LMFDB - Embedded newform 6015.2.a.b.1.17

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:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q+1.02584 q^{2} +1.00000 q^{3} -0.947645 q^{4} +1.00000 q^{5} +1.02584 q^{6} +0.748026 q^{7} -3.02382 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.02584 q^{2} +1.00000 q^{3} -0.947645 q^{4} +1.00000 q^{5} +1.02584 q^{6} +0.748026 q^{7} -3.02382 q^{8} +1.00000 q^{9} +1.02584 q^{10} -1.00435 q^{11} -0.947645 q^{12} -5.81603 q^{13} +0.767357 q^{14} +1.00000 q^{15} -1.20668 q^{16} +6.14432 q^{17} +1.02584 q^{18} -2.92500 q^{19} -0.947645 q^{20} +0.748026 q^{21} -1.03031 q^{22} -0.823418 q^{23} -3.02382 q^{24} +1.00000 q^{25} -5.96633 q^{26} +1.00000 q^{27} -0.708863 q^{28} -0.995609 q^{29} +1.02584 q^{30} -0.390326 q^{31} +4.80978 q^{32} -1.00435 q^{33} +6.30311 q^{34} +0.748026 q^{35} -0.947645 q^{36} +2.17309 q^{37} -3.00060 q^{38} -5.81603 q^{39} -3.02382 q^{40} +2.10191 q^{41} +0.767357 q^{42} -6.36882 q^{43} +0.951767 q^{44} +1.00000 q^{45} -0.844698 q^{46} -10.7884 q^{47} -1.20668 q^{48} -6.44046 q^{49} +1.02584 q^{50} +6.14432 q^{51} +5.51153 q^{52} -7.05171 q^{53} +1.02584 q^{54} -1.00435 q^{55} -2.26190 q^{56} -2.92500 q^{57} -1.02134 q^{58} -10.3898 q^{59} -0.947645 q^{60} +9.39075 q^{61} -0.400413 q^{62} +0.748026 q^{63} +7.34744 q^{64} -5.81603 q^{65} -1.03031 q^{66} +7.10786 q^{67} -5.82263 q^{68} -0.823418 q^{69} +0.767357 q^{70} -7.23069 q^{71} -3.02382 q^{72} +3.76938 q^{73} +2.22925 q^{74} +1.00000 q^{75} +2.77187 q^{76} -0.751279 q^{77} -5.96633 q^{78} +2.43750 q^{79} -1.20668 q^{80} +1.00000 q^{81} +2.15623 q^{82} -4.13397 q^{83} -0.708863 q^{84} +6.14432 q^{85} -6.53341 q^{86} -0.995609 q^{87} +3.03698 q^{88} -13.7319 q^{89} +1.02584 q^{90} -4.35054 q^{91} +0.780309 q^{92} -0.390326 q^{93} -11.0672 q^{94} -2.92500 q^{95} +4.80978 q^{96} -17.1458 q^{97} -6.60690 q^{98} -1.00435 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) $ 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * 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 $

$2$	1.02584	0.725381	0.362690	−	0.931910i	$-0.381858\pi$
$2$	1.02584	0.725381	0.362690	+	0.931910i	$0.381858\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.947645	−0.473823
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.02584	0.418799
$7$	0.748026	0.282727	0.141364	−	0.989958i	$-0.454851\pi$
$7$	0.748026	0.282727	0.141364	+	0.989958i	$0.454851\pi$
$8$	−3.02382	−1.06908
$9$	1.00000	0.333333
$10$	1.02584	0.324400
$11$	−1.00435	−0.302823	−0.151411	−	0.988471i	$-0.548382\pi$
$11$	−1.00435	−0.302823	−0.151411	+	0.988471i	$0.548382\pi$
$12$	−0.947645	−0.273562
$13$	−5.81603	−1.61308	−0.806538	−	0.591182i	$-0.798661\pi$
$13$	−5.81603	−1.61308	−0.806538	+	0.591182i	$0.798661\pi$
$14$	0.767357	0.205085
$15$	1.00000	0.258199
$16$	−1.20668	−0.301669
$17$	6.14432	1.49022	0.745108	−	0.666944i	$-0.232398\pi$
$17$	6.14432	1.49022	0.745108	+	0.666944i	$0.232398\pi$
$18$	1.02584	0.241794
$19$	−2.92500	−0.671042	−0.335521	−	0.942033i	$-0.608912\pi$
$19$	−2.92500	−0.671042	−0.335521	+	0.942033i	$0.608912\pi$
$20$	−0.947645	−0.211900
$21$	0.748026	0.163233
$22$	−1.03031	−0.219662
$23$	−0.823418	−0.171695	−0.0858473	−	0.996308i	$-0.527360\pi$
$23$	−0.823418	−0.171695	−0.0858473	+	0.996308i	$0.527360\pi$
$24$	−3.02382	−0.617235
$25$	1.00000	0.200000
$26$	−5.96633	−1.17009
$27$	1.00000	0.192450
$28$	−0.708863	−0.133963
$29$	−0.995609	−0.184880	−0.0924400	−	0.995718i	$-0.529467\pi$
$29$	−0.995609	−0.184880	−0.0924400	+	0.995718i	$0.529467\pi$
$30$	1.02584	0.187293
$31$	−0.390326	−0.0701046	−0.0350523	−	0.999385i	$-0.511160\pi$
$31$	−0.390326	−0.0701046	−0.0350523	+	0.999385i	$0.511160\pi$
$32$	4.80978	0.850257
$33$	−1.00435	−0.174835
$34$	6.30311	1.08097
$35$	0.748026	0.126439
$36$	−0.947645	−0.157941
$37$	2.17309	0.357254	0.178627	−	0.983917i	$-0.442834\pi$
$37$	2.17309	0.357254	0.178627	+	0.983917i	$0.442834\pi$
$38$	−3.00060	−0.486761
$39$	−5.81603	−0.931310
$40$	−3.02382	−0.478108
$41$	2.10191	0.328263	0.164132	−	0.986438i	$-0.447518\pi$
$41$	2.10191	0.328263	0.164132	+	0.986438i	$0.447518\pi$
$42$	0.767357	0.118406
$43$	−6.36882	−0.971236	−0.485618	−	0.874171i	$-0.661405\pi$
$43$	−6.36882	−0.971236	−0.485618	+	0.874171i	$0.661405\pi$
$44$	0.951767	0.143484
$45$	1.00000	0.149071
$46$	−0.844698	−0.124544
$47$	−10.7884	−1.57365	−0.786827	−	0.617174i	$-0.788278\pi$
$47$	−10.7884	−1.57365	−0.786827	+	0.617174i	$0.788278\pi$
$48$	−1.20668	−0.174169
$49$	−6.44046	−0.920065
$50$	1.02584	0.145076
$51$	6.14432	0.860377
$52$	5.51153	0.764312
$53$	−7.05171	−0.968627	−0.484313	−	0.874895i	$-0.660931\pi$
$53$	−7.05171	−0.968627	−0.484313	+	0.874895i	$0.660931\pi$
$54$	1.02584	0.139600
$55$	−1.00435	−0.135426
$56$	−2.26190	−0.302259
$57$	−2.92500	−0.387426
$58$	−1.02134	−0.134108
$59$	−10.3898	−1.35264	−0.676318	−	0.736610i	$-0.736426\pi$
$59$	−10.3898	−1.35264	−0.676318	+	0.736610i	$0.736426\pi$
$60$	−0.947645	−0.122340
$61$	9.39075	1.20236	0.601181	−	0.799113i	$-0.294697\pi$
$61$	9.39075	1.20236	0.601181	+	0.799113i	$0.294697\pi$
$62$	−0.400413	−0.0508526
$63$	0.748026	0.0942424
$64$	7.34744	0.918430
$65$	−5.81603	−0.721389
$66$	−1.03031	−0.126822
$67$	7.10786	0.868364	0.434182	−	0.900825i	$-0.357038\pi$
$67$	7.10786	0.868364	0.434182	+	0.900825i	$0.357038\pi$
$68$	−5.82263	−0.706098
$69$	−0.823418	−0.0991279
$70$	0.767357	0.0917167
$71$	−7.23069	−0.858125	−0.429062	−	0.903275i	$-0.641156\pi$
$71$	−7.23069	−0.858125	−0.429062	+	0.903275i	$0.641156\pi$
$72$	−3.02382	−0.356361
$73$	3.76938	0.441173	0.220586	−	0.975367i	$-0.429203\pi$
$73$	3.76938	0.441173	0.220586	+	0.975367i	$0.429203\pi$
$74$	2.22925	0.259145
$75$	1.00000	0.115470
$76$	2.77187	0.317955
$77$	−0.751279	−0.0856162
$78$	−5.96633	−0.675554
$79$	2.43750	0.274240	0.137120	−	0.990554i	$-0.456215\pi$
$79$	2.43750	0.274240	0.137120	+	0.990554i	$0.456215\pi$
$80$	−1.20668	−0.134911
$81$	1.00000	0.111111
$82$	2.15623	0.238116
$83$	−4.13397	−0.453762	−0.226881	−	0.973922i	$-0.572853\pi$
$83$	−4.13397	−0.453762	−0.226881	+	0.973922i	$0.572853\pi$
$84$	−0.708863	−0.0773433
$85$	6.14432	0.666445
$86$	−6.53341	−0.704516
$87$	−0.995609	−0.106741
$88$	3.03698	0.323743
$89$	−13.7319	−1.45558	−0.727788	−	0.685802i	$-0.759452\pi$
$89$	−13.7319	−1.45558	−0.727788	+	0.685802i	$0.759452\pi$
$90$	1.02584	0.108133
$91$	−4.35054	−0.456060
$92$	0.780309	0.0813528
$93$	−0.390326	−0.0404749
$94$	−11.0672	−1.14150
$95$	−2.92500	−0.300099
$96$	4.80978	0.490896
$97$	−17.1458	−1.74089	−0.870447	−	0.492261i	$-0.836170\pi$
$97$	−17.1458	−1.74089	−0.870447	+	0.492261i	$0.836170\pi$
$98$	−6.60690	−0.667398
$99$	−1.00435	−0.100941
$100$	−0.947645	−0.0947645
$101$	7.20269	0.716694	0.358347	−	0.933588i	$-0.383340\pi$
$101$	7.20269	0.716694	0.358347	+	0.933588i	$0.383340\pi$
$102$	6.30311	0.624101
$103$	5.16172	0.508599	0.254300	−	0.967125i	$-0.418155\pi$
$103$	5.16172	0.508599	0.254300	+	0.967125i	$0.418155\pi$
$104$	17.5866	1.72451
$105$	0.748026	0.0729998
$106$	−7.23395	−0.702623
$107$	3.14470	0.304010	0.152005	−	0.988380i	$-0.451427\pi$
$107$	3.14470	0.304010	0.152005	+	0.988380i	$0.451427\pi$
$108$	−0.947645	−0.0911872
$109$	−17.3945	−1.66609	−0.833047	−	0.553203i	$-0.813405\pi$
$109$	−17.3945	−1.66609	−0.833047	+	0.553203i	$0.813405\pi$
$110$	−1.03031	−0.0982358
$111$	2.17309	0.206261
$112$	−0.902626	−0.0852901
$113$	−19.7693	−1.85974	−0.929868	−	0.367892i	$-0.880080\pi$
$113$	−19.7693	−1.85974	−0.929868	+	0.367892i	$0.880080\pi$
$114$	−3.00060	−0.281032
$115$	−0.823418	−0.0767842
$116$	0.943485	0.0876003
$117$	−5.81603	−0.537692
$118$	−10.6583	−0.981177
$119$	4.59611	0.421324
$120$	−3.02382	−0.276036
$121$	−9.99128	−0.908298
$122$	9.63344	0.872171
$123$	2.10191	0.189523
$124$	0.369891	0.0332172
$125$	1.00000	0.0894427
$126$	0.767357	0.0683616
$127$	0.295077	0.0261838	0.0130919	−	0.999914i	$-0.495833\pi$
$127$	0.295077	0.0261838	0.0130919	+	0.999914i	$0.495833\pi$
$128$	−2.08224	−0.184046
$129$	−6.36882	−0.560743
$130$	−5.96633	−0.523282
$131$	15.0846	1.31795	0.658973	−	0.752167i	$-0.270991\pi$
$131$	15.0846	1.31795	0.658973	+	0.752167i	$0.270991\pi$
$132$	0.951767	0.0828407
$133$	−2.18798	−0.189722
$134$	7.29155	0.629894
$135$	1.00000	0.0860663
$136$	−18.5793	−1.59316
$137$	−5.24384	−0.448012	−0.224006	−	0.974588i	$-0.571913\pi$
$137$	−5.24384	−0.448012	−0.224006	+	0.974588i	$0.571913\pi$
$138$	−0.844698	−0.0719055
$139$	0.303185	0.0257158	0.0128579	−	0.999917i	$-0.495907\pi$
$139$	0.303185	0.0257158	0.0128579	+	0.999917i	$0.495907\pi$
$140$	−0.708863	−0.0599099
$141$	−10.7884	−0.908549
$142$	−7.41755	−0.622467
$143$	5.84133	0.488476
$144$	−1.20668	−0.100556
$145$	−0.995609	−0.0826809
$146$	3.86679	0.320018
$147$	−6.44046	−0.531200
$148$	−2.05932	−0.169275
$149$	−15.8929	−1.30199	−0.650997	−	0.759080i	$-0.725649\pi$
$149$	−15.8929	−1.30199	−0.650997	+	0.759080i	$0.725649\pi$
$150$	1.02584	0.0837598
$151$	−3.12095	−0.253979	−0.126990	−	0.991904i	$-0.540532\pi$
$151$	−3.12095	−0.253979	−0.126990	+	0.991904i	$0.540532\pi$
$152$	8.84469	0.717399
$153$	6.14432	0.496739
$154$	−0.770695	−0.0621044
$155$	−0.390326	−0.0313517
$156$	5.51153	0.441276
$157$	6.40260	0.510983	0.255492	−	0.966811i	$-0.417763\pi$
$157$	6.40260	0.510983	0.255492	+	0.966811i	$0.417763\pi$
$158$	2.50049	0.198929
$159$	−7.05171	−0.559237
$160$	4.80978	0.380247
$161$	−0.615938	−0.0485427
$162$	1.02584	0.0805979
$163$	10.9364	0.856603	0.428301	−	0.903636i	$-0.359112\pi$
$163$	10.9364	0.856603	0.428301	+	0.903636i	$0.359112\pi$
$164$	−1.99186	−0.155538
$165$	−1.00435	−0.0781885
$166$	−4.24080	−0.329150
$167$	−7.12374	−0.551252	−0.275626	−	0.961265i	$-0.588885\pi$
$167$	−7.12374	−0.551252	−0.275626	+	0.961265i	$0.588885\pi$
$168$	−2.26190	−0.174509
$169$	20.8262	1.60201
$170$	6.30311	0.483426
$171$	−2.92500	−0.223681
$172$	6.03538	0.460194
$173$	−19.1436	−1.45546	−0.727729	−	0.685865i	$-0.759424\pi$
$173$	−19.1436	−1.45546	−0.727729	+	0.685865i	$0.759424\pi$
$174$	−1.02134	−0.0774275
$175$	0.748026	0.0565454
$176$	1.21193	0.0913524
$177$	−10.3898	−0.780945
$178$	−14.0868	−1.05585
$179$	16.5478	1.23684	0.618421	−	0.785847i	$-0.287773\pi$
$179$	16.5478	1.23684	0.618421	+	0.785847i	$0.287773\pi$
$180$	−0.947645	−0.0706333
$181$	−20.8116	−1.54692	−0.773459	−	0.633847i	$-0.781475\pi$
$181$	−20.8116	−1.54692	−0.773459	+	0.633847i	$0.781475\pi$
$182$	−4.46297	−0.330817
$183$	9.39075	0.694184
$184$	2.48987	0.183556
$185$	2.17309	0.159769
$186$	−0.400413	−0.0293597
$187$	−6.17104	−0.451271
$188$	10.2236	0.745633
$189$	0.748026	0.0544109
$190$	−3.00060	−0.217686
$191$	16.0732	1.16301	0.581507	−	0.813541i	$-0.302463\pi$
$191$	16.0732	1.16301	0.581507	+	0.813541i	$0.302463\pi$
$192$	7.34744	0.530256
$193$	−20.3840	−1.46727	−0.733634	−	0.679544i	$-0.762178\pi$
$193$	−20.3840	−1.46727	−0.733634	+	0.679544i	$0.762178\pi$
$194$	−17.5889	−1.26281
$195$	−5.81603	−0.416494
$196$	6.10327	0.435948
$197$	24.7485	1.76326	0.881630	−	0.471941i	$-0.156446\pi$
$197$	24.7485	1.76326	0.881630	+	0.471941i	$0.156446\pi$
$198$	−1.03031	−0.0732206
$199$	−11.3773	−0.806518	−0.403259	−	0.915086i	$-0.632123\pi$
$199$	−11.3773	−0.806518	−0.403259	+	0.915086i	$0.632123\pi$
$200$	−3.02382	−0.213817
$201$	7.10786	0.501350
$202$	7.38883	0.519876
$203$	−0.744741	−0.0522706
$204$	−5.82263	−0.407666
$205$	2.10191	0.146804
$206$	5.29512	0.368928
$207$	−0.823418	−0.0572315
$208$	7.01807	0.486616
$209$	2.93773	0.203207
$210$	0.767357	0.0529527
$211$	4.80163	0.330558	0.165279	−	0.986247i	$-0.447148\pi$
$211$	4.80163	0.330558	0.165279	+	0.986247i	$0.447148\pi$
$212$	6.68252	0.458957
$213$	−7.23069	−0.495438
$214$	3.22597	0.220523
$215$	−6.36882	−0.434350
$216$	−3.02382	−0.205745
$217$	−0.291974	−0.0198205
$218$	−17.8441	−1.20855
$219$	3.76938	0.254711
$220$	0.951767	0.0641681
$221$	−35.7355	−2.40383
$222$	2.22925	0.149618
$223$	23.0540	1.54381	0.771904	−	0.635740i	$-0.219305\pi$
$223$	23.0540	1.54381	0.771904	+	0.635740i	$0.219305\pi$
$224$	3.59784	0.240391
$225$	1.00000	0.0666667
$226$	−20.2802	−1.34902
$227$	−22.3030	−1.48030	−0.740150	−	0.672442i	$-0.765246\pi$
$227$	−22.3030	−1.48030	−0.740150	+	0.672442i	$0.765246\pi$
$228$	2.77187	0.183571
$229$	−0.0731359	−0.00483296	−0.00241648	−	0.999997i	$-0.500769\pi$
$229$	−0.0731359	−0.00483296	−0.00241648	+	0.999997i	$0.500769\pi$
$230$	−0.844698	−0.0556978
$231$	−0.751279	−0.0494305
$232$	3.01055	0.197652
$233$	17.0586	1.11754	0.558772	−	0.829321i	$-0.311273\pi$
$233$	17.0586	1.11754	0.558772	+	0.829321i	$0.311273\pi$
$234$	−5.96633	−0.390031
$235$	−10.7884	−0.703759
$236$	9.84584	0.640910
$237$	2.43750	0.158333
$238$	4.71489	0.305621
$239$	18.1316	1.17283	0.586417	−	0.810009i	$-0.300538\pi$
$239$	18.1316	1.17283	0.586417	+	0.810009i	$0.300538\pi$
$240$	−1.20668	−0.0778907
$241$	19.3493	1.24640	0.623200	−	0.782063i	$-0.285832\pi$
$241$	19.3493	1.24640	0.623200	+	0.782063i	$0.285832\pi$
$242$	−10.2495	−0.658862
$243$	1.00000	0.0641500
$244$	−8.89910	−0.569707
$245$	−6.44046	−0.411466
$246$	2.15623	0.137476
$247$	17.0119	1.08244
$248$	1.18028	0.0749477
$249$	−4.13397	−0.261980
$250$	1.02584	0.0648800
$251$	−27.3332	−1.72525	−0.862627	−	0.505840i	$-0.831183\pi$
$251$	−27.3332	−1.72525	−0.862627	+	0.505840i	$0.831183\pi$
$252$	−0.708863	−0.0446542
$253$	0.827000	0.0519930
$254$	0.302703	0.0189932
$255$	6.14432	0.384772
$256$	−16.8309	−1.05193
$257$	10.4196	0.649954	0.324977	−	0.945722i	$-0.394643\pi$
$257$	10.4196	0.649954	0.324977	+	0.945722i	$0.394643\pi$
$258$	−6.53341	−0.406752
$259$	1.62553	0.101005
$260$	5.51153	0.341811
$261$	−0.995609	−0.0616267
$262$	15.4744	0.956013
$263$	−25.1198	−1.54896	−0.774478	−	0.632601i	$-0.781987\pi$
$263$	−25.1198	−1.54896	−0.774478	+	0.632601i	$0.781987\pi$
$264$	3.03698	0.186913
$265$	−7.05171	−0.433183
$266$	−2.24452	−0.137621
$267$	−13.7319	−0.840377
$268$	−6.73573	−0.411450
$269$	−5.14965	−0.313979	−0.156990	−	0.987600i	$-0.550179\pi$
$269$	−5.14965	−0.313979	−0.156990	+	0.987600i	$0.550179\pi$
$270$	1.02584	0.0624308
$271$	1.18126	0.0717565	0.0358783	−	0.999356i	$-0.488577\pi$
$271$	1.18126	0.0717565	0.0358783	+	0.999356i	$0.488577\pi$
$272$	−7.41421	−0.449553
$273$	−4.35054	−0.263307
$274$	−5.37936	−0.324979
$275$	−1.00435	−0.0605646
$276$	0.780309	0.0469691
$277$	3.66263	0.220066	0.110033	−	0.993928i	$-0.464904\pi$
$277$	3.66263	0.220066	0.110033	+	0.993928i	$0.464904\pi$
$278$	0.311021	0.0186538
$279$	−0.390326	−0.0233682
$280$	−2.26190	−0.135174
$281$	−20.8361	−1.24298	−0.621489	−	0.783423i	$-0.713472\pi$
$281$	−20.8361	−1.24298	−0.621489	+	0.783423i	$0.713472\pi$
$282$	−11.0672	−0.659044
$283$	6.94225	0.412674	0.206337	−	0.978481i	$-0.433846\pi$
$283$	6.94225	0.412674	0.206337	+	0.978481i	$0.433846\pi$
$284$	6.85213	0.406599
$285$	−2.92500	−0.173262
$286$	5.99229	0.354331
$287$	1.57228	0.0928089
$288$	4.80978	0.283419
$289$	20.7527	1.22074
$290$	−1.02134	−0.0599751
$291$	−17.1458	−1.00511
$292$	−3.57204	−0.209038
$293$	11.2754	0.658716	0.329358	−	0.944205i	$-0.393168\pi$
$293$	11.2754	0.658716	0.329358	+	0.944205i	$0.393168\pi$
$294$	−6.60690	−0.385322
$295$	−10.3898	−0.604917
$296$	−6.57104	−0.381934
$297$	−1.00435	−0.0582783
$298$	−16.3036	−0.944442
$299$	4.78902	0.276956
$300$	−0.947645	−0.0547123
$301$	−4.76404	−0.274595
$302$	−3.20161	−0.184232
$303$	7.20269	0.413784
$304$	3.52954	0.202433
$305$	9.39075	0.537713
$306$	6.30311	0.360325
$307$	10.4812	0.598194	0.299097	−	0.954223i	$-0.403315\pi$
$307$	10.4812	0.598194	0.299097	+	0.954223i	$0.403315\pi$
$308$	0.711946	0.0405669
$309$	5.16172	0.293640
$310$	−0.400413	−0.0227420
$311$	4.86109	0.275647	0.137824	−	0.990457i	$-0.455989\pi$
$311$	4.86109	0.275647	0.137824	+	0.990457i	$0.455989\pi$
$312$	17.5866	0.995647
$313$	21.1295	1.19431	0.597155	−	0.802126i	$-0.296298\pi$
$313$	21.1295	1.19431	0.597155	+	0.802126i	$0.296298\pi$
$314$	6.56807	0.370658
$315$	0.748026	0.0421465
$316$	−2.30989	−0.129941
$317$	35.3062	1.98299	0.991496	−	0.130141i	$-0.0415429\pi$
$317$	35.3062	1.98299	0.991496	+	0.130141i	$0.0415429\pi$
$318$	−7.23395	−0.405660
$319$	0.999940	0.0559859
$320$	7.34744	0.410734
$321$	3.14470	0.175520
$322$	−0.631856	−0.0352120
$323$	−17.9722	−0.999998
$324$	−0.947645	−0.0526470
$325$	−5.81603	−0.322615
$326$	11.2190	0.621363
$327$	−17.3945	−0.961919
$328$	−6.35580	−0.350940
$329$	−8.07002	−0.444915
$330$	−1.03031	−0.0567164
$331$	15.9384	0.876051	0.438026	−	0.898962i	$-0.355678\pi$
$331$	15.9384	0.876051	0.438026	+	0.898962i	$0.355678\pi$
$332$	3.91754	0.215003
$333$	2.17309	0.119085
$334$	−7.30784	−0.399867
$335$	7.10786	0.388344
$336$	−0.902626	−0.0492423
$337$	−24.8338	−1.35278	−0.676391	−	0.736543i	$-0.736457\pi$
$337$	−24.8338	−1.35278	−0.676391	+	0.736543i	$0.736457\pi$
$338$	21.3644	1.16207
$339$	−19.7693	−1.07372
$340$	−5.82263	−0.315777
$341$	0.392024	0.0212293
$342$	−3.00060	−0.162254
$343$	−10.0538	−0.542855
$344$	19.2582	1.03833
$345$	−0.823418	−0.0443314
$346$	−19.6383	−1.05576
$347$	20.5868	1.10516	0.552579	−	0.833460i	$-0.313644\pi$
$347$	20.5868	1.10516	0.552579	+	0.833460i	$0.313644\pi$
$348$	0.943485	0.0505761
$349$	−21.6579	−1.15932	−0.579662	−	0.814857i	$-0.696815\pi$
$349$	−21.6579	−1.15932	−0.579662	+	0.814857i	$0.696815\pi$
$350$	0.767357	0.0410170
$351$	−5.81603	−0.310437
$352$	−4.83070	−0.257477
$353$	26.9535	1.43459	0.717295	−	0.696770i	$-0.245380\pi$
$353$	26.9535	1.43459	0.717295	+	0.696770i	$0.245380\pi$
$354$	−10.6583	−0.566483
$355$	−7.23069	−0.383765
$356$	13.0130	0.689685
$357$	4.59611	0.243252
$358$	16.9755	0.897182
$359$	32.9728	1.74024	0.870120	−	0.492840i	$-0.164041\pi$
$359$	32.9728	1.74024	0.870120	+	0.492840i	$0.164041\pi$
$360$	−3.02382	−0.159369
$361$	−10.4444	−0.549703
$362$	−21.3495	−1.12210
$363$	−9.99128	−0.524406
$364$	4.12277	0.216092
$365$	3.76938	0.197298
$366$	9.63344	0.503548
$367$	5.91211	0.308610	0.154305	−	0.988023i	$-0.450686\pi$
$367$	5.91211	0.308610	0.154305	+	0.988023i	$0.450686\pi$
$368$	0.993601	0.0517950
$369$	2.10191	0.109421
$370$	2.22925	0.115893
$371$	−5.27486	−0.273857
$372$	0.369891	0.0191779
$373$	−8.65809	−0.448299	−0.224149	−	0.974555i	$-0.571960\pi$
$373$	−8.65809	−0.448299	−0.224149	+	0.974555i	$0.571960\pi$
$374$	−6.33053	−0.327344
$375$	1.00000	0.0516398
$376$	32.6223	1.68237
$377$	5.79049	0.298226
$378$	0.767357	0.0394686
$379$	−5.15795	−0.264946	−0.132473	−	0.991187i	$-0.542292\pi$
$379$	−5.15795	−0.264946	−0.132473	+	0.991187i	$0.542292\pi$
$380$	2.77187	0.142194
$381$	0.295077	0.0151172
$382$	16.4886	0.843628
$383$	−6.65725	−0.340170	−0.170085	−	0.985429i	$-0.554404\pi$
$383$	−6.65725	−0.340170	−0.170085	+	0.985429i	$0.554404\pi$
$384$	−2.08224	−0.106259
$385$	−0.751279	−0.0382887
$386$	−20.9107	−1.06433
$387$	−6.36882	−0.323745
$388$	16.2482	0.824875
$389$	16.5598	0.839617	0.419809	−	0.907613i	$-0.362097\pi$
$389$	16.5598	0.839617	0.419809	+	0.907613i	$0.362097\pi$
$390$	−5.96633	−0.302117
$391$	−5.05935	−0.255862
$392$	19.4748	0.983626
$393$	15.0846	0.760917
$394$	25.3881	1.27904
$395$	2.43750	0.122644
$396$	0.951767	0.0478281
$397$	−1.85345	−0.0930219	−0.0465110	−	0.998918i	$-0.514810\pi$
$397$	−1.85345	−0.0930219	−0.0465110	+	0.998918i	$0.514810\pi$
$398$	−11.6714	−0.585032
$399$	−2.18798	−0.109536
$400$	−1.20668	−0.0603339
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	7.29155	0.363670
$403$	2.27015	0.113084
$404$	−6.82559	−0.339586
$405$	1.00000	0.0496904
$406$	−0.763988	−0.0379161
$407$	−2.18254	−0.108185
$408$	−18.5793	−0.919814
$409$	22.1379	1.09465	0.547325	−	0.836920i	$-0.315646\pi$
$409$	22.1379	1.09465	0.547325	+	0.836920i	$0.315646\pi$
$410$	2.15623	0.106489
$411$	−5.24384	−0.258660
$412$	−4.89148	−0.240986
$413$	−7.77184	−0.382427
$414$	−0.844698	−0.0415147
$415$	−4.13397	−0.202929
$416$	−27.9738	−1.37153
$417$	0.303185	0.0148471
$418$	3.01365	0.147402
$419$	12.8183	0.626215	0.313107	−	0.949718i	$-0.398630\pi$
$419$	12.8183	0.626215	0.313107	+	0.949718i	$0.398630\pi$
$420$	−0.708863	−0.0345890
$421$	−18.5310	−0.903147	−0.451574	−	0.892234i	$-0.649137\pi$
$421$	−18.5310	−0.903147	−0.451574	+	0.892234i	$0.649137\pi$
$422$	4.92572	0.239780
$423$	−10.7884	−0.524551
$424$	21.3231	1.03554
$425$	6.14432	0.298043
$426$	−7.41755	−0.359382
$427$	7.02452	0.339940
$428$	−2.98006	−0.144047
$429$	5.84133	0.282022
$430$	−6.53341	−0.315069
$431$	−29.1630	−1.40473	−0.702365	−	0.711817i	$-0.747873\pi$
$431$	−29.1630	−1.40473	−0.702365	+	0.711817i	$0.747873\pi$
$432$	−1.20668	−0.0580563
$433$	−26.7124	−1.28371	−0.641857	−	0.766824i	$-0.721836\pi$
$433$	−26.7124	−1.28371	−0.641857	+	0.766824i	$0.721836\pi$
$434$	−0.299520	−0.0143774
$435$	−0.995609	−0.0477358
$436$	16.4838	0.789433
$437$	2.40850	0.115214
$438$	3.86679	0.184763
$439$	0.414402	0.0197783	0.00988917	−	0.999951i	$-0.496852\pi$
$439$	0.414402	0.0197783	0.00988917	+	0.999951i	$0.496852\pi$
$440$	3.03698	0.144782
$441$	−6.44046	−0.306688
$442$	−36.6591	−1.74369
$443$	−34.2358	−1.62659	−0.813295	−	0.581852i	$-0.802328\pi$
$443$	−34.2358	−1.62659	−0.813295	+	0.581852i	$0.802328\pi$
$444$	−2.05932	−0.0977310
$445$	−13.7319	−0.650954
$446$	23.6498	1.11985
$447$	−15.8929	−0.751707
$448$	5.49607	0.259665
$449$	−0.785048	−0.0370487	−0.0185244	−	0.999828i	$-0.505897\pi$
$449$	−0.785048	−0.0370487	−0.0185244	+	0.999828i	$0.505897\pi$
$450$	1.02584	0.0483587
$451$	−2.11105	−0.0994055
$452$	18.7343	0.881185
$453$	−3.12095	−0.146635
$454$	−22.8794	−1.07378
$455$	−4.35054	−0.203956
$456$	8.84469	0.414191
$457$	8.01405	0.374881	0.187441	−	0.982276i	$-0.439981\pi$
$457$	8.01405	0.374881	0.187441	+	0.982276i	$0.439981\pi$
$458$	−0.0750260	−0.00350574
$459$	6.14432	0.286792
$460$	0.780309	0.0363821
$461$	37.6542	1.75373	0.876867	−	0.480734i	$-0.159630\pi$
$461$	37.6542	1.75373	0.876867	+	0.480734i	$0.159630\pi$
$462$	−0.770695	−0.0358560
$463$	40.9814	1.90457	0.952283	−	0.305218i	$-0.0987292\pi$
$463$	40.9814	1.90457	0.952283	+	0.305218i	$0.0987292\pi$
$464$	1.20138	0.0557727
$465$	−0.390326	−0.0181009
$466$	17.4994	0.810645
$467$	−32.2708	−1.49331	−0.746657	−	0.665209i	$-0.768342\pi$
$467$	−32.2708	−1.49331	−0.746657	+	0.665209i	$0.768342\pi$
$468$	5.51153	0.254771
$469$	5.31686	0.245510
$470$	−11.0672	−0.510494
$471$	6.40260	0.295016
$472$	31.4169	1.44608
$473$	6.39652	0.294112
$474$	2.50049	0.114852
$475$	−2.92500	−0.134208
$476$	−4.35548	−0.199633
$477$	−7.05171	−0.322876
$478$	18.6002	0.850751
$479$	−8.66265	−0.395807	−0.197903	−	0.980222i	$-0.563413\pi$
$479$	−8.66265	−0.395807	−0.197903	+	0.980222i	$0.563413\pi$
$480$	4.80978	0.219536
$481$	−12.6388	−0.576278
$482$	19.8494	0.904114
$483$	−0.615938	−0.0280262
$484$	9.46819	0.430372
$485$	−17.1458	−0.778552
$486$	1.02584	0.0465332
$487$	−28.6246	−1.29711	−0.648553	−	0.761169i	$-0.724626\pi$
$487$	−28.6246	−1.29711	−0.648553	+	0.761169i	$0.724626\pi$
$488$	−28.3960	−1.28542
$489$	10.9364	0.494560
$490$	−6.60690	−0.298469
$491$	−30.5551	−1.37893	−0.689467	−	0.724317i	$-0.742155\pi$
$491$	−30.5551	−1.37893	−0.689467	+	0.724317i	$0.742155\pi$
$492$	−1.99186	−0.0898002
$493$	−6.11734	−0.275511
$494$	17.4516	0.785182
$495$	−1.00435	−0.0451422
$496$	0.470998	0.0211484
$497$	−5.40874	−0.242615
$498$	−4.24080	−0.190035
$499$	−16.6476	−0.745251	−0.372625	−	0.927982i	$-0.621542\pi$
$499$	−16.6476	−0.745251	−0.372625	+	0.927982i	$0.621542\pi$
$500$	−0.947645	−0.0423800
$501$	−7.12374	−0.318265
$502$	−28.0396	−1.25147
$503$	−4.74704	−0.211660	−0.105830	−	0.994384i	$-0.533750\pi$
$503$	−4.74704	−0.211660	−0.105830	+	0.994384i	$0.533750\pi$
$504$	−2.26190	−0.100753
$505$	7.20269	0.320515
$506$	0.848373	0.0377148
$507$	20.8262	0.924923
$508$	−0.279628	−0.0124065
$509$	−0.626010	−0.0277474	−0.0138737	−	0.999904i	$-0.504416\pi$
$509$	−0.626010	−0.0277474	−0.0138737	+	0.999904i	$0.504416\pi$
$510$	6.30311	0.279106
$511$	2.81959	0.124731
$512$	−13.1014	−0.579006
$513$	−2.92500	−0.129142
$514$	10.6888	0.471465
$515$	5.16172	0.227453
$516$	6.03538	0.265693
$517$	10.8354	0.476538
$518$	1.66754	0.0732674
$519$	−19.1436	−0.840309
$520$	17.5866	0.771225
$521$	−24.0946	−1.05560	−0.527801	−	0.849368i	$-0.676983\pi$
$521$	−24.0946	−1.05560	−0.527801	+	0.849368i	$0.676983\pi$
$522$	−1.02134	−0.0447028
$523$	−0.531120	−0.0232243	−0.0116121	−	0.999933i	$-0.503696\pi$
$523$	−0.531120	−0.0232243	−0.0116121	+	0.999933i	$0.503696\pi$
$524$	−14.2948	−0.624473
$525$	0.748026	0.0326465
$526$	−25.7690	−1.12358
$527$	−2.39829	−0.104471
$528$	1.21193	0.0527423
$529$	−22.3220	−0.970521
$530$	−7.23395	−0.314223
$531$	−10.3898	−0.450879
$532$	2.07343	0.0898945
$533$	−12.2248	−0.529513
$534$	−14.0868	−0.609594
$535$	3.14470	0.135957
$536$	−21.4929	−0.928353
$537$	16.5478	0.714091
$538$	−5.28273	−0.227755
$539$	6.46847	0.278617
$540$	−0.947645	−0.0407802
$541$	37.3355	1.60518	0.802589	−	0.596533i	$-0.203456\pi$
$541$	37.3355	1.60518	0.802589	+	0.596533i	$0.203456\pi$
$542$	1.21179	0.0520508
$543$	−20.8116	−0.893113
$544$	29.5528	1.26707
$545$	−17.3945	−0.745099
$546$	−4.46297	−0.190998
$547$	−31.6989	−1.35534	−0.677672	−	0.735364i	$-0.737011\pi$
$547$	−31.6989	−1.35534	−0.677672	+	0.735364i	$0.737011\pi$
$548$	4.96930	0.212278
$549$	9.39075	0.400787
$550$	−1.03031	−0.0439324
$551$	2.91216	0.124062
$552$	2.48987	0.105976
$553$	1.82331	0.0775352
$554$	3.75728	0.159632
$555$	2.17309	0.0922426
$556$	−0.287312	−0.0121848
$557$	3.63881	0.154181	0.0770906	−	0.997024i	$-0.475437\pi$
$557$	3.63881	0.154181	0.0770906	+	0.997024i	$0.475437\pi$
$558$	−0.400413	−0.0169509
$559$	37.0412	1.56668
$560$	−0.902626	−0.0381429
$561$	−6.17104	−0.260542
$562$	−21.3746	−0.901632
$563$	−34.9258	−1.47195	−0.735973	−	0.677011i	$-0.763275\pi$
$563$	−34.9258	−1.47195	−0.735973	+	0.677011i	$0.763275\pi$
$564$	10.2236	0.430491
$565$	−19.7693	−0.831700
$566$	7.12166	0.299346
$567$	0.748026	0.0314141
$568$	21.8643	0.917406
$569$	−4.56212	−0.191254	−0.0956270	−	0.995417i	$-0.530486\pi$
$569$	−4.56212	−0.191254	−0.0956270	+	0.995417i	$0.530486\pi$
$570$	−3.00060	−0.125681
$571$	23.0275	0.963673	0.481836	−	0.876261i	$-0.339970\pi$
$571$	23.0275	0.963673	0.481836	+	0.876261i	$0.339970\pi$
$572$	−5.53550	−0.231451
$573$	16.0732	0.671466
$574$	1.61291	0.0673218
$575$	−0.823418	−0.0343389
$576$	7.34744	0.306143
$577$	−44.6583	−1.85915	−0.929576	−	0.368632i	$-0.879826\pi$
$577$	−44.6583	−1.85915	−0.929576	+	0.368632i	$0.879826\pi$
$578$	21.2890	0.885504
$579$	−20.3840	−0.847128
$580$	0.943485	0.0391761
$581$	−3.09231	−0.128291
$582$	−17.5889	−0.729085
$583$	7.08238	0.293322
$584$	−11.3979	−0.471650
$585$	−5.81603	−0.240463
$586$	11.5668	0.477820
$587$	23.3827	0.965107	0.482553	−	0.875867i	$-0.339709\pi$
$587$	23.3827	0.965107	0.482553	+	0.875867i	$0.339709\pi$
$588$	6.10327	0.251695
$589$	1.14171	0.0470432
$590$	−10.6583	−0.438796
$591$	24.7485	1.01802
$592$	−2.62222	−0.107773
$593$	−9.97384	−0.409577	−0.204788	−	0.978806i	$-0.565651\pi$
$593$	−9.97384	−0.409577	−0.204788	+	0.978806i	$0.565651\pi$
$594$	−1.03031	−0.0422739
$595$	4.59611	0.188422
$596$	15.0608	0.616914
$597$	−11.3773	−0.465643
$598$	4.91279	0.200899
$599$	7.60791	0.310851	0.155425	−	0.987848i	$-0.450325\pi$
$599$	7.60791	0.310851	0.155425	+	0.987848i	$0.450325\pi$
$600$	−3.02382	−0.123447
$601$	0.328270	0.0133904	0.00669520	−	0.999978i	$-0.497869\pi$
$601$	0.328270	0.0133904	0.00669520	+	0.999978i	$0.497869\pi$
$602$	−4.88716	−0.199186
$603$	7.10786	0.289455
$604$	2.95755	0.120341
$605$	−9.99128	−0.406203
$606$	7.38883	0.300151
$607$	−26.8088	−1.08813	−0.544067	−	0.839042i	$-0.683116\pi$
$607$	−26.8088	−1.08813	−0.544067	+	0.839042i	$0.683116\pi$
$608$	−14.0686	−0.570558
$609$	−0.744741	−0.0301784
$610$	9.63344	0.390047
$611$	62.7458	2.53842
$612$	−5.82263	−0.235366
$613$	−3.39468	−0.137110	−0.0685549	−	0.997647i	$-0.521839\pi$
$613$	−3.39468	−0.137110	−0.0685549	+	0.997647i	$0.521839\pi$
$614$	10.7521	0.433918
$615$	2.10191	0.0847572
$616$	2.27174	0.0915308
$617$	−28.9617	−1.16595	−0.582976	−	0.812489i	$-0.698112\pi$
$617$	−28.9617	−1.16595	−0.582976	+	0.812489i	$0.698112\pi$
$618$	5.29512	0.213001
$619$	14.3756	0.577806	0.288903	−	0.957358i	$-0.406710\pi$
$619$	14.3756	0.577806	0.288903	+	0.957358i	$0.406710\pi$
$620$	0.369891	0.0148552
$621$	−0.823418	−0.0330426
$622$	4.98672	0.199949
$623$	−10.2718	−0.411531
$624$	7.01807	0.280948
$625$	1.00000	0.0400000
$626$	21.6756	0.866330
$627$	2.93773	0.117322
$628$	−6.06740	−0.242115
$629$	13.3522	0.532386
$630$	0.767357	0.0305722
$631$	−19.1928	−0.764053	−0.382027	−	0.924151i	$-0.624774\pi$
$631$	−19.1928	−0.764053	−0.382027	+	0.924151i	$0.624774\pi$
$632$	−7.37057	−0.293186
$633$	4.80163	0.190848
$634$	36.2186	1.43842
$635$	0.295077	0.0117098
$636$	6.68252	0.264979
$637$	37.4579	1.48414
$638$	1.02578	0.0406111
$639$	−7.23069	−0.286042
$640$	−2.08224	−0.0823079
$641$	−28.9393	−1.14303	−0.571517	−	0.820590i	$-0.693645\pi$
$641$	−28.9393	−1.14303	−0.571517	+	0.820590i	$0.693645\pi$
$642$	3.22597	0.127319
$643$	11.4188	0.450315	0.225158	−	0.974322i	$-0.427710\pi$
$643$	11.4188	0.450315	0.225158	+	0.974322i	$0.427710\pi$
$644$	0.583691	0.0230006
$645$	−6.36882	−0.250772
$646$	−18.4366	−0.725379
$647$	−22.6854	−0.891854	−0.445927	−	0.895069i	$-0.647126\pi$
$647$	−22.6854	−0.891854	−0.445927	+	0.895069i	$0.647126\pi$
$648$	−3.02382	−0.118787
$649$	10.4350	0.409609
$650$	−5.96633	−0.234019
$651$	−0.291974	−0.0114434
$652$	−10.3638	−0.405878
$653$	8.07650	0.316058	0.158029	−	0.987434i	$-0.449486\pi$
$653$	8.07650	0.316058	0.158029	+	0.987434i	$0.449486\pi$
$654$	−17.8441	−0.697758
$655$	15.0846	0.589403
$656$	−2.53633	−0.0990269
$657$	3.76938	0.147058
$658$	−8.27858	−0.322732
$659$	49.3673	1.92308	0.961539	−	0.274668i	$-0.0885681\pi$
$659$	49.3673	1.92308	0.961539	+	0.274668i	$0.0885681\pi$
$660$	0.951767	0.0370475
$661$	−29.5563	−1.14961	−0.574803	−	0.818292i	$-0.694921\pi$
$661$	−29.5563	−1.14961	−0.574803	+	0.818292i	$0.694921\pi$
$662$	16.3503	0.635471
$663$	−35.7355	−1.38785
$664$	12.5004	0.485109
$665$	−2.18798	−0.0848461
$666$	2.22925	0.0863817
$667$	0.819803	0.0317429
$668$	6.75078	0.261195
$669$	23.0540	0.891318
$670$	7.29155	0.281697
$671$	−9.43160	−0.364103
$672$	3.59784	0.138790
$673$	13.5602	0.522707	0.261354	−	0.965243i	$-0.415831\pi$
$673$	13.5602	0.522707	0.261354	+	0.965243i	$0.415831\pi$
$674$	−25.4755	−0.981282
$675$	1.00000	0.0384900
$676$	−19.7358	−0.759070
$677$	4.58404	0.176179	0.0880895	−	0.996113i	$-0.471924\pi$
$677$	4.58404	0.176179	0.0880895	+	0.996113i	$0.471924\pi$
$678$	−20.2802	−0.778856
$679$	−12.8255	−0.492198
$680$	−18.5793	−0.712485
$681$	−22.3030	−0.854652
$682$	0.402155	0.0153993
$683$	32.3458	1.23768	0.618839	−	0.785518i	$-0.287603\pi$
$683$	32.3458	1.23768	0.618839	+	0.785518i	$0.287603\pi$
$684$	2.77187	0.105985
$685$	−5.24384	−0.200357
$686$	−10.3136	−0.393776
$687$	−0.0731359	−0.00279031
$688$	7.68511	0.292992
$689$	41.0129	1.56247
$690$	−0.844698	−0.0321571
$691$	43.0465	1.63757	0.818784	−	0.574102i	$-0.194649\pi$
$691$	43.0465	1.63757	0.818784	+	0.574102i	$0.194649\pi$
$692$	18.1413	0.689629
$693$	−0.751279	−0.0285387
$694$	21.1189	0.801661
$695$	0.303185	0.0115005
$696$	3.01055	0.114114
$697$	12.9148	0.489183
$698$	−22.2177	−0.840951
$699$	17.0586	0.645214
$700$	−0.708863	−0.0267925
$701$	52.5427	1.98451	0.992255	−	0.124220i	$-0.0396430\pi$
$701$	52.5427	1.98451	0.992255	+	0.124220i	$0.0396430\pi$
$702$	−5.96633	−0.225185
$703$	−6.35630	−0.239732
$704$	−7.37940	−0.278122
$705$	−10.7884	−0.406316
$706$	27.6501	1.04062
$707$	5.38780	0.202629
$708$	9.84584	0.370029
$709$	38.5822	1.44898	0.724492	−	0.689283i	$-0.242074\pi$
$709$	38.5822	1.44898	0.724492	+	0.689283i	$0.242074\pi$
$710$	−7.41755	−0.278376
$711$	2.43750	0.0914134
$712$	41.5228	1.55613
$713$	0.321402	0.0120366
$714$	4.71489	0.176450
$715$	5.84133	0.218453
$716$	−15.6815	−0.586044
$717$	18.1316	0.677136
$718$	33.8250	1.26234
$719$	24.0708	0.897690	0.448845	−	0.893610i	$-0.351836\pi$
$719$	24.0708	0.897690	0.448845	+	0.893610i	$0.351836\pi$
$720$	−1.20668	−0.0449702
$721$	3.86110	0.143795
$722$	−10.7143	−0.398744
$723$	19.3493	0.719609
$724$	19.7221	0.732964
$725$	−0.995609	−0.0369760
$726$	−10.2495	−0.380394
$727$	36.8655	1.36727	0.683633	−	0.729826i	$-0.260399\pi$
$727$	36.8655	1.36727	0.683633	+	0.729826i	$0.260399\pi$
$728$	13.1553	0.487566
$729$	1.00000	0.0370370
$730$	3.86679	0.143116
$731$	−39.1321	−1.44735
$732$	−8.89910	−0.328920
$733$	−16.4951	−0.609260	−0.304630	−	0.952471i	$-0.598533\pi$
$733$	−16.4951	−0.609260	−0.304630	+	0.952471i	$0.598533\pi$
$734$	6.06490	0.223859
$735$	−6.44046	−0.237560
$736$	−3.96046	−0.145985
$737$	−7.13878	−0.262960
$738$	2.15623	0.0793719
$739$	−9.55323	−0.351421	−0.175711	−	0.984442i	$-0.556222\pi$
$739$	−9.55323	−0.351421	−0.175711	+	0.984442i	$0.556222\pi$
$740$	−2.05932	−0.0757021
$741$	17.0119	0.624948
$742$	−5.41118	−0.198651
$743$	22.1669	0.813225	0.406613	−	0.913601i	$-0.366710\pi$
$743$	22.1669	0.813225	0.406613	+	0.913601i	$0.366710\pi$
$744$	1.18028	0.0432710
$745$	−15.8929	−0.582270
$746$	−8.88184	−0.325187
$747$	−4.13397	−0.151254
$748$	5.84796	0.213823
$749$	2.35232	0.0859518
$750$	1.02584	0.0374585
$751$	11.8409	0.432079	0.216039	−	0.976385i	$-0.430686\pi$
$751$	11.8409	0.432079	0.216039	+	0.976385i	$0.430686\pi$
$752$	13.0182	0.474723
$753$	−27.3332	−0.996076
$754$	5.94014	0.216327
$755$	−3.12095	−0.113583
$756$	−0.708863	−0.0257811
$757$	19.2164	0.698432	0.349216	−	0.937042i	$-0.386448\pi$
$757$	19.2164	0.698432	0.349216	+	0.937042i	$0.386448\pi$
$758$	−5.29125	−0.192187
$759$	0.827000	0.0300182
$760$	8.84469	0.320831
$761$	43.0644	1.56108	0.780541	−	0.625104i	$-0.214943\pi$
$761$	43.0644	1.56108	0.780541	+	0.625104i	$0.214943\pi$
$762$	0.302703	0.0109658
$763$	−13.0115	−0.471050
$764$	−15.2317	−0.551062
$765$	6.14432	0.222148
$766$	−6.82930	−0.246753
$767$	60.4274	2.18191
$768$	−16.8309	−0.607334
$769$	−17.3642	−0.626169	−0.313084	−	0.949725i	$-0.601362\pi$
$769$	−17.3642	−0.626169	−0.313084	+	0.949725i	$0.601362\pi$
$770$	−0.770695	−0.0277739
$771$	10.4196	0.375251
$772$	19.3168	0.695225
$773$	53.6526	1.92975	0.964874	−	0.262712i	$-0.0846169\pi$
$773$	53.6526	1.92975	0.964874	+	0.262712i	$0.0846169\pi$
$774$	−6.53341	−0.234839
$775$	−0.390326	−0.0140209
$776$	51.8459	1.86116
$777$	1.62553	0.0583155
$778$	16.9878	0.609042
$779$	−6.14809	−0.220278
$780$	5.51153	0.197344
$781$	7.26214	0.259860
$782$	−5.19010	−0.185597
$783$	−0.995609	−0.0355802
$784$	7.77156	0.277556
$785$	6.40260	0.228519
$786$	15.4744	0.551954
$787$	5.96246	0.212539	0.106269	−	0.994337i	$-0.466109\pi$
$787$	5.96246	0.212539	0.106269	+	0.994337i	$0.466109\pi$
$788$	−23.4528	−0.835473
$789$	−25.1198	−0.894290
$790$	2.50049	0.0889636
$791$	−14.7879	−0.525798
$792$	3.03698	0.107914
$793$	−54.6169	−1.93950
$794$	−1.90135	−0.0674763
$795$	−7.05171	−0.250098
$796$	10.7817	0.382146
$797$	−27.1835	−0.962889	−0.481445	−	0.876476i	$-0.659888\pi$
$797$	−27.1835	−0.962889	−0.481445	+	0.876476i	$0.659888\pi$
$798$	−2.24452	−0.0794552
$799$	−66.2875	−2.34508
$800$	4.80978	0.170051
$801$	−13.7319	−0.485192
$802$	−1.02584	−0.0362238
$803$	−3.78578	−0.133597
$804$	−6.73573	−0.237551
$805$	−0.615938	−0.0217090
$806$	2.32882	0.0820290
$807$	−5.14965	−0.181276
$808$	−21.7797	−0.766206
$809$	49.8323	1.75201	0.876005	−	0.482302i	$-0.160199\pi$
$809$	49.8323	1.75201	0.876005	+	0.482302i	$0.160199\pi$
$810$	1.02584	0.0360445
$811$	−47.7107	−1.67535	−0.837674	−	0.546170i	$-0.816085\pi$
$811$	−47.7107	−1.67535	−0.837674	+	0.546170i	$0.816085\pi$
$812$	0.705751	0.0247670
$813$	1.18126	0.0414286
$814$	−2.23895	−0.0784751
$815$	10.9364	0.383084
$816$	−7.41421	−0.259549
$817$	18.6288	0.651740
$818$	22.7100	0.794038
$819$	−4.35054	−0.152020
$820$	−1.99186	−0.0695589
$821$	31.6670	1.10519	0.552593	−	0.833451i	$-0.313639\pi$
$821$	31.6670	1.10519	0.552593	+	0.833451i	$0.313639\pi$
$822$	−5.37936	−0.187627
$823$	−1.76770	−0.0616181	−0.0308090	−	0.999525i	$-0.509808\pi$
$823$	−1.76770	−0.0616181	−0.0308090	+	0.999525i	$0.509808\pi$
$824$	−15.6081	−0.543735
$825$	−1.00435	−0.0349670
$826$	−7.97269	−0.277405
$827$	29.2214	1.01613	0.508065	−	0.861319i	$-0.330361\pi$
$827$	29.2214	1.01613	0.508065	+	0.861319i	$0.330361\pi$
$828$	0.780309	0.0271176
$829$	−16.9147	−0.587472	−0.293736	−	0.955887i	$-0.594899\pi$
$829$	−16.9147	−0.587472	−0.293736	+	0.955887i	$0.594899\pi$
$830$	−4.24080	−0.147200
$831$	3.66263	0.127055
$832$	−42.7329	−1.48150
$833$	−39.5722	−1.37110
$834$	0.311021	0.0107698
$835$	−7.12374	−0.246527
$836$	−2.78392	−0.0962840
$837$	−0.390326	−0.0134916
$838$	13.1496	0.454244
$839$	47.5157	1.64042	0.820212	−	0.572060i	$-0.193856\pi$
$839$	47.5157	1.64042	0.820212	+	0.572060i	$0.193856\pi$
$840$	−2.26190	−0.0780428
$841$	−28.0088	−0.965819
$842$	−19.0099	−0.655126
$843$	−20.8361	−0.717633
$844$	−4.55024	−0.156626
$845$	20.8262	0.716442
$846$	−11.0672	−0.380499
$847$	−7.47373	−0.256801
$848$	8.50914	0.292205
$849$	6.94225	0.238257
$850$	6.30311	0.216195
$851$	−1.78936	−0.0613386
$852$	6.85213	0.234750
$853$	11.8624	0.406161	0.203081	−	0.979162i	$-0.434905\pi$
$853$	11.8624	0.406161	0.203081	+	0.979162i	$0.434905\pi$
$854$	7.20606	0.246586
$855$	−2.92500	−0.100033
$856$	−9.50902	−0.325012
$857$	31.0122	1.05936	0.529678	−	0.848199i	$-0.322313\pi$
$857$	31.0122	1.05936	0.529678	+	0.848199i	$0.322313\pi$
$858$	5.99229	0.204573
$859$	41.1347	1.40350	0.701749	−	0.712424i	$-0.252403\pi$
$859$	41.1347	1.40350	0.701749	+	0.712424i	$0.252403\pi$
$860$	6.03538	0.205805
$861$	1.57228	0.0535832
$862$	−29.9166	−1.01896
$863$	31.2997	1.06545	0.532727	−	0.846287i	$-0.321167\pi$
$863$	31.2997	1.06545	0.532727	+	0.846287i	$0.321167\pi$
$864$	4.80978	0.163632
$865$	−19.1436	−0.650900
$866$	−27.4027	−0.931182
$867$	20.7527	0.704797
$868$	0.276688	0.00939139
$869$	−2.44810	−0.0830462
$870$	−1.02134	−0.0346266
$871$	−41.3395	−1.40074
$872$	52.5979	1.78119
$873$	−17.1458	−0.580298
$874$	2.47075	0.0835742
$875$	0.748026	0.0252879
$876$	−3.57204	−0.120688
$877$	23.4425	0.791599	0.395799	−	0.918337i	$-0.370468\pi$
$877$	23.4425	0.791599	0.395799	+	0.918337i	$0.370468\pi$
$878$	0.425112	0.0143468
$879$	11.2754	0.380310
$880$	1.21193	0.0408540
$881$	−29.0670	−0.979293	−0.489646	−	0.871921i	$-0.662874\pi$
$881$	−29.0670	−0.979293	−0.489646	+	0.871921i	$0.662874\pi$
$882$	−6.60690	−0.222466
$883$	−25.4029	−0.854874	−0.427437	−	0.904045i	$-0.640583\pi$
$883$	−25.4029	−0.854874	−0.427437	+	0.904045i	$0.640583\pi$
$884$	33.8646	1.13899
$885$	−10.3898	−0.349249
$886$	−35.1205	−1.17990
$887$	−29.1111	−0.977457	−0.488728	−	0.872436i	$-0.662539\pi$
$887$	−29.1111	−0.977457	−0.488728	+	0.872436i	$0.662539\pi$
$888$	−6.57104	−0.220510
$889$	0.220725	0.00740288
$890$	−14.0868	−0.472189
$891$	−1.00435	−0.0336470
$892$	−21.8470	−0.731491
$893$	31.5562	1.05599
$894$	−16.3036	−0.545274
$895$	16.5478	0.553133
$896$	−1.55757	−0.0520348
$897$	4.78902	0.159901
$898$	−0.805336	−0.0268744
$899$	0.388612	0.0129609
$900$	−0.947645	−0.0315882
$901$	−43.3280	−1.44346
$902$	−2.16561	−0.0721069
$903$	−4.76404	−0.158537
$904$	59.7788	1.98821
$905$	−20.8116	−0.691802
$906$	−3.20161	−0.106366
$907$	−14.7279	−0.489031	−0.244516	−	0.969645i	$-0.578629\pi$
$907$	−14.7279	−0.489031	−0.244516	+	0.969645i	$0.578629\pi$
$908$	21.1353	0.701400
$909$	7.20269	0.238898
$910$	−4.46297	−0.147946
$911$	−19.7157	−0.653212	−0.326606	−	0.945161i	$-0.605905\pi$
$911$	−19.7157	−0.653212	−0.326606	+	0.945161i	$0.605905\pi$
$912$	3.52954	0.116875
$913$	4.15195	0.137409
$914$	8.22116	0.271932
$915$	9.39075	0.310449
$916$	0.0693069	0.00228997
$917$	11.2837	0.372619
$918$	6.30311	0.208034
$919$	49.3904	1.62924	0.814619	−	0.579997i	$-0.196946\pi$
$919$	49.3904	1.62924	0.814619	+	0.579997i	$0.196946\pi$
$920$	2.48987	0.0820886
$921$	10.4812	0.345367
$922$	38.6274	1.27212
$923$	42.0539	1.38422
$924$	0.711946	0.0234213
$925$	2.17309	0.0714508
$926$	42.0405	1.38154
$927$	5.16172	0.169533
$928$	−4.78866	−0.157196
$929$	3.45692	0.113418	0.0567089	−	0.998391i	$-0.481939\pi$
$929$	3.45692	0.113418	0.0567089	+	0.998391i	$0.481939\pi$
$930$	−0.400413	−0.0131301
$931$	18.8384	0.617402
$932$	−16.1655	−0.529518
$933$	4.86109	0.159145
$934$	−33.1048	−1.08322
$935$	−6.17104	−0.201815
$936$	17.5866	0.574837
$937$	31.7067	1.03581	0.517906	−	0.855438i	$-0.326712\pi$
$937$	31.7067	1.03581	0.517906	+	0.855438i	$0.326712\pi$
$938$	5.45427	0.178088
$939$	21.1295	0.689535
$940$	10.2236	0.333457
$941$	23.8971	0.779022	0.389511	−	0.921022i	$-0.372644\pi$
$941$	23.8971	0.779022	0.389511	+	0.921022i	$0.372644\pi$
$942$	6.56807	0.213999
$943$	−1.73075	−0.0563610
$944$	12.5371	0.408049
$945$	0.748026	0.0243333
$946$	6.56183	0.213343
$947$	14.6405	0.475751	0.237876	−	0.971296i	$-0.423549\pi$
$947$	14.6405	0.475751	0.237876	+	0.971296i	$0.423549\pi$
$948$	−2.30989	−0.0750216
$949$	−21.9228	−0.711645
$950$	−3.00060	−0.0973522
$951$	35.3062	1.14488
$952$	−13.8978	−0.450431
$953$	−43.4488	−1.40745	−0.703723	−	0.710475i	$-0.748480\pi$
$953$	−43.4488	−1.40745	−0.703723	+	0.710475i	$0.748480\pi$
$954$	−7.23395	−0.234208
$955$	16.0732	0.520116
$956$	−17.1823	−0.555715
$957$	0.999940	0.0323235
$958$	−8.88652	−0.287110
$959$	−3.92253	−0.126665
$960$	7.34744	0.237138
$961$	−30.8476	−0.995085
$962$	−12.9654	−0.418021
$963$	3.14470	0.101337
$964$	−18.3363	−0.590572
$965$	−20.3840	−0.656183
$966$	−0.631856	−0.0203296
$967$	−0.858042	−0.0275928	−0.0137964	−	0.999905i	$-0.504392\pi$
$967$	−0.858042	−0.0275928	−0.0137964	+	0.999905i	$0.504392\pi$
$968$	30.2119	0.971046
$969$	−17.9722	−0.577349
$970$	−17.5889	−0.564747
$971$	−26.2055	−0.840974	−0.420487	−	0.907299i	$-0.638141\pi$
$971$	−26.2055	−0.840974	−0.420487	+	0.907299i	$0.638141\pi$
$972$	−0.947645	−0.0303957
$973$	0.226790	0.00727057
$974$	−29.3644	−0.940896
$975$	−5.81603	−0.186262
$976$	−11.3316	−0.362716
$977$	−45.6130	−1.45929	−0.729644	−	0.683827i	$-0.760314\pi$
$977$	−45.6130	−1.45929	−0.729644	+	0.683827i	$0.760314\pi$
$978$	11.2190	0.358744
$979$	13.7916	0.440782
$980$	6.10327	0.194962
$981$	−17.3945	−0.555364
$982$	−31.3448	−1.00025
$983$	19.8991	0.634683	0.317342	−	0.948311i	$-0.397210\pi$
$983$	19.8991	0.634683	0.317342	+	0.948311i	$0.397210\pi$
$984$	−6.35580	−0.202616
$985$	24.7485	0.788554
$986$	−6.27543	−0.199851
$987$	−8.07002	−0.256872
$988$	−16.1213	−0.512885
$989$	5.24420	0.166756
$990$	−1.03031	−0.0327453
$991$	−7.70827	−0.244861	−0.122431	−	0.992477i	$-0.539069\pi$
$991$	−7.70827	−0.244861	−0.122431	+	0.992477i	$0.539069\pi$
$992$	−1.87738	−0.0596070
$993$	15.9384	0.505788
$994$	−5.54852	−0.175988
$995$	−11.3773	−0.360686
$996$	3.91754	0.124132
$997$	−26.0428	−0.824784	−0.412392	−	0.911006i	$-0.635307\pi$
$997$	−26.0428	−0.824784	−0.412392	+	0.911006i	$0.635307\pi$
$998$	−17.0779	−0.540591
$999$	2.17309	0.0687536

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.b.1.17	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.b.1.17	✓	23	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)

\(f(q)\)	\(=\)	\(q+1.02584 q^{2} +1.00000 q^{3} -0.947645 q^{4} +1.00000 q^{5} +1.02584 q^{6} +0.748026 q^{7} -3.02382 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.02584 q^{2} +1.00000 q^{3} -0.947645 q^{4} +1.00000 q^{5} +1.02584 q^{6} +0.748026 q^{7} -3.02382 q^{8} +1.00000 q^{9} +1.02584 q^{10} -1.00435 q^{11} -0.947645 q^{12} -5.81603 q^{13} +0.767357 q^{14} +1.00000 q^{15} -1.20668 q^{16} +6.14432 q^{17} +1.02584 q^{18} -2.92500 q^{19} -0.947645 q^{20} +0.748026 q^{21} -1.03031 q^{22} -0.823418 q^{23} -3.02382 q^{24} +1.00000 q^{25} -5.96633 q^{26} +1.00000 q^{27} -0.708863 q^{28} -0.995609 q^{29} +1.02584 q^{30} -0.390326 q^{31} +4.80978 q^{32} -1.00435 q^{33} +6.30311 q^{34} +0.748026 q^{35} -0.947645 q^{36} +2.17309 q^{37} -3.00060 q^{38} -5.81603 q^{39} -3.02382 q^{40} +2.10191 q^{41} +0.767357 q^{42} -6.36882 q^{43} +0.951767 q^{44} +1.00000 q^{45} -0.844698 q^{46} -10.7884 q^{47} -1.20668 q^{48} -6.44046 q^{49} +1.02584 q^{50} +6.14432 q^{51} +5.51153 q^{52} -7.05171 q^{53} +1.02584 q^{54} -1.00435 q^{55} -2.26190 q^{56} -2.92500 q^{57} -1.02134 q^{58} -10.3898 q^{59} -0.947645 q^{60} +9.39075 q^{61} -0.400413 q^{62} +0.748026 q^{63} +7.34744 q^{64} -5.81603 q^{65} -1.03031 q^{66} +7.10786 q^{67} -5.82263 q^{68} -0.823418 q^{69} +0.767357 q^{70} -7.23069 q^{71} -3.02382 q^{72} +3.76938 q^{73} +2.22925 q^{74} +1.00000 q^{75} +2.77187 q^{76} -0.751279 q^{77} -5.96633 q^{78} +2.43750 q^{79} -1.20668 q^{80} +1.00000 q^{81} +2.15623 q^{82} -4.13397 q^{83} -0.708863 q^{84} +6.14432 q^{85} -6.53341 q^{86} -0.995609 q^{87} +3.03698 q^{88} -13.7319 q^{89} +1.02584 q^{90} -4.35054 q^{91} +0.780309 q^{92} -0.390326 q^{93} -11.0672 q^{94} -2.92500 q^{95} +4.80978 q^{96} -17.1458 q^{97} -6.60690 q^{98} -1.00435 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * q^99

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