LMFDB - Embedded newform 6041.2.a.f.1.16

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			1.16
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)

$f(q)$	$=$	$q-2.32322 q^{2} +2.41590 q^{3} +3.39733 q^{4} +0.249961 q^{5} -5.61265 q^{6} +1.00000 q^{7} -3.24629 q^{8} +2.83657 q^{9} +O(q^{10})$	\(q-2.32322 q^{2} +2.41590 q^{3} +3.39733 q^{4} +0.249961 q^{5} -5.61265 q^{6} +1.00000 q^{7} -3.24629 q^{8} +2.83657 q^{9} -0.580712 q^{10} +3.91510 q^{11} +8.20760 q^{12} +0.778528 q^{13} -2.32322 q^{14} +0.603880 q^{15} +0.747183 q^{16} +3.22662 q^{17} -6.58997 q^{18} +6.57430 q^{19} +0.849198 q^{20} +2.41590 q^{21} -9.09562 q^{22} -3.71094 q^{23} -7.84272 q^{24} -4.93752 q^{25} -1.80869 q^{26} -0.394827 q^{27} +3.39733 q^{28} +9.52419 q^{29} -1.40294 q^{30} +7.29397 q^{31} +4.75672 q^{32} +9.45849 q^{33} -7.49612 q^{34} +0.249961 q^{35} +9.63676 q^{36} -8.87264 q^{37} -15.2735 q^{38} +1.88085 q^{39} -0.811446 q^{40} +4.01810 q^{41} -5.61265 q^{42} +2.12465 q^{43} +13.3009 q^{44} +0.709031 q^{45} +8.62132 q^{46} -13.2644 q^{47} +1.80512 q^{48} +1.00000 q^{49} +11.4709 q^{50} +7.79518 q^{51} +2.64492 q^{52} +4.92230 q^{53} +0.917268 q^{54} +0.978621 q^{55} -3.24629 q^{56} +15.8829 q^{57} -22.1267 q^{58} -3.00791 q^{59} +2.05158 q^{60} +7.07562 q^{61} -16.9455 q^{62} +2.83657 q^{63} -12.5453 q^{64} +0.194601 q^{65} -21.9741 q^{66} +9.24765 q^{67} +10.9619 q^{68} -8.96526 q^{69} -0.580712 q^{70} +13.4447 q^{71} -9.20835 q^{72} +3.92772 q^{73} +20.6131 q^{74} -11.9286 q^{75} +22.3351 q^{76} +3.91510 q^{77} -4.36961 q^{78} +9.95908 q^{79} +0.186766 q^{80} -9.46358 q^{81} -9.33490 q^{82} -17.4886 q^{83} +8.20760 q^{84} +0.806527 q^{85} -4.93601 q^{86} +23.0095 q^{87} -12.7096 q^{88} -1.86575 q^{89} -1.64723 q^{90} +0.778528 q^{91} -12.6073 q^{92} +17.6215 q^{93} +30.8161 q^{94} +1.64332 q^{95} +11.4918 q^{96} +3.66925 q^{97} -2.32322 q^{98} +11.1055 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.32322	−1.64276	−0.821381	−	0.570381i	$-0.806796\pi$
$2$	−2.32322	−1.64276	−0.821381	+	0.570381i	$0.806796\pi$
$3$	2.41590	1.39482	0.697410	−	0.716672i	$-0.254336\pi$
$3$	2.41590	1.39482	0.697410	+	0.716672i	$0.254336\pi$
$4$	3.39733	1.69866
$5$	0.249961	0.111786	0.0558929	−	0.998437i	$-0.482199\pi$
$5$	0.249961	0.111786	0.0558929	+	0.998437i	$0.482199\pi$
$6$	−5.61265	−2.29136
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.24629	−1.14774
$9$	2.83657	0.945524
$10$	−0.580712	−0.183637
$11$	3.91510	1.18045	0.590224	−	0.807240i	$-0.299040\pi$
$11$	3.91510	1.18045	0.590224	+	0.807240i	$0.299040\pi$
$12$	8.20760	2.36933
$13$	0.778528	0.215925	0.107962	−	0.994155i	$-0.465567\pi$
$13$	0.778528	0.215925	0.107962	+	0.994155i	$0.465567\pi$
$14$	−2.32322	−0.620905
$15$	0.603880	0.155921
$16$	0.747183	0.186796
$17$	3.22662	0.782569	0.391285	−	0.920270i	$-0.372031\pi$
$17$	3.22662	0.782569	0.391285	+	0.920270i	$0.372031\pi$
$18$	−6.58997	−1.55327
$19$	6.57430	1.50825	0.754124	−	0.656732i	$-0.228062\pi$
$19$	6.57430	1.50825	0.754124	+	0.656732i	$0.228062\pi$
$20$	0.849198	0.189886
$21$	2.41590	0.527193
$22$	−9.09562	−1.93919
$23$	−3.71094	−0.773785	−0.386892	−	0.922125i	$-0.626452\pi$
$23$	−3.71094	−0.773785	−0.386892	+	0.922125i	$0.626452\pi$
$24$	−7.84272	−1.60089
$25$	−4.93752	−0.987504
$26$	−1.80869	−0.354713
$27$	−0.394827	−0.0759845
$28$	3.39733	0.642035
$29$	9.52419	1.76860	0.884299	−	0.466922i	$-0.154637\pi$
$29$	9.52419	1.76860	0.884299	+	0.466922i	$0.154637\pi$
$30$	−1.40294	−0.256141
$31$	7.29397	1.31004	0.655018	−	0.755614i	$-0.272661\pi$
$31$	7.29397	1.31004	0.655018	+	0.755614i	$0.272661\pi$
$32$	4.75672	0.840878
$33$	9.45849	1.64651
$34$	−7.49612	−1.28557
$35$	0.249961	0.0422510
$36$	9.63676	1.60613
$37$	−8.87264	−1.45865	−0.729327	−	0.684166i	$-0.760166\pi$
$37$	−8.87264	−1.45865	−0.729327	+	0.684166i	$0.760166\pi$
$38$	−15.2735	−2.47769
$39$	1.88085	0.301177
$40$	−0.811446	−0.128301
$41$	4.01810	0.627521	0.313761	−	0.949502i	$-0.398411\pi$
$41$	4.01810	0.627521	0.313761	+	0.949502i	$0.398411\pi$
$42$	−5.61265	−0.866051
$43$	2.12465	0.324005	0.162003	−	0.986790i	$-0.448205\pi$
$43$	2.12465	0.324005	0.162003	+	0.986790i	$0.448205\pi$
$44$	13.3009	2.00518
$45$	0.709031	0.105696
$46$	8.62132	1.27114
$47$	−13.2644	−1.93482	−0.967408	−	0.253223i	$-0.918509\pi$
$47$	−13.2644	−1.93482	−0.967408	+	0.253223i	$0.918509\pi$
$48$	1.80512	0.260546
$49$	1.00000	0.142857
$50$	11.4709	1.62223
$51$	7.79518	1.09154
$52$	2.64492	0.366784
$53$	4.92230	0.676130	0.338065	−	0.941123i	$-0.390228\pi$
$53$	4.92230	0.676130	0.338065	+	0.941123i	$0.390228\pi$
$54$	0.917268	0.124824
$55$	0.978621	0.131957
$56$	−3.24629	−0.433804
$57$	15.8829	2.10374
$58$	−22.1267	−2.90538
$59$	−3.00791	−0.391596	−0.195798	−	0.980644i	$-0.562730\pi$
$59$	−3.00791	−0.391596	−0.195798	+	0.980644i	$0.562730\pi$
$60$	2.05158	0.264858
$61$	7.07562	0.905941	0.452970	−	0.891526i	$-0.350364\pi$
$61$	7.07562	0.905941	0.452970	+	0.891526i	$0.350364\pi$
$62$	−16.9455	−2.15207
$63$	2.83657	0.357374
$64$	−12.5453	−1.56816
$65$	0.194601	0.0241373
$66$	−21.9741	−2.70483
$67$	9.24765	1.12978	0.564890	−	0.825166i	$-0.308918\pi$
$67$	9.24765	1.12978	0.564890	+	0.825166i	$0.308918\pi$
$68$	10.9619	1.32932
$69$	−8.96526	−1.07929
$70$	−0.580712	−0.0694084
$71$	13.4447	1.59559	0.797795	−	0.602928i	$-0.206000\pi$
$71$	13.4447	1.59559	0.797795	+	0.602928i	$0.206000\pi$
$72$	−9.20835	−1.08521
$73$	3.92772	0.459705	0.229852	−	0.973226i	$-0.426176\pi$
$73$	3.92772	0.459705	0.229852	+	0.973226i	$0.426176\pi$
$74$	20.6131	2.39622
$75$	−11.9286	−1.37739
$76$	22.3351	2.56201
$77$	3.91510	0.446167
$78$	−4.36961	−0.494761
$79$	9.95908	1.12048	0.560242	−	0.828329i	$-0.310708\pi$
$79$	9.95908	1.12048	0.560242	+	0.828329i	$0.310708\pi$
$80$	0.186766	0.0208811
$81$	−9.46358	−1.05151
$82$	−9.33490	−1.03087
$83$	−17.4886	−1.91963	−0.959813	−	0.280639i	$-0.909454\pi$
$83$	−17.4886	−1.91963	−0.959813	+	0.280639i	$0.909454\pi$
$84$	8.20760	0.895523
$85$	0.806527	0.0874801
$86$	−4.93601	−0.532263
$87$	23.0095	2.46688
$88$	−12.7096	−1.35484
$89$	−1.86575	−0.197769	−0.0988844	−	0.995099i	$-0.531527\pi$
$89$	−1.86575	−0.197769	−0.0988844	+	0.995099i	$0.531527\pi$
$90$	−1.64723	−0.173633
$91$	0.778528	0.0816120
$92$	−12.6073	−1.31440
$93$	17.6215	1.82726
$94$	30.8161	3.17844
$95$	1.64332	0.168601
$96$	11.4918	1.17287
$97$	3.66925	0.372556	0.186278	−	0.982497i	$-0.440357\pi$
$97$	3.66925	0.372556	0.186278	+	0.982497i	$0.440357\pi$
$98$	−2.32322	−0.234680
$99$	11.1055	1.11614
$100$	−16.7744	−1.67744
$101$	−7.99220	−0.795254	−0.397627	−	0.917547i	$-0.630166\pi$
$101$	−7.99220	−0.795254	−0.397627	+	0.917547i	$0.630166\pi$
$102$	−18.1099	−1.79315
$103$	−9.14245	−0.900832	−0.450416	−	0.892819i	$-0.648724\pi$
$103$	−9.14245	−0.900832	−0.450416	+	0.892819i	$0.648724\pi$
$104$	−2.52733	−0.247825
$105$	0.603880	0.0589326
$106$	−11.4356	−1.11072
$107$	2.38360	0.230431	0.115216	−	0.993341i	$-0.463244\pi$
$107$	2.38360	0.230431	0.115216	+	0.993341i	$0.463244\pi$
$108$	−1.34136	−0.129072
$109$	1.05016	0.100587	0.0502934	−	0.998734i	$-0.483984\pi$
$109$	1.05016	0.100587	0.0502934	+	0.998734i	$0.483984\pi$
$110$	−2.27355	−0.216774
$111$	−21.4354	−2.03456
$112$	0.747183	0.0706021
$113$	−15.7834	−1.48478	−0.742389	−	0.669969i	$-0.766307\pi$
$113$	−15.7834	−1.48478	−0.742389	+	0.669969i	$0.766307\pi$
$114$	−36.8993	−3.45594
$115$	−0.927589	−0.0864981
$116$	32.3568	3.00425
$117$	2.20835	0.204162
$118$	6.98802	0.643299
$119$	3.22662	0.295783
$120$	−1.96037	−0.178957
$121$	4.32801	0.393455
$122$	−16.4382	−1.48824
$123$	9.70732	0.875279
$124$	24.7800	2.22531
$125$	−2.48399	−0.222175
$126$	−6.58997	−0.587081
$127$	−7.24116	−0.642549	−0.321274	−	0.946986i	$-0.604111\pi$
$127$	−7.24116	−0.642549	−0.321274	+	0.946986i	$0.604111\pi$
$128$	19.6319	1.73523
$129$	5.13293	0.451929
$130$	−0.452101	−0.0396519
$131$	20.9396	1.82950	0.914752	−	0.404016i	$-0.132386\pi$
$131$	20.9396	1.82950	0.914752	+	0.404016i	$0.132386\pi$
$132$	32.1336	2.79687
$133$	6.57430	0.570064
$134$	−21.4843	−1.85596
$135$	−0.0986911	−0.00849398
$136$	−10.4745	−0.898185
$137$	−19.9137	−1.70134	−0.850669	−	0.525701i	$-0.823803\pi$
$137$	−19.9137	−1.70134	−0.850669	+	0.525701i	$0.823803\pi$
$138$	20.8282	1.77302
$139$	−13.6921	−1.16135	−0.580675	−	0.814135i	$-0.697211\pi$
$139$	−13.6921	−1.16135	−0.580675	+	0.814135i	$0.697211\pi$
$140$	0.849198	0.0717703
$141$	−32.0455	−2.69872
$142$	−31.2349	−2.62117
$143$	3.04802	0.254888
$144$	2.11944	0.176620
$145$	2.38067	0.197704
$146$	−9.12493	−0.755185
$147$	2.41590	0.199260
$148$	−30.1433	−2.47776
$149$	11.9358	0.977819	0.488909	−	0.872335i	$-0.337395\pi$
$149$	11.9358	0.977819	0.488909	+	0.872335i	$0.337395\pi$
$150$	27.7126	2.26272
$151$	0.0794979	0.00646945	0.00323472	−	0.999995i	$-0.498970\pi$
$151$	0.0794979	0.00646945	0.00323472	+	0.999995i	$0.498970\pi$
$152$	−21.3421	−1.73107
$153$	9.15252	0.739938
$154$	−9.09562	−0.732946
$155$	1.82320	0.146443
$156$	6.38985	0.511598
$157$	−4.64293	−0.370546	−0.185273	−	0.982687i	$-0.559317\pi$
$157$	−4.64293	−0.370546	−0.185273	+	0.982687i	$0.559317\pi$
$158$	−23.1371	−1.84069
$159$	11.8918	0.943079
$160$	1.18899	0.0939981
$161$	−3.71094	−0.292463
$162$	21.9859	1.72738
$163$	16.1775	1.26712	0.633558	−	0.773695i	$-0.281594\pi$
$163$	16.1775	1.26712	0.633558	+	0.773695i	$0.281594\pi$
$164$	13.6508	1.06595
$165$	2.36425	0.184057
$166$	40.6298	3.15349
$167$	−6.40110	−0.495332	−0.247666	−	0.968845i	$-0.579664\pi$
$167$	−6.40110	−0.495332	−0.247666	+	0.968845i	$0.579664\pi$
$168$	−7.84272	−0.605079
$169$	−12.3939	−0.953376
$170$	−1.87373	−0.143709
$171$	18.6485	1.42608
$172$	7.21812	0.550376
$173$	−15.3410	−1.16635	−0.583177	−	0.812345i	$-0.698191\pi$
$173$	−15.3410	−1.16635	−0.583177	+	0.812345i	$0.698191\pi$
$174$	−53.4560	−4.05249
$175$	−4.93752	−0.373241
$176$	2.92530	0.220502
$177$	−7.26681	−0.546207
$178$	4.33453	0.324887
$179$	20.0212	1.49645	0.748227	−	0.663443i	$-0.230905\pi$
$179$	20.0212	1.49645	0.748227	+	0.663443i	$0.230905\pi$
$180$	2.40881	0.179542
$181$	14.5407	1.08080	0.540402	−	0.841407i	$-0.318272\pi$
$181$	14.5407	1.08080	0.540402	+	0.841407i	$0.318272\pi$
$182$	−1.80869	−0.134069
$183$	17.0940	1.26362
$184$	12.0468	0.888102
$185$	−2.21781	−0.163057
$186$	−40.9385	−3.00176
$187$	12.6325	0.923781
$188$	−45.0636	−3.28660
$189$	−0.394827	−0.0287194
$190$	−3.81778	−0.276971
$191$	−8.15118	−0.589799	−0.294899	−	0.955528i	$-0.595286\pi$
$191$	−8.15118	−0.589799	−0.294899	+	0.955528i	$0.595286\pi$
$192$	−30.3081	−2.18730
$193$	16.3978	1.18034	0.590168	−	0.807280i	$-0.299061\pi$
$193$	16.3978	1.18034	0.590168	+	0.807280i	$0.299061\pi$
$194$	−8.52446	−0.612021
$195$	0.470138	0.0336672
$196$	3.39733	0.242666
$197$	10.7579	0.766472	0.383236	−	0.923650i	$-0.374810\pi$
$197$	10.7579	0.766472	0.383236	+	0.923650i	$0.374810\pi$
$198$	−25.8004	−1.83355
$199$	26.3198	1.86576	0.932882	−	0.360182i	$-0.117285\pi$
$199$	26.3198	1.86576	0.932882	+	0.360182i	$0.117285\pi$
$200$	16.0286	1.13340
$201$	22.3414	1.57584
$202$	18.5676	1.30641
$203$	9.52419	0.668467
$204$	26.4828	1.85417
$205$	1.00437	0.0701479
$206$	21.2399	1.47985
$207$	−10.5264	−0.731632
$208$	0.581703	0.0403338
$209$	25.7391	1.78041
$210$	−1.40294	−0.0968122
$211$	−18.4210	−1.26815	−0.634076	−	0.773271i	$-0.718619\pi$
$211$	−18.4210	−1.26815	−0.634076	+	0.773271i	$0.718619\pi$
$212$	16.7227	1.14852
$213$	32.4810	2.22556
$214$	−5.53761	−0.378543
$215$	0.531078	0.0362192
$216$	1.28172	0.0872103
$217$	7.29397	0.495147
$218$	−2.43974	−0.165240
$219$	9.48897	0.641205
$220$	3.32470	0.224151
$221$	2.51201	0.168976
$222$	49.7991	3.34229
$223$	−1.18338	−0.0792452	−0.0396226	−	0.999215i	$-0.512616\pi$
$223$	−1.18338	−0.0792452	−0.0396226	+	0.999215i	$0.512616\pi$
$224$	4.75672	0.317822
$225$	−14.0056	−0.933709
$226$	36.6683	2.43914
$227$	0.425661	0.0282521	0.0141261	−	0.999900i	$-0.495503\pi$
$227$	0.425661	0.0282521	0.0141261	+	0.999900i	$0.495503\pi$
$228$	53.9593	3.57354
$229$	17.1475	1.13314	0.566569	−	0.824015i	$-0.308271\pi$
$229$	17.1475	1.13314	0.566569	+	0.824015i	$0.308271\pi$
$230$	2.15499	0.142096
$231$	9.45849	0.622323
$232$	−30.9183	−2.02989
$233$	−27.5273	−1.80338	−0.901688	−	0.432387i	$-0.857671\pi$
$233$	−27.5273	−1.80338	−0.901688	+	0.432387i	$0.857671\pi$
$234$	−5.13048	−0.335390
$235$	−3.31558	−0.216285
$236$	−10.2189	−0.665191
$237$	24.0601	1.56287
$238$	−7.49612	−0.485901
$239$	−6.62922	−0.428808	−0.214404	−	0.976745i	$-0.568781\pi$
$239$	−6.62922	−0.428808	−0.214404	+	0.976745i	$0.568781\pi$
$240$	0.451208	0.0291254
$241$	20.7738	1.33816	0.669080	−	0.743190i	$-0.266688\pi$
$241$	20.7738	1.33816	0.669080	+	0.743190i	$0.266688\pi$
$242$	−10.0549	−0.646353
$243$	−21.6786	−1.39068
$244$	24.0382	1.53889
$245$	0.249961	0.0159694
$246$	−22.5522	−1.43788
$247$	5.11828	0.325668
$248$	−23.6784	−1.50358
$249$	−42.2508	−2.67753
$250$	5.77084	0.364980
$251$	−22.0828	−1.39386	−0.696928	−	0.717141i	$-0.745450\pi$
$251$	−22.0828	−1.39386	−0.696928	+	0.717141i	$0.745450\pi$
$252$	9.63676	0.607059
$253$	−14.5287	−0.913412
$254$	16.8228	1.05555
$255$	1.94849	0.122019
$256$	−20.5186	−1.28241
$257$	−6.24116	−0.389313	−0.194656	−	0.980872i	$-0.562359\pi$
$257$	−6.24116	−0.389313	−0.194656	+	0.980872i	$0.562359\pi$
$258$	−11.9249	−0.742412
$259$	−8.87264	−0.551319
$260$	0.661125	0.0410012
$261$	27.0160	1.67225
$262$	−48.6473	−3.00544
$263$	−5.24927	−0.323684	−0.161842	−	0.986817i	$-0.551743\pi$
$263$	−5.24927	−0.323684	−0.161842	+	0.986817i	$0.551743\pi$
$264$	−30.7050	−1.88976
$265$	1.23038	0.0755817
$266$	−15.2735	−0.936480
$267$	−4.50746	−0.275852
$268$	31.4173	1.91912
$269$	13.0845	0.797779	0.398889	−	0.916999i	$-0.369396\pi$
$269$	13.0845	0.797779	0.398889	+	0.916999i	$0.369396\pi$
$270$	0.229281	0.0139536
$271$	6.80852	0.413588	0.206794	−	0.978384i	$-0.433697\pi$
$271$	6.80852	0.413588	0.206794	+	0.978384i	$0.433697\pi$
$272$	2.41087	0.146181
$273$	1.88085	0.113834
$274$	46.2637	2.79489
$275$	−19.3309	−1.16570
$276$	−30.4579	−1.83335
$277$	10.0423	0.603386	0.301693	−	0.953405i	$-0.402448\pi$
$277$	10.0423	0.603386	0.301693	+	0.953405i	$0.402448\pi$
$278$	31.8097	1.90782
$279$	20.6899	1.23867
$280$	−0.811446	−0.0484931
$281$	−5.98701	−0.357155	−0.178578	−	0.983926i	$-0.557150\pi$
$281$	−5.98701	−0.357155	−0.178578	+	0.983926i	$0.557150\pi$
$282$	74.4487	4.43335
$283$	−0.833588	−0.0495517	−0.0247758	−	0.999693i	$-0.507887\pi$
$283$	−0.833588	−0.0495517	−0.0247758	+	0.999693i	$0.507887\pi$
$284$	45.6760	2.71037
$285$	3.97009	0.235168
$286$	−7.08120	−0.418720
$287$	4.01810	0.237181
$288$	13.4928	0.795070
$289$	−6.58895	−0.387586
$290$	−5.53081	−0.324781
$291$	8.86454	0.519649
$292$	13.3437	0.780884
$293$	−4.29442	−0.250882	−0.125441	−	0.992101i	$-0.540035\pi$
$293$	−4.29442	−0.250882	−0.125441	+	0.992101i	$0.540035\pi$
$294$	−5.61265	−0.327337
$295$	−0.751859	−0.0437749
$296$	28.8032	1.67415
$297$	−1.54579	−0.0896956
$298$	−27.7294	−1.60632
$299$	−2.88907	−0.167079
$300$	−40.5252	−2.33972
$301$	2.12465	0.122463
$302$	−0.184691	−0.0106278
$303$	−19.3084	−1.10924
$304$	4.91221	0.281734
$305$	1.76863	0.101271
$306$	−21.2633	−1.21554
$307$	−13.5745	−0.774738	−0.387369	−	0.921925i	$-0.626616\pi$
$307$	−13.5745	−0.774738	−0.387369	+	0.921925i	$0.626616\pi$
$308$	13.3009	0.757888
$309$	−22.0872	−1.25650
$310$	−4.23570	−0.240571
$311$	−7.87348	−0.446464	−0.223232	−	0.974765i	$-0.571661\pi$
$311$	−7.87348	−0.446464	−0.223232	+	0.974765i	$0.571661\pi$
$312$	−6.10578	−0.345672
$313$	6.78714	0.383632	0.191816	−	0.981431i	$-0.438562\pi$
$313$	6.78714	0.383632	0.191816	+	0.981431i	$0.438562\pi$
$314$	10.7865	0.608719
$315$	0.709031	0.0399494
$316$	33.8343	1.90333
$317$	6.98076	0.392079	0.196039	−	0.980596i	$-0.437192\pi$
$317$	6.98076	0.392079	0.196039	+	0.980596i	$0.437192\pi$
$318$	−27.6272	−1.54925
$319$	37.2882	2.08774
$320$	−3.13582	−0.175298
$321$	5.75854	0.321410
$322$	8.62132	0.480447
$323$	21.2127	1.18031
$324$	−32.1509	−1.78616
$325$	−3.84400	−0.213227
$326$	−37.5837	−2.08157
$327$	2.53707	0.140300
$328$	−13.0439	−0.720230
$329$	−13.2644	−0.731292
$330$	−5.49266	−0.302361
$331$	−18.4003	−1.01137	−0.505685	−	0.862718i	$-0.668760\pi$
$331$	−18.4003	−1.01137	−0.505685	+	0.862718i	$0.668760\pi$
$332$	−59.4146	−3.26080
$333$	−25.1679	−1.37919
$334$	14.8711	0.813713
$335$	2.31155	0.126293
$336$	1.80512	0.0984773
$337$	11.1747	0.608724	0.304362	−	0.952556i	$-0.401557\pi$
$337$	11.1747	0.608724	0.304362	+	0.952556i	$0.401557\pi$
$338$	28.7937	1.56617
$339$	−38.1311	−2.07100
$340$	2.74004	0.148599
$341$	28.5566	1.54643
$342$	−43.3244	−2.34272
$343$	1.00000	0.0539949
$344$	−6.89722	−0.371873
$345$	−2.24096	−0.120649
$346$	35.6404	1.91604
$347$	−3.12443	−0.167728	−0.0838642	−	0.996477i	$-0.526726\pi$
$347$	−3.12443	−0.167728	−0.0838642	+	0.996477i	$0.526726\pi$
$348$	78.1708	4.19039
$349$	0.948338	0.0507634	0.0253817	−	0.999678i	$-0.491920\pi$
$349$	0.948338	0.0507634	0.0253817	+	0.999678i	$0.491920\pi$
$350$	11.4709	0.613146
$351$	−0.307384	−0.0164069
$352$	18.6230	0.992611
$353$	−27.6077	−1.46941	−0.734706	−	0.678386i	$-0.762680\pi$
$353$	−27.6077	−1.46941	−0.734706	+	0.678386i	$0.762680\pi$
$354$	16.8824	0.897287
$355$	3.36064	0.178364
$356$	−6.33855	−0.335943
$357$	7.79518	0.412565
$358$	−46.5135	−2.45832
$359$	−6.73201	−0.355302	−0.177651	−	0.984094i	$-0.556850\pi$
$359$	−6.73201	−0.355302	−0.177651	+	0.984094i	$0.556850\pi$
$360$	−2.30172	−0.121311
$361$	24.2215	1.27481
$362$	−33.7812	−1.77550
$363$	10.4560	0.548800
$364$	2.64492	0.138631
$365$	0.981774	0.0513884
$366$	−39.7130	−2.07583
$367$	25.3040	1.32086	0.660428	−	0.750889i	$-0.270375\pi$
$367$	25.3040	1.32086	0.660428	+	0.750889i	$0.270375\pi$
$368$	−2.77275	−0.144540
$369$	11.3976	0.593336
$370$	5.15245	0.267863
$371$	4.92230	0.255553
$372$	59.8660	3.10391
$373$	−5.91183	−0.306103	−0.153051	−	0.988218i	$-0.548910\pi$
$373$	−5.91183	−0.306103	−0.153051	+	0.988218i	$0.548910\pi$
$374$	−29.3481	−1.51755
$375$	−6.00107	−0.309894
$376$	43.0602	2.22066
$377$	7.41485	0.381884
$378$	0.917268	0.0471792
$379$	3.53866	0.181769	0.0908843	−	0.995861i	$-0.471031\pi$
$379$	3.53866	0.181769	0.0908843	+	0.995861i	$0.471031\pi$
$380$	5.58289	0.286396
$381$	−17.4939	−0.896240
$382$	18.9369	0.968898
$383$	23.0661	1.17862	0.589310	−	0.807907i	$-0.299400\pi$
$383$	23.0661	1.17862	0.589310	+	0.807907i	$0.299400\pi$
$384$	47.4286	2.42033
$385$	0.978621	0.0498751
$386$	−38.0955	−1.93901
$387$	6.02671	0.306355
$388$	12.4657	0.632848
$389$	8.30924	0.421295	0.210647	−	0.977562i	$-0.432443\pi$
$389$	8.30924	0.421295	0.210647	+	0.977562i	$0.432443\pi$
$390$	−1.09223	−0.0553072
$391$	−11.9738	−0.605540
$392$	−3.24629	−0.163963
$393$	50.5880	2.55183
$394$	−24.9930	−1.25913
$395$	2.48938	0.125254
$396$	37.7289	1.89595
$397$	22.9321	1.15093	0.575466	−	0.817826i	$-0.304821\pi$
$397$	22.9321	1.15093	0.575466	+	0.817826i	$0.304821\pi$
$398$	−61.1466	−3.06500
$399$	15.8829	0.795137
$400$	−3.68923	−0.184461
$401$	−12.2159	−0.610031	−0.305016	−	0.952347i	$-0.598662\pi$
$401$	−12.2159	−0.610031	−0.305016	+	0.952347i	$0.598662\pi$
$402$	−51.9039	−2.58873
$403$	5.67856	0.282869
$404$	−27.1521	−1.35087
$405$	−2.36552	−0.117544
$406$	−22.1267	−1.09813
$407$	−34.7373	−1.72186
$408$	−25.3054	−1.25281
$409$	11.5517	0.571195	0.285597	−	0.958350i	$-0.407808\pi$
$409$	11.5517	0.571195	0.285597	+	0.958350i	$0.407808\pi$
$410$	−2.33336	−0.115236
$411$	−48.1094	−2.37306
$412$	−31.0599	−1.53021
$413$	−3.00791	−0.148010
$414$	24.4550	1.20190
$415$	−4.37147	−0.214587
$416$	3.70324	0.181566
$417$	−33.0788	−1.61988
$418$	−59.7974	−2.92478
$419$	−30.7824	−1.50382	−0.751909	−	0.659266i	$-0.770867\pi$
$419$	−30.7824	−1.50382	−0.751909	+	0.659266i	$0.770867\pi$
$420$	2.05158	0.100107
$421$	0.890721	0.0434111	0.0217056	−	0.999764i	$-0.493090\pi$
$421$	0.890721	0.0434111	0.0217056	+	0.999764i	$0.493090\pi$
$422$	42.7959	2.08327
$423$	−37.6255	−1.82941
$424$	−15.9792	−0.776020
$425$	−15.9315	−0.772790
$426$	−75.4604	−3.65607
$427$	7.07562	0.342413
$428$	8.09787	0.391425
$429$	7.36370	0.355523
$430$	−1.23381	−0.0594995
$431$	−22.2770	−1.07304	−0.536521	−	0.843887i	$-0.680262\pi$
$431$	−22.2770	−1.07304	−0.536521	+	0.843887i	$0.680262\pi$
$432$	−0.295008	−0.0141936
$433$	4.00513	0.192474	0.0962371	−	0.995358i	$-0.469319\pi$
$433$	4.00513	0.192474	0.0962371	+	0.995358i	$0.469319\pi$
$434$	−16.9455	−0.813408
$435$	5.75146	0.275762
$436$	3.56773	0.170863
$437$	−24.3969	−1.16706
$438$	−22.0449	−1.05335
$439$	−25.6374	−1.22361	−0.611804	−	0.791009i	$-0.709556\pi$
$439$	−25.6374	−1.22361	−0.611804	+	0.791009i	$0.709556\pi$
$440$	−3.17689	−0.151452
$441$	2.83657	0.135075
$442$	−5.83594	−0.277588
$443$	−3.71944	−0.176716	−0.0883579	−	0.996089i	$-0.528162\pi$
$443$	−3.71944	−0.176716	−0.0883579	+	0.996089i	$0.528162\pi$
$444$	−72.8231	−3.45603
$445$	−0.466363	−0.0221077
$446$	2.74925	0.130181
$447$	28.8357	1.36388
$448$	−12.5453	−0.592708
$449$	22.2992	1.05236	0.526182	−	0.850372i	$-0.323623\pi$
$449$	22.2992	1.05236	0.526182	+	0.850372i	$0.323623\pi$
$450$	32.5381	1.53386
$451$	15.7313	0.740756
$452$	−53.6214	−2.52214
$453$	0.192059	0.00902372
$454$	−0.988902	−0.0464115
$455$	0.194601	0.00912306
$456$	−51.5604	−2.41454
$457$	1.95251	0.0913345	0.0456672	−	0.998957i	$-0.485459\pi$
$457$	1.95251	0.0913345	0.0456672	+	0.998957i	$0.485459\pi$
$458$	−39.8373	−1.86147
$459$	−1.27395	−0.0594631
$460$	−3.15132	−0.146931
$461$	−6.21417	−0.289423	−0.144711	−	0.989474i	$-0.546225\pi$
$461$	−6.21417	−0.289423	−0.144711	+	0.989474i	$0.546225\pi$
$462$	−21.9741	−1.02233
$463$	−2.94314	−0.136779	−0.0683897	−	0.997659i	$-0.521786\pi$
$463$	−2.94314	−0.136779	−0.0683897	+	0.997659i	$0.521786\pi$
$464$	7.11631	0.330366
$465$	4.40468	0.204262
$466$	63.9519	2.96252
$467$	−3.36550	−0.155737	−0.0778683	−	0.996964i	$-0.524811\pi$
$467$	−3.36550	−0.155737	−0.0778683	+	0.996964i	$0.524811\pi$
$468$	7.50250	0.346803
$469$	9.24765	0.427017
$470$	7.70282	0.355304
$471$	−11.2169	−0.516846
$472$	9.76456	0.449450
$473$	8.31820	0.382471
$474$	−55.8969	−2.56743
$475$	−32.4607	−1.48940
$476$	10.9619	0.502437
$477$	13.9625	0.639297
$478$	15.4011	0.704430
$479$	6.62083	0.302513	0.151257	−	0.988495i	$-0.451668\pi$
$479$	6.62083	0.302513	0.151257	+	0.988495i	$0.451668\pi$
$480$	2.87249	0.131111
$481$	−6.90760	−0.314960
$482$	−48.2621	−2.19828
$483$	−8.96526	−0.407934
$484$	14.7037	0.668348
$485$	0.917168	0.0416465
$486$	50.3640	2.28456
$487$	10.8426	0.491326	0.245663	−	0.969355i	$-0.420994\pi$
$487$	10.8426	0.491326	0.245663	+	0.969355i	$0.420994\pi$
$488$	−22.9696	−1.03978
$489$	39.0831	1.76740
$490$	−0.580712	−0.0262339
$491$	−14.2737	−0.644164	−0.322082	−	0.946712i	$-0.604383\pi$
$491$	−14.2737	−0.644164	−0.322082	+	0.946712i	$0.604383\pi$
$492$	32.9789	1.48681
$493$	30.7309	1.38405
$494$	−11.8909	−0.534995
$495$	2.77593	0.124769
$496$	5.44993	0.244709
$497$	13.4447	0.603077
$498$	98.1576	4.39855
$499$	−26.4167	−1.18257	−0.591286	−	0.806462i	$-0.701380\pi$
$499$	−26.4167	−1.18257	−0.591286	+	0.806462i	$0.701380\pi$
$500$	−8.43892	−0.377400
$501$	−15.4644	−0.690900
$502$	51.3032	2.28977
$503$	16.1977	0.722219	0.361110	−	0.932523i	$-0.382398\pi$
$503$	16.1977	0.722219	0.361110	+	0.932523i	$0.382398\pi$
$504$	−9.20835	−0.410172
$505$	−1.99774	−0.0888981
$506$	33.7533	1.50052
$507$	−29.9424	−1.32979
$508$	−24.6006	−1.09147
$509$	7.46534	0.330895	0.165448	−	0.986219i	$-0.447093\pi$
$509$	7.46534	0.330895	0.165448	+	0.986219i	$0.447093\pi$
$510$	−4.52676	−0.200448
$511$	3.92772	0.173752
$512$	8.40529	0.371465
$513$	−2.59571	−0.114603
$514$	14.4995	0.639548
$515$	−2.28525	−0.100700
$516$	17.4382	0.767676
$517$	−51.9316	−2.28395
$518$	20.6131	0.905686
$519$	−37.0623	−1.62686
$520$	−0.631733	−0.0277033
$521$	−22.5064	−0.986025	−0.493012	−	0.870022i	$-0.664104\pi$
$521$	−22.5064	−0.986025	−0.493012	+	0.870022i	$0.664104\pi$
$522$	−62.7641	−2.74711
$523$	6.29048	0.275063	0.137532	−	0.990497i	$-0.456083\pi$
$523$	6.29048	0.275063	0.137532	+	0.990497i	$0.456083\pi$
$524$	71.1388	3.10771
$525$	−11.9286	−0.520605
$526$	12.1952	0.531736
$527$	23.5348	1.02519
$528$	7.06722	0.307561
$529$	−9.22891	−0.401257
$530$	−2.85844	−0.124163
$531$	−8.53215	−0.370264
$532$	22.3351	0.968348
$533$	3.12820	0.135497
$534$	10.4718	0.453159
$535$	0.595806	0.0257589
$536$	−30.0206	−1.29669
$537$	48.3692	2.08728
$538$	−30.3982	−1.31056
$539$	3.91510	0.168635
$540$	−0.335286	−0.0144284
$541$	−18.1700	−0.781191	−0.390596	−	0.920562i	$-0.627731\pi$
$541$	−18.1700	−0.781191	−0.390596	+	0.920562i	$0.627731\pi$
$542$	−15.8177	−0.679427
$543$	35.1289	1.50753
$544$	15.3481	0.658045
$545$	0.262498	0.0112442
$546$	−4.36961	−0.187002
$547$	25.8143	1.10374	0.551869	−	0.833931i	$-0.313915\pi$
$547$	25.8143	1.10374	0.551869	+	0.833931i	$0.313915\pi$
$548$	−67.6532	−2.89000
$549$	20.0705	0.856588
$550$	44.9098	1.91496
$551$	62.6149	2.66748
$552$	29.1039	1.23874
$553$	9.95908	0.423503
$554$	−23.3305	−0.991219
$555$	−5.35801	−0.227435
$556$	−46.5166	−1.97274
$557$	5.72328	0.242503	0.121252	−	0.992622i	$-0.461309\pi$
$557$	5.72328	0.242503	0.121252	+	0.992622i	$0.461309\pi$
$558$	−48.0670	−2.03484
$559$	1.65410	0.0699608
$560$	0.186766	0.00789231
$561$	30.5189	1.28851
$562$	13.9091	0.586721
$563$	9.19731	0.387620	0.193810	−	0.981039i	$-0.437915\pi$
$563$	9.19731	0.387620	0.193810	+	0.981039i	$0.437915\pi$
$564$	−108.869	−4.58422
$565$	−3.94523	−0.165977
$566$	1.93660	0.0814016
$567$	−9.46358	−0.397433
$568$	−43.6454	−1.83132
$569$	−19.1641	−0.803403	−0.401701	−	0.915771i	$-0.631581\pi$
$569$	−19.1641	−0.803403	−0.401701	+	0.915771i	$0.631581\pi$
$570$	−9.22337	−0.386324
$571$	−12.6880	−0.530975	−0.265487	−	0.964114i	$-0.585533\pi$
$571$	−12.6880	−0.530975	−0.265487	+	0.964114i	$0.585533\pi$
$572$	10.3551	0.432969
$573$	−19.6924	−0.822663
$574$	−9.33490	−0.389631
$575$	18.3228	0.764116
$576$	−35.5855	−1.48273
$577$	−29.8813	−1.24397	−0.621987	−	0.783028i	$-0.713674\pi$
$577$	−29.8813	−1.24397	−0.621987	+	0.783028i	$0.713674\pi$
$578$	15.3076	0.636710
$579$	39.6153	1.64636
$580$	8.08792	0.335833
$581$	−17.4886	−0.725551
$582$	−20.5942	−0.853659
$583$	19.2713	0.798135
$584$	−12.7505	−0.527620
$585$	0.552001	0.0228224
$586$	9.97685	0.412140
$587$	33.1092	1.36656	0.683282	−	0.730155i	$-0.260552\pi$
$587$	33.1092	1.36656	0.683282	+	0.730155i	$0.260552\pi$
$588$	8.20760	0.338476
$589$	47.9527	1.97586
$590$	1.74673	0.0719117
$591$	25.9901	1.06909
$592$	−6.62948	−0.272470
$593$	6.38519	0.262208	0.131104	−	0.991369i	$-0.458148\pi$
$593$	6.38519	0.262208	0.131104	+	0.991369i	$0.458148\pi$
$594$	3.59119	0.147348
$595$	0.806527	0.0330644
$596$	40.5498	1.66099
$597$	63.5861	2.60241
$598$	6.71194	0.274472
$599$	−20.2403	−0.826998	−0.413499	−	0.910505i	$-0.635693\pi$
$599$	−20.2403	−0.826998	−0.413499	+	0.910505i	$0.635693\pi$
$600$	38.7236	1.58088
$601$	−0.800381	−0.0326482	−0.0163241	−	0.999867i	$-0.505196\pi$
$601$	−0.800381	−0.0326482	−0.0163241	+	0.999867i	$0.505196\pi$
$602$	−4.93601	−0.201177
$603$	26.2316	1.06823
$604$	0.270081	0.0109894
$605$	1.08183	0.0439827
$606$	44.8575	1.82221
$607$	41.9841	1.70408	0.852040	−	0.523476i	$-0.175365\pi$
$607$	41.9841	1.70408	0.852040	+	0.523476i	$0.175365\pi$
$608$	31.2721	1.26825
$609$	23.0095	0.932391
$610$	−4.10890	−0.166365
$611$	−10.3267	−0.417775
$612$	31.0941	1.25691
$613$	16.9583	0.684941	0.342470	−	0.939529i	$-0.388736\pi$
$613$	16.9583	0.684941	0.342470	+	0.939529i	$0.388736\pi$
$614$	31.5365	1.27271
$615$	2.42645	0.0978438
$616$	−12.7096	−0.512083
$617$	−14.9102	−0.600261	−0.300131	−	0.953898i	$-0.597030\pi$
$617$	−14.9102	−0.600261	−0.300131	+	0.953898i	$0.597030\pi$
$618$	51.3134	2.06413
$619$	−9.52969	−0.383031	−0.191515	−	0.981490i	$-0.561340\pi$
$619$	−9.52969	−0.383031	−0.191515	+	0.981490i	$0.561340\pi$
$620$	6.19402	0.248758
$621$	1.46518	0.0587956
$622$	18.2918	0.733434
$623$	−1.86575	−0.0747496
$624$	1.40534	0.0562585
$625$	24.0667	0.962668
$626$	−15.7680	−0.630215
$627$	62.1830	2.48335
$628$	−15.7736	−0.629434
$629$	−28.6286	−1.14150
$630$	−1.64723	−0.0656273
$631$	−16.6968	−0.664688	−0.332344	−	0.943158i	$-0.607839\pi$
$631$	−16.6968	−0.664688	−0.332344	+	0.943158i	$0.607839\pi$
$632$	−32.3301	−1.28602
$633$	−44.5032	−1.76884
$634$	−16.2178	−0.644092
$635$	−1.81000	−0.0718278
$636$	40.4003	1.60198
$637$	0.778528	0.0308464
$638$	−86.6284	−3.42965
$639$	38.1368	1.50867
$640$	4.90720	0.193974
$641$	26.5122	1.04717	0.523585	−	0.851973i	$-0.324594\pi$
$641$	26.5122	1.04717	0.523585	+	0.851973i	$0.324594\pi$
$642$	−13.3783	−0.528000
$643$	39.4211	1.55462	0.777309	−	0.629119i	$-0.216584\pi$
$643$	39.4211	1.55462	0.777309	+	0.629119i	$0.216584\pi$
$644$	−12.6073	−0.496797
$645$	1.28303	0.0505193
$646$	−49.2818	−1.93897
$647$	−34.4890	−1.35590	−0.677951	−	0.735107i	$-0.737132\pi$
$647$	−34.4890	−1.35590	−0.677951	+	0.735107i	$0.737132\pi$
$648$	30.7216	1.20686
$649$	−11.7763	−0.462259
$650$	8.93044	0.350281
$651$	17.6215	0.690641
$652$	54.9601	2.15241
$653$	27.1351	1.06188	0.530939	−	0.847410i	$-0.321839\pi$
$653$	27.1351	1.06188	0.530939	+	0.847410i	$0.321839\pi$
$654$	−5.89417	−0.230480
$655$	5.23408	0.204513
$656$	3.00225	0.117218
$657$	11.1413	0.434662
$658$	30.8161	1.20134
$659$	42.3125	1.64826	0.824131	−	0.566399i	$-0.191664\pi$
$659$	42.3125	1.64826	0.824131	+	0.566399i	$0.191664\pi$
$660$	8.03213	0.312650
$661$	−25.9655	−1.00994	−0.504970	−	0.863137i	$-0.668497\pi$
$661$	−25.9655	−1.00994	−0.504970	+	0.863137i	$0.668497\pi$
$662$	42.7477	1.66144
$663$	6.06877	0.235691
$664$	56.7732	2.20323
$665$	1.64332	0.0637251
$666$	58.4704	2.26568
$667$	−35.3437	−1.36851
$668$	−21.7467	−0.841403
$669$	−2.85894	−0.110533
$670$	−5.37023	−0.207470
$671$	27.7018	1.06941
$672$	11.4918	0.443304
$673$	−5.54953	−0.213919	−0.106959	−	0.994263i	$-0.534111\pi$
$673$	−5.54953	−0.213919	−0.106959	+	0.994263i	$0.534111\pi$
$674$	−25.9612	−0.999988
$675$	1.94947	0.0750349
$676$	−42.1061	−1.61947
$677$	38.3481	1.47384	0.736918	−	0.675982i	$-0.236280\pi$
$677$	38.3481	1.47384	0.736918	+	0.675982i	$0.236280\pi$
$678$	88.5868	3.40216
$679$	3.66925	0.140813
$680$	−2.61822	−0.100404
$681$	1.02835	0.0394066
$682$	−66.3431	−2.54041
$683$	41.5552	1.59007	0.795033	−	0.606566i	$-0.207454\pi$
$683$	41.5552	1.59007	0.795033	+	0.606566i	$0.207454\pi$
$684$	63.3550	2.42244
$685$	−4.97763	−0.190185
$686$	−2.32322	−0.0887008
$687$	41.4266	1.58052
$688$	1.58750	0.0605228
$689$	3.83215	0.145993
$690$	5.20624	0.198198
$691$	32.4489	1.23441	0.617207	−	0.786801i	$-0.288264\pi$
$691$	32.4489	1.23441	0.617207	+	0.786801i	$0.288264\pi$
$692$	−52.1184	−1.98125
$693$	11.1055	0.421862
$694$	7.25873	0.275538
$695$	−3.42249	−0.129822
$696$	−74.6956	−2.83133
$697$	12.9649	0.491079
$698$	−2.20319	−0.0833921
$699$	−66.5033	−2.51539
$700$	−16.7744	−0.634012
$701$	20.5210	0.775068	0.387534	−	0.921855i	$-0.373327\pi$
$701$	20.5210	0.775068	0.387534	+	0.921855i	$0.373327\pi$
$702$	0.714119	0.0269527
$703$	−58.3314	−2.20001
$704$	−49.1159	−1.85113
$705$	−8.01012	−0.301679
$706$	64.1387	2.41389
$707$	−7.99220	−0.300578
$708$	−24.6877	−0.927822
$709$	25.5778	0.960593	0.480297	−	0.877106i	$-0.340529\pi$
$709$	25.5778	0.960593	0.480297	+	0.877106i	$0.340529\pi$
$710$	−7.80749	−0.293010
$711$	28.2496	1.05944
$712$	6.05676	0.226987
$713$	−27.0675	−1.01369
$714$	−18.1099	−0.677745
$715$	0.761884	0.0284928
$716$	68.0186	2.54197
$717$	−16.0155	−0.598111
$718$	15.6399	0.583676
$719$	−19.9240	−0.743040	−0.371520	−	0.928425i	$-0.621163\pi$
$719$	−19.9240	−0.743040	−0.371520	+	0.928425i	$0.621163\pi$
$720$	0.529776	0.0197436
$721$	−9.14245	−0.340483
$722$	−56.2716	−2.09421
$723$	50.1875	1.86649
$724$	49.3996	1.83592
$725$	−47.0259	−1.74650
$726$	−24.2916	−0.901546
$727$	4.38569	0.162656	0.0813280	−	0.996687i	$-0.474084\pi$
$727$	4.38569	0.162656	0.0813280	+	0.996687i	$0.474084\pi$
$728$	−2.52733	−0.0936692
$729$	−23.9825	−0.888242
$730$	−2.28087	−0.0844189
$731$	6.85541	0.253557
$732$	58.0739	2.14647
$733$	−36.0771	−1.33254	−0.666270	−	0.745711i	$-0.732110\pi$
$733$	−36.0771	−1.33254	−0.666270	+	0.745711i	$0.732110\pi$
$734$	−58.7865	−2.16985
$735$	0.603880	0.0222744
$736$	−17.6519	−0.650658
$737$	36.2055	1.33365
$738$	−26.4791	−0.974710
$739$	−42.0234	−1.54585	−0.772927	−	0.634495i	$-0.781208\pi$
$739$	−42.0234	−1.54585	−0.772927	+	0.634495i	$0.781208\pi$
$740$	−7.53463	−0.276979
$741$	12.3653	0.454249
$742$	−11.4356	−0.419813
$743$	−50.9812	−1.87032	−0.935160	−	0.354225i	$-0.884745\pi$
$743$	−50.9812	−1.87032	−0.935160	+	0.354225i	$0.884745\pi$
$744$	−57.2045	−2.09722
$745$	2.98348	0.109306
$746$	13.7345	0.502854
$747$	−49.6078	−1.81505
$748$	42.9168	1.56919
$749$	2.38360	0.0870948
$750$	13.9418	0.509081
$751$	−26.6313	−0.971790	−0.485895	−	0.874017i	$-0.661506\pi$
$751$	−26.6313	−0.971790	−0.485895	+	0.874017i	$0.661506\pi$
$752$	−9.91095	−0.361415
$753$	−53.3499	−1.94418
$754$	−17.2263	−0.627345
$755$	0.0198713	0.000723192 0
$756$	−1.34136	−0.0487847
$757$	46.4929	1.68981	0.844907	−	0.534914i	$-0.179656\pi$
$757$	46.4929	1.68981	0.844907	+	0.534914i	$0.179656\pi$
$758$	−8.22106	−0.298602
$759$	−35.0999	−1.27405
$760$	−5.33469	−0.193509
$761$	−10.3478	−0.375106	−0.187553	−	0.982254i	$-0.560056\pi$
$761$	−10.3478	−0.375106	−0.187553	+	0.982254i	$0.560056\pi$
$762$	40.6421	1.47231
$763$	1.05016	0.0380182
$764$	−27.6922	−1.00187
$765$	2.28777	0.0827145
$766$	−53.5874	−1.93619
$767$	−2.34174	−0.0845554
$768$	−49.5708	−1.78873
$769$	41.4044	1.49308	0.746541	−	0.665340i	$-0.231713\pi$
$769$	41.4044	1.49308	0.746541	+	0.665340i	$0.231713\pi$
$770$	−2.27355	−0.0819329
$771$	−15.0780	−0.543021
$772$	55.7086	2.00500
$773$	−22.4816	−0.808605	−0.404303	−	0.914625i	$-0.632486\pi$
$773$	−22.4816	−0.808605	−0.404303	+	0.914625i	$0.632486\pi$
$774$	−14.0013	−0.503268
$775$	−36.0141	−1.29366
$776$	−11.9115	−0.427597
$777$	−21.4354	−0.768991
$778$	−19.3041	−0.692087
$779$	26.4162	0.946458
$780$	1.59721	0.0571893
$781$	52.6373	1.88351
$782$	27.8177	0.994758
$783$	−3.76041	−0.134386
$784$	0.747183	0.0266851
$785$	−1.16055	−0.0414218
$786$	−117.527	−4.19205
$787$	9.60789	0.342484	0.171242	−	0.985229i	$-0.445222\pi$
$787$	9.60789	0.342484	0.171242	+	0.985229i	$0.445222\pi$
$788$	36.5483	1.30198
$789$	−12.6817	−0.451481
$790$	−5.78336	−0.205763
$791$	−15.7834	−0.561193
$792$	−36.0516	−1.28104
$793$	5.50857	0.195615
$794$	−53.2763	−1.89071
$795$	2.97248	0.105423
$796$	89.4171	3.16931
$797$	35.9437	1.27319	0.636596	−	0.771198i	$-0.280342\pi$
$797$	35.9437	1.27319	0.636596	+	0.771198i	$0.280342\pi$
$798$	−36.8993	−1.30622
$799$	−42.7992	−1.51413
$800$	−23.4864	−0.830370
$801$	−5.29232	−0.186995
$802$	28.3801	1.00214
$803$	15.3774	0.542657
$804$	75.9011	2.67682
$805$	−0.927589	−0.0326932
$806$	−13.1925	−0.464687
$807$	31.6109	1.11276
$808$	25.9450	0.912743
$809$	7.44846	0.261874	0.130937	−	0.991391i	$-0.458201\pi$
$809$	7.44846	0.261874	0.130937	+	0.991391i	$0.458201\pi$
$810$	5.49561	0.193096
$811$	−17.3304	−0.608552	−0.304276	−	0.952584i	$-0.598414\pi$
$811$	−17.3304	−0.608552	−0.304276	+	0.952584i	$0.598414\pi$
$812$	32.3568	1.13550
$813$	16.4487	0.576881
$814$	80.7022	2.82861
$815$	4.04373	0.141646
$816$	5.82442	0.203896
$817$	13.9681	0.488681
$818$	−26.8371	−0.938336
$819$	2.20835	0.0771661
$820$	3.41216	0.119158
$821$	−40.4372	−1.41127	−0.705634	−	0.708577i	$-0.749338\pi$
$821$	−40.4372	−1.41127	−0.705634	+	0.708577i	$0.749338\pi$
$822$	111.768	3.89837
$823$	−10.8949	−0.379772	−0.189886	−	0.981806i	$-0.560812\pi$
$823$	−10.8949	−0.379772	−0.189886	+	0.981806i	$0.560812\pi$
$824$	29.6791	1.03392
$825$	−46.7015	−1.62594
$826$	6.98802	0.243144
$827$	−25.3817	−0.882608	−0.441304	−	0.897358i	$-0.645484\pi$
$827$	−25.3817	−0.882608	−0.441304	+	0.897358i	$0.645484\pi$
$828$	−35.7615	−1.24280
$829$	14.4419	0.501587	0.250793	−	0.968041i	$-0.419309\pi$
$829$	14.4419	0.501587	0.250793	+	0.968041i	$0.419309\pi$
$830$	10.1559	0.352515
$831$	24.2613	0.841615
$832$	−9.76684	−0.338604
$833$	3.22662	0.111796
$834$	76.8492	2.66107
$835$	−1.60002	−0.0553711
$836$	87.4440	3.02431
$837$	−2.87985	−0.0995423
$838$	71.5141	2.47042
$839$	36.7760	1.26965	0.634824	−	0.772657i	$-0.281073\pi$
$839$	36.7760	1.26965	0.634824	+	0.772657i	$0.281073\pi$
$840$	−1.96037	−0.0676392
$841$	61.7102	2.12794
$842$	−2.06934	−0.0713141
$843$	−14.4640	−0.498167
$844$	−62.5821	−2.15417
$845$	−3.09798	−0.106574
$846$	87.4121	3.00529
$847$	4.32801	0.148712
$848$	3.67786	0.126298
$849$	−2.01387	−0.0691157
$850$	37.0122	1.26951
$851$	32.9259	1.12868
$852$	110.349	3.78048
$853$	22.3193	0.764200	0.382100	−	0.924121i	$-0.375201\pi$
$853$	22.3193	0.764200	0.382100	+	0.924121i	$0.375201\pi$
$854$	−16.4382	−0.562503
$855$	4.66138	0.159416
$856$	−7.73786	−0.264475
$857$	34.9241	1.19298	0.596491	−	0.802619i	$-0.296561\pi$
$857$	34.9241	1.19298	0.596491	+	0.802619i	$0.296561\pi$
$858$	−17.1075	−0.584039
$859$	−18.2717	−0.623423	−0.311711	−	0.950177i	$-0.600902\pi$
$859$	−18.2717	−0.623423	−0.311711	+	0.950177i	$0.600902\pi$
$860$	1.80424	0.0615242
$861$	9.70732	0.330825
$862$	51.7541	1.76275
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	−1.87808	−0.0638936
$865$	−3.83465	−0.130382
$866$	−9.30477	−0.316189
$867$	−15.9183	−0.540612
$868$	24.7800	0.841088
$869$	38.9908	1.32267
$870$	−13.3619	−0.453010
$871$	7.19956	0.243948
$872$	−3.40912	−0.115447
$873$	10.4081	0.352261
$874$	56.6791	1.91720
$875$	−2.48399	−0.0839741
$876$	32.2371	1.08919
$877$	45.5877	1.53939	0.769694	−	0.638413i	$-0.220409\pi$
$877$	45.5877	1.53939	0.769694	+	0.638413i	$0.220409\pi$
$878$	59.5613	2.01010
$879$	−10.3749	−0.349936
$880$	0.731208	0.0246490
$881$	−5.12342	−0.172612	−0.0863062	−	0.996269i	$-0.527506\pi$
$881$	−5.12342	−0.172612	−0.0863062	+	0.996269i	$0.527506\pi$
$882$	−6.58997	−0.221896
$883$	−9.79563	−0.329649	−0.164825	−	0.986323i	$-0.552706\pi$
$883$	−9.79563	−0.329649	−0.164825	+	0.986323i	$0.552706\pi$
$884$	8.53413	0.287034
$885$	−1.81642	−0.0610581
$886$	8.64105	0.290302
$887$	34.6144	1.16224	0.581119	−	0.813819i	$-0.302615\pi$
$887$	34.6144	1.16224	0.581119	+	0.813819i	$0.302615\pi$
$888$	69.5856	2.33514
$889$	−7.24116	−0.242861
$890$	1.08346	0.0363177
$891$	−37.0508	−1.24125
$892$	−4.02034	−0.134611
$893$	−87.2044	−2.91818
$894$	−66.9915	−2.24053
$895$	5.00451	0.167282
$896$	19.6319	0.655855
$897$	−6.97971	−0.233046
$898$	−51.8058	−1.72878
$899$	69.4691	2.31692
$900$	−47.5817	−1.58606
$901$	15.8824	0.529118
$902$	−36.5471	−1.21688
$903$	5.13293	0.170813
$904$	51.2376	1.70414
$905$	3.63461	0.120819
$906$	−0.446194	−0.0148238
$907$	−8.11052	−0.269305	−0.134653	−	0.990893i	$-0.542992\pi$
$907$	−8.11052	−0.269305	−0.134653	+	0.990893i	$0.542992\pi$
$908$	1.44611	0.0479909
$909$	−22.6705	−0.751932
$910$	−0.452101	−0.0149870
$911$	−41.5161	−1.37549	−0.687746	−	0.725952i	$-0.741400\pi$
$911$	−41.5161	−1.37549	−0.687746	+	0.725952i	$0.741400\pi$
$912$	11.8674	0.392969
$913$	−68.4697	−2.26602
$914$	−4.53610	−0.150041
$915$	4.27282	0.141255
$916$	58.2556	1.92482
$917$	20.9396	0.691488
$918$	2.95967	0.0976836
$919$	−9.47738	−0.312630	−0.156315	−	0.987707i	$-0.549961\pi$
$919$	−9.47738	−0.312630	−0.156315	+	0.987707i	$0.549961\pi$
$920$	3.01123	0.0992772
$921$	−32.7946	−1.08062
$922$	14.4369	0.475453
$923$	10.4671	0.344528
$924$	32.1336	1.05712
$925$	43.8088	1.44043
$926$	6.83755	0.224696
$927$	−25.9332	−0.851758
$928$	45.3039	1.48717
$929$	57.2899	1.87962	0.939810	−	0.341697i	$-0.111002\pi$
$929$	57.2899	1.87962	0.939810	+	0.341697i	$0.111002\pi$
$930$	−10.2330	−0.335554
$931$	6.57430	0.215464
$932$	−93.5194	−3.06333
$933$	−19.0215	−0.622737
$934$	7.81877	0.255838
$935$	3.15763	0.103266
$936$	−7.16896	−0.234325
$937$	36.7691	1.20119	0.600597	−	0.799552i	$-0.294930\pi$
$937$	36.7691	1.20119	0.600597	+	0.799552i	$0.294930\pi$
$938$	−21.4843	−0.701487
$939$	16.3970	0.535097
$940$	−11.2641	−0.367395
$941$	51.1660	1.66796	0.833982	−	0.551792i	$-0.186056\pi$
$941$	51.1660	1.66796	0.833982	+	0.551792i	$0.186056\pi$
$942$	26.0592	0.849054
$943$	−14.9109	−0.485566
$944$	−2.24746	−0.0731485
$945$	−0.0986911	−0.00321042
$946$	−19.3250	−0.628309
$947$	54.9177	1.78458	0.892292	−	0.451459i	$-0.149096\pi$
$947$	54.9177	1.78458	0.892292	+	0.451459i	$0.149096\pi$
$948$	81.7402	2.65480
$949$	3.05784	0.0992617
$950$	75.4133	2.44673
$951$	16.8648	0.546879
$952$	−10.4745	−0.339482
$953$	29.9073	0.968792	0.484396	−	0.874849i	$-0.339039\pi$
$953$	29.9073	0.968792	0.484396	+	0.874849i	$0.339039\pi$
$954$	−32.4378	−1.05021
$955$	−2.03747	−0.0659311
$956$	−22.5216	−0.728401
$957$	90.0844	2.91202
$958$	−15.3816	−0.496957
$959$	−19.9137	−0.643046
$960$	−7.57582	−0.244509
$961$	22.2020	0.716192
$962$	16.0478	0.517403
$963$	6.76125	0.217878
$964$	70.5755	2.27308
$965$	4.09879	0.131945
$966$	20.8282	0.670137
$967$	48.2573	1.55185	0.775925	−	0.630825i	$-0.217284\pi$
$967$	48.2573	1.55185	0.775925	+	0.630825i	$0.217284\pi$
$968$	−14.0500	−0.451584
$969$	51.2479	1.64632
$970$	−2.13078	−0.0684152
$971$	−21.8317	−0.700612	−0.350306	−	0.936635i	$-0.613922\pi$
$971$	−21.8317	−0.700612	−0.350306	+	0.936635i	$0.613922\pi$
$972$	−73.6492	−2.36230
$973$	−13.6921	−0.438949
$974$	−25.1898	−0.807132
$975$	−9.28672	−0.297413
$976$	5.28678	0.169226
$977$	−50.8131	−1.62566	−0.812828	−	0.582504i	$-0.802073\pi$
$977$	−50.8131	−1.62566	−0.812828	+	0.582504i	$0.802073\pi$
$978$	−90.7985	−2.90342
$979$	−7.30459	−0.233456
$980$	0.849198	0.0271266
$981$	2.97884	0.0951072
$982$	33.1609	1.05821
$983$	−62.2006	−1.98389	−0.991945	−	0.126668i	$-0.959572\pi$
$983$	−62.2006	−1.98389	−0.991945	+	0.126668i	$0.959572\pi$
$984$	−31.5128	−1.00459
$985$	2.68906	0.0856807
$986$	−71.3945	−2.27366
$987$	−32.0455	−1.02002
$988$	17.3885	0.553201
$989$	−7.88443	−0.250710
$990$	−6.44908	−0.204965
$991$	22.4166	0.712088	0.356044	−	0.934469i	$-0.384125\pi$
$991$	22.4166	0.712088	0.356044	+	0.934469i	$0.384125\pi$
$992$	34.6954	1.10158
$993$	−44.4532	−1.41068
$994$	−31.2349	−0.990711
$995$	6.57892	0.208566
$996$	−143.540	−4.54823
$997$	62.2275	1.97076	0.985382	−	0.170361i	$-0.0544935\pi$
$997$	62.2275	1.97076	0.985382	+	0.170361i	$0.0544935\pi$
$998$	61.3716	1.94268
$999$	3.50316	0.110835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.f.1.16	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.f.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-2.32322 q^{2} +2.41590 q^{3} +3.39733 q^{4} +0.249961 q^{5} -5.61265 q^{6} +1.00000 q^{7} -3.24629 q^{8} +2.83657 q^{9} +O(q^{10})\)	\(q-2.32322 q^{2} +2.41590 q^{3} +3.39733 q^{4} +0.249961 q^{5} -5.61265 q^{6} +1.00000 q^{7} -3.24629 q^{8} +2.83657 q^{9} -0.580712 q^{10} +3.91510 q^{11} +8.20760 q^{12} +0.778528 q^{13} -2.32322 q^{14} +0.603880 q^{15} +0.747183 q^{16} +3.22662 q^{17} -6.58997 q^{18} +6.57430 q^{19} +0.849198 q^{20} +2.41590 q^{21} -9.09562 q^{22} -3.71094 q^{23} -7.84272 q^{24} -4.93752 q^{25} -1.80869 q^{26} -0.394827 q^{27} +3.39733 q^{28} +9.52419 q^{29} -1.40294 q^{30} +7.29397 q^{31} +4.75672 q^{32} +9.45849 q^{33} -7.49612 q^{34} +0.249961 q^{35} +9.63676 q^{36} -8.87264 q^{37} -15.2735 q^{38} +1.88085 q^{39} -0.811446 q^{40} +4.01810 q^{41} -5.61265 q^{42} +2.12465 q^{43} +13.3009 q^{44} +0.709031 q^{45} +8.62132 q^{46} -13.2644 q^{47} +1.80512 q^{48} +1.00000 q^{49} +11.4709 q^{50} +7.79518 q^{51} +2.64492 q^{52} +4.92230 q^{53} +0.917268 q^{54} +0.978621 q^{55} -3.24629 q^{56} +15.8829 q^{57} -22.1267 q^{58} -3.00791 q^{59} +2.05158 q^{60} +7.07562 q^{61} -16.9455 q^{62} +2.83657 q^{63} -12.5453 q^{64} +0.194601 q^{65} -21.9741 q^{66} +9.24765 q^{67} +10.9619 q^{68} -8.96526 q^{69} -0.580712 q^{70} +13.4447 q^{71} -9.20835 q^{72} +3.92772 q^{73} +20.6131 q^{74} -11.9286 q^{75} +22.3351 q^{76} +3.91510 q^{77} -4.36961 q^{78} +9.95908 q^{79} +0.186766 q^{80} -9.46358 q^{81} -9.33490 q^{82} -17.4886 q^{83} +8.20760 q^{84} +0.806527 q^{85} -4.93601 q^{86} +23.0095 q^{87} -12.7096 q^{88} -1.86575 q^{89} -1.64723 q^{90} +0.778528 q^{91} -12.6073 q^{92} +17.6215 q^{93} +30.8161 q^{94} +1.64332 q^{95} +11.4918 q^{96} +3.66925 q^{97} -2.32322 q^{98} +11.1055 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) \) 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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