LMFDB - Embedded newform 4015.2.a.f.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.595851 q^{2} -0.809318 q^{3} -1.64496 q^{4} -1.00000 q^{5} +0.482233 q^{6} -4.26782 q^{7} +2.17186 q^{8} -2.34500 q^{9} +O(q^{10})$	\(q-0.595851 q^{2} -0.809318 q^{3} -1.64496 q^{4} -1.00000 q^{5} +0.482233 q^{6} -4.26782 q^{7} +2.17186 q^{8} -2.34500 q^{9} +0.595851 q^{10} +1.00000 q^{11} +1.33130 q^{12} -3.12250 q^{13} +2.54298 q^{14} +0.809318 q^{15} +1.99582 q^{16} +2.46096 q^{17} +1.39727 q^{18} +2.20280 q^{19} +1.64496 q^{20} +3.45402 q^{21} -0.595851 q^{22} -0.564424 q^{23} -1.75772 q^{24} +1.00000 q^{25} +1.86054 q^{26} +4.32581 q^{27} +7.02039 q^{28} -5.17442 q^{29} -0.482233 q^{30} +8.87539 q^{31} -5.53292 q^{32} -0.809318 q^{33} -1.46636 q^{34} +4.26782 q^{35} +3.85744 q^{36} -2.41618 q^{37} -1.31254 q^{38} +2.52709 q^{39} -2.17186 q^{40} +6.48547 q^{41} -2.05808 q^{42} -11.6771 q^{43} -1.64496 q^{44} +2.34500 q^{45} +0.336313 q^{46} +9.33297 q^{47} -1.61525 q^{48} +11.2142 q^{49} -0.595851 q^{50} -1.99170 q^{51} +5.13639 q^{52} +10.7445 q^{53} -2.57754 q^{54} -1.00000 q^{55} -9.26908 q^{56} -1.78276 q^{57} +3.08319 q^{58} +5.90401 q^{59} -1.33130 q^{60} +2.22386 q^{61} -5.28841 q^{62} +10.0080 q^{63} -0.694840 q^{64} +3.12250 q^{65} +0.482233 q^{66} +0.968685 q^{67} -4.04818 q^{68} +0.456799 q^{69} -2.54298 q^{70} +2.24687 q^{71} -5.09301 q^{72} +1.00000 q^{73} +1.43968 q^{74} -0.809318 q^{75} -3.62352 q^{76} -4.26782 q^{77} -1.50577 q^{78} -16.8450 q^{79} -1.99582 q^{80} +3.53405 q^{81} -3.86438 q^{82} +6.31217 q^{83} -5.68173 q^{84} -2.46096 q^{85} +6.95780 q^{86} +4.18775 q^{87} +2.17186 q^{88} -1.82969 q^{89} -1.39727 q^{90} +13.3262 q^{91} +0.928455 q^{92} -7.18301 q^{93} -5.56106 q^{94} -2.20280 q^{95} +4.47790 q^{96} -1.63403 q^{97} -6.68202 q^{98} -2.34500 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.595851	−0.421331	−0.210665	−	0.977558i	$-0.567563\pi$
$2$	−0.595851	−0.421331	−0.210665	+	0.977558i	$0.567563\pi$
$3$	−0.809318	−0.467260	−0.233630	−	0.972326i	$-0.575060\pi$
$3$	−0.809318	−0.467260	−0.233630	+	0.972326i	$0.575060\pi$
$4$	−1.64496	−0.822481
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.482233	0.196871
$7$	−4.26782	−1.61308	−0.806541	−	0.591178i	$-0.798663\pi$
$7$	−4.26782	−1.61308	−0.806541	+	0.591178i	$0.798663\pi$
$8$	2.17186	0.767867
$9$	−2.34500	−0.781668
$10$	0.595851	0.188425
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.33130	0.384312
$13$	−3.12250	−0.866025	−0.433012	−	0.901388i	$-0.642549\pi$
$13$	−3.12250	−0.866025	−0.433012	+	0.901388i	$0.642549\pi$
$14$	2.54298	0.679641
$15$	0.809318	0.208965
$16$	1.99582	0.498955
$17$	2.46096	0.596870	0.298435	−	0.954430i	$-0.403535\pi$
$17$	2.46096	0.596870	0.298435	+	0.954430i	$0.403535\pi$
$18$	1.39727	0.329341
$19$	2.20280	0.505356	0.252678	−	0.967550i	$-0.418689\pi$
$19$	2.20280	0.505356	0.252678	+	0.967550i	$0.418689\pi$
$20$	1.64496	0.367824
$21$	3.45402	0.753729
$22$	−0.595851	−0.127036
$23$	−0.564424	−0.117691	−0.0588453	−	0.998267i	$-0.518742\pi$
$23$	−0.564424	−0.117691	−0.0588453	+	0.998267i	$0.518742\pi$
$24$	−1.75772	−0.358794
$25$	1.00000	0.200000
$26$	1.86054	0.364883
$27$	4.32581	0.832502
$28$	7.02039	1.32673
$29$	−5.17442	−0.960866	−0.480433	−	0.877031i	$-0.659520\pi$
$29$	−5.17442	−0.960866	−0.480433	+	0.877031i	$0.659520\pi$
$30$	−0.482233	−0.0880434
$31$	8.87539	1.59407	0.797033	−	0.603935i	$-0.206401\pi$
$31$	8.87539	1.59407	0.797033	+	0.603935i	$0.206401\pi$
$32$	−5.53292	−0.978092
$33$	−0.809318	−0.140884
$34$	−1.46636	−0.251479
$35$	4.26782	0.721392
$36$	3.85744	0.642907
$37$	−2.41618	−0.397218	−0.198609	−	0.980079i	$-0.563642\pi$
$37$	−2.41618	−0.397218	−0.198609	+	0.980079i	$0.563642\pi$
$38$	−1.31254	−0.212922
$39$	2.52709	0.404659
$40$	−2.17186	−0.343400
$41$	6.48547	1.01286	0.506430	−	0.862281i	$-0.330965\pi$
$41$	6.48547	1.01286	0.506430	+	0.862281i	$0.330965\pi$
$42$	−2.05808	−0.317569
$43$	−11.6771	−1.78074	−0.890369	−	0.455240i	$-0.849554\pi$
$43$	−11.6771	−1.78074	−0.890369	+	0.455240i	$0.849554\pi$
$44$	−1.64496	−0.247987
$45$	2.34500	0.349573
$46$	0.336313	0.0495866
$47$	9.33297	1.36135	0.680677	−	0.732584i	$-0.261686\pi$
$47$	9.33297	1.36135	0.680677	+	0.732584i	$0.261686\pi$
$48$	−1.61525	−0.233142
$49$	11.2142	1.60204
$50$	−0.595851	−0.0842661
$51$	−1.99170	−0.278893
$52$	5.13639	0.712288
$53$	10.7445	1.47587	0.737936	−	0.674871i	$-0.235801\pi$
$53$	10.7445	1.47587	0.737936	+	0.674871i	$0.235801\pi$
$54$	−2.57754	−0.350759
$55$	−1.00000	−0.134840
$56$	−9.26908	−1.23863
$57$	−1.78276	−0.236133
$58$	3.08319	0.404842
$59$	5.90401	0.768637	0.384318	−	0.923201i	$-0.374437\pi$
$59$	5.90401	0.768637	0.384318	+	0.923201i	$0.374437\pi$
$60$	−1.33130	−0.171870
$61$	2.22386	0.284736	0.142368	−	0.989814i	$-0.454528\pi$
$61$	2.22386	0.284736	0.142368	+	0.989814i	$0.454528\pi$
$62$	−5.28841	−0.671629
$63$	10.0080	1.26089
$64$	−0.694840	−0.0868550
$65$	3.12250	0.387298
$66$	0.482233	0.0593588
$67$	0.968685	0.118344	0.0591718	−	0.998248i	$-0.481154\pi$
$67$	0.968685	0.118344	0.0591718	+	0.998248i	$0.481154\pi$
$68$	−4.04818	−0.490914
$69$	0.456799	0.0549921
$70$	−2.54298	−0.303945
$71$	2.24687	0.266655	0.133327	−	0.991072i	$-0.457434\pi$
$71$	2.24687	0.266655	0.133327	+	0.991072i	$0.457434\pi$
$72$	−5.09301	−0.600217
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	1.43968	0.167360
$75$	−0.809318	−0.0934520
$76$	−3.62352	−0.415646
$77$	−4.26782	−0.486363
$78$	−1.50577	−0.170495
$79$	−16.8450	−1.89521	−0.947605	−	0.319444i	$-0.896504\pi$
$79$	−16.8450	−1.89521	−0.947605	+	0.319444i	$0.896504\pi$
$80$	−1.99582	−0.223139
$81$	3.53405	0.392673
$82$	−3.86438	−0.426749
$83$	6.31217	0.692851	0.346425	−	0.938078i	$-0.387395\pi$
$83$	6.31217	0.692851	0.346425	+	0.938078i	$0.387395\pi$
$84$	−5.68173	−0.619928
$85$	−2.46096	−0.266928
$86$	6.95780	0.750279
$87$	4.18775	0.448974
$88$	2.17186	0.231521
$89$	−1.82969	−0.193947	−0.0969733	−	0.995287i	$-0.530916\pi$
$89$	−1.82969	−0.193947	−0.0969733	+	0.995287i	$0.530916\pi$
$90$	−1.39727	−0.147286
$91$	13.3262	1.39697
$92$	0.928455	0.0967982
$93$	−7.18301	−0.744844
$94$	−5.56106	−0.573580
$95$	−2.20280	−0.226002
$96$	4.47790	0.457023
$97$	−1.63403	−0.165910	−0.0829552	−	0.996553i	$-0.526436\pi$
$97$	−1.63403	−0.165910	−0.0829552	+	0.996553i	$0.526436\pi$
$98$	−6.68202	−0.674986
$99$	−2.34500	−0.235682
$100$	−1.64496	−0.164496
$101$	4.00908	0.398919	0.199459	−	0.979906i	$-0.436081\pi$
$101$	4.00908	0.398919	0.199459	+	0.979906i	$0.436081\pi$
$102$	1.18676	0.117506
$103$	−9.85912	−0.971447	−0.485724	−	0.874112i	$-0.661444\pi$
$103$	−9.85912	−0.971447	−0.485724	+	0.874112i	$0.661444\pi$
$104$	−6.78161	−0.664992
$105$	−3.45402	−0.337078
$106$	−6.40213	−0.621830
$107$	−5.25132	−0.507664	−0.253832	−	0.967248i	$-0.581691\pi$
$107$	−5.25132	−0.507664	−0.253832	+	0.967248i	$0.581691\pi$
$108$	−7.11579	−0.684717
$109$	8.97424	0.859576	0.429788	−	0.902930i	$-0.358588\pi$
$109$	8.97424	0.859576	0.429788	+	0.902930i	$0.358588\pi$
$110$	0.595851	0.0568122
$111$	1.95546	0.185604
$112$	−8.51779	−0.804855
$113$	−10.5777	−0.995068	−0.497534	−	0.867445i	$-0.665761\pi$
$113$	−10.5777	−0.995068	−0.497534	+	0.867445i	$0.665761\pi$
$114$	1.06226	0.0994900
$115$	0.564424	0.0526328
$116$	8.51172	0.790294
$117$	7.32227	0.676944
$118$	−3.51791	−0.323850
$119$	−10.5029	−0.962800
$120$	1.75772	0.160457
$121$	1.00000	0.0909091
$122$	−1.32509	−0.119968
$123$	−5.24881	−0.473269
$124$	−14.5997	−1.31109
$125$	−1.00000	−0.0894427
$126$	−5.96331	−0.531254
$127$	−17.1549	−1.52225	−0.761125	−	0.648605i	$-0.775353\pi$
$127$	−17.1549	−1.52225	−0.761125	+	0.648605i	$0.775353\pi$
$128$	11.4799	1.01469
$129$	9.45047	0.832068
$130$	−1.86054	−0.163180
$131$	−11.1897	−0.977647	−0.488823	−	0.872383i	$-0.662574\pi$
$131$	−11.1897	−0.977647	−0.488823	+	0.872383i	$0.662574\pi$
$132$	1.33130	0.115875
$133$	−9.40113	−0.815182
$134$	−0.577192	−0.0498618
$135$	−4.32581	−0.372306
$136$	5.34484	0.458316
$137$	−1.15009	−0.0982587	−0.0491293	−	0.998792i	$-0.515645\pi$
$137$	−1.15009	−0.0982587	−0.0491293	+	0.998792i	$0.515645\pi$
$138$	−0.272184	−0.0231698
$139$	7.08584	0.601013	0.300507	−	0.953780i	$-0.402844\pi$
$139$	7.08584	0.601013	0.300507	+	0.953780i	$0.402844\pi$
$140$	−7.02039	−0.593331
$141$	−7.55334	−0.636106
$142$	−1.33880	−0.112350
$143$	−3.12250	−0.261116
$144$	−4.68020	−0.390017
$145$	5.17442	0.429712
$146$	−0.595851	−0.0493130
$147$	−9.07590	−0.748567
$148$	3.97452	0.326704
$149$	14.8979	1.22048	0.610240	−	0.792217i	$-0.291073\pi$
$149$	14.8979	1.22048	0.610240	+	0.792217i	$0.291073\pi$
$150$	0.482233	0.0393742
$151$	−4.07769	−0.331838	−0.165919	−	0.986139i	$-0.553059\pi$
$151$	−4.07769	−0.331838	−0.165919	+	0.986139i	$0.553059\pi$
$152$	4.78416	0.388046
$153$	−5.77095	−0.466554
$154$	2.54298	0.204919
$155$	−8.87539	−0.712888
$156$	−4.15697	−0.332824
$157$	24.0026	1.91562	0.957808	−	0.287410i	$-0.0927941\pi$
$157$	24.0026	1.91562	0.957808	+	0.287410i	$0.0927941\pi$
$158$	10.0371	0.798510
$159$	−8.69573	−0.689616
$160$	5.53292	0.437416
$161$	2.40886	0.189845
$162$	−2.10577	−0.165445
$163$	−3.92595	−0.307504	−0.153752	−	0.988109i	$-0.549136\pi$
$163$	−3.92595	−0.307504	−0.153752	+	0.988109i	$0.549136\pi$
$164$	−10.6683	−0.833058
$165$	0.809318	0.0630053
$166$	−3.76111	−0.291919
$167$	17.1858	1.32988	0.664940	−	0.746897i	$-0.268457\pi$
$167$	17.1858	1.32988	0.664940	+	0.746897i	$0.268457\pi$
$168$	7.50163	0.578764
$169$	−3.25002	−0.250001
$170$	1.46636	0.112465
$171$	−5.16557	−0.395021
$172$	19.2083	1.46462
$173$	−3.85402	−0.293016	−0.146508	−	0.989209i	$-0.546803\pi$
$173$	−3.85402	−0.293016	−0.146508	+	0.989209i	$0.546803\pi$
$174$	−2.49528	−0.189167
$175$	−4.26782	−0.322617
$176$	1.99582	0.150441
$177$	−4.77822	−0.359153
$178$	1.09022	0.0817156
$179$	−22.1646	−1.65666	−0.828331	−	0.560239i	$-0.810709\pi$
$179$	−22.1646	−1.65666	−0.828331	+	0.560239i	$0.810709\pi$
$180$	−3.85744	−0.287517
$181$	−2.66291	−0.197932	−0.0989661	−	0.995091i	$-0.531554\pi$
$181$	−2.66291	−0.197932	−0.0989661	+	0.995091i	$0.531554\pi$
$182$	−7.94046	−0.588586
$183$	−1.79981	−0.133046
$184$	−1.22585	−0.0903706
$185$	2.41618	0.177641
$186$	4.28001	0.313825
$187$	2.46096	0.179963
$188$	−15.3524	−1.11969
$189$	−18.4618	−1.34290
$190$	1.31254	0.0952216
$191$	9.65601	0.698684	0.349342	−	0.936995i	$-0.386405\pi$
$191$	9.65601	0.698684	0.349342	+	0.936995i	$0.386405\pi$
$192$	0.562346	0.0405839
$193$	−17.2371	−1.24075	−0.620377	−	0.784304i	$-0.713021\pi$
$193$	−17.2371	−1.24075	−0.620377	+	0.784304i	$0.713021\pi$
$194$	0.973638	0.0699031
$195$	−2.52709	−0.180969
$196$	−18.4470	−1.31764
$197$	7.88397	0.561710	0.280855	−	0.959750i	$-0.409382\pi$
$197$	7.88397	0.561710	0.280855	+	0.959750i	$0.409382\pi$
$198$	1.39727	0.0992999
$199$	3.63898	0.257961	0.128980	−	0.991647i	$-0.458830\pi$
$199$	3.63898	0.257961	0.128980	+	0.991647i	$0.458830\pi$
$200$	2.17186	0.153573
$201$	−0.783974	−0.0552973
$202$	−2.38882	−0.168077
$203$	22.0835	1.54996
$204$	3.27627	0.229384
$205$	−6.48547	−0.452965
$206$	5.87457	0.409300
$207$	1.32358	0.0919949
$208$	−6.23194	−0.432107
$209$	2.20280	0.152371
$210$	2.05808	0.142021
$211$	−5.46716	−0.376375	−0.188187	−	0.982133i	$-0.560261\pi$
$211$	−5.46716	−0.376375	−0.188187	+	0.982133i	$0.560261\pi$
$212$	−17.6743	−1.21388
$213$	−1.81844	−0.124597
$214$	3.12901	0.213894
$215$	11.6771	0.796370
$216$	9.39503	0.639251
$217$	−37.8785	−2.57136
$218$	−5.34731	−0.362166
$219$	−0.809318	−0.0546887
$220$	1.64496	0.110903
$221$	−7.68433	−0.516904
$222$	−1.16516	−0.0782006
$223$	−17.3693	−1.16313	−0.581566	−	0.813499i	$-0.697560\pi$
$223$	−17.3693	−1.16313	−0.581566	+	0.813499i	$0.697560\pi$
$224$	23.6135	1.57774
$225$	−2.34500	−0.156334
$226$	6.30275	0.419252
$227$	6.84163	0.454095	0.227047	−	0.973884i	$-0.427093\pi$
$227$	6.84163	0.454095	0.227047	+	0.973884i	$0.427093\pi$
$228$	2.93258	0.194215
$229$	11.0636	0.731100	0.365550	−	0.930792i	$-0.380881\pi$
$229$	11.0636	0.731100	0.365550	+	0.930792i	$0.380881\pi$
$230$	−0.336313	−0.0221758
$231$	3.45402	0.227258
$232$	−11.2381	−0.737817
$233$	−22.5926	−1.48009	−0.740045	−	0.672557i	$-0.765196\pi$
$233$	−22.5926	−1.48009	−0.740045	+	0.672557i	$0.765196\pi$
$234$	−4.36298	−0.285217
$235$	−9.33297	−0.608816
$236$	−9.71187	−0.632189
$237$	13.6330	0.885556
$238$	6.25817	0.405657
$239$	17.6913	1.14436	0.572178	−	0.820130i	$-0.306099\pi$
$239$	17.6913	1.14436	0.572178	+	0.820130i	$0.306099\pi$
$240$	1.61525	0.104264
$241$	−24.4995	−1.57815	−0.789076	−	0.614295i	$-0.789440\pi$
$241$	−24.4995	−1.57815	−0.789076	+	0.614295i	$0.789440\pi$
$242$	−0.595851	−0.0383028
$243$	−15.8376	−1.01598
$244$	−3.65817	−0.234190
$245$	−11.2142	−0.716452
$246$	3.12751	0.199403
$247$	−6.87823	−0.437651
$248$	19.2761	1.22403
$249$	−5.10855	−0.323741
$250$	0.595851	0.0376849
$251$	17.4702	1.10271	0.551354	−	0.834271i	$-0.314111\pi$
$251$	17.4702	1.10271	0.551354	+	0.834271i	$0.314111\pi$
$252$	−16.4628	−1.03706
$253$	−0.564424	−0.0354850
$254$	10.2218	0.641370
$255$	1.99170	0.124725
$256$	−5.45061	−0.340663
$257$	23.1341	1.44306	0.721532	−	0.692381i	$-0.243438\pi$
$257$	23.1341	1.44306	0.721532	+	0.692381i	$0.243438\pi$
$258$	−5.63108	−0.350576
$259$	10.3118	0.640745
$260$	−5.13639	−0.318545
$261$	12.1340	0.751078
$262$	6.66738	0.411912
$263$	16.5572	1.02096	0.510480	−	0.859890i	$-0.329468\pi$
$263$	16.5572	1.02096	0.510480	+	0.859890i	$0.329468\pi$
$264$	−1.75772	−0.108180
$265$	−10.7445	−0.660030
$266$	5.60168	0.343461
$267$	1.48080	0.0906235
$268$	−1.59345	−0.0973354
$269$	−14.3793	−0.876722	−0.438361	−	0.898799i	$-0.644441\pi$
$269$	−14.3793	−0.876722	−0.438361	+	0.898799i	$0.644441\pi$
$270$	2.57754	0.156864
$271$	20.5628	1.24910	0.624552	−	0.780984i	$-0.285282\pi$
$271$	20.5628	1.24910	0.624552	+	0.780984i	$0.285282\pi$
$272$	4.91163	0.297811
$273$	−10.7852	−0.652748
$274$	0.685282	0.0413994
$275$	1.00000	0.0603023
$276$	−0.751416	−0.0452299
$277$	−31.7876	−1.90993	−0.954966	−	0.296716i	$-0.904108\pi$
$277$	−31.7876	−1.90993	−0.954966	+	0.296716i	$0.904108\pi$
$278$	−4.22211	−0.253225
$279$	−20.8128	−1.24603
$280$	9.26908	0.553933
$281$	7.10956	0.424121	0.212060	−	0.977257i	$-0.431983\pi$
$281$	7.10956	0.424121	0.212060	+	0.977257i	$0.431983\pi$
$282$	4.50067	0.268011
$283$	−10.2054	−0.606650	−0.303325	−	0.952887i	$-0.598097\pi$
$283$	−10.2054	−0.606650	−0.303325	+	0.952887i	$0.598097\pi$
$284$	−3.69602	−0.219318
$285$	1.78276	0.105602
$286$	1.86054	0.110016
$287$	−27.6788	−1.63383
$288$	12.9747	0.764543
$289$	−10.9437	−0.643747
$290$	−3.08319	−0.181051
$291$	1.32245	0.0775233
$292$	−1.64496	−0.0962641
$293$	−3.98394	−0.232744	−0.116372	−	0.993206i	$-0.537127\pi$
$293$	−3.98394	−0.232744	−0.116372	+	0.993206i	$0.537127\pi$
$294$	5.40789	0.315394
$295$	−5.90401	−0.343745
$296$	−5.24759	−0.305010
$297$	4.32581	0.251009
$298$	−8.87691	−0.514225
$299$	1.76241	0.101923
$300$	1.33130	0.0768625
$301$	49.8356	2.87248
$302$	2.42970	0.139813
$303$	−3.24463	−0.186399
$304$	4.39639	0.252150
$305$	−2.22386	−0.127338
$306$	3.43863	0.196573
$307$	−1.23232	−0.0703323	−0.0351661	−	0.999381i	$-0.511196\pi$
$307$	−1.23232	−0.0703323	−0.0351661	+	0.999381i	$0.511196\pi$
$308$	7.02039	0.400024
$309$	7.97916	0.453919
$310$	5.28841	0.300362
$311$	26.4324	1.49884	0.749421	−	0.662093i	$-0.230332\pi$
$311$	26.4324	1.49884	0.749421	+	0.662093i	$0.230332\pi$
$312$	5.48848	0.310724
$313$	16.0483	0.907103	0.453551	−	0.891230i	$-0.350157\pi$
$313$	16.0483	0.907103	0.453551	+	0.891230i	$0.350157\pi$
$314$	−14.3020	−0.807107
$315$	−10.0080	−0.563889
$316$	27.7094	1.55877
$317$	−26.0000	−1.46030	−0.730152	−	0.683285i	$-0.760551\pi$
$317$	−26.0000	−1.46030	−0.730152	+	0.683285i	$0.760551\pi$
$318$	5.18136	0.290556
$319$	−5.17442	−0.289712
$320$	0.694840	0.0388427
$321$	4.24999	0.237211
$322$	−1.43532	−0.0799873
$323$	5.42099	0.301632
$324$	−5.81338	−0.322966
$325$	−3.12250	−0.173205
$326$	2.33928	0.129561
$327$	−7.26301	−0.401646
$328$	14.0855	0.777742
$329$	−39.8314	−2.19598
$330$	−0.482233	−0.0265461
$331$	0.859079	0.0472193	0.0236096	−	0.999721i	$-0.492484\pi$
$331$	0.859079	0.0472193	0.0236096	+	0.999721i	$0.492484\pi$
$332$	−10.3833	−0.569856
$333$	5.66595	0.310492
$334$	−10.2402	−0.560319
$335$	−0.968685	−0.0529249
$336$	6.89360	0.376077
$337$	−31.3314	−1.70673	−0.853364	−	0.521315i	$-0.825442\pi$
$337$	−31.3314	−1.70673	−0.853364	+	0.521315i	$0.825442\pi$
$338$	1.93653	0.105333
$339$	8.56074	0.464956
$340$	4.04818	0.219543
$341$	8.87539	0.480629
$342$	3.07791	0.166434
$343$	−17.9856	−0.971133
$344$	−25.3609	−1.36737
$345$	−0.456799	−0.0245932
$346$	2.29643	0.123457
$347$	−22.2289	−1.19331	−0.596656	−	0.802497i	$-0.703504\pi$
$347$	−22.2289	−1.19331	−0.596656	+	0.802497i	$0.703504\pi$
$348$	−6.88869	−0.369273
$349$	−11.5384	−0.617634	−0.308817	−	0.951121i	$-0.599933\pi$
$349$	−11.5384	−0.617634	−0.308817	+	0.951121i	$0.599933\pi$
$350$	2.54298	0.135928
$351$	−13.5073	−0.720968
$352$	−5.53292	−0.294906
$353$	3.06199	0.162973	0.0814867	−	0.996674i	$-0.474033\pi$
$353$	3.06199	0.162973	0.0814867	+	0.996674i	$0.474033\pi$
$354$	2.84711	0.151322
$355$	−2.24687	−0.119252
$356$	3.00977	0.159517
$357$	8.50020	0.449878
$358$	13.2068	0.698002
$359$	6.42867	0.339292	0.169646	−	0.985505i	$-0.445738\pi$
$359$	6.42867	0.339292	0.169646	+	0.985505i	$0.445738\pi$
$360$	5.09301	0.268425
$361$	−14.1477	−0.744615
$362$	1.58670	0.0833949
$363$	−0.809318	−0.0424782
$364$	−21.9211	−1.14898
$365$	−1.00000	−0.0523424
$366$	1.07242	0.0560563
$367$	−10.4827	−0.547192	−0.273596	−	0.961845i	$-0.588213\pi$
$367$	−10.4827	−0.547192	−0.273596	+	0.961845i	$0.588213\pi$
$368$	−1.12649	−0.0587223
$369$	−15.2085	−0.791720
$370$	−1.43968	−0.0748456
$371$	−45.8556	−2.38070
$372$	11.8158	0.612620
$373$	19.6656	1.01825	0.509123	−	0.860694i	$-0.329970\pi$
$373$	19.6656	1.01825	0.509123	+	0.860694i	$0.329970\pi$
$374$	−1.46636	−0.0758239
$375$	0.809318	0.0417930
$376$	20.2699	1.04534
$377$	16.1571	0.832134
$378$	11.0005	0.565803
$379$	27.5058	1.41288	0.706439	−	0.707773i	$-0.250300\pi$
$379$	27.5058	1.41288	0.706439	+	0.707773i	$0.250300\pi$
$380$	3.62352	0.185882
$381$	13.8838	0.711287
$382$	−5.75355	−0.294377
$383$	17.7072	0.904794	0.452397	−	0.891817i	$-0.350569\pi$
$383$	17.7072	0.904794	0.452397	+	0.891817i	$0.350569\pi$
$384$	−9.29087	−0.474122
$385$	4.26782	0.217508
$386$	10.2708	0.522768
$387$	27.3828	1.39195
$388$	2.68791	0.136458
$389$	−25.7751	−1.30685	−0.653425	−	0.756991i	$-0.726669\pi$
$389$	−25.7751	−1.30685	−0.653425	+	0.756991i	$0.726669\pi$
$390$	1.50577	0.0762477
$391$	−1.38902	−0.0702459
$392$	24.3557	1.23015
$393$	9.05601	0.456815
$394$	−4.69768	−0.236665
$395$	16.8450	0.847564
$396$	3.85744	0.193844
$397$	−7.73826	−0.388372	−0.194186	−	0.980965i	$-0.562207\pi$
$397$	−7.73826	−0.388372	−0.194186	+	0.980965i	$0.562207\pi$
$398$	−2.16829	−0.108687
$399$	7.60851	0.380902
$400$	1.99582	0.0997910
$401$	5.90858	0.295060	0.147530	−	0.989058i	$-0.452868\pi$
$401$	5.90858	0.295060	0.147530	+	0.989058i	$0.452868\pi$
$402$	0.467132	0.0232984
$403$	−27.7134	−1.38050
$404$	−6.59479	−0.328103
$405$	−3.53405	−0.175609
$406$	−13.1585	−0.653044
$407$	−2.41618	−0.119766
$408$	−4.32568	−0.214153
$409$	−13.3315	−0.659200	−0.329600	−	0.944121i	$-0.606914\pi$
$409$	−13.3315	−0.659200	−0.329600	+	0.944121i	$0.606914\pi$
$410$	3.86438	0.190848
$411$	0.930788	0.0459124
$412$	16.2179	0.798997
$413$	−25.1972	−1.23987
$414$	−0.788655	−0.0387603
$415$	−6.31217	−0.309852
$416$	17.2765	0.847052
$417$	−5.73470	−0.280830
$418$	−1.31254	−0.0641984
$419$	−26.5037	−1.29479	−0.647394	−	0.762155i	$-0.724141\pi$
$419$	−26.5037	−1.29479	−0.647394	+	0.762155i	$0.724141\pi$
$420$	5.68173	0.277240
$421$	7.20607	0.351202	0.175601	−	0.984461i	$-0.443813\pi$
$421$	7.20607	0.351202	0.175601	+	0.984461i	$0.443813\pi$
$422$	3.25761	0.158578
$423$	−21.8858	−1.06413
$424$	23.3355	1.13327
$425$	2.46096	0.119374
$426$	1.08352	0.0524966
$427$	−9.49104	−0.459303
$428$	8.63822	0.417544
$429$	2.52709	0.122009
$430$	−6.95780	−0.335535
$431$	−21.9180	−1.05575	−0.527876	−	0.849321i	$-0.677011\pi$
$431$	−21.9180	−1.05575	−0.527876	+	0.849321i	$0.677011\pi$
$432$	8.63353	0.415381
$433$	−25.8955	−1.24446	−0.622230	−	0.782835i	$-0.713773\pi$
$433$	−25.8955	−1.24446	−0.622230	+	0.782835i	$0.713773\pi$
$434$	22.5700	1.08339
$435$	−4.18775	−0.200787
$436$	−14.7623	−0.706985
$437$	−1.24331	−0.0594757
$438$	0.482233	0.0230420
$439$	19.8266	0.946273	0.473137	−	0.880989i	$-0.343122\pi$
$439$	19.8266	0.946273	0.473137	+	0.880989i	$0.343122\pi$
$440$	−2.17186	−0.103539
$441$	−26.2975	−1.25226
$442$	4.57872	0.217787
$443$	0.762161	0.0362114	0.0181057	−	0.999836i	$-0.494236\pi$
$443$	0.762161	0.0362114	0.0181057	+	0.999836i	$0.494236\pi$
$444$	−3.21665	−0.152656
$445$	1.82969	0.0867355
$446$	10.3495	0.490063
$447$	−12.0571	−0.570282
$448$	2.96545	0.140104
$449$	21.2025	1.00061	0.500305	−	0.865849i	$-0.333221\pi$
$449$	21.2025	1.00061	0.500305	+	0.865849i	$0.333221\pi$
$450$	1.39727	0.0658681
$451$	6.48547	0.305389
$452$	17.3999	0.818424
$453$	3.30015	0.155055
$454$	−4.07659	−0.191324
$455$	−13.3262	−0.624744
$456$	−3.87191	−0.181319
$457$	41.4137	1.93725	0.968627	−	0.248520i	$-0.0799443\pi$
$457$	41.4137	1.93725	0.968627	+	0.248520i	$0.0799443\pi$
$458$	−6.59223	−0.308035
$459$	10.6456	0.496896
$460$	−0.928455	−0.0432895
$461$	16.9780	0.790743	0.395371	−	0.918521i	$-0.370616\pi$
$461$	16.9780	0.790743	0.395371	+	0.918521i	$0.370616\pi$
$462$	−2.05808	−0.0957507
$463$	−11.4102	−0.530276	−0.265138	−	0.964210i	$-0.585417\pi$
$463$	−11.4102	−0.530276	−0.265138	+	0.964210i	$0.585417\pi$
$464$	−10.3272	−0.479429
$465$	7.18301	0.333104
$466$	13.4618	0.623607
$467$	−20.1948	−0.934503	−0.467251	−	0.884125i	$-0.654756\pi$
$467$	−20.1948	−0.934503	−0.467251	+	0.884125i	$0.654756\pi$
$468$	−12.0448	−0.556773
$469$	−4.13417	−0.190898
$470$	5.56106	0.256513
$471$	−19.4257	−0.895091
$472$	12.8227	0.590210
$473$	−11.6771	−0.536913
$474$	−8.12322	−0.373112
$475$	2.20280	0.101071
$476$	17.2769	0.791884
$477$	−25.1959	−1.15364
$478$	−10.5414	−0.482152
$479$	16.3638	0.747683	0.373842	−	0.927493i	$-0.378040\pi$
$479$	16.3638	0.747683	0.373842	+	0.927493i	$0.378040\pi$
$480$	−4.47790	−0.204387
$481$	7.54451	0.344000
$482$	14.5981	0.664924
$483$	−1.94953	−0.0887068
$484$	−1.64496	−0.0747710
$485$	1.63403	0.0741974
$486$	9.43686	0.428065
$487$	−15.3326	−0.694785	−0.347392	−	0.937720i	$-0.612933\pi$
$487$	−15.3326	−0.694785	−0.347392	+	0.937720i	$0.612933\pi$
$488$	4.82991	0.218640
$489$	3.17734	0.143684
$490$	6.68202	0.301863
$491$	11.1477	0.503089	0.251544	−	0.967846i	$-0.419062\pi$
$491$	11.1477	0.503089	0.251544	+	0.967846i	$0.419062\pi$
$492$	8.63409	0.389255
$493$	−12.7340	−0.573512
$494$	4.09840	0.184396
$495$	2.34500	0.105400
$496$	17.7137	0.795367
$497$	−9.58924	−0.430136
$498$	3.04394	0.136402
$499$	10.8383	0.485190	0.242595	−	0.970128i	$-0.422001\pi$
$499$	10.8383	0.485190	0.242595	+	0.970128i	$0.422001\pi$
$500$	1.64496	0.0735649
$501$	−13.9088	−0.621400
$502$	−10.4096	−0.464605
$503$	14.8664	0.662859	0.331430	−	0.943480i	$-0.392469\pi$
$503$	14.8664	0.662859	0.331430	+	0.943480i	$0.392469\pi$
$504$	21.7360	0.968199
$505$	−4.00908	−0.178402
$506$	0.336313	0.0149509
$507$	2.63030	0.116816
$508$	28.2191	1.25202
$509$	8.20927	0.363869	0.181935	−	0.983311i	$-0.441764\pi$
$509$	8.20927	0.363869	0.181935	+	0.983311i	$0.441764\pi$
$510$	−1.18676	−0.0525504
$511$	−4.26782	−0.188797
$512$	−19.7120	−0.871154
$513$	9.52888	0.420710
$514$	−13.7845	−0.608007
$515$	9.85912	0.434445
$516$	−15.5457	−0.684360
$517$	9.33297	0.410464
$518$	−6.14431	−0.269965
$519$	3.11913	0.136915
$520$	6.78161	0.297393
$521$	−4.60926	−0.201935	−0.100968	−	0.994890i	$-0.532194\pi$
$521$	−4.60926	−0.201935	−0.100968	+	0.994890i	$0.532194\pi$
$522$	−7.23008	−0.316452
$523$	36.3055	1.58753	0.793764	−	0.608226i	$-0.208119\pi$
$523$	36.3055	1.58753	0.793764	+	0.608226i	$0.208119\pi$
$524$	18.4066	0.804095
$525$	3.45402	0.150746
$526$	−9.86562	−0.430162
$527$	21.8419	0.951450
$528$	−1.61525	−0.0702949
$529$	−22.6814	−0.986149
$530$	6.40213	0.278091
$531$	−13.8449	−0.600819
$532$	15.4645	0.670471
$533$	−20.2509	−0.877162
$534$	−0.882337	−0.0381824
$535$	5.25132	0.227034
$536$	2.10384	0.0908722
$537$	17.9382	0.774092
$538$	8.56794	0.369390
$539$	11.2142	0.483032
$540$	7.11579	0.306215
$541$	2.16560	0.0931065	0.0465532	−	0.998916i	$-0.485176\pi$
$541$	2.16560	0.0931065	0.0465532	+	0.998916i	$0.485176\pi$
$542$	−12.2524	−0.526285
$543$	2.15514	0.0924859
$544$	−13.6163	−0.583793
$545$	−8.97424	−0.384414
$546$	6.42636	0.275023
$547$	−1.04813	−0.0448148	−0.0224074	−	0.999749i	$-0.507133\pi$
$547$	−1.04813	−0.0448148	−0.0224074	+	0.999749i	$0.507133\pi$
$548$	1.89185	0.0808159
$549$	−5.21497	−0.222569
$550$	−0.595851	−0.0254072
$551$	−11.3982	−0.485580
$552$	0.992100	0.0422266
$553$	71.8913	3.05713
$554$	18.9407	0.804712
$555$	−1.95546	−0.0830046
$556$	−11.6559	−0.494322
$557$	−23.6702	−1.00294	−0.501468	−	0.865176i	$-0.667207\pi$
$557$	−23.6702	−1.00294	−0.501468	+	0.865176i	$0.667207\pi$
$558$	12.4013	0.524991
$559$	36.4616	1.54216
$560$	8.51779	0.359942
$561$	−1.99170	−0.0840895
$562$	−4.23624	−0.178695
$563$	1.61485	0.0680579	0.0340290	−	0.999421i	$-0.489166\pi$
$563$	1.61485	0.0680579	0.0340290	+	0.999421i	$0.489166\pi$
$564$	12.4250	0.523185
$565$	10.5777	0.445008
$566$	6.08092	0.255600
$567$	−15.0827	−0.633414
$568$	4.87988	0.204755
$569$	−34.7353	−1.45618	−0.728089	−	0.685482i	$-0.759591\pi$
$569$	−34.7353	−1.45618	−0.728089	+	0.685482i	$0.759591\pi$
$570$	−1.06226	−0.0444933
$571$	11.0043	0.460515	0.230258	−	0.973130i	$-0.426043\pi$
$571$	11.0043	0.460515	0.230258	+	0.973130i	$0.426043\pi$
$572$	5.13639	0.214763
$573$	−7.81479	−0.326467
$574$	16.4924	0.688381
$575$	−0.564424	−0.0235381
$576$	1.62940	0.0678917
$577$	−30.5986	−1.27384	−0.636918	−	0.770931i	$-0.719791\pi$
$577$	−30.5986	−1.27384	−0.636918	+	0.770931i	$0.719791\pi$
$578$	6.52081	0.271230
$579$	13.9503	0.579755
$580$	−8.51172	−0.353430
$581$	−26.9392	−1.11763
$582$	−0.787983	−0.0326629
$583$	10.7445	0.444992
$584$	2.17186	0.0898720
$585$	−7.32227	−0.302738
$586$	2.37384	0.0980624
$587$	−8.95625	−0.369664	−0.184832	−	0.982770i	$-0.559174\pi$
$587$	−8.95625	−0.369664	−0.184832	+	0.982770i	$0.559174\pi$
$588$	14.9295	0.615682
$589$	19.5507	0.805572
$590$	3.51791	0.144830
$591$	−6.38064	−0.262465
$592$	−4.82226	−0.198194
$593$	−5.85645	−0.240496	−0.120248	−	0.992744i	$-0.538369\pi$
$593$	−5.85645	−0.240496	−0.120248	+	0.992744i	$0.538369\pi$
$594$	−2.57754	−0.105758
$595$	10.5029	0.430577
$596$	−24.5064	−1.00382
$597$	−2.94510	−0.120535
$598$	−1.05014	−0.0429432
$599$	−17.8307	−0.728542	−0.364271	−	0.931293i	$-0.618682\pi$
$599$	−17.8307	−0.728542	−0.364271	+	0.931293i	$0.618682\pi$
$600$	−1.75772	−0.0717587
$601$	−12.4556	−0.508076	−0.254038	−	0.967194i	$-0.581759\pi$
$601$	−12.4556	−0.508076	−0.254038	+	0.967194i	$0.581759\pi$
$602$	−29.6946	−1.21026
$603$	−2.27157	−0.0925054
$604$	6.70765	0.272930
$605$	−1.00000	−0.0406558
$606$	1.93331	0.0785355
$607$	7.74874	0.314512	0.157256	−	0.987558i	$-0.449735\pi$
$607$	7.74874	0.314512	0.157256	+	0.987558i	$0.449735\pi$
$608$	−12.1879	−0.494285
$609$	−17.8726	−0.724233
$610$	1.32509	0.0536514
$611$	−29.1422	−1.17897
$612$	9.49299	0.383732
$613$	10.8730	0.439154	0.219577	−	0.975595i	$-0.429532\pi$
$613$	10.8730	0.439154	0.219577	+	0.975595i	$0.429532\pi$
$614$	0.734280	0.0296331
$615$	5.24881	0.211652
$616$	−9.26908	−0.373462
$617$	−2.07800	−0.0836571	−0.0418285	−	0.999125i	$-0.513318\pi$
$617$	−2.07800	−0.0836571	−0.0418285	+	0.999125i	$0.513318\pi$
$618$	−4.75440	−0.191250
$619$	48.4523	1.94746	0.973732	−	0.227698i	$-0.0731198\pi$
$619$	48.4523	1.94746	0.973732	+	0.227698i	$0.0731198\pi$
$620$	14.5997	0.586337
$621$	−2.44159	−0.0979777
$622$	−15.7498	−0.631508
$623$	7.80877	0.312852
$624$	5.04362	0.201906
$625$	1.00000	0.0400000
$626$	−9.56239	−0.382190
$627$	−1.78276	−0.0711967
$628$	−39.4833	−1.57556
$629$	−5.94612	−0.237087
$630$	5.96331	0.237584
$631$	20.1809	0.803391	0.401695	−	0.915773i	$-0.368421\pi$
$631$	20.1809	0.803391	0.401695	+	0.915773i	$0.368421\pi$
$632$	−36.5849	−1.45527
$633$	4.42467	0.175865
$634$	15.4921	0.615270
$635$	17.1549	0.680771
$636$	14.3041	0.567196
$637$	−35.0164	−1.38740
$638$	3.08319	0.122065
$639$	−5.26893	−0.208436
$640$	−11.4799	−0.453782
$641$	−46.1321	−1.82211	−0.911055	−	0.412285i	$-0.864731\pi$
$641$	−46.1321	−1.82211	−0.911055	+	0.412285i	$0.864731\pi$
$642$	−2.53236	−0.0999444
$643$	9.28223	0.366055	0.183028	−	0.983108i	$-0.441410\pi$
$643$	9.28223	0.366055	0.183028	+	0.983108i	$0.441410\pi$
$644$	−3.96248	−0.156143
$645$	−9.45047	−0.372112
$646$	−3.23010	−0.127087
$647$	14.8667	0.584471	0.292236	−	0.956346i	$-0.405601\pi$
$647$	14.8667	0.584471	0.292236	+	0.956346i	$0.405601\pi$
$648$	7.67545	0.301520
$649$	5.90401	0.231753
$650$	1.86054	0.0729765
$651$	30.6558	1.20149
$652$	6.45804	0.252916
$653$	−2.64870	−0.103651	−0.0518257	−	0.998656i	$-0.516504\pi$
$653$	−2.64870	−0.103651	−0.0518257	+	0.998656i	$0.516504\pi$
$654$	4.32768	0.169226
$655$	11.1897	0.437217
$656$	12.9438	0.505371
$657$	−2.34500	−0.0914873
$658$	23.7336	0.925232
$659$	18.0334	0.702482	0.351241	−	0.936285i	$-0.385760\pi$
$659$	18.0334	0.702482	0.351241	+	0.936285i	$0.385760\pi$
$660$	−1.33130	−0.0518207
$661$	−8.51087	−0.331035	−0.165517	−	0.986207i	$-0.552929\pi$
$661$	−8.51087	−0.331035	−0.165517	+	0.986207i	$0.552929\pi$
$662$	−0.511884	−0.0198949
$663$	6.21907	0.241529
$664$	13.7091	0.532017
$665$	9.40113	0.364560
$666$	−3.37607	−0.130820
$667$	2.92057	0.113085
$668$	−28.2700	−1.09380
$669$	14.0573	0.543486
$670$	0.577192	0.0222989
$671$	2.22386	0.0858513
$672$	−19.1108	−0.737216
$673$	−6.95474	−0.268086	−0.134043	−	0.990976i	$-0.542796\pi$
$673$	−6.95474	−0.268086	−0.134043	+	0.990976i	$0.542796\pi$
$674$	18.6688	0.719097
$675$	4.32581	0.166500
$676$	5.34615	0.205621
$677$	−42.3574	−1.62793	−0.813964	−	0.580916i	$-0.802695\pi$
$677$	−42.3574	−1.62793	−0.813964	+	0.580916i	$0.802695\pi$
$678$	−5.10093	−0.195900
$679$	6.97373	0.267627
$680$	−5.34484	−0.204965
$681$	−5.53705	−0.212180
$682$	−5.28841	−0.202504
$683$	−11.9072	−0.455617	−0.227809	−	0.973706i	$-0.573156\pi$
$683$	−11.9072	−0.455617	−0.227809	+	0.973706i	$0.573156\pi$
$684$	8.49716	0.324897
$685$	1.15009	0.0439426
$686$	10.7168	0.409168
$687$	−8.95393	−0.341614
$688$	−23.3053	−0.888508
$689$	−33.5497	−1.27814
$690$	0.272184	0.0103619
$691$	19.0623	0.725166	0.362583	−	0.931952i	$-0.381895\pi$
$691$	19.0623	0.725166	0.362583	+	0.931952i	$0.381895\pi$
$692$	6.33972	0.241000
$693$	10.0080	0.380174
$694$	13.2451	0.502778
$695$	−7.08584	−0.268781
$696$	9.09520	0.344752
$697$	15.9605	0.604546
$698$	6.87515	0.260228
$699$	18.2846	0.691587
$700$	7.02039	0.265346
$701$	−12.7845	−0.482864	−0.241432	−	0.970418i	$-0.577617\pi$
$701$	−12.7845	−0.482864	−0.241432	+	0.970418i	$0.577617\pi$
$702$	8.04836	0.303766
$703$	−5.32236	−0.200736
$704$	−0.694840	−0.0261878
$705$	7.55334	0.284475
$706$	−1.82449	−0.0686656
$707$	−17.1100	−0.643489
$708$	7.85999	0.295397
$709$	32.1127	1.20602	0.603009	−	0.797735i	$-0.293968\pi$
$709$	32.1127	1.20602	0.603009	+	0.797735i	$0.293968\pi$
$710$	1.33880	0.0502444
$711$	39.5016	1.48143
$712$	−3.97382	−0.148925
$713$	−5.00948	−0.187607
$714$	−5.06485	−0.189547
$715$	3.12250	0.116775
$716$	36.4599	1.36257
$717$	−14.3179	−0.534712
$718$	−3.83053	−0.142954
$719$	10.1124	0.377127	0.188564	−	0.982061i	$-0.439617\pi$
$719$	10.1124	0.377127	0.188564	+	0.982061i	$0.439617\pi$
$720$	4.68020	0.174421
$721$	42.0769	1.56702
$722$	8.42992	0.313729
$723$	19.8279	0.737408
$724$	4.38038	0.162795
$725$	−5.17442	−0.192173
$726$	0.482233	0.0178974
$727$	−28.0754	−1.04126	−0.520630	−	0.853783i	$-0.674303\pi$
$727$	−28.0754	−1.04126	−0.520630	+	0.853783i	$0.674303\pi$
$728$	28.9427	1.07269
$729$	2.21550	0.0820556
$730$	0.595851	0.0220534
$731$	−28.7368	−1.06287
$732$	2.96062	0.109428
$733$	28.3854	1.04844	0.524220	−	0.851583i	$-0.324357\pi$
$733$	28.3854	1.04844	0.524220	+	0.851583i	$0.324357\pi$
$734$	6.24612	0.230549
$735$	9.07590	0.334769
$736$	3.12291	0.115112
$737$	0.968685	0.0356820
$738$	9.06198	0.333576
$739$	25.8459	0.950755	0.475378	−	0.879782i	$-0.342311\pi$
$739$	25.8459	0.950755	0.475378	+	0.879782i	$0.342311\pi$
$740$	−3.97452	−0.146106
$741$	5.56668	0.204497
$742$	27.3231	1.00306
$743$	38.3765	1.40790	0.703949	−	0.710250i	$-0.251418\pi$
$743$	38.3765	1.40790	0.703949	+	0.710250i	$0.251418\pi$
$744$	−15.6005	−0.571941
$745$	−14.8979	−0.545815
$746$	−11.7178	−0.429018
$747$	−14.8021	−0.541579
$748$	−4.04818	−0.148016
$749$	22.4117	0.818904
$750$	−0.482233	−0.0176087
$751$	46.8673	1.71021	0.855107	−	0.518452i	$-0.173492\pi$
$751$	46.8673	1.71021	0.855107	+	0.518452i	$0.173492\pi$
$752$	18.6269	0.679254
$753$	−14.1389	−0.515252
$754$	−9.62724	−0.350603
$755$	4.07769	0.148402
$756$	30.3689	1.10451
$757$	10.0849	0.366542	0.183271	−	0.983062i	$-0.441331\pi$
$757$	10.0849	0.366542	0.183271	+	0.983062i	$0.441331\pi$
$758$	−16.3894	−0.595289
$759$	0.456799	0.0165807
$760$	−4.78416	−0.173540
$761$	−17.0475	−0.617970	−0.308985	−	0.951067i	$-0.599989\pi$
$761$	−17.0475	−0.617970	−0.308985	+	0.951067i	$0.599989\pi$
$762$	−8.27266	−0.299687
$763$	−38.3004	−1.38657
$764$	−15.8838	−0.574654
$765$	5.77095	0.208649
$766$	−10.5508	−0.381217
$767$	−18.4352	−0.665658
$768$	4.41128	0.159178
$769$	−44.0014	−1.58673	−0.793366	−	0.608745i	$-0.791673\pi$
$769$	−44.0014	−1.58673	−0.793366	+	0.608745i	$0.791673\pi$
$770$	−2.54298	−0.0916428
$771$	−18.7228	−0.674286
$772$	28.3544	1.02050
$773$	−5.22786	−0.188033	−0.0940165	−	0.995571i	$-0.529971\pi$
$773$	−5.22786	−0.188033	−0.0940165	+	0.995571i	$0.529971\pi$
$774$	−16.3161	−0.586469
$775$	8.87539	0.318813
$776$	−3.54887	−0.127397
$777$	−8.34554	−0.299395
$778$	15.3581	0.550616
$779$	14.2862	0.511855
$780$	4.15697	0.148843
$781$	2.24687	0.0803994
$782$	0.827651	0.0295967
$783$	−22.3836	−0.799923
$784$	22.3816	0.799343
$785$	−24.0026	−0.856689
$786$	−5.39604	−0.192470
$787$	1.13544	0.0404740	0.0202370	−	0.999795i	$-0.493558\pi$
$787$	1.13544	0.0404740	0.0202370	+	0.999795i	$0.493558\pi$
$788$	−12.9688	−0.461995
$789$	−13.4000	−0.477054
$790$	−10.0371	−0.357105
$791$	45.1437	1.60513
$792$	−5.09301	−0.180972
$793$	−6.94400	−0.246589
$794$	4.61085	0.163633
$795$	8.69573	0.308406
$796$	−5.98599	−0.212168
$797$	−34.0236	−1.20518	−0.602588	−	0.798052i	$-0.705864\pi$
$797$	−34.0236	−1.20518	−0.602588	+	0.798052i	$0.705864\pi$
$798$	−4.53354	−0.160486
$799$	22.9680	0.812551
$800$	−5.53292	−0.195618
$801$	4.29063	0.151602
$802$	−3.52064	−0.124318
$803$	1.00000	0.0352892
$804$	1.28961	0.0454809
$805$	−2.40886	−0.0849011
$806$	16.5130	0.581647
$807$	11.6374	0.409657
$808$	8.70715	0.306317
$809$	−5.32867	−0.187346	−0.0936729	−	0.995603i	$-0.529861\pi$
$809$	−5.32867	−0.187346	−0.0936729	+	0.995603i	$0.529861\pi$
$810$	2.10577	0.0739893
$811$	−17.2414	−0.605426	−0.302713	−	0.953082i	$-0.597892\pi$
$811$	−17.2414	−0.605426	−0.302713	+	0.953082i	$0.597892\pi$
$812$	−36.3265	−1.27481
$813$	−16.6419	−0.583656
$814$	1.43968	0.0504609
$815$	3.92595	0.137520
$816$	−3.97507	−0.139155
$817$	−25.7222	−0.899907
$818$	7.94359	0.277741
$819$	−31.2501	−1.09197
$820$	10.6683	0.372555
$821$	21.2048	0.740051	0.370025	−	0.929022i	$-0.379349\pi$
$821$	21.2048	0.740051	0.370025	+	0.929022i	$0.379349\pi$
$822$	−0.554611	−0.0193443
$823$	8.20917	0.286154	0.143077	−	0.989712i	$-0.454300\pi$
$823$	8.20917	0.286154	0.143077	+	0.989712i	$0.454300\pi$
$824$	−21.4126	−0.745942
$825$	−0.809318	−0.0281768
$826$	15.0138	0.522397
$827$	19.4997	0.678072	0.339036	−	0.940773i	$-0.389899\pi$
$827$	19.4997	0.678072	0.339036	+	0.940773i	$0.389899\pi$
$828$	−2.17723	−0.0756640
$829$	24.7818	0.860709	0.430355	−	0.902660i	$-0.358389\pi$
$829$	24.7818	0.860709	0.430355	+	0.902660i	$0.358389\pi$
$830$	3.76111	0.130550
$831$	25.7263	0.892435
$832$	2.16963	0.0752185
$833$	27.5978	0.956206
$834$	3.41703	0.118322
$835$	−17.1858	−0.594740
$836$	−3.62352	−0.125322
$837$	38.3932	1.32706
$838$	15.7922	0.545534
$839$	−33.2527	−1.14801	−0.574006	−	0.818851i	$-0.694611\pi$
$839$	−33.2527	−1.14801	−0.574006	+	0.818851i	$0.694611\pi$
$840$	−7.50163	−0.258831
$841$	−2.22536	−0.0767367
$842$	−4.29375	−0.147972
$843$	−5.75390	−0.198175
$844$	8.99326	0.309561
$845$	3.25002	0.111804
$846$	13.0407	0.448349
$847$	−4.26782	−0.146644
$848$	21.4441	0.736394
$849$	8.25944	0.283463
$850$	−1.46636	−0.0502959
$851$	1.36375	0.0467488
$852$	2.99126	0.102479
$853$	30.3811	1.04023	0.520115	−	0.854096i	$-0.325889\pi$
$853$	30.3811	1.04023	0.520115	+	0.854096i	$0.325889\pi$
$854$	5.65525	0.193519
$855$	5.16557	0.176659
$856$	−11.4051	−0.389819
$857$	−14.1449	−0.483180	−0.241590	−	0.970378i	$-0.577669\pi$
$857$	−14.1449	−0.483180	−0.241590	+	0.970378i	$0.577669\pi$
$858$	−1.50577	−0.0514062
$859$	41.3353	1.41034	0.705171	−	0.709038i	$-0.250870\pi$
$859$	41.3353	1.41034	0.705171	+	0.709038i	$0.250870\pi$
$860$	−19.2083	−0.654999
$861$	22.4009	0.763422
$862$	13.0599	0.444821
$863$	−48.8768	−1.66379	−0.831894	−	0.554935i	$-0.812743\pi$
$863$	−48.8768	−1.66379	−0.831894	+	0.554935i	$0.812743\pi$
$864$	−23.9344	−0.814264
$865$	3.85402	0.131041
$866$	15.4299	0.524329
$867$	8.85693	0.300797
$868$	62.3087	2.11489
$869$	−16.8450	−0.571427
$870$	2.49528	0.0845979
$871$	−3.02471	−0.102489
$872$	19.4907	0.660040
$873$	3.83180	0.129687
$874$	0.740829	0.0250589
$875$	4.26782	0.144278
$876$	1.33130	0.0449804
$877$	−45.5410	−1.53781	−0.768904	−	0.639364i	$-0.779198\pi$
$877$	−45.5410	−1.53781	−0.768904	+	0.639364i	$0.779198\pi$
$878$	−11.8137	−0.398694
$879$	3.22428	0.108752
$880$	−1.99582	−0.0672791
$881$	18.8600	0.635410	0.317705	−	0.948190i	$-0.397088\pi$
$881$	18.8600	0.635410	0.317705	+	0.948190i	$0.397088\pi$
$882$	15.6694	0.527615
$883$	−4.35838	−0.146671	−0.0733357	−	0.997307i	$-0.523364\pi$
$883$	−4.35838	−0.146671	−0.0733357	+	0.997307i	$0.523364\pi$
$884$	12.6404	0.425143
$885$	4.77822	0.160618
$886$	−0.454135	−0.0152570
$887$	−41.3136	−1.38717	−0.693587	−	0.720373i	$-0.743971\pi$
$887$	−41.3136	−1.38717	−0.693587	+	0.720373i	$0.743971\pi$
$888$	4.24697	0.142519
$889$	73.2139	2.45552
$890$	−1.09022	−0.0365443
$891$	3.53405	0.118395
$892$	28.5718	0.956654
$893$	20.5586	0.687969
$894$	7.18424	0.240277
$895$	22.1646	0.740882
$896$	−48.9939	−1.63677
$897$	−1.42635	−0.0476245
$898$	−12.6336	−0.421588
$899$	−45.9250	−1.53168
$900$	3.85744	0.128581
$901$	26.4418	0.880904
$902$	−3.86438	−0.128670
$903$	−40.3329	−1.34219
$904$	−22.9733	−0.764079
$905$	2.66291	0.0885180
$906$	−1.96640	−0.0653293
$907$	−30.2508	−1.00446	−0.502231	−	0.864734i	$-0.667487\pi$
$907$	−30.2508	−1.00446	−0.502231	+	0.864734i	$0.667487\pi$
$908$	−11.2542	−0.373484
$909$	−9.40132	−0.311822
$910$	7.94046	0.263224
$911$	45.6738	1.51324	0.756620	−	0.653855i	$-0.226849\pi$
$911$	45.6738	1.51324	0.756620	+	0.653855i	$0.226849\pi$
$912$	−3.55808	−0.117820
$913$	6.31217	0.208902
$914$	−24.6764	−0.816224
$915$	1.79981	0.0595000
$916$	−18.1991	−0.601316
$917$	47.7555	1.57702
$918$	−6.34321	−0.209357
$919$	14.0956	0.464970	0.232485	−	0.972600i	$-0.425314\pi$
$919$	14.0956	0.464970	0.232485	+	0.972600i	$0.425314\pi$
$920$	1.22585	0.0404150
$921$	0.997340	0.0328635
$922$	−10.1163	−0.333164
$923$	−7.01585	−0.230930
$924$	−5.68173	−0.186915
$925$	−2.41618	−0.0794435
$926$	6.79877	0.223421
$927$	23.1197	0.759349
$928$	28.6297	0.939815
$929$	12.3219	0.404267	0.202134	−	0.979358i	$-0.435212\pi$
$929$	12.3219	0.404267	0.202134	+	0.979358i	$0.435212\pi$
$930$	−4.28001	−0.140347
$931$	24.7027	0.809599
$932$	37.1640	1.21735
$933$	−21.3922	−0.700350
$934$	12.0331	0.393735
$935$	−2.46096	−0.0804819
$936$	15.9029	0.519803
$937$	−4.40520	−0.143912	−0.0719558	−	0.997408i	$-0.522924\pi$
$937$	−4.40520	−0.143912	−0.0719558	+	0.997408i	$0.522924\pi$
$938$	2.46335	0.0804312
$939$	−12.9882	−0.423853
$940$	15.3524	0.500739
$941$	11.5562	0.376723	0.188361	−	0.982100i	$-0.439682\pi$
$941$	11.5562	0.376723	0.188361	+	0.982100i	$0.439682\pi$
$942$	11.5749	0.377129
$943$	−3.66055	−0.119204
$944$	11.7833	0.383515
$945$	18.4618	0.600561
$946$	6.95780	0.226218
$947$	6.28553	0.204252	0.102126	−	0.994771i	$-0.467435\pi$
$947$	6.28553	0.204252	0.102126	+	0.994771i	$0.467435\pi$
$948$	−22.4257	−0.728353
$949$	−3.12250	−0.101361
$950$	−1.31254	−0.0425844
$951$	21.0422	0.682341
$952$	−22.8108	−0.739302
$953$	−4.95239	−0.160424	−0.0802119	−	0.996778i	$-0.525560\pi$
$953$	−4.95239	−0.160424	−0.0802119	+	0.996778i	$0.525560\pi$
$954$	15.0130	0.486065
$955$	−9.65601	−0.312461
$956$	−29.1015	−0.941210
$957$	4.18775	0.135371
$958$	−9.75042	−0.315022
$959$	4.90836	0.158499
$960$	−0.562346	−0.0181497
$961$	47.7725	1.54105
$962$	−4.49541	−0.144938
$963$	12.3144	0.396825
$964$	40.3008	1.29800
$965$	17.2371	0.554882
$966$	1.16163	0.0373749
$967$	30.6691	0.986251	0.493126	−	0.869958i	$-0.335854\pi$
$967$	30.6691	0.986251	0.493126	+	0.869958i	$0.335854\pi$
$968$	2.17186	0.0698061
$969$	−4.38731	−0.140941
$970$	−0.973638	−0.0312616
$971$	16.8792	0.541679	0.270840	−	0.962624i	$-0.412699\pi$
$971$	16.8792	0.541679	0.270840	+	0.962624i	$0.412699\pi$
$972$	26.0522	0.835626
$973$	−30.2411	−0.969484
$974$	9.13593	0.292734
$975$	2.52709	0.0809318
$976$	4.43843	0.142071
$977$	−49.8939	−1.59625	−0.798124	−	0.602494i	$-0.794174\pi$
$977$	−49.8939	−1.59625	−0.798124	+	0.602494i	$0.794174\pi$
$978$	−1.89323	−0.0605387
$979$	−1.82969	−0.0584771
$980$	18.4470	0.589268
$981$	−21.0446	−0.671903
$982$	−6.64237	−0.211967
$983$	27.9016	0.889923	0.444961	−	0.895550i	$-0.353217\pi$
$983$	27.9016	0.889923	0.444961	+	0.895550i	$0.353217\pi$
$984$	−11.3997	−0.363408
$985$	−7.88397	−0.251204
$986$	7.58759	0.241638
$987$	32.2363	1.02609
$988$	11.3144	0.359960
$989$	6.59082	0.209576
$990$	−1.39727	−0.0444083
$991$	−26.2326	−0.833305	−0.416652	−	0.909066i	$-0.636797\pi$
$991$	−26.2326	−0.833305	−0.416652	+	0.909066i	$0.636797\pi$
$992$	−49.1068	−1.55914
$993$	−0.695269	−0.0220637
$994$	5.71376	0.181230
$995$	−3.63898	−0.115364
$996$	8.40337	0.266271
$997$	6.87518	0.217739	0.108870	−	0.994056i	$-0.465277\pi$
$997$	6.87518	0.217739	0.108870	+	0.994056i	$0.465277\pi$
$998$	−6.45802	−0.204425
$999$	−10.4519	−0.330685

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.f.1.15	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.f.1.15	✓	31	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.595851 q^{2} -0.809318 q^{3} -1.64496 q^{4} -1.00000 q^{5} +0.482233 q^{6} -4.26782 q^{7} +2.17186 q^{8} -2.34500 q^{9} +O(q^{10})\)	\(q-0.595851 q^{2} -0.809318 q^{3} -1.64496 q^{4} -1.00000 q^{5} +0.482233 q^{6} -4.26782 q^{7} +2.17186 q^{8} -2.34500 q^{9} +0.595851 q^{10} +1.00000 q^{11} +1.33130 q^{12} -3.12250 q^{13} +2.54298 q^{14} +0.809318 q^{15} +1.99582 q^{16} +2.46096 q^{17} +1.39727 q^{18} +2.20280 q^{19} +1.64496 q^{20} +3.45402 q^{21} -0.595851 q^{22} -0.564424 q^{23} -1.75772 q^{24} +1.00000 q^{25} +1.86054 q^{26} +4.32581 q^{27} +7.02039 q^{28} -5.17442 q^{29} -0.482233 q^{30} +8.87539 q^{31} -5.53292 q^{32} -0.809318 q^{33} -1.46636 q^{34} +4.26782 q^{35} +3.85744 q^{36} -2.41618 q^{37} -1.31254 q^{38} +2.52709 q^{39} -2.17186 q^{40} +6.48547 q^{41} -2.05808 q^{42} -11.6771 q^{43} -1.64496 q^{44} +2.34500 q^{45} +0.336313 q^{46} +9.33297 q^{47} -1.61525 q^{48} +11.2142 q^{49} -0.595851 q^{50} -1.99170 q^{51} +5.13639 q^{52} +10.7445 q^{53} -2.57754 q^{54} -1.00000 q^{55} -9.26908 q^{56} -1.78276 q^{57} +3.08319 q^{58} +5.90401 q^{59} -1.33130 q^{60} +2.22386 q^{61} -5.28841 q^{62} +10.0080 q^{63} -0.694840 q^{64} +3.12250 q^{65} +0.482233 q^{66} +0.968685 q^{67} -4.04818 q^{68} +0.456799 q^{69} -2.54298 q^{70} +2.24687 q^{71} -5.09301 q^{72} +1.00000 q^{73} +1.43968 q^{74} -0.809318 q^{75} -3.62352 q^{76} -4.26782 q^{77} -1.50577 q^{78} -16.8450 q^{79} -1.99582 q^{80} +3.53405 q^{81} -3.86438 q^{82} +6.31217 q^{83} -5.68173 q^{84} -2.46096 q^{85} +6.95780 q^{86} +4.18775 q^{87} +2.17186 q^{88} -1.82969 q^{89} -1.39727 q^{90} +13.3262 q^{91} +0.928455 q^{92} -7.18301 q^{93} -5.56106 q^{94} -2.20280 q^{95} +4.47790 q^{96} -1.63403 q^{97} -6.68202 q^{98} -2.34500 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * q^99

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