LMFDB - Embedded newform 4015.2.a.c.1.4

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

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-2.15888 q^{2} +1.54599 q^{3} +2.66074 q^{4} +1.00000 q^{5} -3.33759 q^{6} +2.48210 q^{7} -1.42646 q^{8} -0.609922 q^{9} +O(q^{10})$	\(q-2.15888 q^{2} +1.54599 q^{3} +2.66074 q^{4} +1.00000 q^{5} -3.33759 q^{6} +2.48210 q^{7} -1.42646 q^{8} -0.609922 q^{9} -2.15888 q^{10} -1.00000 q^{11} +4.11348 q^{12} +2.62985 q^{13} -5.35854 q^{14} +1.54599 q^{15} -2.24193 q^{16} -6.48465 q^{17} +1.31675 q^{18} -3.23516 q^{19} +2.66074 q^{20} +3.83729 q^{21} +2.15888 q^{22} -1.58706 q^{23} -2.20529 q^{24} +1.00000 q^{25} -5.67752 q^{26} -5.58089 q^{27} +6.60422 q^{28} -1.87344 q^{29} -3.33759 q^{30} +8.57890 q^{31} +7.69298 q^{32} -1.54599 q^{33} +13.9995 q^{34} +2.48210 q^{35} -1.62285 q^{36} -8.41516 q^{37} +6.98430 q^{38} +4.06572 q^{39} -1.42646 q^{40} +3.86543 q^{41} -8.28423 q^{42} -6.54920 q^{43} -2.66074 q^{44} -0.609922 q^{45} +3.42627 q^{46} -8.62747 q^{47} -3.46600 q^{48} -0.839197 q^{49} -2.15888 q^{50} -10.0252 q^{51} +6.99736 q^{52} -5.30695 q^{53} +12.0485 q^{54} -1.00000 q^{55} -3.54062 q^{56} -5.00151 q^{57} +4.04453 q^{58} -13.4645 q^{59} +4.11348 q^{60} -5.12898 q^{61} -18.5208 q^{62} -1.51388 q^{63} -12.1243 q^{64} +2.62985 q^{65} +3.33759 q^{66} +11.8854 q^{67} -17.2540 q^{68} -2.45358 q^{69} -5.35854 q^{70} +2.87529 q^{71} +0.870030 q^{72} +1.00000 q^{73} +18.1673 q^{74} +1.54599 q^{75} -8.60792 q^{76} -2.48210 q^{77} -8.77737 q^{78} -2.79470 q^{79} -2.24193 q^{80} -6.79823 q^{81} -8.34499 q^{82} +2.56421 q^{83} +10.2100 q^{84} -6.48465 q^{85} +14.1389 q^{86} -2.89632 q^{87} +1.42646 q^{88} -12.8857 q^{89} +1.31675 q^{90} +6.52754 q^{91} -4.22276 q^{92} +13.2629 q^{93} +18.6256 q^{94} -3.23516 q^{95} +11.8932 q^{96} +5.21610 q^{97} +1.81172 q^{98} +0.609922 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9} - 3 q^{10} - 23 q^{11} - 18 q^{12} - 5 q^{13} - 17 q^{14} - 5 q^{15} - q^{16} - 36 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 18 q^{21} + 3 q^{22} - 14 q^{23} - 7 q^{24} + 23 q^{25} - 21 q^{26} - 29 q^{27} + 28 q^{28} - 36 q^{29} - 5 q^{30} - 16 q^{31} - 5 q^{32} + 5 q^{33} - 28 q^{34} - 14 q^{36} - 24 q^{37} + q^{38} - 10 q^{39} - 6 q^{40} - 36 q^{41} - 5 q^{42} + 17 q^{43} - 15 q^{44} + 8 q^{45} - 25 q^{46} - 21 q^{47} - 17 q^{48} - 27 q^{49} - 3 q^{50} + 19 q^{51} - 21 q^{52} - 28 q^{53} - 15 q^{54} - 23 q^{55} - 46 q^{56} - 23 q^{57} - 16 q^{58} - 61 q^{59} - 18 q^{60} - 17 q^{61} - 22 q^{62} - 9 q^{63} - 18 q^{64} - 5 q^{65} + 5 q^{66} + 2 q^{67} - 39 q^{68} - 36 q^{69} - 17 q^{70} - 50 q^{71} + 15 q^{72} + 23 q^{73} + 17 q^{74} - 5 q^{75} - 21 q^{76} + 49 q^{78} - 18 q^{79} - q^{80} - 57 q^{81} + 14 q^{82} - 20 q^{83} - 38 q^{84} - 36 q^{85} - 45 q^{86} + 37 q^{87} + 6 q^{88} - 93 q^{89} + q^{90} - 42 q^{91} - 39 q^{92} - 18 q^{93} - 6 q^{94} + 6 q^{95} - 9 q^{96} - 31 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9 - 3 * q^10 - 23 * q^11 - 18 * q^12 - 5 * q^13 - 17 * q^14 - 5 * q^15 - q^16 - 36 * q^17 + q^18 + 6 * q^19 + 15 * q^20 - 18 * q^21 + 3 * q^22 - 14 * q^23 - 7 * q^24 + 23 * q^25 - 21 * q^26 - 29 * q^27 + 28 * q^28 - 36 * q^29 - 5 * q^30 - 16 * q^31 - 5 * q^32 + 5 * q^33 - 28 * q^34 - 14 * q^36 - 24 * q^37 + q^38 - 10 * q^39 - 6 * q^40 - 36 * q^41 - 5 * q^42 + 17 * q^43 - 15 * q^44 + 8 * q^45 - 25 * q^46 - 21 * q^47 - 17 * q^48 - 27 * q^49 - 3 * q^50 + 19 * q^51 - 21 * q^52 - 28 * q^53 - 15 * q^54 - 23 * q^55 - 46 * q^56 - 23 * q^57 - 16 * q^58 - 61 * q^59 - 18 * q^60 - 17 * q^61 - 22 * q^62 - 9 * q^63 - 18 * q^64 - 5 * q^65 + 5 * q^66 + 2 * q^67 - 39 * q^68 - 36 * q^69 - 17 * q^70 - 50 * q^71 + 15 * q^72 + 23 * q^73 + 17 * q^74 - 5 * q^75 - 21 * q^76 + 49 * q^78 - 18 * q^79 - q^80 - 57 * q^81 + 14 * q^82 - 20 * q^83 - 38 * q^84 - 36 * q^85 - 45 * q^86 + 37 * q^87 + 6 * q^88 - 93 * q^89 + q^90 - 42 * q^91 - 39 * q^92 - 18 * q^93 - 6 * q^94 + 6 * q^95 - 9 * q^96 - 31 * q^97 - 31 * q^98 - 8 * 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 $

$2$	−2.15888	−1.52656	−0.763278	−	0.646071i	$-0.776411\pi$
$2$	−2.15888	−1.52656	−0.763278	+	0.646071i	$0.776411\pi$
$3$	1.54599	0.892576	0.446288	−	0.894889i	$-0.352746\pi$
$3$	1.54599	0.892576	0.446288	+	0.894889i	$0.352746\pi$
$4$	2.66074	1.33037
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.33759	−1.36257
$7$	2.48210	0.938144	0.469072	−	0.883160i	$-0.344588\pi$
$7$	2.48210	0.938144	0.469072	+	0.883160i	$0.344588\pi$
$8$	−1.42646	−0.504331
$9$	−0.609922	−0.203307
$10$	−2.15888	−0.682696
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	4.11348	1.18746
$13$	2.62985	0.729389	0.364695	−	0.931127i	$-0.381173\pi$
$13$	2.62985	0.729389	0.364695	+	0.931127i	$0.381173\pi$
$14$	−5.35854	−1.43213
$15$	1.54599	0.399172
$16$	−2.24193	−0.560483
$17$	−6.48465	−1.57276	−0.786379	−	0.617744i	$-0.788047\pi$
$17$	−6.48465	−1.57276	−0.786379	+	0.617744i	$0.788047\pi$
$18$	1.31675	0.310360
$19$	−3.23516	−0.742196	−0.371098	−	0.928594i	$-0.621019\pi$
$19$	−3.23516	−0.742196	−0.371098	+	0.928594i	$0.621019\pi$
$20$	2.66074	0.594960
$21$	3.83729	0.837366
$22$	2.15888	0.460274
$23$	−1.58706	−0.330925	−0.165463	−	0.986216i	$-0.552912\pi$
$23$	−1.58706	−0.330925	−0.165463	+	0.986216i	$0.552912\pi$
$24$	−2.20529	−0.450154
$25$	1.00000	0.200000
$26$	−5.67752	−1.11345
$27$	−5.58089	−1.07404
$28$	6.60422	1.24808
$29$	−1.87344	−0.347890	−0.173945	−	0.984755i	$-0.555651\pi$
$29$	−1.87344	−0.347890	−0.173945	+	0.984755i	$0.555651\pi$
$30$	−3.33759	−0.609359
$31$	8.57890	1.54082	0.770408	−	0.637551i	$-0.220053\pi$
$31$	8.57890	1.54082	0.770408	+	0.637551i	$0.220053\pi$
$32$	7.69298	1.35994
$33$	−1.54599	−0.269122
$34$	13.9995	2.40090
$35$	2.48210	0.419551
$36$	−1.62285	−0.270474
$37$	−8.41516	−1.38344	−0.691722	−	0.722164i	$-0.743148\pi$
$37$	−8.41516	−1.38344	−0.691722	+	0.722164i	$0.743148\pi$
$38$	6.98430	1.13300
$39$	4.06572	0.651036
$40$	−1.42646	−0.225543
$41$	3.86543	0.603679	0.301840	−	0.953359i	$-0.402399\pi$
$41$	3.86543	0.603679	0.301840	+	0.953359i	$0.402399\pi$
$42$	−8.28423	−1.27828
$43$	−6.54920	−0.998743	−0.499372	−	0.866388i	$-0.666436\pi$
$43$	−6.54920	−0.998743	−0.499372	+	0.866388i	$0.666436\pi$
$44$	−2.66074	−0.401122
$45$	−0.609922	−0.0909218
$46$	3.42627	0.505176
$47$	−8.62747	−1.25845	−0.629223	−	0.777225i	$-0.716627\pi$
$47$	−8.62747	−1.25845	−0.629223	+	0.777225i	$0.716627\pi$
$48$	−3.46600	−0.500274
$49$	−0.839197	−0.119885
$50$	−2.15888	−0.305311
$51$	−10.0252	−1.40381
$52$	6.99736	0.970359
$53$	−5.30695	−0.728966	−0.364483	−	0.931210i	$-0.618754\pi$
$53$	−5.30695	−0.728966	−0.364483	+	0.931210i	$0.618754\pi$
$54$	12.0485	1.63959
$55$	−1.00000	−0.134840
$56$	−3.54062	−0.473135
$57$	−5.00151	−0.662466
$58$	4.04453	0.531073
$59$	−13.4645	−1.75293	−0.876465	−	0.481466i	$-0.840104\pi$
$59$	−13.4645	−1.75293	−0.876465	+	0.481466i	$0.840104\pi$
$60$	4.11348	0.531048
$61$	−5.12898	−0.656699	−0.328349	−	0.944556i	$-0.606492\pi$
$61$	−5.12898	−0.656699	−0.328349	+	0.944556i	$0.606492\pi$
$62$	−18.5208	−2.35214
$63$	−1.51388	−0.190732
$64$	−12.1243	−1.51554
$65$	2.62985	0.326193
$66$	3.33759	0.410830
$67$	11.8854	1.45203	0.726016	−	0.687677i	$-0.241370\pi$
$67$	11.8854	1.45203	0.726016	+	0.687677i	$0.241370\pi$
$68$	−17.2540	−2.09235
$69$	−2.45358	−0.295376
$70$	−5.35854	−0.640468
$71$	2.87529	0.341235	0.170617	−	0.985337i	$-0.445424\pi$
$71$	2.87529	0.341235	0.170617	+	0.985337i	$0.445424\pi$
$72$	0.870030	0.102534
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	18.1673	2.11190
$75$	1.54599	0.178515
$76$	−8.60792	−0.987396
$77$	−2.48210	−0.282861
$78$	−8.77737	−0.993842
$79$	−2.79470	−0.314428	−0.157214	−	0.987565i	$-0.550251\pi$
$79$	−2.79470	−0.314428	−0.157214	+	0.987565i	$0.550251\pi$
$80$	−2.24193	−0.250656
$81$	−6.79823	−0.755359
$82$	−8.34499	−0.921550
$83$	2.56421	0.281458	0.140729	−	0.990048i	$-0.455055\pi$
$83$	2.56421	0.281458	0.140729	+	0.990048i	$0.455055\pi$
$84$	10.2100	1.11401
$85$	−6.48465	−0.703359
$86$	14.1389	1.52464
$87$	−2.89632	−0.310518
$88$	1.42646	0.152061
$89$	−12.8857	−1.36588	−0.682940	−	0.730474i	$-0.739299\pi$
$89$	−12.8857	−1.36588	−0.682940	+	0.730474i	$0.739299\pi$
$90$	1.31675	0.138797
$91$	6.52754	0.684272
$92$	−4.22276	−0.440253
$93$	13.2629	1.37530
$94$	18.6256	1.92109
$95$	−3.23516	−0.331920
$96$	11.8932	1.21385
$97$	5.21610	0.529615	0.264807	−	0.964301i	$-0.414692\pi$
$97$	5.21610	0.529615	0.264807	+	0.964301i	$0.414692\pi$
$98$	1.81172	0.183012
$99$	0.609922	0.0612995
$100$	2.66074	0.266074
$101$	15.6773	1.55995	0.779976	−	0.625809i	$-0.215231\pi$
$101$	15.6773	1.55995	0.779976	+	0.625809i	$0.215231\pi$
$102$	21.6431	2.14299
$103$	−15.4343	−1.52079	−0.760395	−	0.649461i	$-0.774995\pi$
$103$	−15.4343	−1.52079	−0.760395	+	0.649461i	$0.774995\pi$
$104$	−3.75138	−0.367853
$105$	3.83729	0.374481
$106$	11.4570	1.11281
$107$	−14.6445	−1.41574	−0.707868	−	0.706345i	$-0.750343\pi$
$107$	−14.6445	−1.41574	−0.707868	+	0.706345i	$0.750343\pi$
$108$	−14.8493	−1.42888
$109$	−3.40817	−0.326443	−0.163222	−	0.986589i	$-0.552189\pi$
$109$	−3.40817	−0.326443	−0.163222	+	0.986589i	$0.552189\pi$
$110$	2.15888	0.205841
$111$	−13.0097	−1.23483
$112$	−5.56469	−0.525814
$113$	−8.18541	−0.770019	−0.385009	−	0.922913i	$-0.625802\pi$
$113$	−8.18541	−0.770019	−0.385009	+	0.922913i	$0.625802\pi$
$114$	10.7976	1.01129
$115$	−1.58706	−0.147994
$116$	−4.98475	−0.462823
$117$	−1.60400	−0.148290
$118$	29.0682	2.67594
$119$	−16.0955	−1.47547
$120$	−2.20529	−0.201315
$121$	1.00000	0.0909091
$122$	11.0728	1.00249
$123$	5.97591	0.538830
$124$	22.8262	2.04986
$125$	1.00000	0.0894427
$126$	3.26829	0.291162
$127$	9.90704	0.879107	0.439554	−	0.898216i	$-0.355137\pi$
$127$	9.90704	0.879107	0.439554	+	0.898216i	$0.355137\pi$
$128$	10.7889	0.953616
$129$	−10.1250	−0.891455
$130$	−5.67752	−0.497951
$131$	−17.9847	−1.57133	−0.785667	−	0.618650i	$-0.787680\pi$
$131$	−17.9847	−1.57133	−0.785667	+	0.618650i	$0.787680\pi$
$132$	−4.11348	−0.358032
$133$	−8.02997	−0.696287
$134$	−25.6591	−2.21661
$135$	−5.58089	−0.480327
$136$	9.25011	0.793190
$137$	11.0454	0.943671	0.471836	−	0.881687i	$-0.343592\pi$
$137$	11.0454	0.943671	0.471836	+	0.881687i	$0.343592\pi$
$138$	5.29697	0.450908
$139$	−1.06629	−0.0904412	−0.0452206	−	0.998977i	$-0.514399\pi$
$139$	−1.06629	−0.0904412	−0.0452206	+	0.998977i	$0.514399\pi$
$140$	6.60422	0.558159
$141$	−13.3380	−1.12326
$142$	−6.20740	−0.520913
$143$	−2.62985	−0.219919
$144$	1.36740	0.113950
$145$	−1.87344	−0.155581
$146$	−2.15888	−0.178670
$147$	−1.29739	−0.107007
$148$	−22.3906	−1.84049
$149$	−9.65827	−0.791236	−0.395618	−	0.918415i	$-0.629470\pi$
$149$	−9.65827	−0.791236	−0.395618	+	0.918415i	$0.629470\pi$
$150$	−3.33759	−0.272513
$151$	17.4030	1.41624	0.708119	−	0.706093i	$-0.249544\pi$
$151$	17.4030	1.41624	0.708119	+	0.706093i	$0.249544\pi$
$152$	4.61483	0.374312
$153$	3.95513	0.319753
$154$	5.35854	0.431803
$155$	8.57890	0.689074
$156$	10.8178	0.866119
$157$	4.57886	0.365433	0.182716	−	0.983166i	$-0.441511\pi$
$157$	4.57886	0.365433	0.182716	+	0.983166i	$0.441511\pi$
$158$	6.03340	0.479992
$159$	−8.20448	−0.650658
$160$	7.69298	0.608183
$161$	−3.93924	−0.310456
$162$	14.6765	1.15310
$163$	16.0420	1.25650	0.628252	−	0.778010i	$-0.283771\pi$
$163$	16.0420	1.25650	0.628252	+	0.778010i	$0.283771\pi$
$164$	10.2849	0.803118
$165$	−1.54599	−0.120355
$166$	−5.53581	−0.429662
$167$	−3.02416	−0.234016	−0.117008	−	0.993131i	$-0.537330\pi$
$167$	−3.02416	−0.234016	−0.117008	+	0.993131i	$0.537330\pi$
$168$	−5.47375	−0.422309
$169$	−6.08389	−0.467991
$170$	13.9995	1.07372
$171$	1.97319	0.150894
$172$	−17.4257	−1.32870
$173$	12.1803	0.926052	0.463026	−	0.886345i	$-0.346764\pi$
$173$	12.1803	0.926052	0.463026	+	0.886345i	$0.346764\pi$
$174$	6.25280	0.474023
$175$	2.48210	0.187629
$176$	2.24193	0.168992
$177$	−20.8160	−1.56462
$178$	27.8186	2.08509
$179$	−7.91094	−0.591292	−0.295646	−	0.955298i	$-0.595535\pi$
$179$	−7.91094	−0.591292	−0.295646	+	0.955298i	$0.595535\pi$
$180$	−1.62285	−0.120960
$181$	−17.1054	−1.27143	−0.635715	−	0.771924i	$-0.719295\pi$
$181$	−17.1054	−1.27143	−0.635715	+	0.771924i	$0.719295\pi$
$182$	−14.0921	−1.04458
$183$	−7.92934	−0.586154
$184$	2.26388	0.166896
$185$	−8.41516	−0.618695
$186$	−28.6329	−2.09947
$187$	6.48465	0.474204
$188$	−22.9555	−1.67420
$189$	−13.8523	−1.00761
$190$	6.98430	0.506694
$191$	8.71486	0.630585	0.315292	−	0.948995i	$-0.397897\pi$
$191$	8.71486	0.630585	0.315292	+	0.948995i	$0.397897\pi$
$192$	−18.7440	−1.35273
$193$	21.0125	1.51251	0.756256	−	0.654276i	$-0.227027\pi$
$193$	21.0125	1.51251	0.756256	+	0.654276i	$0.227027\pi$
$194$	−11.2609	−0.808486
$195$	4.06572	0.291152
$196$	−2.23289	−0.159492
$197$	12.4804	0.889195	0.444598	−	0.895730i	$-0.353347\pi$
$197$	12.4804	0.889195	0.444598	+	0.895730i	$0.353347\pi$
$198$	−1.31675	−0.0935770
$199$	−21.4210	−1.51850	−0.759249	−	0.650800i	$-0.774434\pi$
$199$	−21.4210	−1.51850	−0.759249	+	0.650800i	$0.774434\pi$
$200$	−1.42646	−0.100866
$201$	18.3747	1.29605
$202$	−33.8454	−2.38135
$203$	−4.65007	−0.326371
$204$	−26.6744	−1.86758
$205$	3.86543	0.269974
$206$	33.3208	2.32157
$207$	0.967983	0.0672795
$208$	−5.89595	−0.408810
$209$	3.23516	0.223780
$210$	−8.28423	−0.571666
$211$	22.2986	1.53510	0.767551	−	0.640988i	$-0.221475\pi$
$211$	22.2986	1.53510	0.767551	+	0.640988i	$0.221475\pi$
$212$	−14.1204	−0.969796
$213$	4.44517	0.304578
$214$	31.6156	2.16120
$215$	−6.54920	−0.446652
$216$	7.96094	0.541673
$217$	21.2937	1.44551
$218$	7.35781	0.498334
$219$	1.54599	0.104468
$220$	−2.66074	−0.179387
$221$	−17.0537	−1.14715
$222$	28.0864	1.88504
$223$	−2.54628	−0.170511	−0.0852557	−	0.996359i	$-0.527171\pi$
$223$	−2.54628	−0.170511	−0.0852557	+	0.996359i	$0.527171\pi$
$224$	19.0947	1.27582
$225$	−0.609922	−0.0406615
$226$	17.6713	1.17548
$227$	20.7317	1.37601	0.688006	−	0.725705i	$-0.258486\pi$
$227$	20.7317	1.37601	0.688006	+	0.725705i	$0.258486\pi$
$228$	−13.3077	−0.881327
$229$	9.23091	0.609996	0.304998	−	0.952353i	$-0.401344\pi$
$229$	9.23091	0.609996	0.304998	+	0.952353i	$0.401344\pi$
$230$	3.42627	0.225921
$231$	−3.83729	−0.252475
$232$	2.67240	0.175452
$233$	14.0503	0.920468	0.460234	−	0.887798i	$-0.347766\pi$
$233$	14.0503	0.920468	0.460234	+	0.887798i	$0.347766\pi$
$234$	3.46284	0.226373
$235$	−8.62747	−0.562794
$236$	−35.8256	−2.33205
$237$	−4.32057	−0.280651
$238$	34.7482	2.25239
$239$	−4.51561	−0.292090	−0.146045	−	0.989278i	$-0.546654\pi$
$239$	−4.51561	−0.292090	−0.146045	+	0.989278i	$0.546654\pi$
$240$	−3.46600	−0.223729
$241$	−11.6585	−0.750993	−0.375496	−	0.926824i	$-0.622528\pi$
$241$	−11.6585	−0.750993	−0.375496	+	0.926824i	$0.622528\pi$
$242$	−2.15888	−0.138778
$243$	6.23270	0.399828
$244$	−13.6469	−0.873653
$245$	−0.839197	−0.0536143
$246$	−12.9013	−0.822554
$247$	−8.50798	−0.541350
$248$	−12.2375	−0.777080
$249$	3.96424	0.251223
$250$	−2.15888	−0.136539
$251$	0.454199	0.0286688	0.0143344	−	0.999897i	$-0.495437\pi$
$251$	0.454199	0.0286688	0.0143344	+	0.999897i	$0.495437\pi$
$252$	−4.02806	−0.253744
$253$	1.58706	0.0997777
$254$	−21.3881	−1.34201
$255$	−10.0252	−0.627802
$256$	0.956672	0.0597920
$257$	−17.1381	−1.06905	−0.534524	−	0.845153i	$-0.679509\pi$
$257$	−17.1381	−1.06905	−0.534524	+	0.845153i	$0.679509\pi$
$258$	21.8586	1.36086
$259$	−20.8872	−1.29787
$260$	6.99736	0.433958
$261$	1.14265	0.0707286
$262$	38.8268	2.39873
$263$	−5.44283	−0.335619	−0.167810	−	0.985819i	$-0.553669\pi$
$263$	−5.44283	−0.335619	−0.167810	+	0.985819i	$0.553669\pi$
$264$	2.20529	0.135726
$265$	−5.30695	−0.326004
$266$	17.3357	1.06292
$267$	−19.9211	−1.21915
$268$	31.6240	1.93174
$269$	9.57668	0.583901	0.291950	−	0.956433i	$-0.405696\pi$
$269$	9.57668	0.583901	0.291950	+	0.956433i	$0.405696\pi$
$270$	12.0485	0.733246
$271$	−16.5288	−1.00405	−0.502027	−	0.864852i	$-0.667412\pi$
$271$	−16.5288	−1.00405	−0.502027	+	0.864852i	$0.667412\pi$
$272$	14.5381	0.881504
$273$	10.0915	0.610765
$274$	−23.8456	−1.44057
$275$	−1.00000	−0.0603023
$276$	−6.52834	−0.392960
$277$	−17.7130	−1.06427	−0.532135	−	0.846660i	$-0.678610\pi$
$277$	−17.7130	−1.06427	−0.532135	+	0.846660i	$0.678610\pi$
$278$	2.30198	0.138064
$279$	−5.23246	−0.313259
$280$	−3.54062	−0.211592
$281$	24.6069	1.46793	0.733963	−	0.679190i	$-0.237669\pi$
$281$	24.6069	1.46793	0.733963	+	0.679190i	$0.237669\pi$
$282$	28.7950	1.71472
$283$	22.1338	1.31572	0.657860	−	0.753141i	$-0.271462\pi$
$283$	22.1338	1.31572	0.657860	+	0.753141i	$0.271462\pi$
$284$	7.65042	0.453969
$285$	−5.00151	−0.296264
$286$	5.67752	0.335719
$287$	9.59438	0.566338
$288$	−4.69211	−0.276486
$289$	25.0507	1.47357
$290$	4.04453	0.237503
$291$	8.06403	0.472722
$292$	2.66074	0.155708
$293$	23.1950	1.35507	0.677534	−	0.735491i	$-0.263048\pi$
$293$	23.1950	1.35507	0.677534	+	0.735491i	$0.263048\pi$
$294$	2.80090	0.163352
$295$	−13.4645	−0.783934
$296$	12.0039	0.697713
$297$	5.58089	0.323836
$298$	20.8510	1.20787
$299$	−4.17373	−0.241373
$300$	4.11348	0.237492
$301$	−16.2557	−0.936965
$302$	−37.5709	−2.16196
$303$	24.2370	1.39238
$304$	7.25300	0.415988
$305$	−5.12898	−0.293685
$306$	−8.53863	−0.488121
$307$	18.0656	1.03106	0.515530	−	0.856871i	$-0.327595\pi$
$307$	18.0656	1.03106	0.515530	+	0.856871i	$0.327595\pi$
$308$	−6.60422	−0.376310
$309$	−23.8613	−1.35742
$310$	−18.5208	−1.05191
$311$	−31.3738	−1.77905	−0.889524	−	0.456889i	$-0.848964\pi$
$311$	−31.3738	−1.77905	−0.889524	+	0.456889i	$0.848964\pi$
$312$	−5.79959	−0.328337
$313$	−20.2769	−1.14612	−0.573059	−	0.819514i	$-0.694243\pi$
$313$	−20.2769	−1.14612	−0.573059	+	0.819514i	$0.694243\pi$
$314$	−9.88519	−0.557854
$315$	−1.51388	−0.0852978
$316$	−7.43597	−0.418306
$317$	−1.38516	−0.0777981	−0.0388990	−	0.999243i	$-0.512385\pi$
$317$	−1.38516	−0.0777981	−0.0388990	+	0.999243i	$0.512385\pi$
$318$	17.7125	0.993265
$319$	1.87344	0.104893
$320$	−12.1243	−0.677770
$321$	−22.6402	−1.26365
$322$	8.50433	0.473928
$323$	20.9789	1.16729
$324$	−18.0883	−1.00491
$325$	2.62985	0.145878
$326$	−34.6326	−1.91812
$327$	−5.26899	−0.291376
$328$	−5.51390	−0.304454
$329$	−21.4142	−1.18060
$330$	3.33759	0.183729
$331$	18.9284	1.04040	0.520198	−	0.854045i	$-0.325858\pi$
$331$	18.9284	1.04040	0.520198	+	0.854045i	$0.325858\pi$
$332$	6.82270	0.374444
$333$	5.13259	0.281264
$334$	6.52878	0.357239
$335$	11.8854	0.649369
$336$	−8.60295	−0.469329
$337$	−13.6669	−0.744484	−0.372242	−	0.928136i	$-0.621411\pi$
$337$	−13.6669	−0.744484	−0.372242	+	0.928136i	$0.621411\pi$
$338$	13.1344	0.714415
$339$	−12.6545	−0.687300
$340$	−17.2540	−0.935729
$341$	−8.57890	−0.464573
$342$	−4.25988	−0.230348
$343$	−19.4576	−1.05061
$344$	9.34218	0.503697
$345$	−2.45358	−0.132096
$346$	−26.2958	−1.41367
$347$	−12.0225	−0.645401	−0.322701	−	0.946501i	$-0.604591\pi$
$347$	−12.0225	−0.645401	−0.322701	+	0.946501i	$0.604591\pi$
$348$	−7.70637	−0.413105
$349$	−11.1913	−0.599059	−0.299530	−	0.954087i	$-0.596830\pi$
$349$	−11.1913	−0.599059	−0.299530	+	0.954087i	$0.596830\pi$
$350$	−5.35854	−0.286426
$351$	−14.6769	−0.783396
$352$	−7.69298	−0.410037
$353$	18.5601	0.987853	0.493926	−	0.869504i	$-0.335561\pi$
$353$	18.5601	0.987853	0.493926	+	0.869504i	$0.335561\pi$
$354$	44.9391	2.38848
$355$	2.87529	0.152605
$356$	−34.2855	−1.81713
$357$	−24.8835	−1.31697
$358$	17.0787	0.902640
$359$	1.38210	0.0729445	0.0364723	−	0.999335i	$-0.488388\pi$
$359$	1.38210	0.0729445	0.0364723	+	0.999335i	$0.488388\pi$
$360$	0.870030	0.0458546
$361$	−8.53376	−0.449145
$362$	36.9283	1.94091
$363$	1.54599	0.0811433
$364$	17.3681	0.910336
$365$	1.00000	0.0523424
$366$	17.1185	0.894796
$367$	−2.60727	−0.136098	−0.0680492	−	0.997682i	$-0.521677\pi$
$367$	−2.60727	−0.136098	−0.0680492	+	0.997682i	$0.521677\pi$
$368$	3.55808	0.185478
$369$	−2.35761	−0.122732
$370$	18.1673	0.944472
$371$	−13.1724	−0.683875
$372$	35.2891	1.82965
$373$	−5.42954	−0.281131	−0.140565	−	0.990071i	$-0.544892\pi$
$373$	−5.42954	−0.281131	−0.140565	+	0.990071i	$0.544892\pi$
$374$	−13.9995	−0.723899
$375$	1.54599	0.0798345
$376$	12.3068	0.634673
$377$	−4.92688	−0.253747
$378$	29.9054	1.53817
$379$	−2.83152	−0.145445	−0.0727227	−	0.997352i	$-0.523169\pi$
$379$	−2.83152	−0.145445	−0.0727227	+	0.997352i	$0.523169\pi$
$380$	−8.60792	−0.441577
$381$	15.3162	0.784671
$382$	−18.8143	−0.962623
$383$	−15.9973	−0.817422	−0.408711	−	0.912664i	$-0.634022\pi$
$383$	−15.9973	−0.817422	−0.408711	+	0.912664i	$0.634022\pi$
$384$	16.6796	0.851175
$385$	−2.48210	−0.126499
$386$	−45.3633	−2.30893
$387$	3.99450	0.203052
$388$	13.8787	0.704584
$389$	−34.5123	−1.74984	−0.874921	−	0.484265i	$-0.839087\pi$
$389$	−34.5123	−1.74984	−0.874921	+	0.484265i	$0.839087\pi$
$390$	−8.77737	−0.444460
$391$	10.2915	0.520465
$392$	1.19708	0.0604618
$393$	−27.8042	−1.40253
$394$	−26.9437	−1.35741
$395$	−2.79470	−0.140616
$396$	1.62285	0.0815510
$397$	26.0043	1.30512	0.652560	−	0.757737i	$-0.273695\pi$
$397$	26.0043	1.30512	0.652560	+	0.757737i	$0.273695\pi$
$398$	46.2454	2.31807
$399$	−12.4142	−0.621489
$400$	−2.24193	−0.112097
$401$	−20.6913	−1.03328	−0.516638	−	0.856204i	$-0.672817\pi$
$401$	−20.6913	−1.03328	−0.516638	+	0.856204i	$0.672817\pi$
$402$	−39.6687	−1.97849
$403$	22.5612	1.12385
$404$	41.7133	2.07532
$405$	−6.79823	−0.337807
$406$	10.0389	0.498223
$407$	8.41516	0.417124
$408$	14.3005	0.707983
$409$	20.0193	0.989889	0.494945	−	0.868924i	$-0.335188\pi$
$409$	20.0193	0.989889	0.494945	+	0.868924i	$0.335188\pi$
$410$	−8.34499	−0.412130
$411$	17.0760	0.842299
$412$	−41.0668	−2.02322
$413$	−33.4202	−1.64450
$414$	−2.08976	−0.102706
$415$	2.56421	0.125872
$416$	20.2314	0.991925
$417$	−1.64847	−0.0807257
$418$	−6.98430	−0.341613
$419$	7.51219	0.366995	0.183497	−	0.983020i	$-0.441258\pi$
$419$	7.51219	0.366995	0.183497	+	0.983020i	$0.441258\pi$
$420$	10.2100	0.498199
$421$	10.8076	0.526729	0.263365	−	0.964696i	$-0.415168\pi$
$421$	10.8076	0.526729	0.263365	+	0.964696i	$0.415168\pi$
$422$	−48.1400	−2.34342
$423$	5.26208	0.255851
$424$	7.57017	0.367640
$425$	−6.48465	−0.314552
$426$	−9.59656	−0.464955
$427$	−12.7306	−0.616078
$428$	−38.9652	−1.88345
$429$	−4.06572	−0.196295
$430$	14.1389	0.681839
$431$	7.86062	0.378633	0.189316	−	0.981916i	$-0.439373\pi$
$431$	7.86062	0.378633	0.189316	+	0.981916i	$0.439373\pi$
$432$	12.5120	0.601983
$433$	−18.5781	−0.892807	−0.446403	−	0.894832i	$-0.647295\pi$
$433$	−18.5781	−0.892807	−0.446403	+	0.894832i	$0.647295\pi$
$434$	−45.9703	−2.20665
$435$	−2.89632	−0.138868
$436$	−9.06826	−0.434291
$437$	5.13439	0.245611
$438$	−3.33759	−0.159476
$439$	24.6872	1.17826	0.589129	−	0.808039i	$-0.299471\pi$
$439$	24.6872	1.17826	0.589129	+	0.808039i	$0.299471\pi$
$440$	1.42646	0.0680039
$441$	0.511845	0.0243735
$442$	36.8167	1.75119
$443$	0.0654551	0.00310987	0.00155493	−	0.999999i	$-0.499505\pi$
$443$	0.0654551	0.00310987	0.00155493	+	0.999999i	$0.499505\pi$
$444$	−34.6156	−1.64278
$445$	−12.8857	−0.610840
$446$	5.49710	0.260295
$447$	−14.9316	−0.706239
$448$	−30.0937	−1.42179
$449$	5.96059	0.281298	0.140649	−	0.990060i	$-0.455081\pi$
$449$	5.96059	0.281298	0.140649	+	0.990060i	$0.455081\pi$
$450$	1.31675	0.0620720
$451$	−3.86543	−0.182016
$452$	−21.7793	−1.02441
$453$	26.9049	1.26410
$454$	−44.7572	−2.10056
$455$	6.52754	0.306016
$456$	7.13447	0.334102
$457$	38.9752	1.82318	0.911592	−	0.411096i	$-0.134854\pi$
$457$	38.9752	1.82318	0.911592	+	0.411096i	$0.134854\pi$
$458$	−19.9284	−0.931193
$459$	36.1901	1.68921
$460$	−4.22276	−0.196887
$461$	3.28595	0.153042	0.0765210	−	0.997068i	$-0.475619\pi$
$461$	3.28595	0.153042	0.0765210	+	0.997068i	$0.475619\pi$
$462$	8.28423	0.385417
$463$	1.27325	0.0591729	0.0295864	−	0.999562i	$-0.490581\pi$
$463$	1.27325	0.0591729	0.0295864	+	0.999562i	$0.490581\pi$
$464$	4.20014	0.194986
$465$	13.2629	0.615051
$466$	−30.3329	−1.40514
$467$	−24.2218	−1.12085	−0.560426	−	0.828205i	$-0.689363\pi$
$467$	−24.2218	−1.12085	−0.560426	+	0.828205i	$0.689363\pi$
$468$	−4.26784	−0.197281
$469$	29.5007	1.36222
$470$	18.6256	0.859137
$471$	7.07887	0.326177
$472$	19.2066	0.884056
$473$	6.54920	0.301132
$474$	9.32756	0.428429
$475$	−3.23516	−0.148439
$476$	−42.8261	−1.96293
$477$	3.23683	0.148204
$478$	9.74863	0.445892
$479$	−25.4394	−1.16236	−0.581178	−	0.813776i	$-0.697408\pi$
$479$	−25.4394	−1.16236	−0.581178	+	0.813776i	$0.697408\pi$
$480$	11.8932	0.542850
$481$	−22.1306	−1.00907
$482$	25.1693	1.14643
$483$	−6.09002	−0.277105
$484$	2.66074	0.120943
$485$	5.21610	0.236851
$486$	−13.4556	−0.610360
$487$	−23.5163	−1.06563	−0.532814	−	0.846233i	$-0.678865\pi$
$487$	−23.5163	−1.06563	−0.532814	+	0.846233i	$0.678865\pi$
$488$	7.31630	0.331193
$489$	24.8007	1.12153
$490$	1.81172	0.0818452
$491$	−22.0191	−0.993710	−0.496855	−	0.867834i	$-0.665512\pi$
$491$	−22.0191	−0.993710	−0.496855	+	0.867834i	$0.665512\pi$
$492$	15.9004	0.716844
$493$	12.1486	0.547147
$494$	18.3677	0.826400
$495$	0.609922	0.0274139
$496$	−19.2333	−0.863601
$497$	7.13676	0.320127
$498$	−8.55829	−0.383506
$499$	23.7488	1.06314	0.531570	−	0.847014i	$-0.321602\pi$
$499$	23.7488	1.06314	0.531570	+	0.847014i	$0.321602\pi$
$500$	2.66074	0.118992
$501$	−4.67531	−0.208877
$502$	−0.980560	−0.0437645
$503$	−31.2131	−1.39172	−0.695862	−	0.718176i	$-0.744977\pi$
$503$	−31.2131	−1.39172	−0.695862	+	0.718176i	$0.744977\pi$
$504$	2.15950	0.0961917
$505$	15.6773	0.697632
$506$	−3.42627	−0.152316
$507$	−9.40562	−0.417718
$508$	26.3601	1.16954
$509$	26.9950	1.19653	0.598266	−	0.801297i	$-0.295856\pi$
$509$	26.9950	1.19653	0.598266	+	0.801297i	$0.295856\pi$
$510$	21.6431	0.958374
$511$	2.48210	0.109801
$512$	−23.6432	−1.04489
$513$	18.0551	0.797151
$514$	36.9991	1.63196
$515$	−15.4343	−0.680118
$516$	−26.9400	−1.18597
$517$	8.62747	0.379436
$518$	45.0929	1.98127
$519$	18.8306	0.826572
$520$	−3.75138	−0.164509
$521$	−34.9776	−1.53240	−0.766198	−	0.642605i	$-0.777854\pi$
$521$	−34.9776	−1.53240	−0.766198	+	0.642605i	$0.777854\pi$
$522$	−2.46685	−0.107971
$523$	−9.74931	−0.426308	−0.213154	−	0.977019i	$-0.568374\pi$
$523$	−9.74931	−0.426308	−0.213154	+	0.977019i	$0.568374\pi$
$524$	−47.8527	−2.09046
$525$	3.83729	0.167473
$526$	11.7504	0.512341
$527$	−55.6311	−2.42333
$528$	3.46600	0.150838
$529$	−20.4812	−0.890489
$530$	11.4570	0.497662
$531$	8.21230	0.356383
$532$	−21.3657	−0.926320
$533$	10.1655	0.440317
$534$	43.0072	1.86110
$535$	−14.6445	−0.633136
$536$	−16.9541	−0.732304
$537$	−12.2302	−0.527773
$538$	−20.6749	−0.891357
$539$	0.839197	0.0361468
$540$	−14.8493	−0.639013
$541$	−40.4692	−1.73991	−0.869953	−	0.493135i	$-0.835851\pi$
$541$	−40.4692	−1.73991	−0.869953	+	0.493135i	$0.835851\pi$
$542$	35.6837	1.53274
$543$	−26.4447	−1.13485
$544$	−49.8863	−2.13886
$545$	−3.40817	−0.145990
$546$	−21.7863	−0.932367
$547$	32.7356	1.39967	0.699836	−	0.714304i	$-0.253256\pi$
$547$	32.7356	1.39967	0.699836	+	0.714304i	$0.253256\pi$
$548$	29.3889	1.25543
$549$	3.12828	0.133512
$550$	2.15888	0.0920548
$551$	6.06089	0.258202
$552$	3.49994	0.148967
$553$	−6.93671	−0.294979
$554$	38.2401	1.62467
$555$	−13.0097	−0.552232
$556$	−2.83711	−0.120320
$557$	−39.6113	−1.67839	−0.839193	−	0.543834i	$-0.816972\pi$
$557$	−39.6113	−1.67839	−0.839193	+	0.543834i	$0.816972\pi$
$558$	11.2962	0.478207
$559$	−17.2234	−0.728473
$560$	−5.56469	−0.235151
$561$	10.0252	0.423264
$562$	−53.1233	−2.24087
$563$	−43.7615	−1.84433	−0.922164	−	0.386798i	$-0.873581\pi$
$563$	−43.7615	−1.84433	−0.922164	+	0.386798i	$0.873581\pi$
$564$	−35.4889	−1.49435
$565$	−8.18541	−0.344363
$566$	−47.7842	−2.00852
$567$	−16.8739	−0.708636
$568$	−4.10150	−0.172095
$569$	−6.52817	−0.273675	−0.136838	−	0.990594i	$-0.543694\pi$
$569$	−6.52817	−0.273675	−0.136838	+	0.990594i	$0.543694\pi$
$570$	10.7976	0.452263
$571$	−25.8671	−1.08250	−0.541252	−	0.840861i	$-0.682049\pi$
$571$	−25.8671	−1.08250	−0.541252	+	0.840861i	$0.682049\pi$
$572$	−6.99736	−0.292574
$573$	13.4731	0.562845
$574$	−20.7131	−0.864547
$575$	−1.58706	−0.0661850
$576$	7.39488	0.308120
$577$	−18.7402	−0.780165	−0.390083	−	0.920780i	$-0.627554\pi$
$577$	−18.7402	−0.780165	−0.390083	+	0.920780i	$0.627554\pi$
$578$	−54.0813	−2.24948
$579$	32.4850	1.35003
$580$	−4.98475	−0.206981
$581$	6.36461	0.264049
$582$	−17.4092	−0.721636
$583$	5.30695	0.219792
$584$	−1.42646	−0.0590274
$585$	−1.60400	−0.0663174
$586$	−50.0752	−2.06859
$587$	−33.8341	−1.39648	−0.698242	−	0.715862i	$-0.746034\pi$
$587$	−33.8341	−1.39648	−0.698242	+	0.715862i	$0.746034\pi$
$588$	−3.45202	−0.142359
$589$	−27.7541	−1.14359
$590$	29.0682	1.19672
$591$	19.2946	0.793675
$592$	18.8662	0.775397
$593$	13.8140	0.567274	0.283637	−	0.958932i	$-0.408459\pi$
$593$	13.8140	0.567274	0.283637	+	0.958932i	$0.408459\pi$
$594$	−12.0485	−0.494354
$595$	−16.0955	−0.659852
$596$	−25.6982	−1.05264
$597$	−33.1167	−1.35538
$598$	9.01057	0.368470
$599$	14.1355	0.577563	0.288781	−	0.957395i	$-0.406750\pi$
$599$	14.1355	0.577563	0.288781	+	0.957395i	$0.406750\pi$
$600$	−2.20529	−0.0900307
$601$	13.7865	0.562363	0.281182	−	0.959655i	$-0.409274\pi$
$601$	13.7865	0.562363	0.281182	+	0.959655i	$0.409274\pi$
$602$	35.0941	1.43033
$603$	−7.24916	−0.295209
$604$	46.3050	1.88412
$605$	1.00000	0.0406558
$606$	−52.3246	−2.12554
$607$	−23.7459	−0.963814	−0.481907	−	0.876222i	$-0.660056\pi$
$607$	−23.7459	−0.963814	−0.481907	+	0.876222i	$0.660056\pi$
$608$	−24.8880	−1.00934
$609$	−7.18895	−0.291311
$610$	11.0728	0.448326
$611$	−22.6890	−0.917897
$612$	10.5236	0.425391
$613$	−37.3346	−1.50793	−0.753965	−	0.656914i	$-0.771861\pi$
$613$	−37.3346	−1.50793	−0.753965	+	0.656914i	$0.771861\pi$
$614$	−39.0015	−1.57397
$615$	5.97591	0.240972
$616$	3.54062	0.142656
$617$	−15.9176	−0.640820	−0.320410	−	0.947279i	$-0.603821\pi$
$617$	−15.9176	−0.640820	−0.320410	+	0.947279i	$0.603821\pi$
$618$	51.5135	2.07218
$619$	−27.5360	−1.10677	−0.553383	−	0.832927i	$-0.686663\pi$
$619$	−27.5360	−1.10677	−0.553383	+	0.832927i	$0.686663\pi$
$620$	22.8262	0.916724
$621$	8.85722	0.355428
$622$	67.7322	2.71581
$623$	−31.9835	−1.28139
$624$	−9.11506	−0.364894
$625$	1.00000	0.0400000
$626$	43.7753	1.74961
$627$	5.00151	0.199741
$628$	12.1832	0.486162
$629$	54.5694	2.17582
$630$	3.26829	0.130212
$631$	−3.99688	−0.159113	−0.0795567	−	0.996830i	$-0.525350\pi$
$631$	−3.99688	−0.159113	−0.0795567	+	0.996830i	$0.525350\pi$
$632$	3.98653	0.158576
$633$	34.4734	1.37020
$634$	2.99038	0.118763
$635$	9.90704	0.393149
$636$	−21.8300	−0.865617
$637$	−2.20696	−0.0874430
$638$	−4.04453	−0.160125
$639$	−1.75370	−0.0693755
$640$	10.7889	0.426470
$641$	−16.6301	−0.656849	−0.328424	−	0.944530i	$-0.606518\pi$
$641$	−16.6301	−0.656849	−0.328424	+	0.944530i	$0.606518\pi$
$642$	48.8773	1.92904
$643$	21.2367	0.837495	0.418747	−	0.908103i	$-0.362469\pi$
$643$	21.2367	0.837495	0.418747	+	0.908103i	$0.362469\pi$
$644$	−10.4813	−0.413021
$645$	−10.1250	−0.398671
$646$	−45.2907	−1.78194
$647$	41.9282	1.64837	0.824183	−	0.566324i	$-0.191635\pi$
$647$	41.9282	1.64837	0.824183	+	0.566324i	$0.191635\pi$
$648$	9.69742	0.380951
$649$	13.4645	0.528528
$650$	−5.67752	−0.222691
$651$	32.9197	1.29023
$652$	42.6836	1.67162
$653$	40.4631	1.58344	0.791722	−	0.610882i	$-0.209185\pi$
$653$	40.4631	1.58344	0.791722	+	0.610882i	$0.209185\pi$
$654$	11.3751	0.444801
$655$	−17.9847	−0.702722
$656$	−8.66604	−0.338352
$657$	−0.609922	−0.0237953
$658$	46.2306	1.80226
$659$	20.0252	0.780073	0.390036	−	0.920799i	$-0.372462\pi$
$659$	20.0252	0.780073	0.390036	+	0.920799i	$0.372462\pi$
$660$	−4.11348	−0.160117
$661$	0.697227	0.0271190	0.0135595	−	0.999908i	$-0.495684\pi$
$661$	0.697227	0.0271190	0.0135595	+	0.999908i	$0.495684\pi$
$662$	−40.8640	−1.58822
$663$	−26.3647	−1.02392
$664$	−3.65775	−0.141948
$665$	−8.02997	−0.311389
$666$	−11.0806	−0.429365
$667$	2.97327	0.115126
$668$	−8.04650	−0.311329
$669$	−3.93651	−0.152194
$670$	−25.6591	−0.991297
$671$	5.12898	0.198002
$672$	29.5202	1.13877
$673$	37.5673	1.44811	0.724057	−	0.689740i	$-0.242275\pi$
$673$	37.5673	1.44811	0.724057	+	0.689740i	$0.242275\pi$
$674$	29.5051	1.13650
$675$	−5.58089	−0.214809
$676$	−16.1877	−0.622603
$677$	−30.0485	−1.15486	−0.577429	−	0.816441i	$-0.695944\pi$
$677$	−30.0485	−1.15486	−0.577429	+	0.816441i	$0.695944\pi$
$678$	27.3196	1.04920
$679$	12.9469	0.496855
$680$	9.25011	0.354725
$681$	32.0510	1.22820
$682$	18.5208	0.709197
$683$	26.5924	1.01753	0.508765	−	0.860905i	$-0.330102\pi$
$683$	26.5924	1.01753	0.508765	+	0.860905i	$0.330102\pi$
$684$	5.25016	0.200745
$685$	11.0454	0.422023
$686$	42.0066	1.60382
$687$	14.2709	0.544468
$688$	14.6829	0.559779
$689$	−13.9565	−0.531700
$690$	5.29697	0.201652
$691$	−31.0234	−1.18018	−0.590092	−	0.807336i	$-0.700909\pi$
$691$	−31.0234	−1.18018	−0.590092	+	0.807336i	$0.700909\pi$
$692$	32.4087	1.23199
$693$	1.51388	0.0575077
$694$	25.9551	0.985241
$695$	−1.06629	−0.0404465
$696$	4.13149	0.156604
$697$	−25.0660	−0.949442
$698$	24.1607	0.914497
$699$	21.7216	0.821588
$700$	6.60422	0.249616
$701$	−14.9187	−0.563471	−0.281735	−	0.959492i	$-0.590910\pi$
$701$	−14.9187	−0.563471	−0.281735	+	0.959492i	$0.590910\pi$
$702$	31.6856	1.19590
$703$	27.2244	1.02679
$704$	12.1243	0.456952
$705$	−13.3380	−0.502337
$706$	−40.0689	−1.50801
$707$	38.9126	1.46346
$708$	−55.3859	−2.08153
$709$	−2.31374	−0.0868942	−0.0434471	−	0.999056i	$-0.513834\pi$
$709$	−2.31374	−0.0868942	−0.0434471	+	0.999056i	$0.513834\pi$
$710$	−6.20740	−0.232960
$711$	1.70455	0.0639255
$712$	18.3809	0.688855
$713$	−13.6152	−0.509895
$714$	53.7203	2.01043
$715$	−2.62985	−0.0983508
$716$	−21.0490	−0.786638
$717$	−6.98107	−0.260713
$718$	−2.98378	−0.111354
$719$	14.3027	0.533399	0.266699	−	0.963780i	$-0.414067\pi$
$719$	14.3027	0.533399	0.266699	+	0.963780i	$0.414067\pi$
$720$	1.36740	0.0509601
$721$	−38.3095	−1.42672
$722$	18.4233	0.685645
$723$	−18.0240	−0.670318
$724$	−45.5129	−1.69148
$725$	−1.87344	−0.0695780
$726$	−3.33759	−0.123870
$727$	−18.5021	−0.686205	−0.343103	−	0.939298i	$-0.611478\pi$
$727$	−18.5021	−0.686205	−0.343103	+	0.939298i	$0.611478\pi$
$728$	−9.31129	−0.345099
$729$	30.0304	1.11224
$730$	−2.15888	−0.0799036
$731$	42.4693	1.57078
$732$	−21.0979	−0.779803
$733$	32.0553	1.18399	0.591994	−	0.805942i	$-0.298341\pi$
$733$	32.0553	1.18399	0.591994	+	0.805942i	$0.298341\pi$
$734$	5.62877	0.207762
$735$	−1.29739	−0.0478549
$736$	−12.2092	−0.450038
$737$	−11.8854	−0.437804
$738$	5.08979	0.187358
$739$	23.3970	0.860672	0.430336	−	0.902669i	$-0.358395\pi$
$739$	23.3970	0.860672	0.430336	+	0.902669i	$0.358395\pi$
$740$	−22.3906	−0.823094
$741$	−13.1532	−0.483196
$742$	28.4375	1.04397
$743$	−27.0839	−0.993612	−0.496806	−	0.867861i	$-0.665494\pi$
$743$	−27.0839	−0.993612	−0.496806	+	0.867861i	$0.665494\pi$
$744$	−18.9190	−0.693604
$745$	−9.65827	−0.353852
$746$	11.7217	0.429162
$747$	−1.56397	−0.0572226
$748$	17.2540	0.630868
$749$	−36.3490	−1.32816
$750$	−3.33759	−0.121872
$751$	21.7988	0.795450	0.397725	−	0.917505i	$-0.369800\pi$
$751$	21.7988	0.795450	0.397725	+	0.917505i	$0.369800\pi$
$752$	19.3422	0.705338
$753$	0.702187	0.0255891
$754$	10.6365	0.387359
$755$	17.4030	0.633361
$756$	−36.8575	−1.34049
$757$	16.5698	0.602240	0.301120	−	0.953586i	$-0.402640\pi$
$757$	16.5698	0.602240	0.301120	+	0.953586i	$0.402640\pi$
$758$	6.11290	0.222030
$759$	2.45358	0.0890592
$760$	4.61483	0.167397
$761$	24.3326	0.882057	0.441029	−	0.897493i	$-0.354614\pi$
$761$	24.3326	0.882057	0.441029	+	0.897493i	$0.354614\pi$
$762$	−33.0657	−1.19784
$763$	−8.45940	−0.306251
$764$	23.1880	0.838912
$765$	3.95513	0.142998
$766$	34.5361	1.24784
$767$	−35.4096	−1.27857
$768$	1.47900	0.0533689
$769$	45.4962	1.64064	0.820318	−	0.571908i	$-0.193797\pi$
$769$	45.4962	1.64064	0.820318	+	0.571908i	$0.193797\pi$
$770$	5.35854	0.193108
$771$	−26.4954	−0.954207
$772$	55.9088	2.01220
$773$	15.5199	0.558213	0.279107	−	0.960260i	$-0.409962\pi$
$773$	15.5199	0.558213	0.279107	+	0.960260i	$0.409962\pi$
$774$	−8.62363	−0.309970
$775$	8.57890	0.308163
$776$	−7.44057	−0.267101
$777$	−32.2914	−1.15845
$778$	74.5077	2.67123
$779$	−12.5053	−0.448048
$780$	10.8178	0.387340
$781$	−2.87529	−0.102886
$782$	−22.2181	−0.794519
$783$	10.4555	0.373649
$784$	1.88142	0.0671937
$785$	4.57886	0.163427
$786$	60.0257	2.14105
$787$	5.24801	0.187071	0.0935356	−	0.995616i	$-0.470183\pi$
$787$	5.24801	0.187071	0.0935356	+	0.995616i	$0.470183\pi$
$788$	33.2073	1.18296
$789$	−8.41454	−0.299566
$790$	6.03340	0.214659
$791$	−20.3170	−0.722388
$792$	−0.870030	−0.0309152
$793$	−13.4885	−0.478989
$794$	−56.1402	−1.99234
$795$	−8.20448	−0.290983
$796$	−56.9959	−2.02017
$797$	47.3699	1.67793	0.838964	−	0.544187i	$-0.183162\pi$
$797$	47.3699	1.67793	0.838964	+	0.544187i	$0.183162\pi$
$798$	26.8008	0.948738
$799$	55.9461	1.97923
$800$	7.69298	0.271988
$801$	7.85926	0.277693
$802$	44.6700	1.57735
$803$	−1.00000	−0.0352892
$804$	48.8903	1.72423
$805$	−3.93924	−0.138840
$806$	−48.7068	−1.71563
$807$	14.8054	0.521176
$808$	−22.3631	−0.786732
$809$	−31.8806	−1.12086	−0.560431	−	0.828201i	$-0.689364\pi$
$809$	−31.8806	−1.12086	−0.560431	+	0.828201i	$0.689364\pi$
$810$	14.6765	0.515681
$811$	14.5198	0.509860	0.254930	−	0.966960i	$-0.417948\pi$
$811$	14.5198	0.509860	0.254930	+	0.966960i	$0.417948\pi$
$812$	−12.3726	−0.434195
$813$	−25.5534	−0.896195
$814$	−18.1673	−0.636763
$815$	16.0420	0.561926
$816$	22.4758	0.786810
$817$	21.1877	0.741263
$818$	−43.2191	−1.51112
$819$	−3.98129	−0.139118
$820$	10.2849	0.359165
$821$	−13.1098	−0.457534	−0.228767	−	0.973481i	$-0.573469\pi$
$821$	−13.1098	−0.457534	−0.228767	+	0.973481i	$0.573469\pi$
$822$	−36.8650	−1.28582
$823$	−13.2495	−0.461848	−0.230924	−	0.972972i	$-0.574175\pi$
$823$	−13.2495	−0.461848	−0.230924	+	0.972972i	$0.574175\pi$
$824$	22.0165	0.766981
$825$	−1.54599	−0.0538244
$826$	72.1500	2.51042
$827$	2.05225	0.0713638	0.0356819	−	0.999363i	$-0.488640\pi$
$827$	2.05225	0.0713638	0.0356819	+	0.999363i	$0.488640\pi$
$828$	2.57556	0.0895067
$829$	49.7556	1.72808	0.864041	−	0.503422i	$-0.167926\pi$
$829$	49.7556	1.72808	0.864041	+	0.503422i	$0.167926\pi$
$830$	−5.53581	−0.192151
$831$	−27.3840	−0.949942
$832$	−31.8851	−1.10542
$833$	5.44190	0.188551
$834$	3.55883	0.123232
$835$	−3.02416	−0.104655
$836$	8.60792	0.297711
$837$	−47.8779	−1.65490
$838$	−16.2179	−0.560238
$839$	−4.76280	−0.164430	−0.0822151	−	0.996615i	$-0.526199\pi$
$839$	−4.76280	−0.164430	−0.0822151	+	0.996615i	$0.526199\pi$
$840$	−5.47375	−0.188862
$841$	−25.4902	−0.878973
$842$	−23.3322	−0.804081
$843$	38.0420	1.31024
$844$	59.3310	2.04226
$845$	−6.08389	−0.209292
$846$	−11.3602	−0.390571
$847$	2.48210	0.0852858
$848$	11.8978	0.408573
$849$	34.2186	1.17438
$850$	13.9995	0.480181
$851$	13.3554	0.457816
$852$	11.8275	0.405202
$853$	−17.0994	−0.585473	−0.292736	−	0.956193i	$-0.594566\pi$
$853$	−17.0994	−0.585473	−0.292736	+	0.956193i	$0.594566\pi$
$854$	27.4838	0.940478
$855$	1.97319	0.0674818
$856$	20.8898	0.713999
$857$	4.07500	0.139199	0.0695997	−	0.997575i	$-0.477828\pi$
$857$	4.07500	0.139199	0.0695997	+	0.997575i	$0.477828\pi$
$858$	8.77737	0.299655
$859$	−38.0533	−1.29836	−0.649181	−	0.760634i	$-0.724888\pi$
$859$	−38.0533	−1.29836	−0.649181	+	0.760634i	$0.724888\pi$
$860$	−17.4257	−0.594213
$861$	14.8328	0.505500
$862$	−16.9701	−0.578004
$863$	18.7528	0.638353	0.319177	−	0.947695i	$-0.396594\pi$
$863$	18.7528	0.638353	0.319177	+	0.947695i	$0.396594\pi$
$864$	−42.9337	−1.46063
$865$	12.1803	0.414143
$866$	40.1078	1.36292
$867$	38.7280	1.31527
$868$	56.6569	1.92306
$869$	2.79470	0.0948036
$870$	6.25280	0.211990
$871$	31.2568	1.05910
$872$	4.86162	0.164635
$873$	−3.18141	−0.107675
$874$	−11.0845	−0.374939
$875$	2.48210	0.0839102
$876$	4.11348	0.138981
$877$	−3.20019	−0.108063	−0.0540313	−	0.998539i	$-0.517207\pi$
$877$	−3.20019	−0.108063	−0.0540313	+	0.998539i	$0.517207\pi$
$878$	−53.2967	−1.79868
$879$	35.8593	1.20950
$880$	2.24193	0.0755755
$881$	−40.5018	−1.36454	−0.682270	−	0.731101i	$-0.739007\pi$
$881$	−40.5018	−1.36454	−0.682270	+	0.731101i	$0.739007\pi$
$882$	−1.10501	−0.0372076
$883$	27.5566	0.927354	0.463677	−	0.886004i	$-0.346530\pi$
$883$	27.5566	0.927354	0.463677	+	0.886004i	$0.346530\pi$
$884$	−45.3754	−1.52614
$885$	−20.8160	−0.699721
$886$	−0.141309	−0.00474738
$887$	22.7781	0.764814	0.382407	−	0.923994i	$-0.375095\pi$
$887$	22.7781	0.764814	0.382407	+	0.923994i	$0.375095\pi$
$888$	18.5579	0.622762
$889$	24.5902	0.824730
$890$	27.8186	0.932481
$891$	6.79823	0.227749
$892$	−6.77499	−0.226843
$893$	27.9112	0.934013
$894$	32.2354	1.07811
$895$	−7.91094	−0.264434
$896$	26.7792	0.894629
$897$	−6.45254	−0.215444
$898$	−12.8682	−0.429417
$899$	−16.0721	−0.536034
$900$	−1.62285	−0.0540948
$901$	34.4137	1.14649
$902$	8.34499	0.277858
$903$	−25.1312	−0.836313
$904$	11.6762	0.388344
$905$	−17.1054	−0.568601
$906$	−58.0842	−1.92972
$907$	36.3876	1.20823	0.604116	−	0.796897i	$-0.293527\pi$
$907$	36.3876	1.20823	0.604116	+	0.796897i	$0.293527\pi$
$908$	55.1617	1.83061
$909$	−9.56194	−0.317150
$910$	−14.0921	−0.467150
$911$	−31.1915	−1.03342	−0.516711	−	0.856160i	$-0.672844\pi$
$911$	−31.1915	−1.03342	−0.516711	+	0.856160i	$0.672844\pi$
$912$	11.2131	0.371301
$913$	−2.56421	−0.0848629
$914$	−84.1427	−2.78319
$915$	−7.92934	−0.262136
$916$	24.5611	0.811521
$917$	−44.6398	−1.47414
$918$	−78.1300	−2.57867
$919$	−23.1360	−0.763188	−0.381594	−	0.924330i	$-0.624625\pi$
$919$	−23.1360	−0.763188	−0.381594	+	0.924330i	$0.624625\pi$
$920$	2.26388	0.0746380
$921$	27.9293	0.920300
$922$	−7.09396	−0.233627
$923$	7.56159	0.248893
$924$	−10.2100	−0.335886
$925$	−8.41516	−0.276689
$926$	−2.74879	−0.0903307
$927$	9.41374	0.309188
$928$	−14.4124	−0.473109
$929$	−28.2095	−0.925524	−0.462762	−	0.886483i	$-0.653142\pi$
$929$	−28.2095	−0.925524	−0.462762	+	0.886483i	$0.653142\pi$
$930$	−28.6329	−0.938909
$931$	2.71493	0.0889783
$932$	37.3843	1.22456
$933$	−48.5036	−1.58794
$934$	52.2919	1.71104
$935$	6.48465	0.212071
$936$	2.28805	0.0747872
$937$	21.5018	0.702434	0.351217	−	0.936294i	$-0.385768\pi$
$937$	21.5018	0.702434	0.351217	+	0.936294i	$0.385768\pi$
$938$	−63.6884	−2.07950
$939$	−31.3478	−1.02300
$940$	−22.9555	−0.748725
$941$	−52.1151	−1.69890	−0.849451	−	0.527667i	$-0.823067\pi$
$941$	−52.1151	−1.69890	−0.849451	+	0.527667i	$0.823067\pi$
$942$	−15.2824	−0.497927
$943$	−6.13468	−0.199773
$944$	30.1865	0.982487
$945$	−13.8523	−0.450616
$946$	−14.1389	−0.459695
$947$	30.3610	0.986601	0.493301	−	0.869859i	$-0.335790\pi$
$947$	30.3610	0.986601	0.493301	+	0.869859i	$0.335790\pi$
$948$	−11.4959	−0.373370
$949$	2.62985	0.0853685
$950$	6.98430	0.226601
$951$	−2.14143	−0.0694407
$952$	22.9597	0.744127
$953$	9.02678	0.292406	0.146203	−	0.989255i	$-0.453295\pi$
$953$	9.02678	0.292406	0.146203	+	0.989255i	$0.453295\pi$
$954$	−6.98790	−0.226242
$955$	8.71486	0.282006
$956$	−12.0149	−0.388589
$957$	2.89632	0.0936248
$958$	54.9205	1.77440
$959$	27.4157	0.885300
$960$	−18.7440	−0.604961
$961$	42.5975	1.37411
$962$	47.7772	1.54040
$963$	8.93199	0.287829
$964$	−31.0204	−0.999099
$965$	21.0125	0.676416
$966$	13.1476	0.423017
$967$	8.39892	0.270091	0.135046	−	0.990839i	$-0.456882\pi$
$967$	8.39892	0.270091	0.135046	+	0.990839i	$0.456882\pi$
$968$	−1.42646	−0.0458482
$969$	32.4330	1.04190
$970$	−11.2609	−0.361566
$971$	−6.21739	−0.199526	−0.0997628	−	0.995011i	$-0.531808\pi$
$971$	−6.21739	−0.199526	−0.0997628	+	0.995011i	$0.531808\pi$
$972$	16.5836	0.531920
$973$	−2.64663	−0.0848469
$974$	50.7689	1.62674
$975$	4.06572	0.130207
$976$	11.4988	0.368069
$977$	58.1008	1.85881	0.929404	−	0.369063i	$-0.120321\pi$
$977$	58.1008	1.85881	0.929404	+	0.369063i	$0.120321\pi$
$978$	−53.5416	−1.71207
$979$	12.8857	0.411828
$980$	−2.23289	−0.0713270
$981$	2.07872	0.0663683
$982$	47.5366	1.51695
$983$	−18.6661	−0.595357	−0.297678	−	0.954666i	$-0.596212\pi$
$983$	−18.6661	−0.595357	−0.297678	+	0.954666i	$0.596212\pi$
$984$	−8.52442	−0.271748
$985$	12.4804	0.397660
$986$	−26.2274	−0.835250
$987$	−33.1061	−1.05378
$988$	−22.6375	−0.720196
$989$	10.3940	0.330509
$990$	−1.31675	−0.0418489
$991$	−5.54207	−0.176050	−0.0880248	−	0.996118i	$-0.528055\pi$
$991$	−5.54207	−0.176050	−0.0880248	+	0.996118i	$0.528055\pi$
$992$	65.9973	2.09542
$993$	29.2630	0.928634
$994$	−15.4074	−0.488692
$995$	−21.4210	−0.679093
$996$	10.5478	0.334220
$997$	−14.6787	−0.464878	−0.232439	−	0.972611i	$-0.574671\pi$
$997$	−14.6787	−0.464878	−0.232439	+	0.972611i	$0.574671\pi$
$998$	−51.2706	−1.62294
$999$	46.9641	1.48588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.c.1.4	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.c.1.4	✓	23	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-2.15888 q^{2} +1.54599 q^{3} +2.66074 q^{4} +1.00000 q^{5} -3.33759 q^{6} +2.48210 q^{7} -1.42646 q^{8} -0.609922 q^{9} +O(q^{10})\)	\(q-2.15888 q^{2} +1.54599 q^{3} +2.66074 q^{4} +1.00000 q^{5} -3.33759 q^{6} +2.48210 q^{7} -1.42646 q^{8} -0.609922 q^{9} -2.15888 q^{10} -1.00000 q^{11} +4.11348 q^{12} +2.62985 q^{13} -5.35854 q^{14} +1.54599 q^{15} -2.24193 q^{16} -6.48465 q^{17} +1.31675 q^{18} -3.23516 q^{19} +2.66074 q^{20} +3.83729 q^{21} +2.15888 q^{22} -1.58706 q^{23} -2.20529 q^{24} +1.00000 q^{25} -5.67752 q^{26} -5.58089 q^{27} +6.60422 q^{28} -1.87344 q^{29} -3.33759 q^{30} +8.57890 q^{31} +7.69298 q^{32} -1.54599 q^{33} +13.9995 q^{34} +2.48210 q^{35} -1.62285 q^{36} -8.41516 q^{37} +6.98430 q^{38} +4.06572 q^{39} -1.42646 q^{40} +3.86543 q^{41} -8.28423 q^{42} -6.54920 q^{43} -2.66074 q^{44} -0.609922 q^{45} +3.42627 q^{46} -8.62747 q^{47} -3.46600 q^{48} -0.839197 q^{49} -2.15888 q^{50} -10.0252 q^{51} +6.99736 q^{52} -5.30695 q^{53} +12.0485 q^{54} -1.00000 q^{55} -3.54062 q^{56} -5.00151 q^{57} +4.04453 q^{58} -13.4645 q^{59} +4.11348 q^{60} -5.12898 q^{61} -18.5208 q^{62} -1.51388 q^{63} -12.1243 q^{64} +2.62985 q^{65} +3.33759 q^{66} +11.8854 q^{67} -17.2540 q^{68} -2.45358 q^{69} -5.35854 q^{70} +2.87529 q^{71} +0.870030 q^{72} +1.00000 q^{73} +18.1673 q^{74} +1.54599 q^{75} -8.60792 q^{76} -2.48210 q^{77} -8.77737 q^{78} -2.79470 q^{79} -2.24193 q^{80} -6.79823 q^{81} -8.34499 q^{82} +2.56421 q^{83} +10.2100 q^{84} -6.48465 q^{85} +14.1389 q^{86} -2.89632 q^{87} +1.42646 q^{88} -12.8857 q^{89} +1.31675 q^{90} +6.52754 q^{91} -4.22276 q^{92} +13.2629 q^{93} +18.6256 q^{94} -3.23516 q^{95} +11.8932 q^{96} +5.21610 q^{97} +1.81172 q^{98} +0.609922 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9} - 3 q^{10} - 23 q^{11} - 18 q^{12} - 5 q^{13} - 17 q^{14} - 5 q^{15} - q^{16} - 36 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 18 q^{21} + 3 q^{22} - 14 q^{23} - 7 q^{24} + 23 q^{25} - 21 q^{26} - 29 q^{27} + 28 q^{28} - 36 q^{29} - 5 q^{30} - 16 q^{31} - 5 q^{32} + 5 q^{33} - 28 q^{34} - 14 q^{36} - 24 q^{37} + q^{38} - 10 q^{39} - 6 q^{40} - 36 q^{41} - 5 q^{42} + 17 q^{43} - 15 q^{44} + 8 q^{45} - 25 q^{46} - 21 q^{47} - 17 q^{48} - 27 q^{49} - 3 q^{50} + 19 q^{51} - 21 q^{52} - 28 q^{53} - 15 q^{54} - 23 q^{55} - 46 q^{56} - 23 q^{57} - 16 q^{58} - 61 q^{59} - 18 q^{60} - 17 q^{61} - 22 q^{62} - 9 q^{63} - 18 q^{64} - 5 q^{65} + 5 q^{66} + 2 q^{67} - 39 q^{68} - 36 q^{69} - 17 q^{70} - 50 q^{71} + 15 q^{72} + 23 q^{73} + 17 q^{74} - 5 q^{75} - 21 q^{76} + 49 q^{78} - 18 q^{79} - q^{80} - 57 q^{81} + 14 q^{82} - 20 q^{83} - 38 q^{84} - 36 q^{85} - 45 q^{86} + 37 q^{87} + 6 q^{88} - 93 q^{89} + q^{90} - 42 q^{91} - 39 q^{92} - 18 q^{93} - 6 q^{94} + 6 q^{95} - 9 q^{96} - 31 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9 - 3 * q^10 - 23 * q^11 - 18 * q^12 - 5 * q^13 - 17 * q^14 - 5 * q^15 - q^16 - 36 * q^17 + q^18 + 6 * q^19 + 15 * q^20 - 18 * q^21 + 3 * q^22 - 14 * q^23 - 7 * q^24 + 23 * q^25 - 21 * q^26 - 29 * q^27 + 28 * q^28 - 36 * q^29 - 5 * q^30 - 16 * q^31 - 5 * q^32 + 5 * q^33 - 28 * q^34 - 14 * q^36 - 24 * q^37 + q^38 - 10 * q^39 - 6 * q^40 - 36 * q^41 - 5 * q^42 + 17 * q^43 - 15 * q^44 + 8 * q^45 - 25 * q^46 - 21 * q^47 - 17 * q^48 - 27 * q^49 - 3 * q^50 + 19 * q^51 - 21 * q^52 - 28 * q^53 - 15 * q^54 - 23 * q^55 - 46 * q^56 - 23 * q^57 - 16 * q^58 - 61 * q^59 - 18 * q^60 - 17 * q^61 - 22 * q^62 - 9 * q^63 - 18 * q^64 - 5 * q^65 + 5 * q^66 + 2 * q^67 - 39 * q^68 - 36 * q^69 - 17 * q^70 - 50 * q^71 + 15 * q^72 + 23 * q^73 + 17 * q^74 - 5 * q^75 - 21 * q^76 + 49 * q^78 - 18 * q^79 - q^80 - 57 * q^81 + 14 * q^82 - 20 * q^83 - 38 * q^84 - 36 * q^85 - 45 * q^86 + 37 * q^87 + 6 * q^88 - 93 * q^89 + q^90 - 42 * q^91 - 39 * q^92 - 18 * q^93 - 6 * q^94 + 6 * q^95 - 9 * q^96 - 31 * q^97 - 31 * q^98 - 8 * q^99

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