LMFDB - Embedded newform 8015.2.a.k.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.736107 q^{2} -1.41103 q^{3} -1.45815 q^{4} -1.00000 q^{5} +1.03867 q^{6} -1.00000 q^{7} +2.54557 q^{8} -1.00899 q^{9} +O(q^{10})$	\(q-0.736107 q^{2} -1.41103 q^{3} -1.45815 q^{4} -1.00000 q^{5} +1.03867 q^{6} -1.00000 q^{7} +2.54557 q^{8} -1.00899 q^{9} +0.736107 q^{10} -5.32231 q^{11} +2.05749 q^{12} -0.724260 q^{13} +0.736107 q^{14} +1.41103 q^{15} +1.04248 q^{16} +3.52671 q^{17} +0.742722 q^{18} +1.06587 q^{19} +1.45815 q^{20} +1.41103 q^{21} +3.91779 q^{22} -0.370007 q^{23} -3.59188 q^{24} +1.00000 q^{25} +0.533133 q^{26} +5.65681 q^{27} +1.45815 q^{28} -2.74792 q^{29} -1.03867 q^{30} -9.99102 q^{31} -5.85851 q^{32} +7.50996 q^{33} -2.59604 q^{34} +1.00000 q^{35} +1.47125 q^{36} -6.61551 q^{37} -0.784591 q^{38} +1.02195 q^{39} -2.54557 q^{40} -3.86132 q^{41} -1.03867 q^{42} +0.547640 q^{43} +7.76071 q^{44} +1.00899 q^{45} +0.272365 q^{46} +5.06503 q^{47} -1.47098 q^{48} +1.00000 q^{49} -0.736107 q^{50} -4.97631 q^{51} +1.05608 q^{52} +0.0183487 q^{53} -4.16402 q^{54} +5.32231 q^{55} -2.54557 q^{56} -1.50397 q^{57} +2.02276 q^{58} +12.2734 q^{59} -2.05749 q^{60} +9.07965 q^{61} +7.35446 q^{62} +1.00899 q^{63} +2.22753 q^{64} +0.724260 q^{65} -5.52814 q^{66} +0.894238 q^{67} -5.14246 q^{68} +0.522092 q^{69} -0.736107 q^{70} -4.15737 q^{71} -2.56844 q^{72} +10.2262 q^{73} +4.86973 q^{74} -1.41103 q^{75} -1.55419 q^{76} +5.32231 q^{77} -0.752268 q^{78} +9.94074 q^{79} -1.04248 q^{80} -4.95499 q^{81} +2.84235 q^{82} -1.79586 q^{83} -2.05749 q^{84} -3.52671 q^{85} -0.403122 q^{86} +3.87740 q^{87} -13.5483 q^{88} -13.9211 q^{89} -0.742722 q^{90} +0.724260 q^{91} +0.539525 q^{92} +14.0977 q^{93} -3.72840 q^{94} -1.06587 q^{95} +8.26655 q^{96} +13.5058 q^{97} -0.736107 q^{98} +5.37014 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) $ 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * 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 $

$2$	−0.736107	−0.520506	−0.260253	−	0.965540i	$-0.583806\pi$
$2$	−0.736107	−0.520506	−0.260253	+	0.965540i	$0.583806\pi$
$3$	−1.41103	−0.814660	−0.407330	−	0.913281i	$-0.633540\pi$
$3$	−1.41103	−0.814660	−0.407330	+	0.913281i	$0.633540\pi$
$4$	−1.45815	−0.729073
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.03867	0.424036
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.54557	0.899994
$9$	−1.00899	−0.336329
$10$	0.736107	0.232778
$11$	−5.32231	−1.60474	−0.802369	−	0.596828i	$-0.796427\pi$
$11$	−5.32231	−1.60474	−0.802369	+	0.596828i	$0.796427\pi$
$12$	2.05749	0.593947
$13$	−0.724260	−0.200873	−0.100437	−	0.994943i	$-0.532024\pi$
$13$	−0.724260	−0.200873	−0.100437	+	0.994943i	$0.532024\pi$
$14$	0.736107	0.196733
$15$	1.41103	0.364327
$16$	1.04248	0.260621
$17$	3.52671	0.855354	0.427677	−	0.903932i	$-0.359332\pi$
$17$	3.52671	0.855354	0.427677	+	0.903932i	$0.359332\pi$
$18$	0.742722	0.175061
$19$	1.06587	0.244526	0.122263	−	0.992498i	$-0.460985\pi$
$19$	1.06587	0.244526	0.122263	+	0.992498i	$0.460985\pi$
$20$	1.45815	0.326051
$21$	1.41103	0.307913
$22$	3.91779	0.835276
$23$	−0.370007	−0.0771518	−0.0385759	−	0.999256i	$-0.512282\pi$
$23$	−0.370007	−0.0771518	−0.0385759	+	0.999256i	$0.512282\pi$
$24$	−3.59188	−0.733189
$25$	1.00000	0.200000
$26$	0.533133	0.104556
$27$	5.65681	1.08865
$28$	1.45815	0.275564
$29$	−2.74792	−0.510275	−0.255138	−	0.966905i	$-0.582121\pi$
$29$	−2.74792	−0.510275	−0.255138	+	0.966905i	$0.582121\pi$
$30$	−1.03867	−0.189635
$31$	−9.99102	−1.79444	−0.897220	−	0.441584i	$-0.854417\pi$
$31$	−9.99102	−1.79444	−0.897220	+	0.441584i	$0.854417\pi$
$32$	−5.85851	−1.03565
$33$	7.50996	1.30732
$34$	−2.59604	−0.445217
$35$	1.00000	0.169031
$36$	1.47125	0.245208
$37$	−6.61551	−1.08758	−0.543792	−	0.839220i	$-0.683012\pi$
$37$	−6.61551	−1.08758	−0.543792	+	0.839220i	$0.683012\pi$
$38$	−0.784591	−0.127277
$39$	1.02195	0.163644
$40$	−2.54557	−0.402489
$41$	−3.86132	−0.603038	−0.301519	−	0.953460i	$-0.597494\pi$
$41$	−3.86132	−0.603038	−0.301519	+	0.953460i	$0.597494\pi$
$42$	−1.03867	−0.160271
$43$	0.547640	0.0835143	0.0417571	−	0.999128i	$-0.486704\pi$
$43$	0.547640	0.0835143	0.0417571	+	0.999128i	$0.486704\pi$
$44$	7.76071	1.16997
$45$	1.00899	0.150411
$46$	0.272365	0.0401580
$47$	5.06503	0.738810	0.369405	−	0.929268i	$-0.379561\pi$
$47$	5.06503	0.738810	0.369405	+	0.929268i	$0.379561\pi$
$48$	−1.47098	−0.212317
$49$	1.00000	0.142857
$50$	−0.736107	−0.104101
$51$	−4.97631	−0.696823
$52$	1.05608	0.146451
$53$	0.0183487	0.00252039	0.00126020	−	0.999999i	$-0.499599\pi$
$53$	0.0183487	0.00252039	0.00126020	+	0.999999i	$0.499599\pi$
$54$	−4.16402	−0.566651
$55$	5.32231	0.717661
$56$	−2.54557	−0.340166
$57$	−1.50397	−0.199206
$58$	2.02276	0.265602
$59$	12.2734	1.59786	0.798932	−	0.601421i	$-0.205399\pi$
$59$	12.2734	1.59786	0.798932	+	0.601421i	$0.205399\pi$
$60$	−2.05749	−0.265621
$61$	9.07965	1.16253	0.581265	−	0.813714i	$-0.302558\pi$
$61$	9.07965	1.16253	0.581265	+	0.813714i	$0.302558\pi$
$62$	7.35446	0.934017
$63$	1.00899	0.127120
$64$	2.22753	0.278441
$65$	0.724260	0.0898334
$66$	−5.52814	−0.680466
$67$	0.894238	0.109249	0.0546243	−	0.998507i	$-0.482604\pi$
$67$	0.894238	0.109249	0.0546243	+	0.998507i	$0.482604\pi$
$68$	−5.14246	−0.623615
$69$	0.522092	0.0628525
$70$	−0.736107	−0.0879816
$71$	−4.15737	−0.493389	−0.246695	−	0.969093i	$-0.579344\pi$
$71$	−4.15737	−0.493389	−0.246695	+	0.969093i	$0.579344\pi$
$72$	−2.56844	−0.302694
$73$	10.2262	1.19689	0.598443	−	0.801166i	$-0.295786\pi$
$73$	10.2262	1.19689	0.598443	+	0.801166i	$0.295786\pi$
$74$	4.86973	0.566094
$75$	−1.41103	−0.162932
$76$	−1.55419	−0.178278
$77$	5.32231	0.606534
$78$	−0.752268	−0.0851776
$79$	9.94074	1.11842	0.559210	−	0.829026i	$-0.311104\pi$
$79$	9.94074	1.11842	0.559210	+	0.829026i	$0.311104\pi$
$80$	−1.04248	−0.116553
$81$	−4.95499	−0.550554
$82$	2.84235	0.313885
$83$	−1.79586	−0.197122	−0.0985608	−	0.995131i	$-0.531424\pi$
$83$	−1.79586	−0.197122	−0.0985608	+	0.995131i	$0.531424\pi$
$84$	−2.05749	−0.224491
$85$	−3.52671	−0.382526
$86$	−0.403122	−0.0434697
$87$	3.87740	0.415701
$88$	−13.5483	−1.44425
$89$	−13.9211	−1.47564	−0.737819	−	0.674998i	$-0.764144\pi$
$89$	−13.9211	−1.47564	−0.737819	+	0.674998i	$0.764144\pi$
$90$	−0.742722	−0.0782898
$91$	0.724260	0.0759230
$92$	0.539525	0.0562493
$93$	14.0977	1.46186
$94$	−3.72840	−0.384556
$95$	−1.06587	−0.109355
$96$	8.26655	0.843702
$97$	13.5058	1.37131	0.685655	−	0.727926i	$-0.259516\pi$
$97$	13.5058	1.37131	0.685655	+	0.727926i	$0.259516\pi$
$98$	−0.736107	−0.0743581
$99$	5.37014	0.539719
$100$	−1.45815	−0.145815
$101$	−0.126289	−0.0125662	−0.00628311	−	0.999980i	$-0.502000\pi$
$101$	−0.126289	−0.0125662	−0.00628311	+	0.999980i	$0.502000\pi$
$102$	3.66310	0.362701
$103$	14.2539	1.40448	0.702239	−	0.711941i	$-0.252184\pi$
$103$	14.2539	1.40448	0.702239	+	0.711941i	$0.252184\pi$
$104$	−1.84365	−0.180785
$105$	−1.41103	−0.137703
$106$	−0.0135066	−0.00131188
$107$	10.2980	0.995549	0.497774	−	0.867306i	$-0.334151\pi$
$107$	10.2980	0.995549	0.497774	+	0.867306i	$0.334151\pi$
$108$	−8.24846	−0.793708
$109$	−18.4722	−1.76932	−0.884659	−	0.466238i	$-0.845609\pi$
$109$	−18.4722	−1.76932	−0.884659	+	0.466238i	$0.845609\pi$
$110$	−3.91779	−0.373547
$111$	9.33471	0.886011
$112$	−1.04248	−0.0985053
$113$	10.7590	1.01212	0.506060	−	0.862498i	$-0.331101\pi$
$113$	10.7590	1.01212	0.506060	+	0.862498i	$0.331101\pi$
$114$	1.10708	0.103688
$115$	0.370007	0.0345033
$116$	4.00686	0.372028
$117$	0.730768	0.0675595
$118$	−9.03456	−0.831699
$119$	−3.52671	−0.323293
$120$	3.59188	0.327892
$121$	17.3270	1.57518
$122$	−6.68360	−0.605104
$123$	5.44846	0.491271
$124$	14.5684	1.30828
$125$	−1.00000	−0.0894427
$126$	−0.742722	−0.0661669
$127$	−2.56070	−0.227226	−0.113613	−	0.993525i	$-0.536242\pi$
$127$	−2.56070	−0.227226	−0.113613	+	0.993525i	$0.536242\pi$
$128$	10.0773	0.890718
$129$	−0.772738	−0.0680358
$130$	−0.533133	−0.0467588
$131$	22.6845	1.98195	0.990976	−	0.134040i	$-0.0427949\pi$
$131$	22.6845	1.98195	0.990976	+	0.134040i	$0.0427949\pi$
$132$	−10.9506	−0.953129
$133$	−1.06587	−0.0924222
$134$	−0.658255	−0.0568646
$135$	−5.65681	−0.486861
$136$	8.97748	0.769813
$137$	6.44405	0.550553	0.275276	−	0.961365i	$-0.411231\pi$
$137$	6.44405	0.550553	0.275276	+	0.961365i	$0.411231\pi$
$138$	−0.384316	−0.0327151
$139$	−7.28199	−0.617650	−0.308825	−	0.951119i	$-0.599936\pi$
$139$	−7.28199	−0.617650	−0.308825	+	0.951119i	$0.599936\pi$
$140$	−1.45815	−0.123236
$141$	−7.14692	−0.601879
$142$	3.06027	0.256812
$143$	3.85474	0.322349
$144$	−1.05185	−0.0876542
$145$	2.74792	0.228202
$146$	−7.52757	−0.622986
$147$	−1.41103	−0.116380
$148$	9.64638	0.792928
$149$	0.532837	0.0436517	0.0218259	−	0.999762i	$-0.493052\pi$
$149$	0.532837	0.0436517	0.0218259	+	0.999762i	$0.493052\pi$
$150$	1.03867	0.0848072
$151$	−0.750479	−0.0610732	−0.0305366	−	0.999534i	$-0.509722\pi$
$151$	−0.750479	−0.0610732	−0.0305366	+	0.999534i	$0.509722\pi$
$152$	2.71323	0.220072
$153$	−3.55840	−0.287680
$154$	−3.91779	−0.315705
$155$	9.99102	0.802498
$156$	−1.49016	−0.119308
$157$	2.29329	0.183025	0.0915123	−	0.995804i	$-0.470830\pi$
$157$	2.29329	0.183025	0.0915123	+	0.995804i	$0.470830\pi$
$158$	−7.31745	−0.582145
$159$	−0.0258907	−0.00205327
$160$	5.85851	0.463156
$161$	0.370007	0.0291607
$162$	3.64740	0.286567
$163$	1.74799	0.136913	0.0684567	−	0.997654i	$-0.478193\pi$
$163$	1.74799	0.136913	0.0684567	+	0.997654i	$0.478193\pi$
$164$	5.63038	0.439658
$165$	−7.50996	−0.584650
$166$	1.32195	0.102603
$167$	−19.1282	−1.48019	−0.740093	−	0.672505i	$-0.765218\pi$
$167$	−19.1282	−1.48019	−0.740093	+	0.672505i	$0.765218\pi$
$168$	3.59188	0.277119
$169$	−12.4754	−0.959650
$170$	2.59604	0.199107
$171$	−1.07544	−0.0822412
$172$	−0.798539	−0.0608880
$173$	20.2714	1.54121	0.770603	−	0.637316i	$-0.219955\pi$
$173$	20.2714	1.54121	0.770603	+	0.637316i	$0.219955\pi$
$174$	−2.85418	−0.216375
$175$	−1.00000	−0.0755929
$176$	−5.54842	−0.418228
$177$	−17.3182	−1.30172
$178$	10.2475	0.768079
$179$	−17.9588	−1.34230	−0.671152	−	0.741320i	$-0.734200\pi$
$179$	−17.9588	−1.34230	−0.671152	+	0.741320i	$0.734200\pi$
$180$	−1.47125	−0.109660
$181$	5.06777	0.376684	0.188342	−	0.982103i	$-0.439689\pi$
$181$	5.06777	0.376684	0.188342	+	0.982103i	$0.439689\pi$
$182$	−0.533133	−0.0395184
$183$	−12.8117	−0.947067
$184$	−0.941878	−0.0694362
$185$	6.61551	0.486382
$186$	−10.3774	−0.760907
$187$	−18.7703	−1.37262
$188$	−7.38555	−0.538647
$189$	−5.65681	−0.411472
$190$	0.784591	0.0569202
$191$	0.0602601	0.00436027	0.00218013	−	0.999998i	$-0.499306\pi$
$191$	0.0602601	0.00436027	0.00218013	+	0.999998i	$0.499306\pi$
$192$	−3.14312	−0.226835
$193$	−12.5382	−0.902521	−0.451260	−	0.892392i	$-0.649025\pi$
$193$	−12.5382	−0.902521	−0.451260	+	0.892392i	$0.649025\pi$
$194$	−9.94175	−0.713776
$195$	−1.02195	−0.0731837
$196$	−1.45815	−0.104153
$197$	15.0345	1.07116	0.535582	−	0.844483i	$-0.320092\pi$
$197$	15.0345	1.07116	0.535582	+	0.844483i	$0.320092\pi$
$198$	−3.95300	−0.280927
$199$	−9.52226	−0.675015	−0.337507	−	0.941323i	$-0.609584\pi$
$199$	−9.52226	−0.675015	−0.337507	+	0.941323i	$0.609584\pi$
$200$	2.54557	0.179999
$201$	−1.26180	−0.0890005
$202$	0.0929622	0.00654080
$203$	2.74792	0.192866
$204$	7.25619	0.508035
$205$	3.86132	0.269687
$206$	−10.4924	−0.731040
$207$	0.373332	0.0259484
$208$	−0.755028	−0.0523518
$209$	−5.67287	−0.392401
$210$	1.03867	0.0716752
$211$	8.01795	0.551979	0.275989	−	0.961161i	$-0.410995\pi$
$211$	8.01795	0.551979	0.275989	+	0.961161i	$0.410995\pi$
$212$	−0.0267552	−0.00183755
$213$	5.86619	0.401945
$214$	−7.58046	−0.518190
$215$	−0.547640	−0.0373487
$216$	14.3998	0.979782
$217$	9.99102	0.678234
$218$	13.5975	0.920942
$219$	−14.4295	−0.975055
$220$	−7.76071	−0.523227
$221$	−2.55426	−0.171818
$222$	−6.87135	−0.461175
$223$	−0.114911	−0.00769499	−0.00384749	−	0.999993i	$-0.501225\pi$
$223$	−0.114911	−0.00769499	−0.00384749	+	0.999993i	$0.501225\pi$
$224$	5.85851	0.391438
$225$	−1.00899	−0.0672657
$226$	−7.91977	−0.526815
$227$	−25.2982	−1.67910	−0.839549	−	0.543284i	$-0.817181\pi$
$227$	−25.2982	−1.67910	−0.839549	+	0.543284i	$0.817181\pi$
$228$	2.19301	0.145236
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−0.272365	−0.0179592
$231$	−7.50996	−0.494119
$232$	−6.99501	−0.459245
$233$	−6.31296	−0.413576	−0.206788	−	0.978386i	$-0.566301\pi$
$233$	−6.31296	−0.413576	−0.206788	+	0.978386i	$0.566301\pi$
$234$	−0.537923	−0.0351652
$235$	−5.06503	−0.330406
$236$	−17.8964	−1.16496
$237$	−14.0267	−0.911133
$238$	2.59604	0.168276
$239$	29.0274	1.87763	0.938814	−	0.344425i	$-0.111926\pi$
$239$	29.0274	1.87763	0.938814	+	0.344425i	$0.111926\pi$
$240$	1.47098	0.0949511
$241$	1.25117	0.0805948	0.0402974	−	0.999188i	$-0.487169\pi$
$241$	1.25117	0.0805948	0.0402974	+	0.999188i	$0.487169\pi$
$242$	−12.7545	−0.819893
$243$	−9.97878	−0.640139
$244$	−13.2395	−0.847569
$245$	−1.00000	−0.0638877
$246$	−4.01065	−0.255710
$247$	−0.771963	−0.0491188
$248$	−25.4328	−1.61498
$249$	2.53402	0.160587
$250$	0.736107	0.0465555
$251$	30.5592	1.92888	0.964439	−	0.264306i	$-0.0851429\pi$
$251$	30.5592	1.92888	0.964439	+	0.264306i	$0.0851429\pi$
$252$	−1.47125	−0.0926800
$253$	1.96929	0.123808
$254$	1.88495	0.118272
$255$	4.97631	0.311629
$256$	−11.8730	−0.742066
$257$	−12.9899	−0.810291	−0.405145	−	0.914252i	$-0.632779\pi$
$257$	−12.9899	−0.810291	−0.405145	+	0.914252i	$0.632779\pi$
$258$	0.568818	0.0354131
$259$	6.61551	0.411068
$260$	−1.05608	−0.0654951
$261$	2.77261	0.171620
$262$	−16.6982	−1.03162
$263$	−10.5963	−0.653395	−0.326697	−	0.945129i	$-0.605936\pi$
$263$	−10.5963	−0.653395	−0.326697	+	0.945129i	$0.605936\pi$
$264$	19.1171	1.17658
$265$	−0.0183487	−0.00112715
$266$	0.784591	0.0481064
$267$	19.6432	1.20214
$268$	−1.30393	−0.0796502
$269$	−1.82528	−0.111289	−0.0556445	−	0.998451i	$-0.517721\pi$
$269$	−1.82528	−0.111289	−0.0556445	+	0.998451i	$0.517721\pi$
$270$	4.16402	0.253414
$271$	21.9110	1.33100	0.665501	−	0.746397i	$-0.268218\pi$
$271$	21.9110	1.33100	0.665501	+	0.746397i	$0.268218\pi$
$272$	3.67654	0.222923
$273$	−1.02195	−0.0618515
$274$	−4.74351	−0.286566
$275$	−5.32231	−0.320948
$276$	−0.761287	−0.0458241
$277$	27.6443	1.66099	0.830494	−	0.557028i	$-0.188058\pi$
$277$	27.6443	1.66099	0.830494	+	0.557028i	$0.188058\pi$
$278$	5.36032	0.321491
$279$	10.0808	0.603521
$280$	2.54557	0.152127
$281$	−6.55945	−0.391304	−0.195652	−	0.980673i	$-0.562682\pi$
$281$	−6.55945	−0.391304	−0.195652	+	0.980673i	$0.562682\pi$
$282$	5.26090	0.313282
$283$	23.1127	1.37391	0.686955	−	0.726700i	$-0.258947\pi$
$283$	23.1127	1.37391	0.686955	+	0.726700i	$0.258947\pi$
$284$	6.06206	0.359717
$285$	1.50397	0.0890876
$286$	−2.83750	−0.167785
$287$	3.86132	0.227927
$288$	5.91116	0.348318
$289$	−4.56229	−0.268370
$290$	−2.02276	−0.118781
$291$	−19.0572	−1.11715
$292$	−14.9113	−0.872617
$293$	−22.2030	−1.29712	−0.648558	−	0.761165i	$-0.724628\pi$
$293$	−22.2030	−1.29712	−0.648558	+	0.761165i	$0.724628\pi$
$294$	1.03867	0.0605766
$295$	−12.2734	−0.714587
$296$	−16.8402	−0.978818
$297$	−30.1073	−1.74700
$298$	−0.392225	−0.0227210
$299$	0.267981	0.0154978
$300$	2.05749	0.118789
$301$	−0.547640	−0.0315654
$302$	0.552433	0.0317890
$303$	0.178198	0.0102372
$304$	1.11115	0.0637286
$305$	−9.07965	−0.519899
$306$	2.61937	0.149739
$307$	12.3565	0.705224	0.352612	−	0.935770i	$-0.385294\pi$
$307$	12.3565	0.705224	0.352612	+	0.935770i	$0.385294\pi$
$308$	−7.76071	−0.442207
$309$	−20.1127	−1.14417
$310$	−7.35446	−0.417705
$311$	20.8176	1.18046	0.590228	−	0.807236i	$-0.299038\pi$
$311$	20.8176	1.18046	0.590228	+	0.807236i	$0.299038\pi$
$312$	2.60145	0.147278
$313$	12.9025	0.729293	0.364646	−	0.931146i	$-0.381190\pi$
$313$	12.9025	0.729293	0.364646	+	0.931146i	$0.381190\pi$
$314$	−1.68811	−0.0952655
$315$	−1.00899	−0.0568499
$316$	−14.4951	−0.815410
$317$	2.10633	0.118303	0.0591517	−	0.998249i	$-0.481160\pi$
$317$	2.10633	0.118303	0.0591517	+	0.998249i	$0.481160\pi$
$318$	0.0190583	0.00106874
$319$	14.6253	0.818858
$320$	−2.22753	−0.124523
$321$	−14.5309	−0.811034
$322$	−0.272365	−0.0151783
$323$	3.75900	0.209156
$324$	7.22510	0.401394
$325$	−0.724260	−0.0401747
$326$	−1.28671	−0.0712643
$327$	26.0649	1.44139
$328$	−9.82926	−0.542730
$329$	−5.06503	−0.279244
$330$	5.52814	0.304314
$331$	10.2426	0.562986	0.281493	−	0.959563i	$-0.409170\pi$
$331$	10.2426	0.562986	0.281493	+	0.959563i	$0.409170\pi$
$332$	2.61863	0.143716
$333$	6.67496	0.365786
$334$	14.0804	0.770446
$335$	−0.894238	−0.0488574
$336$	1.47098	0.0802484
$337$	−16.6496	−0.906962	−0.453481	−	0.891266i	$-0.649818\pi$
$337$	−16.6496	−0.906962	−0.453481	+	0.891266i	$0.649818\pi$
$338$	9.18327	0.499504
$339$	−15.1813	−0.824534
$340$	5.14246	0.278889
$341$	53.1753	2.87960
$342$	0.791641	0.0428071
$343$	−1.00000	−0.0539949
$344$	1.39405	0.0751623
$345$	−0.522092	−0.0281085
$346$	−14.9219	−0.802208
$347$	−24.5767	−1.31935	−0.659674	−	0.751552i	$-0.729306\pi$
$347$	−24.5767	−1.31935	−0.659674	+	0.751552i	$0.729306\pi$
$348$	−5.65382	−0.303076
$349$	−33.0531	−1.76929	−0.884647	−	0.466261i	$-0.845601\pi$
$349$	−33.0531	−1.76929	−0.884647	+	0.466261i	$0.845601\pi$
$350$	0.736107	0.0393466
$351$	−4.09700	−0.218682
$352$	31.1808	1.66194
$353$	−9.51574	−0.506472	−0.253236	−	0.967405i	$-0.581495\pi$
$353$	−9.51574	−0.506472	−0.253236	+	0.967405i	$0.581495\pi$
$354$	12.7481	0.677552
$355$	4.15737	0.220650
$356$	20.2991	1.07585
$357$	4.97631	0.263374
$358$	13.2196	0.698677
$359$	32.5815	1.71959	0.859794	−	0.510641i	$-0.170592\pi$
$359$	32.5815	1.71959	0.859794	+	0.510641i	$0.170592\pi$
$360$	2.56844	0.135369
$361$	−17.8639	−0.940207
$362$	−3.73042	−0.196067
$363$	−24.4490	−1.28324
$364$	−1.05608	−0.0553534
$365$	−10.2262	−0.535263
$366$	9.43078	0.492955
$367$	−5.14102	−0.268359	−0.134179	−	0.990957i	$-0.542840\pi$
$367$	−5.14102	−0.268359	−0.134179	+	0.990957i	$0.542840\pi$
$368$	−0.385726	−0.0201074
$369$	3.89602	0.202819
$370$	−4.86973	−0.253165
$371$	−0.0183487	−0.000952620 0
$372$	−20.5564	−1.06580
$373$	−21.4382	−1.11003	−0.555015	−	0.831841i	$-0.687287\pi$
$373$	−21.4382	−1.11003	−0.555015	+	0.831841i	$0.687287\pi$
$374$	13.8169	0.714457
$375$	1.41103	0.0728654
$376$	12.8934	0.664925
$377$	1.99021	0.102501
$378$	4.16402	0.214174
$379$	−3.56294	−0.183016	−0.0915079	−	0.995804i	$-0.529169\pi$
$379$	−3.56294	−0.183016	−0.0915079	+	0.995804i	$0.529169\pi$
$380$	1.55419	0.0797281
$381$	3.61324	0.185112
$382$	−0.0443579	−0.00226955
$383$	7.94373	0.405906	0.202953	−	0.979189i	$-0.434946\pi$
$383$	7.94373	0.405906	0.202953	+	0.979189i	$0.434946\pi$
$384$	−14.2194	−0.725633
$385$	−5.32231	−0.271250
$386$	9.22947	0.469768
$387$	−0.552561	−0.0280882
$388$	−19.6935	−0.999786
$389$	21.1417	1.07193	0.535963	−	0.844241i	$-0.319949\pi$
$389$	21.1417	1.07193	0.535963	+	0.844241i	$0.319949\pi$
$390$	0.752268	0.0380926
$391$	−1.30491	−0.0659921
$392$	2.54557	0.128571
$393$	−32.0085	−1.61462
$394$	−11.0670	−0.557548
$395$	−9.94074	−0.500173
$396$	−7.83045	−0.393495
$397$	−19.5477	−0.981070	−0.490535	−	0.871422i	$-0.663199\pi$
$397$	−19.5477	−0.981070	−0.490535	+	0.871422i	$0.663199\pi$
$398$	7.00940	0.351350
$399$	1.50397	0.0752927
$400$	1.04248	0.0521241
$401$	−4.91521	−0.245454	−0.122727	−	0.992440i	$-0.539164\pi$
$401$	−4.91521	−0.245454	−0.122727	+	0.992440i	$0.539164\pi$
$402$	0.928820	0.0463253
$403$	7.23609	0.360455
$404$	0.184148	0.00916169
$405$	4.95499	0.246215
$406$	−2.02276	−0.100388
$407$	35.2098	1.74529
$408$	−12.6675	−0.627136
$409$	−33.7437	−1.66852	−0.834259	−	0.551372i	$-0.814104\pi$
$409$	−33.7437	−1.66852	−0.834259	+	0.551372i	$0.814104\pi$
$410$	−2.84235	−0.140374
$411$	−9.09277	−0.448513
$412$	−20.7843	−1.02397
$413$	−12.2734	−0.603936
$414$	−0.274812	−0.0135063
$415$	1.79586	0.0881554
$416$	4.24308	0.208034
$417$	10.2751	0.503175
$418$	4.17584	0.204247
$419$	−9.04100	−0.441682	−0.220841	−	0.975310i	$-0.570880\pi$
$419$	−9.04100	−0.441682	−0.220841	+	0.975310i	$0.570880\pi$
$420$	2.05749	0.100395
$421$	19.1910	0.935311	0.467655	−	0.883911i	$-0.345099\pi$
$421$	19.1910	0.935311	0.467655	+	0.883911i	$0.345099\pi$
$422$	−5.90207	−0.287308
$423$	−5.11054	−0.248483
$424$	0.0467080	0.00226834
$425$	3.52671	0.171071
$426$	−4.31815	−0.209215
$427$	−9.07965	−0.439395
$428$	−15.0160	−0.725828
$429$	−5.43916	−0.262605
$430$	0.403122	0.0194403
$431$	−26.6655	−1.28443	−0.642216	−	0.766523i	$-0.721985\pi$
$431$	−26.6655	−1.28443	−0.642216	+	0.766523i	$0.721985\pi$
$432$	5.89712	0.283726
$433$	−28.4582	−1.36761	−0.683806	−	0.729664i	$-0.739677\pi$
$433$	−28.4582	−1.36761	−0.683806	+	0.729664i	$0.739677\pi$
$434$	−7.35446	−0.353025
$435$	−3.87740	−0.185907
$436$	26.9352	1.28996
$437$	−0.394378	−0.0188656
$438$	10.6217	0.507522
$439$	34.3874	1.64122	0.820610	−	0.571488i	$-0.193634\pi$
$439$	34.3874	1.64122	0.820610	+	0.571488i	$0.193634\pi$
$440$	13.5483	0.645890
$441$	−1.00899	−0.0480469
$442$	1.88021	0.0894323
$443$	−4.38974	−0.208563	−0.104281	−	0.994548i	$-0.533254\pi$
$443$	−4.38974	−0.208563	−0.104281	+	0.994548i	$0.533254\pi$
$444$	−13.6114	−0.645967
$445$	13.9211	0.659926
$446$	0.0845866	0.00400529
$447$	−0.751851	−0.0355613
$448$	−2.22753	−0.105241
$449$	7.96931	0.376095	0.188048	−	0.982160i	$-0.439784\pi$
$449$	7.96931	0.376095	0.188048	+	0.982160i	$0.439784\pi$
$450$	0.742722	0.0350122
$451$	20.5512	0.967717
$452$	−15.6882	−0.737910
$453$	1.05895	0.0497539
$454$	18.6222	0.873981
$455$	−0.724260	−0.0339538
$456$	−3.82846	−0.179284
$457$	−34.5390	−1.61566	−0.807832	−	0.589413i	$-0.799359\pi$
$457$	−34.5390	−1.61566	−0.807832	+	0.589413i	$0.799359\pi$
$458$	0.736107	0.0343960
$459$	19.9500	0.931184
$460$	−0.539525	−0.0251555
$461$	18.2909	0.851894	0.425947	−	0.904748i	$-0.359941\pi$
$461$	18.2909	0.851894	0.425947	+	0.904748i	$0.359941\pi$
$462$	5.52814	0.257192
$463$	−15.7515	−0.732036	−0.366018	−	0.930608i	$-0.619279\pi$
$463$	−15.7515	−0.732036	−0.366018	+	0.930608i	$0.619279\pi$
$464$	−2.86465	−0.132988
$465$	−14.0977	−0.653763
$466$	4.64702	0.215269
$467$	0.510221	0.0236102	0.0118051	−	0.999930i	$-0.496242\pi$
$467$	0.510221	0.0236102	0.0118051	+	0.999930i	$0.496242\pi$
$468$	−1.06557	−0.0492558
$469$	−0.894238	−0.0412921
$470$	3.72840	0.171978
$471$	−3.23591	−0.149103
$472$	31.2428	1.43807
$473$	−2.91471	−0.134019
$474$	10.3252	0.474251
$475$	1.06587	0.0489053
$476$	5.14246	0.235704
$477$	−0.0185136	−0.000847681 0
$478$	−21.3673	−0.977317
$479$	14.4410	0.659826	0.329913	−	0.944011i	$-0.392981\pi$
$479$	14.4410	0.659826	0.329913	+	0.944011i	$0.392981\pi$
$480$	−8.26655	−0.377315
$481$	4.79135	0.218467
$482$	−0.920994	−0.0419501
$483$	−0.522092	−0.0237560
$484$	−25.2653	−1.14842
$485$	−13.5058	−0.613269
$486$	7.34545	0.333197
$487$	−15.6901	−0.710985	−0.355492	−	0.934679i	$-0.615687\pi$
$487$	−15.6901	−0.710985	−0.355492	+	0.934679i	$0.615687\pi$
$488$	23.1129	1.04627
$489$	−2.46648	−0.111538
$490$	0.736107	0.0332539
$491$	10.4529	0.471734	0.235867	−	0.971785i	$-0.424207\pi$
$491$	10.4529	0.471734	0.235867	+	0.971785i	$0.424207\pi$
$492$	−7.94465	−0.358172
$493$	−9.69112	−0.436466
$494$	0.568248	0.0255667
$495$	−5.37014	−0.241370
$496$	−10.4155	−0.467668
$497$	4.15737	0.186484
$498$	−1.86531	−0.0835866
$499$	9.12851	0.408648	0.204324	−	0.978903i	$-0.434500\pi$
$499$	9.12851	0.408648	0.204324	+	0.978903i	$0.434500\pi$
$500$	1.45815	0.0652103
$501$	26.9905	1.20585
$502$	−22.4948	−1.00399
$503$	−17.5187	−0.781118	−0.390559	−	0.920578i	$-0.627718\pi$
$503$	−17.5187	−0.781118	−0.390559	+	0.920578i	$0.627718\pi$
$504$	2.56844	0.114407
$505$	0.126289	0.00561978
$506$	−1.44961	−0.0644431
$507$	17.6033	0.781789
$508$	3.73388	0.165664
$509$	−23.3585	−1.03535	−0.517673	−	0.855579i	$-0.673201\pi$
$509$	−23.3585	−1.03535	−0.517673	+	0.855579i	$0.673201\pi$
$510$	−3.66310	−0.162205
$511$	−10.2262	−0.452380
$512$	−11.4148	−0.504468
$513$	6.02940	0.266204
$514$	9.56199	0.421761
$515$	−14.2539	−0.628101
$516$	1.12676	0.0496030
$517$	−26.9577	−1.18560
$518$	−4.86973	−0.213964
$519$	−28.6036	−1.25556
$520$	1.84365	0.0808494
$521$	25.9871	1.13852	0.569258	−	0.822159i	$-0.307230\pi$
$521$	25.9871	1.13852	0.569258	+	0.822159i	$0.307230\pi$
$522$	−2.04094	−0.0893294
$523$	−42.8700	−1.87457	−0.937287	−	0.348560i	$-0.886671\pi$
$523$	−42.8700	−1.87457	−0.937287	+	0.348560i	$0.886671\pi$
$524$	−33.0773	−1.44499
$525$	1.41103	0.0615825
$526$	7.80000	0.340096
$527$	−35.2355	−1.53488
$528$	7.82900	0.340713
$529$	−22.8631	−0.994048
$530$	0.0135066	0.000586691 0
$531$	−12.3837	−0.537407
$532$	1.55419	0.0673826
$533$	2.79660	0.121134
$534$	−14.4595	−0.625724
$535$	−10.2980	−0.445223
$536$	2.27634	0.0983230
$537$	25.3404	1.09352
$538$	1.34360	0.0579266
$539$	−5.32231	−0.229248
$540$	8.24846	0.354957
$541$	4.65293	0.200045	0.100023	−	0.994985i	$-0.468109\pi$
$541$	4.65293	0.200045	0.100023	+	0.994985i	$0.468109\pi$
$542$	−16.1289	−0.692795
$543$	−7.15079	−0.306870
$544$	−20.6613	−0.885846
$545$	18.4722	0.791263
$546$	0.752268	0.0321941
$547$	−14.4417	−0.617483	−0.308742	−	0.951146i	$-0.599908\pi$
$547$	−14.4417	−0.617483	−0.308742	+	0.951146i	$0.599908\pi$
$548$	−9.39637	−0.401393
$549$	−9.16124	−0.390992
$550$	3.91779	0.167055
$551$	−2.92891	−0.124776
$552$	1.32902	0.0565669
$553$	−9.94074	−0.422723
$554$	−20.3492	−0.864555
$555$	−9.33471	−0.396236
$556$	10.6182	0.450312
$557$	−36.9761	−1.56673	−0.783364	−	0.621563i	$-0.786498\pi$
$557$	−36.9761	−1.56673	−0.783364	+	0.621563i	$0.786498\pi$
$558$	−7.42055	−0.314137
$559$	−0.396633	−0.0167758
$560$	1.04248	0.0440529
$561$	26.4855	1.11822
$562$	4.82846	0.203676
$563$	39.6914	1.67279	0.836397	−	0.548124i	$-0.184658\pi$
$563$	39.6914	1.67279	0.836397	+	0.548124i	$0.184658\pi$
$564$	10.4213	0.438814
$565$	−10.7590	−0.452634
$566$	−17.0134	−0.715129
$567$	4.95499	0.208090
$568$	−10.5829	−0.444047
$569$	−31.2803	−1.31134	−0.655669	−	0.755049i	$-0.727613\pi$
$569$	−31.2803	−1.31134	−0.655669	+	0.755049i	$0.727613\pi$
$570$	−1.10708	−0.0463706
$571$	10.6682	0.446451	0.223225	−	0.974767i	$-0.428341\pi$
$571$	10.6682	0.446451	0.223225	+	0.974767i	$0.428341\pi$
$572$	−5.62077	−0.235016
$573$	−0.0850290	−0.00355214
$574$	−2.84235	−0.118637
$575$	−0.370007	−0.0154304
$576$	−2.24755	−0.0936477
$577$	−11.7883	−0.490753	−0.245377	−	0.969428i	$-0.578912\pi$
$577$	−11.7883	−0.490753	−0.245377	+	0.969428i	$0.578912\pi$
$578$	3.35834	0.139688
$579$	17.6918	0.735248
$580$	−4.00686	−0.166376
$581$	1.79586	0.0745050
$582$	14.0281	0.581485
$583$	−0.0976578	−0.00404457
$584$	26.0315	1.07719
$585$	−0.730768	−0.0302135
$586$	16.3438	0.675157
$587$	−7.98038	−0.329385	−0.164693	−	0.986345i	$-0.552663\pi$
$587$	−7.98038	−0.329385	−0.164693	+	0.986345i	$0.552663\pi$
$588$	2.05749	0.0848495
$589$	−10.6491	−0.438788
$590$	9.03456	0.371947
$591$	−21.2142	−0.872635
$592$	−6.89655	−0.283447
$593$	−33.2291	−1.36455	−0.682277	−	0.731093i	$-0.739010\pi$
$593$	−33.2291	−1.36455	−0.682277	+	0.731093i	$0.739010\pi$
$594$	22.1622	0.909327
$595$	3.52671	0.144581
$596$	−0.776955	−0.0318253
$597$	13.4362	0.549908
$598$	−0.197263	−0.00806668
$599$	−37.1924	−1.51964	−0.759821	−	0.650133i	$-0.774713\pi$
$599$	−37.1924	−1.51964	−0.759821	+	0.650133i	$0.774713\pi$
$600$	−3.59188	−0.146638
$601$	48.1694	1.96487	0.982435	−	0.186604i	$-0.0597480\pi$
$601$	48.1694	1.96487	0.982435	+	0.186604i	$0.0597480\pi$
$602$	0.403122	0.0164300
$603$	−0.902274	−0.0367434
$604$	1.09431	0.0445268
$605$	−17.3270	−0.704443
$606$	−0.131173	−0.00532853
$607$	−7.08944	−0.287752	−0.143876	−	0.989596i	$-0.545957\pi$
$607$	−7.08944	−0.287752	−0.143876	+	0.989596i	$0.545957\pi$
$608$	−6.24438	−0.253243
$609$	−3.87740	−0.157120
$610$	6.68360	0.270611
$611$	−3.66840	−0.148407
$612$	5.18867	0.209740
$613$	14.2973	0.577463	0.288732	−	0.957410i	$-0.406766\pi$
$613$	14.2973	0.577463	0.288732	+	0.957410i	$0.406766\pi$
$614$	−9.09572	−0.367073
$615$	−5.44846	−0.219703
$616$	13.5483	0.545877
$617$	15.7741	0.635041	0.317521	−	0.948251i	$-0.397150\pi$
$617$	15.7741	0.635041	0.317521	+	0.948251i	$0.397150\pi$
$618$	14.8051	0.595549
$619$	−14.8687	−0.597623	−0.298811	−	0.954312i	$-0.596590\pi$
$619$	−14.8687	−0.597623	−0.298811	+	0.954312i	$0.596590\pi$
$620$	−14.5684	−0.585079
$621$	−2.09306	−0.0839916
$622$	−15.3240	−0.614435
$623$	13.9211	0.557739
$624$	1.06537	0.0426489
$625$	1.00000	0.0400000
$626$	−9.49763	−0.379602
$627$	8.00460	0.319673
$628$	−3.34395	−0.133438
$629$	−23.3310	−0.930269
$630$	0.742722	0.0295907
$631$	−5.94376	−0.236617	−0.118309	−	0.992977i	$-0.537747\pi$
$631$	−5.94376	−0.236617	−0.118309	+	0.992977i	$0.537747\pi$
$632$	25.3048	1.00657
$633$	−11.3136	−0.449675
$634$	−1.55049	−0.0615777
$635$	2.56070	0.101618
$636$	0.0377524	0.00149698
$637$	−0.724260	−0.0286962
$638$	−10.7658	−0.426221
$639$	4.19473	0.165941
$640$	−10.0773	−0.398341
$641$	−23.3347	−0.921666	−0.460833	−	0.887487i	$-0.652449\pi$
$641$	−23.3347	−0.921666	−0.460833	+	0.887487i	$0.652449\pi$
$642$	10.6963	0.422149
$643$	−14.3405	−0.565535	−0.282768	−	0.959188i	$-0.591253\pi$
$643$	−14.3405	−0.565535	−0.282768	+	0.959188i	$0.591253\pi$
$644$	−0.539525	−0.0212602
$645$	0.772738	0.0304265
$646$	−2.76703	−0.108867
$647$	16.1586	0.635260	0.317630	−	0.948215i	$-0.397113\pi$
$647$	16.1586	0.635260	0.317630	+	0.948215i	$0.397113\pi$
$648$	−12.6133	−0.495495
$649$	−65.3230	−2.56415
$650$	0.533133	0.0209112
$651$	−14.0977	−0.552531
$652$	−2.54883	−0.0998198
$653$	13.2235	0.517476	0.258738	−	0.965948i	$-0.416693\pi$
$653$	13.2235	0.517476	0.258738	+	0.965948i	$0.416693\pi$
$654$	−19.1866	−0.750255
$655$	−22.6845	−0.886356
$656$	−4.02536	−0.157164
$657$	−10.3181	−0.402547
$658$	3.72840	0.145348
$659$	−19.0359	−0.741532	−0.370766	−	0.928726i	$-0.620905\pi$
$659$	−19.0359	−0.741532	−0.370766	+	0.928726i	$0.620905\pi$
$660$	10.9506	0.426252
$661$	−13.6437	−0.530678	−0.265339	−	0.964155i	$-0.585484\pi$
$661$	−13.6437	−0.530678	−0.265339	+	0.964155i	$0.585484\pi$
$662$	−7.53968	−0.293038
$663$	3.60414	0.139973
$664$	−4.57149	−0.177408
$665$	1.06587	0.0413325
$666$	−4.91349	−0.190394
$667$	1.01675	0.0393687
$668$	27.8917	1.07916
$669$	0.162143	0.00626880
$670$	0.658255	0.0254306
$671$	−48.3247	−1.86556
$672$	−8.26655	−0.318889
$673$	−6.13851	−0.236622	−0.118311	−	0.992977i	$-0.537748\pi$
$673$	−6.13851	−0.236622	−0.118311	+	0.992977i	$0.537748\pi$
$674$	12.2559	0.472080
$675$	5.65681	0.217731
$676$	18.1910	0.699655
$677$	20.5443	0.789581	0.394791	−	0.918771i	$-0.370817\pi$
$677$	20.5443	0.789581	0.394791	+	0.918771i	$0.370817\pi$
$678$	11.1751	0.429175
$679$	−13.5058	−0.518307
$680$	−8.97748	−0.344271
$681$	35.6965	1.36789
$682$	−39.1427	−1.49885
$683$	−5.54580	−0.212204	−0.106102	−	0.994355i	$-0.533837\pi$
$683$	−5.54580	−0.212204	−0.106102	+	0.994355i	$0.533837\pi$
$684$	1.56815	0.0599598
$685$	−6.44405	−0.246215
$686$	0.736107	0.0281047
$687$	1.41103	0.0538343
$688$	0.570905	0.0217655
$689$	−0.0132893	−0.000506280 0
$690$	0.384316	0.0146307
$691$	−30.2469	−1.15064	−0.575322	−	0.817927i	$-0.695123\pi$
$691$	−30.2469	−1.15064	−0.575322	+	0.817927i	$0.695123\pi$
$692$	−29.5587	−1.12365
$693$	−5.37014	−0.203995
$694$	18.0911	0.686729
$695$	7.28199	0.276222
$696$	9.87018	0.374128
$697$	−13.6178	−0.515810
$698$	24.3307	0.920929
$699$	8.90780	0.336924
$700$	1.45815	0.0551127
$701$	−8.97825	−0.339104	−0.169552	−	0.985521i	$-0.554232\pi$
$701$	−8.97825	−0.339104	−0.169552	+	0.985521i	$0.554232\pi$
$702$	3.01583	0.113825
$703$	−7.05125	−0.265943
$704$	−11.8556	−0.446825
$705$	7.14692	0.269169
$706$	7.00461	0.263622
$707$	0.126289	0.00474958
$708$	25.2525	0.949046
$709$	31.0760	1.16708	0.583542	−	0.812083i	$-0.301667\pi$
$709$	31.0760	1.16708	0.583542	+	0.812083i	$0.301667\pi$
$710$	−3.06027	−0.114850
$711$	−10.0301	−0.376157
$712$	−35.4372	−1.32807
$713$	3.69675	0.138444
$714$	−3.66310	−0.137088
$715$	−3.85474	−0.144159
$716$	26.1865	0.978637
$717$	−40.9586	−1.52963
$718$	−23.9835	−0.895057
$719$	−9.61381	−0.358535	−0.179267	−	0.983800i	$-0.557373\pi$
$719$	−9.61381	−0.358535	−0.179267	+	0.983800i	$0.557373\pi$
$720$	1.05185	0.0392001
$721$	−14.2539	−0.530843
$722$	13.1498	0.489384
$723$	−1.76544	−0.0656574
$724$	−7.38955	−0.274630
$725$	−2.74792	−0.102055
$726$	17.9971	0.667934
$727$	42.9901	1.59442	0.797208	−	0.603705i	$-0.206310\pi$
$727$	42.9901	1.59442	0.797208	+	0.603705i	$0.206310\pi$
$728$	1.84365	0.0683303
$729$	28.9454	1.07205
$730$	7.52757	0.278608
$731$	1.93137	0.0714342
$732$	18.6813	0.690481
$733$	26.1558	0.966088	0.483044	−	0.875596i	$-0.339531\pi$
$733$	26.1558	0.966088	0.483044	+	0.875596i	$0.339531\pi$
$734$	3.78434	0.139683
$735$	1.41103	0.0520467
$736$	2.16769	0.0799022
$737$	−4.75941	−0.175315
$738$	−2.86789	−0.105568
$739$	8.81438	0.324242	0.162121	−	0.986771i	$-0.448166\pi$
$739$	8.81438	0.324242	0.162121	+	0.986771i	$0.448166\pi$
$740$	−9.64638	−0.354608
$741$	1.08927	0.0400152
$742$	0.0135066	0.000495845 0
$743$	24.2862	0.890974	0.445487	−	0.895288i	$-0.353030\pi$
$743$	24.2862	0.890974	0.445487	+	0.895288i	$0.353030\pi$
$744$	35.8865	1.31566
$745$	−0.532837	−0.0195216
$746$	15.7808	0.577777
$747$	1.81200	0.0662976
$748$	27.3698	1.00074
$749$	−10.2980	−0.376282
$750$	−1.03867	−0.0379269
$751$	24.9952	0.912087	0.456043	−	0.889958i	$-0.349266\pi$
$751$	24.9952	0.912087	0.456043	+	0.889958i	$0.349266\pi$
$752$	5.28020	0.192549
$753$	−43.1200	−1.57138
$754$	−1.46500	−0.0533523
$755$	0.750479	0.0273127
$756$	8.24846	0.299993
$757$	20.6224	0.749534	0.374767	−	0.927119i	$-0.377723\pi$
$757$	20.6224	0.749534	0.374767	+	0.927119i	$0.377723\pi$
$758$	2.62270	0.0952609
$759$	−2.77874	−0.100862
$760$	−2.71323	−0.0984192
$761$	−23.4630	−0.850534	−0.425267	−	0.905068i	$-0.639820\pi$
$761$	−23.4630	−0.850534	−0.425267	+	0.905068i	$0.639820\pi$
$762$	−2.65973	−0.0963519
$763$	18.4722	0.668740
$764$	−0.0878680	−0.00317895
$765$	3.55840	0.128654
$766$	−5.84744	−0.211277
$767$	−8.88915	−0.320969
$768$	16.7533	0.604531
$769$	−17.0587	−0.615153	−0.307577	−	0.951523i	$-0.599518\pi$
$769$	−17.0587	−0.615153	−0.307577	+	0.951523i	$0.599518\pi$
$770$	3.91779	0.141187
$771$	18.3292	0.660112
$772$	18.2826	0.658004
$773$	−37.9128	−1.36363	−0.681815	−	0.731525i	$-0.738809\pi$
$773$	−37.9128	−1.36363	−0.681815	+	0.731525i	$0.738809\pi$
$774$	0.406744	0.0146201
$775$	−9.99102	−0.358888
$776$	34.3800	1.23417
$777$	−9.33471	−0.334881
$778$	−15.5626	−0.557945
$779$	−4.11565	−0.147459
$780$	1.49016	0.0533562
$781$	22.1268	0.791761
$782$	0.960553	0.0343493
$783$	−15.5444	−0.555513
$784$	1.04248	0.0372315
$785$	−2.29329	−0.0818511
$786$	23.5617	0.840419
$787$	−46.9913	−1.67506	−0.837529	−	0.546393i	$-0.816001\pi$
$787$	−46.9913	−1.67506	−0.837529	+	0.546393i	$0.816001\pi$
$788$	−21.9225	−0.780957
$789$	14.9517	0.532295
$790$	7.31745	0.260343
$791$	−10.7590	−0.382546
$792$	13.6700	0.485744
$793$	−6.57602	−0.233521
$794$	14.3892	0.510653
$795$	0.0258907	0.000918248 0
$796$	13.8848	0.492135
$797$	−24.6260	−0.872297	−0.436148	−	0.899875i	$-0.643658\pi$
$797$	−24.6260	−0.872297	−0.436148	+	0.899875i	$0.643658\pi$
$798$	−1.10708	−0.0391903
$799$	17.8629	0.631944
$800$	−5.85851	−0.207130
$801$	14.0462	0.496299
$802$	3.61812	0.127760
$803$	−54.4270	−1.92069
$804$	1.83989	0.0648878
$805$	−0.370007	−0.0130410
$806$	−5.32654	−0.187619
$807$	2.57552	0.0906627
$808$	−0.321477	−0.0113095
$809$	45.1599	1.58774	0.793869	−	0.608088i	$-0.208063\pi$
$809$	45.1599	1.58774	0.793869	+	0.608088i	$0.208063\pi$
$810$	−3.64740	−0.128157
$811$	−50.8429	−1.78533	−0.892667	−	0.450716i	$-0.851169\pi$
$811$	−50.8429	−1.78533	−0.892667	+	0.450716i	$0.851169\pi$
$812$	−4.00686	−0.140613
$813$	−30.9172	−1.08431
$814$	−25.9182	−0.908433
$815$	−1.74799	−0.0612295
$816$	−5.18771	−0.181606
$817$	0.583710	0.0204214
$818$	24.8390	0.868475
$819$	−0.730768	−0.0255351
$820$	−5.63038	−0.196621
$821$	25.0079	0.872783	0.436391	−	0.899757i	$-0.356256\pi$
$821$	25.0079	0.872783	0.436391	+	0.899757i	$0.356256\pi$
$822$	6.69325	0.233454
$823$	17.7161	0.617544	0.308772	−	0.951136i	$-0.400082\pi$
$823$	17.7161	0.617544	0.308772	+	0.951136i	$0.400082\pi$
$824$	36.2842	1.26402
$825$	7.50996	0.261463
$826$	9.03456	0.314352
$827$	21.6655	0.753385	0.376692	−	0.926338i	$-0.377061\pi$
$827$	21.6655	0.753385	0.376692	+	0.926338i	$0.377061\pi$
$828$	−0.544373	−0.0189183
$829$	−52.3428	−1.81794	−0.908970	−	0.416861i	$-0.863130\pi$
$829$	−52.3428	−1.81794	−0.908970	+	0.416861i	$0.863130\pi$
$830$	−1.32195	−0.0458855
$831$	−39.0071	−1.35314
$832$	−1.61331	−0.0559314
$833$	3.52671	0.122193
$834$	−7.56360	−0.261906
$835$	19.1282	0.661959
$836$	8.27187	0.286089
$837$	−56.5173	−1.95352
$838$	6.65514	0.229898
$839$	−4.88352	−0.168598	−0.0842989	−	0.996441i	$-0.526865\pi$
$839$	−4.88352	−0.168598	−0.0842989	+	0.996441i	$0.526865\pi$
$840$	−3.59188	−0.123932
$841$	−21.4490	−0.739619
$842$	−14.1266	−0.486835
$843$	9.25560	0.318780
$844$	−11.6913	−0.402433
$845$	12.4754	0.429168
$846$	3.76191	0.129337
$847$	−17.3270	−0.595363
$848$	0.0191282	0.000656867 0
$849$	−32.6128	−1.11927
$850$	−2.59604	−0.0890434
$851$	2.44779	0.0839091
$852$	−8.55376	−0.293047
$853$	28.4004	0.972410	0.486205	−	0.873845i	$-0.338381\pi$
$853$	28.4004	0.972410	0.486205	+	0.873845i	$0.338381\pi$
$854$	6.68360	0.228708
$855$	1.07544	0.0367794
$856$	26.2143	0.895988
$857$	29.6965	1.01441	0.507206	−	0.861825i	$-0.330678\pi$
$857$	29.6965	1.01441	0.507206	+	0.861825i	$0.330678\pi$
$858$	4.00381	0.136688
$859$	35.5368	1.21250	0.606250	−	0.795274i	$-0.292673\pi$
$859$	35.5368	1.21250	0.606250	+	0.795274i	$0.292673\pi$
$860$	0.798539	0.0272299
$861$	−5.44846	−0.185683
$862$	19.6287	0.668555
$863$	−25.5546	−0.869887	−0.434944	−	0.900458i	$-0.643232\pi$
$863$	−25.5546	−0.869887	−0.434944	+	0.900458i	$0.643232\pi$
$864$	−33.1405	−1.12746
$865$	−20.2714	−0.689248
$866$	20.9483	0.711851
$867$	6.43755	0.218631
$868$	−14.5684	−0.494482
$869$	−52.9077	−1.79477
$870$	2.85418	0.0967659
$871$	−0.647661	−0.0219451
$872$	−47.0223	−1.59238
$873$	−13.6272	−0.461211
$874$	0.290304	0.00981969
$875$	1.00000	0.0338062
$876$	21.0403	0.710886
$877$	9.42601	0.318294	0.159147	−	0.987255i	$-0.449126\pi$
$877$	9.42601	0.318294	0.159147	+	0.987255i	$0.449126\pi$
$878$	−25.3128	−0.854266
$879$	31.3292	1.05671
$880$	5.54842	0.187037
$881$	14.9369	0.503238	0.251619	−	0.967826i	$-0.419037\pi$
$881$	14.9369	0.503238	0.251619	+	0.967826i	$0.419037\pi$
$882$	0.742722	0.0250087
$883$	43.7584	1.47259	0.736294	−	0.676661i	$-0.236574\pi$
$883$	43.7584	1.47259	0.736294	+	0.676661i	$0.236574\pi$
$884$	3.72448	0.125268
$885$	17.3182	0.582145
$886$	3.23132	0.108558
$887$	−24.7688	−0.831654	−0.415827	−	0.909444i	$-0.636508\pi$
$887$	−24.7688	−0.831654	−0.415827	+	0.909444i	$0.636508\pi$
$888$	23.7621	0.797404
$889$	2.56070	0.0858832
$890$	−10.2475	−0.343496
$891$	26.3720	0.883495
$892$	0.167557	0.00561021
$893$	5.39864	0.180659
$894$	0.553443	0.0185099
$895$	17.9588	0.600296
$896$	−10.0773	−0.336660
$897$	−0.378130	−0.0126254
$898$	−5.86627	−0.195760
$899$	27.4545	0.915658
$900$	1.47125	0.0490416
$901$	0.0647108	0.00215583
$902$	−15.1279	−0.503703
$903$	0.772738	0.0257151
$904$	27.3877	0.910902
$905$	−5.06777	−0.168458
$906$	−0.779502	−0.0258972
$907$	4.89448	0.162518	0.0812592	−	0.996693i	$-0.474106\pi$
$907$	4.89448	0.162518	0.0812592	+	0.996693i	$0.474106\pi$
$908$	36.8884	1.22418
$909$	0.127424	0.00422638
$910$	0.533133	0.0176732
$911$	−24.8513	−0.823361	−0.411681	−	0.911328i	$-0.635058\pi$
$911$	−24.8513	−0.823361	−0.411681	+	0.911328i	$0.635058\pi$
$912$	−1.56786	−0.0519171
$913$	9.55814	0.316328
$914$	25.4244	0.840964
$915$	12.8117	0.423541
$916$	1.45815	0.0481785
$917$	−22.6845	−0.749107
$918$	−14.6853	−0.484687
$919$	9.09137	0.299896	0.149948	−	0.988694i	$-0.452089\pi$
$919$	9.09137	0.299896	0.149948	+	0.988694i	$0.452089\pi$
$920$	0.941878	0.0310528
$921$	−17.4354	−0.574518
$922$	−13.4641	−0.443416
$923$	3.01102	0.0991088
$924$	10.9506	0.360249
$925$	−6.61551	−0.217517
$926$	11.5948	0.381029
$927$	−14.3820	−0.472366
$928$	16.0987	0.528466
$929$	2.88575	0.0946783	0.0473392	−	0.998879i	$-0.484926\pi$
$929$	2.88575	0.0946783	0.0473392	+	0.998879i	$0.484926\pi$
$930$	10.3774	0.340288
$931$	1.06587	0.0349323
$932$	9.20523	0.301527
$933$	−29.3743	−0.961671
$934$	−0.375577	−0.0122893
$935$	18.7703	0.613854
$936$	1.86022	0.0608031
$937$	−52.4692	−1.71409	−0.857046	−	0.515239i	$-0.827703\pi$
$937$	−52.4692	−1.71409	−0.857046	+	0.515239i	$0.827703\pi$
$938$	0.658255	0.0214928
$939$	−18.2059	−0.594126
$940$	7.38555	0.240890
$941$	26.1868	0.853665	0.426833	−	0.904331i	$-0.359629\pi$
$941$	26.1868	0.853665	0.426833	+	0.904331i	$0.359629\pi$
$942$	2.38198	0.0776090
$943$	1.42872	0.0465255
$944$	12.7948	0.416436
$945$	5.65681	0.184016
$946$	2.14554	0.0697575
$947$	−7.50904	−0.244011	−0.122005	−	0.992529i	$-0.538933\pi$
$947$	−7.50904	−0.244011	−0.122005	+	0.992529i	$0.538933\pi$
$948$	20.4530	0.664283
$949$	−7.40642	−0.240423
$950$	−0.784591	−0.0254555
$951$	−2.97210	−0.0963770
$952$	−8.97748	−0.290962
$953$	−18.4587	−0.597935	−0.298968	−	0.954263i	$-0.596642\pi$
$953$	−18.4587	−0.597935	−0.298968	+	0.954263i	$0.596642\pi$
$954$	0.0136280	0.000441223 0
$955$	−0.0602601	−0.00194997
$956$	−42.3262	−1.36893
$957$	−20.6367	−0.667091
$958$	−10.6301	−0.343444
$959$	−6.44405	−0.208089
$960$	3.14312	0.101444
$961$	68.8204	2.22001
$962$	−3.52695	−0.113713
$963$	−10.3906	−0.334832
$964$	−1.82439	−0.0587595
$965$	12.5382	0.403620
$966$	0.384316	0.0123652
$967$	7.15757	0.230172	0.115086	−	0.993356i	$-0.463286\pi$
$967$	7.15757	0.230172	0.115086	+	0.993356i	$0.463286\pi$
$968$	44.1071	1.41765
$969$	−5.30407	−0.170391
$970$	9.94175	0.319210
$971$	16.8718	0.541441	0.270721	−	0.962658i	$-0.412738\pi$
$971$	16.8718	0.541441	0.270721	+	0.962658i	$0.412738\pi$
$972$	14.5505	0.466708
$973$	7.28199	0.233450
$974$	11.5496	0.370072
$975$	1.02195	0.0327287
$976$	9.46537	0.302979
$977$	−41.1494	−1.31649	−0.658243	−	0.752806i	$-0.728700\pi$
$977$	−41.1494	−1.31649	−0.658243	+	0.752806i	$0.728700\pi$
$978$	1.81559	0.0580562
$979$	74.0927	2.36801
$980$	1.45815	0.0465788
$981$	18.6382	0.595072
$982$	−7.69447	−0.245540
$983$	−4.49440	−0.143349	−0.0716746	−	0.997428i	$-0.522834\pi$
$983$	−4.49440	−0.143349	−0.0716746	+	0.997428i	$0.522834\pi$
$984$	13.8694	0.442141
$985$	−15.0345	−0.479039
$986$	7.13370	0.227183
$987$	7.14692	0.227489
$988$	1.12564	0.0358112
$989$	−0.202631	−0.00644328
$990$	3.95300	0.125635
$991$	11.3759	0.361367	0.180684	−	0.983541i	$-0.442169\pi$
$991$	11.3759	0.361367	0.180684	+	0.983541i	$0.442169\pi$
$992$	58.5325	1.85841
$993$	−14.4527	−0.458643
$994$	−3.06027	−0.0970659
$995$	9.52226	0.301876
$996$	−3.69497	−0.117080
$997$	41.0324	1.29951	0.649754	−	0.760144i	$-0.274872\pi$
$997$	41.0324	1.29951	0.649754	+	0.760144i	$0.274872\pi$
$998$	−6.71956	−0.212704
$999$	−37.4227	−1.18400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.k.1.20	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.k.1.20	✓	49	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.736107 q^{2} -1.41103 q^{3} -1.45815 q^{4} -1.00000 q^{5} +1.03867 q^{6} -1.00000 q^{7} +2.54557 q^{8} -1.00899 q^{9} +O(q^{10})\)	\(q-0.736107 q^{2} -1.41103 q^{3} -1.45815 q^{4} -1.00000 q^{5} +1.03867 q^{6} -1.00000 q^{7} +2.54557 q^{8} -1.00899 q^{9} +0.736107 q^{10} -5.32231 q^{11} +2.05749 q^{12} -0.724260 q^{13} +0.736107 q^{14} +1.41103 q^{15} +1.04248 q^{16} +3.52671 q^{17} +0.742722 q^{18} +1.06587 q^{19} +1.45815 q^{20} +1.41103 q^{21} +3.91779 q^{22} -0.370007 q^{23} -3.59188 q^{24} +1.00000 q^{25} +0.533133 q^{26} +5.65681 q^{27} +1.45815 q^{28} -2.74792 q^{29} -1.03867 q^{30} -9.99102 q^{31} -5.85851 q^{32} +7.50996 q^{33} -2.59604 q^{34} +1.00000 q^{35} +1.47125 q^{36} -6.61551 q^{37} -0.784591 q^{38} +1.02195 q^{39} -2.54557 q^{40} -3.86132 q^{41} -1.03867 q^{42} +0.547640 q^{43} +7.76071 q^{44} +1.00899 q^{45} +0.272365 q^{46} +5.06503 q^{47} -1.47098 q^{48} +1.00000 q^{49} -0.736107 q^{50} -4.97631 q^{51} +1.05608 q^{52} +0.0183487 q^{53} -4.16402 q^{54} +5.32231 q^{55} -2.54557 q^{56} -1.50397 q^{57} +2.02276 q^{58} +12.2734 q^{59} -2.05749 q^{60} +9.07965 q^{61} +7.35446 q^{62} +1.00899 q^{63} +2.22753 q^{64} +0.724260 q^{65} -5.52814 q^{66} +0.894238 q^{67} -5.14246 q^{68} +0.522092 q^{69} -0.736107 q^{70} -4.15737 q^{71} -2.56844 q^{72} +10.2262 q^{73} +4.86973 q^{74} -1.41103 q^{75} -1.55419 q^{76} +5.32231 q^{77} -0.752268 q^{78} +9.94074 q^{79} -1.04248 q^{80} -4.95499 q^{81} +2.84235 q^{82} -1.79586 q^{83} -2.05749 q^{84} -3.52671 q^{85} -0.403122 q^{86} +3.87740 q^{87} -13.5483 q^{88} -13.9211 q^{89} -0.742722 q^{90} +0.724260 q^{91} +0.539525 q^{92} +14.0977 q^{93} -3.72840 q^{94} -1.06587 q^{95} +8.26655 q^{96} +13.5058 q^{97} -0.736107 q^{98} +5.37014 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * q^99

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