LMFDB - Embedded newform 6015.2.a.d.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.319268 q^{2} -1.00000 q^{3} -1.89807 q^{4} +1.00000 q^{5} +0.319268 q^{6} +0.830562 q^{7} +1.24453 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.319268 q^{2} -1.00000 q^{3} -1.89807 q^{4} +1.00000 q^{5} +0.319268 q^{6} +0.830562 q^{7} +1.24453 q^{8} +1.00000 q^{9} -0.319268 q^{10} -4.09418 q^{11} +1.89807 q^{12} -4.03690 q^{13} -0.265172 q^{14} -1.00000 q^{15} +3.39880 q^{16} +4.73743 q^{17} -0.319268 q^{18} +4.81525 q^{19} -1.89807 q^{20} -0.830562 q^{21} +1.30714 q^{22} -7.15657 q^{23} -1.24453 q^{24} +1.00000 q^{25} +1.28885 q^{26} -1.00000 q^{27} -1.57646 q^{28} -8.77658 q^{29} +0.319268 q^{30} +7.47946 q^{31} -3.57419 q^{32} +4.09418 q^{33} -1.51251 q^{34} +0.830562 q^{35} -1.89807 q^{36} +11.6457 q^{37} -1.53736 q^{38} +4.03690 q^{39} +1.24453 q^{40} +0.611381 q^{41} +0.265172 q^{42} -2.50141 q^{43} +7.77104 q^{44} +1.00000 q^{45} +2.28487 q^{46} +1.23402 q^{47} -3.39880 q^{48} -6.31017 q^{49} -0.319268 q^{50} -4.73743 q^{51} +7.66231 q^{52} +5.98540 q^{53} +0.319268 q^{54} -4.09418 q^{55} +1.03366 q^{56} -4.81525 q^{57} +2.80209 q^{58} -4.67265 q^{59} +1.89807 q^{60} +4.06374 q^{61} -2.38795 q^{62} +0.830562 q^{63} -5.65647 q^{64} -4.03690 q^{65} -1.30714 q^{66} -0.0446029 q^{67} -8.99197 q^{68} +7.15657 q^{69} -0.265172 q^{70} -2.66203 q^{71} +1.24453 q^{72} -9.28858 q^{73} -3.71811 q^{74} -1.00000 q^{75} -9.13968 q^{76} -3.40047 q^{77} -1.28885 q^{78} -0.567417 q^{79} +3.39880 q^{80} +1.00000 q^{81} -0.195195 q^{82} +3.28314 q^{83} +1.57646 q^{84} +4.73743 q^{85} +0.798620 q^{86} +8.77658 q^{87} -5.09533 q^{88} +18.6762 q^{89} -0.319268 q^{90} -3.35289 q^{91} +13.5836 q^{92} -7.47946 q^{93} -0.393984 q^{94} +4.81525 q^{95} +3.57419 q^{96} -14.6565 q^{97} +2.01464 q^{98} -4.09418 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * 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 $

$2$	−0.319268	−0.225757	−0.112878	−	0.993609i	$-0.536007\pi$
$2$	−0.319268	−0.225757	−0.112878	+	0.993609i	$0.536007\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.89807	−0.949034
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.319268	0.130341
$7$	0.830562	0.313923	0.156961	−	0.987605i	$-0.449830\pi$
$7$	0.830562	0.313923	0.156961	+	0.987605i	$0.449830\pi$
$8$	1.24453	0.440008
$9$	1.00000	0.333333
$10$	−0.319268	−0.100962
$11$	−4.09418	−1.23444	−0.617221	−	0.786790i	$-0.711742\pi$
$11$	−4.09418	−1.23444	−0.617221	+	0.786790i	$0.711742\pi$
$12$	1.89807	0.547925
$13$	−4.03690	−1.11963	−0.559817	−	0.828616i	$-0.689129\pi$
$13$	−4.03690	−1.11963	−0.559817	+	0.828616i	$0.689129\pi$
$14$	−0.265172	−0.0708702
$15$	−1.00000	−0.258199
$16$	3.39880	0.849699
$17$	4.73743	1.14900	0.574498	−	0.818506i	$-0.305197\pi$
$17$	4.73743	1.14900	0.574498	+	0.818506i	$0.305197\pi$
$18$	−0.319268	−0.0752523
$19$	4.81525	1.10469	0.552347	−	0.833614i	$-0.313732\pi$
$19$	4.81525	1.10469	0.552347	+	0.833614i	$0.313732\pi$
$20$	−1.89807	−0.424421
$21$	−0.830562	−0.181243
$22$	1.30714	0.278684
$23$	−7.15657	−1.49225	−0.746124	−	0.665807i	$-0.768087\pi$
$23$	−7.15657	−1.49225	−0.746124	+	0.665807i	$0.768087\pi$
$24$	−1.24453	−0.254039
$25$	1.00000	0.200000
$26$	1.28885	0.252765
$27$	−1.00000	−0.192450
$28$	−1.57646	−0.297923
$29$	−8.77658	−1.62977	−0.814885	−	0.579622i	$-0.803200\pi$
$29$	−8.77658	−1.62977	−0.814885	+	0.579622i	$0.803200\pi$
$30$	0.319268	0.0582902
$31$	7.47946	1.34335	0.671675	−	0.740846i	$-0.265575\pi$
$31$	7.47946	1.34335	0.671675	+	0.740846i	$0.265575\pi$
$32$	−3.57419	−0.631833
$33$	4.09418	0.712706
$34$	−1.51251	−0.259394
$35$	0.830562	0.140391
$36$	−1.89807	−0.316345
$37$	11.6457	1.91455	0.957273	−	0.289186i	$-0.0933845\pi$
$37$	11.6457	1.91455	0.957273	+	0.289186i	$0.0933845\pi$
$38$	−1.53736	−0.249392
$39$	4.03690	0.646421
$40$	1.24453	0.196777
$41$	0.611381	0.0954816	0.0477408	−	0.998860i	$-0.484798\pi$
$41$	0.611381	0.0954816	0.0477408	+	0.998860i	$0.484798\pi$
$42$	0.265172	0.0409169
$43$	−2.50141	−0.381461	−0.190731	−	0.981642i	$-0.561086\pi$
$43$	−2.50141	−0.381461	−0.190731	+	0.981642i	$0.561086\pi$
$44$	7.77104	1.17153
$45$	1.00000	0.149071
$46$	2.28487	0.336885
$47$	1.23402	0.180001	0.0900004	−	0.995942i	$-0.471313\pi$
$47$	1.23402	0.180001	0.0900004	+	0.995942i	$0.471313\pi$
$48$	−3.39880	−0.490574
$49$	−6.31017	−0.901452
$50$	−0.319268	−0.0451514
$51$	−4.73743	−0.663373
$52$	7.66231	1.06257
$53$	5.98540	0.822158	0.411079	−	0.911600i	$-0.365152\pi$
$53$	5.98540	0.822158	0.411079	+	0.911600i	$0.365152\pi$
$54$	0.319268	0.0434469
$55$	−4.09418	−0.552059
$56$	1.03366	0.138128
$57$	−4.81525	−0.637796
$58$	2.80209	0.367932
$59$	−4.67265	−0.608327	−0.304163	−	0.952620i	$-0.598377\pi$
$59$	−4.67265	−0.608327	−0.304163	+	0.952620i	$0.598377\pi$
$60$	1.89807	0.245039
$61$	4.06374	0.520309	0.260155	−	0.965567i	$-0.416226\pi$
$61$	4.06374	0.520309	0.260155	+	0.965567i	$0.416226\pi$
$62$	−2.38795	−0.303270
$63$	0.830562	0.104641
$64$	−5.65647	−0.707059
$65$	−4.03690	−0.500716
$66$	−1.30714	−0.160898
$67$	−0.0446029	−0.00544911	−0.00272455	−	0.999996i	$-0.500867\pi$
$67$	−0.0446029	−0.00544911	−0.00272455	+	0.999996i	$0.500867\pi$
$68$	−8.99197	−1.09044
$69$	7.15657	0.861549
$70$	−0.265172	−0.0316941
$71$	−2.66203	−0.315924	−0.157962	−	0.987445i	$-0.550492\pi$
$71$	−2.66203	−0.315924	−0.157962	+	0.987445i	$0.550492\pi$
$72$	1.24453	0.146669
$73$	−9.28858	−1.08715	−0.543573	−	0.839362i	$-0.682929\pi$
$73$	−9.28858	−1.08715	−0.543573	+	0.839362i	$0.682929\pi$
$74$	−3.71811	−0.432222
$75$	−1.00000	−0.115470
$76$	−9.13968	−1.04839
$77$	−3.40047	−0.387520
$78$	−1.28885	−0.145934
$79$	−0.567417	−0.0638394	−0.0319197	−	0.999490i	$-0.510162\pi$
$79$	−0.567417	−0.0638394	−0.0319197	+	0.999490i	$0.510162\pi$
$80$	3.39880	0.379997
$81$	1.00000	0.111111
$82$	−0.195195	−0.0215556
$83$	3.28314	0.360372	0.180186	−	0.983633i	$-0.442330\pi$
$83$	3.28314	0.360372	0.180186	+	0.983633i	$0.442330\pi$
$84$	1.57646	0.172006
$85$	4.73743	0.513847
$86$	0.798620	0.0861174
$87$	8.77658	0.940948
$88$	−5.09533	−0.543164
$89$	18.6762	1.97967	0.989835	−	0.142220i	$-0.0454241\pi$
$89$	18.6762	1.97967	0.989835	+	0.142220i	$0.0454241\pi$
$90$	−0.319268	−0.0336538
$91$	−3.35289	−0.351479
$92$	13.5836	1.41619
$93$	−7.47946	−0.775583
$94$	−0.393984	−0.0406364
$95$	4.81525	0.494035
$96$	3.57419	0.364789
$97$	−14.6565	−1.48814	−0.744072	−	0.668100i	$-0.767108\pi$
$97$	−14.6565	−1.48814	−0.744072	+	0.668100i	$0.767108\pi$
$98$	2.01464	0.203509
$99$	−4.09418	−0.411481
$100$	−1.89807	−0.189807
$101$	−11.6625	−1.16046	−0.580232	−	0.814451i	$-0.697038\pi$
$101$	−11.6625	−1.16046	−0.580232	+	0.814451i	$0.697038\pi$
$102$	1.51251	0.149761
$103$	8.83498	0.870536	0.435268	−	0.900301i	$-0.356654\pi$
$103$	8.83498	0.870536	0.435268	+	0.900301i	$0.356654\pi$
$104$	−5.02404	−0.492648
$105$	−0.830562	−0.0810545
$106$	−1.91095	−0.185608
$107$	8.07270	0.780418	0.390209	−	0.920726i	$-0.372403\pi$
$107$	8.07270	0.780418	0.390209	+	0.920726i	$0.372403\pi$
$108$	1.89807	0.182642
$109$	−0.798062	−0.0764405	−0.0382202	−	0.999269i	$-0.512169\pi$
$109$	−0.798062	−0.0764405	−0.0382202	+	0.999269i	$0.512169\pi$
$110$	1.30714	0.124631
$111$	−11.6457	−1.10536
$112$	2.82291	0.266740
$113$	−17.1999	−1.61803	−0.809015	−	0.587788i	$-0.799999\pi$
$113$	−17.1999	−1.61803	−0.809015	+	0.587788i	$0.799999\pi$
$114$	1.53736	0.143987
$115$	−7.15657	−0.667353
$116$	16.6585	1.54671
$117$	−4.03690	−0.373211
$118$	1.49183	0.137334
$119$	3.93473	0.360696
$120$	−1.24453	−0.113609
$121$	5.76233	0.523848
$122$	−1.29742	−0.117463
$123$	−0.611381	−0.0551264
$124$	−14.1965	−1.27488
$125$	1.00000	0.0894427
$126$	−0.265172	−0.0236234
$127$	9.77907	0.867752	0.433876	−	0.900973i	$-0.357146\pi$
$127$	9.77907	0.867752	0.433876	+	0.900973i	$0.357146\pi$
$128$	8.95431	0.791456
$129$	2.50141	0.220237
$130$	1.28885	0.113040
$131$	12.7636	1.11516	0.557582	−	0.830122i	$-0.311729\pi$
$131$	12.7636	1.11516	0.557582	+	0.830122i	$0.311729\pi$
$132$	−7.77104	−0.676382
$133$	3.99936	0.346789
$134$	0.0142403	0.00123017
$135$	−1.00000	−0.0860663
$136$	5.89588	0.505567
$137$	0.792763	0.0677303	0.0338652	−	0.999426i	$-0.489218\pi$
$137$	0.792763	0.0677303	0.0338652	+	0.999426i	$0.489218\pi$
$138$	−2.28487	−0.194501
$139$	6.06206	0.514177	0.257088	−	0.966388i	$-0.417237\pi$
$139$	6.06206	0.514177	0.257088	+	0.966388i	$0.417237\pi$
$140$	−1.57646	−0.133235
$141$	−1.23402	−0.103923
$142$	0.849901	0.0713221
$143$	16.5278	1.38212
$144$	3.39880	0.283233
$145$	−8.77658	−0.728856
$146$	2.96555	0.245431
$147$	6.31017	0.520454
$148$	−22.1044	−1.81697
$149$	−9.13639	−0.748482	−0.374241	−	0.927331i	$-0.622097\pi$
$149$	−9.13639	−0.748482	−0.374241	+	0.927331i	$0.622097\pi$
$150$	0.319268	0.0260682
$151$	20.6111	1.67731	0.838656	−	0.544662i	$-0.183342\pi$
$151$	20.6111	1.67731	0.838656	+	0.544662i	$0.183342\pi$
$152$	5.99273	0.486074
$153$	4.73743	0.382999
$154$	1.08566	0.0874852
$155$	7.47946	0.600764
$156$	−7.66231	−0.613475
$157$	−7.51435	−0.599710	−0.299855	−	0.953985i	$-0.596938\pi$
$157$	−7.51435	−0.599710	−0.299855	+	0.953985i	$0.596938\pi$
$158$	0.181158	0.0144122
$159$	−5.98540	−0.474673
$160$	−3.57419	−0.282564
$161$	−5.94397	−0.468450
$162$	−0.319268	−0.0250841
$163$	15.0678	1.18020	0.590102	−	0.807329i	$-0.299088\pi$
$163$	15.0678	1.18020	0.590102	+	0.807329i	$0.299088\pi$
$164$	−1.16044	−0.0906153
$165$	4.09418	0.318732
$166$	−1.04820	−0.0813564
$167$	−0.206036	−0.0159435	−0.00797176	−	0.999968i	$-0.502538\pi$
$167$	−0.206036	−0.0159435	−0.00797176	+	0.999968i	$0.502538\pi$
$168$	−1.03366	−0.0797485
$169$	3.29654	0.253580
$170$	−1.51251	−0.116004
$171$	4.81525	0.368232
$172$	4.74784	0.362019
$173$	5.61834	0.427155	0.213577	−	0.976926i	$-0.431488\pi$
$173$	5.61834	0.427155	0.213577	+	0.976926i	$0.431488\pi$
$174$	−2.80209	−0.212426
$175$	0.830562	0.0627846
$176$	−13.9153	−1.04890
$177$	4.67265	0.351218
$178$	−5.96271	−0.446924
$179$	3.49899	0.261527	0.130763	−	0.991414i	$-0.458257\pi$
$179$	3.49899	0.261527	0.130763	+	0.991414i	$0.458257\pi$
$180$	−1.89807	−0.141474
$181$	−11.2656	−0.837369	−0.418685	−	0.908132i	$-0.637509\pi$
$181$	−11.2656	−0.837369	−0.418685	+	0.908132i	$0.637509\pi$
$182$	1.07047	0.0793487
$183$	−4.06374	−0.300401
$184$	−8.90656	−0.656600
$185$	11.6457	0.856211
$186$	2.38795	0.175093
$187$	−19.3959	−1.41837
$188$	−2.34226	−0.170827
$189$	−0.830562	−0.0604145
$190$	−1.53736	−0.111532
$191$	−24.2035	−1.75130	−0.875652	−	0.482943i	$-0.839568\pi$
$191$	−24.2035	−1.75130	−0.875652	+	0.482943i	$0.839568\pi$
$192$	5.65647	0.408220
$193$	−15.2924	−1.10077	−0.550385	−	0.834911i	$-0.685519\pi$
$193$	−15.2924	−1.10077	−0.550385	+	0.834911i	$0.685519\pi$
$194$	4.67936	0.335958
$195$	4.03690	0.289088
$196$	11.9771	0.855509
$197$	−20.4242	−1.45517	−0.727583	−	0.686020i	$-0.759356\pi$
$197$	−20.4242	−1.45517	−0.727583	+	0.686020i	$0.759356\pi$
$198$	1.30714	0.0928946
$199$	−17.4784	−1.23901	−0.619505	−	0.784992i	$-0.712667\pi$
$199$	−17.4784	−1.23901	−0.619505	+	0.784992i	$0.712667\pi$
$200$	1.24453	0.0880015
$201$	0.0446029	0.00314604
$202$	3.72347	0.261983
$203$	−7.28949	−0.511622
$204$	8.99197	0.629564
$205$	0.611381	0.0427007
$206$	−2.82073	−0.196530
$207$	−7.15657	−0.497416
$208$	−13.7206	−0.951352
$209$	−19.7145	−1.36368
$210$	0.265172	0.0182986
$211$	−6.54142	−0.450330	−0.225165	−	0.974321i	$-0.572292\pi$
$211$	−6.54142	−0.450330	−0.225165	+	0.974321i	$0.572292\pi$
$212$	−11.3607	−0.780255
$213$	2.66203	0.182399
$214$	−2.57736	−0.176185
$215$	−2.50141	−0.170595
$216$	−1.24453	−0.0846795
$217$	6.21215	0.421708
$218$	0.254796	0.0172570
$219$	9.28858	0.627664
$220$	7.77104	0.523923
$221$	−19.1245	−1.28646
$222$	3.71811	0.249543
$223$	−21.4831	−1.43862	−0.719308	−	0.694691i	$-0.755541\pi$
$223$	−21.4831	−1.43862	−0.719308	+	0.694691i	$0.755541\pi$
$224$	−2.96858	−0.198347
$225$	1.00000	0.0666667
$226$	5.49138	0.365281
$227$	17.4304	1.15690	0.578449	−	0.815719i	$-0.303658\pi$
$227$	17.4304	1.15690	0.578449	+	0.815719i	$0.303658\pi$
$228$	9.13968	0.605290
$229$	4.99561	0.330119	0.165059	−	0.986284i	$-0.447218\pi$
$229$	4.99561	0.330119	0.165059	+	0.986284i	$0.447218\pi$
$230$	2.28487	0.150660
$231$	3.40047	0.223735
$232$	−10.9227	−0.717112
$233$	3.77667	0.247418	0.123709	−	0.992319i	$-0.460521\pi$
$233$	3.77667	0.247418	0.123709	+	0.992319i	$0.460521\pi$
$234$	1.28885	0.0842550
$235$	1.23402	0.0804988
$236$	8.86900	0.577323
$237$	0.567417	0.0368577
$238$	−1.25623	−0.0814296
$239$	−7.57510	−0.489992	−0.244996	−	0.969524i	$-0.578787\pi$
$239$	−7.57510	−0.489992	−0.244996	+	0.969524i	$0.578787\pi$
$240$	−3.39880	−0.219391
$241$	9.85305	0.634691	0.317345	−	0.948310i	$-0.397209\pi$
$241$	9.85305	0.634691	0.317345	+	0.948310i	$0.397209\pi$
$242$	−1.83973	−0.118262
$243$	−1.00000	−0.0641500
$244$	−7.71326	−0.493791
$245$	−6.31017	−0.403142
$246$	0.195195	0.0124452
$247$	−19.4387	−1.23685
$248$	9.30840	0.591084
$249$	−3.28314	−0.208061
$250$	−0.319268	−0.0201923
$251$	20.1124	1.26948	0.634740	−	0.772726i	$-0.281107\pi$
$251$	20.1124	1.26948	0.634740	+	0.772726i	$0.281107\pi$
$252$	−1.57646	−0.0993078
$253$	29.3003	1.84209
$254$	−3.12215	−0.195901
$255$	−4.73743	−0.296670
$256$	8.45411	0.528382
$257$	−8.16926	−0.509584	−0.254792	−	0.966996i	$-0.582007\pi$
$257$	−8.16926	−0.509584	−0.254792	+	0.966996i	$0.582007\pi$
$258$	−0.798620	−0.0497199
$259$	9.67250	0.601020
$260$	7.66231	0.475196
$261$	−8.77658	−0.543257
$262$	−4.07502	−0.251756
$263$	−11.2508	−0.693756	−0.346878	−	0.937910i	$-0.612758\pi$
$263$	−11.2508	−0.693756	−0.346878	+	0.937910i	$0.612758\pi$
$264$	5.09533	0.313596
$265$	5.98540	0.367680
$266$	−1.27687	−0.0782900
$267$	−18.6762	−1.14296
$268$	0.0846592	0.00517139
$269$	−14.0298	−0.855411	−0.427705	−	0.903918i	$-0.640678\pi$
$269$	−14.0298	−0.855411	−0.427705	+	0.903918i	$0.640678\pi$
$270$	0.319268	0.0194301
$271$	12.5942	0.765042	0.382521	−	0.923947i	$-0.375056\pi$
$271$	12.5942	0.765042	0.382521	+	0.923947i	$0.375056\pi$
$272$	16.1016	0.976301
$273$	3.35289	0.202926
$274$	−0.253104	−0.0152906
$275$	−4.09418	−0.246888
$276$	−13.5836	−0.817639
$277$	−0.747970	−0.0449411	−0.0224706	−	0.999748i	$-0.507153\pi$
$277$	−0.747970	−0.0449411	−0.0224706	+	0.999748i	$0.507153\pi$
$278$	−1.93542	−0.116079
$279$	7.47946	0.447783
$280$	1.03366	0.0617729
$281$	−27.6962	−1.65221	−0.826107	−	0.563513i	$-0.809450\pi$
$281$	−27.6962	−1.65221	−0.826107	+	0.563513i	$0.809450\pi$
$282$	0.393984	0.0234614
$283$	−14.5904	−0.867308	−0.433654	−	0.901080i	$-0.642776\pi$
$283$	−14.5904	−0.867308	−0.433654	+	0.901080i	$0.642776\pi$
$284$	5.05271	0.299823
$285$	−4.81525	−0.285231
$286$	−5.27680	−0.312024
$287$	0.507790	0.0299739
$288$	−3.57419	−0.210611
$289$	5.44327	0.320193
$290$	2.80209	0.164544
$291$	14.6565	0.859180
$292$	17.6303	1.03174
$293$	−4.67766	−0.273272	−0.136636	−	0.990621i	$-0.543629\pi$
$293$	−4.67766	−0.273272	−0.136636	+	0.990621i	$0.543629\pi$
$294$	−2.01464	−0.117496
$295$	−4.67265	−0.272052
$296$	14.4935	0.842415
$297$	4.09418	0.237569
$298$	2.91696	0.168975
$299$	28.8903	1.67077
$300$	1.89807	0.109585
$301$	−2.07757	−0.119749
$302$	−6.58049	−0.378665
$303$	11.6625	0.669994
$304$	16.3661	0.938658
$305$	4.06374	0.232689
$306$	−1.51251	−0.0864646
$307$	−4.25138	−0.242639	−0.121319	−	0.992614i	$-0.538713\pi$
$307$	−4.25138	−0.242639	−0.121319	+	0.992614i	$0.538713\pi$
$308$	6.45432	0.367769
$309$	−8.83498	−0.502604
$310$	−2.38795	−0.135627
$311$	−24.8680	−1.41014	−0.705068	−	0.709140i	$-0.749083\pi$
$311$	−24.8680	−1.41014	−0.705068	+	0.709140i	$0.749083\pi$
$312$	5.02404	0.284430
$313$	−18.2042	−1.02896	−0.514480	−	0.857502i	$-0.672015\pi$
$313$	−18.2042	−1.02896	−0.514480	+	0.857502i	$0.672015\pi$
$314$	2.39909	0.135389
$315$	0.830562	0.0467968
$316$	1.07700	0.0605858
$317$	−2.58899	−0.145412	−0.0727060	−	0.997353i	$-0.523163\pi$
$317$	−2.58899	−0.145412	−0.0727060	+	0.997353i	$0.523163\pi$
$318$	1.91095	0.107161
$319$	35.9329	2.01186
$320$	−5.65647	−0.316206
$321$	−8.07270	−0.450574
$322$	1.89772	0.105756
$323$	22.8119	1.26929
$324$	−1.89807	−0.105448
$325$	−4.03690	−0.223927
$326$	−4.81068	−0.266439
$327$	0.798062	0.0441329
$328$	0.760882	0.0420127
$329$	1.02493	0.0565063
$330$	−1.30714	−0.0719558
$331$	−20.4082	−1.12174	−0.560868	−	0.827905i	$-0.689532\pi$
$331$	−20.4082	−1.12174	−0.560868	+	0.827905i	$0.689532\pi$
$332$	−6.23163	−0.342005
$333$	11.6457	0.638182
$334$	0.0657807	0.00359936
$335$	−0.0446029	−0.00243691
$336$	−2.82291	−0.154002
$337$	−11.5872	−0.631198	−0.315599	−	0.948893i	$-0.602205\pi$
$337$	−11.5872	−0.631198	−0.315599	+	0.948893i	$0.602205\pi$
$338$	−1.05248	−0.0572475
$339$	17.1999	0.934170
$340$	−8.99197	−0.487658
$341$	−30.6223	−1.65829
$342$	−1.53736	−0.0831308
$343$	−11.0549	−0.596909
$344$	−3.11308	−0.167846
$345$	7.15657	0.385297
$346$	−1.79376	−0.0964331
$347$	−26.1385	−1.40319	−0.701595	−	0.712576i	$-0.747529\pi$
$347$	−26.1385	−1.40319	−0.701595	+	0.712576i	$0.747529\pi$
$348$	−16.6585	−0.892992
$349$	7.77730	0.416309	0.208155	−	0.978096i	$-0.433254\pi$
$349$	7.77730	0.416309	0.208155	+	0.978096i	$0.433254\pi$
$350$	−0.265172	−0.0141740
$351$	4.03690	0.215474
$352$	14.6334	0.779962
$353$	−16.2452	−0.864645	−0.432323	−	0.901719i	$-0.642306\pi$
$353$	−16.2452	−0.864645	−0.432323	+	0.901719i	$0.642306\pi$
$354$	−1.49183	−0.0792898
$355$	−2.66203	−0.141286
$356$	−35.4486	−1.87877
$357$	−3.93473	−0.208248
$358$	−1.11712	−0.0590414
$359$	−29.3633	−1.54973	−0.774867	−	0.632125i	$-0.782183\pi$
$359$	−29.3633	−1.54973	−0.774867	+	0.632125i	$0.782183\pi$
$360$	1.24453	0.0655925
$361$	4.18666	0.220351
$362$	3.59677	0.189042
$363$	−5.76233	−0.302444
$364$	6.36402	0.333565
$365$	−9.28858	−0.486186
$366$	1.29742	0.0678175
$367$	6.78710	0.354284	0.177142	−	0.984185i	$-0.443315\pi$
$367$	6.78710	0.354284	0.177142	+	0.984185i	$0.443315\pi$
$368$	−24.3237	−1.26796
$369$	0.611381	0.0318272
$370$	−3.71811	−0.193295
$371$	4.97124	0.258094
$372$	14.1965	0.736055
$373$	21.2007	1.09773	0.548865	−	0.835911i	$-0.315060\pi$
$373$	21.2007	1.09773	0.548865	+	0.835911i	$0.315060\pi$
$374$	6.19250	0.320207
$375$	−1.00000	−0.0516398
$376$	1.53578	0.0792017
$377$	35.4302	1.82475
$378$	0.265172	0.0136390
$379$	−10.3396	−0.531110	−0.265555	−	0.964096i	$-0.585555\pi$
$379$	−10.3396	−0.531110	−0.265555	+	0.964096i	$0.585555\pi$
$380$	−9.13968	−0.468856
$381$	−9.77907	−0.500997
$382$	7.72741	0.395369
$383$	27.5532	1.40790	0.703952	−	0.710247i	$-0.251417\pi$
$383$	27.5532	1.40790	0.703952	+	0.710247i	$0.251417\pi$
$384$	−8.95431	−0.456948
$385$	−3.40047	−0.173304
$386$	4.88237	0.248506
$387$	−2.50141	−0.127154
$388$	27.8191	1.41230
$389$	22.8713	1.15962	0.579811	−	0.814751i	$-0.303126\pi$
$389$	22.8713	1.15962	0.579811	+	0.814751i	$0.303126\pi$
$390$	−1.28885	−0.0652636
$391$	−33.9038	−1.71459
$392$	−7.85319	−0.396646
$393$	−12.7636	−0.643840
$394$	6.52081	0.328514
$395$	−0.567417	−0.0285499
$396$	7.77104	0.390509
$397$	25.5742	1.28353	0.641765	−	0.766901i	$-0.278202\pi$
$397$	25.5742	1.28353	0.641765	+	0.766901i	$0.278202\pi$
$398$	5.58030	0.279715
$399$	−3.99936	−0.200219
$400$	3.39880	0.169940
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−0.0142403	−0.000710241 0
$403$	−30.1938	−1.50406
$404$	22.1363	1.10132
$405$	1.00000	0.0496904
$406$	2.32730	0.115502
$407$	−47.6797	−2.36340
$408$	−5.89588	−0.291889
$409$	35.5509	1.75788	0.878940	−	0.476933i	$-0.158252\pi$
$409$	35.5509	1.75788	0.878940	+	0.476933i	$0.158252\pi$
$410$	−0.195195	−0.00963997
$411$	−0.792763	−0.0391041
$412$	−16.7694	−0.826168
$413$	−3.88092	−0.190968
$414$	2.28487	0.112295
$415$	3.28314	0.161163
$416$	14.4286	0.707422
$417$	−6.06206	−0.296860
$418$	6.29422	0.307861
$419$	−14.6522	−0.715809	−0.357905	−	0.933758i	$-0.616509\pi$
$419$	−14.6522	−0.715809	−0.357905	+	0.933758i	$0.616509\pi$
$420$	1.57646	0.0769235
$421$	−2.55482	−0.124514	−0.0622571	−	0.998060i	$-0.519830\pi$
$421$	−2.55482	−0.124514	−0.0622571	+	0.998060i	$0.519830\pi$
$422$	2.08847	0.101665
$423$	1.23402	0.0600002
$424$	7.44900	0.361756
$425$	4.73743	0.229799
$426$	−0.849901	−0.0411778
$427$	3.37519	0.163337
$428$	−15.3225	−0.740643
$429$	−16.5278	−0.797970
$430$	0.798620	0.0385129
$431$	−40.7945	−1.96500	−0.982500	−	0.186260i	$-0.940363\pi$
$431$	−40.7945	−1.96500	−0.982500	+	0.186260i	$0.940363\pi$
$432$	−3.39880	−0.163525
$433$	−1.86713	−0.0897283	−0.0448642	−	0.998993i	$-0.514286\pi$
$433$	−1.86713	−0.0897283	−0.0448642	+	0.998993i	$0.514286\pi$
$434$	−1.98334	−0.0952035
$435$	8.77658	0.420805
$436$	1.51478	0.0725446
$437$	−34.4607	−1.64848
$438$	−2.96555	−0.141699
$439$	−13.0320	−0.621984	−0.310992	−	0.950412i	$-0.600661\pi$
$439$	−13.0320	−0.621984	−0.310992	+	0.950412i	$0.600661\pi$
$440$	−5.09533	−0.242910
$441$	−6.31017	−0.300484
$442$	6.10586	0.290426
$443$	−21.5281	−1.02283	−0.511415	−	0.859334i	$-0.670879\pi$
$443$	−21.5281	−1.02283	−0.511415	+	0.859334i	$0.670879\pi$
$444$	22.1044	1.04903
$445$	18.6762	0.885335
$446$	6.85888	0.324778
$447$	9.13639	0.432136
$448$	−4.69805	−0.221962
$449$	−35.1628	−1.65943	−0.829717	−	0.558184i	$-0.811498\pi$
$449$	−35.1628	−1.65943	−0.829717	+	0.558184i	$0.811498\pi$
$450$	−0.319268	−0.0150505
$451$	−2.50310	−0.117867
$452$	32.6466	1.53556
$453$	−20.6111	−0.968396
$454$	−5.56498	−0.261178
$455$	−3.35289	−0.157186
$456$	−5.99273	−0.280635
$457$	−29.2681	−1.36910	−0.684551	−	0.728965i	$-0.740002\pi$
$457$	−29.2681	−1.36910	−0.684551	+	0.728965i	$0.740002\pi$
$458$	−1.59494	−0.0745266
$459$	−4.73743	−0.221124
$460$	13.5836	0.633341
$461$	10.8319	0.504492	0.252246	−	0.967663i	$-0.418831\pi$
$461$	10.8319	0.504492	0.252246	+	0.967663i	$0.418831\pi$
$462$	−1.08566	−0.0505096
$463$	−13.4796	−0.626450	−0.313225	−	0.949679i	$-0.601409\pi$
$463$	−13.4796	−0.626450	−0.313225	+	0.949679i	$0.601409\pi$
$464$	−29.8298	−1.38481
$465$	−7.47946	−0.346851
$466$	−1.20577	−0.0558563
$467$	−12.4949	−0.578195	−0.289097	−	0.957300i	$-0.593355\pi$
$467$	−12.4949	−0.578195	−0.289097	+	0.957300i	$0.593355\pi$
$468$	7.66231	0.354190
$469$	−0.0370454	−0.00171060
$470$	−0.393984	−0.0181731
$471$	7.51435	0.346243
$472$	−5.81525	−0.267668
$473$	10.2412	0.470892
$474$	−0.181158	−0.00832088
$475$	4.81525	0.220939
$476$	−7.46839	−0.342313
$477$	5.98540	0.274053
$478$	2.41849	0.110619
$479$	−7.84405	−0.358404	−0.179202	−	0.983812i	$-0.557352\pi$
$479$	−7.84405	−0.358404	−0.179202	+	0.983812i	$0.557352\pi$
$480$	3.57419	0.163139
$481$	−47.0126	−2.14359
$482$	−3.14577	−0.143286
$483$	5.94397	0.270460
$484$	−10.9373	−0.497150
$485$	−14.6565	−0.665518
$486$	0.319268	0.0144823
$487$	5.32347	0.241230	0.120615	−	0.992699i	$-0.461513\pi$
$487$	5.32347	0.241230	0.120615	+	0.992699i	$0.461513\pi$
$488$	5.05745	0.228940
$489$	−15.0678	−0.681391
$490$	2.01464	0.0910120
$491$	−18.2609	−0.824103	−0.412051	−	0.911161i	$-0.635188\pi$
$491$	−18.2609	−0.824103	−0.412051	+	0.911161i	$0.635188\pi$
$492$	1.16044	0.0523168
$493$	−41.5785	−1.87260
$494$	6.20616	0.279228
$495$	−4.09418	−0.184020
$496$	25.4211	1.14144
$497$	−2.21098	−0.0991759
$498$	1.04820	0.0469711
$499$	−33.2713	−1.48943	−0.744713	−	0.667385i	$-0.767414\pi$
$499$	−33.2713	−1.48943	−0.744713	+	0.667385i	$0.767414\pi$
$500$	−1.89807	−0.0848842
$501$	0.206036	0.00920499
$502$	−6.42124	−0.286594
$503$	−16.8233	−0.750112	−0.375056	−	0.927002i	$-0.622377\pi$
$503$	−16.8233	−0.750112	−0.375056	+	0.927002i	$0.622377\pi$
$504$	1.03366	0.0460428
$505$	−11.6625	−0.518975
$506$	−9.35465	−0.415865
$507$	−3.29654	−0.146405
$508$	−18.5613	−0.823526
$509$	−22.0390	−0.976861	−0.488430	−	0.872603i	$-0.662430\pi$
$509$	−22.0390	−0.976861	−0.488430	+	0.872603i	$0.662430\pi$
$510$	1.51251	0.0669752
$511$	−7.71474	−0.341280
$512$	−20.6077	−0.910742
$513$	−4.81525	−0.212599
$514$	2.60819	0.115042
$515$	8.83498	0.389316
$516$	−4.74784	−0.209012
$517$	−5.05231	−0.222201
$518$	−3.08812	−0.135684
$519$	−5.61834	−0.246618
$520$	−5.02404	−0.220319
$521$	−38.3357	−1.67952	−0.839759	−	0.542959i	$-0.817304\pi$
$521$	−38.3357	−1.67952	−0.839759	+	0.542959i	$0.817304\pi$
$522$	2.80209	0.122644
$523$	10.4042	0.454945	0.227472	−	0.973785i	$-0.426954\pi$
$523$	10.4042	0.454945	0.227472	+	0.973785i	$0.426954\pi$
$524$	−24.2262	−1.05833
$525$	−0.830562	−0.0362487
$526$	3.59203	0.156620
$527$	35.4334	1.54350
$528$	13.9153	0.605585
$529$	28.2164	1.22680
$530$	−1.91095	−0.0830063
$531$	−4.67265	−0.202776
$532$	−7.59107	−0.329114
$533$	−2.46808	−0.106904
$534$	5.96271	0.258032
$535$	8.07270	0.349013
$536$	−0.0555096	−0.00239765
$537$	−3.49899	−0.150992
$538$	4.47926	0.193115
$539$	25.8350	1.11279
$540$	1.89807	0.0816798
$541$	−31.1403	−1.33883	−0.669413	−	0.742891i	$-0.733454\pi$
$541$	−31.1403	−1.33883	−0.669413	+	0.742891i	$0.733454\pi$
$542$	−4.02093	−0.172714
$543$	11.2656	0.483455
$544$	−16.9325	−0.725974
$545$	−0.798062	−0.0341852
$546$	−1.07047	−0.0458120
$547$	−15.0866	−0.645057	−0.322528	−	0.946560i	$-0.604533\pi$
$547$	−15.0866	−0.645057	−0.322528	+	0.946560i	$0.604533\pi$
$548$	−1.50472	−0.0642784
$549$	4.06374	0.173436
$550$	1.30714	0.0557368
$551$	−42.2615	−1.80040
$552$	8.90656	0.379088
$553$	−0.471275	−0.0200407
$554$	0.238803	0.0101458
$555$	−11.6457	−0.494334
$556$	−11.5062	−0.487971
$557$	8.86651	0.375686	0.187843	−	0.982199i	$-0.439850\pi$
$557$	8.86651	0.375686	0.187843	+	0.982199i	$0.439850\pi$
$558$	−2.38795	−0.101090
$559$	10.0979	0.427097
$560$	2.82291	0.119290
$561$	19.3959	0.818896
$562$	8.84251	0.372999
$563$	35.1151	1.47992	0.739962	−	0.672649i	$-0.234843\pi$
$563$	35.1151	1.47992	0.739962	+	0.672649i	$0.234843\pi$
$564$	2.34226	0.0986269
$565$	−17.1999	−0.723605
$566$	4.65824	0.195801
$567$	0.830562	0.0348803
$568$	−3.31297	−0.139009
$569$	15.6554	0.656307	0.328153	−	0.944624i	$-0.393574\pi$
$569$	15.6554	0.656307	0.328153	+	0.944624i	$0.393574\pi$
$570$	1.53736	0.0643928
$571$	−26.2755	−1.09960	−0.549798	−	0.835297i	$-0.685295\pi$
$571$	−26.2755	−1.09960	−0.549798	+	0.835297i	$0.685295\pi$
$572$	−31.3709	−1.31168
$573$	24.2035	1.01112
$574$	−0.162121	−0.00676680
$575$	−7.15657	−0.298449
$576$	−5.65647	−0.235686
$577$	33.8850	1.41065	0.705326	−	0.708883i	$-0.250801\pi$
$577$	33.8850	1.41065	0.705326	+	0.708883i	$0.250801\pi$
$578$	−1.73787	−0.0722857
$579$	15.2924	0.635529
$580$	16.6585	0.691709
$581$	2.72685	0.113129
$582$	−4.67936	−0.193966
$583$	−24.5053	−1.01491
$584$	−11.5599	−0.478352
$585$	−4.03690	−0.166905
$586$	1.49343	0.0616930
$587$	25.8562	1.06720	0.533600	−	0.845737i	$-0.320839\pi$
$587$	25.8562	1.06720	0.533600	+	0.845737i	$0.320839\pi$
$588$	−11.9771	−0.493928
$589$	36.0155	1.48399
$590$	1.49183	0.0614176
$591$	20.4242	0.840140
$592$	39.5815	1.62679
$593$	32.6329	1.34007	0.670036	−	0.742328i	$-0.266279\pi$
$593$	32.6329	1.34007	0.670036	+	0.742328i	$0.266279\pi$
$594$	−1.30714	−0.0536327
$595$	3.93473	0.161308
$596$	17.3415	0.710335
$597$	17.4784	0.715343
$598$	−9.22377	−0.377188
$599$	8.47845	0.346420	0.173210	−	0.984885i	$-0.444586\pi$
$599$	8.47845	0.346420	0.173210	+	0.984885i	$0.444586\pi$
$600$	−1.24453	−0.0508077
$601$	−9.77293	−0.398646	−0.199323	−	0.979934i	$-0.563874\pi$
$601$	−9.77293	−0.398646	−0.199323	+	0.979934i	$0.563874\pi$
$602$	0.663303	0.0270342
$603$	−0.0446029	−0.00181637
$604$	−39.1214	−1.59183
$605$	5.76233	0.234272
$606$	−3.72347	−0.151256
$607$	−12.6129	−0.511940	−0.255970	−	0.966685i	$-0.582395\pi$
$607$	−12.6129	−0.511940	−0.255970	+	0.966685i	$0.582395\pi$
$608$	−17.2106	−0.697983
$609$	7.28949	0.295385
$610$	−1.29742	−0.0525312
$611$	−4.98162	−0.201535
$612$	−8.99197	−0.363479
$613$	−42.3368	−1.70997	−0.854983	−	0.518657i	$-0.826432\pi$
$613$	−42.3368	−1.70997	−0.854983	+	0.518657i	$0.826432\pi$
$614$	1.35733	0.0547774
$615$	−0.611381	−0.0246533
$616$	−4.23199	−0.170512
$617$	−17.8070	−0.716884	−0.358442	−	0.933552i	$-0.616692\pi$
$617$	−17.8070	−0.716884	−0.358442	+	0.933552i	$0.616692\pi$
$618$	2.82073	0.113466
$619$	1.45609	0.0585254	0.0292627	−	0.999572i	$-0.490684\pi$
$619$	1.45609	0.0585254	0.0292627	+	0.999572i	$0.490684\pi$
$620$	−14.1965	−0.570146
$621$	7.15657	0.287183
$622$	7.93957	0.318348
$623$	15.5117	0.621464
$624$	13.7206	0.549263
$625$	1.00000	0.0400000
$626$	5.81202	0.232295
$627$	19.7145	0.787322
$628$	14.2627	0.569145
$629$	55.1709	2.19981
$630$	−0.265172	−0.0105647
$631$	−14.7912	−0.588827	−0.294414	−	0.955678i	$-0.595124\pi$
$631$	−14.7912	−0.588827	−0.294414	+	0.955678i	$0.595124\pi$
$632$	−0.706168	−0.0280898
$633$	6.54142	0.259998
$634$	0.826581	0.0328277
$635$	9.77907	0.388070
$636$	11.3607	0.450481
$637$	25.4735	1.00930
$638$	−11.4722	−0.454191
$639$	−2.66203	−0.105308
$640$	8.95431	0.353950
$641$	−36.9403	−1.45905	−0.729527	−	0.683952i	$-0.760260\pi$
$641$	−36.9403	−1.45905	−0.729527	+	0.683952i	$0.760260\pi$
$642$	2.57736	0.101720
$643$	25.9220	1.02226	0.511132	−	0.859502i	$-0.329226\pi$
$643$	25.9220	1.02226	0.511132	+	0.859502i	$0.329226\pi$
$644$	11.2821	0.444575
$645$	2.50141	0.0984928
$646$	−7.28313	−0.286551
$647$	34.9523	1.37412	0.687058	−	0.726602i	$-0.258902\pi$
$647$	34.9523	1.37412	0.687058	+	0.726602i	$0.258902\pi$
$648$	1.24453	0.0488897
$649$	19.1307	0.750944
$650$	1.28885	0.0505530
$651$	−6.21215	−0.243473
$652$	−28.5998	−1.12005
$653$	6.34495	0.248297	0.124149	−	0.992264i	$-0.460380\pi$
$653$	6.34495	0.248297	0.124149	+	0.992264i	$0.460380\pi$
$654$	−0.254796	−0.00996331
$655$	12.7636	0.498716
$656$	2.07796	0.0811307
$657$	−9.28858	−0.362382
$658$	−0.327228	−0.0127567
$659$	5.63342	0.219447	0.109723	−	0.993962i	$-0.465004\pi$
$659$	5.63342	0.219447	0.109723	+	0.993962i	$0.465004\pi$
$660$	−7.77104	−0.302487
$661$	−46.3173	−1.80153	−0.900766	−	0.434304i	$-0.856994\pi$
$661$	−46.3173	−1.80153	−0.900766	+	0.434304i	$0.856994\pi$
$662$	6.51569	0.253240
$663$	19.1245	0.742735
$664$	4.08597	0.158566
$665$	3.99936	0.155089
$666$	−3.71811	−0.144074
$667$	62.8102	2.43202
$668$	0.391070	0.0151309
$669$	21.4831	0.830586
$670$	0.0142403	0.000550150 0
$671$	−16.6377	−0.642292
$672$	2.96858	0.114516
$673$	−14.0192	−0.540400	−0.270200	−	0.962804i	$-0.587090\pi$
$673$	−14.0192	−0.540400	−0.270200	+	0.962804i	$0.587090\pi$
$674$	3.69944	0.142497
$675$	−1.00000	−0.0384900
$676$	−6.25706	−0.240656
$677$	27.5911	1.06041	0.530205	−	0.847869i	$-0.322115\pi$
$677$	27.5911	1.06041	0.530205	+	0.847869i	$0.322115\pi$
$678$	−5.49138	−0.210895
$679$	−12.1731	−0.467162
$680$	5.89588	0.226097
$681$	−17.4304	−0.667935
$682$	9.77672	0.374370
$683$	46.3585	1.77386	0.886928	−	0.461907i	$-0.152835\pi$
$683$	46.3585	1.77386	0.886928	+	0.461907i	$0.152835\pi$
$684$	−9.13968	−0.349464
$685$	0.792763	0.0302899
$686$	3.52948	0.134756
$687$	−4.99561	−0.190594
$688$	−8.50178	−0.324127
$689$	−24.1624	−0.920516
$690$	−2.28487	−0.0869833
$691$	30.2762	1.15176	0.575881	−	0.817534i	$-0.304659\pi$
$691$	30.2762	1.15176	0.575881	+	0.817534i	$0.304659\pi$
$692$	−10.6640	−0.405384
$693$	−3.40047	−0.129173
$694$	8.34521	0.316780
$695$	6.06206	0.229947
$696$	10.9227	0.414025
$697$	2.89638	0.109708
$698$	−2.48305	−0.0939847
$699$	−3.77667	−0.142847
$700$	−1.57646	−0.0595847
$701$	−46.6610	−1.76236	−0.881181	−	0.472779i	$-0.843251\pi$
$701$	−46.6610	−1.76236	−0.881181	+	0.472779i	$0.843251\pi$
$702$	−1.28885	−0.0486446
$703$	56.0771	2.11499
$704$	23.1586	0.872823
$705$	−1.23402	−0.0464760
$706$	5.18658	0.195200
$707$	−9.68644	−0.364296
$708$	−8.86900	−0.333317
$709$	−27.5476	−1.03457	−0.517287	−	0.855812i	$-0.673058\pi$
$709$	−27.5476	−1.03457	−0.517287	+	0.855812i	$0.673058\pi$
$710$	0.849901	0.0318962
$711$	−0.567417	−0.0212798
$712$	23.2430	0.871070
$713$	−53.5272	−2.00461
$714$	1.25623	0.0470134
$715$	16.5278	0.618105
$716$	−6.64132	−0.248198
$717$	7.57510	0.282897
$718$	9.37476	0.349863
$719$	32.9773	1.22984	0.614922	−	0.788588i	$-0.289187\pi$
$719$	32.9773	1.22984	0.614922	+	0.788588i	$0.289187\pi$
$720$	3.39880	0.126666
$721$	7.33799	0.273281
$722$	−1.33667	−0.0497457
$723$	−9.85305	−0.366439
$724$	21.3830	0.794692
$725$	−8.77658	−0.325954
$726$	1.83973	0.0682788
$727$	39.2331	1.45507	0.727537	−	0.686069i	$-0.240665\pi$
$727$	39.2331	1.45507	0.727537	+	0.686069i	$0.240665\pi$
$728$	−4.17277	−0.154653
$729$	1.00000	0.0370370
$730$	2.96555	0.109760
$731$	−11.8503	−0.438297
$732$	7.71326	0.285090
$733$	38.8243	1.43401	0.717004	−	0.697069i	$-0.245513\pi$
$733$	38.8243	1.43401	0.717004	+	0.697069i	$0.245513\pi$
$734$	−2.16691	−0.0799820
$735$	6.31017	0.232754
$736$	25.5789	0.942851
$737$	0.182612	0.00672661
$738$	−0.195195	−0.00718521
$739$	−51.2469	−1.88515	−0.942574	−	0.333998i	$-0.891602\pi$
$739$	−51.2469	−1.88515	−0.942574	+	0.333998i	$0.891602\pi$
$740$	−22.1044	−0.812573
$741$	19.4387	0.714098
$742$	−1.58716	−0.0582665
$743$	10.4503	0.383384	0.191692	−	0.981455i	$-0.438603\pi$
$743$	10.4503	0.383384	0.191692	+	0.981455i	$0.438603\pi$
$744$	−9.30840	−0.341263
$745$	−9.13639	−0.334731
$746$	−6.76871	−0.247820
$747$	3.28314	0.120124
$748$	36.8148	1.34608
$749$	6.70488	0.244991
$750$	0.319268	0.0116580
$751$	24.7519	0.903211	0.451605	−	0.892218i	$-0.350852\pi$
$751$	24.7519	0.903211	0.451605	+	0.892218i	$0.350852\pi$
$752$	4.19419	0.152946
$753$	−20.1124	−0.732935
$754$	−11.3117	−0.411949
$755$	20.6111	0.750117
$756$	1.57646	0.0573354
$757$	−7.45003	−0.270776	−0.135388	−	0.990793i	$-0.543228\pi$
$757$	−7.45003	−0.270776	−0.135388	+	0.990793i	$0.543228\pi$
$758$	3.30111	0.119902
$759$	−29.3003	−1.06353
$760$	5.99273	0.217379
$761$	−38.2835	−1.38778	−0.693889	−	0.720082i	$-0.744104\pi$
$761$	−38.2835	−1.38778	−0.693889	+	0.720082i	$0.744104\pi$
$762$	3.12215	0.113103
$763$	−0.662840	−0.0239964
$764$	45.9399	1.66205
$765$	4.73743	0.171282
$766$	−8.79688	−0.317844
$767$	18.8630	0.681103
$768$	−8.45411	−0.305061
$769$	26.0007	0.937611	0.468805	−	0.883301i	$-0.344685\pi$
$769$	26.0007	0.937611	0.468805	+	0.883301i	$0.344685\pi$
$770$	1.08566	0.0391246
$771$	8.16926	0.294209
$772$	29.0260	1.04467
$773$	−20.8763	−0.750869	−0.375434	−	0.926849i	$-0.622506\pi$
$773$	−20.8763	−0.750869	−0.375434	+	0.926849i	$0.622506\pi$
$774$	0.798620	0.0287058
$775$	7.47946	0.268670
$776$	−18.2405	−0.654794
$777$	−9.67250	−0.346999
$778$	−7.30209	−0.261793
$779$	2.94395	0.105478
$780$	−7.66231	−0.274355
$781$	10.8988	0.389990
$782$	10.8244	0.387080
$783$	8.77658	0.313649
$784$	−21.4470	−0.765963
$785$	−7.51435	−0.268199
$786$	4.07502	0.145351
$787$	1.59505	0.0568576	0.0284288	−	0.999596i	$-0.490950\pi$
$787$	1.59505	0.0568576	0.0284288	+	0.999596i	$0.490950\pi$
$788$	38.7666	1.38100
$789$	11.2508	0.400540
$790$	0.181158	0.00644533
$791$	−14.2856	−0.507936
$792$	−5.09533	−0.181055
$793$	−16.4049	−0.582556
$794$	−8.16502	−0.289766
$795$	−5.98540	−0.212280
$796$	33.1752	1.17586
$797$	−14.7333	−0.521879	−0.260940	−	0.965355i	$-0.584032\pi$
$797$	−14.7333	−0.521879	−0.260940	+	0.965355i	$0.584032\pi$
$798$	1.27687	0.0452007
$799$	5.84610	0.206820
$800$	−3.57419	−0.126367
$801$	18.6762	0.659890
$802$	−0.319268	−0.0112738
$803$	38.0291	1.34202
$804$	−0.0846592	−0.00298570
$805$	−5.94397	−0.209497
$806$	9.63992	0.339552
$807$	14.0298	0.493872
$808$	−14.5144	−0.510613
$809$	−20.3065	−0.713938	−0.356969	−	0.934116i	$-0.616190\pi$
$809$	−20.3065	−0.713938	−0.356969	+	0.934116i	$0.616190\pi$
$810$	−0.319268	−0.0112179
$811$	36.1942	1.27095	0.635475	−	0.772121i	$-0.280804\pi$
$811$	36.1942	1.27095	0.635475	+	0.772121i	$0.280804\pi$
$812$	13.8360	0.485547
$813$	−12.5942	−0.441697
$814$	15.2226	0.533553
$815$	15.0678	0.527803
$816$	−16.1016	−0.563668
$817$	−12.0449	−0.421398
$818$	−11.3503	−0.396853
$819$	−3.35289	−0.117160
$820$	−1.16044	−0.0405244
$821$	−33.9059	−1.18333	−0.591663	−	0.806186i	$-0.701528\pi$
$821$	−33.9059	−1.18333	−0.591663	+	0.806186i	$0.701528\pi$
$822$	0.253104	0.00882802
$823$	46.1534	1.60881	0.804403	−	0.594085i	$-0.202486\pi$
$823$	46.1534	1.60881	0.804403	+	0.594085i	$0.202486\pi$
$824$	10.9954	0.383043
$825$	4.09418	0.142541
$826$	1.23906	0.0431122
$827$	−0.176284	−0.00612999	−0.00306500	−	0.999995i	$-0.500976\pi$
$827$	−0.176284	−0.00612999	−0.00306500	+	0.999995i	$0.500976\pi$
$828$	13.5836	0.472064
$829$	32.8128	1.13964	0.569818	−	0.821771i	$-0.307014\pi$
$829$	32.8128	1.13964	0.569818	+	0.821771i	$0.307014\pi$
$830$	−1.04820	−0.0363837
$831$	0.747970	0.0259468
$832$	22.8346	0.791647
$833$	−29.8940	−1.03577
$834$	1.93542	0.0670182
$835$	−0.206036	−0.00713016
$836$	37.4195	1.29418
$837$	−7.47946	−0.258528
$838$	4.67800	0.161599
$839$	13.0791	0.451542	0.225771	−	0.974180i	$-0.427510\pi$
$839$	13.0791	0.451542	0.225771	+	0.974180i	$0.427510\pi$
$840$	−1.03366	−0.0356646
$841$	48.0284	1.65615
$842$	0.815673	0.0281099
$843$	27.6962	0.953907
$844$	12.4160	0.427378
$845$	3.29654	0.113405
$846$	−0.393984	−0.0135455
$847$	4.78597	0.164448
$848$	20.3431	0.698587
$849$	14.5904	0.500740
$850$	−1.51251	−0.0518788
$851$	−83.3434	−2.85698
$852$	−5.05271	−0.173103
$853$	−7.89267	−0.270240	−0.135120	−	0.990829i	$-0.543142\pi$
$853$	−7.89267	−0.270240	−0.135120	+	0.990829i	$0.543142\pi$
$854$	−1.07759	−0.0368744
$855$	4.81525	0.164678
$856$	10.0467	0.343390
$857$	−32.2239	−1.10075	−0.550373	−	0.834919i	$-0.685514\pi$
$857$	−32.2239	−1.10075	−0.550373	+	0.834919i	$0.685514\pi$
$858$	5.27680	0.180147
$859$	−15.8042	−0.539232	−0.269616	−	0.962968i	$-0.586897\pi$
$859$	−15.8042	−0.539232	−0.269616	+	0.962968i	$0.586897\pi$
$860$	4.74784	0.161900
$861$	−0.507790	−0.0173054
$862$	13.0244	0.443612
$863$	−14.5564	−0.495507	−0.247753	−	0.968823i	$-0.579692\pi$
$863$	−14.5564	−0.495507	−0.247753	+	0.968823i	$0.579692\pi$
$864$	3.57419	0.121596
$865$	5.61834	0.191029
$866$	0.596114	0.0202568
$867$	−5.44327	−0.184863
$868$	−11.7911	−0.400215
$869$	2.32311	0.0788061
$870$	−2.80209	−0.0949996
$871$	0.180057	0.00610100
$872$	−0.993212	−0.0336344
$873$	−14.6565	−0.496048
$874$	11.0022	0.372155
$875$	0.830562	0.0280781
$876$	−17.6303	−0.595674
$877$	44.0641	1.48794	0.743970	−	0.668213i	$-0.232941\pi$
$877$	44.0641	1.48794	0.743970	+	0.668213i	$0.232941\pi$
$878$	4.16071	0.140417
$879$	4.67766	0.157774
$880$	−13.9153	−0.469084
$881$	54.4002	1.83279	0.916395	−	0.400275i	$-0.131085\pi$
$881$	54.4002	1.83279	0.916395	+	0.400275i	$0.131085\pi$
$882$	2.01464	0.0678363
$883$	−8.24344	−0.277414	−0.138707	−	0.990333i	$-0.544295\pi$
$883$	−8.24344	−0.277414	−0.138707	+	0.990333i	$0.544295\pi$
$884$	36.2997	1.22089
$885$	4.67265	0.157069
$886$	6.87324	0.230911
$887$	20.6953	0.694880	0.347440	−	0.937702i	$-0.387051\pi$
$887$	20.6953	0.694880	0.347440	+	0.937702i	$0.387051\pi$
$888$	−14.4935	−0.486369
$889$	8.12212	0.272407
$890$	−5.96271	−0.199871
$891$	−4.09418	−0.137160
$892$	40.7764	1.36530
$893$	5.94213	0.198846
$894$	−2.91696	−0.0975577
$895$	3.49899	0.116958
$896$	7.43710	0.248456
$897$	−28.8903	−0.964620
$898$	11.2264	0.374629
$899$	−65.6441	−2.18935
$900$	−1.89807	−0.0632689
$901$	28.3554	0.944656
$902$	0.799162	0.0266092
$903$	2.07757	0.0691373
$904$	−21.4058	−0.711945
$905$	−11.2656	−0.374483
$906$	6.58049	0.218622
$907$	43.4417	1.44246	0.721230	−	0.692696i	$-0.243577\pi$
$907$	43.4417	1.44246	0.721230	+	0.692696i	$0.243577\pi$
$908$	−33.0841	−1.09793
$909$	−11.6625	−0.386821
$910$	1.07047	0.0354858
$911$	13.9697	0.462836	0.231418	−	0.972854i	$-0.425663\pi$
$911$	13.9697	0.462836	0.231418	+	0.972854i	$0.425663\pi$
$912$	−16.3661	−0.541935
$913$	−13.4418	−0.444858
$914$	9.34437	0.309084
$915$	−4.06374	−0.134343
$916$	−9.48200	−0.313294
$917$	10.6010	0.350075
$918$	1.51251	0.0499204
$919$	−11.4889	−0.378983	−0.189492	−	0.981882i	$-0.560684\pi$
$919$	−11.4889	−0.378983	−0.189492	+	0.981882i	$0.560684\pi$
$920$	−8.90656	−0.293641
$921$	4.25138	0.140088
$922$	−3.45828	−0.113893
$923$	10.7463	0.353720
$924$	−6.45432	−0.212332
$925$	11.6457	0.382909
$926$	4.30361	0.141425
$927$	8.83498	0.290179
$928$	31.3692	1.02974
$929$	34.0887	1.11841	0.559207	−	0.829028i	$-0.311106\pi$
$929$	34.0887	1.11841	0.559207	+	0.829028i	$0.311106\pi$
$930$	2.38795	0.0783041
$931$	−30.3851	−0.995830
$932$	−7.16838	−0.234808
$933$	24.8680	0.814142
$934$	3.98922	0.130531
$935$	−19.3959	−0.634314
$936$	−5.02404	−0.164216
$937$	44.8806	1.46619	0.733093	−	0.680129i	$-0.238076\pi$
$937$	44.8806	1.46619	0.733093	+	0.680129i	$0.238076\pi$
$938$	0.0118274	0.000386179 0
$939$	18.2042	0.594071
$940$	−2.34226	−0.0763961
$941$	−39.0480	−1.27293	−0.636464	−	0.771307i	$-0.719604\pi$
$941$	−39.0480	−1.27293	−0.636464	+	0.771307i	$0.719604\pi$
$942$	−2.39909	−0.0781667
$943$	−4.37539	−0.142482
$944$	−15.8814	−0.516895
$945$	−0.830562	−0.0270182
$946$	−3.26970	−0.106307
$947$	−38.7041	−1.25771	−0.628857	−	0.777521i	$-0.716477\pi$
$947$	−38.7041	−1.25771	−0.628857	+	0.777521i	$0.716477\pi$
$948$	−1.07700	−0.0349792
$949$	37.4970	1.21721
$950$	−1.53736	−0.0498785
$951$	2.58899	0.0839536
$952$	4.89689	0.158709
$953$	−32.8925	−1.06549	−0.532746	−	0.846275i	$-0.678840\pi$
$953$	−32.8925	−1.06549	−0.532746	+	0.846275i	$0.678840\pi$
$954$	−1.91095	−0.0618692
$955$	−24.2035	−0.783207
$956$	14.3780	0.465019
$957$	−35.9329	−1.16155
$958$	2.50436	0.0809121
$959$	0.658439	0.0212621
$960$	5.65647	0.182562
$961$	24.9423	0.804589
$962$	15.0096	0.483930
$963$	8.07270	0.260139
$964$	−18.7018	−0.602343
$965$	−15.2924	−0.492279
$966$	−1.89772	−0.0610582
$967$	−34.5567	−1.11127	−0.555635	−	0.831427i	$-0.687525\pi$
$967$	−34.5567	−1.11127	−0.555635	+	0.831427i	$0.687525\pi$
$968$	7.17139	0.230497
$969$	−22.8119	−0.732825
$970$	4.67936	0.150245
$971$	−23.0713	−0.740395	−0.370197	−	0.928953i	$-0.620710\pi$
$971$	−23.0713	−0.740395	−0.370197	+	0.928953i	$0.620710\pi$
$972$	1.89807	0.0608806
$973$	5.03491	0.161412
$974$	−1.69962	−0.0544592
$975$	4.03690	0.129284
$976$	13.8118	0.442106
$977$	8.91407	0.285186	0.142593	−	0.989781i	$-0.454456\pi$
$977$	8.91407	0.285186	0.142593	+	0.989781i	$0.454456\pi$
$978$	4.81068	0.153829
$979$	−76.4636	−2.44379
$980$	11.9771	0.382595
$981$	−0.798062	−0.0254802
$982$	5.83013	0.186047
$983$	−24.6132	−0.785040	−0.392520	−	0.919744i	$-0.628397\pi$
$983$	−24.6132	−0.785040	−0.392520	+	0.919744i	$0.628397\pi$
$984$	−0.760882	−0.0242560
$985$	−20.4242	−0.650770
$986$	13.2747	0.422752
$987$	−1.02493	−0.0326239
$988$	36.8959	1.17382
$989$	17.9015	0.569234
$990$	1.30714	0.0415437
$991$	12.2445	0.388959	0.194480	−	0.980907i	$-0.437698\pi$
$991$	12.2445	0.388959	0.194480	+	0.980907i	$0.437698\pi$
$992$	−26.7330	−0.848773
$993$	20.4082	0.647635
$994$	0.705895	0.0223896
$995$	−17.4784	−0.554102
$996$	6.23163	0.197457
$997$	43.3820	1.37392	0.686961	−	0.726694i	$-0.258944\pi$
$997$	43.3820	1.37392	0.686961	+	0.726694i	$0.258944\pi$
$998$	10.6225	0.336248
$999$	−11.6457	−0.368455

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.d.1.13	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.d.1.13	✓	29	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.319268 q^{2} -1.00000 q^{3} -1.89807 q^{4} +1.00000 q^{5} +0.319268 q^{6} +0.830562 q^{7} +1.24453 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.319268 q^{2} -1.00000 q^{3} -1.89807 q^{4} +1.00000 q^{5} +0.319268 q^{6} +0.830562 q^{7} +1.24453 q^{8} +1.00000 q^{9} -0.319268 q^{10} -4.09418 q^{11} +1.89807 q^{12} -4.03690 q^{13} -0.265172 q^{14} -1.00000 q^{15} +3.39880 q^{16} +4.73743 q^{17} -0.319268 q^{18} +4.81525 q^{19} -1.89807 q^{20} -0.830562 q^{21} +1.30714 q^{22} -7.15657 q^{23} -1.24453 q^{24} +1.00000 q^{25} +1.28885 q^{26} -1.00000 q^{27} -1.57646 q^{28} -8.77658 q^{29} +0.319268 q^{30} +7.47946 q^{31} -3.57419 q^{32} +4.09418 q^{33} -1.51251 q^{34} +0.830562 q^{35} -1.89807 q^{36} +11.6457 q^{37} -1.53736 q^{38} +4.03690 q^{39} +1.24453 q^{40} +0.611381 q^{41} +0.265172 q^{42} -2.50141 q^{43} +7.77104 q^{44} +1.00000 q^{45} +2.28487 q^{46} +1.23402 q^{47} -3.39880 q^{48} -6.31017 q^{49} -0.319268 q^{50} -4.73743 q^{51} +7.66231 q^{52} +5.98540 q^{53} +0.319268 q^{54} -4.09418 q^{55} +1.03366 q^{56} -4.81525 q^{57} +2.80209 q^{58} -4.67265 q^{59} +1.89807 q^{60} +4.06374 q^{61} -2.38795 q^{62} +0.830562 q^{63} -5.65647 q^{64} -4.03690 q^{65} -1.30714 q^{66} -0.0446029 q^{67} -8.99197 q^{68} +7.15657 q^{69} -0.265172 q^{70} -2.66203 q^{71} +1.24453 q^{72} -9.28858 q^{73} -3.71811 q^{74} -1.00000 q^{75} -9.13968 q^{76} -3.40047 q^{77} -1.28885 q^{78} -0.567417 q^{79} +3.39880 q^{80} +1.00000 q^{81} -0.195195 q^{82} +3.28314 q^{83} +1.57646 q^{84} +4.73743 q^{85} +0.798620 q^{86} +8.77658 q^{87} -5.09533 q^{88} +18.6762 q^{89} -0.319268 q^{90} -3.35289 q^{91} +13.5836 q^{92} -7.47946 q^{93} -0.393984 q^{94} +4.81525 q^{95} +3.57419 q^{96} -14.6565 q^{97} +2.01464 q^{98} -4.09418 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * q^99

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