LMFDB - Embedded newform 6041.2.a.f.1.3

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:	$0$
Dimension:	$132$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-2.77966 q^{2} -1.97929 q^{3} +5.72652 q^{4} -3.34292 q^{5} +5.50177 q^{6} +1.00000 q^{7} -10.3585 q^{8} +0.917605 q^{9} +O(q^{10})$	\(q-2.77966 q^{2} -1.97929 q^{3} +5.72652 q^{4} -3.34292 q^{5} +5.50177 q^{6} +1.00000 q^{7} -10.3585 q^{8} +0.917605 q^{9} +9.29218 q^{10} -6.19168 q^{11} -11.3345 q^{12} -4.77059 q^{13} -2.77966 q^{14} +6.61661 q^{15} +17.3400 q^{16} +6.95085 q^{17} -2.55063 q^{18} +5.45695 q^{19} -19.1433 q^{20} -1.97929 q^{21} +17.2108 q^{22} -5.40623 q^{23} +20.5025 q^{24} +6.17509 q^{25} +13.2606 q^{26} +4.12167 q^{27} +5.72652 q^{28} +1.50514 q^{29} -18.3920 q^{30} +6.57683 q^{31} -27.4824 q^{32} +12.2552 q^{33} -19.3210 q^{34} -3.34292 q^{35} +5.25469 q^{36} +2.34769 q^{37} -15.1685 q^{38} +9.44241 q^{39} +34.6275 q^{40} +3.44238 q^{41} +5.50177 q^{42} -10.2289 q^{43} -35.4568 q^{44} -3.06748 q^{45} +15.0275 q^{46} +4.97411 q^{47} -34.3210 q^{48} +1.00000 q^{49} -17.1647 q^{50} -13.7578 q^{51} -27.3189 q^{52} -0.487931 q^{53} -11.4569 q^{54} +20.6983 q^{55} -10.3585 q^{56} -10.8009 q^{57} -4.18379 q^{58} -1.04347 q^{59} +37.8902 q^{60} -11.8056 q^{61} -18.2814 q^{62} +0.917605 q^{63} +41.7118 q^{64} +15.9477 q^{65} -34.0652 q^{66} -7.29417 q^{67} +39.8042 q^{68} +10.7005 q^{69} +9.29218 q^{70} -0.563675 q^{71} -9.50499 q^{72} -13.1235 q^{73} -6.52579 q^{74} -12.2223 q^{75} +31.2494 q^{76} -6.19168 q^{77} -26.2467 q^{78} +2.20459 q^{79} -57.9662 q^{80} -10.9108 q^{81} -9.56864 q^{82} -16.2511 q^{83} -11.3345 q^{84} -23.2361 q^{85} +28.4328 q^{86} -2.97912 q^{87} +64.1364 q^{88} +1.00906 q^{89} +8.52655 q^{90} -4.77059 q^{91} -30.9589 q^{92} -13.0175 q^{93} -13.8263 q^{94} -18.2421 q^{95} +54.3958 q^{96} -3.71356 q^{97} -2.77966 q^{98} -5.68152 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) $ 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * 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 $

$2$	−2.77966	−1.96552	−0.982759	−	0.184891i	$-0.940807\pi$
$2$	−2.77966	−1.96552	−0.982759	+	0.184891i	$0.940807\pi$
$3$	−1.97929	−1.14275	−0.571373	−	0.820690i	$-0.693589\pi$
$3$	−1.97929	−1.14275	−0.571373	+	0.820690i	$0.693589\pi$
$4$	5.72652	2.86326
$5$	−3.34292	−1.49500	−0.747499	−	0.664263i	$-0.768745\pi$
$5$	−3.34292	−1.49500	−0.747499	+	0.664263i	$0.768745\pi$
$6$	5.50177	2.24609
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−10.3585	−3.66227
$9$	0.917605	0.305868
$10$	9.29218	2.93844
$11$	−6.19168	−1.86686	−0.933431	−	0.358756i	$-0.883201\pi$
$11$	−6.19168	−1.86686	−0.933431	+	0.358756i	$0.883201\pi$
$12$	−11.3345	−3.27198
$13$	−4.77059	−1.32312	−0.661562	−	0.749890i	$-0.730106\pi$
$13$	−4.77059	−1.32312	−0.661562	+	0.749890i	$0.730106\pi$
$14$	−2.77966	−0.742896
$15$	6.61661	1.70840
$16$	17.3400	4.33500
$17$	6.95085	1.68583	0.842915	−	0.538047i	$-0.180838\pi$
$17$	6.95085	1.68583	0.842915	+	0.538047i	$0.180838\pi$
$18$	−2.55063	−0.601190
$19$	5.45695	1.25191	0.625955	−	0.779859i	$-0.284709\pi$
$19$	5.45695	1.25191	0.625955	+	0.779859i	$0.284709\pi$
$20$	−19.1433	−4.28057
$21$	−1.97929	−0.431917
$22$	17.2108	3.66935
$23$	−5.40623	−1.12728	−0.563639	−	0.826022i	$-0.690599\pi$
$23$	−5.40623	−1.12728	−0.563639	+	0.826022i	$0.690599\pi$
$24$	20.5025	4.18505
$25$	6.17509	1.23502
$26$	13.2606	2.60063
$27$	4.12167	0.793216
$28$	5.72652	1.08221
$29$	1.50514	0.279498	0.139749	−	0.990187i	$-0.455370\pi$
$29$	1.50514	0.279498	0.139749	+	0.990187i	$0.455370\pi$
$30$	−18.3920	−3.35790
$31$	6.57683	1.18123	0.590617	−	0.806952i	$-0.298885\pi$
$31$	6.57683	1.18123	0.590617	+	0.806952i	$0.298885\pi$
$32$	−27.4824	−4.85825
$33$	12.2552	2.13335
$34$	−19.3210	−3.31353
$35$	−3.34292	−0.565056
$36$	5.25469	0.875781
$37$	2.34769	0.385958	0.192979	−	0.981203i	$-0.438185\pi$
$37$	2.34769	0.385958	0.192979	+	0.981203i	$0.438185\pi$
$38$	−15.1685	−2.46065
$39$	9.44241	1.51200
$40$	34.6275	5.47509
$41$	3.44238	0.537609	0.268804	−	0.963195i	$-0.413371\pi$
$41$	3.44238	0.537609	0.268804	+	0.963195i	$0.413371\pi$
$42$	5.50177	0.848941
$43$	−10.2289	−1.55989	−0.779945	−	0.625848i	$-0.784753\pi$
$43$	−10.2289	−1.55989	−0.779945	+	0.625848i	$0.784753\pi$
$44$	−35.4568	−5.34531
$45$	−3.06748	−0.457273
$46$	15.0275	2.21568
$47$	4.97411	0.725548	0.362774	−	0.931877i	$-0.381830\pi$
$47$	4.97411	0.725548	0.362774	+	0.931877i	$0.381830\pi$
$48$	−34.3210	−4.95381
$49$	1.00000	0.142857
$50$	−17.1647	−2.42745
$51$	−13.7578	−1.92648
$52$	−27.3189	−3.78845
$53$	−0.487931	−0.0670224	−0.0335112	−	0.999438i	$-0.510669\pi$
$53$	−0.487931	−0.0670224	−0.0335112	+	0.999438i	$0.510669\pi$
$54$	−11.4569	−1.55908
$55$	20.6983	2.79095
$56$	−10.3585	−1.38421
$57$	−10.8009	−1.43062
$58$	−4.18379	−0.549359
$59$	−1.04347	−0.135848	−0.0679241	−	0.997690i	$-0.521638\pi$
$59$	−1.04347	−0.135848	−0.0679241	+	0.997690i	$0.521638\pi$
$60$	37.8902	4.89160
$61$	−11.8056	−1.51156	−0.755778	−	0.654828i	$-0.772741\pi$
$61$	−11.8056	−1.51156	−0.755778	+	0.654828i	$0.772741\pi$
$62$	−18.2814	−2.32174
$63$	0.917605	0.115607
$64$	41.7118	5.21398
$65$	15.9477	1.97807
$66$	−34.0652	−4.19314
$67$	−7.29417	−0.891125	−0.445563	−	0.895251i	$-0.646996\pi$
$67$	−7.29417	−0.891125	−0.445563	+	0.895251i	$0.646996\pi$
$68$	39.8042	4.82697
$69$	10.7005	1.28819
$70$	9.29218	1.11063
$71$	−0.563675	−0.0668959	−0.0334479	−	0.999440i	$-0.510649\pi$
$71$	−0.563675	−0.0668959	−0.0334479	+	0.999440i	$0.510649\pi$
$72$	−9.50499	−1.12017
$73$	−13.1235	−1.53599	−0.767996	−	0.640455i	$-0.778746\pi$
$73$	−13.1235	−1.53599	−0.767996	+	0.640455i	$0.778746\pi$
$74$	−6.52579	−0.758607
$75$	−12.2223	−1.41131
$76$	31.2494	3.58455
$77$	−6.19168	−0.705608
$78$	−26.2467	−2.97185
$79$	2.20459	0.248036	0.124018	−	0.992280i	$-0.460422\pi$
$79$	2.20459	0.248036	0.124018	+	0.992280i	$0.460422\pi$
$80$	−57.9662	−6.48082
$81$	−10.9108	−1.21231
$82$	−9.56864	−1.05668
$83$	−16.2511	−1.78379	−0.891894	−	0.452244i	$-0.850623\pi$
$83$	−16.2511	−1.78379	−0.891894	+	0.452244i	$0.850623\pi$
$84$	−11.3345	−1.23669
$85$	−23.2361	−2.52031
$86$	28.4328	3.06599
$87$	−2.97912	−0.319396
$88$	64.1364	6.83696
$89$	1.00906	0.106960	0.0534800	−	0.998569i	$-0.482969\pi$
$89$	1.00906	0.106960	0.0534800	+	0.998569i	$0.482969\pi$
$90$	8.52655	0.898777
$91$	−4.77059	−0.500094
$92$	−30.9589	−3.22769
$93$	−13.0175	−1.34985
$94$	−13.8263	−1.42608
$95$	−18.2421	−1.87160
$96$	54.3958	5.55175
$97$	−3.71356	−0.377055	−0.188527	−	0.982068i	$-0.560371\pi$
$97$	−3.71356	−0.377055	−0.188527	+	0.982068i	$0.560371\pi$
$98$	−2.77966	−0.280788
$99$	−5.68152	−0.571014
$100$	35.3618	3.53618
$101$	−12.4218	−1.23602	−0.618009	−	0.786171i	$-0.712060\pi$
$101$	−12.4218	−1.23602	−0.618009	+	0.786171i	$0.712060\pi$
$102$	38.2420	3.78652
$103$	15.1733	1.49507	0.747534	−	0.664224i	$-0.231238\pi$
$103$	15.1733	1.49507	0.747534	+	0.664224i	$0.231238\pi$
$104$	49.4161	4.84564
$105$	6.61661	0.645715
$106$	1.35628	0.131734
$107$	3.95507	0.382351	0.191176	−	0.981556i	$-0.438770\pi$
$107$	3.95507	0.382351	0.191176	+	0.981556i	$0.438770\pi$
$108$	23.6028	2.27118
$109$	0.553679	0.0530328	0.0265164	−	0.999648i	$-0.491559\pi$
$109$	0.553679	0.0530328	0.0265164	+	0.999648i	$0.491559\pi$
$110$	−57.5342	−5.48567
$111$	−4.64677	−0.441052
$112$	17.3400	1.63848
$113$	−3.96232	−0.372744	−0.186372	−	0.982479i	$-0.559673\pi$
$113$	−3.96232	−0.372744	−0.186372	+	0.982479i	$0.559673\pi$
$114$	30.0229	2.81190
$115$	18.0726	1.68528
$116$	8.61924	0.800277
$117$	−4.37752	−0.404702
$118$	2.90049	0.267012
$119$	6.95085	0.637184
$120$	−68.5380	−6.25663
$121$	27.3369	2.48518
$122$	32.8157	2.97099
$123$	−6.81347	−0.614350
$124$	37.6623	3.38218
$125$	−3.92822	−0.351351
$126$	−2.55063	−0.227228
$127$	−4.95798	−0.439949	−0.219975	−	0.975506i	$-0.570597\pi$
$127$	−4.95798	−0.439949	−0.219975	+	0.975506i	$0.570597\pi$
$128$	−60.9799	−5.38991
$129$	20.2460	1.78256
$130$	−44.3292	−3.88793
$131$	9.81299	0.857365	0.428682	−	0.903455i	$-0.358978\pi$
$131$	9.81299	0.857365	0.428682	+	0.903455i	$0.358978\pi$
$132$	70.1794	6.10834
$133$	5.45695	0.473178
$134$	20.2753	1.75152
$135$	−13.7784	−1.18586
$136$	−72.0002	−6.17397
$137$	6.21435	0.530928	0.265464	−	0.964121i	$-0.414475\pi$
$137$	6.21435	0.530928	0.265464	+	0.964121i	$0.414475\pi$
$138$	−29.7438	−2.53196
$139$	−19.0566	−1.61636	−0.808179	−	0.588937i	$-0.799547\pi$
$139$	−19.0566	−1.61636	−0.808179	+	0.588937i	$0.799547\pi$
$140$	−19.1433	−1.61790
$141$	−9.84523	−0.829118
$142$	1.56682	0.131485
$143$	29.5380	2.47009
$144$	15.9113	1.32594
$145$	−5.03157	−0.417849
$146$	36.4790	3.01902
$147$	−1.97929	−0.163249
$148$	13.4441	1.10510
$149$	−18.1028	−1.48304	−0.741521	−	0.670930i	$-0.765895\pi$
$149$	−18.1028	−1.48304	−0.741521	+	0.670930i	$0.765895\pi$
$150$	33.9739	2.77396
$151$	−6.79550	−0.553010	−0.276505	−	0.961012i	$-0.589176\pi$
$151$	−6.79550	−0.553010	−0.276505	+	0.961012i	$0.589176\pi$
$152$	−56.5257	−4.58484
$153$	6.37814	0.515642
$154$	17.2108	1.38688
$155$	−21.9858	−1.76594
$156$	54.0722	4.32924
$157$	−7.64318	−0.609992	−0.304996	−	0.952354i	$-0.598655\pi$
$157$	−7.64318	−0.609992	−0.304996	+	0.952354i	$0.598655\pi$
$158$	−6.12802	−0.487519
$159$	0.965759	0.0765896
$160$	91.8714	7.26307
$161$	−5.40623	−0.426071
$162$	30.3284	2.38282
$163$	20.1932	1.58165	0.790826	−	0.612042i	$-0.209651\pi$
$163$	20.1932	1.58165	0.790826	+	0.612042i	$0.209651\pi$
$164$	19.7128	1.53931
$165$	−40.9680	−3.18935
$166$	45.1725	3.50607
$167$	−16.7923	−1.29943	−0.649715	−	0.760178i	$-0.725112\pi$
$167$	−16.7923	−1.29943	−0.649715	+	0.760178i	$0.725112\pi$
$168$	20.5025	1.58180
$169$	9.75857	0.750659
$170$	64.5886	4.95372
$171$	5.00733	0.382920
$172$	−58.5759	−4.46637
$173$	−8.99218	−0.683663	−0.341831	−	0.939761i	$-0.611047\pi$
$173$	−8.99218	−0.683663	−0.341831	+	0.939761i	$0.611047\pi$
$174$	8.28096	0.627778
$175$	6.17509	0.466793
$176$	−107.364	−8.09285
$177$	2.06533	0.155240
$178$	−2.80484	−0.210232
$179$	10.2297	0.764607	0.382303	−	0.924037i	$-0.375131\pi$
$179$	10.2297	0.764607	0.382303	+	0.924037i	$0.375131\pi$
$180$	−17.5660	−1.30929
$181$	18.1511	1.34916	0.674581	−	0.738201i	$-0.264324\pi$
$181$	18.1511	1.34916	0.674581	+	0.738201i	$0.264324\pi$
$182$	13.2606	0.982944
$183$	23.3668	1.72733
$184$	56.0003	4.12840
$185$	−7.84813	−0.577006
$186$	36.1842	2.65315
$187$	−43.0375	−3.14721
$188$	28.4843	2.07743
$189$	4.12167	0.299807
$190$	50.7070	3.67867
$191$	−13.9354	−1.00833	−0.504165	−	0.863607i	$-0.668200\pi$
$191$	−13.9354	−1.00833	−0.504165	+	0.863607i	$0.668200\pi$
$192$	−82.5599	−5.95825
$193$	−15.9732	−1.14978	−0.574890	−	0.818231i	$-0.694955\pi$
$193$	−15.9732	−1.14978	−0.574890	+	0.818231i	$0.694955\pi$
$194$	10.3224	0.741108
$195$	−31.5652	−2.26043
$196$	5.72652	0.409037
$197$	−1.76439	−0.125708	−0.0628539	−	0.998023i	$-0.520020\pi$
$197$	−1.76439	−0.125708	−0.0628539	+	0.998023i	$0.520020\pi$
$198$	15.7927	1.12234
$199$	1.77239	0.125641	0.0628207	−	0.998025i	$-0.479990\pi$
$199$	1.77239	0.125641	0.0628207	+	0.998025i	$0.479990\pi$
$200$	−63.9645	−4.52297
$201$	14.4373	1.01833
$202$	34.5285	2.42941
$203$	1.50514	0.105640
$204$	−78.7842	−5.51600
$205$	−11.5076	−0.803724
$206$	−42.1766	−2.93858
$207$	−4.96079	−0.344798
$208$	−82.7221	−5.73575
$209$	−33.7877	−2.33715
$210$	−18.3920	−1.26917
$211$	5.21318	0.358890	0.179445	−	0.983768i	$-0.442570\pi$
$211$	5.21318	0.358890	0.179445	+	0.983768i	$0.442570\pi$
$212$	−2.79415	−0.191903
$213$	1.11568	0.0764450
$214$	−10.9938	−0.751518
$215$	34.1943	2.33203
$216$	−42.6942	−2.90497
$217$	6.57683	0.446464
$218$	−1.53904	−0.104237
$219$	25.9753	1.75525
$220$	118.529	7.99123
$221$	−33.1597	−2.23056
$222$	12.9165	0.866895
$223$	−28.4440	−1.90475	−0.952376	−	0.304926i	$-0.901368\pi$
$223$	−28.4440	−1.90475	−0.952376	+	0.304926i	$0.901368\pi$
$224$	−27.4824	−1.83625
$225$	5.66629	0.377753
$226$	11.0139	0.732635
$227$	−25.5923	−1.69862	−0.849312	−	0.527892i	$-0.822983\pi$
$227$	−25.5923	−1.69862	−0.849312	+	0.527892i	$0.822983\pi$
$228$	−61.8517	−4.09623
$229$	−6.29749	−0.416150	−0.208075	−	0.978113i	$-0.566720\pi$
$229$	−6.29749	−0.416150	−0.208075	+	0.978113i	$0.566720\pi$
$230$	−50.2357	−3.31244
$231$	12.2552	0.806330
$232$	−15.5910	−1.02360
$233$	8.65776	0.567188	0.283594	−	0.958944i	$-0.408473\pi$
$233$	8.65776	0.567188	0.283594	+	0.958944i	$0.408473\pi$
$234$	12.1680	0.795449
$235$	−16.6280	−1.08469
$236$	−5.97545	−0.388969
$237$	−4.36353	−0.283442
$238$	−19.3210	−1.25240
$239$	13.7734	0.890927	0.445463	−	0.895300i	$-0.353039\pi$
$239$	13.7734	0.890927	0.445463	+	0.895300i	$0.353039\pi$
$240$	114.732	7.40593
$241$	−26.0178	−1.67595	−0.837977	−	0.545705i	$-0.816262\pi$
$241$	−26.0178	−1.67595	−0.837977	+	0.545705i	$0.816262\pi$
$242$	−75.9874	−4.88466
$243$	9.23070	0.592150
$244$	−67.6052	−4.32798
$245$	−3.34292	−0.213571
$246$	18.9392	1.20752
$247$	−26.0329	−1.65643
$248$	−68.1259	−4.32600
$249$	32.1657	2.03842
$250$	10.9191	0.690586
$251$	−24.2358	−1.52975	−0.764877	−	0.644177i	$-0.777200\pi$
$251$	−24.2358	−1.52975	−0.764877	+	0.644177i	$0.777200\pi$
$252$	5.25469	0.331014
$253$	33.4737	2.10447
$254$	13.7815	0.864728
$255$	45.9911	2.88008
$256$	86.0799	5.38000
$257$	9.51267	0.593384	0.296692	−	0.954973i	$-0.404117\pi$
$257$	9.51267	0.593384	0.296692	+	0.954973i	$0.404117\pi$
$258$	−56.2769	−3.50365
$259$	2.34769	0.145878
$260$	91.3248	5.66372
$261$	1.38113	0.0854897
$262$	−27.2768	−1.68517
$263$	24.7176	1.52415	0.762076	−	0.647488i	$-0.224180\pi$
$263$	24.7176	1.52415	0.762076	+	0.647488i	$0.224180\pi$
$264$	−126.945	−7.81291
$265$	1.63111	0.100198
$266$	−15.1685	−0.930039
$267$	−1.99722	−0.122228
$268$	−41.7702	−2.55152
$269$	31.5595	1.92422	0.962110	−	0.272663i	$-0.0879044\pi$
$269$	31.5595	1.92422	0.962110	+	0.272663i	$0.0879044\pi$
$270$	38.2993	2.33082
$271$	−15.9783	−0.970610	−0.485305	−	0.874345i	$-0.661292\pi$
$271$	−15.9783	−0.970610	−0.485305	+	0.874345i	$0.661292\pi$
$272$	120.528	7.30807
$273$	9.44241	0.571481
$274$	−17.2738	−1.04355
$275$	−38.2342	−2.30561
$276$	61.2768	3.68843
$277$	−8.23691	−0.494908	−0.247454	−	0.968900i	$-0.579594\pi$
$277$	−8.23691	−0.494908	−0.247454	+	0.968900i	$0.579594\pi$
$278$	52.9708	3.17698
$279$	6.03493	0.361302
$280$	34.6275	2.06939
$281$	10.1158	0.603456	0.301728	−	0.953394i	$-0.402437\pi$
$281$	10.1158	0.603456	0.301728	+	0.953394i	$0.402437\pi$
$282$	27.3664	1.62965
$283$	7.96966	0.473747	0.236873	−	0.971541i	$-0.423877\pi$
$283$	7.96966	0.473747	0.236873	+	0.971541i	$0.423877\pi$
$284$	−3.22789	−0.191540
$285$	36.1065	2.13877
$286$	−82.1057	−4.85501
$287$	3.44238	0.203197
$288$	−25.2180	−1.48599
$289$	31.3144	1.84202
$290$	13.9861	0.821290
$291$	7.35023	0.430878
$292$	−75.1521	−4.39795
$293$	5.84491	0.341464	0.170732	−	0.985318i	$-0.445387\pi$
$293$	5.84491	0.341464	0.170732	+	0.985318i	$0.445387\pi$
$294$	5.50177	0.320870
$295$	3.48823	0.203093
$296$	−24.3185	−1.41348
$297$	−25.5201	−1.48083
$298$	50.3197	2.91494
$299$	25.7909	1.49153
$300$	−69.9913	−4.04095
$301$	−10.2289	−0.589583
$302$	18.8892	1.08695
$303$	24.5864	1.41245
$304$	94.6236	5.42703
$305$	39.4652	2.25977
$306$	−17.7291	−1.01350
$307$	4.74578	0.270856	0.135428	−	0.990787i	$-0.456759\pi$
$307$	4.74578	0.270856	0.135428	+	0.990787i	$0.456759\pi$
$308$	−35.4568	−2.02034
$309$	−30.0324	−1.70848
$310$	61.1131	3.47099
$311$	27.0039	1.53125	0.765626	−	0.643285i	$-0.222429\pi$
$311$	27.0039	1.53125	0.765626	+	0.643285i	$0.222429\pi$
$312$	−97.8089	−5.53734
$313$	−4.28084	−0.241967	−0.120984	−	0.992654i	$-0.538605\pi$
$313$	−4.28084	−0.241967	−0.120984	+	0.992654i	$0.538605\pi$
$314$	21.2455	1.19895
$315$	−3.06748	−0.172833
$316$	12.6246	0.710191
$317$	−17.1471	−0.963078	−0.481539	−	0.876425i	$-0.659922\pi$
$317$	−17.1471	−0.963078	−0.481539	+	0.876425i	$0.659922\pi$
$318$	−2.68448	−0.150538
$319$	−9.31938	−0.521785
$320$	−139.439	−7.79488
$321$	−7.82825	−0.436931
$322$	15.0275	0.837450
$323$	37.9305	2.11051
$324$	−62.4810	−3.47117
$325$	−29.4588	−1.63408
$326$	−56.1302	−3.10876
$327$	−1.09589	−0.0606030
$328$	−35.6578	−1.96887
$329$	4.97411	0.274232
$330$	113.877	6.26873
$331$	−4.46118	−0.245209	−0.122604	−	0.992456i	$-0.539125\pi$
$331$	−4.46118	−0.245209	−0.122604	+	0.992456i	$0.539125\pi$
$332$	−93.0622	−5.10745
$333$	2.15425	0.118052
$334$	46.6770	2.55405
$335$	24.3838	1.33223
$336$	−34.3210	−1.87236
$337$	−4.95466	−0.269898	−0.134949	−	0.990853i	$-0.543087\pi$
$337$	−4.95466	−0.269898	−0.134949	+	0.990853i	$0.543087\pi$
$338$	−27.1255	−1.47543
$339$	7.84260	0.425952
$340$	−133.062	−7.21631
$341$	−40.7216	−2.20520
$342$	−13.9187	−0.752636
$343$	1.00000	0.0539949
$344$	105.956	5.71274
$345$	−35.7709	−1.92584
$346$	24.9952	1.34375
$347$	−5.88572	−0.315962	−0.157981	−	0.987442i	$-0.550498\pi$
$347$	−5.88572	−0.315962	−0.157981	+	0.987442i	$0.550498\pi$
$348$	−17.0600	−0.914513
$349$	4.55226	0.243677	0.121838	−	0.992550i	$-0.461121\pi$
$349$	4.55226	0.243677	0.121838	+	0.992550i	$0.461121\pi$
$350$	−17.1647	−0.917489
$351$	−19.6628	−1.04952
$352$	170.162	9.06968
$353$	−21.2818	−1.13272	−0.566359	−	0.824159i	$-0.691648\pi$
$353$	−21.2818	−1.13272	−0.566359	+	0.824159i	$0.691648\pi$
$354$	−5.74093	−0.305127
$355$	1.88432	0.100009
$356$	5.77840	0.306255
$357$	−13.7578	−0.728139
$358$	−28.4352	−1.50285
$359$	15.0025	0.791800	0.395900	−	0.918294i	$-0.370433\pi$
$359$	15.0025	0.791800	0.395900	+	0.918294i	$0.370433\pi$
$360$	31.7744	1.67466
$361$	10.7783	0.567281
$362$	−50.4540	−2.65180
$363$	−54.1078	−2.83992
$364$	−27.3189	−1.43190
$365$	43.8708	2.29630
$366$	−64.9519	−3.39509
$367$	−12.3509	−0.644714	−0.322357	−	0.946618i	$-0.604475\pi$
$367$	−12.3509	−0.644714	−0.322357	+	0.946618i	$0.604475\pi$
$368$	−93.7441	−4.88675
$369$	3.15874	0.164438
$370$	21.8152	1.13412
$371$	−0.487931	−0.0253321
$372$	−74.5449	−3.86497
$373$	12.0320	0.622991	0.311496	−	0.950248i	$-0.399170\pi$
$373$	12.0320	0.622991	0.311496	+	0.950248i	$0.399170\pi$
$374$	119.630	6.18590
$375$	7.77510	0.401504
$376$	−51.5242	−2.65716
$377$	−7.18043	−0.369811
$378$	−11.4569	−0.589277
$379$	−0.172165	−0.00884354	−0.00442177	−	0.999990i	$-0.501407\pi$
$379$	−0.172165	−0.00884354	−0.00442177	+	0.999990i	$0.501407\pi$
$380$	−104.464	−5.35889
$381$	9.81330	0.502750
$382$	38.7357	1.98189
$383$	2.84338	0.145290	0.0726450	−	0.997358i	$-0.476856\pi$
$383$	2.84338	0.145290	0.0726450	+	0.997358i	$0.476856\pi$
$384$	120.697	6.15930
$385$	20.6983	1.05488
$386$	44.4002	2.25991
$387$	−9.38608	−0.477121
$388$	−21.2658	−1.07961
$389$	−30.1133	−1.52681	−0.763403	−	0.645923i	$-0.776473\pi$
$389$	−30.1133	−1.52681	−0.763403	+	0.645923i	$0.776473\pi$
$390$	87.7405	4.44291
$391$	−37.5779	−1.90040
$392$	−10.3585	−0.523182
$393$	−19.4228	−0.979750
$394$	4.90441	0.247081
$395$	−7.36976	−0.370813
$396$	−32.5353	−1.63496
$397$	−21.5186	−1.07999	−0.539995	−	0.841668i	$-0.681574\pi$
$397$	−21.5186	−1.07999	−0.539995	+	0.841668i	$0.681574\pi$
$398$	−4.92665	−0.246951
$399$	−10.8009	−0.540722
$400$	107.076	5.35380
$401$	2.97108	0.148368	0.0741842	−	0.997245i	$-0.476365\pi$
$401$	2.97108	0.148368	0.0741842	+	0.997245i	$0.476365\pi$
$402$	−40.1309	−2.00155
$403$	−31.3754	−1.56292
$404$	−71.1338	−3.53904
$405$	36.4739	1.81240
$406$	−4.18379	−0.207638
$407$	−14.5362	−0.720530
$408$	142.510	7.05528
$409$	5.28633	0.261392	0.130696	−	0.991422i	$-0.458279\pi$
$409$	5.28633	0.261392	0.130696	+	0.991422i	$0.458279\pi$
$410$	31.9872	1.57973
$411$	−12.3000	−0.606715
$412$	86.8901	4.28077
$413$	−1.04347	−0.0513458
$414$	13.7893	0.677708
$415$	54.3260	2.66676
$416$	131.107	6.42807
$417$	37.7186	1.84709
$418$	93.9184	4.59370
$419$	−6.47399	−0.316275	−0.158138	−	0.987417i	$-0.550549\pi$
$419$	−6.47399	−0.316275	−0.158138	+	0.987417i	$0.550549\pi$
$420$	37.8902	1.84885
$421$	22.2759	1.08566	0.542830	−	0.839843i	$-0.317353\pi$
$421$	22.2759	1.08566	0.542830	+	0.839843i	$0.317353\pi$
$422$	−14.4909	−0.705405
$423$	4.56427	0.221922
$424$	5.05422	0.245454
$425$	42.9221	2.08203
$426$	−3.10121	−0.150254
$427$	−11.8056	−0.571315
$428$	22.6488	1.09477
$429$	−58.4644	−2.82269
$430$	−95.0486	−4.58365
$431$	−30.6431	−1.47603	−0.738014	−	0.674786i	$-0.764236\pi$
$431$	−30.6431	−1.47603	−0.738014	+	0.674786i	$0.764236\pi$
$432$	71.4698	3.43859
$433$	−37.4271	−1.79863	−0.899316	−	0.437299i	$-0.855935\pi$
$433$	−37.4271	−1.79863	−0.899316	+	0.437299i	$0.855935\pi$
$434$	−18.2814	−0.877533
$435$	9.95896	0.477496
$436$	3.17065	0.151847
$437$	−29.5015	−1.41125
$438$	−72.2026	−3.44997
$439$	2.97048	0.141773	0.0708865	−	0.997484i	$-0.477417\pi$
$439$	2.97048	0.141773	0.0708865	+	0.997484i	$0.477417\pi$
$440$	−214.402	−10.2212
$441$	0.917605	0.0436955
$442$	92.1728	4.38421
$443$	4.06562	0.193163	0.0965816	−	0.995325i	$-0.469209\pi$
$443$	4.06562	0.193163	0.0965816	+	0.995325i	$0.469209\pi$
$444$	−26.6098	−1.26285
$445$	−3.37320	−0.159905
$446$	79.0648	3.74382
$447$	35.8308	1.69474
$448$	41.7118	1.97070
$449$	−22.5341	−1.06345	−0.531725	−	0.846917i	$-0.678456\pi$
$449$	−22.5341	−1.06345	−0.531725	+	0.846917i	$0.678456\pi$
$450$	−15.7504	−0.742480
$451$	−21.3141	−1.00364
$452$	−22.6903	−1.06726
$453$	13.4503	0.631950
$454$	71.1381	3.33867
$455$	15.9477	0.747639
$456$	111.881	5.23931
$457$	−1.86633	−0.0873033	−0.0436517	−	0.999047i	$-0.513899\pi$
$457$	−1.86633	−0.0873033	−0.0436517	+	0.999047i	$0.513899\pi$
$458$	17.5049	0.817950
$459$	28.6491	1.33723
$460$	103.493	4.82539
$461$	30.9483	1.44141	0.720703	−	0.693244i	$-0.243819\pi$
$461$	30.9483	1.44141	0.720703	+	0.693244i	$0.243819\pi$
$462$	−34.0652	−1.58486
$463$	2.28236	0.106070	0.0530351	−	0.998593i	$-0.483110\pi$
$463$	2.28236	0.106070	0.0530351	+	0.998593i	$0.483110\pi$
$464$	26.0992	1.21163
$465$	43.5163	2.01802
$466$	−24.0656	−1.11482
$467$	2.09724	0.0970489	0.0485244	−	0.998822i	$-0.484548\pi$
$467$	2.09724	0.0970489	0.0485244	+	0.998822i	$0.484548\pi$
$468$	−25.0680	−1.15877
$469$	−7.29417	−0.336814
$470$	46.2203	2.13198
$471$	15.1281	0.697066
$472$	10.8087	0.497513
$473$	63.3340	2.91210
$474$	12.1291	0.557110
$475$	33.6972	1.54613
$476$	39.8042	1.82442
$477$	−0.447728	−0.0205001
$478$	−38.2854	−1.75113
$479$	−15.4198	−0.704548	−0.352274	−	0.935897i	$-0.614592\pi$
$479$	−15.4198	−0.704548	−0.352274	+	0.935897i	$0.614592\pi$
$480$	−181.841	−8.29985
$481$	−11.1999	−0.510670
$482$	72.3207	3.29412
$483$	10.7005	0.486891
$484$	156.546	7.11571
$485$	12.4141	0.563696
$486$	−25.6582	−1.16388
$487$	−34.8612	−1.57971	−0.789855	−	0.613293i	$-0.789844\pi$
$487$	−34.8612	−1.57971	−0.789855	+	0.613293i	$0.789844\pi$
$488$	122.288	5.53573
$489$	−39.9682	−1.80743
$490$	9.29218	0.419778
$491$	27.5227	1.24208	0.621042	−	0.783777i	$-0.286710\pi$
$491$	27.5227	1.24208	0.621042	+	0.783777i	$0.286710\pi$
$492$	−39.0175	−1.75905
$493$	10.4620	0.471187
$494$	72.3627	3.25575
$495$	18.9928	0.853665
$496$	114.042	5.12065
$497$	−0.563675	−0.0252843
$498$	−89.4097	−4.00654
$499$	5.96452	0.267009	0.133504	−	0.991048i	$-0.457377\pi$
$499$	5.96452	0.267009	0.133504	+	0.991048i	$0.457377\pi$
$500$	−22.4950	−1.00601
$501$	33.2370	1.48492
$502$	67.3675	3.00676
$503$	−1.14699	−0.0511419	−0.0255709	−	0.999673i	$-0.508140\pi$
$503$	−1.14699	−0.0511419	−0.0255709	+	0.999673i	$0.508140\pi$
$504$	−9.50499	−0.423386
$505$	41.5251	1.84784
$506$	−93.0455	−4.13638
$507$	−19.3151	−0.857813
$508$	−28.3920	−1.25969
$509$	11.8883	0.526939	0.263469	−	0.964668i	$-0.415133\pi$
$509$	11.8883	0.526939	0.263469	+	0.964668i	$0.415133\pi$
$510$	−127.840	−5.66084
$511$	−13.1235	−0.580550
$512$	−117.313	−5.18456
$513$	22.4918	0.993036
$514$	−26.4420	−1.16631
$515$	−50.7230	−2.23512
$516$	115.939	5.10393
$517$	−30.7981	−1.35450
$518$	−6.52579	−0.286727
$519$	17.7982	0.781253
$520$	−165.194	−7.24422
$521$	−4.25156	−0.186264	−0.0931321	−	0.995654i	$-0.529688\pi$
$521$	−4.25156	−0.186264	−0.0931321	+	0.995654i	$0.529688\pi$
$522$	−3.83907	−0.168032
$523$	−17.5335	−0.766685	−0.383343	−	0.923606i	$-0.625227\pi$
$523$	−17.5335	−0.766685	−0.383343	+	0.923606i	$0.625227\pi$
$524$	56.1943	2.45486
$525$	−12.2223	−0.533426
$526$	−68.7065	−2.99575
$527$	45.7146	1.99136
$528$	212.505	9.24807
$529$	6.22734	0.270754
$530$	−4.53394	−0.196942
$531$	−0.957493	−0.0415517
$532$	31.2494	1.35483
$533$	−16.4222	−0.711324
$534$	5.55161	0.240242
$535$	−13.2215	−0.571614
$536$	75.5565	3.26354
$537$	−20.2477	−0.873751
$538$	−87.7249	−3.78209
$539$	−6.19168	−0.266695
$540$	−78.9023	−3.39541
$541$	45.7987	1.96904	0.984521	−	0.175268i	$-0.0560790\pi$
$541$	45.7987	1.96904	0.984521	+	0.175268i	$0.0560790\pi$
$542$	44.4142	1.90775
$543$	−35.9264	−1.54175
$544$	−191.026	−8.19018
$545$	−1.85090	−0.0792839
$546$	−26.2467	−1.12326
$547$	−0.206296	−0.00882059	−0.00441030	−	0.999990i	$-0.501404\pi$
$547$	−0.206296	−0.00882059	−0.00441030	+	0.999990i	$0.501404\pi$
$548$	35.5866	1.52018
$549$	−10.8329	−0.462337
$550$	106.278	4.53171
$551$	8.21350	0.349907
$552$	−110.841	−4.71771
$553$	2.20459	0.0937487
$554$	22.8958	0.972750
$555$	15.5338	0.659371
$556$	−109.128	−4.62805
$557$	−41.0407	−1.73895	−0.869476	−	0.493975i	$-0.835543\pi$
$557$	−41.0407	−1.73895	−0.869476	+	0.493975i	$0.835543\pi$
$558$	−16.7751	−0.710145
$559$	48.7978	2.06393
$560$	−57.9662	−2.44952
$561$	85.1838	3.59646
$562$	−28.1184	−1.18610
$563$	17.9057	0.754637	0.377318	−	0.926084i	$-0.376846\pi$
$563$	17.9057	0.754637	0.377318	+	0.926084i	$0.376846\pi$
$564$	−56.3789	−2.37398
$565$	13.2457	0.557251
$566$	−22.1530	−0.931158
$567$	−10.9108	−0.458211
$568$	5.83881	0.244991
$569$	20.5517	0.861573	0.430787	−	0.902454i	$-0.358236\pi$
$569$	20.5517	0.861573	0.430787	+	0.902454i	$0.358236\pi$
$570$	−100.364	−4.20379
$571$	33.0094	1.38140	0.690701	−	0.723140i	$-0.257302\pi$
$571$	33.0094	1.38140	0.690701	+	0.723140i	$0.257302\pi$
$572$	169.150	7.07252
$573$	27.5822	1.15227
$574$	−9.56864	−0.399387
$575$	−33.3840	−1.39221
$576$	38.2750	1.59479
$577$	29.4541	1.22619	0.613094	−	0.790010i	$-0.289925\pi$
$577$	29.4541	1.22619	0.613094	+	0.790010i	$0.289925\pi$
$578$	−87.0434	−3.62053
$579$	31.6157	1.31391
$580$	−28.8134	−1.19641
$581$	−16.2511	−0.674209
$582$	−20.4312	−0.846898
$583$	3.02111	0.125122
$584$	135.940	5.62522
$585$	14.6337	0.605029
$586$	−16.2469	−0.671153
$587$	36.8284	1.52007	0.760035	−	0.649883i	$-0.225182\pi$
$587$	36.8284	1.52007	0.760035	+	0.649883i	$0.225182\pi$
$588$	−11.3345	−0.467426
$589$	35.8894	1.47880
$590$	−9.69610	−0.399182
$591$	3.49225	0.143652
$592$	40.7090	1.67313
$593$	−9.34275	−0.383661	−0.191830	−	0.981428i	$-0.561442\pi$
$593$	−9.34275	−0.383661	−0.191830	+	0.981428i	$0.561442\pi$
$594$	70.9372	2.91059
$595$	−23.2361	−0.952588
$596$	−103.666	−4.24633
$597$	−3.50808	−0.143576
$598$	−71.6901	−2.93163
$599$	6.60359	0.269815	0.134908	−	0.990858i	$-0.456926\pi$
$599$	6.60359	0.269815	0.134908	+	0.990858i	$0.456926\pi$
$600$	126.604	5.16861
$601$	−33.3652	−1.36100	−0.680498	−	0.732750i	$-0.738237\pi$
$601$	−33.3652	−1.36100	−0.680498	+	0.732750i	$0.738237\pi$
$602$	28.4328	1.15884
$603$	−6.69317	−0.272567
$604$	−38.9146	−1.58341
$605$	−91.3851	−3.71533
$606$	−68.3420	−2.77620
$607$	9.80090	0.397806	0.198903	−	0.980019i	$-0.436262\pi$
$607$	9.80090	0.397806	0.198903	+	0.980019i	$0.436262\pi$
$608$	−149.970	−6.08210
$609$	−2.97912	−0.120720
$610$	−109.700	−4.44162
$611$	−23.7295	−0.959991
$612$	36.5246	1.47642
$613$	−2.04850	−0.0827382	−0.0413691	−	0.999144i	$-0.513172\pi$
$613$	−2.04850	−0.0827382	−0.0413691	+	0.999144i	$0.513172\pi$
$614$	−13.1917	−0.532372
$615$	22.7769	0.918452
$616$	64.1364	2.58413
$617$	21.1575	0.851768	0.425884	−	0.904778i	$-0.359963\pi$
$617$	21.1575	0.851768	0.425884	+	0.904778i	$0.359963\pi$
$618$	83.4799	3.35805
$619$	14.1691	0.569506	0.284753	−	0.958601i	$-0.408088\pi$
$619$	14.1691	0.569506	0.284753	+	0.958601i	$0.408088\pi$
$620$	−125.902	−5.05635
$621$	−22.2827	−0.894174
$622$	−75.0618	−3.00970
$623$	1.00906	0.0404271
$624$	163.731	6.55450
$625$	−17.7437	−0.709749
$626$	11.8993	0.475591
$627$	66.8758	2.67076
$628$	−43.7688	−1.74657
$629$	16.3185	0.650659
$630$	8.52655	0.339706
$631$	−22.2323	−0.885055	−0.442527	−	0.896755i	$-0.645918\pi$
$631$	−22.2323	−0.885055	−0.442527	+	0.896755i	$0.645918\pi$
$632$	−22.8362	−0.908375
$633$	−10.3184	−0.410120
$634$	47.6632	1.89295
$635$	16.5741	0.657723
$636$	5.53044	0.219296
$637$	−4.77059	−0.189018
$638$	25.9047	1.02558
$639$	−0.517231	−0.0204613
$640$	203.851	8.05791
$641$	−6.35933	−0.251178	−0.125589	−	0.992082i	$-0.540082\pi$
$641$	−6.35933	−0.251178	−0.125589	+	0.992082i	$0.540082\pi$
$642$	21.7599	0.858795
$643$	11.6601	0.459830	0.229915	−	0.973211i	$-0.426155\pi$
$643$	11.6601	0.459830	0.229915	+	0.973211i	$0.426155\pi$
$644$	−30.9589	−1.21995
$645$	−67.6806	−2.66492
$646$	−105.434	−4.14824
$647$	10.4861	0.412252	0.206126	−	0.978525i	$-0.433914\pi$
$647$	10.4861	0.412252	0.206126	+	0.978525i	$0.433914\pi$
$648$	113.019	4.43982
$649$	6.46083	0.253610
$650$	81.8856	3.21182
$651$	−13.0175	−0.510195
$652$	115.637	4.52868
$653$	−12.2095	−0.477793	−0.238897	−	0.971045i	$-0.576786\pi$
$653$	−12.2095	−0.477793	−0.238897	+	0.971045i	$0.576786\pi$
$654$	3.04621	0.119116
$655$	−32.8040	−1.28176
$656$	59.6908	2.33053
$657$	−12.0422	−0.469812
$658$	−13.8263	−0.539007
$659$	32.8898	1.28121	0.640603	−	0.767872i	$-0.278684\pi$
$659$	32.8898	1.28121	0.640603	+	0.767872i	$0.278684\pi$
$660$	−234.604	−9.13195
$661$	24.1826	0.940595	0.470298	−	0.882508i	$-0.344147\pi$
$661$	24.1826	0.940595	0.470298	+	0.882508i	$0.344147\pi$
$662$	12.4006	0.481962
$663$	65.6328	2.54897
$664$	168.336	6.53272
$665$	−18.2421	−0.707400
$666$	−5.98810	−0.232034
$667$	−8.13716	−0.315072
$668$	−96.1617	−3.72061
$669$	56.2991	2.17665
$670$	−67.7788	−2.61852
$671$	73.0967	2.82187
$672$	54.3958	2.09836
$673$	−1.75396	−0.0676103	−0.0338051	−	0.999428i	$-0.510763\pi$
$673$	−1.75396	−0.0676103	−0.0338051	+	0.999428i	$0.510763\pi$
$674$	13.7723	0.530489
$675$	25.4517	0.979636
$676$	55.8826	2.14933
$677$	30.6664	1.17860	0.589302	−	0.807913i	$-0.299403\pi$
$677$	30.6664	1.17860	0.589302	+	0.807913i	$0.299403\pi$
$678$	−21.7998	−0.837216
$679$	−3.71356	−0.142513
$680$	240.691	9.23007
$681$	50.6548	1.94110
$682$	113.192	4.33436
$683$	−29.6528	−1.13463	−0.567316	−	0.823500i	$-0.692018\pi$
$683$	−29.6528	−1.13463	−0.567316	+	0.823500i	$0.692018\pi$
$684$	28.6746	1.09640
$685$	−20.7740	−0.793736
$686$	−2.77966	−0.106128
$687$	12.4646	0.475553
$688$	−177.369	−6.76212
$689$	2.32772	0.0886791
$690$	99.4311	3.78528
$691$	32.8988	1.25153	0.625765	−	0.780012i	$-0.284787\pi$
$691$	32.8988	1.25153	0.625765	+	0.780012i	$0.284787\pi$
$692$	−51.4939	−1.95750
$693$	−5.68152	−0.215823
$694$	16.3603	0.621029
$695$	63.7045	2.41645
$696$	30.8592	1.16971
$697$	23.9275	0.906317
$698$	−12.6537	−0.478951
$699$	−17.1362	−0.648152
$700$	35.3618	1.33655
$701$	10.3374	0.390437	0.195218	−	0.980760i	$-0.437458\pi$
$701$	10.3374	0.390437	0.195218	+	0.980760i	$0.437458\pi$
$702$	54.6560	2.06286
$703$	12.8112	0.483185
$704$	−258.266	−9.73378
$705$	32.9118	1.23953
$706$	59.1563	2.22638
$707$	−12.4218	−0.467171
$708$	11.8272	0.444492
$709$	46.3400	1.74033	0.870167	−	0.492757i	$-0.164011\pi$
$709$	46.3400	1.74033	0.870167	+	0.492757i	$0.164011\pi$
$710$	−5.23776	−0.196570
$711$	2.02294	0.0758663
$712$	−10.4523	−0.391717
$713$	−35.5559	−1.33158
$714$	38.2420	1.43117
$715$	−98.7431	−3.69278
$716$	58.5808	2.18927
$717$	−27.2616	−1.01810
$718$	−41.7018	−1.55630
$719$	−24.2676	−0.905030	−0.452515	−	0.891757i	$-0.649473\pi$
$719$	−24.2676	−0.905030	−0.452515	+	0.891757i	$0.649473\pi$
$720$	−53.1901	−1.98228
$721$	15.1733	0.565083
$722$	−29.9601	−1.11500
$723$	51.4969	1.91519
$724$	103.943	3.86300
$725$	9.29440	0.345185
$726$	150.401	5.58192
$727$	−32.4213	−1.20244	−0.601220	−	0.799083i	$-0.705319\pi$
$727$	−32.4213	−1.20244	−0.601220	+	0.799083i	$0.705319\pi$
$728$	49.4161	1.83148
$729$	14.4622	0.535636
$730$	−121.946	−4.51343
$731$	−71.0995	−2.62971
$732$	133.811	4.94578
$733$	−17.3482	−0.640770	−0.320385	−	0.947288i	$-0.603812\pi$
$733$	−17.3482	−0.640770	−0.320385	+	0.947288i	$0.603812\pi$
$734$	34.3314	1.26720
$735$	6.61661	0.244057
$736$	148.576	5.47659
$737$	45.1632	1.66361
$738$	−8.78024	−0.323205
$739$	−25.6340	−0.942961	−0.471481	−	0.881876i	$-0.656280\pi$
$739$	−25.6340	−0.942961	−0.471481	+	0.881876i	$0.656280\pi$
$740$	−44.9425	−1.65212
$741$	51.5268	1.89288
$742$	1.35628	0.0497907
$743$	−14.1137	−0.517783	−0.258891	−	0.965906i	$-0.583357\pi$
$743$	−14.1137	−0.517783	−0.258891	+	0.965906i	$0.583357\pi$
$744$	134.841	4.94352
$745$	60.5162	2.21714
$746$	−33.4448	−1.22450
$747$	−14.9121	−0.545604
$748$	−246.455	−9.01129
$749$	3.95507	0.144515
$750$	−21.6122	−0.789164
$751$	−18.5451	−0.676719	−0.338360	−	0.941017i	$-0.609872\pi$
$751$	−18.5451	−0.676719	−0.338360	+	0.941017i	$0.609872\pi$
$752$	86.2511	3.14525
$753$	47.9699	1.74812
$754$	19.9592	0.726870
$755$	22.7168	0.826749
$756$	23.6028	0.858427
$757$	28.9796	1.05328	0.526641	−	0.850088i	$-0.323451\pi$
$757$	28.9796	1.05328	0.526641	+	0.850088i	$0.323451\pi$
$758$	0.478561	0.0173821
$759$	−66.2542	−2.40488
$760$	188.961	6.85432
$761$	−40.7998	−1.47899	−0.739495	−	0.673162i	$-0.764936\pi$
$761$	−40.7998	−1.47899	−0.739495	+	0.673162i	$0.764936\pi$
$762$	−27.2776	−0.988165
$763$	0.553679	0.0200445
$764$	−79.8013	−2.88711
$765$	−21.3216	−0.770884
$766$	−7.90364	−0.285570
$767$	4.97797	0.179744
$768$	−170.378	−6.14797
$769$	−19.0973	−0.688668	−0.344334	−	0.938847i	$-0.611895\pi$
$769$	−19.0973	−0.688668	−0.344334	+	0.938847i	$0.611895\pi$
$770$	−57.5342	−2.07339
$771$	−18.8284	−0.678087
$772$	−91.4711	−3.29212
$773$	−6.93671	−0.249496	−0.124748	−	0.992188i	$-0.539812\pi$
$773$	−6.93671	−0.249496	−0.124748	+	0.992188i	$0.539812\pi$
$774$	26.0901	0.937790
$775$	40.6125	1.45884
$776$	38.4668	1.38088
$777$	−4.64677	−0.166702
$778$	83.7048	3.00096
$779$	18.7849	0.673038
$780$	−180.759	−6.47220
$781$	3.49009	0.124885
$782$	104.454	3.73526
$783$	6.20371	0.221703
$784$	17.3400	0.619286
$785$	25.5505	0.911937
$786$	53.9888	1.92572
$787$	−39.9308	−1.42338	−0.711689	−	0.702494i	$-0.752070\pi$
$787$	−39.9308	−1.42338	−0.711689	+	0.702494i	$0.752070\pi$
$788$	−10.1038	−0.359934
$789$	−48.9234	−1.74172
$790$	20.4854	0.728840
$791$	−3.96232	−0.140884
$792$	58.8519	2.09121
$793$	56.3199	1.99998
$794$	59.8146	2.12274
$795$	−3.22845	−0.114501
$796$	10.1496	0.359744
$797$	−38.3478	−1.35835	−0.679175	−	0.733977i	$-0.737662\pi$
$797$	−38.3478	−1.35835	−0.679175	+	0.733977i	$0.737662\pi$
$798$	30.0229	1.06280
$799$	34.5743	1.22315
$800$	−169.706	−6.00002
$801$	0.925918	0.0327157
$802$	−8.25859	−0.291621
$803$	81.2567	2.86749
$804$	82.6756	2.91574
$805$	18.0726	0.636975
$806$	87.2130	3.07195
$807$	−62.4656	−2.19889
$808$	128.671	4.52663
$809$	−35.0181	−1.23117	−0.615585	−	0.788071i	$-0.711080\pi$
$809$	−35.0181	−1.23117	−0.615585	+	0.788071i	$0.711080\pi$
$810$	−101.385	−3.56231
$811$	−7.23577	−0.254082	−0.127041	−	0.991897i	$-0.540548\pi$
$811$	−7.23577	−0.254082	−0.127041	+	0.991897i	$0.540548\pi$
$812$	8.61924	0.302476
$813$	31.6257	1.10916
$814$	40.4056	1.41622
$815$	−67.5041	−2.36456
$816$	−238.560	−8.35127
$817$	−55.8185	−1.95284
$818$	−14.6942	−0.513772
$819$	−4.37752	−0.152963
$820$	−65.8984	−2.30127
$821$	−7.16809	−0.250168	−0.125084	−	0.992146i	$-0.539920\pi$
$821$	−7.16809	−0.250168	−0.125084	+	0.992146i	$0.539920\pi$
$822$	34.1899	1.19251
$823$	−10.3114	−0.359433	−0.179716	−	0.983718i	$-0.557518\pi$
$823$	−10.3114	−0.359433	−0.179716	+	0.983718i	$0.557518\pi$
$824$	−157.172	−5.47535
$825$	75.6767	2.63472
$826$	2.90049	0.100921
$827$	−11.5523	−0.401713	−0.200857	−	0.979621i	$-0.564373\pi$
$827$	−11.5523	−0.401713	−0.200857	+	0.979621i	$0.564373\pi$
$828$	−28.4080	−0.987248
$829$	8.47299	0.294279	0.147140	−	0.989116i	$-0.452993\pi$
$829$	8.47299	0.294279	0.147140	+	0.989116i	$0.452993\pi$
$830$	−151.008	−5.24156
$831$	16.3033	0.565554
$832$	−198.990	−6.89874
$833$	6.95085	0.240833
$834$	−104.845	−3.63048
$835$	56.1354	1.94265
$836$	−193.486	−6.69186
$837$	27.1075	0.936973
$838$	17.9955	0.621645
$839$	39.9674	1.37983	0.689914	−	0.723891i	$-0.257648\pi$
$839$	39.9674	1.37983	0.689914	+	0.723891i	$0.257648\pi$
$840$	−68.5380	−2.36479
$841$	−26.7345	−0.921881
$842$	−61.9194	−2.13388
$843$	−20.0221	−0.689597
$844$	29.8534	1.02760
$845$	−32.6221	−1.12223
$846$	−12.6871	−0.436192
$847$	27.3369	0.939308
$848$	−8.46072	−0.290542
$849$	−15.7743	−0.541372
$850$	−119.309	−4.09227
$851$	−12.6922	−0.435082
$852$	6.38895	0.218882
$853$	48.7968	1.67077	0.835385	−	0.549665i	$-0.185245\pi$
$853$	48.7968	1.67077	0.835385	+	0.549665i	$0.185245\pi$
$854$	32.8157	1.12293
$855$	−16.7391	−0.572464
$856$	−40.9685	−1.40027
$857$	22.9315	0.783325	0.391662	−	0.920109i	$-0.371900\pi$
$857$	22.9315	0.783325	0.391662	+	0.920109i	$0.371900\pi$
$858$	162.511	5.54804
$859$	21.8748	0.746359	0.373179	−	0.927759i	$-0.378268\pi$
$859$	21.8748	0.746359	0.373179	+	0.927759i	$0.378268\pi$
$860$	195.814	6.67721
$861$	−6.81347	−0.232203
$862$	85.1776	2.90116
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	−113.273	−3.85364
$865$	30.0601	1.02207
$866$	104.035	3.53524
$867$	−61.9803	−2.10496
$868$	37.6623	1.27834
$869$	−13.6501	−0.463049
$870$	−27.6825	−0.938526
$871$	34.7975	1.17907
$872$	−5.73527	−0.194221
$873$	−3.40758	−0.115329
$874$	82.0043	2.77384
$875$	−3.92822	−0.132798
$876$	148.748	5.02574
$877$	−24.2205	−0.817868	−0.408934	−	0.912564i	$-0.634099\pi$
$877$	−24.2205	−0.817868	−0.408934	+	0.912564i	$0.634099\pi$
$878$	−8.25692	−0.278658
$879$	−11.5688	−0.390206
$880$	358.908	12.0988
$881$	1.47634	0.0497390	0.0248695	−	0.999691i	$-0.492083\pi$
$881$	1.47634	0.0497390	0.0248695	+	0.999691i	$0.492083\pi$
$882$	−2.55063	−0.0858843
$883$	−23.4755	−0.790013	−0.395007	−	0.918678i	$-0.629258\pi$
$883$	−23.4755	−0.790013	−0.395007	+	0.918678i	$0.629258\pi$
$884$	−189.890	−6.38668
$885$	−6.90424	−0.232083
$886$	−11.3010	−0.379666
$887$	47.2922	1.58792	0.793958	−	0.607973i	$-0.208017\pi$
$887$	47.2922	1.58792	0.793958	+	0.607973i	$0.208017\pi$
$888$	48.1334	1.61525
$889$	−4.95798	−0.166285
$890$	9.37636	0.314296
$891$	67.5563	2.26322
$892$	−162.885	−5.45380
$893$	27.1435	0.908322
$894$	−99.5976	−3.33104
$895$	−34.1972	−1.14309
$896$	−60.9799	−2.03720
$897$	−51.0478	−1.70444
$898$	62.6372	2.09023
$899$	9.89908	0.330153
$900$	32.4481	1.08160
$901$	−3.39154	−0.112988
$902$	59.2460	1.97268
$903$	20.2460	0.673743
$904$	41.0436	1.36509
$905$	−60.6777	−2.01699
$906$	−37.3873	−1.24211
$907$	7.54661	0.250581	0.125291	−	0.992120i	$-0.460014\pi$
$907$	7.54661	0.250581	0.125291	+	0.992120i	$0.460014\pi$
$908$	−146.555	−4.86360
$909$	−11.3983	−0.378059
$910$	−44.3292	−1.46950
$911$	−40.8777	−1.35434	−0.677170	−	0.735827i	$-0.736794\pi$
$911$	−40.8777	−1.35434	−0.677170	+	0.735827i	$0.736794\pi$
$912$	−187.288	−6.20172
$913$	100.622	3.33009
$914$	5.18777	0.171596
$915$	−78.1133	−2.58235
$916$	−36.0627	−1.19154
$917$	9.81299	0.324053
$918$	−79.6349	−2.62834
$919$	−48.0843	−1.58615	−0.793077	−	0.609121i	$-0.791522\pi$
$919$	−48.0843	−1.58615	−0.793077	+	0.609121i	$0.791522\pi$
$920$	−187.204	−6.17194
$921$	−9.39329	−0.309519
$922$	−86.0258	−2.83311
$923$	2.68906	0.0885116
$924$	70.1794	2.30873
$925$	14.4972	0.476665
$926$	−6.34419	−0.208483
$927$	13.9231	0.457294
$928$	−41.3650	−1.35787
$929$	0.944216	0.0309787	0.0154894	−	0.999880i	$-0.495069\pi$
$929$	0.944216	0.0309787	0.0154894	+	0.999880i	$0.495069\pi$
$930$	−120.961	−3.96646
$931$	5.45695	0.178844
$932$	49.5788	1.62401
$933$	−53.4487	−1.74983
$934$	−5.82963	−0.190751
$935$	143.871	4.70507
$936$	45.3444	1.48213
$937$	30.4214	0.993823	0.496912	−	0.867801i	$-0.334467\pi$
$937$	30.4214	0.993823	0.496912	+	0.867801i	$0.334467\pi$
$938$	20.2753	0.662013
$939$	8.47304	0.276507
$940$	−95.2208	−3.10576
$941$	−0.250786	−0.00817539	−0.00408769	−	0.999992i	$-0.501301\pi$
$941$	−0.250786	−0.00817539	−0.00408769	+	0.999992i	$0.501301\pi$
$942$	−42.0510	−1.37010
$943$	−18.6103	−0.606034
$944$	−18.0938	−0.588902
$945$	−13.7784	−0.448211
$946$	−176.047	−5.72378
$947$	43.2058	1.40400	0.702001	−	0.712176i	$-0.252290\pi$
$947$	43.2058	1.40400	0.702001	+	0.712176i	$0.252290\pi$
$948$	−24.9879	−0.811568
$949$	62.6070	2.03231
$950$	−93.6667	−3.03895
$951$	33.9392	1.10055
$952$	−72.0002	−2.33354
$953$	12.0748	0.391141	0.195570	−	0.980690i	$-0.437344\pi$
$953$	12.0748	0.391141	0.195570	+	0.980690i	$0.437344\pi$
$954$	1.24453	0.0402932
$955$	46.5849	1.50745
$956$	78.8736	2.55096
$957$	18.4458	0.596268
$958$	42.8618	1.38480
$959$	6.21435	0.200672
$960$	275.991	8.90757
$961$	12.2547	0.395312
$962$	31.1319	1.00373
$963$	3.62920	0.116949
$964$	−148.992	−4.79870
$965$	53.3972	1.71892
$966$	−29.7438	−0.956992
$967$	−1.52583	−0.0490673	−0.0245336	−	0.999699i	$-0.507810\pi$
$967$	−1.52583	−0.0490673	−0.0245336	+	0.999699i	$0.507810\pi$
$968$	−283.169	−9.10139
$969$	−75.0756	−2.41177
$970$	−34.5071	−1.10795
$971$	−16.4589	−0.528191	−0.264095	−	0.964497i	$-0.585073\pi$
$971$	−16.4589	−0.528191	−0.264095	+	0.964497i	$0.585073\pi$
$972$	52.8598	1.69548
$973$	−19.0566	−0.610926
$974$	96.9023	3.10495
$975$	58.3077	1.86734
$976$	−204.710	−6.55260
$977$	−29.3602	−0.939315	−0.469657	−	0.882849i	$-0.655623\pi$
$977$	−29.3602	−0.939315	−0.469657	+	0.882849i	$0.655623\pi$
$978$	111.098	3.55253
$979$	−6.24777	−0.199680
$980$	−19.1433	−0.611510
$981$	0.508059	0.0162211
$982$	−76.5039	−2.44134
$983$	30.8785	0.984872	0.492436	−	0.870349i	$-0.336107\pi$
$983$	30.8785	0.984872	0.492436	+	0.870349i	$0.336107\pi$
$984$	70.5772	2.24992
$985$	5.89822	0.187933
$986$	−29.0809	−0.926126
$987$	−9.84523	−0.313377
$988$	−149.078	−4.74280
$989$	55.2997	1.75843
$990$	−52.7937	−1.67789
$991$	38.0520	1.20876	0.604381	−	0.796695i	$-0.293420\pi$
$991$	38.0520	1.20876	0.604381	+	0.796695i	$0.293420\pi$
$992$	−180.747	−5.73873
$993$	8.82999	0.280211
$994$	1.56682	0.0496967
$995$	−5.92496	−0.187834
$996$	184.197	5.83652
$997$	−4.21961	−0.133636	−0.0668181	−	0.997765i	$-0.521285\pi$
$997$	−4.21961	−0.133636	−0.0668181	+	0.997765i	$0.521285\pi$
$998$	−16.5794	−0.524810
$999$	9.67641	0.306148

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.f.1.3	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.f.1.3	✓	132	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)

\(f(q)\)	\(=\)	\(q-2.77966 q^{2} -1.97929 q^{3} +5.72652 q^{4} -3.34292 q^{5} +5.50177 q^{6} +1.00000 q^{7} -10.3585 q^{8} +0.917605 q^{9} +O(q^{10})\)	\(q-2.77966 q^{2} -1.97929 q^{3} +5.72652 q^{4} -3.34292 q^{5} +5.50177 q^{6} +1.00000 q^{7} -10.3585 q^{8} +0.917605 q^{9} +9.29218 q^{10} -6.19168 q^{11} -11.3345 q^{12} -4.77059 q^{13} -2.77966 q^{14} +6.61661 q^{15} +17.3400 q^{16} +6.95085 q^{17} -2.55063 q^{18} +5.45695 q^{19} -19.1433 q^{20} -1.97929 q^{21} +17.2108 q^{22} -5.40623 q^{23} +20.5025 q^{24} +6.17509 q^{25} +13.2606 q^{26} +4.12167 q^{27} +5.72652 q^{28} +1.50514 q^{29} -18.3920 q^{30} +6.57683 q^{31} -27.4824 q^{32} +12.2552 q^{33} -19.3210 q^{34} -3.34292 q^{35} +5.25469 q^{36} +2.34769 q^{37} -15.1685 q^{38} +9.44241 q^{39} +34.6275 q^{40} +3.44238 q^{41} +5.50177 q^{42} -10.2289 q^{43} -35.4568 q^{44} -3.06748 q^{45} +15.0275 q^{46} +4.97411 q^{47} -34.3210 q^{48} +1.00000 q^{49} -17.1647 q^{50} -13.7578 q^{51} -27.3189 q^{52} -0.487931 q^{53} -11.4569 q^{54} +20.6983 q^{55} -10.3585 q^{56} -10.8009 q^{57} -4.18379 q^{58} -1.04347 q^{59} +37.8902 q^{60} -11.8056 q^{61} -18.2814 q^{62} +0.917605 q^{63} +41.7118 q^{64} +15.9477 q^{65} -34.0652 q^{66} -7.29417 q^{67} +39.8042 q^{68} +10.7005 q^{69} +9.29218 q^{70} -0.563675 q^{71} -9.50499 q^{72} -13.1235 q^{73} -6.52579 q^{74} -12.2223 q^{75} +31.2494 q^{76} -6.19168 q^{77} -26.2467 q^{78} +2.20459 q^{79} -57.9662 q^{80} -10.9108 q^{81} -9.56864 q^{82} -16.2511 q^{83} -11.3345 q^{84} -23.2361 q^{85} +28.4328 q^{86} -2.97912 q^{87} +64.1364 q^{88} +1.00906 q^{89} +8.52655 q^{90} -4.77059 q^{91} -30.9589 q^{92} -13.0175 q^{93} -13.8263 q^{94} -18.2421 q^{95} +54.3958 q^{96} -3.71356 q^{97} -2.77966 q^{98} -5.68152 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * q^99

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