LMFDB - Embedded newform 4011.2.a.k.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.05296 q^{2} +1.00000 q^{3} -0.891266 q^{4} +4.03535 q^{5} -1.05296 q^{6} +1.00000 q^{7} +3.04440 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.05296 q^{2} +1.00000 q^{3} -0.891266 q^{4} +4.03535 q^{5} -1.05296 q^{6} +1.00000 q^{7} +3.04440 q^{8} +1.00000 q^{9} -4.24908 q^{10} +0.242041 q^{11} -0.891266 q^{12} +0.703933 q^{13} -1.05296 q^{14} +4.03535 q^{15} -1.42311 q^{16} +4.01294 q^{17} -1.05296 q^{18} +4.25330 q^{19} -3.59657 q^{20} +1.00000 q^{21} -0.254861 q^{22} -2.98887 q^{23} +3.04440 q^{24} +11.2841 q^{25} -0.741217 q^{26} +1.00000 q^{27} -0.891266 q^{28} +10.0301 q^{29} -4.24908 q^{30} -2.29314 q^{31} -4.59031 q^{32} +0.242041 q^{33} -4.22548 q^{34} +4.03535 q^{35} -0.891266 q^{36} -2.34105 q^{37} -4.47857 q^{38} +0.703933 q^{39} +12.2852 q^{40} -1.99832 q^{41} -1.05296 q^{42} -2.90817 q^{43} -0.215723 q^{44} +4.03535 q^{45} +3.14717 q^{46} -11.4157 q^{47} -1.42311 q^{48} +1.00000 q^{49} -11.8817 q^{50} +4.01294 q^{51} -0.627391 q^{52} -12.6763 q^{53} -1.05296 q^{54} +0.976721 q^{55} +3.04440 q^{56} +4.25330 q^{57} -10.5613 q^{58} +12.5298 q^{59} -3.59657 q^{60} +13.5317 q^{61} +2.41460 q^{62} +1.00000 q^{63} +7.67966 q^{64} +2.84062 q^{65} -0.254861 q^{66} -0.658447 q^{67} -3.57659 q^{68} -2.98887 q^{69} -4.24908 q^{70} -0.254382 q^{71} +3.04440 q^{72} +9.21154 q^{73} +2.46505 q^{74} +11.2841 q^{75} -3.79082 q^{76} +0.242041 q^{77} -0.741217 q^{78} +12.4284 q^{79} -5.74277 q^{80} +1.00000 q^{81} +2.10416 q^{82} -15.4511 q^{83} -0.891266 q^{84} +16.1936 q^{85} +3.06221 q^{86} +10.0301 q^{87} +0.736870 q^{88} -1.66122 q^{89} -4.24908 q^{90} +0.703933 q^{91} +2.66387 q^{92} -2.29314 q^{93} +12.0204 q^{94} +17.1635 q^{95} -4.59031 q^{96} -7.34461 q^{97} -1.05296 q^{98} +0.242041 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) $ 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.05296	−0.744558	−0.372279	−	0.928121i	$-0.621424\pi$
$2$	−1.05296	−0.744558	−0.372279	+	0.928121i	$0.621424\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.891266	−0.445633
$5$	4.03535	1.80466	0.902332	−	0.431042i	$-0.141854\pi$
$5$	4.03535	1.80466	0.902332	+	0.431042i	$0.141854\pi$
$6$	−1.05296	−0.429871
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.04440	1.07636
$9$	1.00000	0.333333
$10$	−4.24908	−1.34368
$11$	0.242041	0.0729782	0.0364891	−	0.999334i	$-0.488383\pi$
$11$	0.242041	0.0729782	0.0364891	+	0.999334i	$0.488383\pi$
$12$	−0.891266	−0.257286
$13$	0.703933	0.195236	0.0976180	−	0.995224i	$-0.468878\pi$
$13$	0.703933	0.195236	0.0976180	+	0.995224i	$0.468878\pi$
$14$	−1.05296	−0.281417
$15$	4.03535	1.04192
$16$	−1.42311	−0.355779
$17$	4.01294	0.973281	0.486640	−	0.873602i	$-0.338222\pi$
$17$	4.01294	0.973281	0.486640	+	0.873602i	$0.338222\pi$
$18$	−1.05296	−0.248186
$19$	4.25330	0.975774	0.487887	−	0.872907i	$-0.337768\pi$
$19$	4.25330	0.975774	0.487887	+	0.872907i	$0.337768\pi$
$20$	−3.59657	−0.804217
$21$	1.00000	0.218218
$22$	−0.254861	−0.0543365
$23$	−2.98887	−0.623222	−0.311611	−	0.950210i	$-0.600868\pi$
$23$	−2.98887	−0.623222	−0.311611	+	0.950210i	$0.600868\pi$
$24$	3.04440	0.621436
$25$	11.2841	2.25681
$26$	−0.741217	−0.145365
$27$	1.00000	0.192450
$28$	−0.891266	−0.168433
$29$	10.0301	1.86254	0.931270	−	0.364330i	$-0.118702\pi$
$29$	10.0301	1.86254	0.931270	+	0.364330i	$0.118702\pi$
$30$	−4.24908	−0.775773
$31$	−2.29314	−0.411860	−0.205930	−	0.978567i	$-0.566022\pi$
$31$	−2.29314	−0.411860	−0.205930	+	0.978567i	$0.566022\pi$
$32$	−4.59031	−0.811460
$33$	0.242041	0.0421340
$34$	−4.22548	−0.724664
$35$	4.03535	0.682099
$36$	−0.891266	−0.148544
$37$	−2.34105	−0.384867	−0.192433	−	0.981310i	$-0.561638\pi$
$37$	−2.34105	−0.384867	−0.192433	+	0.981310i	$0.561638\pi$
$38$	−4.47857	−0.726520
$39$	0.703933	0.112720
$40$	12.2852	1.94246
$41$	−1.99832	−0.312085	−0.156043	−	0.987750i	$-0.549874\pi$
$41$	−1.99832	−0.312085	−0.156043	+	0.987750i	$0.549874\pi$
$42$	−1.05296	−0.162476
$43$	−2.90817	−0.443493	−0.221746	−	0.975104i	$-0.571176\pi$
$43$	−2.90817	−0.443493	−0.221746	+	0.975104i	$0.571176\pi$
$44$	−0.215723	−0.0325215
$45$	4.03535	0.601555
$46$	3.14717	0.464025
$47$	−11.4157	−1.66516	−0.832579	−	0.553907i	$-0.813136\pi$
$47$	−11.4157	−1.66516	−0.832579	+	0.553907i	$0.813136\pi$
$48$	−1.42311	−0.205409
$49$	1.00000	0.142857
$50$	−11.8817	−1.68033
$51$	4.01294	0.561924
$52$	−0.627391	−0.0870035
$53$	−12.6763	−1.74122	−0.870612	−	0.491970i	$-0.836277\pi$
$53$	−12.6763	−1.74122	−0.870612	+	0.491970i	$0.836277\pi$
$54$	−1.05296	−0.143290
$55$	0.976721	0.131701
$56$	3.04440	0.406825
$57$	4.25330	0.563363
$58$	−10.5613	−1.38677
$59$	12.5298	1.63124	0.815622	−	0.578585i	$-0.196395\pi$
$59$	12.5298	1.63124	0.815622	+	0.578585i	$0.196395\pi$
$60$	−3.59657	−0.464315
$61$	13.5317	1.73255	0.866275	−	0.499567i	$-0.166508\pi$
$61$	13.5317	1.73255	0.866275	+	0.499567i	$0.166508\pi$
$62$	2.41460	0.306654
$63$	1.00000	0.125988
$64$	7.67966	0.959958
$65$	2.84062	0.352335
$66$	−0.254861	−0.0313712
$67$	−0.658447	−0.0804421	−0.0402211	−	0.999191i	$-0.512806\pi$
$67$	−0.658447	−0.0804421	−0.0402211	+	0.999191i	$0.512806\pi$
$68$	−3.57659	−0.433726
$69$	−2.98887	−0.359817
$70$	−4.24908	−0.507862
$71$	−0.254382	−0.0301896	−0.0150948	−	0.999886i	$-0.504805\pi$
$71$	−0.254382	−0.0301896	−0.0150948	+	0.999886i	$0.504805\pi$
$72$	3.04440	0.358786
$73$	9.21154	1.07813	0.539065	−	0.842264i	$-0.318778\pi$
$73$	9.21154	1.07813	0.539065	+	0.842264i	$0.318778\pi$
$74$	2.46505	0.286556
$75$	11.2841	1.30297
$76$	−3.79082	−0.434837
$77$	0.242041	0.0275832
$78$	−0.741217	−0.0839263
$79$	12.4284	1.39831	0.699153	−	0.714973i	$-0.253561\pi$
$79$	12.4284	1.39831	0.699153	+	0.714973i	$0.253561\pi$
$80$	−5.74277	−0.642061
$81$	1.00000	0.111111
$82$	2.10416	0.232366
$83$	−15.4511	−1.69598	−0.847991	−	0.530010i	$-0.822188\pi$
$83$	−15.4511	−1.69598	−0.847991	+	0.530010i	$0.822188\pi$
$84$	−0.891266	−0.0972450
$85$	16.1936	1.75644
$86$	3.06221	0.330206
$87$	10.0301	1.07534
$88$	0.736870	0.0785506
$89$	−1.66122	−0.176089	−0.0880446	−	0.996117i	$-0.528062\pi$
$89$	−1.66122	−0.176089	−0.0880446	+	0.996117i	$0.528062\pi$
$90$	−4.24908	−0.447892
$91$	0.703933	0.0737922
$92$	2.66387	0.277728
$93$	−2.29314	−0.237788
$94$	12.0204	1.23981
$95$	17.1635	1.76094
$96$	−4.59031	−0.468497
$97$	−7.34461	−0.745732	−0.372866	−	0.927885i	$-0.621625\pi$
$97$	−7.34461	−0.745732	−0.372866	+	0.927885i	$0.621625\pi$
$98$	−1.05296	−0.106365
$99$	0.242041	0.0243261
$100$	−10.0571	−1.00571
$101$	12.5805	1.25180	0.625902	−	0.779902i	$-0.284731\pi$
$101$	12.5805	1.25180	0.625902	+	0.779902i	$0.284731\pi$
$102$	−4.22548	−0.418385
$103$	−18.0142	−1.77499	−0.887497	−	0.460814i	$-0.847558\pi$
$103$	−18.0142	−1.77499	−0.887497	+	0.460814i	$0.847558\pi$
$104$	2.14305	0.210144
$105$	4.03535	0.393810
$106$	13.3477	1.29644
$107$	3.88063	0.375154	0.187577	−	0.982250i	$-0.439937\pi$
$107$	3.88063	0.375154	0.187577	+	0.982250i	$0.439937\pi$
$108$	−0.891266	−0.0857621
$109$	−10.2580	−0.982538	−0.491269	−	0.871008i	$-0.663467\pi$
$109$	−10.2580	−0.982538	−0.491269	+	0.871008i	$0.663467\pi$
$110$	−1.02845	−0.0980591
$111$	−2.34105	−0.222203
$112$	−1.42311	−0.134472
$113$	−9.50367	−0.894030	−0.447015	−	0.894526i	$-0.647513\pi$
$113$	−9.50367	−0.894030	−0.447015	+	0.894526i	$0.647513\pi$
$114$	−4.47857	−0.419457
$115$	−12.0611	−1.12471
$116$	−8.93947	−0.830009
$117$	0.703933	0.0650786
$118$	−13.1935	−1.21456
$119$	4.01294	0.367866
$120$	12.2852	1.12148
$121$	−10.9414	−0.994674
$122$	−14.2483	−1.28998
$123$	−1.99832	−0.180182
$124$	2.04380	0.183538
$125$	25.3584	2.26812
$126$	−1.05296	−0.0938055
$127$	−15.5231	−1.37745	−0.688727	−	0.725020i	$-0.741830\pi$
$127$	−15.5231	−1.37745	−0.688727	+	0.725020i	$0.741830\pi$
$128$	1.09421	0.0967152
$129$	−2.90817	−0.256051
$130$	−2.99107	−0.262334
$131$	−0.0467292	−0.00408275	−0.00204138	−	0.999998i	$-0.500650\pi$
$131$	−0.0467292	−0.00408275	−0.00204138	+	0.999998i	$0.500650\pi$
$132$	−0.215723	−0.0187763
$133$	4.25330	0.368808
$134$	0.693322	0.0598939
$135$	4.03535	0.347308
$136$	12.2170	1.04760
$137$	7.16171	0.611866	0.305933	−	0.952053i	$-0.401032\pi$
$137$	7.16171	0.611866	0.305933	+	0.952053i	$0.401032\pi$
$138$	3.14717	0.267905
$139$	0.455855	0.0386651	0.0193326	−	0.999813i	$-0.493846\pi$
$139$	0.455855	0.0386651	0.0193326	+	0.999813i	$0.493846\pi$
$140$	−3.59657	−0.303966
$141$	−11.4157	−0.961379
$142$	0.267855	0.0224779
$143$	0.170381	0.0142480
$144$	−1.42311	−0.118593
$145$	40.4749	3.36126
$146$	−9.69943	−0.802731
$147$	1.00000	0.0824786
$148$	2.08650	0.171509
$149$	−13.5690	−1.11162	−0.555809	−	0.831310i	$-0.687592\pi$
$149$	−13.5690	−1.11162	−0.555809	+	0.831310i	$0.687592\pi$
$150$	−11.8817	−0.970137
$151$	15.4698	1.25891	0.629457	−	0.777035i	$-0.283277\pi$
$151$	15.4698	1.25891	0.629457	+	0.777035i	$0.283277\pi$
$152$	12.9487	1.05028
$153$	4.01294	0.324427
$154$	−0.254861	−0.0205373
$155$	−9.25362	−0.743269
$156$	−0.627391	−0.0502315
$157$	7.42231	0.592365	0.296183	−	0.955131i	$-0.404286\pi$
$157$	7.42231	0.592365	0.296183	+	0.955131i	$0.404286\pi$
$158$	−13.0867	−1.04112
$159$	−12.6763	−1.00530
$160$	−18.5235	−1.46441
$161$	−2.98887	−0.235556
$162$	−1.05296	−0.0827287
$163$	−20.2695	−1.58763	−0.793813	−	0.608161i	$-0.791907\pi$
$163$	−20.2695	−1.58763	−0.793813	+	0.608161i	$0.791907\pi$
$164$	1.78103	0.139075
$165$	0.976721	0.0760376
$166$	16.2695	1.26276
$167$	−6.83591	−0.528979	−0.264489	−	0.964389i	$-0.585203\pi$
$167$	−6.83591	−0.528979	−0.264489	+	0.964389i	$0.585203\pi$
$168$	3.04440	0.234881
$169$	−12.5045	−0.961883
$170$	−17.0513	−1.30778
$171$	4.25330	0.325258
$172$	2.59196	0.197635
$173$	−1.77811	−0.135187	−0.0675934	−	0.997713i	$-0.521532\pi$
$173$	−1.77811	−0.135187	−0.0675934	+	0.997713i	$0.521532\pi$
$174$	−10.5613	−0.800652
$175$	11.2841	0.852994
$176$	−0.344452	−0.0259641
$177$	12.5298	0.941799
$178$	1.74921	0.131109
$179$	1.28946	0.0963790	0.0481895	−	0.998838i	$-0.484655\pi$
$179$	1.28946	0.0963790	0.0481895	+	0.998838i	$0.484655\pi$
$180$	−3.59657	−0.268072
$181$	−5.06947	−0.376811	−0.188405	−	0.982091i	$-0.560332\pi$
$181$	−5.06947	−0.376811	−0.188405	+	0.982091i	$0.560332\pi$
$182$	−0.741217	−0.0549426
$183$	13.5317	1.00029
$184$	−9.09930	−0.670809
$185$	−9.44697	−0.694555
$186$	2.41460	0.177047
$187$	0.971297	0.0710282
$188$	10.1745	0.742049
$189$	1.00000	0.0727393
$190$	−18.0726	−1.31112
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	7.67966	0.554232
$193$	17.2568	1.24217	0.621086	−	0.783742i	$-0.286692\pi$
$193$	17.2568	1.24217	0.621086	+	0.783742i	$0.286692\pi$
$194$	7.73361	0.555241
$195$	2.84062	0.203421
$196$	−0.891266	−0.0636618
$197$	−14.4183	−1.02726	−0.513632	−	0.858011i	$-0.671700\pi$
$197$	−14.4183	−1.02726	−0.513632	+	0.858011i	$0.671700\pi$
$198$	−0.254861	−0.0181122
$199$	−23.9644	−1.69879	−0.849397	−	0.527754i	$-0.823034\pi$
$199$	−23.9644	−1.69879	−0.849397	+	0.527754i	$0.823034\pi$
$200$	34.3532	2.42914
$201$	−0.658447	−0.0464433
$202$	−13.2468	−0.932041
$203$	10.0301	0.703974
$204$	−3.57659	−0.250412
$205$	−8.06392	−0.563209
$206$	18.9683	1.32159
$207$	−2.98887	−0.207741
$208$	−1.00178	−0.0694608
$209$	1.02947	0.0712102
$210$	−4.24908	−0.293214
$211$	−1.75726	−0.120975	−0.0604874	−	0.998169i	$-0.519265\pi$
$211$	−1.75726	−0.120975	−0.0604874	+	0.998169i	$0.519265\pi$
$212$	11.2980	0.775947
$213$	−0.254382	−0.0174300
$214$	−4.08616	−0.279324
$215$	−11.7355	−0.800355
$216$	3.04440	0.207145
$217$	−2.29314	−0.155668
$218$	10.8013	0.731557
$219$	9.21154	0.622459
$220$	−0.870518	−0.0586903
$221$	2.82484	0.190019
$222$	2.46505	0.165443
$223$	7.38323	0.494418	0.247209	−	0.968962i	$-0.420487\pi$
$223$	7.38323	0.494418	0.247209	+	0.968962i	$0.420487\pi$
$224$	−4.59031	−0.306703
$225$	11.2841	0.752270
$226$	10.0070	0.665657
$227$	−27.3050	−1.81230	−0.906148	−	0.422960i	$-0.860991\pi$
$227$	−27.3050	−1.81230	−0.906148	+	0.422960i	$0.860991\pi$
$228$	−3.79082	−0.251053
$229$	17.3416	1.14597	0.572983	−	0.819567i	$-0.305786\pi$
$229$	17.3416	1.14597	0.572983	+	0.819567i	$0.305786\pi$
$230$	12.6999	0.837409
$231$	0.242041	0.0159251
$232$	30.5356	2.00476
$233$	20.7871	1.36181	0.680904	−	0.732372i	$-0.261587\pi$
$233$	20.7871	1.36181	0.680904	+	0.732372i	$0.261587\pi$
$234$	−0.741217	−0.0484549
$235$	−46.0665	−3.00505
$236$	−11.1674	−0.726936
$237$	12.4284	0.807312
$238$	−4.22548	−0.273897
$239$	10.0817	0.652134	0.326067	−	0.945347i	$-0.394277\pi$
$239$	10.0817	0.652134	0.326067	+	0.945347i	$0.394277\pi$
$240$	−5.74277	−0.370694
$241$	−23.1519	−1.49135	−0.745673	−	0.666312i	$-0.767872\pi$
$241$	−23.1519	−1.49135	−0.745673	+	0.666312i	$0.767872\pi$
$242$	11.5209	0.740593
$243$	1.00000	0.0641500
$244$	−12.0603	−0.772081
$245$	4.03535	0.257809
$246$	2.10416	0.134156
$247$	2.99404	0.190506
$248$	−6.98124	−0.443309
$249$	−15.4511	−0.979176
$250$	−26.7014	−1.68875
$251$	−10.8383	−0.684107	−0.342053	−	0.939680i	$-0.611122\pi$
$251$	−10.8383	−0.684107	−0.342053	+	0.939680i	$0.611122\pi$
$252$	−0.891266	−0.0561445
$253$	−0.723429	−0.0454816
$254$	16.3453	1.02560
$255$	16.1936	1.01408
$256$	−16.5115	−1.03197
$257$	22.0869	1.37774	0.688871	−	0.724884i	$-0.258107\pi$
$257$	22.0869	1.37774	0.688871	+	0.724884i	$0.258107\pi$
$258$	3.06221	0.190645
$259$	−2.34105	−0.145466
$260$	−2.53174	−0.157012
$261$	10.0301	0.620847
$262$	0.0492042	0.00303985
$263$	11.8714	0.732024	0.366012	−	0.930610i	$-0.380723\pi$
$263$	11.8714	0.732024	0.366012	+	0.930610i	$0.380723\pi$
$264$	0.736870	0.0453512
$265$	−51.1533	−3.14232
$266$	−4.47857	−0.274599
$267$	−1.66122	−0.101665
$268$	0.586851	0.0358476
$269$	9.70585	0.591776	0.295888	−	0.955223i	$-0.404384\pi$
$269$	9.70585	0.591776	0.295888	+	0.955223i	$0.404384\pi$
$270$	−4.24908	−0.258591
$271$	16.1823	0.983007	0.491503	−	0.870876i	$-0.336448\pi$
$271$	16.1823	0.983007	0.491503	+	0.870876i	$0.336448\pi$
$272$	−5.71087	−0.346273
$273$	0.703933	0.0426040
$274$	−7.54103	−0.455570
$275$	2.73121	0.164698
$276$	2.66387	0.160346
$277$	24.1835	1.45305	0.726523	−	0.687143i	$-0.241135\pi$
$277$	24.1835	1.45305	0.726523	+	0.687143i	$0.241135\pi$
$278$	−0.480000	−0.0287885
$279$	−2.29314	−0.137287
$280$	12.2852	0.734182
$281$	27.2646	1.62647	0.813234	−	0.581937i	$-0.197705\pi$
$281$	27.2646	1.62647	0.813234	+	0.581937i	$0.197705\pi$
$282$	12.0204	0.715803
$283$	23.7230	1.41019	0.705093	−	0.709115i	$-0.250905\pi$
$283$	23.7230	1.41019	0.705093	+	0.709115i	$0.250905\pi$
$284$	0.226722	0.0134535
$285$	17.1635	1.01668
$286$	−0.179405	−0.0106084
$287$	−1.99832	−0.117957
$288$	−4.59031	−0.270487
$289$	−0.896320	−0.0527247
$290$	−42.6186	−2.50265
$291$	−7.34461	−0.430548
$292$	−8.20993	−0.480450
$293$	6.54608	0.382426	0.191213	−	0.981549i	$-0.438758\pi$
$293$	6.54608	0.382426	0.191213	+	0.981549i	$0.438758\pi$
$294$	−1.05296	−0.0614101
$295$	50.5622	2.94385
$296$	−7.12710	−0.414254
$297$	0.242041	0.0140447
$298$	14.2877	0.827665
$299$	−2.10396	−0.121675
$300$	−10.0571	−0.580646
$301$	−2.90817	−0.167624
$302$	−16.2892	−0.937335
$303$	12.5805	0.722729
$304$	−6.05293	−0.347159
$305$	54.6049	3.12667
$306$	−4.22548	−0.241555
$307$	−2.66553	−0.152130	−0.0760651	−	0.997103i	$-0.524236\pi$
$307$	−2.66553	−0.152130	−0.0760651	+	0.997103i	$0.524236\pi$
$308$	−0.215723	−0.0122920
$309$	−18.0142	−1.02479
$310$	9.74374	0.553407
$311$	19.1884	1.08807	0.544037	−	0.839061i	$-0.316895\pi$
$311$	19.1884	1.08807	0.544037	+	0.839061i	$0.316895\pi$
$312$	2.14305	0.121327
$313$	−3.38032	−0.191067	−0.0955336	−	0.995426i	$-0.530456\pi$
$313$	−3.38032	−0.191067	−0.0955336	+	0.995426i	$0.530456\pi$
$314$	−7.81543	−0.441050
$315$	4.03535	0.227366
$316$	−11.0770	−0.623131
$317$	15.7083	0.882264	0.441132	−	0.897442i	$-0.354577\pi$
$317$	15.7083	0.882264	0.441132	+	0.897442i	$0.354577\pi$
$318$	13.3477	0.748502
$319$	2.42769	0.135925
$320$	30.9901	1.73240
$321$	3.88063	0.216595
$322$	3.14717	0.175385
$323$	17.0682	0.949702
$324$	−0.891266	−0.0495148
$325$	7.94322	0.440611
$326$	21.3430	1.18208
$327$	−10.2580	−0.567269
$328$	−6.08369	−0.335915
$329$	−11.4157	−0.629370
$330$	−1.02845	−0.0566145
$331$	20.4115	1.12192	0.560958	−	0.827844i	$-0.310433\pi$
$331$	20.4115	1.12192	0.560958	+	0.827844i	$0.310433\pi$
$332$	13.7711	0.755785
$333$	−2.34105	−0.128289
$334$	7.19797	0.393856
$335$	−2.65707	−0.145171
$336$	−1.42311	−0.0776373
$337$	−27.1765	−1.48040	−0.740198	−	0.672389i	$-0.765268\pi$
$337$	−27.1765	−1.48040	−0.740198	+	0.672389i	$0.765268\pi$
$338$	13.1668	0.716178
$339$	−9.50367	−0.516168
$340$	−14.4328	−0.782729
$341$	−0.555034	−0.0300568
$342$	−4.47857	−0.242173
$343$	1.00000	0.0539949
$344$	−8.85365	−0.477357
$345$	−12.0611	−0.649349
$346$	1.87228	0.100655
$347$	−4.34445	−0.233222	−0.116611	−	0.993178i	$-0.537203\pi$
$347$	−4.34445	−0.233222	−0.116611	+	0.993178i	$0.537203\pi$
$348$	−8.93947	−0.479206
$349$	−4.30353	−0.230363	−0.115181	−	0.993344i	$-0.536745\pi$
$349$	−4.30353	−0.230363	−0.115181	+	0.993344i	$0.536745\pi$
$350$	−11.8817	−0.635104
$351$	0.703933	0.0375732
$352$	−1.11104	−0.0592189
$353$	−15.7281	−0.837123	−0.418562	−	0.908188i	$-0.637466\pi$
$353$	−15.7281	−0.837123	−0.418562	+	0.908188i	$0.637466\pi$
$354$	−13.1935	−0.701225
$355$	−1.02652	−0.0544820
$356$	1.48059	0.0784711
$357$	4.01294	0.212387
$358$	−1.35776	−0.0717598
$359$	15.4356	0.814659	0.407330	−	0.913281i	$-0.366460\pi$
$359$	15.4356	0.814659	0.407330	+	0.913281i	$0.366460\pi$
$360$	12.2852	0.647488
$361$	−0.909453	−0.0478659
$362$	5.33797	0.280558
$363$	−10.9414	−0.574275
$364$	−0.627391	−0.0328842
$365$	37.1718	1.94566
$366$	−14.2483	−0.744773
$367$	0.836030	0.0436404	0.0218202	−	0.999762i	$-0.493054\pi$
$367$	0.836030	0.0436404	0.0218202	+	0.999762i	$0.493054\pi$
$368$	4.25350	0.221729
$369$	−1.99832	−0.104028
$370$	9.94732	0.517137
$371$	−12.6763	−0.658121
$372$	2.04380	0.105966
$373$	−20.8636	−1.08028	−0.540139	−	0.841576i	$-0.681628\pi$
$373$	−20.8636	−1.08028	−0.540139	+	0.841576i	$0.681628\pi$
$374$	−1.02274	−0.0528847
$375$	25.3584	1.30950
$376$	−34.7541	−1.79231
$377$	7.06051	0.363635
$378$	−1.05296	−0.0541587
$379$	−13.4660	−0.691703	−0.345851	−	0.938289i	$-0.612410\pi$
$379$	−13.4660	−0.691703	−0.345851	+	0.938289i	$0.612410\pi$
$380$	−15.2973	−0.784734
$381$	−15.5231	−0.795274
$382$	−1.05296	−0.0538744
$383$	35.3283	1.80519	0.902595	−	0.430491i	$-0.141660\pi$
$383$	35.3283	1.80519	0.902595	+	0.430491i	$0.141660\pi$
$384$	1.09421	0.0558385
$385$	0.976721	0.0497783
$386$	−18.1708	−0.924870
$387$	−2.90817	−0.147831
$388$	6.54599	0.332323
$389$	18.8371	0.955079	0.477540	−	0.878610i	$-0.341529\pi$
$389$	18.8371	0.955079	0.477540	+	0.878610i	$0.341529\pi$
$390$	−2.99107	−0.151459
$391$	−11.9941	−0.606569
$392$	3.04440	0.153765
$393$	−0.0467292	−0.00235718
$394$	15.1820	0.764858
$395$	50.1530	2.52347
$396$	−0.215723	−0.0108405
$397$	−20.9744	−1.05267	−0.526337	−	0.850276i	$-0.676435\pi$
$397$	−20.9744	−1.05267	−0.526337	+	0.850276i	$0.676435\pi$
$398$	25.2337	1.26485
$399$	4.25330	0.212931
$400$	−16.0585	−0.802925
$401$	28.3104	1.41375	0.706876	−	0.707338i	$-0.250104\pi$
$401$	28.3104	1.41375	0.706876	+	0.707338i	$0.250104\pi$
$402$	0.693322	0.0345797
$403$	−1.61422	−0.0804099
$404$	−11.2125	−0.557845
$405$	4.03535	0.200518
$406$	−10.5613	−0.524150
$407$	−0.566631	−0.0280869
$408$	12.2170	0.604831
$409$	22.4833	1.11173	0.555865	−	0.831273i	$-0.312387\pi$
$409$	22.4833	1.11173	0.555865	+	0.831273i	$0.312387\pi$
$410$	8.49103	0.419342
$411$	7.16171	0.353261
$412$	16.0555	0.790995
$413$	12.5298	0.616552
$414$	3.14717	0.154675
$415$	−62.3508	−3.06068
$416$	−3.23127	−0.158426
$417$	0.455855	0.0223233
$418$	−1.08400	−0.0530201
$419$	−22.4624	−1.09736	−0.548680	−	0.836033i	$-0.684869\pi$
$419$	−22.4624	−1.09736	−0.548680	+	0.836033i	$0.684869\pi$
$420$	−3.59657	−0.175495
$421$	−0.878103	−0.0427961	−0.0213981	−	0.999771i	$-0.506812\pi$
$421$	−0.878103	−0.0427961	−0.0213981	+	0.999771i	$0.506812\pi$
$422$	1.85033	0.0900728
$423$	−11.4157	−0.555052
$424$	−38.5917	−1.87418
$425$	45.2822	2.19651
$426$	0.267855	0.0129776
$427$	13.5317	0.654842
$428$	−3.45867	−0.167181
$429$	0.170381	0.00822606
$430$	12.3571	0.595911
$431$	26.8052	1.29116	0.645581	−	0.763691i	$-0.276615\pi$
$431$	26.8052	1.29116	0.645581	+	0.763691i	$0.276615\pi$
$432$	−1.42311	−0.0684696
$433$	4.29193	0.206257	0.103128	−	0.994668i	$-0.467115\pi$
$433$	4.29193	0.206257	0.103128	+	0.994668i	$0.467115\pi$
$434$	2.41460	0.115904
$435$	40.4749	1.94062
$436$	9.14260	0.437851
$437$	−12.7125	−0.608123
$438$	−9.69943	−0.463457
$439$	−34.0131	−1.62336	−0.811679	−	0.584104i	$-0.801446\pi$
$439$	−34.0131	−1.62336	−0.811679	+	0.584104i	$0.801446\pi$
$440$	2.97353	0.141757
$441$	1.00000	0.0476190
$442$	−2.97446	−0.141481
$443$	−28.7097	−1.36404	−0.682018	−	0.731335i	$-0.738898\pi$
$443$	−28.7097	−1.36404	−0.682018	+	0.731335i	$0.738898\pi$
$444$	2.08650	0.0990209
$445$	−6.70361	−0.317782
$446$	−7.77428	−0.368123
$447$	−13.5690	−0.641793
$448$	7.67966	0.362830
$449$	24.7552	1.16827	0.584134	−	0.811657i	$-0.301434\pi$
$449$	24.7552	1.16827	0.584134	+	0.811657i	$0.301434\pi$
$450$	−11.8817	−0.560109
$451$	−0.483676	−0.0227754
$452$	8.47029	0.398409
$453$	15.4698	0.726835
$454$	28.7512	1.34936
$455$	2.84062	0.133170
$456$	12.9487	0.606380
$457$	−40.2076	−1.88083	−0.940415	−	0.340029i	$-0.889563\pi$
$457$	−40.2076	−1.88083	−0.940415	+	0.340029i	$0.889563\pi$
$458$	−18.2601	−0.853239
$459$	4.01294	0.187308
$460$	10.7497	0.501205
$461$	1.72791	0.0804770	0.0402385	−	0.999190i	$-0.487188\pi$
$461$	1.72791	0.0804770	0.0402385	+	0.999190i	$0.487188\pi$
$462$	−0.254861	−0.0118572
$463$	−1.54250	−0.0716860	−0.0358430	−	0.999357i	$-0.511412\pi$
$463$	−1.54250	−0.0716860	−0.0358430	+	0.999357i	$0.511412\pi$
$464$	−14.2740	−0.662652
$465$	−9.25362	−0.429126
$466$	−21.8881	−1.01395
$467$	3.79890	0.175792	0.0878961	−	0.996130i	$-0.471986\pi$
$467$	3.79890	0.175792	0.0878961	+	0.996130i	$0.471986\pi$
$468$	−0.627391	−0.0290012
$469$	−0.658447	−0.0304043
$470$	48.5064	2.23743
$471$	7.42231	0.342002
$472$	38.1458	1.75580
$473$	−0.703898	−0.0323653
$474$	−13.0867	−0.601091
$475$	47.9944	2.20214
$476$	−3.57659	−0.163933
$477$	−12.6763	−0.580408
$478$	−10.6157	−0.485552
$479$	8.12704	0.371334	0.185667	−	0.982613i	$-0.440555\pi$
$479$	8.12704	0.371334	0.185667	+	0.982613i	$0.440555\pi$
$480$	−18.5235	−0.845479
$481$	−1.64794	−0.0751398
$482$	24.3781	1.11039
$483$	−2.98887	−0.135998
$484$	9.75171	0.443259
$485$	−29.6381	−1.34580
$486$	−1.05296	−0.0477634
$487$	17.2720	0.782670	0.391335	−	0.920248i	$-0.372013\pi$
$487$	17.2720	0.782670	0.391335	+	0.920248i	$0.372013\pi$
$488$	41.1958	1.86484
$489$	−20.2695	−0.916617
$490$	−4.24908	−0.191954
$491$	26.6876	1.20440	0.602198	−	0.798347i	$-0.294292\pi$
$491$	26.6876	1.20440	0.602198	+	0.798347i	$0.294292\pi$
$492$	1.78103	0.0802952
$493$	40.2501	1.81277
$494$	−3.15262	−0.141843
$495$	0.976721	0.0439003
$496$	3.26340	0.146531
$497$	−0.254382	−0.0114106
$498$	16.2695	0.729054
$499$	25.9229	1.16047	0.580234	−	0.814450i	$-0.302961\pi$
$499$	25.9229	1.16047	0.580234	+	0.814450i	$0.302961\pi$
$500$	−22.6010	−1.01075
$501$	−6.83591	−0.305406
$502$	11.4123	0.509358
$503$	−35.7092	−1.59219	−0.796097	−	0.605168i	$-0.793106\pi$
$503$	−35.7092	−1.59219	−0.796097	+	0.605168i	$0.793106\pi$
$504$	3.04440	0.135608
$505$	50.7666	2.25908
$506$	0.761745	0.0338637
$507$	−12.5045	−0.555343
$508$	13.8352	0.613839
$509$	−24.3262	−1.07824	−0.539120	−	0.842229i	$-0.681243\pi$
$509$	−24.3262	−1.07824	−0.539120	+	0.842229i	$0.681243\pi$
$510$	−17.0513	−0.755044
$511$	9.21154	0.407495
$512$	15.1976	0.671645
$513$	4.25330	0.187788
$514$	−23.2567	−1.02581
$515$	−72.6937	−3.20327
$516$	2.59196	0.114105
$517$	−2.76308	−0.121520
$518$	2.46505	0.108308
$519$	−1.77811	−0.0780502
$520$	8.64798	0.379239
$521$	−29.7608	−1.30384	−0.651922	−	0.758286i	$-0.726037\pi$
$521$	−29.7608	−1.30384	−0.651922	+	0.758286i	$0.726037\pi$
$522$	−10.5613	−0.462257
$523$	−41.7387	−1.82511	−0.912553	−	0.408959i	$-0.865892\pi$
$523$	−41.7387	−1.82511	−0.912553	+	0.408959i	$0.865892\pi$
$524$	0.0416481	0.00181941
$525$	11.2841	0.492476
$526$	−12.5002	−0.545035
$527$	−9.20223	−0.400855
$528$	−0.344452	−0.0149904
$529$	−14.0667	−0.611595
$530$	53.8626	2.33964
$531$	12.5298	0.543748
$532$	−3.79082	−0.164353
$533$	−1.40668	−0.0609303
$534$	1.74921	0.0756956
$535$	15.6597	0.677027
$536$	−2.00458	−0.0865845
$537$	1.28946	0.0556444
$538$	−10.2199	−0.440612
$539$	0.242041	0.0104255
$540$	−3.59657	−0.154772
$541$	−39.9913	−1.71936	−0.859679	−	0.510834i	$-0.829337\pi$
$541$	−39.9913	−1.71936	−0.859679	+	0.510834i	$0.829337\pi$
$542$	−17.0394	−0.731906
$543$	−5.06947	−0.217552
$544$	−18.4206	−0.789778
$545$	−41.3946	−1.77315
$546$	−0.741217	−0.0317211
$547$	27.5893	1.17964	0.589818	−	0.807537i	$-0.299200\pi$
$547$	27.5893	1.17964	0.589818	+	0.807537i	$0.299200\pi$
$548$	−6.38299	−0.272668
$549$	13.5317	0.577517
$550$	−2.87586	−0.122627
$551$	42.6609	1.81742
$552$	−9.09930	−0.387292
$553$	12.4284	0.528510
$554$	−25.4644	−1.08188
$555$	−9.44697	−0.401001
$556$	−0.406288	−0.0172305
$557$	23.9736	1.01580	0.507898	−	0.861417i	$-0.330423\pi$
$557$	23.9736	1.01580	0.507898	+	0.861417i	$0.330423\pi$
$558$	2.41460	0.102218
$559$	−2.04716	−0.0865857
$560$	−5.74277	−0.242676
$561$	0.971297	0.0410082
$562$	−28.7086	−1.21100
$563$	−23.7106	−0.999283	−0.499642	−	0.866232i	$-0.666535\pi$
$563$	−23.7106	−0.999283	−0.499642	+	0.866232i	$0.666535\pi$
$564$	10.1745	0.428422
$565$	−38.3506	−1.61342
$566$	−24.9795	−1.04997
$567$	1.00000	0.0419961
$568$	−0.774440	−0.0324948
$569$	9.78615	0.410257	0.205128	−	0.978735i	$-0.434239\pi$
$569$	9.78615	0.410257	0.205128	+	0.978735i	$0.434239\pi$
$570$	−18.0726	−0.756978
$571$	36.6005	1.53168	0.765841	−	0.643030i	$-0.222323\pi$
$571$	36.6005	1.53168	0.765841	+	0.643030i	$0.222323\pi$
$572$	−0.151855	−0.00634936
$573$	1.00000	0.0417756
$574$	2.10416	0.0878260
$575$	−33.7265	−1.40649
$576$	7.67966	0.319986
$577$	−7.88762	−0.328366	−0.164183	−	0.986430i	$-0.552499\pi$
$577$	−7.88762	−0.328366	−0.164183	+	0.986430i	$0.552499\pi$
$578$	0.943793	0.0392566
$579$	17.2568	0.717169
$580$	−36.0739	−1.49789
$581$	−15.4511	−0.641021
$582$	7.73361	0.320568
$583$	−3.06819	−0.127071
$584$	28.0436	1.16045
$585$	2.84062	0.117445
$586$	−6.89279	−0.284739
$587$	12.7537	0.526403	0.263202	−	0.964741i	$-0.415222\pi$
$587$	12.7537	0.526403	0.263202	+	0.964741i	$0.415222\pi$
$588$	−0.891266	−0.0367552
$589$	−9.75341	−0.401882
$590$	−53.2402	−2.19187
$591$	−14.4183	−0.593091
$592$	3.33159	0.136927
$593$	−26.0545	−1.06993	−0.534965	−	0.844874i	$-0.679675\pi$
$593$	−26.0545	−1.06993	−0.534965	+	0.844874i	$0.679675\pi$
$594$	−0.254861	−0.0104571
$595$	16.1936	0.663873
$596$	12.0936	0.495374
$597$	−23.9644	−0.980799
$598$	2.21540	0.0905943
$599$	8.76146	0.357984	0.178992	−	0.983851i	$-0.442716\pi$
$599$	8.76146	0.357984	0.178992	+	0.983851i	$0.442716\pi$
$600$	34.3532	1.40246
$601$	−27.8477	−1.13593	−0.567966	−	0.823052i	$-0.692269\pi$
$601$	−27.8477	−1.13593	−0.567966	+	0.823052i	$0.692269\pi$
$602$	3.06221	0.124806
$603$	−0.658447	−0.0268140
$604$	−13.7877	−0.561013
$605$	−44.1524	−1.79505
$606$	−13.2468	−0.538114
$607$	−11.6537	−0.473009	−0.236504	−	0.971630i	$-0.576002\pi$
$607$	−11.6537	−0.473009	−0.236504	+	0.971630i	$0.576002\pi$
$608$	−19.5240	−0.791801
$609$	10.0301	0.406440
$610$	−57.4971	−2.32799
$611$	−8.03592	−0.325099
$612$	−3.57659	−0.144575
$613$	36.5730	1.47717	0.738585	−	0.674161i	$-0.235495\pi$
$613$	36.5730	1.47717	0.738585	+	0.674161i	$0.235495\pi$
$614$	2.80671	0.113270
$615$	−8.06392	−0.325169
$616$	0.736870	0.0296894
$617$	1.87578	0.0755160	0.0377580	−	0.999287i	$-0.487978\pi$
$617$	1.87578	0.0755160	0.0377580	+	0.999287i	$0.487978\pi$
$618$	18.9683	0.763018
$619$	−16.1253	−0.648132	−0.324066	−	0.946034i	$-0.605050\pi$
$619$	−16.1253	−0.648132	−0.324066	+	0.946034i	$0.605050\pi$
$620$	8.24743	0.331225
$621$	−2.98887	−0.119939
$622$	−20.2047	−0.810134
$623$	−1.66122	−0.0665554
$624$	−1.00178	−0.0401032
$625$	45.9096	1.83638
$626$	3.55936	0.142261
$627$	1.02947	0.0411132
$628$	−6.61525	−0.263977
$629$	−9.39450	−0.374583
$630$	−4.24908	−0.169287
$631$	−4.08230	−0.162514	−0.0812569	−	0.996693i	$-0.525893\pi$
$631$	−4.08230	−0.162514	−0.0812569	+	0.996693i	$0.525893\pi$
$632$	37.8370	1.50508
$633$	−1.75726	−0.0698448
$634$	−16.5403	−0.656897
$635$	−62.6413	−2.48584
$636$	11.2980	0.447993
$637$	0.703933	0.0278908
$638$	−2.55628	−0.101204
$639$	−0.254382	−0.0100632
$640$	4.41551	0.174538
$641$	−28.9955	−1.14525	−0.572626	−	0.819817i	$-0.694075\pi$
$641$	−28.9955	−1.14525	−0.572626	+	0.819817i	$0.694075\pi$
$642$	−4.08616	−0.161268
$643$	24.3779	0.961369	0.480685	−	0.876894i	$-0.340388\pi$
$643$	24.3779	0.961369	0.480685	+	0.876894i	$0.340388\pi$
$644$	2.66387	0.104971
$645$	−11.7355	−0.462085
$646$	−17.9722	−0.707108
$647$	4.98540	0.195996	0.0979982	−	0.995187i	$-0.468756\pi$
$647$	4.98540	0.195996	0.0979982	+	0.995187i	$0.468756\pi$
$648$	3.04440	0.119595
$649$	3.03273	0.119045
$650$	−8.36393	−0.328060
$651$	−2.29314	−0.0898752
$652$	18.0655	0.707499
$653$	26.3245	1.03016	0.515079	−	0.857143i	$-0.327763\pi$
$653$	26.3245	1.03016	0.515079	+	0.857143i	$0.327763\pi$
$654$	10.8013	0.422365
$655$	−0.188569	−0.00736799
$656$	2.84384	0.111033
$657$	9.21154	0.359377
$658$	12.0204	0.468603
$659$	−15.9080	−0.619688	−0.309844	−	0.950787i	$-0.600277\pi$
$659$	−15.9080	−0.619688	−0.309844	+	0.950787i	$0.600277\pi$
$660$	−0.870518	−0.0338849
$661$	41.6787	1.62112	0.810558	−	0.585659i	$-0.199164\pi$
$661$	41.6787	1.62112	0.810558	+	0.585659i	$0.199164\pi$
$662$	−21.4926	−0.835333
$663$	2.82484	0.109708
$664$	−47.0395	−1.82548
$665$	17.1635	0.665574
$666$	2.46505	0.0955186
$667$	−29.9786	−1.16077
$668$	6.09261	0.235730
$669$	7.38323	0.285452
$670$	2.79780	0.108088
$671$	3.27522	0.126438
$672$	−4.59031	−0.177075
$673$	17.2366	0.664422	0.332211	−	0.943205i	$-0.392205\pi$
$673$	17.2366	0.664422	0.332211	+	0.943205i	$0.392205\pi$
$674$	28.6159	1.10224
$675$	11.2841	0.434323
$676$	11.1448	0.428647
$677$	−40.3066	−1.54911	−0.774554	−	0.632507i	$-0.782026\pi$
$677$	−40.3066	−1.54911	−0.774554	+	0.632507i	$0.782026\pi$
$678$	10.0070	0.384318
$679$	−7.34461	−0.281860
$680$	49.2998	1.89056
$681$	−27.3050	−1.04633
$682$	0.584431	0.0223790
$683$	−8.58517	−0.328502	−0.164251	−	0.986419i	$-0.552521\pi$
$683$	−8.58517	−0.328502	−0.164251	+	0.986419i	$0.552521\pi$
$684$	−3.79082	−0.144946
$685$	28.9000	1.10421
$686$	−1.05296	−0.0402024
$687$	17.3416	0.661624
$688$	4.13867	0.157785
$689$	−8.92327	−0.339950
$690$	12.6999	0.483478
$691$	−39.4606	−1.50115	−0.750577	−	0.660783i	$-0.770224\pi$
$691$	−39.4606	−1.50115	−0.750577	+	0.660783i	$0.770224\pi$
$692$	1.58476	0.0602437
$693$	0.242041	0.00919439
$694$	4.57455	0.173647
$695$	1.83954	0.0697776
$696$	30.5356	1.15745
$697$	−8.01914	−0.303747
$698$	4.53146	0.171518
$699$	20.7871	0.786241
$700$	−10.0571	−0.380122
$701$	37.3103	1.40919	0.704595	−	0.709610i	$-0.251129\pi$
$701$	37.3103	1.40919	0.704595	+	0.709610i	$0.251129\pi$
$702$	−0.741217	−0.0279754
$703$	−9.95719	−0.375543
$704$	1.85880	0.0700560
$705$	−46.0665	−1.73497
$706$	16.5612	0.623287
$707$	12.5805	0.473137
$708$	−11.1674	−0.419697
$709$	3.27180	0.122875	0.0614375	−	0.998111i	$-0.480432\pi$
$709$	3.27180	0.122875	0.0614375	+	0.998111i	$0.480432\pi$
$710$	1.08089	0.0405650
$711$	12.4284	0.466102
$712$	−5.05742	−0.189535
$713$	6.85389	0.256680
$714$	−4.22548	−0.158135
$715$	0.687546	0.0257128
$716$	−1.14925	−0.0429496
$717$	10.0817	0.376510
$718$	−16.2531	−0.606561
$719$	11.1094	0.414312	0.207156	−	0.978308i	$-0.433579\pi$
$719$	11.1094	0.414312	0.207156	+	0.978308i	$0.433579\pi$
$720$	−5.74277	−0.214020
$721$	−18.0142	−0.670885
$722$	0.957622	0.0356390
$723$	−23.1519	−0.861029
$724$	4.51824	0.167919
$725$	113.180	4.20340
$726$	11.5209	0.427582
$727$	22.2739	0.826094	0.413047	−	0.910710i	$-0.364465\pi$
$727$	22.2739	0.826094	0.413047	+	0.910710i	$0.364465\pi$
$728$	2.14305	0.0794269
$729$	1.00000	0.0370370
$730$	−39.1406	−1.44866
$731$	−11.6703	−0.431643
$732$	−12.0603	−0.445761
$733$	9.56507	0.353294	0.176647	−	0.984274i	$-0.443475\pi$
$733$	9.56507	0.353294	0.176647	+	0.984274i	$0.443475\pi$
$734$	−0.880310	−0.0324928
$735$	4.03535	0.148846
$736$	13.7198	0.505719
$737$	−0.159371	−0.00587052
$738$	2.10416	0.0774552
$739$	6.21910	0.228773	0.114387	−	0.993436i	$-0.463510\pi$
$739$	6.21910	0.228773	0.114387	+	0.993436i	$0.463510\pi$
$740$	8.41976	0.309516
$741$	2.99404	0.109989
$742$	13.3477	0.490009
$743$	15.6828	0.575345	0.287673	−	0.957729i	$-0.407118\pi$
$743$	15.6828	0.575345	0.287673	+	0.957729i	$0.407118\pi$
$744$	−6.98124	−0.255945
$745$	−54.7558	−2.00610
$746$	21.9687	0.804331
$747$	−15.4511	−0.565328
$748$	−0.865683	−0.0316525
$749$	3.88063	0.141795
$750$	−26.7014	−0.974999
$751$	−21.3556	−0.779276	−0.389638	−	0.920968i	$-0.627400\pi$
$751$	−21.3556	−0.779276	−0.389638	+	0.920968i	$0.627400\pi$
$752$	16.2459	0.592427
$753$	−10.8383	−0.394969
$754$	−7.43447	−0.270747
$755$	62.4261	2.27192
$756$	−0.891266	−0.0324150
$757$	−0.171891	−0.00624747	−0.00312373	−	0.999995i	$-0.500994\pi$
$757$	−0.171891	−0.00624747	−0.00312373	+	0.999995i	$0.500994\pi$
$758$	14.1792	0.515013
$759$	−0.723429	−0.0262588
$760$	52.2527	1.89541
$761$	24.2819	0.880217	0.440109	−	0.897945i	$-0.354940\pi$
$761$	24.2819	0.880217	0.440109	+	0.897945i	$0.354940\pi$
$762$	16.3453	0.592128
$763$	−10.2580	−0.371365
$764$	−0.891266	−0.0322449
$765$	16.1936	0.585481
$766$	−37.1994	−1.34407
$767$	8.82016	0.318478
$768$	−16.5115	−0.595807
$769$	8.46796	0.305362	0.152681	−	0.988275i	$-0.451209\pi$
$769$	8.46796	0.305362	0.152681	+	0.988275i	$0.451209\pi$
$770$	−1.02845	−0.0370629
$771$	22.0869	0.795440
$772$	−15.3804	−0.553553
$773$	7.60774	0.273631	0.136816	−	0.990597i	$-0.456313\pi$
$773$	7.60774	0.273631	0.136816	+	0.990597i	$0.456313\pi$
$774$	3.06221	0.110069
$775$	−25.8759	−0.929490
$776$	−22.3599	−0.802674
$777$	−2.34105	−0.0839848
$778$	−19.8348	−0.711112
$779$	−8.49945	−0.304525
$780$	−2.53174	−0.0906510
$781$	−0.0615709	−0.00220318
$782$	12.6294	0.451626
$783$	10.0301	0.358446
$784$	−1.42311	−0.0508255
$785$	29.9516	1.06902
$786$	0.0492042	0.00175506
$787$	0.991189	0.0353321	0.0176660	−	0.999844i	$-0.494376\pi$
$787$	0.991189	0.0353321	0.0176660	+	0.999844i	$0.494376\pi$
$788$	12.8506	0.457782
$789$	11.8714	0.422634
$790$	−52.8093	−1.87887
$791$	−9.50367	−0.337912
$792$	0.736870	0.0261835
$793$	9.52538	0.338256
$794$	22.0853	0.783778
$795$	−51.1533	−1.81422
$796$	21.3587	0.757038
$797$	26.9612	0.955014	0.477507	−	0.878628i	$-0.341541\pi$
$797$	26.9612	0.955014	0.477507	+	0.878628i	$0.341541\pi$
$798$	−4.47857	−0.158540
$799$	−45.8107	−1.62067
$800$	−51.7973	−1.83131
$801$	−1.66122	−0.0586964
$802$	−29.8098	−1.05262
$803$	2.22957	0.0786799
$804$	0.586851	0.0206966
$805$	−12.0611	−0.425099
$806$	1.69971	0.0598699
$807$	9.70585	0.341662
$808$	38.3000	1.34739
$809$	27.4553	0.965276	0.482638	−	0.875820i	$-0.339679\pi$
$809$	27.4553	0.965276	0.482638	+	0.875820i	$0.339679\pi$
$810$	−4.24908	−0.149297
$811$	−4.67630	−0.164207	−0.0821035	−	0.996624i	$-0.526164\pi$
$811$	−4.67630	−0.164207	−0.0821035	+	0.996624i	$0.526164\pi$
$812$	−8.93947	−0.313714
$813$	16.1823	0.567539
$814$	0.596643	0.0209123
$815$	−81.7944	−2.86513
$816$	−5.71087	−0.199921
$817$	−12.3693	−0.432748
$818$	−23.6741	−0.827747
$819$	0.703933	0.0245974
$820$	7.18710	0.250984
$821$	−30.8440	−1.07646	−0.538232	−	0.842797i	$-0.680907\pi$
$821$	−30.8440	−1.07646	−0.538232	+	0.842797i	$0.680907\pi$
$822$	−7.54103	−0.263024
$823$	42.2238	1.47183	0.735915	−	0.677074i	$-0.236752\pi$
$823$	42.2238	1.47183	0.735915	+	0.677074i	$0.236752\pi$
$824$	−54.8425	−1.91053
$825$	2.73121	0.0950884
$826$	−13.1935	−0.459059
$827$	−49.5199	−1.72198	−0.860988	−	0.508625i	$-0.830154\pi$
$827$	−49.5199	−1.72198	−0.860988	+	0.508625i	$0.830154\pi$
$828$	2.66387	0.0925760
$829$	−22.7322	−0.789523	−0.394762	−	0.918784i	$-0.629173\pi$
$829$	−22.7322	−0.789523	−0.394762	+	0.918784i	$0.629173\pi$
$830$	65.6531	2.27885
$831$	24.1835	0.838916
$832$	5.40597	0.187418
$833$	4.01294	0.139040
$834$	−0.480000	−0.0166210
$835$	−27.5853	−0.954629
$836$	−0.917534	−0.0317336
$837$	−2.29314	−0.0792625
$838$	23.6521	0.817048
$839$	−37.6376	−1.29939	−0.649697	−	0.760193i	$-0.725104\pi$
$839$	−37.6376	−1.29939	−0.649697	+	0.760193i	$0.725104\pi$
$840$	12.2852	0.423880
$841$	71.6026	2.46905
$842$	0.924611	0.0318642
$843$	27.2646	0.939042
$844$	1.56619	0.0539103
$845$	−50.4599	−1.73588
$846$	12.0204	0.413269
$847$	−10.9414	−0.375952
$848$	18.0398	0.619490
$849$	23.7230	0.814171
$850$	−47.6806	−1.63543
$851$	6.99709	0.239857
$852$	0.226722	0.00776736
$853$	44.5605	1.52572	0.762860	−	0.646563i	$-0.223794\pi$
$853$	44.5605	1.52572	0.762860	+	0.646563i	$0.223794\pi$
$854$	−14.2483	−0.487568
$855$	17.1635	0.586981
$856$	11.8142	0.403800
$857$	−3.77540	−0.128965	−0.0644826	−	0.997919i	$-0.520540\pi$
$857$	−3.77540	−0.128965	−0.0644826	+	0.997919i	$0.520540\pi$
$858$	−0.179405	−0.00612479
$859$	−13.5092	−0.460929	−0.230465	−	0.973081i	$-0.574025\pi$
$859$	−13.5092	−0.460929	−0.230465	+	0.973081i	$0.574025\pi$
$860$	10.4595	0.356664
$861$	−1.99832	−0.0681026
$862$	−28.2250	−0.961346
$863$	−24.7250	−0.841649	−0.420825	−	0.907142i	$-0.638259\pi$
$863$	−24.7250	−0.841649	−0.420825	+	0.907142i	$0.638259\pi$
$864$	−4.59031	−0.156166
$865$	−7.17528	−0.243967
$866$	−4.51925	−0.153570
$867$	−0.896320	−0.0304406
$868$	2.04380	0.0693710
$869$	3.00819	0.102046
$870$	−42.6186	−1.44491
$871$	−0.463503	−0.0157052
$872$	−31.2295	−1.05756
$873$	−7.34461	−0.248577
$874$	13.3859	0.452783
$875$	25.3584	0.857269
$876$	−8.20993	−0.277388
$877$	−35.5091	−1.19906	−0.599528	−	0.800354i	$-0.704645\pi$
$877$	−35.5091	−1.19906	−0.599528	+	0.800354i	$0.704645\pi$
$878$	35.8146	1.20868
$879$	6.54608	0.220794
$880$	−1.38999	−0.0468564
$881$	−35.5736	−1.19850	−0.599252	−	0.800560i	$-0.704535\pi$
$881$	−35.5736	−1.19850	−0.599252	+	0.800560i	$0.704535\pi$
$882$	−1.05296	−0.0354552
$883$	−12.7841	−0.430218	−0.215109	−	0.976590i	$-0.569011\pi$
$883$	−12.7841	−0.430218	−0.215109	+	0.976590i	$0.569011\pi$
$884$	−2.51768	−0.0846789
$885$	50.5622	1.69963
$886$	30.2302	1.01561
$887$	−3.95881	−0.132924	−0.0664619	−	0.997789i	$-0.521171\pi$
$887$	−3.95881	−0.132924	−0.0664619	+	0.997789i	$0.521171\pi$
$888$	−7.12710	−0.239170
$889$	−15.5231	−0.520629
$890$	7.05867	0.236607
$891$	0.242041	0.00810869
$892$	−6.58042	−0.220329
$893$	−48.5546	−1.62482
$894$	14.2877	0.477853
$895$	5.20344	0.173932
$896$	1.09421	0.0365549
$897$	−2.10396	−0.0702492
$898$	−26.0663	−0.869845
$899$	−23.0004	−0.767106
$900$	−10.0571	−0.335236
$901$	−50.8692	−1.69470
$902$	0.509294	0.0169576
$903$	−2.90817	−0.0967780
$904$	−28.9330	−0.962296
$905$	−20.4571	−0.680017
$906$	−16.2892	−0.541171
$907$	18.9117	0.627953	0.313977	−	0.949431i	$-0.398339\pi$
$907$	18.9117	0.627953	0.313977	+	0.949431i	$0.398339\pi$
$908$	24.3360	0.807619
$909$	12.5805	0.417268
$910$	−2.99107	−0.0991530
$911$	0.701355	0.0232369	0.0116185	−	0.999933i	$-0.496302\pi$
$911$	0.701355	0.0232369	0.0116185	+	0.999933i	$0.496302\pi$
$912$	−6.05293	−0.200433
$913$	−3.73981	−0.123770
$914$	42.3371	1.40039
$915$	54.6049	1.80518
$916$	−15.4560	−0.510680
$917$	−0.0467292	−0.00154313
$918$	−4.22548	−0.139462
$919$	30.1511	0.994593	0.497296	−	0.867581i	$-0.334326\pi$
$919$	30.1511	0.994593	0.497296	+	0.867581i	$0.334326\pi$
$920$	−36.7189	−1.21059
$921$	−2.66553	−0.0878324
$922$	−1.81943	−0.0599198
$923$	−0.179068	−0.00589409
$924$	−0.215723	−0.00709677
$925$	−26.4166	−0.868571
$926$	1.62420	0.0533744
$927$	−18.0142	−0.591665
$928$	−46.0412	−1.51138
$929$	7.10755	0.233191	0.116596	−	0.993179i	$-0.462802\pi$
$929$	7.10755	0.233191	0.116596	+	0.993179i	$0.462802\pi$
$930$	9.74374	0.319510
$931$	4.25330	0.139396
$932$	−18.5268	−0.606867
$933$	19.1884	0.628200
$934$	−4.00011	−0.130888
$935$	3.91952	0.128182
$936$	2.14305	0.0700479
$937$	−17.3737	−0.567573	−0.283786	−	0.958887i	$-0.591591\pi$
$937$	−17.3737	−0.567573	−0.283786	+	0.958887i	$0.591591\pi$
$938$	0.693322	0.0226378
$939$	−3.38032	−0.110313
$940$	41.0575	1.33915
$941$	0.0550425	0.00179434	0.000897168	−	1.00000i	$-0.499714\pi$
$941$	0.0550425	0.00179434	0.000897168		1.00000i	$0.499714\pi$
$942$	−7.81543	−0.254641
$943$	5.97271	0.194498
$944$	−17.8314	−0.580362
$945$	4.03535	0.131270
$946$	0.741180	0.0240978
$947$	−20.5347	−0.667289	−0.333644	−	0.942699i	$-0.608278\pi$
$947$	−20.5347	−0.667289	−0.333644	+	0.942699i	$0.608278\pi$
$948$	−11.0770	−0.359765
$949$	6.48431	0.210490
$950$	−50.5364	−1.63962
$951$	15.7083	0.509376
$952$	12.2170	0.395955
$953$	41.7049	1.35095	0.675476	−	0.737382i	$-0.263938\pi$
$953$	41.7049	1.35095	0.675476	+	0.737382i	$0.263938\pi$
$954$	13.3477	0.432148
$955$	4.03535	0.130581
$956$	−8.98551	−0.290612
$957$	2.42769	0.0784762
$958$	−8.55749	−0.276480
$959$	7.16171	0.231264
$960$	30.9901	1.00020
$961$	−25.7415	−0.830371
$962$	1.73523	0.0559460
$963$	3.88063	0.125051
$964$	20.6345	0.664592
$965$	69.6373	2.24170
$966$	3.14717	0.101259
$967$	−40.2000	−1.29275	−0.646373	−	0.763022i	$-0.723715\pi$
$967$	−40.2000	−1.29275	−0.646373	+	0.763022i	$0.723715\pi$
$968$	−33.3101	−1.07063
$969$	17.0682	0.548310
$970$	31.2078	1.00202
$971$	−24.1565	−0.775218	−0.387609	−	0.921824i	$-0.626699\pi$
$971$	−24.1565	−0.775218	−0.387609	+	0.921824i	$0.626699\pi$
$972$	−0.891266	−0.0285874
$973$	0.455855	0.0146141
$974$	−18.1868	−0.582743
$975$	7.94322	0.254387
$976$	−19.2571	−0.616404
$977$	−31.1444	−0.996398	−0.498199	−	0.867063i	$-0.666005\pi$
$977$	−31.1444	−0.996398	−0.498199	+	0.867063i	$0.666005\pi$
$978$	21.3430	0.682475
$979$	−0.402084	−0.0128507
$980$	−3.59657	−0.114888
$981$	−10.2580	−0.327513
$982$	−28.1011	−0.896743
$983$	41.9046	1.33655	0.668274	−	0.743915i	$-0.267033\pi$
$983$	41.9046	1.33655	0.668274	+	0.743915i	$0.267033\pi$
$984$	−6.08369	−0.193941
$985$	−58.1830	−1.85386
$986$	−42.3819	−1.34972
$987$	−11.4157	−0.363367
$988$	−2.66848	−0.0848957
$989$	8.69214	0.276394
$990$	−1.02845	−0.0326864
$991$	−57.0580	−1.81251	−0.906254	−	0.422735i	$-0.861070\pi$
$991$	−57.0580	−1.81251	−0.906254	+	0.422735i	$0.861070\pi$
$992$	10.5262	0.334208
$993$	20.4115	0.647739
$994$	0.267855	0.00849585
$995$	−96.7049	−3.06575
$996$	13.7711	0.436353
$997$	−56.2937	−1.78284	−0.891420	−	0.453179i	$-0.850290\pi$
$997$	−56.2937	−1.78284	−0.891420	+	0.453179i	$0.850290\pi$
$998$	−27.2959	−0.864036
$999$	−2.34105	−0.0740676

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.k.1.8	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.k.1.8	✓	27	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-1.05296 q^{2} +1.00000 q^{3} -0.891266 q^{4} +4.03535 q^{5} -1.05296 q^{6} +1.00000 q^{7} +3.04440 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.05296 q^{2} +1.00000 q^{3} -0.891266 q^{4} +4.03535 q^{5} -1.05296 q^{6} +1.00000 q^{7} +3.04440 q^{8} +1.00000 q^{9} -4.24908 q^{10} +0.242041 q^{11} -0.891266 q^{12} +0.703933 q^{13} -1.05296 q^{14} +4.03535 q^{15} -1.42311 q^{16} +4.01294 q^{17} -1.05296 q^{18} +4.25330 q^{19} -3.59657 q^{20} +1.00000 q^{21} -0.254861 q^{22} -2.98887 q^{23} +3.04440 q^{24} +11.2841 q^{25} -0.741217 q^{26} +1.00000 q^{27} -0.891266 q^{28} +10.0301 q^{29} -4.24908 q^{30} -2.29314 q^{31} -4.59031 q^{32} +0.242041 q^{33} -4.22548 q^{34} +4.03535 q^{35} -0.891266 q^{36} -2.34105 q^{37} -4.47857 q^{38} +0.703933 q^{39} +12.2852 q^{40} -1.99832 q^{41} -1.05296 q^{42} -2.90817 q^{43} -0.215723 q^{44} +4.03535 q^{45} +3.14717 q^{46} -11.4157 q^{47} -1.42311 q^{48} +1.00000 q^{49} -11.8817 q^{50} +4.01294 q^{51} -0.627391 q^{52} -12.6763 q^{53} -1.05296 q^{54} +0.976721 q^{55} +3.04440 q^{56} +4.25330 q^{57} -10.5613 q^{58} +12.5298 q^{59} -3.59657 q^{60} +13.5317 q^{61} +2.41460 q^{62} +1.00000 q^{63} +7.67966 q^{64} +2.84062 q^{65} -0.254861 q^{66} -0.658447 q^{67} -3.57659 q^{68} -2.98887 q^{69} -4.24908 q^{70} -0.254382 q^{71} +3.04440 q^{72} +9.21154 q^{73} +2.46505 q^{74} +11.2841 q^{75} -3.79082 q^{76} +0.242041 q^{77} -0.741217 q^{78} +12.4284 q^{79} -5.74277 q^{80} +1.00000 q^{81} +2.10416 q^{82} -15.4511 q^{83} -0.891266 q^{84} +16.1936 q^{85} +3.06221 q^{86} +10.0301 q^{87} +0.736870 q^{88} -1.66122 q^{89} -4.24908 q^{90} +0.703933 q^{91} +2.66387 q^{92} -2.29314 q^{93} +12.0204 q^{94} +17.1635 q^{95} -4.59031 q^{96} -7.34461 q^{97} -1.05296 q^{98} +0.242041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * q^99

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