LMFDB - Embedded newform 6015.2.a.h.1.11

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:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-1.46868 q^{2} +1.00000 q^{3} +0.157024 q^{4} -1.00000 q^{5} -1.46868 q^{6} -1.36125 q^{7} +2.70674 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.46868 q^{2} +1.00000 q^{3} +0.157024 q^{4} -1.00000 q^{5} -1.46868 q^{6} -1.36125 q^{7} +2.70674 q^{8} +1.00000 q^{9} +1.46868 q^{10} +0.919947 q^{11} +0.157024 q^{12} -2.49744 q^{13} +1.99924 q^{14} -1.00000 q^{15} -4.28939 q^{16} -0.335196 q^{17} -1.46868 q^{18} -2.84577 q^{19} -0.157024 q^{20} -1.36125 q^{21} -1.35111 q^{22} +6.04761 q^{23} +2.70674 q^{24} +1.00000 q^{25} +3.66795 q^{26} +1.00000 q^{27} -0.213748 q^{28} +0.957827 q^{29} +1.46868 q^{30} +9.05824 q^{31} +0.886259 q^{32} +0.919947 q^{33} +0.492296 q^{34} +1.36125 q^{35} +0.157024 q^{36} -5.39210 q^{37} +4.17953 q^{38} -2.49744 q^{39} -2.70674 q^{40} -3.36782 q^{41} +1.99924 q^{42} -2.20909 q^{43} +0.144454 q^{44} -1.00000 q^{45} -8.88201 q^{46} +6.54392 q^{47} -4.28939 q^{48} -5.14701 q^{49} -1.46868 q^{50} -0.335196 q^{51} -0.392158 q^{52} -2.32031 q^{53} -1.46868 q^{54} -0.919947 q^{55} -3.68454 q^{56} -2.84577 q^{57} -1.40674 q^{58} -11.0470 q^{59} -0.157024 q^{60} -2.16395 q^{61} -13.3037 q^{62} -1.36125 q^{63} +7.27715 q^{64} +2.49744 q^{65} -1.35111 q^{66} -7.99431 q^{67} -0.0526338 q^{68} +6.04761 q^{69} -1.99924 q^{70} +2.00279 q^{71} +2.70674 q^{72} +7.50619 q^{73} +7.91928 q^{74} +1.00000 q^{75} -0.446853 q^{76} -1.25227 q^{77} +3.66795 q^{78} +8.79976 q^{79} +4.28939 q^{80} +1.00000 q^{81} +4.94625 q^{82} -4.52944 q^{83} -0.213748 q^{84} +0.335196 q^{85} +3.24444 q^{86} +0.957827 q^{87} +2.49006 q^{88} -5.84771 q^{89} +1.46868 q^{90} +3.39964 q^{91} +0.949619 q^{92} +9.05824 q^{93} -9.61094 q^{94} +2.84577 q^{95} +0.886259 q^{96} +3.98142 q^{97} +7.55932 q^{98} +0.919947 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - 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 $

$2$	−1.46868	−1.03851	−0.519257	−	0.854618i	$-0.673791\pi$
$2$	−1.46868	−1.03851	−0.519257	+	0.854618i	$0.673791\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.157024	0.0785119
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.46868	−0.599587
$7$	−1.36125	−0.514502	−0.257251	−	0.966345i	$-0.582817\pi$
$7$	−1.36125	−0.514502	−0.257251	+	0.966345i	$0.582817\pi$
$8$	2.70674	0.956979
$9$	1.00000	0.333333
$10$	1.46868	0.464438
$11$	0.919947	0.277374	0.138687	−	0.990336i	$-0.455712\pi$
$11$	0.919947	0.277374	0.138687	+	0.990336i	$0.455712\pi$
$12$	0.157024	0.0453289
$13$	−2.49744	−0.692666	−0.346333	−	0.938112i	$-0.612573\pi$
$13$	−2.49744	−0.692666	−0.346333	+	0.938112i	$0.612573\pi$
$14$	1.99924	0.534318
$15$	−1.00000	−0.258199
$16$	−4.28939	−1.07235
$17$	−0.335196	−0.0812970	−0.0406485	−	0.999174i	$-0.512942\pi$
$17$	−0.335196	−0.0812970	−0.0406485	+	0.999174i	$0.512942\pi$
$18$	−1.46868	−0.346171
$19$	−2.84577	−0.652864	−0.326432	−	0.945221i	$-0.605846\pi$
$19$	−2.84577	−0.652864	−0.326432	+	0.945221i	$0.605846\pi$
$20$	−0.157024	−0.0351116
$21$	−1.36125	−0.297048
$22$	−1.35111	−0.288057
$23$	6.04761	1.26101	0.630507	−	0.776184i	$-0.282847\pi$
$23$	6.04761	1.26101	0.630507	+	0.776184i	$0.282847\pi$
$24$	2.70674	0.552512
$25$	1.00000	0.200000
$26$	3.66795	0.719344
$27$	1.00000	0.192450
$28$	−0.213748	−0.0403946
$29$	0.957827	0.177864	0.0889320	−	0.996038i	$-0.471655\pi$
$29$	0.957827	0.177864	0.0889320	+	0.996038i	$0.471655\pi$
$30$	1.46868	0.268143
$31$	9.05824	1.62691	0.813454	−	0.581629i	$-0.197584\pi$
$31$	9.05824	1.62691	0.813454	+	0.581629i	$0.197584\pi$
$32$	0.886259	0.156670
$33$	0.919947	0.160142
$34$	0.492296	0.0844281
$35$	1.36125	0.230092
$36$	0.157024	0.0261706
$37$	−5.39210	−0.886456	−0.443228	−	0.896409i	$-0.646167\pi$
$37$	−5.39210	−0.886456	−0.443228	+	0.896409i	$0.646167\pi$
$38$	4.17953	0.678008
$39$	−2.49744	−0.399911
$40$	−2.70674	−0.427974
$41$	−3.36782	−0.525964	−0.262982	−	0.964801i	$-0.584706\pi$
$41$	−3.36782	−0.525964	−0.262982	+	0.964801i	$0.584706\pi$
$42$	1.99924	0.308489
$43$	−2.20909	−0.336882	−0.168441	−	0.985712i	$-0.553873\pi$
$43$	−2.20909	−0.336882	−0.168441	+	0.985712i	$0.553873\pi$
$44$	0.144454	0.0217772
$45$	−1.00000	−0.149071
$46$	−8.88201	−1.30958
$47$	6.54392	0.954529	0.477265	−	0.878760i	$-0.341628\pi$
$47$	6.54392	0.954529	0.477265	+	0.878760i	$0.341628\pi$
$48$	−4.28939	−0.619120
$49$	−5.14701	−0.735287
$50$	−1.46868	−0.207703
$51$	−0.335196	−0.0469368
$52$	−0.392158	−0.0543826
$53$	−2.32031	−0.318719	−0.159360	−	0.987221i	$-0.550943\pi$
$53$	−2.32031	−0.318719	−0.159360	+	0.987221i	$0.550943\pi$
$54$	−1.46868	−0.199862
$55$	−0.919947	−0.124046
$56$	−3.68454	−0.492368
$57$	−2.84577	−0.376931
$58$	−1.40674	−0.184714
$59$	−11.0470	−1.43820	−0.719100	−	0.694906i	$-0.755446\pi$
$59$	−11.0470	−1.43820	−0.719100	+	0.694906i	$0.755446\pi$
$60$	−0.157024	−0.0202717
$61$	−2.16395	−0.277065	−0.138532	−	0.990358i	$-0.544239\pi$
$61$	−2.16395	−0.277065	−0.138532	+	0.990358i	$0.544239\pi$
$62$	−13.3037	−1.68957
$63$	−1.36125	−0.171501
$64$	7.27715	0.909644
$65$	2.49744	0.309770
$66$	−1.35111	−0.166310
$67$	−7.99431	−0.976661	−0.488330	−	0.872659i	$-0.662394\pi$
$67$	−7.99431	−0.976661	−0.488330	+	0.872659i	$0.662394\pi$
$68$	−0.0526338	−0.00638278
$69$	6.04761	0.728047
$70$	−1.99924	−0.238954
$71$	2.00279	0.237688	0.118844	−	0.992913i	$-0.462081\pi$
$71$	2.00279	0.237688	0.118844	+	0.992913i	$0.462081\pi$
$72$	2.70674	0.318993
$73$	7.50619	0.878534	0.439267	−	0.898357i	$-0.355238\pi$
$73$	7.50619	0.878534	0.439267	+	0.898357i	$0.355238\pi$
$74$	7.91928	0.920597
$75$	1.00000	0.115470
$76$	−0.446853	−0.0512576
$77$	−1.25227	−0.142710
$78$	3.66795	0.415313
$79$	8.79976	0.990050	0.495025	−	0.868879i	$-0.335159\pi$
$79$	8.79976	0.990050	0.495025	+	0.868879i	$0.335159\pi$
$80$	4.28939	0.479569
$81$	1.00000	0.111111
$82$	4.94625	0.546222
$83$	−4.52944	−0.497171	−0.248585	−	0.968610i	$-0.579966\pi$
$83$	−4.52944	−0.497171	−0.248585	+	0.968610i	$0.579966\pi$
$84$	−0.213748	−0.0233218
$85$	0.335196	0.0363571
$86$	3.24444	0.349857
$87$	0.957827	0.102690
$88$	2.49006	0.265441
$89$	−5.84771	−0.619856	−0.309928	−	0.950760i	$-0.600305\pi$
$89$	−5.84771	−0.619856	−0.309928	+	0.950760i	$0.600305\pi$
$90$	1.46868	0.154813
$91$	3.39964	0.356379
$92$	0.949619	0.0990046
$93$	9.05824	0.939296
$94$	−9.61094	−0.991292
$95$	2.84577	0.291970
$96$	0.886259	0.0904534
$97$	3.98142	0.404252	0.202126	−	0.979360i	$-0.435215\pi$
$97$	3.98142	0.404252	0.202126	+	0.979360i	$0.435215\pi$
$98$	7.55932	0.763606
$99$	0.919947	0.0924581
$100$	0.157024	0.0157024
$101$	8.45817	0.841619	0.420810	−	0.907149i	$-0.361746\pi$
$101$	8.45817	0.841619	0.420810	+	0.907149i	$0.361746\pi$
$102$	0.492296	0.0487446
$103$	5.67895	0.559563	0.279782	−	0.960064i	$-0.409738\pi$
$103$	5.67895	0.559563	0.279782	+	0.960064i	$0.409738\pi$
$104$	−6.75994	−0.662867
$105$	1.36125	0.132844
$106$	3.40780	0.330995
$107$	0.879789	0.0850524	0.0425262	−	0.999095i	$-0.486459\pi$
$107$	0.879789	0.0850524	0.0425262	+	0.999095i	$0.486459\pi$
$108$	0.157024	0.0151096
$109$	−2.85590	−0.273545	−0.136773	−	0.990602i	$-0.543673\pi$
$109$	−2.85590	−0.273545	−0.136773	+	0.990602i	$0.543673\pi$
$110$	1.35111	0.128823
$111$	−5.39210	−0.511796
$112$	5.83891	0.551726
$113$	15.5210	1.46009	0.730047	−	0.683397i	$-0.239498\pi$
$113$	15.5210	1.46009	0.730047	+	0.683397i	$0.239498\pi$
$114$	4.17953	0.391448
$115$	−6.04761	−0.563943
$116$	0.150402	0.0139644
$117$	−2.49744	−0.230889
$118$	16.2246	1.49359
$119$	0.456284	0.0418275
$120$	−2.70674	−0.247091
$121$	−10.1537	−0.923063
$122$	3.17815	0.287736
$123$	−3.36782	−0.303666
$124$	1.42236	0.127732
$125$	−1.00000	−0.0894427
$126$	1.99924	0.178106
$127$	20.0754	1.78141	0.890703	−	0.454587i	$-0.150213\pi$
$127$	20.0754	1.78141	0.890703	+	0.454587i	$0.150213\pi$
$128$	−12.4603	−1.10135
$129$	−2.20909	−0.194499
$130$	−3.66795	−0.321700
$131$	14.5947	1.27514	0.637571	−	0.770392i	$-0.279939\pi$
$131$	14.5947	1.27514	0.637571	+	0.770392i	$0.279939\pi$
$132$	0.144454	0.0125731
$133$	3.87379	0.335900
$134$	11.7411	1.01428
$135$	−1.00000	−0.0860663
$136$	−0.907290	−0.0777994
$137$	−20.5811	−1.75836	−0.879181	−	0.476488i	$-0.841909\pi$
$137$	−20.5811	−1.75836	−0.879181	+	0.476488i	$0.841909\pi$
$138$	−8.88201	−0.756087
$139$	9.82167	0.833063	0.416532	−	0.909121i	$-0.363246\pi$
$139$	9.82167	0.833063	0.416532	+	0.909121i	$0.363246\pi$
$140$	0.213748	0.0180650
$141$	6.54392	0.551098
$142$	−2.94146	−0.246842
$143$	−2.29752	−0.192128
$144$	−4.28939	−0.357449
$145$	−0.957827	−0.0795432
$146$	−11.0242	−0.912370
$147$	−5.14701	−0.424518
$148$	−0.846688	−0.0695973
$149$	2.99513	0.245371	0.122685	−	0.992446i	$-0.460849\pi$
$149$	2.99513	0.245371	0.122685	+	0.992446i	$0.460849\pi$
$150$	−1.46868	−0.119917
$151$	−8.31318	−0.676517	−0.338259	−	0.941053i	$-0.609838\pi$
$151$	−8.31318	−0.676517	−0.338259	+	0.941053i	$0.609838\pi$
$152$	−7.70277	−0.624777
$153$	−0.335196	−0.0270990
$154$	1.83919	0.148206
$155$	−9.05824	−0.727576
$156$	−0.392158	−0.0313978
$157$	10.4685	0.835476	0.417738	−	0.908567i	$-0.362823\pi$
$157$	10.4685	0.835476	0.417738	+	0.908567i	$0.362823\pi$
$158$	−12.9240	−1.02818
$159$	−2.32031	−0.184013
$160$	−0.886259	−0.0700649
$161$	−8.23228	−0.648795
$162$	−1.46868	−0.115390
$163$	16.7071	1.30860	0.654302	−	0.756234i	$-0.272963\pi$
$163$	16.7071	1.30860	0.654302	+	0.756234i	$0.272963\pi$
$164$	−0.528827	−0.0412945
$165$	−0.919947	−0.0716178
$166$	6.65230	0.516319
$167$	−16.1323	−1.24835	−0.624176	−	0.781284i	$-0.714565\pi$
$167$	−16.1323	−1.24835	−0.624176	+	0.781284i	$0.714565\pi$
$168$	−3.68454	−0.284269
$169$	−6.76277	−0.520213
$170$	−0.492296	−0.0377574
$171$	−2.84577	−0.217621
$172$	−0.346879	−0.0264493
$173$	−16.4730	−1.25242	−0.626211	−	0.779654i	$-0.715395\pi$
$173$	−16.4730	−1.25242	−0.626211	+	0.779654i	$0.715395\pi$
$174$	−1.40674	−0.106645
$175$	−1.36125	−0.102900
$176$	−3.94601	−0.297442
$177$	−11.0470	−0.830345
$178$	8.58841	0.643729
$179$	8.69897	0.650191	0.325096	−	0.945681i	$-0.394604\pi$
$179$	8.69897	0.650191	0.325096	+	0.945681i	$0.394604\pi$
$180$	−0.157024	−0.0117039
$181$	7.22646	0.537138	0.268569	−	0.963260i	$-0.413449\pi$
$181$	7.22646	0.537138	0.268569	+	0.963260i	$0.413449\pi$
$182$	−4.99298	−0.370104
$183$	−2.16395	−0.159963
$184$	16.3693	1.20676
$185$	5.39210	0.396435
$186$	−13.3037	−0.975473
$187$	−0.308362	−0.0225497
$188$	1.02755	0.0749419
$189$	−1.36125	−0.0990160
$190$	−4.17953	−0.303215
$191$	6.51038	0.471075	0.235537	−	0.971865i	$-0.424315\pi$
$191$	6.51038	0.471075	0.235537	+	0.971865i	$0.424315\pi$
$192$	7.27715	0.525183
$193$	4.27238	0.307533	0.153766	−	0.988107i	$-0.450860\pi$
$193$	4.27238	0.307533	0.153766	+	0.988107i	$0.450860\pi$
$194$	−5.84743	−0.419821
$195$	2.49744	0.178846
$196$	−0.808203	−0.0577288
$197$	−27.4336	−1.95456	−0.977280	−	0.211953i	$-0.932018\pi$
$197$	−27.4336	−1.95456	−0.977280	+	0.211953i	$0.932018\pi$
$198$	−1.35111	−0.0960191
$199$	−9.51015	−0.674157	−0.337078	−	0.941477i	$-0.609439\pi$
$199$	−9.51015	−0.674157	−0.337078	+	0.941477i	$0.609439\pi$
$200$	2.70674	0.191396
$201$	−7.99431	−0.563875
$202$	−12.4223	−0.874033
$203$	−1.30384	−0.0915115
$204$	−0.0526338	−0.00368510
$205$	3.36782	0.235218
$206$	−8.34056	−0.581114
$207$	6.04761	0.420338
$208$	10.7125	0.742779
$209$	−2.61796	−0.181088
$210$	−1.99924	−0.137960
$211$	−2.20047	−0.151487	−0.0757434	−	0.997127i	$-0.524133\pi$
$211$	−2.20047	−0.151487	−0.0757434	+	0.997127i	$0.524133\pi$
$212$	−0.364344	−0.0250233
$213$	2.00279	0.137229
$214$	−1.29213	−0.0883281
$215$	2.20909	0.150658
$216$	2.70674	0.184171
$217$	−12.3305	−0.837049
$218$	4.19440	0.284081
$219$	7.50619	0.507222
$220$	−0.144454	−0.00973906
$221$	0.837133	0.0563117
$222$	7.91928	0.531507
$223$	15.6826	1.05018	0.525092	−	0.851045i	$-0.324031\pi$
$223$	15.6826	1.05018	0.525092	+	0.851045i	$0.324031\pi$
$224$	−1.20642	−0.0806071
$225$	1.00000	0.0666667
$226$	−22.7954	−1.51633
$227$	10.5916	0.702987	0.351494	−	0.936190i	$-0.385674\pi$
$227$	10.5916	0.702987	0.351494	+	0.936190i	$0.385674\pi$
$228$	−0.446853	−0.0295936
$229$	0.953698	0.0630222	0.0315111	−	0.999503i	$-0.489968\pi$
$229$	0.953698	0.0630222	0.0315111	+	0.999503i	$0.489968\pi$
$230$	8.88201	0.585662
$231$	−1.25227	−0.0823936
$232$	2.59259	0.170212
$233$	20.4543	1.34000	0.670002	−	0.742359i	$-0.266293\pi$
$233$	20.4543	1.34000	0.670002	+	0.742359i	$0.266293\pi$
$234$	3.66795	0.239781
$235$	−6.54392	−0.426879
$236$	−1.73465	−0.112916
$237$	8.79976	0.571606
$238$	−0.670136	−0.0434384
$239$	−11.7121	−0.757594	−0.378797	−	0.925480i	$-0.623662\pi$
$239$	−11.7121	−0.757594	−0.378797	+	0.925480i	$0.623662\pi$
$240$	4.28939	0.276879
$241$	13.3356	0.859019	0.429509	−	0.903062i	$-0.358687\pi$
$241$	13.3356	0.859019	0.429509	+	0.903062i	$0.358687\pi$
$242$	14.9125	0.958615
$243$	1.00000	0.0641500
$244$	−0.339791	−0.0217529
$245$	5.14701	0.328830
$246$	4.94625	0.315361
$247$	7.10715	0.452217
$248$	24.5184	1.55692
$249$	−4.52944	−0.287042
$250$	1.46868	0.0928875
$251$	18.9529	1.19630	0.598148	−	0.801385i	$-0.295903\pi$
$251$	18.9529	1.19630	0.598148	+	0.801385i	$0.295903\pi$
$252$	−0.213748	−0.0134649
$253$	5.56348	0.349773
$254$	−29.4844	−1.85001
$255$	0.335196	0.0209908
$256$	3.74595	0.234122
$257$	2.58334	0.161144	0.0805722	−	0.996749i	$-0.474325\pi$
$257$	2.58334	0.161144	0.0805722	+	0.996749i	$0.474325\pi$
$258$	3.24444	0.201990
$259$	7.33997	0.456084
$260$	0.392158	0.0243206
$261$	0.957827	0.0592880
$262$	−21.4349	−1.32425
$263$	12.5570	0.774297	0.387149	−	0.922017i	$-0.373460\pi$
$263$	12.5570	0.774297	0.387149	+	0.922017i	$0.373460\pi$
$264$	2.49006	0.153253
$265$	2.32031	0.142536
$266$	−5.68936	−0.348837
$267$	−5.84771	−0.357874
$268$	−1.25530	−0.0766795
$269$	−15.5178	−0.946137	−0.473068	−	0.881026i	$-0.656854\pi$
$269$	−15.5178	−0.946137	−0.473068	+	0.881026i	$0.656854\pi$
$270$	1.46868	0.0893811
$271$	15.4115	0.936183	0.468092	−	0.883680i	$-0.344942\pi$
$271$	15.4115	0.936183	0.468092	+	0.883680i	$0.344942\pi$
$272$	1.43779	0.0871786
$273$	3.39964	0.205755
$274$	30.2271	1.82608
$275$	0.919947	0.0554749
$276$	0.949619	0.0571603
$277$	12.5502	0.754067	0.377033	−	0.926200i	$-0.376944\pi$
$277$	12.5502	0.754067	0.377033	+	0.926200i	$0.376944\pi$
$278$	−14.4249	−0.865148
$279$	9.05824	0.542303
$280$	3.68454	0.220194
$281$	11.4738	0.684470	0.342235	−	0.939614i	$-0.388816\pi$
$281$	11.4738	0.684470	0.342235	+	0.939614i	$0.388816\pi$
$282$	−9.61094	−0.572323
$283$	10.9529	0.651081	0.325541	−	0.945528i	$-0.394454\pi$
$283$	10.9529	0.651081	0.325541	+	0.945528i	$0.394454\pi$
$284$	0.314486	0.0186613
$285$	2.84577	0.168569
$286$	3.37432	0.199528
$287$	4.58442	0.270610
$288$	0.886259	0.0522233
$289$	−16.8876	−0.993391
$290$	1.40674	0.0826068
$291$	3.98142	0.233395
$292$	1.17865	0.0689754
$293$	−17.2645	−1.00861	−0.504303	−	0.863527i	$-0.668250\pi$
$293$	−17.2645	−1.00861	−0.504303	+	0.863527i	$0.668250\pi$
$294$	7.55932	0.440868
$295$	11.0470	0.643183
$296$	−14.5950	−0.848319
$297$	0.919947	0.0533807
$298$	−4.39889	−0.254821
$299$	−15.1036	−0.873462
$300$	0.157024	0.00906578
$301$	3.00711	0.173327
$302$	12.2094	0.702573
$303$	8.45817	0.485909
$304$	12.2066	0.700097
$305$	2.16395	0.123907
$306$	0.492296	0.0281427
$307$	10.0092	0.571256	0.285628	−	0.958341i	$-0.407798\pi$
$307$	10.0092	0.571256	0.285628	+	0.958341i	$0.407798\pi$
$308$	−0.196637	−0.0112044
$309$	5.67895	0.323064
$310$	13.3037	0.755598
$311$	−7.58733	−0.430238	−0.215119	−	0.976588i	$-0.569014\pi$
$311$	−7.58733	−0.430238	−0.215119	+	0.976588i	$0.569014\pi$
$312$	−6.75994	−0.382706
$313$	27.3727	1.54720	0.773598	−	0.633676i	$-0.218455\pi$
$313$	27.3727	1.54720	0.773598	+	0.633676i	$0.218455\pi$
$314$	−15.3749	−0.867654
$315$	1.36125	0.0766975
$316$	1.38177	0.0777307
$317$	−2.17285	−0.122039	−0.0610197	−	0.998137i	$-0.519435\pi$
$317$	−2.17285	−0.122039	−0.0610197	+	0.998137i	$0.519435\pi$
$318$	3.40780	0.191100
$319$	0.881150	0.0493349
$320$	−7.27715	−0.406805
$321$	0.879789	0.0491050
$322$	12.0906	0.673783
$323$	0.953890	0.0530759
$324$	0.157024	0.00872355
$325$	−2.49744	−0.138533
$326$	−24.5374	−1.35900
$327$	−2.85590	−0.157932
$328$	−9.11582	−0.503337
$329$	−8.90789	−0.491108
$330$	1.35111	0.0743761
$331$	−29.4874	−1.62077	−0.810387	−	0.585894i	$-0.800743\pi$
$331$	−29.4874	−1.62077	−0.810387	+	0.585894i	$0.800743\pi$
$332$	−0.711230	−0.0390338
$333$	−5.39210	−0.295485
$334$	23.6932	1.29643
$335$	7.99431	0.436776
$336$	5.83891	0.318539
$337$	22.1814	1.20830	0.604149	−	0.796872i	$-0.293513\pi$
$337$	22.1814	1.20830	0.604149	+	0.796872i	$0.293513\pi$
$338$	9.93235	0.540249
$339$	15.5210	0.842986
$340$	0.0526338	0.00285447
$341$	8.33310	0.451263
$342$	4.17953	0.226003
$343$	16.5351	0.892810
$344$	−5.97943	−0.322389
$345$	−6.04761	−0.325592
$346$	24.1936	1.30066
$347$	16.5148	0.886563	0.443282	−	0.896382i	$-0.353814\pi$
$347$	16.5148	0.886563	0.443282	+	0.896382i	$0.353814\pi$
$348$	0.150402	0.00806238
$349$	20.3478	1.08920	0.544598	−	0.838697i	$-0.316682\pi$
$349$	20.3478	1.08920	0.544598	+	0.838697i	$0.316682\pi$
$350$	1.99924	0.106864
$351$	−2.49744	−0.133304
$352$	0.815311	0.0434562
$353$	25.9199	1.37958	0.689788	−	0.724012i	$-0.257704\pi$
$353$	25.9199	1.37958	0.689788	+	0.724012i	$0.257704\pi$
$354$	16.2246	0.862326
$355$	−2.00279	−0.106297
$356$	−0.918229	−0.0486661
$357$	0.456284	0.0241491
$358$	−12.7760	−0.675233
$359$	23.7770	1.25490	0.627452	−	0.778656i	$-0.284098\pi$
$359$	23.7770	1.25490	0.627452	+	0.778656i	$0.284098\pi$
$360$	−2.70674	−0.142658
$361$	−10.9016	−0.573769
$362$	−10.6134	−0.557826
$363$	−10.1537	−0.532931
$364$	0.533824	0.0279800
$365$	−7.50619	−0.392892
$366$	3.17815	0.166124
$367$	18.9663	0.990034	0.495017	−	0.868883i	$-0.335162\pi$
$367$	18.9663	0.990034	0.495017	+	0.868883i	$0.335162\pi$
$368$	−25.9406	−1.35225
$369$	−3.36782	−0.175321
$370$	−7.91928	−0.411704
$371$	3.15851	0.163982
$372$	1.42236	0.0737459
$373$	−0.307344	−0.0159137	−0.00795684	−	0.999968i	$-0.502533\pi$
$373$	−0.307344	−0.0159137	−0.00795684	+	0.999968i	$0.502533\pi$
$374$	0.452886	0.0234182
$375$	−1.00000	−0.0516398
$376$	17.7127	0.913464
$377$	−2.39212	−0.123200
$378$	1.99924	0.102830
$379$	30.7333	1.57867	0.789333	−	0.613965i	$-0.210427\pi$
$379$	30.7333	1.57867	0.789333	+	0.613965i	$0.210427\pi$
$380$	0.446853	0.0229231
$381$	20.0754	1.02849
$382$	−9.56168	−0.489218
$383$	4.93572	0.252203	0.126102	−	0.992017i	$-0.459753\pi$
$383$	4.93572	0.252203	0.126102	+	0.992017i	$0.459753\pi$
$384$	−12.4603	−0.635864
$385$	1.25227	0.0638218
$386$	−6.27477	−0.319377
$387$	−2.20909	−0.112294
$388$	0.625177	0.0317386
$389$	12.5502	0.636320	0.318160	−	0.948037i	$-0.396935\pi$
$389$	12.5502	0.636320	0.318160	+	0.948037i	$0.396935\pi$
$390$	−3.66795	−0.185734
$391$	−2.02713	−0.102517
$392$	−13.9316	−0.703654
$393$	14.5947	0.736203
$394$	40.2911	2.02984
$395$	−8.79976	−0.442764
$396$	0.144454	0.00725907
$397$	−25.3275	−1.27115	−0.635575	−	0.772039i	$-0.719237\pi$
$397$	−25.3275	−1.27115	−0.635575	+	0.772039i	$0.719237\pi$
$398$	13.9674	0.700122
$399$	3.87379	0.193932
$400$	−4.28939	−0.214470
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	11.7411	0.585593
$403$	−22.6225	−1.12691
$404$	1.32813	0.0660771
$405$	−1.00000	−0.0496904
$406$	1.91492	0.0950360
$407$	−4.96045	−0.245880
$408$	−0.907290	−0.0449175
$409$	0.974472	0.0481845	0.0240923	−	0.999710i	$-0.492330\pi$
$409$	0.974472	0.0481845	0.0240923	+	0.999710i	$0.492330\pi$
$410$	−4.94625	−0.244278
$411$	−20.5811	−1.01519
$412$	0.891730	0.0439324
$413$	15.0377	0.739958
$414$	−8.88201	−0.436527
$415$	4.52944	0.222342
$416$	−2.21338	−0.108520
$417$	9.82167	0.480969
$418$	3.84494	0.188062
$419$	−33.9865	−1.66035	−0.830173	−	0.557505i	$-0.811759\pi$
$419$	−33.9865	−1.66035	−0.830173	+	0.557505i	$0.811759\pi$
$420$	0.213748	0.0104298
$421$	0.596409	0.0290672	0.0145336	−	0.999894i	$-0.495374\pi$
$421$	0.596409	0.0290672	0.0145336	+	0.999894i	$0.495374\pi$
$422$	3.23179	0.157321
$423$	6.54392	0.318176
$424$	−6.28049	−0.305008
$425$	−0.335196	−0.0162594
$426$	−2.94146	−0.142514
$427$	2.94566	0.142551
$428$	0.138148	0.00667763
$429$	−2.29752	−0.110925
$430$	−3.24444	−0.156461
$431$	−3.04313	−0.146583	−0.0732913	−	0.997311i	$-0.523350\pi$
$431$	−3.04313	−0.146583	−0.0732913	+	0.997311i	$0.523350\pi$
$432$	−4.28939	−0.206373
$433$	7.71018	0.370528	0.185264	−	0.982689i	$-0.440686\pi$
$433$	7.71018	0.370528	0.185264	+	0.982689i	$0.440686\pi$
$434$	18.1096	0.869287
$435$	−0.957827	−0.0459243
$436$	−0.448444	−0.0214766
$437$	−17.2101	−0.823271
$438$	−11.0242	−0.526757
$439$	31.8341	1.51936	0.759678	−	0.650299i	$-0.225356\pi$
$439$	31.8341	1.51936	0.759678	+	0.650299i	$0.225356\pi$
$440$	−2.49006	−0.118709
$441$	−5.14701	−0.245096
$442$	−1.22948	−0.0584805
$443$	−36.0248	−1.71159	−0.855795	−	0.517315i	$-0.826932\pi$
$443$	−36.0248	−1.71159	−0.855795	+	0.517315i	$0.826932\pi$
$444$	−0.846688	−0.0401820
$445$	5.84771	0.277208
$446$	−23.0327	−1.09063
$447$	2.99513	0.141665
$448$	−9.90599	−0.468014
$449$	38.8632	1.83407	0.917035	−	0.398807i	$-0.130576\pi$
$449$	38.8632	1.83407	0.917035	+	0.398807i	$0.130576\pi$
$450$	−1.46868	−0.0692343
$451$	−3.09821	−0.145889
$452$	2.43717	0.114635
$453$	−8.31318	−0.390587
$454$	−15.5556	−0.730062
$455$	−3.39964	−0.159377
$456$	−7.70277	−0.360715
$457$	30.5916	1.43101	0.715506	−	0.698606i	$-0.246196\pi$
$457$	30.5916	1.43101	0.715506	+	0.698606i	$0.246196\pi$
$458$	−1.40068	−0.0654494
$459$	−0.335196	−0.0156456
$460$	−0.949619	−0.0442762
$461$	7.30757	0.340347	0.170174	−	0.985414i	$-0.445567\pi$
$461$	7.30757	0.340347	0.170174	+	0.985414i	$0.445567\pi$
$462$	1.83919	0.0855669
$463$	20.9889	0.975439	0.487719	−	0.873000i	$-0.337829\pi$
$463$	20.9889	0.975439	0.487719	+	0.873000i	$0.337829\pi$
$464$	−4.10850	−0.190732
$465$	−9.05824	−0.420066
$466$	−30.0408	−1.39161
$467$	−39.0693	−1.80791	−0.903956	−	0.427626i	$-0.859350\pi$
$467$	−39.0693	−1.80791	−0.903956	+	0.427626i	$0.859350\pi$
$468$	−0.392158	−0.0181275
$469$	10.8822	0.502494
$470$	9.61094	0.443319
$471$	10.4685	0.482362
$472$	−29.9015	−1.37633
$473$	−2.03224	−0.0934425
$474$	−12.9240	−0.593621
$475$	−2.84577	−0.130573
$476$	0.0716475	0.00328396
$477$	−2.32031	−0.106240
$478$	17.2014	0.786772
$479$	29.9814	1.36988	0.684942	−	0.728597i	$-0.259827\pi$
$479$	29.9814	1.36988	0.684942	+	0.728597i	$0.259827\pi$
$480$	−0.886259	−0.0404520
$481$	13.4665	0.614018
$482$	−19.5857	−0.892103
$483$	−8.23228	−0.374582
$484$	−1.59437	−0.0724715
$485$	−3.98142	−0.180787
$486$	−1.46868	−0.0666207
$487$	40.2790	1.82522	0.912609	−	0.408834i	$-0.134065\pi$
$487$	40.2790	1.82522	0.912609	+	0.408834i	$0.134065\pi$
$488$	−5.85725	−0.265145
$489$	16.7071	0.755523
$490$	−7.55932	−0.341495
$491$	−2.85049	−0.128641	−0.0643204	−	0.997929i	$-0.520488\pi$
$491$	−2.85049	−0.128641	−0.0643204	+	0.997929i	$0.520488\pi$
$492$	−0.528827	−0.0238414
$493$	−0.321060	−0.0144598
$494$	−10.4381	−0.469634
$495$	−0.919947	−0.0413485
$496$	−38.8544	−1.74461
$497$	−2.72629	−0.122291
$498$	6.65230	0.298097
$499$	−17.5085	−0.783790	−0.391895	−	0.920010i	$-0.628180\pi$
$499$	−17.5085	−0.783790	−0.391895	+	0.920010i	$0.628180\pi$
$500$	−0.157024	−0.00702232
$501$	−16.1323	−0.720736
$502$	−27.8358	−1.24237
$503$	26.5017	1.18165	0.590827	−	0.806798i	$-0.298802\pi$
$503$	26.5017	1.18165	0.590827	+	0.806798i	$0.298802\pi$
$504$	−3.68454	−0.164123
$505$	−8.45817	−0.376384
$506$	−8.17098	−0.363244
$507$	−6.76277	−0.300345
$508$	3.15232	0.139862
$509$	−29.3425	−1.30058	−0.650291	−	0.759686i	$-0.725353\pi$
$509$	−29.3425	−1.30058	−0.650291	+	0.759686i	$0.725353\pi$
$510$	−0.492296	−0.0217992
$511$	−10.2178	−0.452008
$512$	19.4191	0.858209
$513$	−2.84577	−0.125644
$514$	−3.79410	−0.167351
$515$	−5.67895	−0.250244
$516$	−0.346879	−0.0152705
$517$	6.02006	0.264762
$518$	−10.7801	−0.473649
$519$	−16.4730	−0.723086
$520$	6.75994	0.296443
$521$	−16.8487	−0.738154	−0.369077	−	0.929399i	$-0.620326\pi$
$521$	−16.8487	−0.738154	−0.369077	+	0.929399i	$0.620326\pi$
$522$	−1.40674	−0.0615715
$523$	−14.1016	−0.616619	−0.308310	−	0.951286i	$-0.599763\pi$
$523$	−14.1016	−0.616619	−0.308310	+	0.951286i	$0.599763\pi$
$524$	2.29171	0.100114
$525$	−1.36125	−0.0594096
$526$	−18.4422	−0.804119
$527$	−3.03629	−0.132263
$528$	−3.94601	−0.171728
$529$	13.5736	0.590156
$530$	−3.40780	−0.148025
$531$	−11.0470	−0.479400
$532$	0.608277	0.0263722
$533$	8.41093	0.364318
$534$	8.58841	0.371657
$535$	−0.879789	−0.0380366
$536$	−21.6386	−0.934644
$537$	8.69897	0.375388
$538$	22.7907	0.982577
$539$	−4.73498	−0.203950
$540$	−0.157024	−0.00675723
$541$	−9.05094	−0.389130	−0.194565	−	0.980890i	$-0.562330\pi$
$541$	−9.05094	−0.389130	−0.194565	+	0.980890i	$0.562330\pi$
$542$	−22.6346	−0.972240
$543$	7.22646	0.310117
$544$	−0.297070	−0.0127368
$545$	2.85590	0.122333
$546$	−4.99298	−0.213680
$547$	23.1019	0.987767	0.493884	−	0.869528i	$-0.335577\pi$
$547$	23.1019	0.987767	0.493884	+	0.869528i	$0.335577\pi$
$548$	−3.23172	−0.138052
$549$	−2.16395	−0.0923549
$550$	−1.35111	−0.0576115
$551$	−2.72575	−0.116121
$552$	16.3693	0.696725
$553$	−11.9786	−0.509383
$554$	−18.4322	−0.783109
$555$	5.39210	0.228882
$556$	1.54224	0.0654054
$557$	32.3369	1.37016	0.685080	−	0.728468i	$-0.259767\pi$
$557$	32.3369	1.37016	0.685080	+	0.728468i	$0.259767\pi$
$558$	−13.3037	−0.563189
$559$	5.51707	0.233347
$560$	−5.83891	−0.246739
$561$	−0.308362	−0.0130191
$562$	−16.8514	−0.710831
$563$	42.8994	1.80800	0.903998	−	0.427538i	$-0.140619\pi$
$563$	42.8994	1.80800	0.903998	+	0.427538i	$0.140619\pi$
$564$	1.02755	0.0432677
$565$	−15.5210	−0.652974
$566$	−16.0863	−0.676157
$567$	−1.36125	−0.0571669
$568$	5.42104	0.227462
$569$	14.7481	0.618272	0.309136	−	0.951018i	$-0.399960\pi$
$569$	14.7481	0.618272	0.309136	+	0.951018i	$0.399960\pi$
$570$	−4.17953	−0.175061
$571$	−27.4910	−1.15046	−0.575230	−	0.817991i	$-0.695088\pi$
$571$	−27.4910	−1.15046	−0.575230	+	0.817991i	$0.695088\pi$
$572$	−0.360765	−0.0150843
$573$	6.51038	0.271975
$574$	−6.73306	−0.281032
$575$	6.04761	0.252203
$576$	7.27715	0.303215
$577$	31.7976	1.32375	0.661877	−	0.749613i	$-0.269760\pi$
$577$	31.7976	1.32375	0.661877	+	0.749613i	$0.269760\pi$
$578$	24.8026	1.03165
$579$	4.27238	0.177554
$580$	−0.150402	−0.00624509
$581$	6.16568	0.255796
$582$	−5.84743	−0.242384
$583$	−2.13456	−0.0884046
$584$	20.3173	0.840738
$585$	2.49744	0.103257
$586$	25.3561	1.04745
$587$	9.66717	0.399007	0.199503	−	0.979897i	$-0.436067\pi$
$587$	9.66717	0.399007	0.199503	+	0.979897i	$0.436067\pi$
$588$	−0.808203	−0.0333297
$589$	−25.7777	−1.06215
$590$	−16.2246	−0.667955
$591$	−27.4336	−1.12847
$592$	23.1288	0.950589
$593$	27.6757	1.13651	0.568253	−	0.822854i	$-0.307620\pi$
$593$	27.6757	1.13651	0.568253	+	0.822854i	$0.307620\pi$
$594$	−1.35111	−0.0554366
$595$	−0.456284	−0.0187058
$596$	0.470307	0.0192645
$597$	−9.51015	−0.389225
$598$	22.1823	0.907103
$599$	27.0872	1.10675	0.553377	−	0.832931i	$-0.313339\pi$
$599$	27.0872	1.10675	0.553377	+	0.832931i	$0.313339\pi$
$600$	2.70674	0.110502
$601$	0.180058	0.00734471	0.00367235	−	0.999993i	$-0.498831\pi$
$601$	0.180058	0.00734471	0.00367235	+	0.999993i	$0.498831\pi$
$602$	−4.41648	−0.180002
$603$	−7.99431	−0.325554
$604$	−1.30537	−0.0531147
$605$	10.1537	0.412807
$606$	−12.4223	−0.504623
$607$	−36.5361	−1.48295	−0.741477	−	0.670978i	$-0.765874\pi$
$607$	−36.5361	−1.48295	−0.741477	+	0.670978i	$0.765874\pi$
$608$	−2.52209	−0.102284
$609$	−1.30384	−0.0528342
$610$	−3.17815	−0.128679
$611$	−16.3431	−0.661170
$612$	−0.0526338	−0.00212759
$613$	13.9673	0.564133	0.282067	−	0.959395i	$-0.408980\pi$
$613$	13.9673	0.564133	0.282067	+	0.959395i	$0.408980\pi$
$614$	−14.7003	−0.593258
$615$	3.36782	0.135803
$616$	−3.38958	−0.136570
$617$	0.574755	0.0231388	0.0115694	−	0.999933i	$-0.496317\pi$
$617$	0.574755	0.0231388	0.0115694	+	0.999933i	$0.496317\pi$
$618$	−8.34056	−0.335507
$619$	24.1300	0.969865	0.484933	−	0.874551i	$-0.338844\pi$
$619$	24.1300	0.969865	0.484933	+	0.874551i	$0.338844\pi$
$620$	−1.42236	−0.0571234
$621$	6.04761	0.242682
$622$	11.1434	0.446808
$623$	7.96016	0.318917
$624$	10.7125	0.428844
$625$	1.00000	0.0400000
$626$	−40.2018	−1.60679
$627$	−2.61796	−0.104551
$628$	1.64380	0.0655948
$629$	1.80741	0.0720662
$630$	−1.99924	−0.0796514
$631$	13.7667	0.548043	0.274022	−	0.961724i	$-0.411646\pi$
$631$	13.7667	0.548043	0.274022	+	0.961724i	$0.411646\pi$
$632$	23.8187	0.947457
$633$	−2.20047	−0.0874609
$634$	3.19122	0.126740
$635$	−20.0754	−0.796669
$636$	−0.364344	−0.0144472
$637$	12.8544	0.509309
$638$	−1.29413	−0.0512350
$639$	2.00279	0.0792292
$640$	12.4603	0.492538
$641$	39.0883	1.54390	0.771948	−	0.635686i	$-0.219282\pi$
$641$	39.0883	1.54390	0.771948	+	0.635686i	$0.219282\pi$
$642$	−1.29213	−0.0509963
$643$	−5.30464	−0.209195	−0.104597	−	0.994515i	$-0.533355\pi$
$643$	−5.30464	−0.209195	−0.104597	+	0.994515i	$0.533355\pi$
$644$	−1.29266	−0.0509381
$645$	2.20909	0.0869827
$646$	−1.40096	−0.0551200
$647$	−35.8774	−1.41049	−0.705243	−	0.708965i	$-0.749162\pi$
$647$	−35.8774	−1.41049	−0.705243	+	0.708965i	$0.749162\pi$
$648$	2.70674	0.106331
$649$	−10.1627	−0.398920
$650$	3.66795	0.143869
$651$	−12.3305	−0.483270
$652$	2.62342	0.102741
$653$	−5.26399	−0.205996	−0.102998	−	0.994682i	$-0.532843\pi$
$653$	−5.26399	−0.205996	−0.102998	+	0.994682i	$0.532843\pi$
$654$	4.19440	0.164014
$655$	−14.5947	−0.570261
$656$	14.4459	0.564017
$657$	7.50619	0.292845
$658$	13.0828	0.510022
$659$	−15.0435	−0.586011	−0.293006	−	0.956111i	$-0.594655\pi$
$659$	−15.0435	−0.586011	−0.293006	+	0.956111i	$0.594655\pi$
$660$	−0.144454	−0.00562285
$661$	−9.21991	−0.358613	−0.179306	−	0.983793i	$-0.557385\pi$
$661$	−9.21991	−0.358613	−0.179306	+	0.983793i	$0.557385\pi$
$662$	43.3076	1.68320
$663$	0.837133	0.0325116
$664$	−12.2600	−0.475782
$665$	−3.87379	−0.150219
$666$	7.91928	0.306866
$667$	5.79257	0.224289
$668$	−2.53315	−0.0980105
$669$	15.6826	0.606325
$670$	−11.7411	−0.453598
$671$	−1.99071	−0.0768507
$672$	−1.20642	−0.0465385
$673$	36.9303	1.42356	0.711780	−	0.702403i	$-0.247889\pi$
$673$	36.9303	1.42356	0.711780	+	0.702403i	$0.247889\pi$
$674$	−32.5774	−1.25483
$675$	1.00000	0.0384900
$676$	−1.06192	−0.0408429
$677$	−9.85325	−0.378691	−0.189346	−	0.981910i	$-0.560637\pi$
$677$	−9.85325	−0.378691	−0.189346	+	0.981910i	$0.560637\pi$
$678$	−22.7954	−0.875453
$679$	−5.41969	−0.207988
$680$	0.907290	0.0347930
$681$	10.5916	0.405870
$682$	−12.2387	−0.468643
$683$	29.9282	1.14517	0.572586	−	0.819845i	$-0.305940\pi$
$683$	29.9282	1.14517	0.572586	+	0.819845i	$0.305940\pi$
$684$	−0.446853	−0.0170859
$685$	20.5811	0.786363
$686$	−24.2847	−0.927195
$687$	0.953698	0.0363859
$688$	9.47563	0.361255
$689$	5.79485	0.220766
$690$	8.88201	0.338132
$691$	13.5513	0.515515	0.257757	−	0.966210i	$-0.417017\pi$
$691$	13.5513	0.515515	0.257757	+	0.966210i	$0.417017\pi$
$692$	−2.58666	−0.0983300
$693$	−1.25227	−0.0475699
$694$	−24.2550	−0.920709
$695$	−9.82167	−0.372557
$696$	2.59259	0.0982720
$697$	1.12888	0.0427593
$698$	−29.8845	−1.13114
$699$	20.4543	0.773651
$700$	−0.213748	−0.00807891
$701$	27.2744	1.03014	0.515070	−	0.857148i	$-0.327766\pi$
$701$	27.2744	1.03014	0.515070	+	0.857148i	$0.327766\pi$
$702$	3.66795	0.138438
$703$	15.3447	0.578735
$704$	6.69459	0.252312
$705$	−6.54392	−0.246458
$706$	−38.0680	−1.43271
$707$	−11.5136	−0.433015
$708$	−1.73465	−0.0651920
$709$	−43.1294	−1.61976	−0.809880	−	0.586596i	$-0.800468\pi$
$709$	−43.1294	−1.61976	−0.809880	+	0.586596i	$0.800468\pi$
$710$	2.94146	0.110391
$711$	8.79976	0.330017
$712$	−15.8282	−0.593189
$713$	54.7807	2.05155
$714$	−0.670136	−0.0250792
$715$	2.29752	0.0859222
$716$	1.36594	0.0510478
$717$	−11.7121	−0.437397
$718$	−34.9209	−1.30324
$719$	−31.8177	−1.18660	−0.593301	−	0.804981i	$-0.702175\pi$
$719$	−31.8177	−1.18660	−0.593301	+	0.804981i	$0.702175\pi$
$720$	4.28939	0.159856
$721$	−7.73044	−0.287897
$722$	16.0110	0.595867
$723$	13.3356	0.495955
$724$	1.13473	0.0421718
$725$	0.957827	0.0355728
$726$	14.9125	0.553456
$727$	0.255546	0.00947768	0.00473884	−	0.999989i	$-0.498492\pi$
$727$	0.255546	0.00947768	0.00473884	+	0.999989i	$0.498492\pi$
$728$	9.20194	0.341047
$729$	1.00000	0.0370370
$730$	11.0242	0.408024
$731$	0.740477	0.0273875
$732$	−0.339791	−0.0125590
$733$	22.6092	0.835092	0.417546	−	0.908656i	$-0.362890\pi$
$733$	22.6092	0.835092	0.417546	+	0.908656i	$0.362890\pi$
$734$	−27.8555	−1.02816
$735$	5.14701	0.189850
$736$	5.35975	0.197563
$737$	−7.35434	−0.270901
$738$	4.94625	0.182074
$739$	33.4310	1.22978	0.614890	−	0.788613i	$-0.289200\pi$
$739$	33.4310	1.22978	0.614890	+	0.788613i	$0.289200\pi$
$740$	0.846688	0.0311249
$741$	7.10715	0.261088
$742$	−4.63885	−0.170298
$743$	−49.4394	−1.81375	−0.906877	−	0.421395i	$-0.861540\pi$
$743$	−49.4394	−1.81375	−0.906877	+	0.421395i	$0.861540\pi$
$744$	24.5184	0.898886
$745$	−2.99513	−0.109733
$746$	0.451391	0.0165266
$747$	−4.52944	−0.165724
$748$	−0.0484203	−0.00177042
$749$	−1.19761	−0.0437597
$750$	1.46868	0.0536286
$751$	−21.6690	−0.790714	−0.395357	−	0.918527i	$-0.629379\pi$
$751$	−21.6690	−0.790714	−0.395357	+	0.918527i	$0.629379\pi$
$752$	−28.0694	−1.02359
$753$	18.9529	0.690682
$754$	3.51326	0.127945
$755$	8.31318	0.302548
$756$	−0.213748	−0.00777394
$757$	13.9263	0.506158	0.253079	−	0.967446i	$-0.418557\pi$
$757$	13.9263	0.506158	0.253079	+	0.967446i	$0.418557\pi$
$758$	−45.1375	−1.63947
$759$	5.56348	0.201942
$760$	7.70277	0.279409
$761$	−45.0292	−1.63231	−0.816154	−	0.577834i	$-0.803898\pi$
$761$	−45.0292	−1.63231	−0.816154	+	0.577834i	$0.803898\pi$
$762$	−29.4844	−1.06811
$763$	3.88758	0.140740
$764$	1.02229	0.0369850
$765$	0.335196	0.0121190
$766$	−7.24899	−0.261917
$767$	27.5893	0.996193
$768$	3.74595	0.135170
$769$	21.3798	0.770977	0.385488	−	0.922713i	$-0.374033\pi$
$769$	21.3798	0.770977	0.385488	+	0.922713i	$0.374033\pi$
$770$	−1.83919	−0.0662798
$771$	2.58334	0.0930368
$772$	0.670866	0.0241450
$773$	−6.08087	−0.218714	−0.109357	−	0.994003i	$-0.534879\pi$
$773$	−6.08087	−0.218714	−0.109357	+	0.994003i	$0.534879\pi$
$774$	3.24444	0.116619
$775$	9.05824	0.325382
$776$	10.7767	0.386860
$777$	7.33997	0.263320
$778$	−18.4322	−0.660827
$779$	9.58402	0.343383
$780$	0.392158	0.0140415
$781$	1.84246	0.0659285
$782$	2.97721	0.106465
$783$	0.957827	0.0342300
$784$	22.0775	0.788484
$785$	−10.4685	−0.373636
$786$	−21.4349	−0.764558
$787$	31.3146	1.11624	0.558122	−	0.829759i	$-0.311522\pi$
$787$	31.3146	1.11624	0.558122	+	0.829759i	$0.311522\pi$
$788$	−4.30772	−0.153456
$789$	12.5570	0.447041
$790$	12.9240	0.459817
$791$	−21.1279	−0.751222
$792$	2.49006	0.0884805
$793$	5.40433	0.191913
$794$	37.1980	1.32011
$795$	2.32031	0.0822930
$796$	−1.49332	−0.0529294
$797$	18.7397	0.663793	0.331897	−	0.943316i	$-0.392311\pi$
$797$	18.7397	0.663793	0.331897	+	0.943316i	$0.392311\pi$
$798$	−5.68936	−0.201401
$799$	−2.19350	−0.0776003
$800$	0.886259	0.0313340
$801$	−5.84771	−0.206619
$802$	1.46868	0.0518609
$803$	6.90530	0.243683
$804$	−1.25530	−0.0442709
$805$	8.23228	0.290150
$806$	33.2252	1.17031
$807$	−15.5178	−0.546252
$808$	22.8941	0.805411
$809$	4.78936	0.168385	0.0841924	−	0.996450i	$-0.473169\pi$
$809$	4.78936	0.168385	0.0841924	+	0.996450i	$0.473169\pi$
$810$	1.46868	0.0516042
$811$	19.5289	0.685754	0.342877	−	0.939380i	$-0.388599\pi$
$811$	19.5289	0.685754	0.342877	+	0.939380i	$0.388599\pi$
$812$	−0.204734	−0.00718474
$813$	15.4115	0.540506
$814$	7.28531	0.255350
$815$	−16.7071	−0.585225
$816$	1.43779	0.0503326
$817$	6.28654	0.219938
$818$	−1.43119	−0.0500403
$819$	3.39964	0.118793
$820$	0.528827	0.0184675
$821$	18.2653	0.637463	0.318732	−	0.947845i	$-0.396743\pi$
$821$	18.2653	0.637463	0.318732	+	0.947845i	$0.396743\pi$
$822$	30.2271	1.05429
$823$	−51.8385	−1.80698	−0.903488	−	0.428613i	$-0.859003\pi$
$823$	−51.8385	−1.80698	−0.903488	+	0.428613i	$0.859003\pi$
$824$	15.3715	0.535490
$825$	0.919947	0.0320284
$826$	−22.0856	−0.768457
$827$	−31.5242	−1.09620	−0.548102	−	0.836411i	$-0.684650\pi$
$827$	−31.5242	−1.09620	−0.548102	+	0.836411i	$0.684650\pi$
$828$	0.949619	0.0330015
$829$	−28.3375	−0.984203	−0.492101	−	0.870538i	$-0.663771\pi$
$829$	−28.3375	−0.984203	−0.492101	+	0.870538i	$0.663771\pi$
$830$	−6.65230	−0.230905
$831$	12.5502	0.435361
$832$	−18.1743	−0.630080
$833$	1.72526	0.0597766
$834$	−14.4249	−0.499493
$835$	16.1323	0.558280
$836$	−0.411081	−0.0142175
$837$	9.05824	0.313099
$838$	49.9153	1.72429
$839$	−34.3234	−1.18497	−0.592487	−	0.805580i	$-0.701854\pi$
$839$	−34.3234	−1.18497	−0.592487	+	0.805580i	$0.701854\pi$
$840$	3.68454	0.127129
$841$	−28.0826	−0.968364
$842$	−0.875934	−0.0301867
$843$	11.4738	0.395179
$844$	−0.345526	−0.0118935
$845$	6.76277	0.232646
$846$	−9.61094	−0.330431
$847$	13.8217	0.474918
$848$	9.95273	0.341778
$849$	10.9529	0.375902
$850$	0.492296	0.0168856
$851$	−32.6093	−1.11783
$852$	0.314486	0.0107741
$853$	−16.5395	−0.566302	−0.283151	−	0.959075i	$-0.591380\pi$
$853$	−16.5395	−0.566302	−0.283151	+	0.959075i	$0.591380\pi$
$854$	−4.32624	−0.148041
$855$	2.84577	0.0973232
$856$	2.38136	0.0813933
$857$	50.6338	1.72962	0.864809	−	0.502100i	$-0.167439\pi$
$857$	50.6338	1.72962	0.864809	+	0.502100i	$0.167439\pi$
$858$	3.37432	0.115197
$859$	49.4645	1.68771	0.843853	−	0.536574i	$-0.180282\pi$
$859$	49.4645	1.68771	0.843853	+	0.536574i	$0.180282\pi$
$860$	0.346879	0.0118285
$861$	4.58442	0.156237
$862$	4.46939	0.152228
$863$	43.2848	1.47343	0.736716	−	0.676202i	$-0.236375\pi$
$863$	43.2848	1.47343	0.736716	+	0.676202i	$0.236375\pi$
$864$	0.886259	0.0301511
$865$	16.4730	0.560100
$866$	−11.3238	−0.384798
$867$	−16.8876	−0.573534
$868$	−1.93618	−0.0657183
$869$	8.09531	0.274615
$870$	1.40674	0.0476931
$871$	19.9654	0.676500
$872$	−7.73018	−0.261777
$873$	3.98142	0.134751
$874$	25.2761	0.854978
$875$	1.36125	0.0460185
$876$	1.17865	0.0398229
$877$	10.2947	0.347626	0.173813	−	0.984779i	$-0.444391\pi$
$877$	10.2947	0.347626	0.173813	+	0.984779i	$0.444391\pi$
$878$	−46.7541	−1.57787
$879$	−17.2645	−0.582319
$880$	3.94601	0.133020
$881$	−35.3839	−1.19211	−0.596056	−	0.802943i	$-0.703266\pi$
$881$	−35.3839	−1.19211	−0.596056	+	0.802943i	$0.703266\pi$
$882$	7.55932	0.254535
$883$	43.0587	1.44904	0.724521	−	0.689253i	$-0.242061\pi$
$883$	43.0587	1.44904	0.724521	+	0.689253i	$0.242061\pi$
$884$	0.131450	0.00442114
$885$	11.0470	0.371342
$886$	52.9090	1.77751
$887$	54.7241	1.83746	0.918728	−	0.394891i	$-0.129218\pi$
$887$	54.7241	1.83746	0.918728	+	0.394891i	$0.129218\pi$
$888$	−14.5950	−0.489777
$889$	−27.3276	−0.916537
$890$	−8.58841	−0.287884
$891$	0.919947	0.0308194
$892$	2.46254	0.0824520
$893$	−18.6225	−0.623178
$894$	−4.39889	−0.147121
$895$	−8.69897	−0.290774
$896$	16.9616	0.566646
$897$	−15.1036	−0.504294
$898$	−57.0777	−1.90471
$899$	8.67624	0.289369
$900$	0.157024	0.00523413
$901$	0.777759	0.0259109
$902$	4.55028	0.151508
$903$	3.00711	0.100070
$904$	42.0114	1.39728
$905$	−7.22646	−0.240216
$906$	12.2094	0.405631
$907$	10.0638	0.334162	0.167081	−	0.985943i	$-0.446566\pi$
$907$	10.0638	0.334162	0.167081	+	0.985943i	$0.446566\pi$
$908$	1.66313	0.0551929
$909$	8.45817	0.280540
$910$	4.99298	0.165516
$911$	−4.10147	−0.135888	−0.0679440	−	0.997689i	$-0.521644\pi$
$911$	−4.10147	−0.135888	−0.0679440	+	0.997689i	$0.521644\pi$
$912$	12.2066	0.404201
$913$	−4.16684	−0.137902
$914$	−44.9292	−1.48613
$915$	2.16395	0.0715378
$916$	0.149753	0.00494799
$917$	−19.8669	−0.656064
$918$	0.492296	0.0162482
$919$	−19.2852	−0.636160	−0.318080	−	0.948064i	$-0.603038\pi$
$919$	−19.2852	−0.636160	−0.318080	+	0.948064i	$0.603038\pi$
$920$	−16.3693	−0.539681
$921$	10.0092	0.329815
$922$	−10.7325	−0.353456
$923$	−5.00186	−0.164638
$924$	−0.196637	−0.00646888
$925$	−5.39210	−0.177291
$926$	−30.8261	−1.01301
$927$	5.67895	0.186521
$928$	0.848883	0.0278660
$929$	4.98931	0.163694	0.0818470	−	0.996645i	$-0.473918\pi$
$929$	4.98931	0.163694	0.0818470	+	0.996645i	$0.473918\pi$
$930$	13.3037	0.436245
$931$	14.6472	0.480042
$932$	3.21181	0.105206
$933$	−7.58733	−0.248398
$934$	57.3803	1.87754
$935$	0.308362	0.0100845
$936$	−6.75994	−0.220956
$937$	9.71436	0.317354	0.158677	−	0.987331i	$-0.449277\pi$
$937$	9.71436	0.317354	0.158677	+	0.987331i	$0.449277\pi$
$938$	−15.9825	−0.521848
$939$	27.3727	0.893275
$940$	−1.02755	−0.0335150
$941$	15.6983	0.511751	0.255875	−	0.966710i	$-0.417636\pi$
$941$	15.6983	0.511751	0.255875	+	0.966710i	$0.417636\pi$
$942$	−15.3749	−0.500940
$943$	−20.3672	−0.663249
$944$	47.3850	1.54225
$945$	1.36125	0.0442813
$946$	2.98471	0.0970414
$947$	−17.6324	−0.572975	−0.286488	−	0.958084i	$-0.592488\pi$
$947$	−17.6324	−0.572975	−0.286488	+	0.958084i	$0.592488\pi$
$948$	1.38177	0.0448779
$949$	−18.7463	−0.608531
$950$	4.17953	0.135602
$951$	−2.17285	−0.0704594
$952$	1.23504	0.0400280
$953$	24.5941	0.796683	0.398341	−	0.917237i	$-0.369586\pi$
$953$	24.5941	0.796683	0.398341	+	0.917237i	$0.369586\pi$
$954$	3.40780	0.110332
$955$	−6.51038	−0.210671
$956$	−1.83908	−0.0594801
$957$	0.881150	0.0284835
$958$	−44.0331	−1.42264
$959$	28.0159	0.904681
$960$	−7.27715	−0.234869
$961$	51.0518	1.64683
$962$	−19.7779	−0.637667
$963$	0.879789	0.0283508
$964$	2.09400	0.0674432
$965$	−4.27238	−0.137533
$966$	12.0906	0.389009
$967$	−5.63472	−0.181200	−0.0906002	−	0.995887i	$-0.528879\pi$
$967$	−5.63472	−0.181200	−0.0906002	+	0.995887i	$0.528879\pi$
$968$	−27.4835	−0.883352
$969$	0.953890	0.0306434
$970$	5.84743	0.187750
$971$	4.15637	0.133384	0.0666921	−	0.997774i	$-0.478755\pi$
$971$	4.15637	0.133384	0.0666921	+	0.997774i	$0.478755\pi$
$972$	0.157024	0.00503654
$973$	−13.3697	−0.428613
$974$	−59.1571	−1.89551
$975$	−2.49744	−0.0799822
$976$	9.28201	0.297110
$977$	−14.7777	−0.472780	−0.236390	−	0.971658i	$-0.575964\pi$
$977$	−14.7777	−0.472780	−0.236390	+	0.971658i	$0.575964\pi$
$978$	−24.5374	−0.784621
$979$	−5.37958	−0.171932
$980$	0.808203	0.0258171
$981$	−2.85590	−0.0911818
$982$	4.18646	0.133595
$983$	−56.0457	−1.78758	−0.893790	−	0.448486i	$-0.851963\pi$
$983$	−56.0457	−1.78758	−0.893790	+	0.448486i	$0.851963\pi$
$984$	−9.11582	−0.290602
$985$	27.4336	0.874106
$986$	0.471535	0.0150167
$987$	−8.90789	−0.283541
$988$	1.11599	0.0355044
$989$	−13.3597	−0.424813
$990$	1.35111	0.0429410
$991$	−42.2566	−1.34232	−0.671162	−	0.741311i	$-0.734205\pi$
$991$	−42.2566	−1.34232	−0.671162	+	0.741311i	$0.734205\pi$
$992$	8.02795	0.254888
$993$	−29.4874	−0.935755
$994$	4.00405	0.127001
$995$	9.51015	0.301492
$996$	−0.711230	−0.0225362
$997$	−22.4959	−0.712452	−0.356226	−	0.934400i	$-0.615937\pi$
$997$	−22.4959	−0.712452	−0.356226	+	0.934400i	$0.615937\pi$
$998$	25.7145	0.813977
$999$	−5.39210	−0.170599

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.h.1.11	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.h.1.11	✓	39	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)

\(f(q)\)	\(=\)	\(q-1.46868 q^{2} +1.00000 q^{3} +0.157024 q^{4} -1.00000 q^{5} -1.46868 q^{6} -1.36125 q^{7} +2.70674 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.46868 q^{2} +1.00000 q^{3} +0.157024 q^{4} -1.00000 q^{5} -1.46868 q^{6} -1.36125 q^{7} +2.70674 q^{8} +1.00000 q^{9} +1.46868 q^{10} +0.919947 q^{11} +0.157024 q^{12} -2.49744 q^{13} +1.99924 q^{14} -1.00000 q^{15} -4.28939 q^{16} -0.335196 q^{17} -1.46868 q^{18} -2.84577 q^{19} -0.157024 q^{20} -1.36125 q^{21} -1.35111 q^{22} +6.04761 q^{23} +2.70674 q^{24} +1.00000 q^{25} +3.66795 q^{26} +1.00000 q^{27} -0.213748 q^{28} +0.957827 q^{29} +1.46868 q^{30} +9.05824 q^{31} +0.886259 q^{32} +0.919947 q^{33} +0.492296 q^{34} +1.36125 q^{35} +0.157024 q^{36} -5.39210 q^{37} +4.17953 q^{38} -2.49744 q^{39} -2.70674 q^{40} -3.36782 q^{41} +1.99924 q^{42} -2.20909 q^{43} +0.144454 q^{44} -1.00000 q^{45} -8.88201 q^{46} +6.54392 q^{47} -4.28939 q^{48} -5.14701 q^{49} -1.46868 q^{50} -0.335196 q^{51} -0.392158 q^{52} -2.32031 q^{53} -1.46868 q^{54} -0.919947 q^{55} -3.68454 q^{56} -2.84577 q^{57} -1.40674 q^{58} -11.0470 q^{59} -0.157024 q^{60} -2.16395 q^{61} -13.3037 q^{62} -1.36125 q^{63} +7.27715 q^{64} +2.49744 q^{65} -1.35111 q^{66} -7.99431 q^{67} -0.0526338 q^{68} +6.04761 q^{69} -1.99924 q^{70} +2.00279 q^{71} +2.70674 q^{72} +7.50619 q^{73} +7.91928 q^{74} +1.00000 q^{75} -0.446853 q^{76} -1.25227 q^{77} +3.66795 q^{78} +8.79976 q^{79} +4.28939 q^{80} +1.00000 q^{81} +4.94625 q^{82} -4.52944 q^{83} -0.213748 q^{84} +0.335196 q^{85} +3.24444 q^{86} +0.957827 q^{87} +2.49006 q^{88} -5.84771 q^{89} +1.46868 q^{90} +3.39964 q^{91} +0.949619 q^{92} +9.05824 q^{93} -9.61094 q^{94} +2.84577 q^{95} +0.886259 q^{96} +3.98142 q^{97} +7.55932 q^{98} +0.919947 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - q^99

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