LMFDB - Embedded newform 161.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,2,Mod(1,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, 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("161.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	161.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:	$1.28559147254$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.2147108.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 9x^{3} + 17x^{2} + 16x - 27 $ x^5 - 2x^4 - 9x^3 + 17x^2 + 16x - 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.54577$ of defining polynomial
Character	$\chi$	$=$	161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.54577 q^{2} +2.46268 q^{3} +4.48096 q^{4} +2.78847 q^{5} -6.26943 q^{6} +1.00000 q^{7} -6.31597 q^{8} +3.06481 q^{9} +O(q^{10})$	\(q-2.54577 q^{2} +2.46268 q^{3} +4.48096 q^{4} +2.78847 q^{5} -6.26943 q^{6} +1.00000 q^{7} -6.31597 q^{8} +3.06481 q^{9} -7.09882 q^{10} -4.70095 q^{11} +11.0352 q^{12} -2.32579 q^{13} -2.54577 q^{14} +6.86713 q^{15} +7.11710 q^{16} -1.82655 q^{17} -7.80231 q^{18} +7.09155 q^{19} +12.4950 q^{20} +2.46268 q^{21} +11.9675 q^{22} -1.00000 q^{23} -15.5542 q^{24} +2.77558 q^{25} +5.92093 q^{26} +0.159610 q^{27} +4.48096 q^{28} -9.98866 q^{29} -17.4821 q^{30} +3.53732 q^{31} -5.48658 q^{32} -11.5769 q^{33} +4.64998 q^{34} +2.78847 q^{35} +13.7333 q^{36} -0.166179 q^{37} -18.0535 q^{38} -5.72768 q^{39} -17.6119 q^{40} +7.25116 q^{41} -6.26943 q^{42} -9.57695 q^{43} -21.0648 q^{44} +8.54614 q^{45} +2.54577 q^{46} +4.66542 q^{47} +17.5272 q^{48} +1.00000 q^{49} -7.06600 q^{50} -4.49821 q^{51} -10.4218 q^{52} -0.961924 q^{53} -0.406330 q^{54} -13.1085 q^{55} -6.31597 q^{56} +17.4642 q^{57} +25.4289 q^{58} +13.8800 q^{59} +30.7713 q^{60} +0.954652 q^{61} -9.00521 q^{62} +3.06481 q^{63} -0.266598 q^{64} -6.48540 q^{65} +29.4723 q^{66} -11.9221 q^{67} -8.18469 q^{68} -2.46268 q^{69} -7.09882 q^{70} +4.59958 q^{71} -19.3572 q^{72} -7.59806 q^{73} +0.423055 q^{74} +6.83537 q^{75} +31.7770 q^{76} -4.70095 q^{77} +14.5814 q^{78} +5.73902 q^{79} +19.8458 q^{80} -8.80137 q^{81} -18.4598 q^{82} -5.57695 q^{83} +11.0352 q^{84} -5.09328 q^{85} +24.3807 q^{86} -24.5989 q^{87} +29.6910 q^{88} -11.2284 q^{89} -21.7565 q^{90} -2.32579 q^{91} -4.48096 q^{92} +8.71129 q^{93} -11.8771 q^{94} +19.7746 q^{95} -13.5117 q^{96} -1.68805 q^{97} -2.54577 q^{98} -14.4075 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} + 12 q^{4} - 4 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) $ 5 * q + 2 * q^2 + 12 * q^4 - 4 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 11 * q^9	\( 5 q + 2 q^{2} + 12 q^{4} - 4 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 11 q^{9} - 8 q^{10} - 4 q^{11} + 3 q^{12} - 6 q^{13} + 2 q^{14} + 10 q^{15} + 10 q^{16} - 12 q^{17} - 19 q^{18} + 6 q^{19} + 14 q^{22} - 5 q^{23} - 36 q^{24} + 19 q^{25} + q^{26} + 12 q^{28} - 4 q^{29} - 48 q^{30} + 30 q^{31} + 8 q^{32} - 22 q^{33} + 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{37} - 40 q^{38} + 16 q^{39} - 50 q^{40} + 6 q^{41} - 3 q^{42} - 12 q^{43} - 26 q^{44} - 12 q^{45} - 2 q^{46} + 10 q^{47} + 25 q^{48} + 5 q^{49} - 2 q^{50} - 4 q^{51} - 21 q^{52} + 16 q^{53} + 33 q^{54} + 18 q^{55} + 3 q^{56} + 6 q^{57} + 13 q^{58} + 22 q^{59} + 30 q^{60} - 18 q^{61} + 15 q^{62} + 11 q^{63} + 25 q^{64} - 26 q^{65} + 4 q^{66} - 2 q^{67} + 12 q^{68} - 8 q^{70} + 4 q^{71} - 41 q^{72} - 2 q^{73} + 38 q^{74} - 30 q^{75} + 10 q^{76} - 4 q^{77} + 41 q^{78} + 30 q^{79} - 10 q^{80} - 3 q^{81} - 7 q^{82} + 8 q^{83} + 3 q^{84} - 12 q^{85} + 8 q^{86} - 12 q^{87} + 4 q^{88} - 20 q^{89} + 34 q^{90} - 6 q^{91} - 12 q^{92} - 26 q^{93} - 25 q^{94} + 8 q^{95} - q^{96} - 12 q^{97} + 2 q^{98} - 8 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 + 12 * q^4 - 4 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 11 * q^9 - 8 * q^10 - 4 * q^11 + 3 * q^12 - 6 * q^13 + 2 * q^14 + 10 * q^15 + 10 * q^16 - 12 * q^17 - 19 * q^18 + 6 * q^19 + 14 * q^22 - 5 * q^23 - 36 * q^24 + 19 * q^25 + q^26 + 12 * q^28 - 4 * q^29 - 48 * q^30 + 30 * q^31 + 8 * q^32 - 22 * q^33 + 6 * q^34 - 4 * q^35 - q^36 + 4 * q^37 - 40 * q^38 + 16 * q^39 - 50 * q^40 + 6 * q^41 - 3 * q^42 - 12 * q^43 - 26 * q^44 - 12 * q^45 - 2 * q^46 + 10 * q^47 + 25 * q^48 + 5 * q^49 - 2 * q^50 - 4 * q^51 - 21 * q^52 + 16 * q^53 + 33 * q^54 + 18 * q^55 + 3 * q^56 + 6 * q^57 + 13 * q^58 + 22 * q^59 + 30 * q^60 - 18 * q^61 + 15 * q^62 + 11 * q^63 + 25 * q^64 - 26 * q^65 + 4 * q^66 - 2 * q^67 + 12 * q^68 - 8 * q^70 + 4 * q^71 - 41 * q^72 - 2 * q^73 + 38 * q^74 - 30 * q^75 + 10 * q^76 - 4 * q^77 + 41 * q^78 + 30 * q^79 - 10 * q^80 - 3 * q^81 - 7 * q^82 + 8 * q^83 + 3 * q^84 - 12 * q^85 + 8 * q^86 - 12 * q^87 + 4 * q^88 - 20 * q^89 + 34 * q^90 - 6 * q^91 - 12 * q^92 - 26 * q^93 - 25 * q^94 + 8 * q^95 - q^96 - 12 * 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 $

$2$	−2.54577	−1.80013	−0.900067	−	0.435752i	$-0.856483\pi$
$2$	−2.54577	−1.80013	−0.900067	+	0.435752i	$0.856483\pi$
$3$	2.46268	1.42183	0.710916	−	0.703277i	$-0.248281\pi$
$3$	2.46268	1.42183	0.710916	+	0.703277i	$0.248281\pi$
$4$	4.48096	2.24048
$5$	2.78847	1.24704	0.623521	−	0.781806i	$-0.285701\pi$
$5$	2.78847	1.24704	0.623521	+	0.781806i	$0.285701\pi$
$6$	−6.26943	−2.55949
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−6.31597	−2.23303
$9$	3.06481	1.02160
$10$	−7.09882	−2.24484
$11$	−4.70095	−1.41739	−0.708694	−	0.705516i	$-0.750715\pi$
$11$	−4.70095	−1.41739	−0.708694	+	0.705516i	$0.750715\pi$
$12$	11.0352	3.18559
$13$	−2.32579	−0.645058	−0.322529	−	0.946560i	$-0.604533\pi$
$13$	−2.32579	−0.645058	−0.322529	+	0.946560i	$0.604533\pi$
$14$	−2.54577	−0.680387
$15$	6.86713	1.77308
$16$	7.11710	1.77927
$17$	−1.82655	−0.443003	−0.221502	−	0.975160i	$-0.571096\pi$
$17$	−1.82655	−0.443003	−0.221502	+	0.975160i	$0.571096\pi$
$18$	−7.80231	−1.83902
$19$	7.09155	1.62691	0.813456	−	0.581626i	$-0.197583\pi$
$19$	7.09155	1.62691	0.813456	+	0.581626i	$0.197583\pi$
$20$	12.4950	2.79398
$21$	2.46268	0.537402
$22$	11.9675	2.55149
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−15.5542	−3.17499
$25$	2.77558	0.555116
$26$	5.92093	1.16119
$27$	0.159610	0.0307169
$28$	4.48096	0.846822
$29$	−9.98866	−1.85485	−0.927424	−	0.374012i	$-0.877982\pi$
$29$	−9.98866	−1.85485	−0.927424	+	0.374012i	$0.877982\pi$
$30$	−17.4821	−3.19179
$31$	3.53732	0.635321	0.317660	−	0.948205i	$-0.397103\pi$
$31$	3.53732	0.635321	0.317660	+	0.948205i	$0.397103\pi$
$32$	−5.48658	−0.969900
$33$	−11.5769	−2.01529
$34$	4.64998	0.797465
$35$	2.78847	0.471338
$36$	13.7333	2.28888
$37$	−0.166179	−0.0273197	−0.0136599	−	0.999907i	$-0.504348\pi$
$37$	−0.166179	−0.0273197	−0.0136599	+	0.999907i	$0.504348\pi$
$38$	−18.0535	−2.92866
$39$	−5.72768	−0.917163
$40$	−17.6119	−2.78469
$41$	7.25116	1.13244	0.566220	−	0.824254i	$-0.308405\pi$
$41$	7.25116	1.13244	0.566220	+	0.824254i	$0.308405\pi$
$42$	−6.26943	−0.967395
$43$	−9.57695	−1.46047	−0.730235	−	0.683196i	$-0.760590\pi$
$43$	−9.57695	−1.46047	−0.730235	+	0.683196i	$0.760590\pi$
$44$	−21.0648	−3.17563
$45$	8.54614	1.27398
$46$	2.54577	0.375354
$47$	4.66542	0.680521	0.340261	−	0.940331i	$-0.389485\pi$
$47$	4.66542	0.680521	0.340261	+	0.940331i	$0.389485\pi$
$48$	17.5272	2.52983
$49$	1.00000	0.142857
$50$	−7.06600	−0.999283
$51$	−4.49821	−0.629875
$52$	−10.4218	−1.44524
$53$	−0.961924	−0.132130	−0.0660652	−	0.997815i	$-0.521045\pi$
$53$	−0.961924	−0.132130	−0.0660652	+	0.997815i	$0.521045\pi$
$54$	−0.406330	−0.0552945
$55$	−13.1085	−1.76754
$56$	−6.31597	−0.844007
$57$	17.4642	2.31319
$58$	25.4289	3.33897
$59$	13.8800	1.80702	0.903512	−	0.428562i	$-0.140980\pi$
$59$	13.8800	1.80702	0.903512	+	0.428562i	$0.140980\pi$
$60$	30.7713	3.97256
$61$	0.954652	0.122231	0.0611153	−	0.998131i	$-0.480534\pi$
$61$	0.954652	0.122231	0.0611153	+	0.998131i	$0.480534\pi$
$62$	−9.00521	−1.14366
$63$	3.06481	0.386130
$64$	−0.266598	−0.0333248
$65$	−6.48540	−0.804415
$66$	29.4723	3.62779
$67$	−11.9221	−1.45652	−0.728259	−	0.685302i	$-0.759670\pi$
$67$	−11.9221	−1.45652	−0.728259	+	0.685302i	$0.759670\pi$
$68$	−8.18469	−0.992540
$69$	−2.46268	−0.296472
$70$	−7.09882	−0.848471
$71$	4.59958	0.545870	0.272935	−	0.962033i	$-0.412006\pi$
$71$	4.59958	0.545870	0.272935	+	0.962033i	$0.412006\pi$
$72$	−19.3572	−2.28127
$73$	−7.59806	−0.889286	−0.444643	−	0.895708i	$-0.646669\pi$
$73$	−7.59806	−0.889286	−0.444643	+	0.895708i	$0.646669\pi$
$74$	0.423055	0.0491791
$75$	6.83537	0.789281
$76$	31.7770	3.64507
$77$	−4.70095	−0.535723
$78$	14.5814	1.65102
$79$	5.73902	0.645690	0.322845	−	0.946452i	$-0.395361\pi$
$79$	5.73902	0.645690	0.322845	+	0.946452i	$0.395361\pi$
$80$	19.8458	2.21883
$81$	−8.80137	−0.977930
$82$	−18.4598	−2.03854
$83$	−5.57695	−0.612149	−0.306075	−	0.952008i	$-0.599016\pi$
$83$	−5.57695	−0.612149	−0.306075	+	0.952008i	$0.599016\pi$
$84$	11.0352	1.20404
$85$	−5.09328	−0.552444
$86$	24.3807	2.62904
$87$	−24.5989	−2.63728
$88$	29.6910	3.16507
$89$	−11.2284	−1.19021	−0.595106	−	0.803647i	$-0.702890\pi$
$89$	−11.2284	−1.19021	−0.595106	+	0.803647i	$0.702890\pi$
$90$	−21.7565	−2.29334
$91$	−2.32579	−0.243809
$92$	−4.48096	−0.467173
$93$	8.71129	0.903319
$94$	−11.8771	−1.22503
$95$	19.7746	2.02883
$96$	−13.5117	−1.37903
$97$	−1.68805	−0.171396	−0.0856979	−	0.996321i	$-0.527312\pi$
$97$	−1.68805	−0.171396	−0.0856979	+	0.996321i	$0.527312\pi$
$98$	−2.54577	−0.257162
$99$	−14.4075	−1.44801
$100$	12.4373	1.24373
$101$	3.12810	0.311258	0.155629	−	0.987816i	$-0.450260\pi$
$101$	3.12810	0.311258	0.155629	+	0.987816i	$0.450260\pi$
$102$	11.4514	1.13386
$103$	1.03808	0.102285	0.0511423	−	0.998691i	$-0.483714\pi$
$103$	1.03808	0.102285	0.0511423	+	0.998691i	$0.483714\pi$
$104$	14.6896	1.44043
$105$	6.86713	0.670163
$106$	2.44884	0.237853
$107$	8.21965	0.794624	0.397312	−	0.917684i	$-0.369943\pi$
$107$	8.21965	0.794624	0.397312	+	0.917684i	$0.369943\pi$
$108$	0.715204	0.0688206
$109$	6.99848	0.670333	0.335166	−	0.942159i	$-0.391207\pi$
$109$	6.99848	0.670333	0.335166	+	0.942159i	$0.391207\pi$
$110$	33.3712	3.18182
$111$	−0.409247	−0.0388440
$112$	7.11710	0.672503
$113$	2.65158	0.249439	0.124720	−	0.992192i	$-0.460197\pi$
$113$	2.65158	0.249439	0.124720	+	0.992192i	$0.460197\pi$
$114$	−44.4600	−4.16406
$115$	−2.78847	−0.260026
$116$	−44.7588	−4.15575
$117$	−7.12810	−0.658993
$118$	−35.3354	−3.25289
$119$	−1.82655	−0.167439
$120$	−43.3725	−3.95935
$121$	11.0989	1.00899
$122$	−2.43033	−0.220031
$123$	17.8573	1.61014
$124$	15.8506	1.42342
$125$	−6.20274	−0.554790
$126$	−7.80231	−0.695085
$127$	−0.847744	−0.0752251	−0.0376126	−	0.999292i	$-0.511975\pi$
$127$	−0.847744	−0.0752251	−0.0376126	+	0.999292i	$0.511975\pi$
$128$	11.6519	1.02989
$129$	−23.5850	−2.07654
$130$	16.5104	1.44805
$131$	−3.40769	−0.297732	−0.148866	−	0.988857i	$-0.547562\pi$
$131$	−3.40769	−0.297732	−0.148866	+	0.988857i	$0.547562\pi$
$132$	−51.8759	−4.51521
$133$	7.09155	0.614915
$134$	30.3510	2.62193
$135$	0.445067	0.0383052
$136$	11.5364	0.989240
$137$	−14.4092	−1.23107	−0.615533	−	0.788111i	$-0.711059\pi$
$137$	−14.4092	−1.23107	−0.615533	+	0.788111i	$0.711059\pi$
$138$	6.26943	0.533690
$139$	2.60685	0.221110	0.110555	−	0.993870i	$-0.464737\pi$
$139$	2.60685	0.221110	0.110555	+	0.993870i	$0.464737\pi$
$140$	12.4950	1.05602
$141$	11.4895	0.967587
$142$	−11.7095	−0.982638
$143$	10.9334	0.914298
$144$	21.8126	1.81771
$145$	−27.8531	−2.31307
$146$	19.3429	1.60083
$147$	2.46268	0.203119
$148$	−0.744643	−0.0612093
$149$	−0.00887233	−0.000726849 0	−0.000363425	−	1.00000i	$-0.500116\pi$
$149$	−0.00887233	−0.000726849 0	−0.000363425		1.00000i	$0.500116\pi$
$150$	−17.4013	−1.42081
$151$	13.1070	1.06663	0.533316	−	0.845916i	$-0.320946\pi$
$151$	13.1070	1.06663	0.533316	+	0.845916i	$0.320946\pi$
$152$	−44.7900	−3.63295
$153$	−5.59803	−0.452574
$154$	11.9675	0.964372
$155$	9.86371	0.792272
$156$	−25.6655	−2.05489
$157$	−0.249603	−0.0199205	−0.00996025	−	0.999950i	$-0.503170\pi$
$157$	−0.249603	−0.0199205	−0.00996025	+	0.999950i	$0.503170\pi$
$158$	−14.6103	−1.16233
$159$	−2.36892	−0.187867
$160$	−15.2992	−1.20951
$161$	−1.00000	−0.0788110
$162$	22.4063	1.76040
$163$	−0.150737	−0.0118066	−0.00590332	−	0.999983i	$-0.501879\pi$
$163$	−0.150737	−0.0118066	−0.00590332	+	0.999983i	$0.501879\pi$
$164$	32.4922	2.53721
$165$	−32.2820	−2.51315
$166$	14.1976	1.10195
$167$	11.8235	0.914931	0.457465	−	0.889227i	$-0.348757\pi$
$167$	11.8235	0.914931	0.457465	+	0.889227i	$0.348757\pi$
$168$	−15.5542	−1.20003
$169$	−7.59071	−0.583900
$170$	12.9663	0.994473
$171$	21.7343	1.66206
$172$	−42.9139	−3.27216
$173$	6.78120	0.515565	0.257783	−	0.966203i	$-0.417008\pi$
$173$	6.78120	0.515565	0.257783	+	0.966203i	$0.417008\pi$
$174$	62.6233	4.74746
$175$	2.77558	0.209814
$176$	−33.4571	−2.52192
$177$	34.1821	2.56928
$178$	28.5851	2.14254
$179$	20.5624	1.53690	0.768451	−	0.639908i	$-0.221028\pi$
$179$	20.5624	1.53690	0.768451	+	0.639908i	$0.221028\pi$
$180$	38.2949	2.85434
$181$	−1.69693	−0.126131	−0.0630657	−	0.998009i	$-0.520088\pi$
$181$	−1.69693	−0.126131	−0.0630657	+	0.998009i	$0.520088\pi$
$182$	5.92093	0.438889
$183$	2.35101	0.173791
$184$	6.31597	0.465619
$185$	−0.463386	−0.0340688
$186$	−22.1770	−1.62609
$187$	8.58651	0.627907
$188$	20.9056	1.52470
$189$	0.159610	0.0116099
$190$	−50.3416	−3.65216
$191$	15.8873	1.14956	0.574782	−	0.818307i	$-0.305087\pi$
$191$	15.8873	1.14956	0.574782	+	0.818307i	$0.305087\pi$
$192$	−0.656548	−0.0473822
$193$	−21.1919	−1.52543	−0.762714	−	0.646736i	$-0.776134\pi$
$193$	−21.1919	−1.52543	−0.762714	+	0.646736i	$0.776134\pi$
$194$	4.29740	0.308535
$195$	−15.9715	−1.14374
$196$	4.48096	0.320069
$197$	18.5146	1.31911	0.659554	−	0.751657i	$-0.270745\pi$
$197$	18.5146	1.31911	0.659554	+	0.751657i	$0.270745\pi$
$198$	36.6783	2.60661
$199$	12.3192	0.873286	0.436643	−	0.899635i	$-0.356167\pi$
$199$	12.3192	0.873286	0.436643	+	0.899635i	$0.356167\pi$
$200$	−17.5305	−1.23959
$201$	−29.3604	−2.07092
$202$	−7.96344	−0.560306
$203$	−9.98866	−0.701066
$204$	−20.1563	−1.41122
$205$	20.2197	1.41220
$206$	−2.64271	−0.184126
$207$	−3.06481	−0.213019
$208$	−16.5529	−1.14773
$209$	−33.3370	−2.30597
$210$	−17.4821	−1.20638
$211$	−3.49259	−0.240440	−0.120220	−	0.992747i	$-0.538360\pi$
$211$	−3.49259	−0.240440	−0.120220	+	0.992747i	$0.538360\pi$
$212$	−4.31035	−0.296036
$213$	11.3273	0.776134
$214$	−20.9254	−1.43043
$215$	−26.7050	−1.82127
$216$	−1.00809	−0.0685917
$217$	3.53732	0.240129
$218$	−17.8165	−1.20669
$219$	−18.7116	−1.26441
$220$	−58.7385	−3.96015
$221$	4.24817	0.285763
$222$	1.04185	0.0699244
$223$	9.77808	0.654789	0.327394	−	0.944888i	$-0.393829\pi$
$223$	9.77808	0.654789	0.327394	+	0.944888i	$0.393829\pi$
$224$	−5.48658	−0.366588
$225$	8.50663	0.567108
$226$	−6.75032	−0.449024
$227$	8.25924	0.548185	0.274093	−	0.961703i	$-0.411622\pi$
$227$	8.25924	0.548185	0.274093	+	0.961703i	$0.411622\pi$
$228$	78.2566	5.18267
$229$	3.13841	0.207392	0.103696	−	0.994609i	$-0.466933\pi$
$229$	3.13841	0.207392	0.103696	+	0.994609i	$0.466933\pi$
$230$	7.09882	0.468082
$231$	−11.5769	−0.761707
$232$	63.0881	4.14193
$233$	8.84601	0.579521	0.289761	−	0.957099i	$-0.406424\pi$
$233$	8.84601	0.579521	0.289761	+	0.957099i	$0.406424\pi$
$234$	18.1465	1.18628
$235$	13.0094	0.848639
$236$	62.1958	4.04860
$237$	14.1334	0.918063
$238$	4.64998	0.301413
$239$	−10.3793	−0.671379	−0.335689	−	0.941973i	$-0.608969\pi$
$239$	−10.3793	−0.671379	−0.335689	+	0.941973i	$0.608969\pi$
$240$	48.8740	3.15480
$241$	−2.47813	−0.159630	−0.0798151	−	0.996810i	$-0.525433\pi$
$241$	−2.47813	−0.159630	−0.0798151	+	0.996810i	$0.525433\pi$
$242$	−28.2553	−1.81632
$243$	−22.1538	−1.42117
$244$	4.27776	0.273855
$245$	2.78847	0.178149
$246$	−45.4607	−2.89847
$247$	−16.4934	−1.04945
$248$	−22.3416	−1.41869
$249$	−13.7343	−0.870373
$250$	15.7908	0.998695
$251$	−9.66697	−0.610174	−0.305087	−	0.952324i	$-0.598686\pi$
$251$	−9.66697	−0.610174	−0.305087	+	0.952324i	$0.598686\pi$
$252$	13.7333	0.865117
$253$	4.70095	0.295546
$254$	2.15816	0.135415
$255$	−12.5431	−0.785482
$256$	−29.1298	−1.82061
$257$	16.2773	1.01535	0.507676	−	0.861548i	$-0.330505\pi$
$257$	16.2773	1.01535	0.507676	+	0.861548i	$0.330505\pi$
$258$	60.0420	3.73805
$259$	−0.166179	−0.0103259
$260$	−29.0608	−1.80228
$261$	−30.6134	−1.89492
$262$	8.67522	0.535957
$263$	−9.03331	−0.557017	−0.278509	−	0.960434i	$-0.589840\pi$
$263$	−9.03331	−0.557017	−0.278509	+	0.960434i	$0.589840\pi$
$264$	73.1196	4.50020
$265$	−2.68230	−0.164772
$266$	−18.0535	−1.10693
$267$	−27.6521	−1.69228
$268$	−53.4226	−3.26330
$269$	−17.6238	−1.07454	−0.537272	−	0.843409i	$-0.680545\pi$
$269$	−17.6238	−1.07454	−0.537272	+	0.843409i	$0.680545\pi$
$270$	−1.13304	−0.0689546
$271$	23.9935	1.45750	0.728750	−	0.684780i	$-0.240102\pi$
$271$	23.9935	1.45750	0.728750	+	0.684780i	$0.240102\pi$
$272$	−12.9997	−0.788224
$273$	−5.72768	−0.346655
$274$	36.6827	2.21608
$275$	−13.0479	−0.786815
$276$	−11.0352	−0.664241
$277$	16.5641	0.995239	0.497620	−	0.867395i	$-0.334208\pi$
$277$	16.5641	0.995239	0.497620	+	0.867395i	$0.334208\pi$
$278$	−6.63645	−0.398028
$279$	10.8412	0.649046
$280$	−17.6119	−1.05251
$281$	−19.5228	−1.16463	−0.582316	−	0.812962i	$-0.697854\pi$
$281$	−19.5228	−1.16463	−0.582316	+	0.812962i	$0.697854\pi$
$282$	−29.2495	−1.74179
$283$	−15.7324	−0.935191	−0.467596	−	0.883942i	$-0.654880\pi$
$283$	−15.7324	−0.935191	−0.467596	+	0.883942i	$0.654880\pi$
$284$	20.6105	1.22301
$285$	48.6985	2.88465
$286$	−27.8340	−1.64586
$287$	7.25116	0.428022
$288$	−16.8153	−0.990853
$289$	−13.6637	−0.803748
$290$	70.9077	4.16384
$291$	−4.15714	−0.243696
$292$	−34.0466	−1.99243
$293$	−8.16268	−0.476869	−0.238434	−	0.971159i	$-0.576634\pi$
$293$	−8.16268	−0.476869	−0.238434	+	0.971159i	$0.576634\pi$
$294$	−6.26943	−0.365641
$295$	38.7041	2.25344
$296$	1.04958	0.0610058
$297$	−0.750316	−0.0435377
$298$	0.0225869	0.00130843
$299$	2.32579	0.134504
$300$	30.6291	1.76837
$301$	−9.57695	−0.552006
$302$	−33.3674	−1.92008
$303$	7.70353	0.442556
$304$	50.4712	2.89472
$305$	2.66202	0.152427
$306$	14.2513	0.814693
$307$	30.5542	1.74382	0.871910	−	0.489667i	$-0.162882\pi$
$307$	30.5542	1.74382	0.871910	+	0.489667i	$0.162882\pi$
$308$	−21.0648	−1.20028
$309$	2.55645	0.145431
$310$	−25.1108	−1.42620
$311$	25.3573	1.43788	0.718941	−	0.695071i	$-0.244627\pi$
$311$	25.3573	1.43788	0.718941	+	0.695071i	$0.244627\pi$
$312$	36.1759	2.04805
$313$	−6.15654	−0.347988	−0.173994	−	0.984747i	$-0.555667\pi$
$313$	−6.15654	−0.347988	−0.173994	+	0.984747i	$0.555667\pi$
$314$	0.635433	0.0358595
$315$	8.54614	0.481521
$316$	25.7163	1.44666
$317$	−4.48063	−0.251657	−0.125829	−	0.992052i	$-0.540159\pi$
$317$	−4.48063	−0.251657	−0.125829	+	0.992052i	$0.540159\pi$
$318$	6.03072	0.338186
$319$	46.9562	2.62904
$320$	−0.743402	−0.0415575
$321$	20.2424	1.12982
$322$	2.54577	0.141870
$323$	−12.9531	−0.720727
$324$	−39.4386	−2.19103
$325$	−6.45541	−0.358082
$326$	0.383743	0.0212535
$327$	17.2350	0.953100
$328$	−45.7981	−2.52878
$329$	4.66542	0.257213
$330$	82.1826	4.52401
$331$	−1.62894	−0.0895349	−0.0447674	−	0.998997i	$-0.514255\pi$
$331$	−1.62894	−0.0895349	−0.0447674	+	0.998997i	$0.514255\pi$
$332$	−24.9901	−1.37151
$333$	−0.509308	−0.0279099
$334$	−30.1000	−1.64700
$335$	−33.2445	−1.81634
$336$	17.5272	0.956185
$337$	4.91650	0.267819	0.133909	−	0.990994i	$-0.457247\pi$
$337$	4.91650	0.267819	0.133909	+	0.990994i	$0.457247\pi$
$338$	19.3242	1.05110
$339$	6.53000	0.354661
$340$	−22.8228	−1.23774
$341$	−16.6287	−0.900497
$342$	−55.3305	−2.99193
$343$	1.00000	0.0539949
$344$	60.4877	3.26128
$345$	−6.86713	−0.369714
$346$	−17.2634	−0.928086
$347$	33.8004	1.81450	0.907249	−	0.420593i	$-0.138178\pi$
$347$	33.8004	1.81450	0.907249	+	0.420593i	$0.138178\pi$
$348$	−110.227	−5.90878
$349$	3.26430	0.174734	0.0873669	−	0.996176i	$-0.472155\pi$
$349$	3.26430	0.174734	0.0873669	+	0.996176i	$0.472155\pi$
$350$	−7.06600	−0.377693
$351$	−0.371218	−0.0198142
$352$	25.7921	1.37473
$353$	11.1070	0.591165	0.295583	−	0.955317i	$-0.404486\pi$
$353$	11.1070	0.591165	0.295583	+	0.955317i	$0.404486\pi$
$354$	−87.0199	−4.62505
$355$	12.8258	0.680723
$356$	−50.3142	−2.66665
$357$	−4.49821	−0.238071
$358$	−52.3471	−2.76663
$359$	−19.0760	−1.00679	−0.503397	−	0.864056i	$-0.667916\pi$
$359$	−19.0760	−1.00679	−0.503397	+	0.864056i	$0.667916\pi$
$360$	−53.9772	−2.84485
$361$	31.2900	1.64684
$362$	4.31999	0.227054
$363$	27.3331	1.43461
$364$	−10.4218	−0.546249
$365$	−21.1870	−1.10898
$366$	−5.98513	−0.312848
$367$	−31.9319	−1.66683	−0.833416	−	0.552647i	$-0.813618\pi$
$367$	−31.9319	−1.66683	−0.833416	+	0.552647i	$0.813618\pi$
$368$	−7.11710	−0.371004
$369$	22.2234	1.15691
$370$	1.17968	0.0613285
$371$	−0.961924	−0.0499406
$372$	39.0350	2.02387
$373$	20.8038	1.07718	0.538590	−	0.842568i	$-0.318957\pi$
$373$	20.8038	1.07718	0.538590	+	0.842568i	$0.318957\pi$
$374$	−21.8593	−1.13032
$375$	−15.2754	−0.788817
$376$	−29.4666	−1.51963
$377$	23.2315	1.19648
$378$	−0.406330	−0.0208993
$379$	−26.5314	−1.36282	−0.681412	−	0.731900i	$-0.738634\pi$
$379$	−26.5314	−1.36282	−0.681412	+	0.731900i	$0.738634\pi$
$380$	88.6092	4.54555
$381$	−2.08773	−0.106957
$382$	−40.4454	−2.06937
$383$	−20.4224	−1.04354	−0.521768	−	0.853088i	$-0.674727\pi$
$383$	−20.4224	−1.04354	−0.521768	+	0.853088i	$0.674727\pi$
$384$	28.6949	1.46433
$385$	−13.1085	−0.668069
$386$	53.9498	2.74597
$387$	−29.3515	−1.49202
$388$	−7.56410	−0.384009
$389$	1.10846	0.0562012	0.0281006	−	0.999605i	$-0.491054\pi$
$389$	1.10846	0.0562012	0.0281006	+	0.999605i	$0.491054\pi$
$390$	40.6598	2.05889
$391$	1.82655	0.0923725
$392$	−6.31597	−0.319005
$393$	−8.39207	−0.423324
$394$	−47.1339	−2.37457
$395$	16.0031	0.805204
$396$	−64.5595	−3.24424
$397$	−19.3304	−0.970166	−0.485083	−	0.874468i	$-0.661211\pi$
$397$	−19.3304	−0.970166	−0.485083	+	0.874468i	$0.661211\pi$
$398$	−31.3619	−1.57203
$399$	17.4642	0.874305
$400$	19.7541	0.987703
$401$	34.3076	1.71324	0.856620	−	0.515947i	$-0.172560\pi$
$401$	34.3076	1.71324	0.856620	+	0.515947i	$0.172560\pi$
$402$	74.7449	3.72794
$403$	−8.22705	−0.409819
$404$	14.0169	0.697368
$405$	−24.5424	−1.21952
$406$	25.4289	1.26201
$407$	0.781200	0.0387227
$408$	28.4106	1.40653
$409$	−11.1492	−0.551293	−0.275647	−	0.961259i	$-0.588892\pi$
$409$	−11.1492	−0.551293	−0.275647	+	0.961259i	$0.588892\pi$
$410$	−51.4746	−2.54215
$411$	−35.4854	−1.75037
$412$	4.65158	0.229167
$413$	13.8800	0.682991
$414$	7.80231	0.383463
$415$	−15.5512	−0.763376
$416$	12.7606	0.625642
$417$	6.41985	0.314381
$418$	84.8684	4.15105
$419$	−36.8881	−1.80210	−0.901052	−	0.433711i	$-0.857204\pi$
$419$	−36.8881	−1.80210	−0.901052	+	0.433711i	$0.857204\pi$
$420$	30.7713	1.50149
$421$	21.8055	1.06273	0.531367	−	0.847142i	$-0.321679\pi$
$421$	21.8055	1.06273	0.531367	+	0.847142i	$0.321679\pi$
$422$	8.89134	0.432824
$423$	14.2986	0.695223
$424$	6.07548	0.295052
$425$	−5.06973	−0.245918
$426$	−28.8368	−1.39715
$427$	0.954652	0.0461988
$428$	36.8319	1.78034
$429$	26.9255	1.29998
$430$	67.9850	3.27853
$431$	17.1450	0.825846	0.412923	−	0.910766i	$-0.364508\pi$
$431$	17.1450	0.825846	0.412923	+	0.910766i	$0.364508\pi$
$432$	1.13596	0.0546537
$433$	2.68890	0.129220	0.0646102	−	0.997911i	$-0.479420\pi$
$433$	2.68890	0.129220	0.0646102	+	0.997911i	$0.479420\pi$
$434$	−9.00521	−0.432264
$435$	−68.5934	−3.28880
$436$	31.3599	1.50187
$437$	−7.09155	−0.339235
$438$	47.6355	2.27611
$439$	23.9686	1.14396	0.571979	−	0.820268i	$-0.306176\pi$
$439$	23.9686	1.14396	0.571979	+	0.820268i	$0.306176\pi$
$440$	82.7926	3.94698
$441$	3.06481	0.145943
$442$	−10.8149	−0.514411
$443$	−28.5038	−1.35426	−0.677128	−	0.735865i	$-0.736776\pi$
$443$	−28.5038	−1.35426	−0.677128	+	0.735865i	$0.736776\pi$
$444$	−1.83382	−0.0870293
$445$	−31.3102	−1.48425
$446$	−24.8928	−1.17871
$447$	−0.0218497	−0.00103346
$448$	−0.266598	−0.0125956
$449$	1.18398	0.0558753	0.0279376	−	0.999610i	$-0.491106\pi$
$449$	1.18398	0.0558753	0.0279376	+	0.999610i	$0.491106\pi$
$450$	−21.6559	−1.02087
$451$	−34.0873	−1.60511
$452$	11.8816	0.558864
$453$	32.2784	1.51657
$454$	−21.0262	−0.986807
$455$	−6.48540	−0.304040
$456$	−110.304	−5.16544
$457$	33.3173	1.55852	0.779260	−	0.626701i	$-0.215595\pi$
$457$	33.3173	1.55852	0.779260	+	0.626701i	$0.215595\pi$
$458$	−7.98969	−0.373334
$459$	−0.291534	−0.0136077
$460$	−12.4950	−0.582584
$461$	−1.59002	−0.0740545	−0.0370273	−	0.999314i	$-0.511789\pi$
$461$	−1.59002	−0.0740545	−0.0370273	+	0.999314i	$0.511789\pi$
$462$	29.4723	1.37117
$463$	30.4569	1.41545	0.707726	−	0.706487i	$-0.249721\pi$
$463$	30.4569	1.41545	0.707726	+	0.706487i	$0.249721\pi$
$464$	−71.0903	−3.30028
$465$	24.2912	1.12648
$466$	−22.5199	−1.04322
$467$	27.6450	1.27926	0.639628	−	0.768685i	$-0.279088\pi$
$467$	27.6450	1.27926	0.639628	+	0.768685i	$0.279088\pi$
$468$	−31.9408	−1.47646
$469$	−11.9221	−0.550512
$470$	−33.1190	−1.52766
$471$	−0.614693	−0.0283236
$472$	−87.6658	−4.03514
$473$	45.0207	2.07005
$474$	−35.9804	−1.65264
$475$	19.6832	0.903125
$476$	−8.18469	−0.375145
$477$	−2.94812	−0.134985
$478$	26.4232	1.20857
$479$	36.3245	1.65971	0.829855	−	0.557979i	$-0.188423\pi$
$479$	36.3245	1.65971	0.829855	+	0.557979i	$0.188423\pi$
$480$	−37.6771	−1.71971
$481$	0.386498	0.0176228
$482$	6.30875	0.287356
$483$	−2.46268	−0.112056
$484$	49.7338	2.26063
$485$	−4.70709	−0.213738
$486$	56.3986	2.55829
$487$	31.6204	1.43286	0.716428	−	0.697661i	$-0.245776\pi$
$487$	31.6204	1.43286	0.716428	+	0.697661i	$0.245776\pi$
$488$	−6.02955	−0.272945
$489$	−0.371218	−0.0167871
$490$	−7.09882	−0.320692
$491$	−41.6773	−1.88087	−0.940436	−	0.339972i	$-0.889582\pi$
$491$	−41.6773	−1.88087	−0.940436	+	0.339972i	$0.889582\pi$
$492$	80.0179	3.60749
$493$	18.2448	0.821703
$494$	41.9886	1.88915
$495$	−40.1750	−1.80573
$496$	25.1754	1.13041
$497$	4.59958	0.206319
$498$	34.9643	1.56679
$499$	−27.7258	−1.24118	−0.620588	−	0.784137i	$-0.713106\pi$
$499$	−27.7258	−1.24118	−0.620588	+	0.784137i	$0.713106\pi$
$500$	−27.7942	−1.24300
$501$	29.1176	1.30088
$502$	24.6099	1.09839
$503$	−29.0492	−1.29524	−0.647620	−	0.761963i	$-0.724236\pi$
$503$	−29.0492	−1.29524	−0.647620	+	0.761963i	$0.724236\pi$
$504$	−19.3572	−0.862240
$505$	8.72263	0.388152
$506$	−11.9675	−0.532022
$507$	−18.6935	−0.830208
$508$	−3.79871	−0.168540
$509$	−8.20421	−0.363645	−0.181823	−	0.983331i	$-0.558200\pi$
$509$	−8.20421	−0.363645	−0.181823	+	0.983331i	$0.558200\pi$
$510$	31.9320	1.41397
$511$	−7.59806	−0.336118
$512$	50.8542	2.24746
$513$	1.13188	0.0499737
$514$	−41.4384	−1.82777
$515$	2.89465	0.127553
$516$	−105.683	−4.65245
$517$	−21.9319	−0.964563
$518$	0.423055	0.0185880
$519$	16.7000	0.733046
$520$	40.9616	1.79628
$521$	−9.59168	−0.420219	−0.210110	−	0.977678i	$-0.567382\pi$
$521$	−9.59168	−0.420219	−0.210110	+	0.977678i	$0.567382\pi$
$522$	77.9347	3.41111
$523$	−6.06424	−0.265171	−0.132585	−	0.991172i	$-0.542328\pi$
$523$	−6.06424	−0.265171	−0.132585	+	0.991172i	$0.542328\pi$
$524$	−15.2697	−0.667062
$525$	6.83537	0.298320
$526$	22.9967	1.00271
$527$	−6.46108	−0.281449
$528$	−82.3942	−3.58575
$529$	1.00000	0.0434783
$530$	6.82853	0.296612
$531$	42.5396	1.84606
$532$	31.7770	1.37771
$533$	−16.8647	−0.730489
$534$	70.3960	3.04633
$535$	22.9203	0.990930
$536$	75.2997	3.25245
$537$	50.6386	2.18522
$538$	44.8663	1.93432
$539$	−4.70095	−0.202484
$540$	1.99433	0.0858222
$541$	−28.6760	−1.23288	−0.616438	−	0.787403i	$-0.711425\pi$
$541$	−28.6760	−1.23288	−0.616438	+	0.787403i	$0.711425\pi$
$542$	−61.0819	−2.62369
$543$	−4.17899	−0.179338
$544$	10.0215	0.429669
$545$	19.5151	0.835934
$546$	14.5814	0.624026
$547$	−24.5492	−1.04965	−0.524824	−	0.851211i	$-0.675869\pi$
$547$	−24.5492	−1.04965	−0.524824	+	0.851211i	$0.675869\pi$
$548$	−64.5673	−2.75818
$549$	2.92583	0.124871
$550$	33.2169	1.41637
$551$	−70.8350	−3.01767
$552$	15.5542	0.662032
$553$	5.73902	0.244048
$554$	−42.1684	−1.79156
$555$	−1.14117	−0.0484401
$556$	11.6812	0.495393
$557$	−5.82872	−0.246971	−0.123485	−	0.992346i	$-0.539407\pi$
$557$	−5.82872	−0.246971	−0.123485	+	0.992346i	$0.539407\pi$
$558$	−27.5993	−1.16837
$559$	22.2740	0.942088
$560$	19.8458	0.838639
$561$	21.1458	0.892778
$562$	49.7006	2.09649
$563$	−30.9619	−1.30489	−0.652445	−	0.757836i	$-0.726257\pi$
$563$	−30.9619	−1.30489	−0.652445	+	0.757836i	$0.726257\pi$
$564$	51.4838	2.16786
$565$	7.39385	0.311062
$566$	40.0510	1.68347
$567$	−8.80137	−0.369623
$568$	−29.0508	−1.21894
$569$	6.77249	0.283918	0.141959	−	0.989873i	$-0.454660\pi$
$569$	6.77249	0.283918	0.141959	+	0.989873i	$0.454660\pi$
$570$	−123.975	−5.19276
$571$	−26.7220	−1.11828	−0.559140	−	0.829073i	$-0.688868\pi$
$571$	−26.7220	−1.11828	−0.559140	+	0.829073i	$0.688868\pi$
$572$	48.9922	2.04847
$573$	39.1254	1.63449
$574$	−18.4598	−0.770497
$575$	−2.77558	−0.115750
$576$	−0.817074	−0.0340447
$577$	−3.13787	−0.130631	−0.0653157	−	0.997865i	$-0.520805\pi$
$577$	−3.13787	−0.130631	−0.0653157	+	0.997865i	$0.520805\pi$
$578$	34.7847	1.44685
$579$	−52.1890	−2.16890
$580$	−124.809	−5.18240
$581$	−5.57695	−0.231371
$582$	10.5831	0.438685
$583$	4.52196	0.187280
$584$	47.9891	1.98580
$585$	−19.8765	−0.821793
$586$	20.7803	0.858428
$587$	31.4784	1.29925	0.649626	−	0.760254i	$-0.274925\pi$
$587$	31.4784	1.29925	0.649626	+	0.760254i	$0.274925\pi$
$588$	11.0352	0.455084
$589$	25.0850	1.03361
$590$	−98.5317	−4.05649
$591$	45.5955	1.87555
$592$	−1.18271	−0.0486093
$593$	15.4196	0.633209	0.316604	−	0.948558i	$-0.397457\pi$
$593$	15.4196	0.633209	0.316604	+	0.948558i	$0.397457\pi$
$594$	1.91013	0.0783738
$595$	−5.09328	−0.208804
$596$	−0.0397566	−0.00162849
$597$	30.3383	1.24167
$598$	−5.92093	−0.242125
$599$	−18.7196	−0.764862	−0.382431	−	0.923984i	$-0.624913\pi$
$599$	−18.7196	−0.764862	−0.382431	+	0.923984i	$0.624913\pi$
$600$	−43.1720	−1.76249
$601$	12.5523	0.512017	0.256009	−	0.966675i	$-0.417592\pi$
$601$	12.5523	0.512017	0.256009	+	0.966675i	$0.417592\pi$
$602$	24.3807	0.993684
$603$	−36.5390	−1.48798
$604$	58.7319	2.38977
$605$	30.9490	1.25825
$606$	−19.6114	−0.796660
$607$	20.5171	0.832761	0.416381	−	0.909190i	$-0.363298\pi$
$607$	20.5171	0.832761	0.416381	+	0.909190i	$0.363298\pi$
$608$	−38.9084	−1.57794
$609$	−24.5989	−0.996798
$610$	−6.77690	−0.274389
$611$	−10.8508	−0.438976
$612$	−25.0845	−1.01398
$613$	−24.9165	−1.00637	−0.503184	−	0.864179i	$-0.667838\pi$
$613$	−24.9165	−1.00637	−0.503184	+	0.864179i	$0.667838\pi$
$614$	−77.7840	−3.13911
$615$	49.7946	2.00791
$616$	29.6910	1.19629
$617$	−8.77553	−0.353289	−0.176645	−	0.984275i	$-0.556524\pi$
$617$	−8.77553	−0.353289	−0.176645	+	0.984275i	$0.556524\pi$
$618$	−6.50815	−0.261796
$619$	−14.6150	−0.587427	−0.293714	−	0.955893i	$-0.594891\pi$
$619$	−14.6150	−0.587427	−0.293714	+	0.955893i	$0.594891\pi$
$620$	44.1989	1.77507
$621$	−0.159610	−0.00640491
$622$	−64.5540	−2.58838
$623$	−11.2284	−0.449858
$624$	−40.7645	−1.63189
$625$	−31.1741	−1.24696
$626$	15.6731	0.626425
$627$	−82.0984	−3.27870
$628$	−1.11846	−0.0446315
$629$	0.303535	0.0121027
$630$	−21.7565	−0.866801
$631$	18.5826	0.739760	0.369880	−	0.929079i	$-0.379399\pi$
$631$	18.5826	0.739760	0.369880	+	0.929079i	$0.379399\pi$
$632$	−36.2475	−1.44185
$633$	−8.60114	−0.341865
$634$	11.4067	0.453016
$635$	−2.36391	−0.0938089
$636$	−10.6150	−0.420913
$637$	−2.32579	−0.0921511
$638$	−119.540	−4.73262
$639$	14.0968	0.557662
$640$	32.4909	1.28432
$641$	9.57505	0.378192	0.189096	−	0.981959i	$-0.439444\pi$
$641$	9.57505	0.378192	0.189096	+	0.981959i	$0.439444\pi$
$642$	−51.5326	−2.03383
$643$	23.7204	0.935443	0.467722	−	0.883876i	$-0.345075\pi$
$643$	23.7204	0.935443	0.467722	+	0.883876i	$0.345075\pi$
$644$	−4.48096	−0.176575
$645$	−65.7661	−2.58954
$646$	32.9755	1.29741
$647$	−20.1385	−0.791727	−0.395864	−	0.918309i	$-0.629555\pi$
$647$	−20.1385	−0.791727	−0.395864	+	0.918309i	$0.629555\pi$
$648$	55.5891	2.18375
$649$	−65.2492	−2.56126
$650$	16.4340	0.644595
$651$	8.71129	0.341422
$652$	−0.675448	−0.0264526
$653$	−32.6863	−1.27911	−0.639557	−	0.768744i	$-0.720882\pi$
$653$	−32.6863	−1.27911	−0.639557	+	0.768744i	$0.720882\pi$
$654$	−43.8765	−1.71571
$655$	−9.50226	−0.371284
$656$	51.6072	2.01492
$657$	−23.2866	−0.908498
$658$	−11.8771	−0.463018
$659$	37.3251	1.45398	0.726989	−	0.686649i	$-0.240919\pi$
$659$	37.3251	1.45398	0.726989	+	0.686649i	$0.240919\pi$
$660$	−144.654	−5.63066
$661$	−9.68312	−0.376630	−0.188315	−	0.982109i	$-0.560303\pi$
$661$	−9.68312	−0.376630	−0.188315	+	0.982109i	$0.560303\pi$
$662$	4.14692	0.161175
$663$	10.4619	0.406306
$664$	35.2238	1.36695
$665$	19.7746	0.766825
$666$	1.29658	0.0502416
$667$	9.98866	0.386762
$668$	52.9807	2.04988
$669$	24.0803	0.930999
$670$	84.6329	3.26966
$671$	−4.48777	−0.173248
$672$	−13.5117	−0.521226
$673$	38.5622	1.48646	0.743232	−	0.669034i	$-0.233292\pi$
$673$	38.5622	1.48646	0.743232	+	0.669034i	$0.233292\pi$
$674$	−12.5163	−0.482109
$675$	0.443009	0.0170514
$676$	−34.0137	−1.30822
$677$	2.70428	0.103934	0.0519669	−	0.998649i	$-0.483451\pi$
$677$	2.70428	0.103934	0.0519669	+	0.998649i	$0.483451\pi$
$678$	−16.6239	−0.638437
$679$	−1.68805	−0.0647815
$680$	32.1690	1.23362
$681$	20.3399	0.779427
$682$	42.3330	1.62101
$683$	−10.6222	−0.406446	−0.203223	−	0.979132i	$-0.565142\pi$
$683$	−10.6222	−0.406446	−0.203223	+	0.979132i	$0.565142\pi$
$684$	97.3904	3.72381
$685$	−40.1798	−1.53519
$686$	−2.54577	−0.0971981
$687$	7.72892	0.294877
$688$	−68.1601	−2.59858
$689$	2.23723	0.0852318
$690$	17.4821	0.665534
$691$	23.7327	0.902833	0.451416	−	0.892313i	$-0.350919\pi$
$691$	23.7327	0.902833	0.451416	+	0.892313i	$0.350919\pi$
$692$	30.3863	1.15511
$693$	−14.4075	−0.547296
$694$	−86.0481	−3.26634
$695$	7.26913	0.275734
$696$	155.366	5.88913
$697$	−13.2446	−0.501674
$698$	−8.31016	−0.314544
$699$	21.7849	0.823982
$700$	12.4373	0.470084
$701$	22.5615	0.852138	0.426069	−	0.904691i	$-0.359898\pi$
$701$	22.5615	0.852138	0.426069	+	0.904691i	$0.359898\pi$
$702$	0.945037	0.0356681
$703$	−1.17847	−0.0444468
$704$	1.25327	0.0472342
$705$	32.0380	1.20662
$706$	−28.2759	−1.06418
$707$	3.12810	0.117644
$708$	153.169	5.75643
$709$	−16.7030	−0.627294	−0.313647	−	0.949540i	$-0.601551\pi$
$709$	−16.7030	−0.627294	−0.313647	+	0.949540i	$0.601551\pi$
$710$	−32.6516	−1.22539
$711$	17.5890	0.659640
$712$	70.9185	2.65778
$713$	−3.53732	−0.132474
$714$	11.4514	0.428559
$715$	30.4875	1.14017
$716$	92.1391	3.44340
$717$	−25.5608	−0.954587
$718$	48.5632	1.81236
$719$	27.7469	1.03479	0.517393	−	0.855748i	$-0.326903\pi$
$719$	27.7469	1.03479	0.517393	+	0.855748i	$0.326903\pi$
$720$	60.8237	2.26677
$721$	1.03808	0.0386600
$722$	−79.6573	−2.96454
$723$	−6.10284	−0.226967
$724$	−7.60386	−0.282595
$725$	−27.7243	−1.02966
$726$	−69.5838	−2.58250
$727$	−41.4981	−1.53908	−0.769539	−	0.638600i	$-0.779514\pi$
$727$	−41.4981	−1.53908	−0.769539	+	0.638600i	$0.779514\pi$
$728$	14.6896	0.544433
$729$	−28.1537	−1.04273
$730$	53.9373	1.99631
$731$	17.4928	0.646993
$732$	10.5348	0.389376
$733$	35.7212	1.31939	0.659697	−	0.751532i	$-0.270685\pi$
$733$	35.7212	1.31939	0.659697	+	0.751532i	$0.270685\pi$
$734$	81.2914	3.00052
$735$	6.86713	0.253298
$736$	5.48658	0.202238
$737$	56.0452	2.06445
$738$	−56.5758	−2.08258
$739$	−44.4520	−1.63519	−0.817597	−	0.575791i	$-0.804694\pi$
$739$	−44.4520	−1.63519	−0.817597	+	0.575791i	$0.804694\pi$
$740$	−2.07642	−0.0763306
$741$	−40.6181	−1.49214
$742$	2.44884	0.0898998
$743$	−17.0898	−0.626964	−0.313482	−	0.949594i	$-0.601496\pi$
$743$	−17.0898	−0.626964	−0.313482	+	0.949594i	$0.601496\pi$
$744$	−55.0202	−2.01714
$745$	−0.0247402	−0.000906412 0
$746$	−52.9617	−1.93907
$747$	−17.0923	−0.625374
$748$	38.4758	1.40681
$749$	8.21965	0.300339
$750$	38.8876	1.41998
$751$	−40.9748	−1.49519	−0.747596	−	0.664154i	$-0.768792\pi$
$751$	−40.9748	−1.49519	−0.747596	+	0.664154i	$0.768792\pi$
$752$	33.2042	1.21083
$753$	−23.8067	−0.867564
$754$	−59.1422	−2.15383
$755$	36.5485	1.33014
$756$	0.715204	0.0260117
$757$	−23.7095	−0.861737	−0.430868	−	0.902415i	$-0.641793\pi$
$757$	−23.7095	−0.861737	−0.430868	+	0.902415i	$0.641793\pi$
$758$	67.5429	2.45327
$759$	11.5769	0.420216
$760$	−124.896	−4.53044
$761$	−42.7680	−1.55034	−0.775170	−	0.631753i	$-0.782336\pi$
$761$	−42.7680	−1.55034	−0.775170	+	0.631753i	$0.782336\pi$
$762$	5.31488	0.192538
$763$	6.99848	0.253362
$764$	71.1904	2.57558
$765$	−15.6099	−0.564379
$766$	51.9908	1.87850
$767$	−32.2820	−1.16564
$768$	−71.7375	−2.58860
$769$	35.6281	1.28478	0.642392	−	0.766376i	$-0.277942\pi$
$769$	35.6281	1.28478	0.642392	+	0.766376i	$0.277942\pi$
$770$	33.3712	1.20261
$771$	40.0859	1.44366
$772$	−94.9602	−3.41769
$773$	16.9388	0.609246	0.304623	−	0.952473i	$-0.401470\pi$
$773$	16.9388	0.609246	0.304623	+	0.952473i	$0.401470\pi$
$774$	74.7223	2.68584
$775$	9.81810	0.352677
$776$	10.6617	0.382732
$777$	−0.409247	−0.0146817
$778$	−2.82189	−0.101170
$779$	51.4219	1.84238
$780$	−71.5676	−2.56253
$781$	−21.6224	−0.773709
$782$	−4.64998	−0.166283
$783$	−1.59429	−0.0569751
$784$	7.11710	0.254182
$785$	−0.696011	−0.0248417
$786$	21.3643	0.762040
$787$	−15.4748	−0.551619	−0.275809	−	0.961212i	$-0.588946\pi$
$787$	−15.4748	−0.551619	−0.275809	+	0.961212i	$0.588946\pi$
$788$	82.9630	2.95544
$789$	−22.2462	−0.791985
$790$	−40.7403	−1.44947
$791$	2.65158	0.0942792
$792$	90.9974	3.23345
$793$	−2.22032	−0.0788458
$794$	49.2109	1.74643
$795$	−6.60566	−0.234278
$796$	55.2020	1.95658
$797$	28.1935	0.998664	0.499332	−	0.866411i	$-0.333579\pi$
$797$	28.1935	0.998664	0.499332	+	0.866411i	$0.333579\pi$
$798$	−44.4600	−1.57387
$799$	−8.52161	−0.301473
$800$	−15.2284	−0.538407
$801$	−34.4131	−1.21593
$802$	−87.3394	−3.08406
$803$	35.7181	1.26046
$804$	−131.563	−4.63986
$805$	−2.78847	−0.0982807
$806$	20.9442	0.737728
$807$	−43.4020	−1.52782
$808$	−19.7570	−0.695049
$809$	−30.7565	−1.08134	−0.540670	−	0.841235i	$-0.681829\pi$
$809$	−30.7565	−1.08134	−0.540670	+	0.841235i	$0.681829\pi$
$810$	62.4793	2.19530
$811$	1.27477	0.0447632	0.0223816	−	0.999750i	$-0.492875\pi$
$811$	1.27477	0.0447632	0.0223816	+	0.999750i	$0.492875\pi$
$812$	−44.7588	−1.57073
$813$	59.0883	2.07232
$814$	−1.98876	−0.0697059
$815$	−0.420327	−0.0147234
$816$	−32.0142	−1.12072
$817$	−67.9154	−2.37606
$818$	28.3834	0.992402
$819$	−7.12810	−0.249076
$820$	90.6035	3.16401
$821$	−5.88860	−0.205513	−0.102757	−	0.994707i	$-0.532766\pi$
$821$	−5.88860	−0.205513	−0.102757	+	0.994707i	$0.532766\pi$
$822$	90.3378	3.15089
$823$	13.3985	0.467043	0.233522	−	0.972352i	$-0.424975\pi$
$823$	13.3985	0.467043	0.233522	+	0.972352i	$0.424975\pi$
$824$	−6.55645	−0.228405
$825$	−32.1327	−1.11872
$826$	−35.3354	−1.22948
$827$	30.5493	1.06230	0.531151	−	0.847277i	$-0.321760\pi$
$827$	30.5493	1.06230	0.531151	+	0.847277i	$0.321760\pi$
$828$	−13.7333	−0.477265
$829$	−33.2608	−1.15520	−0.577598	−	0.816321i	$-0.696010\pi$
$829$	−33.2608	−1.15520	−0.577598	+	0.816321i	$0.696010\pi$
$830$	39.5897	1.37418
$831$	40.7921	1.41506
$832$	0.620052	0.0214964
$833$	−1.82655	−0.0632861
$834$	−16.3435	−0.565929
$835$	32.9695	1.14096
$836$	−149.382	−5.16648
$837$	0.564589	0.0195151
$838$	93.9089	3.24403
$839$	19.4516	0.671543	0.335772	−	0.941943i	$-0.391003\pi$
$839$	19.4516	0.671543	0.335772	+	0.941943i	$0.391003\pi$
$840$	−43.3725	−1.49649
$841$	70.7733	2.44046
$842$	−55.5118	−1.91306
$843$	−48.0785	−1.65591
$844$	−15.6502	−0.538701
$845$	−21.1665	−0.728149
$846$	−36.4011	−1.25149
$847$	11.0989	0.381363
$848$	−6.84611	−0.235096
$849$	−38.7438	−1.32968
$850$	12.9064	0.442685
$851$	0.166179	0.00569655
$852$	50.7572	1.73891
$853$	−43.9900	−1.50619	−0.753094	−	0.657913i	$-0.771439\pi$
$853$	−43.9900	−1.50619	−0.753094	+	0.657913i	$0.771439\pi$
$854$	−2.43033	−0.0831641
$855$	60.6054	2.07266
$856$	−51.9150	−1.77442
$857$	−50.9265	−1.73962	−0.869808	−	0.493391i	$-0.835757\pi$
$857$	−50.9265	−1.73962	−0.869808	+	0.493391i	$0.835757\pi$
$858$	−68.5463	−2.34013
$859$	19.0473	0.649885	0.324943	−	0.945734i	$-0.394655\pi$
$859$	19.0473	0.649885	0.324943	+	0.945734i	$0.394655\pi$
$860$	−119.664	−4.08052
$861$	17.8573	0.608575
$862$	−43.6473	−1.48663
$863$	−30.6481	−1.04327	−0.521637	−	0.853168i	$-0.674678\pi$
$863$	−30.6481	−1.04327	−0.521637	+	0.853168i	$0.674678\pi$
$864$	−0.875711	−0.0297923
$865$	18.9092	0.642932
$866$	−6.84534	−0.232614
$867$	−33.6494	−1.14279
$868$	15.8506	0.538004
$869$	−26.9788	−0.915194
$870$	174.623	5.92028
$871$	27.7283	0.939538
$872$	−44.2022	−1.49687
$873$	−5.17357	−0.175099
$874$	18.0535	0.610668
$875$	−6.20274	−0.209691
$876$	−83.8461	−2.83290
$877$	15.6561	0.528668	0.264334	−	0.964431i	$-0.414848\pi$
$877$	15.6561	0.528668	0.264334	+	0.964431i	$0.414848\pi$
$878$	−61.0186	−2.05928
$879$	−20.1021	−0.678027
$880$	−93.2942	−3.14495
$881$	−51.9258	−1.74943	−0.874713	−	0.484642i	$-0.838950\pi$
$881$	−51.9258	−1.74943	−0.874713	+	0.484642i	$0.838950\pi$
$882$	−7.80231	−0.262718
$883$	18.1603	0.611144	0.305572	−	0.952169i	$-0.401152\pi$
$883$	18.1603	0.611144	0.305572	+	0.952169i	$0.401152\pi$
$884$	19.0359	0.640246
$885$	95.3158	3.20401
$886$	72.5642	2.43784
$887$	−29.5677	−0.992786	−0.496393	−	0.868098i	$-0.665342\pi$
$887$	−29.5677	−0.992786	−0.496393	+	0.868098i	$0.665342\pi$
$888$	2.58479	0.0867399
$889$	−0.847744	−0.0284324
$890$	79.7087	2.67184
$891$	41.3748	1.38611
$892$	43.8152	1.46704
$893$	33.0850	1.10715
$894$	0.0556245	0.00186036
$895$	57.3376	1.91658
$896$	11.6519	0.389261
$897$	5.72768	0.191242
$898$	−3.01413	−0.100583
$899$	−35.3330	−1.17842
$900$	38.1179	1.27060
$901$	1.75700	0.0585342
$902$	86.7785	2.88941
$903$	−23.5850	−0.784859
$904$	−16.7473	−0.557006
$905$	−4.73183	−0.157291
$906$	−82.1734	−2.73003
$907$	30.4350	1.01058	0.505289	−	0.862950i	$-0.331386\pi$
$907$	30.4350	1.01058	0.505289	+	0.862950i	$0.331386\pi$
$908$	37.0094	1.22820
$909$	9.58705	0.317982
$910$	16.5104	0.547313
$911$	−48.2859	−1.59978	−0.799892	−	0.600144i	$-0.795110\pi$
$911$	−48.2859	−1.59978	−0.799892	+	0.600144i	$0.795110\pi$
$912$	124.295	4.11581
$913$	26.2169	0.867653
$914$	−84.8184	−2.80554
$915$	6.55571	0.216725
$916$	14.0631	0.464658
$917$	−3.40769	−0.112532
$918$	0.742181	0.0244956
$919$	−28.4097	−0.937150	−0.468575	−	0.883424i	$-0.655232\pi$
$919$	−28.4097	−0.937150	−0.468575	+	0.883424i	$0.655232\pi$
$920$	17.6119	0.580647
$921$	75.2453	2.47942
$922$	4.04783	0.133308
$923$	−10.6976	−0.352117
$924$	−51.8759	−1.70659
$925$	−0.461244	−0.0151656
$926$	−77.5363	−2.54800
$927$	3.18151	0.104494
$928$	54.8036	1.79902
$929$	27.0080	0.886104	0.443052	−	0.896496i	$-0.353896\pi$
$929$	27.0080	0.886104	0.443052	+	0.896496i	$0.353896\pi$
$930$	−61.8399	−2.02781
$931$	7.09155	0.232416
$932$	39.6386	1.29841
$933$	62.4471	2.04443
$934$	−70.3778	−2.30283
$935$	23.9432	0.783028
$936$	45.0209	1.47155
$937$	15.3639	0.501917	0.250958	−	0.967998i	$-0.419254\pi$
$937$	15.3639	0.501917	0.250958	+	0.967998i	$0.419254\pi$
$938$	30.3510	0.990995
$939$	−15.1616	−0.494780
$940$	58.2946	1.90136
$941$	−46.8015	−1.52569	−0.762843	−	0.646584i	$-0.776197\pi$
$941$	−46.8015	−1.52569	−0.762843	+	0.646584i	$0.776197\pi$
$942$	1.56487	0.0509862
$943$	−7.25116	−0.236130
$944$	98.7855	3.21519
$945$	0.445067	0.0144780
$946$	−114.613	−3.72637
$947$	13.1326	0.426753	0.213376	−	0.976970i	$-0.431554\pi$
$947$	13.1326	0.426753	0.213376	+	0.976970i	$0.431554\pi$
$948$	63.3312	2.05690
$949$	17.6715	0.573641
$950$	−50.1088	−1.62575
$951$	−11.0344	−0.357814
$952$	11.5364	0.373897
$953$	3.29495	0.106734	0.0533670	−	0.998575i	$-0.483005\pi$
$953$	3.29495	0.106734	0.0533670	+	0.998575i	$0.483005\pi$
$954$	7.50524	0.242991
$955$	44.3013	1.43356
$956$	−46.5091	−1.50421
$957$	115.638	3.73805
$958$	−92.4740	−2.98770
$959$	−14.4092	−0.465299
$960$	−1.83076	−0.0590877
$961$	−18.4874	−0.596368
$962$	−0.983936	−0.0317234
$963$	25.1917	0.811790
$964$	−11.1044	−0.357648
$965$	−59.0931	−1.90227
$966$	6.26943	0.201716
$967$	1.39392	0.0448254	0.0224127	−	0.999749i	$-0.492865\pi$
$967$	1.39392	0.0448254	0.0224127	+	0.999749i	$0.492865\pi$
$968$	−70.1003	−2.25311
$969$	−31.8993	−1.02475
$970$	11.9832	0.384757
$971$	−10.8178	−0.347158	−0.173579	−	0.984820i	$-0.555533\pi$
$971$	−10.8178	−0.347158	−0.173579	+	0.984820i	$0.555533\pi$
$972$	−99.2704	−3.18410
$973$	2.60685	0.0835718
$974$	−80.4983	−2.57933
$975$	−15.8976	−0.509132
$976$	6.79435	0.217482
$977$	23.4628	0.750642	0.375321	−	0.926895i	$-0.377532\pi$
$977$	23.4628	0.750642	0.375321	+	0.926895i	$0.377532\pi$
$978$	0.945037	0.0302190
$979$	52.7843	1.68699
$980$	12.4950	0.399139
$981$	21.4490	0.684815
$982$	106.101	3.38582
$983$	57.3568	1.82940	0.914700	−	0.404134i	$-0.132427\pi$
$983$	57.3568	1.82940	0.914700	+	0.404134i	$0.132427\pi$
$984$	−112.786	−3.59549
$985$	51.6273	1.64498
$986$	−46.4470	−1.47918
$987$	11.4895	0.365713
$988$	−73.9065	−2.35128
$989$	9.57695	0.304529
$990$	102.276	3.25056
$991$	20.1069	0.638718	0.319359	−	0.947634i	$-0.396532\pi$
$991$	20.1069	0.638718	0.319359	+	0.947634i	$0.396532\pi$
$992$	−19.4078	−0.616198
$993$	−4.01157	−0.127303
$994$	−11.7095	−0.371402
$995$	34.3518	1.08903
$996$	−61.5427	−1.95005
$997$	−12.2818	−0.388970	−0.194485	−	0.980906i	$-0.562303\pi$
$997$	−12.2818	−0.388970	−0.194485	+	0.980906i	$0.562303\pi$
$998$	70.5836	2.23428
$999$	−0.0265238	−0.000839176 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.2.a.d.1.1	✓	5
3.2	odd	2		1449.2.a.r.1.5		5
4.3	odd	2		2576.2.a.bd.1.2		5
5.4	even	2		4025.2.a.p.1.5		5
7.6	odd	2		1127.2.a.h.1.1		5
23.22	odd	2		3703.2.a.j.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.2.a.d.1.1	✓	5	1.1	even	1	trivial
1127.2.a.h.1.1		5	7.6	odd	2
1449.2.a.r.1.5		5	3.2	odd	2
2576.2.a.bd.1.2		5	4.3	odd	2
3703.2.a.j.1.1		5	23.22	odd	2
4025.2.a.p.1.5		5	5.4	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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	161.a (trivial)

\(f(q)\)	\(=\)	\(q-2.54577 q^{2} +2.46268 q^{3} +4.48096 q^{4} +2.78847 q^{5} -6.26943 q^{6} +1.00000 q^{7} -6.31597 q^{8} +3.06481 q^{9} +O(q^{10})\)	\(q-2.54577 q^{2} +2.46268 q^{3} +4.48096 q^{4} +2.78847 q^{5} -6.26943 q^{6} +1.00000 q^{7} -6.31597 q^{8} +3.06481 q^{9} -7.09882 q^{10} -4.70095 q^{11} +11.0352 q^{12} -2.32579 q^{13} -2.54577 q^{14} +6.86713 q^{15} +7.11710 q^{16} -1.82655 q^{17} -7.80231 q^{18} +7.09155 q^{19} +12.4950 q^{20} +2.46268 q^{21} +11.9675 q^{22} -1.00000 q^{23} -15.5542 q^{24} +2.77558 q^{25} +5.92093 q^{26} +0.159610 q^{27} +4.48096 q^{28} -9.98866 q^{29} -17.4821 q^{30} +3.53732 q^{31} -5.48658 q^{32} -11.5769 q^{33} +4.64998 q^{34} +2.78847 q^{35} +13.7333 q^{36} -0.166179 q^{37} -18.0535 q^{38} -5.72768 q^{39} -17.6119 q^{40} +7.25116 q^{41} -6.26943 q^{42} -9.57695 q^{43} -21.0648 q^{44} +8.54614 q^{45} +2.54577 q^{46} +4.66542 q^{47} +17.5272 q^{48} +1.00000 q^{49} -7.06600 q^{50} -4.49821 q^{51} -10.4218 q^{52} -0.961924 q^{53} -0.406330 q^{54} -13.1085 q^{55} -6.31597 q^{56} +17.4642 q^{57} +25.4289 q^{58} +13.8800 q^{59} +30.7713 q^{60} +0.954652 q^{61} -9.00521 q^{62} +3.06481 q^{63} -0.266598 q^{64} -6.48540 q^{65} +29.4723 q^{66} -11.9221 q^{67} -8.18469 q^{68} -2.46268 q^{69} -7.09882 q^{70} +4.59958 q^{71} -19.3572 q^{72} -7.59806 q^{73} +0.423055 q^{74} +6.83537 q^{75} +31.7770 q^{76} -4.70095 q^{77} +14.5814 q^{78} +5.73902 q^{79} +19.8458 q^{80} -8.80137 q^{81} -18.4598 q^{82} -5.57695 q^{83} +11.0352 q^{84} -5.09328 q^{85} +24.3807 q^{86} -24.5989 q^{87} +29.6910 q^{88} -11.2284 q^{89} -21.7565 q^{90} -2.32579 q^{91} -4.48096 q^{92} +8.71129 q^{93} -11.8771 q^{94} +19.7746 q^{95} -13.5117 q^{96} -1.68805 q^{97} -2.54577 q^{98} -14.4075 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} + 12 q^{4} - 4 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) \) 5 * q + 2 * q^2 + 12 * q^4 - 4 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 11 * q^9	\( 5 q + 2 q^{2} + 12 q^{4} - 4 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 11 q^{9} - 8 q^{10} - 4 q^{11} + 3 q^{12} - 6 q^{13} + 2 q^{14} + 10 q^{15} + 10 q^{16} - 12 q^{17} - 19 q^{18} + 6 q^{19} + 14 q^{22} - 5 q^{23} - 36 q^{24} + 19 q^{25} + q^{26} + 12 q^{28} - 4 q^{29} - 48 q^{30} + 30 q^{31} + 8 q^{32} - 22 q^{33} + 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{37} - 40 q^{38} + 16 q^{39} - 50 q^{40} + 6 q^{41} - 3 q^{42} - 12 q^{43} - 26 q^{44} - 12 q^{45} - 2 q^{46} + 10 q^{47} + 25 q^{48} + 5 q^{49} - 2 q^{50} - 4 q^{51} - 21 q^{52} + 16 q^{53} + 33 q^{54} + 18 q^{55} + 3 q^{56} + 6 q^{57} + 13 q^{58} + 22 q^{59} + 30 q^{60} - 18 q^{61} + 15 q^{62} + 11 q^{63} + 25 q^{64} - 26 q^{65} + 4 q^{66} - 2 q^{67} + 12 q^{68} - 8 q^{70} + 4 q^{71} - 41 q^{72} - 2 q^{73} + 38 q^{74} - 30 q^{75} + 10 q^{76} - 4 q^{77} + 41 q^{78} + 30 q^{79} - 10 q^{80} - 3 q^{81} - 7 q^{82} + 8 q^{83} + 3 q^{84} - 12 q^{85} + 8 q^{86} - 12 q^{87} + 4 q^{88} - 20 q^{89} + 34 q^{90} - 6 q^{91} - 12 q^{92} - 26 q^{93} - 25 q^{94} + 8 q^{95} - q^{96} - 12 q^{97} + 2 q^{98} - 8 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 + 12 * q^4 - 4 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 11 * q^9 - 8 * q^10 - 4 * q^11 + 3 * q^12 - 6 * q^13 + 2 * q^14 + 10 * q^15 + 10 * q^16 - 12 * q^17 - 19 * q^18 + 6 * q^19 + 14 * q^22 - 5 * q^23 - 36 * q^24 + 19 * q^25 + q^26 + 12 * q^28 - 4 * q^29 - 48 * q^30 + 30 * q^31 + 8 * q^32 - 22 * q^33 + 6 * q^34 - 4 * q^35 - q^36 + 4 * q^37 - 40 * q^38 + 16 * q^39 - 50 * q^40 + 6 * q^41 - 3 * q^42 - 12 * q^43 - 26 * q^44 - 12 * q^45 - 2 * q^46 + 10 * q^47 + 25 * q^48 + 5 * q^49 - 2 * q^50 - 4 * q^51 - 21 * q^52 + 16 * q^53 + 33 * q^54 + 18 * q^55 + 3 * q^56 + 6 * q^57 + 13 * q^58 + 22 * q^59 + 30 * q^60 - 18 * q^61 + 15 * q^62 + 11 * q^63 + 25 * q^64 - 26 * q^65 + 4 * q^66 - 2 * q^67 + 12 * q^68 - 8 * q^70 + 4 * q^71 - 41 * q^72 - 2 * q^73 + 38 * q^74 - 30 * q^75 + 10 * q^76 - 4 * q^77 + 41 * q^78 + 30 * q^79 - 10 * q^80 - 3 * q^81 - 7 * q^82 + 8 * q^83 + 3 * q^84 - 12 * q^85 + 8 * q^86 - 12 * q^87 + 4 * q^88 - 20 * q^89 + 34 * q^90 - 6 * q^91 - 12 * q^92 - 26 * q^93 - 25 * q^94 + 8 * q^95 - q^96 - 12 * q^97 + 2 * q^98 - 8 * q^99

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