LMFDB - Embedded newform 4015.2.a.h.1.14

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:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-0.742421 q^{2} +0.782455 q^{3} -1.44881 q^{4} +1.00000 q^{5} -0.580911 q^{6} +0.262449 q^{7} +2.56047 q^{8} -2.38776 q^{9} +O(q^{10})$	\(q-0.742421 q^{2} +0.782455 q^{3} -1.44881 q^{4} +1.00000 q^{5} -0.580911 q^{6} +0.262449 q^{7} +2.56047 q^{8} -2.38776 q^{9} -0.742421 q^{10} +1.00000 q^{11} -1.13363 q^{12} -1.63020 q^{13} -0.194848 q^{14} +0.782455 q^{15} +0.996674 q^{16} -3.94785 q^{17} +1.77273 q^{18} +3.18333 q^{19} -1.44881 q^{20} +0.205355 q^{21} -0.742421 q^{22} -4.37745 q^{23} +2.00345 q^{24} +1.00000 q^{25} +1.21030 q^{26} -4.21568 q^{27} -0.380239 q^{28} +4.80588 q^{29} -0.580911 q^{30} -0.406340 q^{31} -5.86089 q^{32} +0.782455 q^{33} +2.93097 q^{34} +0.262449 q^{35} +3.45942 q^{36} +6.86756 q^{37} -2.36337 q^{38} -1.27556 q^{39} +2.56047 q^{40} +10.8431 q^{41} -0.152460 q^{42} -9.75665 q^{43} -1.44881 q^{44} -2.38776 q^{45} +3.24991 q^{46} +7.88801 q^{47} +0.779853 q^{48} -6.93112 q^{49} -0.742421 q^{50} -3.08902 q^{51} +2.36185 q^{52} -3.45344 q^{53} +3.12981 q^{54} +1.00000 q^{55} +0.671993 q^{56} +2.49082 q^{57} -3.56799 q^{58} +5.96161 q^{59} -1.13363 q^{60} +6.28533 q^{61} +0.301675 q^{62} -0.626667 q^{63} +2.35790 q^{64} -1.63020 q^{65} -0.580911 q^{66} +15.0832 q^{67} +5.71969 q^{68} -3.42516 q^{69} -0.194848 q^{70} -0.367892 q^{71} -6.11380 q^{72} +1.00000 q^{73} -5.09862 q^{74} +0.782455 q^{75} -4.61205 q^{76} +0.262449 q^{77} +0.947003 q^{78} -9.69406 q^{79} +0.996674 q^{80} +3.86471 q^{81} -8.05015 q^{82} -7.65958 q^{83} -0.297520 q^{84} -3.94785 q^{85} +7.24354 q^{86} +3.76039 q^{87} +2.56047 q^{88} -0.317007 q^{89} +1.77273 q^{90} -0.427845 q^{91} +6.34210 q^{92} -0.317943 q^{93} -5.85622 q^{94} +3.18333 q^{95} -4.58589 q^{96} +9.10851 q^{97} +5.14581 q^{98} -2.38776 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * 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 $

$2$	−0.742421	−0.524971	−0.262486	−	0.964936i	$-0.584542\pi$
$2$	−0.742421	−0.524971	−0.262486	+	0.964936i	$0.584542\pi$
$3$	0.782455	0.451751	0.225875	−	0.974156i	$-0.427476\pi$
$3$	0.782455	0.451751	0.225875	+	0.974156i	$0.427476\pi$
$4$	−1.44881	−0.724405
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.580911	−0.237156
$7$	0.262449	0.0991965	0.0495982	−	0.998769i	$-0.484206\pi$
$7$	0.262449	0.0991965	0.0495982	+	0.998769i	$0.484206\pi$
$8$	2.56047	0.905263
$9$	−2.38776	−0.795921
$10$	−0.742421	−0.234774
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.13363	−0.327251
$13$	−1.63020	−0.452137	−0.226068	−	0.974111i	$-0.572587\pi$
$13$	−1.63020	−0.452137	−0.226068	+	0.974111i	$0.572587\pi$
$14$	−0.194848	−0.0520753
$15$	0.782455	0.202029
$16$	0.996674	0.249169
$17$	−3.94785	−0.957495	−0.478747	−	0.877953i	$-0.658909\pi$
$17$	−3.94785	−0.957495	−0.478747	+	0.877953i	$0.658909\pi$
$18$	1.77273	0.417836
$19$	3.18333	0.730307	0.365153	−	0.930947i	$-0.381017\pi$
$19$	3.18333	0.730307	0.365153	+	0.930947i	$0.381017\pi$
$20$	−1.44881	−0.323964
$21$	0.205355	0.0448121
$22$	−0.742421	−0.158285
$23$	−4.37745	−0.912762	−0.456381	−	0.889784i	$-0.650855\pi$
$23$	−4.37745	−0.912762	−0.456381	+	0.889784i	$0.650855\pi$
$24$	2.00345	0.408953
$25$	1.00000	0.200000
$26$	1.21030	0.237359
$27$	−4.21568	−0.811309
$28$	−0.380239	−0.0718584
$29$	4.80588	0.892430	0.446215	−	0.894926i	$-0.352772\pi$
$29$	4.80588	0.892430	0.446215	+	0.894926i	$0.352772\pi$
$30$	−0.580911	−0.106059
$31$	−0.406340	−0.0729808	−0.0364904	−	0.999334i	$-0.511618\pi$
$31$	−0.406340	−0.0729808	−0.0364904	+	0.999334i	$0.511618\pi$
$32$	−5.86089	−1.03607
$33$	0.782455	0.136208
$34$	2.93097	0.502657
$35$	0.262449	0.0443620
$36$	3.45942	0.576570
$37$	6.86756	1.12902	0.564510	−	0.825426i	$-0.309065\pi$
$37$	6.86756	1.12902	0.564510	+	0.825426i	$0.309065\pi$
$38$	−2.36337	−0.383390
$39$	−1.27556	−0.204253
$40$	2.56047	0.404846
$41$	10.8431	1.69341	0.846704	−	0.532064i	$-0.178584\pi$
$41$	10.8431	1.69341	0.846704	+	0.532064i	$0.178584\pi$
$42$	−0.152460	−0.0235250
$43$	−9.75665	−1.48787	−0.743937	−	0.668249i	$-0.767044\pi$
$43$	−9.75665	−1.48787	−0.743937	+	0.668249i	$0.767044\pi$
$44$	−1.44881	−0.218416
$45$	−2.38776	−0.355947
$46$	3.24991	0.479174
$47$	7.88801	1.15058	0.575292	−	0.817948i	$-0.304888\pi$
$47$	7.88801	1.15058	0.575292	+	0.817948i	$0.304888\pi$
$48$	0.779853	0.112562
$49$	−6.93112	−0.990160
$50$	−0.742421	−0.104994
$51$	−3.08902	−0.432549
$52$	2.36185	0.327530
$53$	−3.45344	−0.474367	−0.237184	−	0.971465i	$-0.576224\pi$
$53$	−3.45344	−0.474367	−0.237184	+	0.971465i	$0.576224\pi$
$54$	3.12981	0.425914
$55$	1.00000	0.134840
$56$	0.671993	0.0897989
$57$	2.49082	0.329917
$58$	−3.56799	−0.468500
$59$	5.96161	0.776135	0.388067	−	0.921631i	$-0.373143\pi$
$59$	5.96161	0.776135	0.388067	+	0.921631i	$0.373143\pi$
$60$	−1.13363	−0.146351
$61$	6.28533	0.804754	0.402377	−	0.915474i	$-0.368184\pi$
$61$	6.28533	0.804754	0.402377	+	0.915474i	$0.368184\pi$
$62$	0.301675	0.0383128
$63$	−0.626667	−0.0789526
$64$	2.35790	0.294738
$65$	−1.63020	−0.202202
$66$	−0.580911	−0.0715053
$67$	15.0832	1.84270	0.921351	−	0.388732i	$-0.127087\pi$
$67$	15.0832	1.84270	0.921351	+	0.388732i	$0.127087\pi$
$68$	5.71969	0.693614
$69$	−3.42516	−0.412341
$70$	−0.194848	−0.0232888
$71$	−0.367892	−0.0436607	−0.0218304	−	0.999762i	$-0.506949\pi$
$71$	−0.367892	−0.0436607	−0.0218304	+	0.999762i	$0.506949\pi$
$72$	−6.11380	−0.720518
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−5.09862	−0.592703
$75$	0.782455	0.0903502
$76$	−4.61205	−0.529038
$77$	0.262449	0.0299089
$78$	0.947003	0.107227
$79$	−9.69406	−1.09067	−0.545334	−	0.838219i	$-0.683597\pi$
$79$	−9.69406	−1.09067	−0.545334	+	0.838219i	$0.683597\pi$
$80$	0.996674	0.111432
$81$	3.86471	0.429412
$82$	−8.05015	−0.888990
$83$	−7.65958	−0.840748	−0.420374	−	0.907351i	$-0.638101\pi$
$83$	−7.65958	−0.840748	−0.420374	+	0.907351i	$0.638101\pi$
$84$	−0.297520	−0.0324621
$85$	−3.94785	−0.428205
$86$	7.24354	0.781091
$87$	3.76039	0.403156
$88$	2.56047	0.272947
$89$	−0.317007	−0.0336026	−0.0168013	−	0.999859i	$-0.505348\pi$
$89$	−0.317007	−0.0336026	−0.0168013	+	0.999859i	$0.505348\pi$
$90$	1.77273	0.186862
$91$	−0.427845	−0.0448504
$92$	6.34210	0.661210
$93$	−0.317943	−0.0329691
$94$	−5.85622	−0.604023
$95$	3.18333	0.326603
$96$	−4.58589	−0.468045
$97$	9.10851	0.924829	0.462414	−	0.886664i	$-0.346983\pi$
$97$	9.10851	0.924829	0.462414	+	0.886664i	$0.346983\pi$
$98$	5.14581	0.519805
$99$	−2.38776	−0.239979
$100$	−1.44881	−0.144881
$101$	2.57120	0.255844	0.127922	−	0.991784i	$-0.459169\pi$
$101$	2.57120	0.255844	0.127922	+	0.991784i	$0.459169\pi$
$102$	2.29335	0.227076
$103$	2.19580	0.216359	0.108179	−	0.994131i	$-0.465498\pi$
$103$	2.19580	0.216359	0.108179	+	0.994131i	$0.465498\pi$
$104$	−4.17408	−0.409303
$105$	0.205355	0.0200406
$106$	2.56391	0.249029
$107$	13.3236	1.28804	0.644021	−	0.765008i	$-0.277265\pi$
$107$	13.3236	1.28804	0.644021	+	0.765008i	$0.277265\pi$
$108$	6.10773	0.587717
$109$	−2.88532	−0.276364	−0.138182	−	0.990407i	$-0.544126\pi$
$109$	−2.88532	−0.276364	−0.138182	+	0.990407i	$0.544126\pi$
$110$	−0.742421	−0.0707871
$111$	5.37356	0.510036
$112$	0.261576	0.0247166
$113$	−7.43713	−0.699626	−0.349813	−	0.936820i	$-0.613755\pi$
$113$	−7.43713	−0.699626	−0.349813	+	0.936820i	$0.613755\pi$
$114$	−1.84923	−0.173197
$115$	−4.37745	−0.408200
$116$	−6.96281	−0.646481
$117$	3.89254	0.359865
$118$	−4.42602	−0.407448
$119$	−1.03611	−0.0949801
$120$	2.00345	0.182889
$121$	1.00000	0.0909091
$122$	−4.66636	−0.422472
$123$	8.48424	0.764998
$124$	0.588709	0.0528677
$125$	1.00000	0.0894427
$126$	0.465251	0.0414478
$127$	4.34669	0.385706	0.192853	−	0.981228i	$-0.438226\pi$
$127$	4.34669	0.385706	0.192853	+	0.981228i	$0.438226\pi$
$128$	9.97123	0.881340
$129$	−7.63414	−0.672149
$130$	1.21030	0.106150
$131$	0.0689576	0.00602485	0.00301243	−	0.999995i	$-0.499041\pi$
$131$	0.0689576	0.00602485	0.00301243	+	0.999995i	$0.499041\pi$
$132$	−1.13363	−0.0986698
$133$	0.835463	0.0724438
$134$	−11.1981	−0.967365
$135$	−4.21568	−0.362828
$136$	−10.1084	−0.866785
$137$	4.15943	0.355364	0.177682	−	0.984088i	$-0.443140\pi$
$137$	4.15943	0.355364	0.177682	+	0.984088i	$0.443140\pi$
$138$	2.54291	0.216467
$139$	4.87694	0.413656	0.206828	−	0.978377i	$-0.433686\pi$
$139$	4.87694	0.413656	0.206828	+	0.978377i	$0.433686\pi$
$140$	−0.380239	−0.0321361
$141$	6.17201	0.519777
$142$	0.273131	0.0229206
$143$	−1.63020	−0.136324
$144$	−2.37982	−0.198318
$145$	4.80588	0.399107
$146$	−0.742421	−0.0614432
$147$	−5.42329	−0.447306
$148$	−9.94979	−0.817868
$149$	6.06732	0.497055	0.248527	−	0.968625i	$-0.420053\pi$
$149$	6.06732	0.497055	0.248527	+	0.968625i	$0.420053\pi$
$150$	−0.580911	−0.0474312
$151$	10.4720	0.852203	0.426102	−	0.904675i	$-0.359887\pi$
$151$	10.4720	0.852203	0.426102	+	0.904675i	$0.359887\pi$
$152$	8.15083	0.661119
$153$	9.42654	0.762090
$154$	−0.194848	−0.0157013
$155$	−0.406340	−0.0326380
$156$	1.84805	0.147962
$157$	−5.00866	−0.399735	−0.199867	−	0.979823i	$-0.564051\pi$
$157$	−5.00866	−0.399735	−0.199867	+	0.979823i	$0.564051\pi$
$158$	7.19708	0.572569
$159$	−2.70217	−0.214296
$160$	−5.86089	−0.463344
$161$	−1.14886	−0.0905427
$162$	−2.86924	−0.225429
$163$	11.8436	0.927661	0.463830	−	0.885924i	$-0.346475\pi$
$163$	11.8436	0.927661	0.463830	+	0.885924i	$0.346475\pi$
$164$	−15.7096	−1.22671
$165$	0.782455	0.0609141
$166$	5.68663	0.441368
$167$	−12.4359	−0.962321	−0.481161	−	0.876632i	$-0.659785\pi$
$167$	−12.4359	−0.962321	−0.481161	+	0.876632i	$0.659785\pi$
$168$	0.525805	0.0405667
$169$	−10.3424	−0.795572
$170$	2.93097	0.224795
$171$	−7.60105	−0.581266
$172$	14.1355	1.07782
$173$	5.89071	0.447862	0.223931	−	0.974605i	$-0.428111\pi$
$173$	5.89071	0.447862	0.223931	+	0.974605i	$0.428111\pi$
$174$	−2.79179	−0.211645
$175$	0.262449	0.0198393
$176$	0.996674	0.0751271
$177$	4.66469	0.350620
$178$	0.235352	0.0176404
$179$	11.4631	0.856792	0.428396	−	0.903591i	$-0.359079\pi$
$179$	11.4631	0.856792	0.428396	+	0.903591i	$0.359079\pi$
$180$	3.45942	0.257850
$181$	14.7852	1.09898	0.549489	−	0.835501i	$-0.314822\pi$
$181$	14.7852	1.09898	0.549489	+	0.835501i	$0.314822\pi$
$182$	0.317641	0.0235451
$183$	4.91799	0.363548
$184$	−11.2083	−0.826290
$185$	6.86756	0.504913
$186$	0.236047	0.0173078
$187$	−3.94785	−0.288696
$188$	−11.4282	−0.833489
$189$	−1.10640	−0.0804790
$190$	−2.36337	−0.171457
$191$	−5.07748	−0.367393	−0.183697	−	0.982983i	$-0.558806\pi$
$191$	−5.07748	−0.367393	−0.183697	+	0.982983i	$0.558806\pi$
$192$	1.84495	0.133148
$193$	19.7757	1.42349	0.711743	−	0.702440i	$-0.247906\pi$
$193$	19.7757	1.42349	0.711743	+	0.702440i	$0.247906\pi$
$194$	−6.76235	−0.485508
$195$	−1.27556	−0.0913448
$196$	10.0419	0.717277
$197$	−1.83202	−0.130526	−0.0652631	−	0.997868i	$-0.520789\pi$
$197$	−1.83202	−0.130526	−0.0652631	+	0.997868i	$0.520789\pi$
$198$	1.77273	0.125982
$199$	14.5281	1.02987	0.514935	−	0.857229i	$-0.327816\pi$
$199$	14.5281	1.02987	0.514935	+	0.857229i	$0.327816\pi$
$200$	2.56047	0.181053
$201$	11.8019	0.832442
$202$	−1.90891	−0.134311
$203$	1.26130	0.0885259
$204$	4.47540	0.313341
$205$	10.8431	0.757315
$206$	−1.63021	−0.113582
$207$	10.4523	0.726487
$208$	−1.62478	−0.112658
$209$	3.18333	0.220196
$210$	−0.152460	−0.0105207
$211$	−5.07473	−0.349359	−0.174679	−	0.984625i	$-0.555889\pi$
$211$	−5.07473	−0.349359	−0.174679	+	0.984625i	$0.555889\pi$
$212$	5.00339	0.343634
$213$	−0.287859	−0.0197238
$214$	−9.89173	−0.676185
$215$	−9.75665	−0.665398
$216$	−10.7941	−0.734448
$217$	−0.106643	−0.00723943
$218$	2.14212	0.145083
$219$	0.782455	0.0528734
$220$	−1.44881	−0.0976788
$221$	6.43580	0.432919
$222$	−3.98944	−0.267754
$223$	6.09231	0.407971	0.203986	−	0.978974i	$-0.434610\pi$
$223$	6.09231	0.407971	0.203986	+	0.978974i	$0.434610\pi$
$224$	−1.53819	−0.102774
$225$	−2.38776	−0.159184
$226$	5.52148	0.367283
$227$	−18.1291	−1.20327	−0.601635	−	0.798771i	$-0.705484\pi$
$227$	−18.1291	−1.20327	−0.601635	+	0.798771i	$0.705484\pi$
$228$	−3.60872	−0.238993
$229$	−14.2432	−0.941219	−0.470610	−	0.882342i	$-0.655966\pi$
$229$	−14.2432	−0.941219	−0.470610	+	0.882342i	$0.655966\pi$
$230$	3.24991	0.214293
$231$	0.205355	0.0135113
$232$	12.3053	0.807884
$233$	−16.0599	−1.05212	−0.526060	−	0.850447i	$-0.676331\pi$
$233$	−16.0599	−1.05212	−0.526060	+	0.850447i	$0.676331\pi$
$234$	−2.88990	−0.188919
$235$	7.88801	0.514557
$236$	−8.63724	−0.562236
$237$	−7.58517	−0.492710
$238$	0.769230	0.0498618
$239$	11.4599	0.741280	0.370640	−	0.928777i	$-0.379138\pi$
$239$	11.4599	0.741280	0.370640	+	0.928777i	$0.379138\pi$
$240$	0.779853	0.0503393
$241$	16.0377	1.03308	0.516538	−	0.856264i	$-0.327221\pi$
$241$	16.0377	1.03308	0.516538	+	0.856264i	$0.327221\pi$
$242$	−0.742421	−0.0477246
$243$	15.6710	1.00530
$244$	−9.10625	−0.582968
$245$	−6.93112	−0.442813
$246$	−6.29888	−0.401602
$247$	−5.18948	−0.330198
$248$	−1.04042	−0.0660668
$249$	−5.99328	−0.379808
$250$	−0.742421	−0.0469548
$251$	9.70512	0.612582	0.306291	−	0.951938i	$-0.400912\pi$
$251$	9.70512	0.612582	0.306291	+	0.951938i	$0.400912\pi$
$252$	0.907921	0.0571937
$253$	−4.37745	−0.275208
$254$	−3.22707	−0.202485
$255$	−3.08902	−0.193442
$256$	−12.1187	−0.757416
$257$	−24.8525	−1.55025	−0.775127	−	0.631805i	$-0.782314\pi$
$257$	−24.8525	−1.55025	−0.775127	+	0.631805i	$0.782314\pi$
$258$	5.66775	0.352859
$259$	1.80239	0.111995
$260$	2.36185	0.146476
$261$	−11.4753	−0.710304
$262$	−0.0511956	−0.00316287
$263$	28.4980	1.75726	0.878631	−	0.477502i	$-0.158458\pi$
$263$	28.4980	1.75726	0.878631	+	0.477502i	$0.158458\pi$
$264$	2.00345	0.123304
$265$	−3.45344	−0.212143
$266$	−0.620265	−0.0380309
$267$	−0.248044	−0.0151800
$268$	−21.8527	−1.33486
$269$	12.2506	0.746930	0.373465	−	0.927644i	$-0.378170\pi$
$269$	12.2506	0.746930	0.373465	+	0.927644i	$0.378170\pi$
$270$	3.12981	0.190474
$271$	−3.50279	−0.212779	−0.106390	−	0.994325i	$-0.533929\pi$
$271$	−3.50279	−0.212779	−0.106390	+	0.994325i	$0.533929\pi$
$272$	−3.93472	−0.238578
$273$	−0.334770	−0.0202612
$274$	−3.08805	−0.186556
$275$	1.00000	0.0603023
$276$	4.96241	0.298702
$277$	32.6492	1.96170	0.980850	−	0.194765i	$-0.0623944\pi$
$277$	32.6492	1.96170	0.980850	+	0.194765i	$0.0623944\pi$
$278$	−3.62074	−0.217158
$279$	0.970243	0.0580869
$280$	0.671993	0.0401593
$281$	18.0971	1.07958	0.539791	−	0.841799i	$-0.318503\pi$
$281$	18.0971	1.07958	0.539791	+	0.841799i	$0.318503\pi$
$282$	−4.58223	−0.272868
$283$	12.3586	0.734642	0.367321	−	0.930094i	$-0.380275\pi$
$283$	12.3586	0.734642	0.367321	+	0.930094i	$0.380275\pi$
$284$	0.533005	0.0316280
$285$	2.49082	0.147543
$286$	1.21030	0.0715663
$287$	2.84576	0.167980
$288$	13.9944	0.824629
$289$	−1.41446	−0.0832038
$290$	−3.56799	−0.209520
$291$	7.12700	0.417792
$292$	−1.44881	−0.0847852
$293$	15.1921	0.887532	0.443766	−	0.896143i	$-0.353642\pi$
$293$	15.1921	0.887532	0.443766	+	0.896143i	$0.353642\pi$
$294$	4.02637	0.234823
$295$	5.96161	0.347098
$296$	17.5842	1.02206
$297$	−4.21568	−0.244619
$298$	−4.50451	−0.260939
$299$	7.13613	0.412693
$300$	−1.13363	−0.0654501
$301$	−2.56062	−0.147592
$302$	−7.77467	−0.447382
$303$	2.01185	0.115578
$304$	3.17274	0.181969
$305$	6.28533	0.359897
$306$	−6.99846	−0.400075
$307$	11.9756	0.683482	0.341741	−	0.939794i	$-0.388983\pi$
$307$	11.9756	0.683482	0.341741	+	0.939794i	$0.388983\pi$
$308$	−0.380239	−0.0216661
$309$	1.71812	0.0977402
$310$	0.301675	0.0171340
$311$	23.6122	1.33892	0.669461	−	0.742847i	$-0.266525\pi$
$311$	23.6122	1.33892	0.669461	+	0.742847i	$0.266525\pi$
$312$	−3.26603	−0.184903
$313$	−22.2454	−1.25738	−0.628692	−	0.777654i	$-0.716409\pi$
$313$	−22.2454	−1.25738	−0.628692	+	0.777654i	$0.716409\pi$
$314$	3.71854	0.209849
$315$	−0.626667	−0.0353087
$316$	14.0449	0.790085
$317$	−13.7589	−0.772776	−0.386388	−	0.922336i	$-0.626277\pi$
$317$	−13.7589	−0.772776	−0.386388	+	0.922336i	$0.626277\pi$
$318$	2.00615	0.112499
$319$	4.80588	0.269078
$320$	2.35790	0.131811
$321$	10.4251	0.581874
$322$	0.852937	0.0475323
$323$	−12.5673	−0.699265
$324$	−5.59923	−0.311068
$325$	−1.63020	−0.0904274
$326$	−8.79293	−0.486995
$327$	−2.25764	−0.124848
$328$	27.7634	1.53298
$329$	2.07020	0.114134
$330$	−0.580911	−0.0319781
$331$	23.3190	1.28173	0.640865	−	0.767653i	$-0.278576\pi$
$331$	23.3190	1.28173	0.640865	+	0.767653i	$0.278576\pi$
$332$	11.0973	0.609042
$333$	−16.3981	−0.898611
$334$	9.23270	0.505191
$335$	15.0832	0.824081
$336$	0.204672	0.0111658
$337$	15.9904	0.871051	0.435526	−	0.900176i	$-0.356563\pi$
$337$	15.9904	0.871051	0.435526	+	0.900176i	$0.356563\pi$
$338$	7.67845	0.417652
$339$	−5.81922	−0.316057
$340$	5.71969	0.310194
$341$	−0.406340	−0.0220045
$342$	5.64318	0.305148
$343$	−3.65621	−0.197417
$344$	−24.9816	−1.34692
$345$	−3.42516	−0.184404
$346$	−4.37339	−0.235115
$347$	11.2907	0.606114	0.303057	−	0.952972i	$-0.401993\pi$
$347$	11.2907	0.606114	0.303057	+	0.952972i	$0.401993\pi$
$348$	−5.44809	−0.292048
$349$	9.58688	0.513174	0.256587	−	0.966521i	$-0.417402\pi$
$349$	9.58688	0.513174	0.256587	+	0.966521i	$0.417402\pi$
$350$	−0.194848	−0.0104151
$351$	6.87242	0.366823
$352$	−5.86089	−0.312387
$353$	−7.39528	−0.393611	−0.196806	−	0.980443i	$-0.563057\pi$
$353$	−7.39528	−0.393611	−0.196806	+	0.980443i	$0.563057\pi$
$354$	−3.46316	−0.184065
$355$	−0.367892	−0.0195257
$356$	0.459283	0.0243419
$357$	−0.810710	−0.0429073
$358$	−8.51045	−0.449791
$359$	11.3521	0.599141	0.299570	−	0.954074i	$-0.403157\pi$
$359$	11.3521	0.599141	0.299570	+	0.954074i	$0.403157\pi$
$360$	−6.11380	−0.322225
$361$	−8.86639	−0.466652
$362$	−10.9769	−0.576932
$363$	0.782455	0.0410683
$364$	0.619867	0.0324898
$365$	1.00000	0.0523424
$366$	−3.65122	−0.190852
$367$	−5.33937	−0.278713	−0.139356	−	0.990242i	$-0.544503\pi$
$367$	−5.33937	−0.278713	−0.139356	+	0.990242i	$0.544503\pi$
$368$	−4.36289	−0.227432
$369$	−25.8908	−1.34782
$370$	−5.09862	−0.265065
$371$	−0.906354	−0.0470555
$372$	0.460639	0.0238830
$373$	−7.74645	−0.401096	−0.200548	−	0.979684i	$-0.564272\pi$
$373$	−7.74645	−0.401096	−0.200548	+	0.979684i	$0.564272\pi$
$374$	2.93097	0.151557
$375$	0.782455	0.0404058
$376$	20.1970	1.04158
$377$	−7.83456	−0.403500
$378$	0.821417	0.0422491
$379$	18.3349	0.941800	0.470900	−	0.882187i	$-0.343929\pi$
$379$	18.3349	0.941800	0.470900	+	0.882187i	$0.343929\pi$
$380$	−4.61205	−0.236593
$381$	3.40109	0.174243
$382$	3.76963	0.192871
$383$	−20.7955	−1.06260	−0.531300	−	0.847184i	$-0.678296\pi$
$383$	−20.7955	−1.06260	−0.531300	+	0.847184i	$0.678296\pi$
$384$	7.80204	0.398146
$385$	0.262449	0.0133756
$386$	−14.6819	−0.747289
$387$	23.2966	1.18423
$388$	−13.1965	−0.669951
$389$	18.1668	0.921095	0.460548	−	0.887635i	$-0.347653\pi$
$389$	18.1668	0.921095	0.460548	+	0.887635i	$0.347653\pi$
$390$	0.947003	0.0479534
$391$	17.2815	0.873965
$392$	−17.7469	−0.896355
$393$	0.0539562	0.00272173
$394$	1.36013	0.0685225
$395$	−9.69406	−0.487761
$396$	3.45942	0.173842
$397$	21.6082	1.08449	0.542243	−	0.840221i	$-0.317575\pi$
$397$	21.6082	1.08449	0.542243	+	0.840221i	$0.317575\pi$
$398$	−10.7860	−0.540652
$399$	0.653712	0.0327266
$400$	0.996674	0.0498337
$401$	3.30414	0.165001	0.0825003	−	0.996591i	$-0.473709\pi$
$401$	3.30414	0.165001	0.0825003	+	0.996591i	$0.473709\pi$
$402$	−8.76198	−0.437008
$403$	0.662416	0.0329973
$404$	−3.72518	−0.185335
$405$	3.86471	0.192039
$406$	−0.936416	−0.0464735
$407$	6.86756	0.340412
$408$	−7.90934	−0.391571
$409$	−22.9983	−1.13719	−0.568596	−	0.822617i	$-0.692513\pi$
$409$	−22.9983	−1.13719	−0.568596	+	0.822617i	$0.692513\pi$
$410$	−8.05015	−0.397568
$411$	3.25456	0.160536
$412$	−3.18130	−0.156731
$413$	1.56462	0.0769898
$414$	−7.76003	−0.381384
$415$	−7.65958	−0.375994
$416$	9.55444	0.468445
$417$	3.81598	0.186870
$418$	−2.36337	−0.115596
$419$	16.3517	0.798834	0.399417	−	0.916769i	$-0.369213\pi$
$419$	16.3517	0.798834	0.399417	+	0.916769i	$0.369213\pi$
$420$	−0.297520	−0.0145175
$421$	−22.5554	−1.09928	−0.549642	−	0.835400i	$-0.685236\pi$
$421$	−22.5554	−1.09928	−0.549642	+	0.835400i	$0.685236\pi$
$422$	3.76759	0.183403
$423$	−18.8347	−0.915774
$424$	−8.84244	−0.429427
$425$	−3.94785	−0.191499
$426$	0.213712	0.0103544
$427$	1.64958	0.0798287
$428$	−19.3034	−0.933064
$429$	−1.27556	−0.0615846
$430$	7.24354	0.349315
$431$	−13.9230	−0.670649	−0.335324	−	0.942103i	$-0.608846\pi$
$431$	−13.9230	−0.670649	−0.335324	+	0.942103i	$0.608846\pi$
$432$	−4.20166	−0.202153
$433$	−13.3480	−0.641464	−0.320732	−	0.947170i	$-0.603929\pi$
$433$	−13.3480	−0.641464	−0.320732	+	0.947170i	$0.603929\pi$
$434$	0.0791744	0.00380049
$435$	3.76039	0.180297
$436$	4.18028	0.200199
$437$	−13.9349	−0.666596
$438$	−0.580911	−0.0277570
$439$	6.22477	0.297092	0.148546	−	0.988905i	$-0.452541\pi$
$439$	6.22477	0.297092	0.148546	+	0.988905i	$0.452541\pi$
$440$	2.56047	0.122066
$441$	16.5499	0.788089
$442$	−4.77807	−0.227270
$443$	−6.34420	−0.301422	−0.150711	−	0.988578i	$-0.548156\pi$
$443$	−6.34420	−0.301422	−0.150711	+	0.988578i	$0.548156\pi$
$444$	−7.78527	−0.369473
$445$	−0.317007	−0.0150276
$446$	−4.52306	−0.214173
$447$	4.74741	0.224545
$448$	0.618830	0.0292369
$449$	29.2233	1.37913	0.689567	−	0.724222i	$-0.257801\pi$
$449$	29.2233	1.37913	0.689567	+	0.724222i	$0.257801\pi$
$450$	1.77273	0.0835671
$451$	10.8431	0.510582
$452$	10.7750	0.506813
$453$	8.19391	0.384983
$454$	13.4594	0.631682
$455$	−0.427845	−0.0200577
$456$	6.37766	0.298661
$457$	−9.50883	−0.444804	−0.222402	−	0.974955i	$-0.571390\pi$
$457$	−9.50883	−0.444804	−0.222402	+	0.974955i	$0.571390\pi$
$458$	10.5745	0.494113
$459$	16.6429	0.776824
$460$	6.34210	0.295702
$461$	12.4996	0.582163	0.291081	−	0.956698i	$-0.405985\pi$
$461$	12.4996	0.582163	0.291081	+	0.956698i	$0.405985\pi$
$462$	−0.152460	−0.00709307
$463$	1.84423	0.0857085	0.0428543	−	0.999081i	$-0.486355\pi$
$463$	1.84423	0.0857085	0.0428543	+	0.999081i	$0.486355\pi$
$464$	4.78990	0.222365
$465$	−0.317943	−0.0147442
$466$	11.9232	0.552333
$467$	4.85468	0.224648	0.112324	−	0.993672i	$-0.464171\pi$
$467$	4.85468	0.224648	0.112324	+	0.993672i	$0.464171\pi$
$468$	−5.63955	−0.260688
$469$	3.95856	0.182789
$470$	−5.85622	−0.270127
$471$	−3.91905	−0.180580
$472$	15.2645	0.702606
$473$	−9.75665	−0.448611
$474$	5.63139	0.258658
$475$	3.18333	0.146061
$476$	1.50113	0.0688041
$477$	8.24601	0.377559
$478$	−8.50808	−0.389150
$479$	−21.3478	−0.975407	−0.487703	−	0.873009i	$-0.662165\pi$
$479$	−21.3478	−0.975407	−0.487703	+	0.873009i	$0.662165\pi$
$480$	−4.58589	−0.209316
$481$	−11.1955	−0.510471
$482$	−11.9067	−0.542335
$483$	−0.898931	−0.0409028
$484$	−1.44881	−0.0658550
$485$	9.10851	0.413596
$486$	−11.6345	−0.527751
$487$	−24.5936	−1.11444	−0.557220	−	0.830365i	$-0.688132\pi$
$487$	−24.5936	−1.11444	−0.557220	+	0.830365i	$0.688132\pi$
$488$	16.0934	0.728514
$489$	9.26707	0.419072
$490$	5.14581	0.232464
$491$	−15.1991	−0.685927	−0.342963	−	0.939349i	$-0.611431\pi$
$491$	−15.1991	−0.685927	−0.342963	+	0.939349i	$0.611431\pi$
$492$	−12.2921	−0.554169
$493$	−18.9729	−0.854497
$494$	3.85278	0.173345
$495$	−2.38776	−0.107322
$496$	−0.404988	−0.0181845
$497$	−0.0965528	−0.00433099
$498$	4.44954	0.199388
$499$	−21.0788	−0.943617	−0.471809	−	0.881701i	$-0.656399\pi$
$499$	−21.0788	−0.943617	−0.471809	+	0.881701i	$0.656399\pi$
$500$	−1.44881	−0.0647928
$501$	−9.73056	−0.434729
$502$	−7.20529	−0.321588
$503$	2.49171	0.111100	0.0555499	−	0.998456i	$-0.482309\pi$
$503$	2.49171	0.111100	0.0555499	+	0.998456i	$0.482309\pi$
$504$	−1.60456	−0.0714728
$505$	2.57120	0.114417
$506$	3.24991	0.144476
$507$	−8.09250	−0.359400
$508$	−6.29753	−0.279408
$509$	7.72200	0.342271	0.171136	−	0.985247i	$-0.445256\pi$
$509$	7.72200	0.342271	0.171136	+	0.985247i	$0.445256\pi$
$510$	2.29335	0.101551
$511$	0.262449	0.0116101
$512$	−10.9453	−0.483719
$513$	−13.4199	−0.592504
$514$	18.4510	0.813839
$515$	2.19580	0.0967585
$516$	11.0604	0.486908
$517$	7.88801	0.346914
$518$	−1.33813	−0.0587940
$519$	4.60922	0.202322
$520$	−4.17408	−0.183046
$521$	−5.25200	−0.230094	−0.115047	−	0.993360i	$-0.536702\pi$
$521$	−5.25200	−0.230094	−0.115047	+	0.993360i	$0.536702\pi$
$522$	8.51951	0.372889
$523$	−8.35019	−0.365128	−0.182564	−	0.983194i	$-0.558440\pi$
$523$	−8.35019	−0.365128	−0.182564	+	0.983194i	$0.558440\pi$
$524$	−0.0999065	−0.00436443
$525$	0.205355	0.00896242
$526$	−21.1575	−0.922511
$527$	1.60417	0.0698787
$528$	0.779853	0.0339387
$529$	−3.83791	−0.166866
$530$	2.56391	0.111369
$531$	−14.2349	−0.617742
$532$	−1.21043	−0.0524787
$533$	−17.6764	−0.765652
$534$	0.184153	0.00796907
$535$	13.3236	0.576030
$536$	38.6200	1.66813
$537$	8.96936	0.387057
$538$	−9.09508	−0.392117
$539$	−6.93112	−0.298544
$540$	6.10773	0.262835
$541$	18.9737	0.815744	0.407872	−	0.913039i	$-0.366271\pi$
$541$	18.9737	0.815744	0.407872	+	0.913039i	$0.366271\pi$
$542$	2.60054	0.111703
$543$	11.5688	0.496464
$544$	23.1379	0.992031
$545$	−2.88532	−0.123594
$546$	0.248540	0.0106365
$547$	−20.6868	−0.884502	−0.442251	−	0.896891i	$-0.645820\pi$
$547$	−20.6868	−0.884502	−0.442251	+	0.896891i	$0.645820\pi$
$548$	−6.02622	−0.257427
$549$	−15.0079	−0.640521
$550$	−0.742421	−0.0316569
$551$	15.2987	0.651747
$552$	−8.77002	−0.373277
$553$	−2.54420	−0.108190
$554$	−24.2395	−1.02984
$555$	5.37356	0.228095
$556$	−7.06576	−0.299655
$557$	−18.7538	−0.794624	−0.397312	−	0.917684i	$-0.630057\pi$
$557$	−18.7538	−0.794624	−0.397312	+	0.917684i	$0.630057\pi$
$558$	−0.720329	−0.0304940
$559$	15.9053	0.672723
$560$	0.261576	0.0110536
$561$	−3.08902	−0.130418
$562$	−13.4357	−0.566749
$563$	40.2870	1.69789	0.848947	−	0.528478i	$-0.177237\pi$
$563$	40.2870	1.69789	0.848947	+	0.528478i	$0.177237\pi$
$564$	−8.94208	−0.376529
$565$	−7.43713	−0.312882
$566$	−9.17528	−0.385666
$567$	1.01429	0.0425961
$568$	−0.941976	−0.0395244
$569$	−12.6667	−0.531015	−0.265507	−	0.964109i	$-0.585539\pi$
$569$	−12.6667	−0.531015	−0.265507	+	0.964109i	$0.585539\pi$
$570$	−1.84923	−0.0774559
$571$	−20.6223	−0.863016	−0.431508	−	0.902109i	$-0.642018\pi$
$571$	−20.6223	−0.863016	−0.431508	+	0.902109i	$0.642018\pi$
$572$	2.36185	0.0987541
$573$	−3.97290	−0.165970
$574$	−2.11275	−0.0881847
$575$	−4.37745	−0.182552
$576$	−5.63011	−0.234588
$577$	−26.8082	−1.11604	−0.558020	−	0.829828i	$-0.688439\pi$
$577$	−26.8082	−1.11604	−0.558020	+	0.829828i	$0.688439\pi$
$578$	1.05013	0.0436796
$579$	15.4736	0.643061
$580$	−6.96281	−0.289115
$581$	−2.01025	−0.0833992
$582$	−5.29124	−0.219329
$583$	−3.45344	−0.143027
$584$	2.56047	0.105953
$585$	3.89254	0.160937
$586$	−11.2789	−0.465929
$587$	12.7941	0.528068	0.264034	−	0.964513i	$-0.414947\pi$
$587$	12.7941	0.528068	0.264034	+	0.964513i	$0.414947\pi$
$588$	7.85732	0.324031
$589$	−1.29351	−0.0532983
$590$	−4.42602	−0.182216
$591$	−1.43348	−0.0589653
$592$	6.84472	0.281316
$593$	22.1445	0.909367	0.454684	−	0.890653i	$-0.349752\pi$
$593$	22.1445	0.909367	0.454684	+	0.890653i	$0.349752\pi$
$594$	3.12981	0.128418
$595$	−1.03611	−0.0424764
$596$	−8.79040	−0.360069
$597$	11.3676	0.465244
$598$	−5.29802	−0.216652
$599$	7.17355	0.293103	0.146552	−	0.989203i	$-0.453183\pi$
$599$	7.17355	0.293103	0.146552	+	0.989203i	$0.453183\pi$
$600$	2.00345	0.0817907
$601$	37.7082	1.53815	0.769075	−	0.639158i	$-0.220717\pi$
$601$	37.7082	1.53815	0.769075	+	0.639158i	$0.220717\pi$
$602$	1.90106	0.0774815
$603$	−36.0150	−1.46665
$604$	−15.1720	−0.617341
$605$	1.00000	0.0406558
$606$	−1.49364	−0.0606750
$607$	−6.75720	−0.274266	−0.137133	−	0.990553i	$-0.543789\pi$
$607$	−6.75720	−0.274266	−0.137133	+	0.990553i	$0.543789\pi$
$608$	−18.6572	−0.756648
$609$	0.986911	0.0399916
$610$	−4.66636	−0.188935
$611$	−12.8590	−0.520221
$612$	−13.6573	−0.552062
$613$	31.3503	1.26623	0.633114	−	0.774059i	$-0.281777\pi$
$613$	31.3503	1.26623	0.633114	+	0.774059i	$0.281777\pi$
$614$	−8.89092	−0.358808
$615$	8.48424	0.342118
$616$	0.671993	0.0270754
$617$	−4.15148	−0.167132	−0.0835662	−	0.996502i	$-0.526631\pi$
$617$	−4.15148	−0.167132	−0.0835662	+	0.996502i	$0.526631\pi$
$618$	−1.27557	−0.0513108
$619$	−6.53303	−0.262585	−0.131292	−	0.991344i	$-0.541913\pi$
$619$	−6.53303	−0.262585	−0.131292	+	0.991344i	$0.541913\pi$
$620$	0.588709	0.0236431
$621$	18.4540	0.740532
$622$	−17.5302	−0.702895
$623$	−0.0831981	−0.00333326
$624$	−1.27132	−0.0508935
$625$	1.00000	0.0400000
$626$	16.5155	0.660090
$627$	2.49082	0.0994736
$628$	7.25660	0.289570
$629$	−27.1121	−1.08103
$630$	0.465251	0.0185360
$631$	35.0672	1.39600	0.698002	−	0.716095i	$-0.254072\pi$
$631$	35.0672	1.39600	0.698002	+	0.716095i	$0.254072\pi$
$632$	−24.8214	−0.987341
$633$	−3.97075	−0.157823
$634$	10.2149	0.405685
$635$	4.34669	0.172493
$636$	3.91493	0.155237
$637$	11.2991	0.447688
$638$	−3.56799	−0.141258
$639$	0.878438	0.0347505
$640$	9.97123	0.394147
$641$	11.4969	0.454099	0.227049	−	0.973883i	$-0.427092\pi$
$641$	11.4969	0.454099	0.227049	+	0.973883i	$0.427092\pi$
$642$	−7.73984	−0.305467
$643$	−47.7381	−1.88261	−0.941304	−	0.337561i	$-0.890398\pi$
$643$	−47.7381	−1.88261	−0.941304	+	0.337561i	$0.890398\pi$
$644$	1.66448	0.0655897
$645$	−7.63414	−0.300594
$646$	9.33025	0.367094
$647$	10.8148	0.425174	0.212587	−	0.977142i	$-0.431811\pi$
$647$	10.8148	0.425174	0.212587	+	0.977142i	$0.431811\pi$
$648$	9.89546	0.388731
$649$	5.96161	0.234013
$650$	1.21030	0.0474717
$651$	−0.0834438	−0.00327042
$652$	−17.1591	−0.672003
$653$	32.3593	1.26632	0.633158	−	0.774022i	$-0.281758\pi$
$653$	32.3593	1.26632	0.633158	+	0.774022i	$0.281758\pi$
$654$	1.67612	0.0655413
$655$	0.0689576	0.00269440
$656$	10.8070	0.421944
$657$	−2.38776	−0.0931555
$658$	−1.53696	−0.0599170
$659$	2.31484	0.0901734	0.0450867	−	0.998983i	$-0.485644\pi$
$659$	2.31484	0.0901734	0.0450867	+	0.998983i	$0.485644\pi$
$660$	−1.13363	−0.0441265
$661$	−27.3510	−1.06383	−0.531915	−	0.846798i	$-0.678527\pi$
$661$	−27.3510	−1.06383	−0.531915	+	0.846798i	$0.678527\pi$
$662$	−17.3126	−0.672871
$663$	5.03572	0.195571
$664$	−19.6121	−0.761098
$665$	0.835463	0.0323979
$666$	12.1743	0.471745
$667$	−21.0375	−0.814576
$668$	18.0173	0.697111
$669$	4.76696	0.184301
$670$	−11.1981	−0.432619
$671$	6.28533	0.242642
$672$	−1.20356	−0.0464284
$673$	3.27968	0.126423	0.0632113	−	0.998000i	$-0.479866\pi$
$673$	3.27968	0.126423	0.0632113	+	0.998000i	$0.479866\pi$
$674$	−11.8716	−0.457277
$675$	−4.21568	−0.162262
$676$	14.9842	0.576317
$677$	−7.22766	−0.277781	−0.138891	−	0.990308i	$-0.544354\pi$
$677$	−7.22766	−0.277781	−0.138891	+	0.990308i	$0.544354\pi$
$678$	4.32031	0.165921
$679$	2.39052	0.0917397
$680$	−10.1084	−0.387638
$681$	−14.1852	−0.543579
$682$	0.301675	0.0115517
$683$	−15.8438	−0.606245	−0.303122	−	0.952952i	$-0.598029\pi$
$683$	−15.8438	−0.606245	−0.303122	+	0.952952i	$0.598029\pi$
$684$	11.0125	0.421073
$685$	4.15943	0.158923
$686$	2.71445	0.103638
$687$	−11.1447	−0.425196
$688$	−9.72420	−0.370732
$689$	5.62981	0.214479
$690$	2.54291	0.0968070
$691$	−18.6355	−0.708928	−0.354464	−	0.935070i	$-0.615337\pi$
$691$	−18.6355	−0.708928	−0.354464	+	0.935070i	$0.615337\pi$
$692$	−8.53452	−0.324434
$693$	−0.626667	−0.0238051
$694$	−8.38242	−0.318192
$695$	4.87694	0.184993
$696$	9.62836	0.364962
$697$	−42.8070	−1.62143
$698$	−7.11750	−0.269401
$699$	−12.5662	−0.475296
$700$	−0.380239	−0.0143717
$701$	28.0362	1.05891	0.529456	−	0.848337i	$-0.322396\pi$
$701$	28.0362	1.05891	0.529456	+	0.848337i	$0.322396\pi$
$702$	−5.10223	−0.192571
$703$	21.8617	0.824531
$704$	2.35790	0.0888668
$705$	6.17201	0.232451
$706$	5.49041	0.206634
$707$	0.674810	0.0253788
$708$	−6.75825	−0.253991
$709$	11.7009	0.439436	0.219718	−	0.975563i	$-0.429486\pi$
$709$	11.7009	0.439436	0.219718	+	0.975563i	$0.429486\pi$
$710$	0.273131	0.0102504
$711$	23.1471	0.868085
$712$	−0.811686	−0.0304192
$713$	1.77873	0.0666141
$714$	0.601888	0.0225251
$715$	−1.63020	−0.0609661
$716$	−16.6079	−0.620665
$717$	8.96687	0.334874
$718$	−8.42804	−0.314532
$719$	1.97747	0.0737473	0.0368736	−	0.999320i	$-0.488260\pi$
$719$	1.97747	0.0737473	0.0368736	+	0.999320i	$0.488260\pi$
$720$	−2.37982	−0.0886907
$721$	0.576286	0.0214620
$722$	6.58260	0.244979
$723$	12.5487	0.466693
$724$	−21.4210	−0.796105
$725$	4.80588	0.178486
$726$	−0.580911	−0.0215596
$727$	−20.3130	−0.753369	−0.376684	−	0.926342i	$-0.622936\pi$
$727$	−20.3130	−0.753369	−0.376684	+	0.926342i	$0.622936\pi$
$728$	−1.09548	−0.0406014
$729$	0.667751	0.0247315
$730$	−0.742421	−0.0274782
$731$	38.5178	1.42463
$732$	−7.12523	−0.263356
$733$	−31.2218	−1.15320	−0.576601	−	0.817026i	$-0.695621\pi$
$733$	−31.2218	−1.15320	−0.576601	+	0.817026i	$0.695621\pi$
$734$	3.96406	0.146316
$735$	−5.42329	−0.200041
$736$	25.6558	0.945685
$737$	15.0832	0.555596
$738$	19.2218	0.707566
$739$	−10.5084	−0.386557	−0.193278	−	0.981144i	$-0.561912\pi$
$739$	−10.5084	−0.386557	−0.193278	+	0.981144i	$0.561912\pi$
$740$	−9.94979	−0.365762
$741$	−4.06053	−0.149167
$742$	0.672896	0.0247028
$743$	−30.7966	−1.12982	−0.564910	−	0.825153i	$-0.691089\pi$
$743$	−30.7966	−1.12982	−0.564910	+	0.825153i	$0.691089\pi$
$744$	−0.814083	−0.0298457
$745$	6.06732	0.222290
$746$	5.75113	0.210564
$747$	18.2893	0.669169
$748$	5.71969	0.209133
$749$	3.49677	0.127769
$750$	−0.580911	−0.0212119
$751$	−32.9457	−1.20220	−0.601102	−	0.799172i	$-0.705272\pi$
$751$	−32.9457	−1.20220	−0.601102	+	0.799172i	$0.705272\pi$
$752$	7.86177	0.286689
$753$	7.59383	0.276734
$754$	5.81654	0.211826
$755$	10.4720	0.381117
$756$	1.60297	0.0582994
$757$	8.72273	0.317033	0.158517	−	0.987356i	$-0.449329\pi$
$757$	8.72273	0.317033	0.158517	+	0.987356i	$0.449329\pi$
$758$	−13.6122	−0.494418
$759$	−3.42516	−0.124325
$760$	8.15083	0.295662
$761$	1.00156	0.0363065	0.0181533	−	0.999835i	$-0.494221\pi$
$761$	1.00156	0.0363065	0.0181533	+	0.999835i	$0.494221\pi$
$762$	−2.52504	−0.0914725
$763$	−0.757250	−0.0274143
$764$	7.35631	0.266142
$765$	9.42654	0.340817
$766$	15.4390	0.557834
$767$	−9.71862	−0.350919
$768$	−9.48231	−0.342163
$769$	−5.68964	−0.205174	−0.102587	−	0.994724i	$-0.532712\pi$
$769$	−5.68964	−0.205174	−0.102587	+	0.994724i	$0.532712\pi$
$770$	−0.194848	−0.00702183
$771$	−19.4460	−0.700329
$772$	−28.6512	−1.03118
$773$	38.9512	1.40098	0.700489	−	0.713663i	$-0.252965\pi$
$773$	38.9512	1.40098	0.700489	+	0.713663i	$0.252965\pi$
$774$	−17.2959	−0.621687
$775$	−0.406340	−0.0145962
$776$	23.3221	0.837213
$777$	1.41029	0.0505937
$778$	−13.4874	−0.483548
$779$	34.5172	1.23671
$780$	1.84805	0.0661707
$781$	−0.367892	−0.0131642
$782$	−12.8302	−0.458806
$783$	−20.2601	−0.724036
$784$	−6.90807	−0.246717
$785$	−5.00866	−0.178767
$786$	−0.0400582	−0.00142883
$787$	1.56057	0.0556283	0.0278142	−	0.999613i	$-0.491145\pi$
$787$	1.56057	0.0556283	0.0278142	+	0.999613i	$0.491145\pi$
$788$	2.65425	0.0945539
$789$	22.2984	0.793844
$790$	7.19708	0.256060
$791$	−1.95187	−0.0694004
$792$	−6.11380	−0.217244
$793$	−10.2464	−0.363859
$794$	−16.0424	−0.569324
$795$	−2.70217	−0.0958360
$796$	−21.0485	−0.746043
$797$	7.67988	0.272035	0.136018	−	0.990706i	$-0.456570\pi$
$797$	7.67988	0.272035	0.136018	+	0.990706i	$0.456570\pi$
$798$	−0.485330	−0.0171805
$799$	−31.1407	−1.10168
$800$	−5.86089	−0.207214
$801$	0.756937	0.0267451
$802$	−2.45306	−0.0866206
$803$	1.00000	0.0352892
$804$	−17.0987	−0.603026
$805$	−1.14886	−0.0404919
$806$	−0.491792	−0.0173226
$807$	9.58552	0.337426
$808$	6.58348	0.231606
$809$	−2.30974	−0.0812060	−0.0406030	−	0.999175i	$-0.512928\pi$
$809$	−2.30974	−0.0812060	−0.0406030	+	0.999175i	$0.512928\pi$
$810$	−2.86924	−0.100815
$811$	26.1957	0.919856	0.459928	−	0.887956i	$-0.347875\pi$
$811$	26.1957	0.919856	0.459928	+	0.887956i	$0.347875\pi$
$812$	−1.82738	−0.0641286
$813$	−2.74077	−0.0961232
$814$	−5.09862	−0.178707
$815$	11.8436	0.414863
$816$	−3.07874	−0.107778
$817$	−31.0587	−1.08660
$818$	17.0744	0.596993
$819$	1.02159	0.0356974
$820$	−15.7096	−0.548603
$821$	23.4241	0.817505	0.408753	−	0.912645i	$-0.365964\pi$
$821$	23.4241	0.817505	0.408753	+	0.912645i	$0.365964\pi$
$822$	−2.41626	−0.0842767
$823$	−27.4849	−0.958063	−0.479032	−	0.877798i	$-0.659012\pi$
$823$	−27.4849	−0.958063	−0.479032	+	0.877798i	$0.659012\pi$
$824$	5.62228	0.195861
$825$	0.782455	0.0272416
$826$	−1.16161	−0.0404174
$827$	43.5697	1.51507	0.757534	−	0.652795i	$-0.226404\pi$
$827$	43.5697	1.51507	0.757534	+	0.652795i	$0.226404\pi$
$828$	−15.1434	−0.526271
$829$	−51.9306	−1.80362	−0.901811	−	0.432130i	$-0.857762\pi$
$829$	−51.9306	−1.80362	−0.901811	+	0.432130i	$0.857762\pi$
$830$	5.68663	0.197386
$831$	25.5465	0.886200
$832$	−3.84386	−0.133262
$833$	27.3630	0.948073
$834$	−2.83307	−0.0981011
$835$	−12.4359	−0.430363
$836$	−4.61205	−0.159511
$837$	1.71300	0.0592099
$838$	−12.1399	−0.419364
$839$	−10.9087	−0.376609	−0.188305	−	0.982111i	$-0.560299\pi$
$839$	−10.9087	−0.376609	−0.188305	+	0.982111i	$0.560299\pi$
$840$	0.525805	0.0181420
$841$	−5.90350	−0.203569
$842$	16.7456	0.577093
$843$	14.1602	0.487702
$844$	7.35232	0.253077
$845$	−10.3424	−0.355791
$846$	13.9833	0.480755
$847$	0.262449	0.00901786
$848$	−3.44196	−0.118197
$849$	9.67005	0.331875
$850$	2.93097	0.100531
$851$	−30.0624	−1.03053
$852$	0.417053	0.0142880
$853$	−8.21416	−0.281247	−0.140624	−	0.990063i	$-0.544911\pi$
$853$	−8.21416	−0.281247	−0.140624	+	0.990063i	$0.544911\pi$
$854$	−1.22468	−0.0419078
$855$	−7.60105	−0.259950
$856$	34.1147	1.16602
$857$	10.7298	0.366524	0.183262	−	0.983064i	$-0.441334\pi$
$857$	10.7298	0.366524	0.183262	+	0.983064i	$0.441334\pi$
$858$	0.947003	0.0323302
$859$	17.3576	0.592233	0.296116	−	0.955152i	$-0.404308\pi$
$859$	17.3576	0.592233	0.296116	+	0.955152i	$0.404308\pi$
$860$	14.1355	0.482018
$861$	2.22668	0.0758851
$862$	10.3367	0.352071
$863$	−2.48905	−0.0847282	−0.0423641	−	0.999102i	$-0.513489\pi$
$863$	−2.48905	−0.0847282	−0.0423641	+	0.999102i	$0.513489\pi$
$864$	24.7077	0.840572
$865$	5.89071	0.200290
$866$	9.90984	0.336750
$867$	−1.10676	−0.0375874
$868$	0.154506	0.00524428
$869$	−9.69406	−0.328849
$870$	−2.79179	−0.0946506
$871$	−24.5886	−0.833153
$872$	−7.38778	−0.250182
$873$	−21.7490	−0.736091
$874$	10.3456	0.349944
$875$	0.262449	0.00887240
$876$	−1.13363	−0.0383018
$877$	−39.3816	−1.32982	−0.664911	−	0.746923i	$-0.731530\pi$
$877$	−39.3816	−1.32982	−0.664911	+	0.746923i	$0.731530\pi$
$878$	−4.62140	−0.155965
$879$	11.8871	0.400943
$880$	0.996674	0.0335979
$881$	40.7335	1.37235	0.686173	−	0.727438i	$-0.259289\pi$
$881$	40.7335	1.37235	0.686173	+	0.727438i	$0.259289\pi$
$882$	−12.2870	−0.413724
$883$	−9.37698	−0.315561	−0.157780	−	0.987474i	$-0.550434\pi$
$883$	−9.37698	−0.315561	−0.157780	+	0.987474i	$0.550434\pi$
$884$	−9.32425	−0.313609
$885$	4.66469	0.156802
$886$	4.71007	0.158238
$887$	−40.2547	−1.35162	−0.675810	−	0.737076i	$-0.736206\pi$
$887$	−40.2547	−1.35162	−0.675810	+	0.737076i	$0.736206\pi$
$888$	13.7588	0.461716
$889$	1.14078	0.0382607
$890$	0.235352	0.00788903
$891$	3.86471	0.129473
$892$	−8.82661	−0.295537
$893$	25.1101	0.840279
$894$	−3.52458	−0.117880
$895$	11.4631	0.383169
$896$	2.61694	0.0874258
$897$	5.58371	0.186435
$898$	−21.6960	−0.724006
$899$	−1.95282	−0.0651302
$900$	3.45942	0.115314
$901$	13.6337	0.454204
$902$	−8.05015	−0.268041
$903$	−2.00357	−0.0666748
$904$	−19.0425	−0.633345
$905$	14.7852	0.491478
$906$	−6.08333	−0.202105
$907$	−3.40449	−0.113044	−0.0565222	−	0.998401i	$-0.518001\pi$
$907$	−3.40449	−0.113044	−0.0565222	+	0.998401i	$0.518001\pi$
$908$	26.2656	0.871656
$909$	−6.13942	−0.203632
$910$	0.317641	0.0105297
$911$	−44.2734	−1.46684	−0.733422	−	0.679774i	$-0.762078\pi$
$911$	−44.2734	−1.46684	−0.733422	+	0.679774i	$0.762078\pi$
$912$	2.48253	0.0822048
$913$	−7.65958	−0.253495
$914$	7.05956	0.233509
$915$	4.91799	0.162584
$916$	20.6357	0.681824
$917$	0.0180979	0.000597644 0
$918$	−12.3560	−0.407810
$919$	−40.5443	−1.33743	−0.668716	−	0.743518i	$-0.733156\pi$
$919$	−40.5443	−1.33743	−0.668716	+	0.743518i	$0.733156\pi$
$920$	−11.2083	−0.369528
$921$	9.37036	0.308764
$922$	−9.27994	−0.305619
$923$	0.599738	0.0197406
$924$	−0.297520	−0.00978769
$925$	6.86756	0.225804
$926$	−1.36919	−0.0449945
$927$	−5.24305	−0.172204
$928$	−28.1668	−0.924619
$929$	3.21196	0.105381	0.0526904	−	0.998611i	$-0.483220\pi$
$929$	3.21196	0.105381	0.0526904	+	0.998611i	$0.483220\pi$
$930$	0.236047	0.00774030
$931$	−22.0641	−0.723120
$932$	23.2678	0.762161
$933$	18.4755	0.604859
$934$	−3.60422	−0.117934
$935$	−3.94785	−0.129109
$936$	9.96673	0.325773
$937$	4.41039	0.144081	0.0720406	−	0.997402i	$-0.477049\pi$
$937$	4.41039	0.144081	0.0720406	+	0.997402i	$0.477049\pi$
$938$	−2.93892	−0.0959592
$939$	−17.4060	−0.568024
$940$	−11.4282	−0.372748
$941$	−35.1747	−1.14666	−0.573331	−	0.819324i	$-0.694349\pi$
$941$	−35.1747	−1.14666	−0.573331	+	0.819324i	$0.694349\pi$
$942$	2.90959	0.0947995
$943$	−47.4652	−1.54568
$944$	5.94178	0.193388
$945$	−1.10640	−0.0359913
$946$	7.24354	0.235508
$947$	−33.4352	−1.08650	−0.543249	−	0.839572i	$-0.682806\pi$
$947$	−33.4352	−1.08650	−0.543249	+	0.839572i	$0.682806\pi$
$948$	10.9895	0.356922
$949$	−1.63020	−0.0529186
$950$	−2.36337	−0.0766780
$951$	−10.7657	−0.349102
$952$	−2.65293	−0.0859819
$953$	−44.4917	−1.44123	−0.720613	−	0.693337i	$-0.756140\pi$
$953$	−44.4917	−1.44123	−0.720613	+	0.693337i	$0.756140\pi$
$954$	−6.12201	−0.198207
$955$	−5.07748	−0.164303
$956$	−16.6032	−0.536987
$957$	3.76039	0.121556
$958$	15.8491	0.512060
$959$	1.09164	0.0352508
$960$	1.84495	0.0595456
$961$	−30.8349	−0.994674
$962$	8.31179	0.267983
$963$	−31.8136	−1.02518
$964$	−23.2355	−0.748366
$965$	19.7757	0.636602
$966$	0.667385	0.0214728
$967$	−21.9377	−0.705469	−0.352735	−	0.935723i	$-0.614748\pi$
$967$	−21.9377	−0.705469	−0.352735	+	0.935723i	$0.614748\pi$
$968$	2.56047	0.0822966
$969$	−9.83337	−0.315893
$970$	−6.76235	−0.217126
$971$	−10.5663	−0.339089	−0.169544	−	0.985523i	$-0.554230\pi$
$971$	−10.5663	−0.339089	−0.169544	+	0.985523i	$0.554230\pi$
$972$	−22.7043	−0.728242
$973$	1.27995	0.0410332
$974$	18.2588	0.585049
$975$	−1.27556	−0.0408506
$976$	6.26442	0.200519
$977$	14.8859	0.476242	0.238121	−	0.971235i	$-0.423469\pi$
$977$	14.8859	0.476242	0.238121	+	0.971235i	$0.423469\pi$
$978$	−6.88007	−0.220000
$979$	−0.317007	−0.0101316
$980$	10.0419	0.320776
$981$	6.88946	0.219964
$982$	11.2842	0.360092
$983$	−36.1008	−1.15144	−0.575719	−	0.817648i	$-0.695278\pi$
$983$	−36.1008	−1.15144	−0.575719	+	0.817648i	$0.695278\pi$
$984$	21.7236	0.692525
$985$	−1.83202	−0.0583731
$986$	14.0859	0.448586
$987$	1.61984	0.0515601
$988$	7.51857	0.239198
$989$	42.7093	1.35808
$990$	1.77273	0.0563409
$991$	−60.5793	−1.92436	−0.962182	−	0.272406i	$-0.912181\pi$
$991$	−60.5793	−1.92436	−0.962182	+	0.272406i	$0.912181\pi$
$992$	2.38151	0.0756131
$993$	18.2461	0.579023
$994$	0.0716829	0.00227364
$995$	14.5281	0.460572
$996$	8.68312	0.275135
$997$	−0.797706	−0.0252636	−0.0126318	−	0.999920i	$-0.504021\pi$
$997$	−0.797706	−0.0252636	−0.0126318	+	0.999920i	$0.504021\pi$
$998$	15.6494	0.495372
$999$	−28.9515	−0.915984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.14	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.14	✓	37	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)

\(f(q)\)	\(=\)	\(q-0.742421 q^{2} +0.782455 q^{3} -1.44881 q^{4} +1.00000 q^{5} -0.580911 q^{6} +0.262449 q^{7} +2.56047 q^{8} -2.38776 q^{9} +O(q^{10})\)	\(q-0.742421 q^{2} +0.782455 q^{3} -1.44881 q^{4} +1.00000 q^{5} -0.580911 q^{6} +0.262449 q^{7} +2.56047 q^{8} -2.38776 q^{9} -0.742421 q^{10} +1.00000 q^{11} -1.13363 q^{12} -1.63020 q^{13} -0.194848 q^{14} +0.782455 q^{15} +0.996674 q^{16} -3.94785 q^{17} +1.77273 q^{18} +3.18333 q^{19} -1.44881 q^{20} +0.205355 q^{21} -0.742421 q^{22} -4.37745 q^{23} +2.00345 q^{24} +1.00000 q^{25} +1.21030 q^{26} -4.21568 q^{27} -0.380239 q^{28} +4.80588 q^{29} -0.580911 q^{30} -0.406340 q^{31} -5.86089 q^{32} +0.782455 q^{33} +2.93097 q^{34} +0.262449 q^{35} +3.45942 q^{36} +6.86756 q^{37} -2.36337 q^{38} -1.27556 q^{39} +2.56047 q^{40} +10.8431 q^{41} -0.152460 q^{42} -9.75665 q^{43} -1.44881 q^{44} -2.38776 q^{45} +3.24991 q^{46} +7.88801 q^{47} +0.779853 q^{48} -6.93112 q^{49} -0.742421 q^{50} -3.08902 q^{51} +2.36185 q^{52} -3.45344 q^{53} +3.12981 q^{54} +1.00000 q^{55} +0.671993 q^{56} +2.49082 q^{57} -3.56799 q^{58} +5.96161 q^{59} -1.13363 q^{60} +6.28533 q^{61} +0.301675 q^{62} -0.626667 q^{63} +2.35790 q^{64} -1.63020 q^{65} -0.580911 q^{66} +15.0832 q^{67} +5.71969 q^{68} -3.42516 q^{69} -0.194848 q^{70} -0.367892 q^{71} -6.11380 q^{72} +1.00000 q^{73} -5.09862 q^{74} +0.782455 q^{75} -4.61205 q^{76} +0.262449 q^{77} +0.947003 q^{78} -9.69406 q^{79} +0.996674 q^{80} +3.86471 q^{81} -8.05015 q^{82} -7.65958 q^{83} -0.297520 q^{84} -3.94785 q^{85} +7.24354 q^{86} +3.76039 q^{87} +2.56047 q^{88} -0.317007 q^{89} +1.77273 q^{90} -0.427845 q^{91} +6.34210 q^{92} -0.317943 q^{93} -5.85622 q^{94} +3.18333 q^{95} -4.58589 q^{96} +9.10851 q^{97} +5.14581 q^{98} -2.38776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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