	0.0213867
$188$	23.2550	1.69605
$189$	−1.24988	−0.0909155
$190$	6.52261	0.473200
$191$	−17.1376	−1.24003	−0.620015	−	0.784590i	$-0.712873\pi$
$191$	−17.1376	−1.24003	−0.620015	+	0.784590i	$0.712873\pi$
$192$	12.4207	0.896390
$193$	20.4544	1.47234	0.736169	−	0.676798i	$-0.236633\pi$
$193$	20.4544	1.47234	0.736169	+	0.676798i	$0.236633\pi$
$194$	9.81215	0.704472
$195$	3.59705	0.257590
$196$	4.22552	0.301823
$197$	24.7722	1.76495	0.882475	−	0.470360i	$-0.155876\pi$
$197$	24.7722	1.76495	0.882475	+	0.470360i	$0.155876\pi$
$198$	6.02640	0.428277
$199$	−1.44139	−0.102178	−0.0510888	−	0.998694i	$-0.516269\pi$
$199$	−1.44139	−0.102178	−0.0510888	+	0.998694i	$0.516269\pi$
$200$	24.9529	1.76443
$201$	3.23485	0.228169
$202$	−28.0962	−1.97684
$203$	−3.27897	−0.230138
$204$	4.55008	0.318569
$205$	−1.72603	−0.120551
$206$	−37.8095	−2.63432
$207$	9.79779	0.680993
$208$	−10.7225	−0.743474
$209$	2.54203	0.175836
$210$	4.52327	0.312136
$211$	4.75808	0.327560	0.163780	−	0.986497i	$-0.447631\pi$
$211$	4.75808	0.327560	0.163780	+	0.986497i	$0.447631\pi$
$212$	46.2297	3.17507
$213$	13.3717	0.916216
$214$	−12.7373	−0.870704
$215$	6.14338	0.418975
$216$	6.94048	0.472240
$217$	8.26482	0.561053
$218$	−30.4008	−2.05900
$219$	15.2128	1.02799
$220$	−2.08053	−0.140269
$221$	0.838643	0.0564133
$222$	−21.6975	−1.45624
$223$	−20.2212	−1.35411	−0.677055	−	0.735932i	$-0.736744\pi$
$223$	−20.2212	−1.35411	−0.677055	+	0.735932i	$0.736744\pi$
$224$	−2.37773	−0.158869
$225$	−15.6856	−1.04570
$226$	3.57801	0.238005
$227$	16.4888	1.09440	0.547200	−	0.837002i	$-0.315694\pi$
$227$	16.4888	1.09440	0.547200	+	0.837002i	$0.315694\pi$
$228$	39.5489	2.61919
$229$	19.0917	1.26162	0.630808	−	0.775939i	$-0.282724\pi$
$229$	19.0917	1.26162	0.630808	+	0.775939i	$0.282724\pi$
$230$	−4.98355	−0.328605
$231$	1.76284	0.115986
$232$	18.2078	1.19540
$233$	−0.222291	−0.0145628	−0.00728139	−	0.999973i	$-0.502318\pi$
$233$	−0.222291	−0.0145628	−0.00728139	+	0.999973i	$0.502318\pi$
$234$	17.2810	1.12970
$235$	3.91615	0.255461
$236$	−29.9270	−1.94808
$237$	32.1935	2.09119
$238$	1.05459	0.0683589
$239$	−15.5111	−1.00333	−0.501665	−	0.865062i	$-0.667279\pi$
$239$	−15.5111	−1.00333	−0.501665	+	0.865062i	$0.667279\pi$
$240$	−9.79673	−0.632376
$241$	12.3643	0.796454	0.398227	−	0.917287i	$-0.369626\pi$
$241$	12.3643	0.796454	0.398227	+	0.917287i	$0.369626\pi$
$242$	26.2515	1.68751
$243$	22.3158	1.43156
$244$	−20.8219	−1.33298
$245$	0.711578	0.0454611
$246$	−15.4190	−0.983078
$247$	7.28942	0.463814
$248$	−45.8938	−2.91426
$249$	9.82537	0.622657
$250$	16.8556	1.06604
$251$	6.95369	0.438913	0.219457	−	0.975622i	$-0.429572\pi$
$251$	6.95369	0.438913	0.219457	+	0.975622i	$0.429572\pi$
$252$	14.7496	0.929138
$253$	−1.94222	−0.122106
$254$	3.90418	0.244970
$255$	0.766232	0.0479833
$256$	−32.4662	−2.02914
$257$	16.9335	1.05628	0.528142	−	0.849156i	$-0.322889\pi$
$257$	16.9335	1.05628	0.528142	+	0.849156i	$0.322889\pi$
$258$	54.8801	3.41669
$259$	−3.41334	−0.212095
$260$	−5.96602	−0.369997
$261$	−11.4456	−0.708462
$262$	22.1230	1.36677
$263$	15.9816	0.985465	0.492732	−	0.870181i	$-0.335998\pi$
$263$	15.9816	0.985465	0.492732	+	0.870181i	$0.335998\pi$
$264$	−9.78887	−0.602463
$265$	7.78507	0.478233
$266$	9.16641	0.562028
$267$	−39.5789	−2.42219
$268$	−5.36528	−0.327736
$269$	15.1780	0.925421	0.462710	−	0.886510i	$-0.346877\pi$
$269$	15.1780	0.925421	0.462710	+	0.886510i	$0.346877\pi$
$270$	2.21911	0.135051
$271$	−22.6330	−1.37486	−0.687429	−	0.726251i	$-0.741261\pi$
$271$	−22.6330	−1.37486	−0.687429	+	0.726251i	$0.741261\pi$
$272$	−2.28408	−0.138493
$273$	5.05503	0.305945
$274$	27.4585	1.65883
$275$	3.10935	0.187501
$276$	−30.2170	−1.81885
$277$	20.9715	1.26006	0.630028	−	0.776573i	$-0.283044\pi$
$277$	20.9715	1.26006	0.630028	+	0.776573i	$0.283044\pi$
$278$	−2.92422	−0.175383
$279$	28.8492	1.72716
$280$	−3.95133	−0.236137
$281$	13.7814	0.822129	0.411065	−	0.911606i	$-0.365157\pi$
$281$	13.7814	0.822129	0.411065	+	0.911606i	$0.365157\pi$
$282$	34.9838	2.08325
$283$	8.70483	0.517448	0.258724	−	0.965951i	$-0.416698\pi$
$283$	8.70483	0.517448	0.258724	+	0.965951i	$0.416698\pi$
$284$	−22.1782	−1.31603
$285$	6.66003	0.394506
$286$	−3.42562	−0.202561
$287$	−2.42563	−0.143181
$288$	−8.29970	−0.489064
$289$	−16.8214	−0.989491
$290$	5.82167	0.341860
$291$	10.0189	0.587317
$292$	−25.2318	−1.47658
$293$	28.3746	1.65766	0.828830	−	0.559500i	$-0.189007\pi$
$293$	28.3746	1.65766	0.828830	+	0.559500i	$0.189007\pi$
$294$	6.35668	0.370729
$295$	−5.03970	−0.293423
$296$	18.9540	1.10168
$297$	0.864846	0.0501835
$298$	−18.6537	−1.08058
$299$	−5.56942	−0.322088
$300$	48.3752	2.79294
$301$	8.63345	0.497624
$302$	23.9355	1.37733
$303$	−28.6881	−1.64809
$304$	−19.8530	−1.13865
$305$	−3.50640	−0.200776
$306$	3.68115	0.210437
$307$	−2.13239	−0.121702	−0.0608510	−	0.998147i	$-0.519381\pi$
$307$	−2.13239	−0.121702	−0.0608510	+	0.998147i	$0.519381\pi$
$308$	−2.92382	−0.166600
$309$	−38.6061	−2.19622
$310$	−14.6738	−0.833419
$311$	−12.9262	−0.732976	−0.366488	−	0.930423i	$-0.619440\pi$
$311$	−12.9262	−0.732976	−0.366488	+	0.930423i	$0.619440\pi$
$312$	−28.0701	−1.58916
$313$	−27.7673	−1.56950	−0.784752	−	0.619810i	$-0.787209\pi$
$313$	−27.7673	−1.56950	−0.784752	+	0.619810i	$0.787209\pi$
$314$	−3.56810	−0.201359
$315$	2.48383	0.139948
$316$	−53.3957	−3.00374
$317$	23.0973	1.29727	0.648636	−	0.761099i	$-0.275340\pi$
$317$	23.0973	1.29727	0.648636	+	0.761099i	$0.275340\pi$
$318$	69.5457	3.89993
$319$	2.26886	0.127032
$320$	−3.46919	−0.193934
$321$	−13.0056	−0.725904
$322$	−7.00352	−0.390291
$323$	1.55277	0.0863983
$324$	−30.7936	−1.71075
$325$	8.91624	0.494584
$326$	46.3245	2.56568
$327$	−31.0412	−1.71658
$328$	13.4693	0.743718
$329$	5.50347	0.303416
$330$	−3.12984	−0.172292
$331$	1.49015	0.0819061	0.0409530	−	0.999161i	$-0.486961\pi$
$331$	1.49015	0.0819061	0.0409530	+	0.999161i	$0.486961\pi$
$332$	−16.2962	−0.894372
$333$	−11.9146	−0.652916
$334$	14.2059	0.777312
$335$	−0.903512	−0.0493641
$336$	−13.7676	−0.751084
$337$	−32.4547	−1.76792	−0.883961	−	0.467561i	$-0.845133\pi$
$337$	−32.4547	−1.76792	−0.883961	+	0.467561i	$0.845133\pi$
$338$	22.6131	1.22999
$339$	3.65338	0.198425
$340$	−1.27086	−0.0689222
$341$	−5.71878	−0.309689
$342$	31.9962	1.73016
$343$	1.00000	0.0539949
$344$	−47.9408	−2.58479
$345$	−5.08854	−0.273958
$346$	−16.1878	−0.870261
$347$	−22.1678	−1.19003	−0.595016	−	0.803714i	$-0.702854\pi$
$347$	−22.1678	−1.19003	−0.595016	+	0.803714i	$0.702854\pi$
$348$	35.2988	1.89221
$349$	9.98305	0.534380	0.267190	−	0.963644i	$-0.413905\pi$
$349$	9.98305	0.534380	0.267190	+	0.963644i	$0.413905\pi$
$350$	11.2121	0.599313
$351$	2.47999	0.132372
$352$	1.64525	0.0876922
$353$	−19.2732	−1.02581	−0.512903	−	0.858446i	$-0.671430\pi$
$353$	−19.2732	−1.02581	−0.512903	+	0.858446i	$0.671430\pi$
$354$	−45.0207	−2.39283
$355$	−3.73480	−0.198223
$356$	65.6451	3.47918
$357$	1.07681	0.0569907
$358$	−16.5930	−0.876968
$359$	−4.29341	−0.226598	−0.113299	−	0.993561i	$-0.536142\pi$
$359$	−4.29341	−0.226598	−0.113299	+	0.993561i	$0.536142\pi$
$360$	−13.7925	−0.726928
$361$	−5.50347	−0.289656
$362$	20.4845	1.07664
$363$	26.8045	1.40687
$364$	−8.38421	−0.439452
$365$	−4.24904	−0.222405
$366$	−31.3234	−1.63730
$367$	20.5202	1.07114	0.535572	−	0.844490i	$-0.320096\pi$
$367$	20.5202	1.07114	0.535572	+	0.844490i	$0.320096\pi$
$368$	15.1686	0.790715
$369$	−8.46691	−0.440770
$370$	6.06025	0.315057
$371$	10.9406	0.568006
$372$	−88.9727	−4.61302
$373$	7.32981	0.379523	0.189761	−	0.981830i	$-0.439229\pi$
$373$	7.32981	0.379523	0.189761	+	0.981830i	$0.439229\pi$
$374$	−0.729715	−0.0377327
$375$	17.2107	0.888757
$376$	−30.5602	−1.57602
$377$	6.50607	0.335080
$378$	3.11858	0.160402
$379$	3.82748	0.196605	0.0983023	−	0.995157i	$-0.468659\pi$
$379$	3.82748	0.196605	0.0983023	+	0.995157i	$0.468659\pi$
$380$	−11.0462	−0.566660
$381$	3.98643	0.204231
$382$	42.7599	2.18779
$383$	−4.48496	−0.229171	−0.114585	−	0.993413i	$-0.536554\pi$
$383$	−4.48496	−0.229171	−0.114585	+	0.993413i	$0.536554\pi$
$384$	−43.1063	−2.19976
$385$	−0.492371	−0.0250935
$386$	−51.0357	−2.59765
$387$	30.1359	1.53190
$388$	−16.6172	−0.843609
$389$	25.7010	1.30309	0.651547	−	0.758609i	$-0.274120\pi$
$389$	25.7010	1.30309	0.651547	+	0.758609i	$0.274120\pi$
$390$	−8.97500	−0.454467
$391$	−1.18638	−0.0599978
$392$	−5.55291	−0.280464
$393$	22.5891	1.13947
$394$	−61.8092	−3.11390
$395$	−8.99183	−0.452428
$396$	−10.2059	−0.512865
$397$	−13.5204	−0.678571	−0.339286	−	0.940683i	$-0.610185\pi$
$397$	−13.5204	−0.678571	−0.339286	+	0.940683i	$0.610185\pi$
$398$	3.59642	0.180272
$399$	9.35952	0.468562
$400$	−24.2838	−1.21419
$401$	−7.07751	−0.353434	−0.176717	−	0.984262i	$-0.556548\pi$
$401$	−7.07751	−0.353434	−0.176717	+	0.984262i	$0.556548\pi$
$402$	−8.07127	−0.402558
$403$	−16.3989	−0.816888
$404$	47.5817	2.36728
$405$	−5.18564	−0.257676
$406$	8.18135	0.406034
$407$	2.36184	0.117072
$408$	−5.97941	−0.296025
$409$	25.5980	1.26574	0.632871	−	0.774258i	$-0.281876\pi$
$409$	25.5980	1.26574	0.632871	+	0.774258i	$0.281876\pi$
$410$	4.30661	0.212688
$411$	28.0370	1.38296
$412$	64.0316	3.15461
$413$	−7.08243	−0.348504
$414$	−24.4465	−1.20148
$415$	−2.74428	−0.134712
$416$	4.71785	0.231312
$417$	−2.98582	−0.146216
$418$	−6.34262	−0.310228
$419$	−15.8997	−0.776749	−0.388374	−	0.921502i	$-0.626963\pi$
$419$	−15.8997	−0.776749	−0.388374	+	0.921502i	$0.626963\pi$
$420$	−7.66030	−0.373784
$421$	−21.5022	−1.04795	−0.523977	−	0.851732i	$-0.675552\pi$
$421$	−21.5022	−1.04795	−0.523977	+	0.851732i	$0.675552\pi$
$422$	−11.8719	−0.577914
$423$	19.2104	0.934042
$424$	−60.7520	−2.95038
$425$	1.89931	0.0921300
$426$	−33.3638	−1.61648
$427$	−4.92764	−0.238465
$428$	21.5710	1.04267
$429$	−3.49779	−0.168875
$430$	−15.3283	−0.739198
$431$	10.5369	0.507545	0.253773	−	0.967264i	$-0.418328\pi$
$431$	10.5369	0.507545	0.253773	+	0.967264i	$0.418328\pi$
$432$	−6.75437	−0.324970
$433$	−25.4924	−1.22509	−0.612543	−	0.790437i	$-0.709854\pi$
$433$	−25.4924	−1.22509	−0.612543	+	0.790437i	$0.709854\pi$
$434$	−20.6216	−0.989867
$435$	5.94432	0.285008
$436$	51.4846	2.46566
$437$	−10.3119	−0.493286
$438$	−37.9576	−1.81368
$439$	−12.4437	−0.593903	−0.296952	−	0.954893i	$-0.595970\pi$
$439$	−12.4437	−0.593903	−0.296952	+	0.954893i	$0.595970\pi$
$440$	2.73409	0.130343
$441$	3.49060	0.166219
$442$	−2.09250	−0.0995300
$443$	−19.3351	−0.918636	−0.459318	−	0.888272i	$-0.651906\pi$
$443$	−19.3351	−0.918636	−0.459318	+	0.888272i	$0.651906\pi$
$444$	36.7454	1.74386
$445$	11.0546	0.524039
$446$	50.4539	2.38906
$447$	−19.0467	−0.900877
$448$	−4.87534	−0.230338
$449$	−40.5000	−1.91131	−0.955656	−	0.294487i	$-0.904851\pi$
$449$	−40.5000	−1.91131	−0.955656	+	0.294487i	$0.904851\pi$
$450$	39.1370	1.84494
$451$	1.67840	0.0790326
$452$	−6.05946	−0.285013
$453$	24.4397	1.14828
$454$	−41.1412	−1.93085
$455$	−1.41190	−0.0661909
$456$	−51.9725	−2.43384
$457$	−2.09105	−0.0978151	−0.0489075	−	0.998803i	$-0.515574\pi$
$457$	−2.09105	−0.0978151	−0.0489075	+	0.998803i	$0.515574\pi$
$458$	−47.6357	−2.22587
$459$	0.528281	0.0246580
$460$	8.43978	0.393507
$461$	17.9055	0.833941	0.416971	−	0.908920i	$-0.363092\pi$
$461$	17.9055	0.833941	0.416971	+	0.908920i	$0.363092\pi$
$462$	−4.39846	−0.204635
$463$	−8.68166	−0.403471	−0.201736	−	0.979440i	$-0.564658\pi$
$463$	−8.68166	−0.403471	−0.201736	+	0.979440i	$0.564658\pi$
$464$	−17.7196	−0.822610
$465$	−14.9830	−0.694819
$466$	0.554639	0.0256932
$467$	−7.25534	−0.335737	−0.167869	−	0.985809i	$-0.553688\pi$
$467$	−7.25534	−0.335737	−0.167869	+	0.985809i	$0.553688\pi$
$468$	−29.2659	−1.35282
$469$	−1.26973	−0.0586307
$470$	−9.77118	−0.450711
$471$	−3.64327	−0.167873
$472$	39.3281	1.81022
$473$	−5.97385	−0.274678
$474$	−80.3259	−3.68949
$475$	16.5086	0.757468
$476$	−1.78598	−0.0818602
$477$	38.1892	1.74856
$478$	38.7017	1.77018
$479$	−3.85516	−0.176147	−0.0880734	−	0.996114i	$-0.528071\pi$
$479$	−3.85516	−0.176147	−0.0880734	+	0.996114i	$0.528071\pi$
$480$	4.31050	0.196746
$481$	6.77269	0.308808
$482$	−30.8502	−1.40519
$483$	−7.15106	−0.325385
$484$	−44.4577	−2.02080
$485$	−2.79833	−0.127066
$486$	−55.6801	−2.52570
$487$	−18.2498	−0.826979	−0.413490	−	0.910509i	$-0.635690\pi$
$487$	−18.2498	−0.826979	−0.413490	+	0.910509i	$0.635690\pi$
$488$	27.3627	1.23865
$489$	47.3005	2.13900
$490$	−1.77546	−0.0802070
$491$	8.57354	0.386919	0.193459	−	0.981108i	$-0.438029\pi$
$491$	8.57354	0.386919	0.193459	+	0.981108i	$0.438029\pi$
$492$	26.1125	1.17724
$493$	1.38590	0.0624179
$494$	−18.1878	−0.818309
$495$	−1.71867	−0.0772484
$496$	44.6632	2.00544
$497$	−5.24862	−0.235433
$498$	−24.5153	−1.09856
$499$	−25.7119	−1.15102	−0.575511	−	0.817794i	$-0.695197\pi$
$499$	−25.7119	−1.15102	−0.575511	+	0.817794i	$0.695197\pi$
$500$	−28.5454	−1.27659
$501$	14.5052	0.648044
$502$	−17.3502	−0.774375
$503$	−23.6888	−1.05623	−0.528115	−	0.849173i	$-0.677101\pi$
$503$	−23.6888	−1.05623	−0.528115	+	0.849173i	$0.677101\pi$
$504$	−19.3830	−0.863386
$505$	8.01276	0.356563
$506$	4.84603	0.215432
$507$	23.0895	1.02544
$508$	−6.61184	−0.293353
$509$	0.0212579	0.000942239 0	0.000471120	−	1.00000i	$-0.499850\pi$
$509$	0.0212579	0.000942239 0	0.000471120		1.00000i	$0.499850\pi$
$510$	−1.91183	−0.0846571
$511$	−5.97129	−0.264154
$512$	47.1666	2.08449
$513$	4.59177	0.202732
$514$	−42.2509	−1.86361
$515$	10.7829	0.475152
$516$	−92.9410	−4.09150
$517$	−3.80808	−0.167479
$518$	8.51663	0.374199
$519$	−16.5288	−0.725534
$520$	7.84015	0.343813
$521$	1.37639	0.0603006	0.0301503	−	0.999545i	$-0.490401\pi$
$521$	1.37639	0.0603006	0.0301503	+	0.999545i	$0.490401\pi$
$522$	28.5578	1.24994
$523$	20.2239	0.884328	0.442164	−	0.896934i	$-0.354211\pi$
$523$	20.2239	0.884328	0.442164	+	0.896934i	$0.354211\pi$
$524$	−37.4660	−1.63671
$525$	11.4483	0.499646
$526$	−39.8756	−1.73866
$527$	−3.49325	−0.152168
$528$	9.52639	0.414583
$529$	−15.1213	−0.657447
$530$	−19.4245	−0.843748
$531$	−24.7219	−1.07284
$532$	−15.5236	−0.673032
$533$	4.81290	0.208470
$534$	98.7533	4.27348
$535$	3.63255	0.157049
$536$	7.05069	0.304544
$537$	−16.9426	−0.731126
$538$	−37.8707	−1.63272
$539$	−0.691942	−0.0298041
$540$	−3.75813	−0.161724
$541$	−34.1697	−1.46907	−0.734535	−	0.678571i	$-0.762599\pi$
$541$	−34.1697	−1.46907	−0.734535	+	0.678571i	$0.762599\pi$
$542$	56.4717	2.42567
$543$	20.9161	0.897594
$544$	1.00498	0.0430882
$545$	8.67000	0.371382
$546$	−12.6128	−0.539779
$547$	−32.8830	−1.40598	−0.702989	−	0.711201i	$-0.748152\pi$
$547$	−32.8830	−1.40598	−0.702989	+	0.711201i	$0.748152\pi$
$548$	−46.5017	−1.98646
$549$	−17.2004	−0.734096
$550$	−7.75814	−0.330808
$551$	12.0461	0.513183
$552$	39.7092	1.69013
$553$	−12.6365	−0.537357
$554$	−52.3260	−2.22312
$555$	6.18792	0.262663
$556$	4.95225	0.210022
$557$	43.0519	1.82417	0.912083	−	0.410005i	$-0.134473\pi$
$557$	43.0519	1.82417	0.912083	+	0.410005i	$0.134473\pi$
$558$	−71.9816	−3.04722
$559$	−17.1304	−0.724537
$560$	3.84537	0.162497
$561$	−0.745088	−0.0314577
$562$	−34.3860	−1.45048
$563$	−32.2466	−1.35903	−0.679517	−	0.733660i	$-0.737811\pi$
$563$	−32.2466	−1.35903	−0.679517	+	0.733660i	$0.737811\pi$
$564$	−59.2461	−2.49471
$565$	−1.02041	−0.0429291
$566$	−21.7194	−0.912935
$567$	−7.28752	−0.306047
$568$	29.1451	1.22290
$569$	10.0184	0.419993	0.209996	−	0.977702i	$-0.432655\pi$
$569$	10.0184	0.419993	0.209996	+	0.977702i	$0.432655\pi$
$570$	−16.6174	−0.696028
$571$	34.8403	1.45802	0.729010	−	0.684503i	$-0.239981\pi$
$571$	34.8403	1.45802	0.729010	+	0.684503i	$0.239981\pi$
$572$	5.80139	0.242568
$573$	43.6607	1.82395
$574$	6.05220	0.252614
$575$	−12.6133	−0.526010
$576$	−17.0179	−0.709078
$577$	40.1824	1.67282	0.836408	−	0.548108i	$-0.184652\pi$
$577$	40.1824	1.67282	0.836408	+	0.548108i	$0.184652\pi$
$578$	41.9710	1.74576
$579$	−52.1109	−2.16565
$580$	−9.85916	−0.409380
$581$	−3.85662	−0.159999
$582$	−24.9981	−1.03620
$583$	−7.57025	−0.313528
$584$	33.1580	1.37209
$585$	−4.92838	−0.203763
$586$	−70.7974	−2.92461
$587$	−26.7136	−1.10259	−0.551294	−	0.834311i	$-0.685866\pi$
$587$	−26.7136	−1.10259	−0.551294	+	0.834311i	$0.685866\pi$
$588$	−10.7652	−0.443950
$589$	−30.3630	−1.25109
$590$	12.5746	0.517687
$591$	−63.1114	−2.59606
$592$	−18.4457	−0.758115
$593$	22.7352	0.933624	0.466812	−	0.884357i	$-0.345402\pi$
$593$	22.7352	0.933624	0.466812	+	0.884357i	$0.345402\pi$
$594$	−2.15788	−0.0885388
$595$	−0.300759	−0.0123299
$596$	31.5906	1.29400
$597$	3.67219	0.150293
$598$	13.8963	0.568260
$599$	21.7930	0.890436	0.445218	−	0.895422i	$-0.353126\pi$
$599$	21.7930	0.890436	0.445218	+	0.895422i	$0.353126\pi$
$600$	−63.5715	−2.59530
$601$	10.4977	0.428210	0.214105	−	0.976811i	$-0.431316\pi$
$601$	10.4977	0.428210	0.214105	+	0.976811i	$0.431316\pi$
$602$	−21.5413	−0.877959
$603$	−4.43212	−0.180490
$604$	−40.5354	−1.64936
$605$	−7.48667	−0.304376
$606$	71.5797	2.90773
$607$	0.240747	0.00977161	0.00488580	−	0.999988i	$-0.498445\pi$
$607$	0.240747	0.00977161	0.00488580	+	0.999988i	$0.498445\pi$
$608$	8.73521	0.354260
$609$	8.35371	0.338509
$610$	8.74882	0.354229
$611$	−10.9199	−0.441771
$612$	−6.23413	−0.252000
$613$	−13.8900	−0.561013	−0.280506	−	0.959852i	$-0.590502\pi$
$613$	−13.8900	−0.561013	−0.280506	+	0.959852i	$0.590502\pi$
$614$	5.32053	0.214719
$615$	4.39734	0.177318
$616$	3.84229	0.154810
$617$	1.14954	0.0462789	0.0231394	−	0.999732i	$-0.492634\pi$
$617$	1.14954	0.0462789	0.0231394	+	0.999732i	$0.492634\pi$
$618$	96.3261	3.87480
$619$	−7.59635	−0.305323	−0.152662	−	0.988279i	$-0.548784\pi$
$619$	−7.59635	−0.305323	−0.152662	+	0.988279i	$0.548784\pi$
$620$	24.8506	0.998024
$621$	−3.50830	−0.140783
$622$	32.2521	1.29319
$623$	15.5354	0.622411
$624$	27.3174	1.09357
$625$	17.6612	0.706449
$626$	69.2823	2.76908
$627$	−6.47625	−0.258636
$628$	6.04268	0.241129
$629$	1.44270	0.0575241
$630$	−6.19741	−0.246911
$631$	−48.4801	−1.92996	−0.964982	−	0.262317i	$-0.915513\pi$
$631$	−48.4801	−1.92996	−0.964982	+	0.262317i	$0.915513\pi$
$632$	70.1691	2.79118
$633$	−12.1220	−0.481806
$634$	−57.6300	−2.28878
$635$	−1.11343	−0.0441852
$636$	−117.778	−4.67019
$637$	−1.98418	−0.0786162
$638$	−5.66102	−0.224122
$639$	−18.3208	−0.724761
$640$	12.0399	0.475917
$641$	−16.4400	−0.649341	−0.324671	−	0.945827i	$-0.605253\pi$
$641$	−16.4400	−0.649341	−0.324671	+	0.945827i	$0.605253\pi$
$642$	32.4504	1.28071
$643$	22.6231	0.892167	0.446083	−	0.894991i	$-0.352818\pi$
$643$	22.6231	0.892167	0.446083	+	0.894991i	$0.352818\pi$
$644$	11.8607	0.467375
$645$	−15.6513	−0.616268
$646$	−3.87431	−0.152433
$647$	−1.29153	−0.0507753	−0.0253877	−	0.999678i	$-0.508082\pi$
$647$	−1.29153	−0.0507753	−0.0253877	+	0.999678i	$0.508082\pi$
$648$	40.4669	1.58969
$649$	4.90063	0.192367
$650$	−22.2469	−0.872595
$651$	−21.0560	−0.825250
$652$	−78.4519	−3.07241
$653$	2.47483	0.0968475	0.0484238	−	0.998827i	$-0.484580\pi$
$653$	2.47483	0.0968475	0.0484238	+	0.998827i	$0.484580\pi$
$654$	77.4510	3.02857
$655$	−6.30927	−0.246524
$656$	−13.1081	−0.511787
$657$	−20.8434	−0.813178
$658$	−13.7317	−0.535318
$659$	−23.3937	−0.911288	−0.455644	−	0.890162i	$-0.650591\pi$
$659$	−23.3937	−0.911288	−0.455644	+	0.890162i	$0.650591\pi$
$660$	5.30048	0.206321
$661$	12.1849	0.473938	0.236969	−	0.971517i	$-0.423846\pi$
$661$	12.1849	0.473938	0.236969	+	0.971517i	$0.423846\pi$
$662$	−3.71807	−0.144507
$663$	−2.13658	−0.0829780
$664$	21.4154	0.831080
$665$	−2.61417	−0.101373
$666$	29.7281	1.15194
$667$	−9.20376	−0.356371
$668$	−24.0581	−0.930836
$669$	51.5168	1.99175
$670$	2.25435	0.0870933
$671$	3.40964	0.131628
$672$	6.05766	0.233679
$673$	−45.4308	−1.75123	−0.875614	−	0.483012i	$-0.839543\pi$
$673$	−45.4308	−1.75123	−0.875614	+	0.483012i	$0.839543\pi$
$674$	80.9778	3.11915
$675$	5.61654	0.216181
$676$	−38.2960	−1.47292
$677$	−37.1820	−1.42902	−0.714511	−	0.699624i	$-0.753351\pi$
$677$	−37.1820	−1.42902	−0.714511	+	0.699624i	$0.753351\pi$
$678$	−9.11556	−0.350081
$679$	−3.93257	−0.150918
$680$	1.67008	0.0640448
$681$	−42.0079	−1.60975
$682$	14.2689	0.546385
$683$	−46.3292	−1.77274	−0.886369	−	0.462980i	$-0.846780\pi$
$683$	−46.3292	−1.77274	−0.886369	+	0.462980i	$0.846780\pi$
$684$	−54.1866	−2.07188
$685$	−7.83089	−0.299203
$686$	−2.49510	−0.0952634
$687$	−48.6393	−1.85570
$688$	46.6553	1.77871
$689$	−21.7081	−0.827013
$690$	12.6964	0.483344
$691$	−12.9879	−0.494082	−0.247041	−	0.969005i	$-0.579458\pi$
$691$	−12.9879	−0.494082	−0.247041	+	0.969005i	$0.579458\pi$
$692$	27.4145	1.04214
$693$	−2.41529	−0.0917494
$694$	55.3110	2.09958
$695$	0.833958	0.0316338
$696$	−46.3874	−1.75831
$697$	1.02523	0.0388333
$698$	−24.9087	−0.942808
$699$	0.566324	0.0214203
$700$	−18.9881	−0.717681
$701$	31.3364	1.18356	0.591779	−	0.806100i	$-0.298426\pi$
$701$	31.3364	1.18356	0.591779	+	0.806100i	$0.298426\pi$
$702$	−6.18783	−0.233545
$703$	12.5398	0.472948
$704$	3.37346	0.127142
$705$	−9.97703	−0.375757
$706$	48.0885	1.80983
$707$	11.2605	0.423496
$708$	76.2439	2.86542
$709$	−44.0152	−1.65302	−0.826512	−	0.562919i	$-0.809678\pi$
$709$	−44.0152	−1.65302	−0.826512	+	0.562919i	$0.809678\pi$
$710$	9.31871	0.349725
$711$	−44.1088	−1.65421
$712$	−86.2664	−3.23297
$713$	23.1986	0.868794
$714$	−2.68674	−0.100549
$715$	0.976954	0.0365360
$716$	28.1007	1.05017
$717$	39.5171	1.47579
$718$	10.7125	0.399787
$719$	−22.5107	−0.839508	−0.419754	−	0.907638i	$-0.637884\pi$
$719$	−22.5107	−0.839508	−0.419754	+	0.907638i	$0.637884\pi$
$720$	13.4227	0.500233
$721$	15.1535	0.564347
$722$	13.7317	0.511041
$723$	−31.5001	−1.17150
$724$	−34.6911	−1.28928
$725$	14.7345	0.547227
$726$	−66.8800	−2.48215
$727$	−0.149821	−0.00555654	−0.00277827	−	0.999996i	$-0.500884\pi$
$727$	−0.149821	−0.00555654	−0.00277827	+	0.999996i	$0.500884\pi$
$728$	11.0180	0.408354
$729$	−34.9906	−1.29595
$730$	10.6018	0.392389
$731$	−3.64905	−0.134965
$732$	53.0471	1.96068
$733$	−25.0783	−0.926288	−0.463144	−	0.886283i	$-0.653279\pi$
$733$	−25.0783	−0.926288	−0.463144	+	0.886283i	$0.653279\pi$
$734$	−51.1998	−1.88982
$735$	−1.81286	−0.0668684
$736$	−6.67407	−0.246009
$737$	0.878580	0.0323629
$738$	21.1258	0.777651
$739$	−12.5961	−0.463354	−0.231677	−	0.972793i	$-0.574421\pi$
$739$	−12.5961	−0.463354	−0.231677	+	0.972793i	$0.574421\pi$
$740$	−10.2632	−0.377283
$741$	−18.5710	−0.682223
$742$	−27.2978	−1.00213
$743$	20.4615	0.750660	0.375330	−	0.926891i	$-0.377529\pi$
$743$	20.4615	0.750660	0.375330	+	0.926891i	$0.377529\pi$
$744$	116.922	4.28657
$745$	5.31985	0.194904
$746$	−18.2886	−0.669593
$747$	−13.4619	−0.492545
$748$	1.23579	0.0451851
$749$	5.10493	0.186530
$750$	−42.9424	−1.56804
$751$	−2.30423	−0.0840825	−0.0420412	−	0.999116i	$-0.513386\pi$
$751$	−2.30423	−0.0840825	−0.0420412	+	0.999116i	$0.513386\pi$
$752$	29.7408	1.08454
$753$	−17.7157	−0.645595
$754$	−16.2333	−0.591182
$755$	−6.82616	−0.248429
$756$	−5.28141	−0.192083
$757$	13.0860	0.475618	0.237809	−	0.971312i	$-0.423571\pi$
$757$	13.0860	0.475618	0.237809	+	0.971312i	$0.423571\pi$
$758$	−9.54995	−0.346870
$759$	4.94812	0.179605
$760$	14.5162	0.526559
$761$	33.2559	1.20553	0.602763	−	0.797920i	$-0.294067\pi$
$761$	33.2559	1.20553	0.602763	+	0.797920i	$0.294067\pi$
$762$	−9.94654	−0.360325
$763$	12.1842	0.441097
$764$	−72.4151	−2.61989
$765$	−1.04983	−0.0379566
$766$	11.1904	0.404326
$767$	14.0528	0.507419
$768$	82.7131	2.98465
$769$	22.7956	0.822030	0.411015	−	0.911629i	$-0.365174\pi$
$769$	22.7956	0.822030	0.411015	+	0.911629i	$0.365174\pi$
$770$	1.22851	0.0442726
$771$	−43.1410	−1.55368
$772$	86.4304	3.11070
$773$	−1.52437	−0.0548277	−0.0274139	−	0.999624i	$-0.508727\pi$
$773$	−1.52437	−0.0548277	−0.0274139	+	0.999624i	$0.508727\pi$
$774$	−75.1921	−2.70273
$775$	−37.1393	−1.33408
$776$	21.8372	0.783909
$777$	8.69605	0.311969
$778$	−64.1266	−2.29905
$779$	8.91120	0.319277
$780$	15.1994	0.544227
$781$	3.63174	0.129954
$782$	2.96014	0.105854
$783$	4.09832	0.146462
$784$	5.40401	0.193000
$785$	1.01759	0.0363192
$786$	−56.3621	−2.01037
$787$	35.0913	1.25087	0.625436	−	0.780276i	$-0.284921\pi$
$787$	35.0913	1.25087	0.625436	+	0.780276i	$0.284921\pi$
$788$	104.676	3.72892
$789$	−40.7156	−1.44952
$790$	22.4355	0.798220
$791$	−1.43401	−0.0509876
$792$	13.4119	0.476571
$793$	9.77734	0.347203
$794$	33.7348	1.19720
$795$	−19.8338	−0.703431
$796$	−6.09064	−0.215877
$797$	−3.76401	−0.133328	−0.0666640	−	0.997775i	$-0.521236\pi$
$797$	−3.76401	−0.133328	−0.0666640	+	0.997775i	$0.521236\pi$
$798$	−23.3529	−0.826685
$799$	−2.32612	−0.0822922
$800$	10.6847	0.377761
$801$	54.2277	1.91604
$802$	17.6591	0.623564
$803$	4.13179	0.145808
$804$	13.6689	0.482066
$805$	1.99733	0.0703968
$806$	40.9169	1.44124
$807$	−38.6685	−1.36120
$808$	−62.5288	−2.19975
$809$	21.2991	0.748836	0.374418	−	0.927260i	$-0.377843\pi$
$809$	21.2991	0.748836	0.374418	+	0.927260i	$0.377843\pi$
$810$	12.9387	0.454619
$811$	−15.5970	−0.547684	−0.273842	−	0.961775i	$-0.588295\pi$
$811$	−15.5970	−0.547684	−0.273842	+	0.961775i	$0.588295\pi$
$812$	−13.8554	−0.486228
$813$	57.6614	2.02227
$814$	−5.89302	−0.206550
$815$	−13.2113	−0.462772
$816$	5.81908	0.203708
$817$	−31.7173	−1.10965
$818$	−63.8697	−2.23315
$819$	−6.92599	−0.242014
$820$	−7.29337	−0.254695
$821$	−36.1953	−1.26323	−0.631613	−	0.775284i	$-0.717607\pi$
$821$	−36.1953	−1.26323	−0.631613	+	0.775284i	$0.717607\pi$
$822$	−69.9550	−2.43996
$823$	41.9472	1.46219	0.731094	−	0.682277i	$-0.239010\pi$
$823$	41.9472	1.46219	0.731094	+	0.682277i	$0.239010\pi$
$824$	−84.1461	−2.93137
$825$	−7.92159	−0.275794
$826$	17.6714	0.614866
$827$	−27.5605	−0.958371	−0.479186	−	0.877714i	$-0.659068\pi$
$827$	−27.5605	−0.958371	−0.479186	+	0.877714i	$0.659068\pi$
$828$	41.4008	1.43878
$829$	19.7940	0.687474	0.343737	−	0.939066i	$-0.388307\pi$
$829$	19.7940	0.687474	0.343737	+	0.939066i	$0.388307\pi$
$830$	6.84726	0.237672
$831$	−53.4284	−1.85341
$832$	9.67358	0.335371
$833$	−0.422664	−0.0146445
$834$	7.44992	0.257970
$835$	−4.05138	−0.140204
$836$	10.7414	0.371500
$837$	−10.3301	−0.357059
$838$	39.6712	1.37042
$839$	−6.77829	−0.234012	−0.117006	−	0.993131i	$-0.537330\pi$
$839$	−6.77829	−0.234012	−0.117006	+	0.993131i	$0.537330\pi$
$840$	10.0667	0.347333
$841$	−18.2484	−0.629254
$842$	53.6502	1.84891
$843$	−35.1104	−1.20927
$844$	20.1054	0.692056
$845$	−6.44904	−0.221854
$846$	−47.9319	−1.64793
$847$	−10.5212	−0.361513
$848$	59.1230	2.03029
$849$	−22.1770	−0.761112
$850$	−4.73896	−0.162545
$851$	−9.58093	−0.328430
$852$	56.5026	1.93575
$853$	42.1401	1.44285	0.721426	−	0.692492i	$-0.243487\pi$
$853$	42.1401	1.44285	0.721426	+	0.692492i	$0.243487\pi$
$854$	12.2950	0.420725
$855$	−9.12501	−0.312069
$856$	−28.3472	−0.968887
$857$	−11.5726	−0.395313	−0.197656	−	0.980271i	$-0.563333\pi$
$857$	−11.5726	−0.395313	−0.197656	+	0.980271i	$0.563333\pi$
$858$	8.72734	0.297946
$859$	−27.8286	−0.949498	−0.474749	−	0.880121i	$-0.657461\pi$
$859$	−27.8286	−0.949498	−0.474749	+	0.880121i	$0.657461\pi$
$860$	25.9590	0.885194
$861$	6.17970	0.210604
$862$	−26.2907	−0.895463
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	2.97188	0.101105
$865$	4.61660	0.156969
$866$	63.6061	2.16142
$867$	42.8552	1.45544
$868$	34.9232	1.18537
$869$	8.74370	0.296610
$870$	−14.8317	−0.502840
$871$	2.51938	0.0853658
$872$	−67.6577	−2.29118
$873$	−13.7270	−0.464589
$874$	25.7293	0.870305
$875$	−6.75548	−0.228377
$876$	64.2823	2.17190
$877$	14.7626	0.498498	0.249249	−	0.968439i	$-0.419816\pi$
$877$	14.7626	0.498498	0.249249	+	0.968439i	$0.419816\pi$
$878$	31.0482	1.04782
$879$	−72.2889	−2.43824
$880$	−2.66078	−0.0896947
$881$	−37.6074	−1.26702	−0.633512	−	0.773733i	$-0.718387\pi$
$881$	−37.6074	−1.26702	−0.633512	+	0.773733i	$0.718387\pi$
$882$	−8.70939	−0.293261
$883$	−9.30220	−0.313044	−0.156522	−	0.987674i	$-0.550028\pi$
$883$	−9.30220	−0.313044	−0.156522	+	0.987674i	$0.550028\pi$
$884$	3.54371	0.119188
$885$	12.8395	0.431594
$886$	48.2429	1.62075
$887$	2.12825	0.0714595	0.0357298	−	0.999361i	$-0.488624\pi$
$887$	2.12825	0.0714595	0.0357298	+	0.999361i	$0.488624\pi$
$888$	−48.2884	−1.62045
$889$	−1.56474	−0.0524796
$890$	−27.5824	−0.924564
$891$	5.04254	0.168931
$892$	−85.4451	−2.86091
$893$	−20.2184	−0.676584
$894$	47.5233	1.58942
$895$	4.73216	0.158179
$896$	16.9199	0.565255
$897$	14.1890	0.473757
$898$	101.051	3.37213
$899$	−27.1001	−0.903838
$900$	−66.2797	−2.20932
$901$	−4.62419	−0.154054
$902$	−4.18777	−0.139437
$903$	−21.9952	−0.731953
$904$	7.96294	0.264843
$905$	−5.84198	−0.194194
$906$	−60.9795	−2.02591
$907$	−3.76599	−0.125048	−0.0625238	−	0.998043i	$-0.519915\pi$
$907$	−3.76599	−0.125048	−0.0625238	+	0.998043i	$0.519915\pi$
$908$	69.6738	2.31221
$909$	39.3061	1.30370
$910$	3.52283	0.116781
$911$	32.3235	1.07093	0.535463	−	0.844558i	$-0.320137\pi$
$911$	32.3235	1.07093	0.535463	+	0.844558i	$0.320137\pi$
$912$	50.5789	1.67484
$913$	2.66856	0.0883163
$914$	5.21737	0.172575
$915$	8.93313	0.295320
$916$	80.6725	2.66549
$917$	−8.86660	−0.292801
$918$	−1.31811	−0.0435042
$919$	−26.1981	−0.864196	−0.432098	−	0.901827i	$-0.642227\pi$
$919$	−26.1981	−0.864196	−0.432098	+	0.901827i	$0.642227\pi$
$920$	−11.0910	−0.365660
$921$	5.43262	0.179011
$922$	−44.6760	−1.47132
$923$	10.4142	0.342788
$924$	7.44891	0.245051
$925$	15.3384	0.504323
$926$	21.6616	0.711845
$927$	52.8949	1.73730
$928$	7.79649	0.255932
$929$	44.1717	1.44923	0.724614	−	0.689155i	$-0.242018\pi$
$929$	44.1717	1.44923	0.724614	+	0.689155i	$0.242018\pi$
$930$	37.3841	1.22587
$931$	−3.67376	−0.120403
$932$	−0.939297	−0.0307677
$933$	32.9315	1.07813
$934$	18.1028	0.592342
$935$	0.208108	0.00680585
$936$	38.4594	1.25708
$937$	−29.7672	−0.972450	−0.486225	−	0.873834i	$-0.661627\pi$
$937$	−29.7672	−0.972450	−0.486225	+	0.873834i	$0.661627\pi$
$938$	3.16810	0.103442
$939$	70.7419	2.30857
$940$	16.5478	0.539729
$941$	14.9252	0.486549	0.243275	−	0.969957i	$-0.421778\pi$
$941$	14.9252	0.486549	0.243275	+	0.969957i	$0.421778\pi$
$942$	9.09032	0.296179
$943$	−6.80853	−0.221716
$944$	−38.2735	−1.24570
$945$	−0.889388	−0.0289318
$946$	14.9054	0.484615
$947$	−31.5872	−1.02645	−0.513224	−	0.858255i	$-0.671549\pi$
$947$	−31.5872	−1.02645	−0.513224	+	0.858255i	$0.671549\pi$
$948$	136.034	4.41819
$949$	11.8481	0.384607
$950$	−41.1907	−1.33640
$951$	−58.8441	−1.90815
$952$	2.34702	0.0760672
$953$	−9.77149	−0.316530	−0.158265	−	0.987397i	$-0.550590\pi$
$953$	−9.77149	−0.316530	−0.158265	+	0.987397i	$0.550590\pi$
$954$	−95.2858	−3.08499
$955$	−12.1947	−0.394611
$956$	−65.5425	−2.11980
$957$	−5.78028	−0.186850
$958$	9.61901	0.310776
$959$	−11.0050	−0.355369
$960$	8.83833	0.285256
$961$	37.3073	1.20346
$962$	−16.8986	−0.544831
$963$	17.8193	0.574217
$964$	52.2456	1.68272
$965$	14.5549	0.468538
$966$	17.8426	0.574077
$967$	45.2131	1.45395	0.726977	−	0.686662i	$-0.240925\pi$
$967$	45.2131	1.45395	0.726977	+	0.686662i	$0.240925\pi$
$968$	58.4233	1.87780
$969$	−3.95593	−0.127083
$970$	6.98211	0.224182
$971$	9.61326	0.308504	0.154252	−	0.988032i	$-0.450703\pi$
$971$	9.61326	0.308504	0.154252	+	0.988032i	$0.450703\pi$
$972$	94.2960	3.02454
$973$	1.17198	0.0375721
$974$	45.5352	1.45904
$975$	−22.7156	−0.727481
$976$	−26.6290	−0.852374
$977$	59.8251	1.91397	0.956987	−	0.290130i	$-0.0936985\pi$
$977$	59.8251	1.91397	0.956987	+	0.290130i	$0.0936985\pi$
$978$	−118.019	−3.77384
$979$	−10.7496	−0.343558
$980$	3.00679	0.0960484
$981$	42.5301	1.35788
$982$	−21.3918	−0.682641
$983$	−24.6705	−0.786868	−0.393434	−	0.919353i	$-0.628713\pi$
$983$	−24.6705	−0.786868	−0.393434	+	0.919353i	$0.628713\pi$
$984$	−34.3153	−1.09393
$985$	17.6274	0.561655
$986$	−3.45796	−0.110124
$987$	−14.0210	−0.446293
$988$	30.8016	0.979930
$989$	24.2333	0.770574
$990$	4.28825	0.136290
$991$	51.2087	1.62670	0.813349	−	0.581776i	$-0.197642\pi$
$991$	51.2087	1.62670	0.813349	+	0.581776i	$0.197642\pi$
$992$	−19.6515	−0.623936
$993$	−3.79640	−0.120475
$994$	13.0958	0.415375
$995$	−1.02566	−0.0325157
$996$	41.5173	1.31553
$997$	16.1553	0.511642	0.255821	−	0.966724i	$-0.417654\pi$
$997$	16.1553	0.511642	0.255821	+	0.966724i	$0.417654\pi$
$998$	64.1538	2.03075
$999$	4.26627	0.134979

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.c.1.5	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.c.1.5	✓	83	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49510 q^{2} -2.54767 q^{3} +4.22552 q^{4} +0.711578 q^{5} +6.35668 q^{6} +1.00000 q^{7} -5.55291 q^{8} +3.49060 q^{9} +O(q^{10})\)	\(q-2.49510 q^{2} -2.54767 q^{3} +4.22552 q^{4} +0.711578 q^{5} +6.35668 q^{6} +1.00000 q^{7} -5.55291 q^{8} +3.49060 q^{9} -1.77546 q^{10} -0.691942 q^{11} -10.7652 q^{12} -1.98418 q^{13} -2.49510 q^{14} -1.81286 q^{15} +5.40401 q^{16} -0.422664 q^{17} -8.70939 q^{18} -3.67376 q^{19} +3.00679 q^{20} -2.54767 q^{21} +1.72647 q^{22} +2.80691 q^{23} +14.1469 q^{24} -4.49366 q^{25} +4.95073 q^{26} -1.24988 q^{27} +4.22552 q^{28} -3.27897 q^{29} +4.52327 q^{30} +8.26482 q^{31} -2.37773 q^{32} +1.76284 q^{33} +1.05459 q^{34} +0.711578 q^{35} +14.7496 q^{36} -3.41334 q^{37} +9.16641 q^{38} +5.05503 q^{39} -3.95133 q^{40} -2.42563 q^{41} +6.35668 q^{42} +8.63345 q^{43} -2.92382 q^{44} +2.48383 q^{45} -7.00352 q^{46} +5.50347 q^{47} -13.7676 q^{48} +1.00000 q^{49} +11.2121 q^{50} +1.07681 q^{51} -8.38421 q^{52} +10.9406 q^{53} +3.11858 q^{54} -0.492371 q^{55} -5.55291 q^{56} +9.35952 q^{57} +8.18135 q^{58} -7.08243 q^{59} -7.66030 q^{60} -4.92764 q^{61} -20.6216 q^{62} +3.49060 q^{63} -4.87534 q^{64} -1.41190 q^{65} -4.39846 q^{66} -1.26973 q^{67} -1.78598 q^{68} -7.15106 q^{69} -1.77546 q^{70} -5.24862 q^{71} -19.3830 q^{72} -5.97129 q^{73} +8.51663 q^{74} +11.4483 q^{75} -15.5236 q^{76} -0.691942 q^{77} -12.6128 q^{78} -12.6365 q^{79} +3.84537 q^{80} -7.28752 q^{81} +6.05220 q^{82} -3.85662 q^{83} -10.7652 q^{84} -0.300759 q^{85} -21.5413 q^{86} +8.35371 q^{87} +3.84229 q^{88} +15.5354 q^{89} -6.19741 q^{90} -1.98418 q^{91} +11.8607 q^{92} -21.0560 q^{93} -13.7317 q^{94} -2.61417 q^{95} +6.05766 q^{96} -3.93257 q^{97} -2.49510 q^{98} -2.41529 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * q^99

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