LMFDB - Embedded newform 4015.2.a.i.1.7

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:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-1.83787 q^{2} -3.02191 q^{3} +1.37778 q^{4} +1.00000 q^{5} +5.55388 q^{6} +4.06050 q^{7} +1.14356 q^{8} +6.13192 q^{9} +O(q^{10})$	\(q-1.83787 q^{2} -3.02191 q^{3} +1.37778 q^{4} +1.00000 q^{5} +5.55388 q^{6} +4.06050 q^{7} +1.14356 q^{8} +6.13192 q^{9} -1.83787 q^{10} -1.00000 q^{11} -4.16352 q^{12} -1.29808 q^{13} -7.46269 q^{14} -3.02191 q^{15} -4.85728 q^{16} +3.26974 q^{17} -11.2697 q^{18} +2.74349 q^{19} +1.37778 q^{20} -12.2705 q^{21} +1.83787 q^{22} +0.430174 q^{23} -3.45574 q^{24} +1.00000 q^{25} +2.38570 q^{26} -9.46437 q^{27} +5.59448 q^{28} +4.65898 q^{29} +5.55388 q^{30} +6.89181 q^{31} +6.63995 q^{32} +3.02191 q^{33} -6.00938 q^{34} +4.06050 q^{35} +8.44843 q^{36} -5.08475 q^{37} -5.04219 q^{38} +3.92267 q^{39} +1.14356 q^{40} +12.5732 q^{41} +22.5516 q^{42} +11.7702 q^{43} -1.37778 q^{44} +6.13192 q^{45} -0.790605 q^{46} -5.13774 q^{47} +14.6783 q^{48} +9.48768 q^{49} -1.83787 q^{50} -9.88086 q^{51} -1.78846 q^{52} +10.1485 q^{53} +17.3943 q^{54} -1.00000 q^{55} +4.64344 q^{56} -8.29057 q^{57} -8.56262 q^{58} -2.54267 q^{59} -4.16352 q^{60} +3.78877 q^{61} -12.6663 q^{62} +24.8987 q^{63} -2.48882 q^{64} -1.29808 q^{65} -5.55388 q^{66} -9.87204 q^{67} +4.50499 q^{68} -1.29994 q^{69} -7.46269 q^{70} +5.70174 q^{71} +7.01223 q^{72} -1.00000 q^{73} +9.34514 q^{74} -3.02191 q^{75} +3.77993 q^{76} -4.06050 q^{77} -7.20937 q^{78} +5.19297 q^{79} -4.85728 q^{80} +10.2047 q^{81} -23.1079 q^{82} -11.9656 q^{83} -16.9060 q^{84} +3.26974 q^{85} -21.6321 q^{86} -14.0790 q^{87} -1.14356 q^{88} +6.71964 q^{89} -11.2697 q^{90} -5.27085 q^{91} +0.592684 q^{92} -20.8264 q^{93} +9.44252 q^{94} +2.74349 q^{95} -20.0653 q^{96} -18.1476 q^{97} -17.4372 q^{98} -6.13192 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9}+O(q^{10}) $ 38 * q + 4 * q^2 + 5 * q^3 + 50 * q^4 + 38 * q^5 + 11 * q^6 + 15 * q^8 + 63 * q^9	\( 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9} + 4 q^{10} - 38 q^{11} + 12 q^{12} - q^{13} + 23 q^{14} + 5 q^{15} + 74 q^{16} + 26 q^{17} + 16 q^{18} - 10 q^{19} + 50 q^{20} + 21 q^{21} - 4 q^{22} + 10 q^{23} + 41 q^{24} + 38 q^{25} + 25 q^{26} + 5 q^{27} + 2 q^{28} + 28 q^{29} + 11 q^{30} + 24 q^{31} + 39 q^{32} - 5 q^{33} + 38 q^{34} + 111 q^{36} + 12 q^{37} + 19 q^{38} - 18 q^{39} + 15 q^{40} + 62 q^{41} - 17 q^{42} - 32 q^{43} - 50 q^{44} + 63 q^{45} - 9 q^{46} + 31 q^{47} + 53 q^{48} + 88 q^{49} + 4 q^{50} - 3 q^{51} - 21 q^{52} + 30 q^{53} + 49 q^{54} - 38 q^{55} + 32 q^{56} + 49 q^{57} + 12 q^{58} + 31 q^{59} + 12 q^{60} + 25 q^{61} + 12 q^{62} + 15 q^{63} + 137 q^{64} - q^{65} - 11 q^{66} + 20 q^{67} + 75 q^{68} + 92 q^{69} + 23 q^{70} + 32 q^{71} + 6 q^{72} - 38 q^{73} + 55 q^{74} + 5 q^{75} - 57 q^{76} - 17 q^{78} - 2 q^{79} + 74 q^{80} + 118 q^{81} + 14 q^{82} + 4 q^{83} + 22 q^{84} + 26 q^{85} + 5 q^{86} + 24 q^{87} - 15 q^{88} + 143 q^{89} + 16 q^{90} + 66 q^{91} + 29 q^{92} - 8 q^{93} - 7 q^{94} - 10 q^{95} + 59 q^{96} + 41 q^{97} - 10 q^{98} - 63 q^{99}+O(q^{100}) \) 38 * q + 4 * q^2 + 5 * q^3 + 50 * q^4 + 38 * q^5 + 11 * q^6 + 15 * q^8 + 63 * q^9 + 4 * q^10 - 38 * q^11 + 12 * q^12 - q^13 + 23 * q^14 + 5 * q^15 + 74 * q^16 + 26 * q^17 + 16 * q^18 - 10 * q^19 + 50 * q^20 + 21 * q^21 - 4 * q^22 + 10 * q^23 + 41 * q^24 + 38 * q^25 + 25 * q^26 + 5 * q^27 + 2 * q^28 + 28 * q^29 + 11 * q^30 + 24 * q^31 + 39 * q^32 - 5 * q^33 + 38 * q^34 + 111 * q^36 + 12 * q^37 + 19 * q^38 - 18 * q^39 + 15 * q^40 + 62 * q^41 - 17 * q^42 - 32 * q^43 - 50 * q^44 + 63 * q^45 - 9 * q^46 + 31 * q^47 + 53 * q^48 + 88 * q^49 + 4 * q^50 - 3 * q^51 - 21 * q^52 + 30 * q^53 + 49 * q^54 - 38 * q^55 + 32 * q^56 + 49 * q^57 + 12 * q^58 + 31 * q^59 + 12 * q^60 + 25 * q^61 + 12 * q^62 + 15 * q^63 + 137 * q^64 - q^65 - 11 * q^66 + 20 * q^67 + 75 * q^68 + 92 * q^69 + 23 * q^70 + 32 * q^71 + 6 * q^72 - 38 * q^73 + 55 * q^74 + 5 * q^75 - 57 * q^76 - 17 * q^78 - 2 * q^79 + 74 * q^80 + 118 * q^81 + 14 * q^82 + 4 * q^83 + 22 * q^84 + 26 * q^85 + 5 * q^86 + 24 * q^87 - 15 * q^88 + 143 * q^89 + 16 * q^90 + 66 * q^91 + 29 * q^92 - 8 * q^93 - 7 * q^94 - 10 * q^95 + 59 * q^96 + 41 * q^97 - 10 * q^98 - 63 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.83787	−1.29957	−0.649786	−	0.760117i	$-0.725142\pi$
$2$	−1.83787	−1.29957	−0.649786	+	0.760117i	$0.725142\pi$
$3$	−3.02191	−1.74470	−0.872349	−	0.488883i	$-0.837404\pi$
$3$	−3.02191	−1.74470	−0.872349	+	0.488883i	$0.837404\pi$
$4$	1.37778	0.688890
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	5.55388	2.26736
$7$	4.06050	1.53473	0.767363	−	0.641213i	$-0.221569\pi$
$7$	4.06050	1.53473	0.767363	+	0.641213i	$0.221569\pi$
$8$	1.14356	0.404310
$9$	6.13192	2.04397
$10$	−1.83787	−0.581187
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.16352	−1.20191
$13$	−1.29808	−0.360022	−0.180011	−	0.983665i	$-0.557613\pi$
$13$	−1.29808	−0.360022	−0.180011	+	0.983665i	$0.557613\pi$
$14$	−7.46269	−1.99449
$15$	−3.02191	−0.780253
$16$	−4.85728	−1.21432
$17$	3.26974	0.793029	0.396515	−	0.918028i	$-0.370220\pi$
$17$	3.26974	0.793029	0.396515	+	0.918028i	$0.370220\pi$
$18$	−11.2697	−2.65629
$19$	2.74349	0.629400	0.314700	−	0.949191i	$-0.398096\pi$
$19$	2.74349	0.629400	0.314700	+	0.949191i	$0.398096\pi$
$20$	1.37778	0.308081
$21$	−12.2705	−2.67763
$22$	1.83787	0.391836
$23$	0.430174	0.0896974	0.0448487	−	0.998994i	$-0.485719\pi$
$23$	0.430174	0.0896974	0.0448487	+	0.998994i	$0.485719\pi$
$24$	−3.45574	−0.705400
$25$	1.00000	0.200000
$26$	2.38570	0.467875
$27$	−9.46437	−1.82142
$28$	5.59448	1.05726
$29$	4.65898	0.865151	0.432576	−	0.901598i	$-0.357605\pi$
$29$	4.65898	0.865151	0.432576	+	0.901598i	$0.357605\pi$
$30$	5.55388	1.01400
$31$	6.89181	1.23781	0.618903	−	0.785468i	$-0.287578\pi$
$31$	6.89181	1.23781	0.618903	+	0.785468i	$0.287578\pi$
$32$	6.63995	1.17379
$33$	3.02191	0.526046
$34$	−6.00938	−1.03060
$35$	4.06050	0.686350
$36$	8.44843	1.40807
$37$	−5.08475	−0.835928	−0.417964	−	0.908463i	$-0.637256\pi$
$37$	−5.08475	−0.835928	−0.417964	+	0.908463i	$0.637256\pi$
$38$	−5.04219	−0.817951
$39$	3.92267	0.628130
$40$	1.14356	0.180813
$41$	12.5732	1.96360	0.981798	−	0.189927i	$-0.0608253\pi$
$41$	12.5732	1.96360	0.981798	+	0.189927i	$0.0608253\pi$
$42$	22.5516	3.47978
$43$	11.7702	1.79493	0.897467	−	0.441082i	$-0.145405\pi$
$43$	11.7702	1.79493	0.897467	+	0.441082i	$0.145405\pi$
$44$	−1.37778	−0.207708
$45$	6.13192	0.914093
$46$	−0.790605	−0.116568
$47$	−5.13774	−0.749417	−0.374708	−	0.927143i	$-0.622257\pi$
$47$	−5.13774	−0.749417	−0.374708	+	0.927143i	$0.622257\pi$
$48$	14.6783	2.11862
$49$	9.48768	1.35538
$50$	−1.83787	−0.259915
$51$	−9.88086	−1.38360
$52$	−1.78846	−0.248015
$53$	10.1485	1.39401	0.697003	−	0.717068i	$-0.254516\pi$
$53$	10.1485	1.39401	0.697003	+	0.717068i	$0.254516\pi$
$54$	17.3943	2.36707
$55$	−1.00000	−0.134840
$56$	4.64344	0.620506
$57$	−8.29057	−1.09811
$58$	−8.56262	−1.12433
$59$	−2.54267	−0.331028	−0.165514	−	0.986207i	$-0.552928\pi$
$59$	−2.54267	−0.331028	−0.165514	+	0.986207i	$0.552928\pi$
$60$	−4.16352	−0.537508
$61$	3.78877	0.485103	0.242551	−	0.970139i	$-0.422016\pi$
$61$	3.78877	0.485103	0.242551	+	0.970139i	$0.422016\pi$
$62$	−12.6663	−1.60862
$63$	24.8987	3.13694
$64$	−2.48882	−0.311102
$65$	−1.29808	−0.161007
$66$	−5.55388	−0.683636
$67$	−9.87204	−1.20606	−0.603031	−	0.797718i	$-0.706041\pi$
$67$	−9.87204	−1.20606	−0.603031	+	0.797718i	$0.706041\pi$
$68$	4.50499	0.546310
$69$	−1.29994	−0.156495
$70$	−7.46269	−0.891962
$71$	5.70174	0.676672	0.338336	−	0.941025i	$-0.390136\pi$
$71$	5.70174	0.676672	0.338336	+	0.941025i	$0.390136\pi$
$72$	7.01223	0.826400
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	9.34514	1.08635
$75$	−3.02191	−0.348940
$76$	3.77993	0.433587
$77$	−4.06050	−0.462737
$78$	−7.20937	−0.816300
$79$	5.19297	0.584255	0.292128	−	0.956379i	$-0.405637\pi$
$79$	5.19297	0.584255	0.292128	+	0.956379i	$0.405637\pi$
$80$	−4.85728	−0.543061
$81$	10.2047	1.13385
$82$	−23.1079	−2.55184
$83$	−11.9656	−1.31339	−0.656696	−	0.754155i	$-0.728047\pi$
$83$	−11.9656	−1.31339	−0.656696	+	0.754155i	$0.728047\pi$
$84$	−16.9060	−1.84459
$85$	3.26974	0.354653
$86$	−21.6321	−2.33265
$87$	−14.0790	−1.50943
$88$	−1.14356	−0.121904
$89$	6.71964	0.712280	0.356140	−	0.934433i	$-0.384093\pi$
$89$	6.71964	0.712280	0.356140	+	0.934433i	$0.384093\pi$
$90$	−11.2697	−1.18793
$91$	−5.27085	−0.552535
$92$	0.592684	0.0617916
$93$	−20.8264	−2.15960
$94$	9.44252	0.973922
$95$	2.74349	0.281476
$96$	−20.0653	−2.04791
$97$	−18.1476	−1.84261	−0.921304	−	0.388843i	$-0.872875\pi$
$97$	−18.1476	−1.84261	−0.921304	+	0.388843i	$0.872875\pi$
$98$	−17.4372	−1.76142
$99$	−6.13192	−0.616281
$100$	1.37778	0.137778
$101$	18.8042	1.87109	0.935545	−	0.353208i	$-0.114909\pi$
$101$	18.8042	1.87109	0.935545	+	0.353208i	$0.114909\pi$
$102$	18.1598	1.79809
$103$	5.77324	0.568854	0.284427	−	0.958698i	$-0.408197\pi$
$103$	5.77324	0.568854	0.284427	+	0.958698i	$0.408197\pi$
$104$	−1.48443	−0.145561
$105$	−12.2705	−1.19747
$106$	−18.6517	−1.81161
$107$	4.00898	0.387563	0.193781	−	0.981045i	$-0.437925\pi$
$107$	4.00898	0.387563	0.193781	+	0.981045i	$0.437925\pi$
$108$	−13.0398	−1.25476
$109$	10.0402	0.961680	0.480840	−	0.876808i	$-0.340332\pi$
$109$	10.0402	0.961680	0.480840	+	0.876808i	$0.340332\pi$
$110$	1.83787	0.175234
$111$	15.3657	1.45844
$112$	−19.7230	−1.86365
$113$	−0.132097	−0.0124267	−0.00621334	−	0.999981i	$-0.501978\pi$
$113$	−0.132097	−0.0124267	−0.00621334	+	0.999981i	$0.501978\pi$
$114$	15.2370	1.42708
$115$	0.430174	0.0401139
$116$	6.41905	0.595994
$117$	−7.95970	−0.735875
$118$	4.67311	0.430195
$119$	13.2768	1.21708
$120$	−3.45574	−0.315464
$121$	1.00000	0.0909091
$122$	−6.96329	−0.630426
$123$	−37.9949	−3.42588
$124$	9.49539	0.852711
$125$	1.00000	0.0894427
$126$	−45.7606	−4.07668
$127$	−4.70330	−0.417350	−0.208675	−	0.977985i	$-0.566915\pi$
$127$	−4.70330	−0.417350	−0.208675	+	0.977985i	$0.566915\pi$
$128$	−8.70576	−0.769488
$129$	−35.5683	−3.13162
$130$	2.38570	0.209240
$131$	−14.1002	−1.23194	−0.615970	−	0.787769i	$-0.711236\pi$
$131$	−14.1002	−1.23194	−0.615970	+	0.787769i	$0.711236\pi$
$132$	4.16352	0.362388
$133$	11.1400	0.965956
$134$	18.1436	1.56737
$135$	−9.46437	−0.814563
$136$	3.73916	0.320630
$137$	−16.7297	−1.42932	−0.714658	−	0.699474i	$-0.753418\pi$
$137$	−16.7297	−1.42932	−0.714658	+	0.699474i	$0.753418\pi$
$138$	2.38913	0.203377
$139$	−7.66584	−0.650208	−0.325104	−	0.945678i	$-0.605399\pi$
$139$	−7.66584	−0.650208	−0.325104	+	0.945678i	$0.605399\pi$
$140$	5.59448	0.472820
$141$	15.5258	1.30751
$142$	−10.4791	−0.879384
$143$	1.29808	0.108551
$144$	−29.7845	−2.48204
$145$	4.65898	0.386907
$146$	1.83787	0.152104
$147$	−28.6709	−2.36473
$148$	−7.00567	−0.575863
$149$	3.61988	0.296552	0.148276	−	0.988946i	$-0.452628\pi$
$149$	3.61988	0.296552	0.148276	+	0.988946i	$0.452628\pi$
$150$	5.55388	0.453473
$151$	14.9864	1.21957	0.609787	−	0.792565i	$-0.291255\pi$
$151$	14.9864	1.21957	0.609787	+	0.792565i	$0.291255\pi$
$152$	3.13735	0.254473
$153$	20.0498	1.62093
$154$	7.46269	0.601361
$155$	6.89181	0.553563
$156$	5.40457	0.432712
$157$	−3.99048	−0.318475	−0.159238	−	0.987240i	$-0.550904\pi$
$157$	−3.99048	−0.318475	−0.159238	+	0.987240i	$0.550904\pi$
$158$	−9.54403	−0.759282
$159$	−30.6679	−2.43212
$160$	6.63995	0.524934
$161$	1.74672	0.137661
$162$	−18.7549	−1.47353
$163$	−17.0145	−1.33268	−0.666340	−	0.745648i	$-0.732140\pi$
$163$	−17.0145	−1.33268	−0.666340	+	0.745648i	$0.732140\pi$
$164$	17.3230	1.35270
$165$	3.02191	0.235255
$166$	21.9912	1.70685
$167$	21.8127	1.68792	0.843959	−	0.536407i	$-0.180219\pi$
$167$	21.8127	1.68792	0.843959	+	0.536407i	$0.180219\pi$
$168$	−14.0320	−1.08260
$169$	−11.3150	−0.870384
$170$	−6.00938	−0.460898
$171$	16.8229	1.28648
$172$	16.2167	1.23651
$173$	2.55969	0.194609	0.0973047	−	0.995255i	$-0.468978\pi$
$173$	2.55969	0.194609	0.0973047	+	0.995255i	$0.468978\pi$
$174$	25.8754	1.96161
$175$	4.06050	0.306945
$176$	4.85728	0.366131
$177$	7.68372	0.577544
$178$	−12.3498	−0.925660
$179$	0.528103	0.0394723	0.0197361	−	0.999805i	$-0.493717\pi$
$179$	0.528103	0.0394723	0.0197361	+	0.999805i	$0.493717\pi$
$180$	8.44843	0.629709
$181$	−20.8616	−1.55063	−0.775316	−	0.631574i	$-0.782409\pi$
$181$	−20.8616	−1.55063	−0.775316	+	0.631574i	$0.782409\pi$
$182$	9.68715	0.718059
$183$	−11.4493	−0.846358
$184$	0.491930	0.0362656
$185$	−5.08475	−0.373839
$186$	38.2763	2.80655
$187$	−3.26974	−0.239107
$188$	−7.07868	−0.516266
$189$	−38.4301	−2.79538
$190$	−5.04219	−0.365799
$191$	11.3077	0.818199	0.409099	−	0.912490i	$-0.365843\pi$
$191$	11.3077	0.818199	0.409099	+	0.912490i	$0.365843\pi$
$192$	7.52097	0.542780
$193$	1.30199	0.0937195	0.0468597	−	0.998901i	$-0.485079\pi$
$193$	1.30199	0.0937195	0.0468597	+	0.998901i	$0.485079\pi$
$194$	33.3530	2.39460
$195$	3.92267	0.280908
$196$	13.0719	0.933710
$197$	−0.861954	−0.0614117	−0.0307058	−	0.999528i	$-0.509776\pi$
$197$	−0.861954	−0.0614117	−0.0307058	+	0.999528i	$0.509776\pi$
$198$	11.2697	0.800902
$199$	−11.0738	−0.785001	−0.392500	−	0.919752i	$-0.628390\pi$
$199$	−11.0738	−0.785001	−0.392500	+	0.919752i	$0.628390\pi$
$200$	1.14356	0.0808621
$201$	29.8324	2.10421
$202$	−34.5598	−2.43162
$203$	18.9178	1.32777
$204$	−13.6136	−0.953146
$205$	12.5732	0.878147
$206$	−10.6105	−0.739267
$207$	2.63779	0.183339
$208$	6.30513	0.437182
$209$	−2.74349	−0.189771
$210$	22.5516	1.55621
$211$	−20.9856	−1.44471	−0.722355	−	0.691523i	$-0.756940\pi$
$211$	−20.9856	−1.44471	−0.722355	+	0.691523i	$0.756940\pi$
$212$	13.9824	0.960317
$213$	−17.2301	−1.18059
$214$	−7.36800	−0.503666
$215$	11.7702	0.802719
$216$	−10.8231	−0.736419
$217$	27.9842	1.89969
$218$	−18.4527	−1.24977
$219$	3.02191	0.204202
$220$	−1.37778	−0.0928899
$221$	−4.24438	−0.285508
$222$	−28.2401	−1.89535
$223$	18.6732	1.25045	0.625226	−	0.780444i	$-0.285007\pi$
$223$	18.6732	1.25045	0.625226	+	0.780444i	$0.285007\pi$
$224$	26.9615	1.80144
$225$	6.13192	0.408795
$226$	0.242778	0.0161494
$227$	5.58704	0.370825	0.185412	−	0.982661i	$-0.440638\pi$
$227$	5.58704	0.370825	0.185412	+	0.982661i	$0.440638\pi$
$228$	−11.4226	−0.756479
$229$	−13.5344	−0.894381	−0.447190	−	0.894439i	$-0.647575\pi$
$229$	−13.5344	−0.894381	−0.447190	+	0.894439i	$0.647575\pi$
$230$	−0.790605	−0.0521309
$231$	12.2705	0.807337
$232$	5.32784	0.349790
$233$	−6.12405	−0.401200	−0.200600	−	0.979673i	$-0.564289\pi$
$233$	−6.12405	−0.401200	−0.200600	+	0.979673i	$0.564289\pi$
$234$	14.6289	0.956323
$235$	−5.13774	−0.335149
$236$	−3.50324	−0.228042
$237$	−15.6927	−1.01935
$238$	−24.4011	−1.58169
$239$	−17.5141	−1.13289	−0.566447	−	0.824099i	$-0.691682\pi$
$239$	−17.5141	−1.13289	−0.566447	+	0.824099i	$0.691682\pi$
$240$	14.6783	0.947477
$241$	14.9483	0.962906	0.481453	−	0.876472i	$-0.340109\pi$
$241$	14.9483	0.962906	0.481453	+	0.876472i	$0.340109\pi$
$242$	−1.83787	−0.118143
$243$	−2.44449	−0.156814
$244$	5.22009	0.334182
$245$	9.48768	0.606146
$246$	69.8298	4.45219
$247$	−3.56126	−0.226598
$248$	7.88121	0.500458
$249$	36.1588	2.29147
$250$	−1.83787	−0.116237
$251$	−19.4423	−1.22719	−0.613593	−	0.789623i	$-0.710276\pi$
$251$	−19.4423	−1.22719	−0.613593	+	0.789623i	$0.710276\pi$
$252$	34.3049	2.16100
$253$	−0.430174	−0.0270448
$254$	8.64407	0.542377
$255$	−9.88086	−0.618763
$256$	20.9777	1.31111
$257$	0.570465	0.0355846	0.0177923	−	0.999842i	$-0.494336\pi$
$257$	0.570465	0.0355846	0.0177923	+	0.999842i	$0.494336\pi$
$258$	65.3701	4.06977
$259$	−20.6467	−1.28292
$260$	−1.78846	−0.110916
$261$	28.5685	1.76835
$262$	25.9144	1.60100
$263$	9.36122	0.577238	0.288619	−	0.957444i	$-0.406804\pi$
$263$	9.36122	0.577238	0.288619	+	0.957444i	$0.406804\pi$
$264$	3.45574	0.212686
$265$	10.1485	0.623419
$266$	−20.4738	−1.25533
$267$	−20.3061	−1.24271
$268$	−13.6015	−0.830844
$269$	10.5361	0.642397	0.321199	−	0.947012i	$-0.395914\pi$
$269$	10.5361	0.642397	0.321199	+	0.947012i	$0.395914\pi$
$270$	17.3943	1.05858
$271$	−2.20171	−0.133744	−0.0668722	−	0.997762i	$-0.521302\pi$
$271$	−2.20171	−0.133744	−0.0668722	+	0.997762i	$0.521302\pi$
$272$	−15.8821	−0.962992
$273$	15.9280	0.964007
$274$	30.7471	1.85750
$275$	−1.00000	−0.0603023
$276$	−1.79104	−0.107808
$277$	5.52008	0.331669	0.165835	−	0.986154i	$-0.446968\pi$
$277$	5.52008	0.331669	0.165835	+	0.986154i	$0.446968\pi$
$278$	14.0889	0.844993
$279$	42.2600	2.53004
$280$	4.64344	0.277499
$281$	2.16841	0.129356	0.0646782	−	0.997906i	$-0.479398\pi$
$281$	2.16841	0.129356	0.0646782	+	0.997906i	$0.479398\pi$
$282$	−28.5344	−1.69920
$283$	4.90207	0.291398	0.145699	−	0.989329i	$-0.453457\pi$
$283$	4.90207	0.291398	0.145699	+	0.989329i	$0.453457\pi$
$284$	7.85573	0.466152
$285$	−8.29057	−0.491091
$286$	−2.38570	−0.141069
$287$	51.0533	3.01358
$288$	40.7156	2.39919
$289$	−6.30878	−0.371105
$290$	−8.56262	−0.502814
$291$	54.8403	3.21480
$292$	−1.37778	−0.0806285
$293$	29.8775	1.74546	0.872732	−	0.488200i	$-0.162346\pi$
$293$	29.8775	1.74546	0.872732	+	0.488200i	$0.162346\pi$
$294$	52.6935	3.07315
$295$	−2.54267	−0.148040
$296$	−5.81473	−0.337975
$297$	9.46437	0.549178
$298$	−6.65288	−0.385391
$299$	−0.558398	−0.0322930
$300$	−4.16352	−0.240381
$301$	47.7928	2.75473
$302$	−27.5431	−1.58493
$303$	−56.8246	−3.26449
$304$	−13.3259	−0.764293
$305$	3.78877	0.216944
$306$	−36.8490	−2.10652
$307$	−16.3968	−0.935816	−0.467908	−	0.883777i	$-0.654992\pi$
$307$	−16.3968	−0.935816	−0.467908	+	0.883777i	$0.654992\pi$
$308$	−5.59448	−0.318775
$309$	−17.4462	−0.992478
$310$	−12.6663	−0.719396
$311$	20.1282	1.14137	0.570683	−	0.821170i	$-0.306679\pi$
$311$	20.1282	1.14137	0.570683	+	0.821170i	$0.306679\pi$
$312$	4.48582	0.253959
$313$	−29.4167	−1.66273	−0.831365	−	0.555726i	$-0.812440\pi$
$313$	−29.4167	−1.66273	−0.831365	+	0.555726i	$0.812440\pi$
$314$	7.33400	0.413882
$315$	24.8987	1.40288
$316$	7.15477	0.402487
$317$	−24.9531	−1.40150	−0.700752	−	0.713405i	$-0.747152\pi$
$317$	−24.9531	−1.40150	−0.700752	+	0.713405i	$0.747152\pi$
$318$	56.3637	3.16072
$319$	−4.65898	−0.260853
$320$	−2.48882	−0.139129
$321$	−12.1148	−0.676180
$322$	−3.21025	−0.178900
$323$	8.97051	0.499133
$324$	14.0598	0.781100
$325$	−1.29808	−0.0720044
$326$	31.2705	1.73191
$327$	−30.3407	−1.67784
$328$	14.3782	0.793902
$329$	−20.8618	−1.15015
$330$	−5.55388	−0.305731
$331$	−12.5359	−0.689037	−0.344518	−	0.938780i	$-0.611958\pi$
$331$	−12.5359	−0.689037	−0.344518	+	0.938780i	$0.611958\pi$
$332$	−16.4859	−0.904782
$333$	−31.1793	−1.70862
$334$	−40.0890	−2.19357
$335$	−9.87204	−0.539367
$336$	59.6011	3.25151
$337$	31.1164	1.69502	0.847509	−	0.530781i	$-0.178101\pi$
$337$	31.1164	1.69502	0.847509	+	0.530781i	$0.178101\pi$
$338$	20.7955	1.13113
$339$	0.399186	0.0216808
$340$	4.50499	0.244317
$341$	−6.89181	−0.373212
$342$	−30.9183	−1.67187
$343$	10.1012	0.545416
$344$	13.4599	0.725710
$345$	−1.29994	−0.0699866
$346$	−4.70438	−0.252909
$347$	4.25660	0.228506	0.114253	−	0.993452i	$-0.463552\pi$
$347$	4.25660	0.228506	0.114253	+	0.993452i	$0.463552\pi$
$348$	−19.3978	−1.03983
$349$	28.7330	1.53804	0.769022	−	0.639223i	$-0.220744\pi$
$349$	28.7330	1.53804	0.769022	+	0.639223i	$0.220744\pi$
$350$	−7.46269	−0.398898
$351$	12.2855	0.655751
$352$	−6.63995	−0.353910
$353$	6.98673	0.371866	0.185933	−	0.982562i	$-0.440469\pi$
$353$	6.98673	0.371866	0.185933	+	0.982562i	$0.440469\pi$
$354$	−14.1217	−0.750560
$355$	5.70174	0.302617
$356$	9.25818	0.490682
$357$	−40.1213	−2.12344
$358$	−0.970586	−0.0512971
$359$	−35.5167	−1.87450	−0.937249	−	0.348662i	$-0.886636\pi$
$359$	−35.5167	−1.87450	−0.937249	+	0.348662i	$0.886636\pi$
$360$	7.01223	0.369577
$361$	−11.4733	−0.603856
$362$	38.3410	2.01516
$363$	−3.02191	−0.158609
$364$	−7.26206	−0.380636
$365$	−1.00000	−0.0523424
$366$	21.0424	1.09990
$367$	5.02885	0.262504	0.131252	−	0.991349i	$-0.458100\pi$
$367$	5.02885	0.262504	0.131252	+	0.991349i	$0.458100\pi$
$368$	−2.08947	−0.108921
$369$	77.0976	4.01354
$370$	9.34514	0.485830
$371$	41.2081	2.13942
$372$	−28.6942	−1.48772
$373$	−17.0528	−0.882962	−0.441481	−	0.897271i	$-0.645547\pi$
$373$	−17.0528	−0.882962	−0.441481	+	0.897271i	$0.645547\pi$
$374$	6.00938	0.310737
$375$	−3.02191	−0.156051
$376$	−5.87533	−0.302997
$377$	−6.04772	−0.311473
$378$	70.6297	3.63280
$379$	−31.9363	−1.64046	−0.820228	−	0.572037i	$-0.806153\pi$
$379$	−31.9363	−1.64046	−0.820228	+	0.572037i	$0.806153\pi$
$380$	3.77993	0.193906
$381$	14.2129	0.728150
$382$	−20.7822	−1.06331
$383$	−30.6656	−1.56694	−0.783468	−	0.621432i	$-0.786551\pi$
$383$	−30.6656	−1.56694	−0.783468	+	0.621432i	$0.786551\pi$
$384$	26.3080	1.34252
$385$	−4.06050	−0.206942
$386$	−2.39290	−0.121795
$387$	72.1737	3.66880
$388$	−25.0034	−1.26935
$389$	23.1980	1.17619	0.588094	−	0.808793i	$-0.299879\pi$
$389$	23.1980	1.17619	0.588094	+	0.808793i	$0.299879\pi$
$390$	−7.20937	−0.365061
$391$	1.40656	0.0711327
$392$	10.8498	0.547995
$393$	42.6095	2.14937
$394$	1.58416	0.0798090
$395$	5.19297	0.261287
$396$	−8.44843	−0.424550
$397$	9.06741	0.455080	0.227540	−	0.973769i	$-0.426932\pi$
$397$	9.06741	0.455080	0.227540	+	0.973769i	$0.426932\pi$
$398$	20.3522	1.02017
$399$	−33.6639	−1.68530
$400$	−4.85728	−0.242864
$401$	3.52967	0.176263	0.0881317	−	0.996109i	$-0.471910\pi$
$401$	3.52967	0.176263	0.0881317	+	0.996109i	$0.471910\pi$
$402$	−54.8282	−2.73458
$403$	−8.94610	−0.445637
$404$	25.9081	1.28897
$405$	10.2047	0.507075
$406$	−34.7685	−1.72553
$407$	5.08475	0.252042
$408$	−11.2994	−0.559403
$409$	22.1451	1.09501	0.547503	−	0.836803i	$-0.315578\pi$
$409$	22.1451	1.09501	0.547503	+	0.836803i	$0.315578\pi$
$410$	−23.1079	−1.14122
$411$	50.5557	2.49373
$412$	7.95425	0.391878
$413$	−10.3245	−0.508037
$414$	−4.84792	−0.238262
$415$	−11.9656	−0.587367
$416$	−8.61916	−0.422589
$417$	23.1655	1.13442
$418$	5.04219	0.246622
$419$	−10.6471	−0.520146	−0.260073	−	0.965589i	$-0.583747\pi$
$419$	−10.6471	−0.520146	−0.260073	+	0.965589i	$0.583747\pi$
$420$	−16.9060	−0.824928
$421$	−8.40422	−0.409597	−0.204798	−	0.978804i	$-0.565654\pi$
$421$	−8.40422	−0.409597	−0.204798	+	0.978804i	$0.565654\pi$
$422$	38.5689	1.87751
$423$	−31.5042	−1.53179
$424$	11.6055	0.563611
$425$	3.26974	0.158606
$426$	31.6668	1.53426
$427$	15.3843	0.744499
$428$	5.52349	0.266988
$429$	−3.92267	−0.189388
$430$	−21.6321	−1.04319
$431$	26.1731	1.26071	0.630357	−	0.776306i	$-0.282909\pi$
$431$	26.1731	1.26071	0.630357	+	0.776306i	$0.282909\pi$
$432$	45.9711	2.21179
$433$	−39.3399	−1.89055	−0.945277	−	0.326270i	$-0.894208\pi$
$433$	−39.3399	−1.89055	−0.945277	+	0.326270i	$0.894208\pi$
$434$	−51.4314	−2.46879
$435$	−14.0790	−0.675037
$436$	13.8332	0.662492
$437$	1.18018	0.0564555
$438$	−5.55388	−0.265375
$439$	−9.91856	−0.473387	−0.236694	−	0.971584i	$-0.576064\pi$
$439$	−9.91856	−0.473387	−0.236694	+	0.971584i	$0.576064\pi$
$440$	−1.14356	−0.0545172
$441$	58.1777	2.77037
$442$	7.80063	0.371038
$443$	15.0588	0.715466	0.357733	−	0.933824i	$-0.383550\pi$
$443$	15.0588	0.715466	0.357733	+	0.933824i	$0.383550\pi$
$444$	21.1705	1.00471
$445$	6.71964	0.318541
$446$	−34.3190	−1.62505
$447$	−10.9389	−0.517394
$448$	−10.1059	−0.477457
$449$	24.3573	1.14949	0.574745	−	0.818332i	$-0.305101\pi$
$449$	24.3573	1.14949	0.574745	+	0.818332i	$0.305101\pi$
$450$	−11.2697	−0.531258
$451$	−12.5732	−0.592047
$452$	−0.182001	−0.00856061
$453$	−45.2875	−2.12779
$454$	−10.2683	−0.481914
$455$	−5.27085	−0.247101
$456$	−9.48079	−0.443979
$457$	1.59552	0.0746353	0.0373177	−	0.999303i	$-0.488119\pi$
$457$	1.59552	0.0746353	0.0373177	+	0.999303i	$0.488119\pi$
$458$	24.8746	1.16231
$459$	−30.9461	−1.44444
$460$	0.592684	0.0276340
$461$	−24.1401	−1.12432	−0.562159	−	0.827029i	$-0.690029\pi$
$461$	−24.1401	−1.12432	−0.562159	+	0.827029i	$0.690029\pi$
$462$	−22.5516	−1.04919
$463$	−1.33172	−0.0618903	−0.0309451	−	0.999521i	$-0.509852\pi$
$463$	−1.33172	−0.0618903	−0.0309451	+	0.999521i	$0.509852\pi$
$464$	−22.6300	−1.05057
$465$	−20.8264	−0.965801
$466$	11.2552	0.521388
$467$	−16.2323	−0.751142	−0.375571	−	0.926794i	$-0.622553\pi$
$467$	−16.2323	−0.751142	−0.375571	+	0.926794i	$0.622553\pi$
$468$	−10.9667	−0.506937
$469$	−40.0855	−1.85097
$470$	9.44252	0.435551
$471$	12.0589	0.555643
$472$	−2.90770	−0.133838
$473$	−11.7702	−0.541193
$474$	28.8412	1.32472
$475$	2.74349	0.125880
$476$	18.2925	0.838436
$477$	62.2299	2.84931
$478$	32.1887	1.47228
$479$	−2.34314	−0.107061	−0.0535305	−	0.998566i	$-0.517047\pi$
$479$	−2.34314	−0.107061	−0.0535305	+	0.998566i	$0.517047\pi$
$480$	−20.0653	−0.915851
$481$	6.60040	0.300952
$482$	−27.4731	−1.25137
$483$	−5.27843	−0.240177
$484$	1.37778	0.0626263
$485$	−18.1476	−0.824039
$486$	4.49266	0.203791
$487$	−37.5886	−1.70330	−0.851651	−	0.524109i	$-0.824398\pi$
$487$	−37.5886	−1.70330	−0.851651	+	0.524109i	$0.824398\pi$
$488$	4.33270	0.196132
$489$	51.4163	2.32512
$490$	−17.4372	−0.787731
$491$	−23.7250	−1.07069	−0.535347	−	0.844632i	$-0.679819\pi$
$491$	−23.7250	−1.07069	−0.535347	+	0.844632i	$0.679819\pi$
$492$	−52.3486	−2.36006
$493$	15.2337	0.686090
$494$	6.54515	0.294480
$495$	−6.13192	−0.275609
$496$	−33.4755	−1.50309
$497$	23.1519	1.03851
$498$	−66.4554	−2.97794
$499$	3.05942	0.136958	0.0684792	−	0.997653i	$-0.478185\pi$
$499$	3.05942	0.136958	0.0684792	+	0.997653i	$0.478185\pi$
$500$	1.37778	0.0616162
$501$	−65.9160	−2.94491
$502$	35.7324	1.59482
$503$	10.0927	0.450010	0.225005	−	0.974358i	$-0.427760\pi$
$503$	10.0927	0.450010	0.225005	+	0.974358i	$0.427760\pi$
$504$	28.4732	1.26830
$505$	18.8042	0.836777
$506$	0.790605	0.0351467
$507$	34.1929	1.51856
$508$	−6.48011	−0.287508
$509$	17.0014	0.753572	0.376786	−	0.926300i	$-0.377029\pi$
$509$	17.0014	0.753572	0.376786	+	0.926300i	$0.377029\pi$
$510$	18.1598	0.804128
$511$	−4.06050	−0.179626
$512$	−21.1429	−0.934392
$513$	−25.9654	−1.14640
$514$	−1.04844	−0.0462448
$515$	5.77324	0.254399
$516$	−49.0053	−2.15734
$517$	5.13774	0.225958
$518$	37.9459	1.66725
$519$	−7.73514	−0.339535
$520$	−1.48443	−0.0650967
$521$	8.73002	0.382469	0.191234	−	0.981544i	$-0.438751\pi$
$521$	8.73002	0.382469	0.191234	+	0.981544i	$0.438751\pi$
$522$	−52.5053	−2.29810
$523$	5.89849	0.257923	0.128961	−	0.991650i	$-0.458836\pi$
$523$	5.89849	0.257923	0.128961	+	0.991650i	$0.458836\pi$
$524$	−19.4270	−0.848671
$525$	−12.2705	−0.535527
$526$	−17.2047	−0.750163
$527$	22.5344	0.981616
$528$	−14.6783	−0.638789
$529$	−22.8150	−0.991954
$530$	−18.6517	−0.810178
$531$	−15.5915	−0.676612
$532$	15.3484	0.665437
$533$	−16.3209	−0.706937
$534$	37.3201	1.61500
$535$	4.00898	0.173323
$536$	−11.2893	−0.487623
$537$	−1.59588	−0.0688672
$538$	−19.3640	−0.834842
$539$	−9.48768	−0.408663
$540$	−13.0398	−0.561144
$541$	16.9098	0.727010	0.363505	−	0.931592i	$-0.381580\pi$
$541$	16.9098	0.727010	0.363505	+	0.931592i	$0.381580\pi$
$542$	4.04646	0.173811
$543$	63.0419	2.70538
$544$	21.7109	0.930848
$545$	10.0402	0.430077
$546$	−29.2737	−1.25280
$547$	17.5563	0.750653	0.375327	−	0.926893i	$-0.377531\pi$
$547$	17.5563	0.750653	0.375327	+	0.926893i	$0.377531\pi$
$548$	−23.0499	−0.984642
$549$	23.2325	0.991537
$550$	1.83787	0.0783672
$551$	12.7819	0.544526
$552$	−1.48657	−0.0632725
$553$	21.0861	0.896672
$554$	−10.1452	−0.431029
$555$	15.3657	0.652236
$556$	−10.5618	−0.447922
$557$	15.3065	0.648559	0.324280	−	0.945961i	$-0.394878\pi$
$557$	15.3065	0.648559	0.324280	+	0.945961i	$0.394878\pi$
$558$	−77.6686	−3.28797
$559$	−15.2786	−0.646215
$560$	−19.7230	−0.833449
$561$	9.88086	0.417170
$562$	−3.98526	−0.168108
$563$	−15.9399	−0.671787	−0.335893	−	0.941900i	$-0.609038\pi$
$563$	−15.9399	−0.671787	−0.335893	+	0.941900i	$0.609038\pi$
$564$	21.3911	0.900728
$565$	−0.132097	−0.00555738
$566$	−9.00938	−0.378693
$567$	41.4361	1.74015
$568$	6.52029	0.273585
$569$	33.5105	1.40483	0.702416	−	0.711767i	$-0.252105\pi$
$569$	33.5105	1.40483	0.702416	+	0.711767i	$0.252105\pi$
$570$	15.2370	0.638209
$571$	−28.7498	−1.20314	−0.601570	−	0.798820i	$-0.705458\pi$
$571$	−28.7498	−1.20314	−0.601570	+	0.798820i	$0.705458\pi$
$572$	1.78846	0.0747794
$573$	−34.1709	−1.42751
$574$	−93.8295	−3.91637
$575$	0.430174	0.0179395
$576$	−15.2612	−0.635885
$577$	15.2530	0.634992	0.317496	−	0.948260i	$-0.397158\pi$
$577$	15.2530	0.634992	0.317496	+	0.948260i	$0.397158\pi$
$578$	11.5947	0.482277
$579$	−3.93450	−0.163512
$580$	6.41905	0.266537
$581$	−48.5862	−2.01570
$582$	−100.790	−4.17786
$583$	−10.1485	−0.420309
$584$	−1.14356	−0.0473210
$585$	−7.95970	−0.329093
$586$	−54.9111	−2.26836
$587$	−32.4360	−1.33878	−0.669388	−	0.742913i	$-0.733444\pi$
$587$	−32.4360	−1.33878	−0.669388	+	0.742913i	$0.733444\pi$
$588$	−39.5022	−1.62904
$589$	18.9076	0.779075
$590$	4.67311	0.192389
$591$	2.60475	0.107145
$592$	24.6981	1.01509
$593$	28.2890	1.16169	0.580845	−	0.814014i	$-0.302722\pi$
$593$	28.2890	1.16169	0.580845	+	0.814014i	$0.302722\pi$
$594$	−17.3943	−0.713697
$595$	13.2768	0.544296
$596$	4.98740	0.204292
$597$	33.4640	1.36959
$598$	1.02627	0.0419671
$599$	32.3531	1.32191	0.660957	−	0.750424i	$-0.270151\pi$
$599$	32.3531	1.32191	0.660957	+	0.750424i	$0.270151\pi$
$600$	−3.45574	−0.141080
$601$	40.0585	1.63402	0.817010	−	0.576624i	$-0.195630\pi$
$601$	40.0585	1.63402	0.817010	+	0.576624i	$0.195630\pi$
$602$	−87.8371	−3.57997
$603$	−60.5346	−2.46516
$604$	20.6479	0.840152
$605$	1.00000	0.0406558
$606$	104.436	4.24244
$607$	−39.3092	−1.59551	−0.797755	−	0.602982i	$-0.793979\pi$
$607$	−39.3092	−1.59551	−0.797755	+	0.602982i	$0.793979\pi$
$608$	18.2166	0.738782
$609$	−57.1679	−2.31656
$610$	−6.96329	−0.281935
$611$	6.66919	0.269806
$612$	27.6242	1.11664
$613$	46.0351	1.85934	0.929671	−	0.368392i	$-0.120092\pi$
$613$	46.0351	1.85934	0.929671	+	0.368392i	$0.120092\pi$
$614$	30.1353	1.21616
$615$	−37.9949	−1.53210
$616$	−4.64344	−0.187089
$617$	23.4296	0.943240	0.471620	−	0.881802i	$-0.343669\pi$
$617$	23.4296	0.943240	0.471620	+	0.881802i	$0.343669\pi$
$618$	32.0639	1.28980
$619$	16.1738	0.650080	0.325040	−	0.945700i	$-0.394622\pi$
$619$	16.1738	0.650080	0.325040	+	0.945700i	$0.394622\pi$
$620$	9.49539	0.381344
$621$	−4.07132	−0.163377
$622$	−36.9931	−1.48329
$623$	27.2851	1.09315
$624$	−19.0535	−0.762751
$625$	1.00000	0.0400000
$626$	54.0642	2.16084
$627$	8.29057	0.331094
$628$	−5.49800	−0.219394
$629$	−16.6258	−0.662916
$630$	−45.7606	−1.82315
$631$	34.2606	1.36389	0.681947	−	0.731402i	$-0.261133\pi$
$631$	34.2606	1.36389	0.681947	+	0.731402i	$0.261133\pi$
$632$	5.93849	0.236220
$633$	63.4166	2.52058
$634$	45.8606	1.82136
$635$	−4.70330	−0.186645
$636$	−42.2536	−1.67546
$637$	−12.3157	−0.487967
$638$	8.56262	0.338997
$639$	34.9626	1.38310
$640$	−8.70576	−0.344125
$641$	23.9922	0.947637	0.473818	−	0.880623i	$-0.342875\pi$
$641$	23.9922	0.947637	0.473818	+	0.880623i	$0.342875\pi$
$642$	22.2654	0.878745
$643$	−18.4169	−0.726291	−0.363146	−	0.931732i	$-0.618297\pi$
$643$	−18.4169	−0.726291	−0.363146	+	0.931732i	$0.618297\pi$
$644$	2.40660	0.0948332
$645$	−35.5683	−1.40050
$646$	−16.4867	−0.648659
$647$	12.1824	0.478940	0.239470	−	0.970904i	$-0.423026\pi$
$647$	12.1824	0.478940	0.239470	+	0.970904i	$0.423026\pi$
$648$	11.6697	0.458429
$649$	2.54267	0.0998086
$650$	2.38570	0.0935749
$651$	−84.5657	−3.31439
$652$	−23.4422	−0.918069
$653$	−5.60044	−0.219162	−0.109581	−	0.993978i	$-0.534951\pi$
$653$	−5.60044	−0.219162	−0.109581	+	0.993978i	$0.534951\pi$
$654$	55.7623	2.18048
$655$	−14.1002	−0.550941
$656$	−61.0713	−2.38444
$657$	−6.13192	−0.239229
$658$	38.3414	1.49470
$659$	−24.8425	−0.967725	−0.483863	−	0.875144i	$-0.660767\pi$
$659$	−24.8425	−0.967725	−0.483863	+	0.875144i	$0.660767\pi$
$660$	4.16352	0.162065
$661$	46.2735	1.79983	0.899915	−	0.436065i	$-0.143628\pi$
$661$	46.2735	1.79983	0.899915	+	0.436065i	$0.143628\pi$
$662$	23.0394	0.895453
$663$	12.8261	0.498125
$664$	−13.6834	−0.531018
$665$	11.1400	0.431989
$666$	57.3036	2.22047
$667$	2.00417	0.0776018
$668$	30.0531	1.16279
$669$	−56.4287	−2.18166
$670$	18.1436	0.700947
$671$	−3.78877	−0.146264
$672$	−81.4752	−3.14297
$673$	35.9970	1.38758	0.693792	−	0.720176i	$-0.255939\pi$
$673$	35.9970	1.38758	0.693792	+	0.720176i	$0.255939\pi$
$674$	−57.1880	−2.20280
$675$	−9.46437	−0.364284
$676$	−15.5896	−0.599599
$677$	1.99399	0.0766354	0.0383177	−	0.999266i	$-0.487800\pi$
$677$	1.99399	0.0766354	0.0383177	+	0.999266i	$0.487800\pi$
$678$	−0.733653	−0.0281758
$679$	−73.6883	−2.82790
$680$	3.73916	0.143390
$681$	−16.8835	−0.646977
$682$	12.6663	0.485017
$683$	1.93167	0.0739135	0.0369567	−	0.999317i	$-0.488234\pi$
$683$	1.93167	0.0739135	0.0369567	+	0.999317i	$0.488234\pi$
$684$	23.1782	0.886241
$685$	−16.7297	−0.639210
$686$	−18.5648	−0.708807
$687$	40.8998	1.56042
$688$	−57.1710	−2.17963
$689$	−13.1736	−0.501873
$690$	2.38913	0.0909528
$691$	−21.1788	−0.805678	−0.402839	−	0.915271i	$-0.631977\pi$
$691$	−21.1788	−0.805678	−0.402839	+	0.915271i	$0.631977\pi$
$692$	3.52669	0.134064
$693$	−24.8987	−0.945823
$694$	−7.82310	−0.296961
$695$	−7.66584	−0.290782
$696$	−16.1002	−0.610278
$697$	41.1110	1.55719
$698$	−52.8077	−1.99880
$699$	18.5063	0.699973
$700$	5.59448	0.211451
$701$	−8.81302	−0.332863	−0.166432	−	0.986053i	$-0.553224\pi$
$701$	−8.81302	−0.332863	−0.166432	+	0.986053i	$0.553224\pi$
$702$	−22.5792	−0.852196
$703$	−13.9500	−0.526133
$704$	2.48882	0.0938008
$705$	15.5258	0.584735
$706$	−12.8407	−0.483267
$707$	76.3546	2.87161
$708$	10.5865	0.397864
$709$	22.8473	0.858050	0.429025	−	0.903293i	$-0.358857\pi$
$709$	22.8473	0.858050	0.429025	+	0.903293i	$0.358857\pi$
$710$	−10.4791	−0.393272
$711$	31.8429	1.19420
$712$	7.68432	0.287982
$713$	2.96467	0.111028
$714$	73.7378	2.75957
$715$	1.29808	0.0485453
$716$	0.727609	0.0271920
$717$	52.9260	1.97656
$718$	65.2751	2.43605
$719$	44.7326	1.66824	0.834122	−	0.551581i	$-0.185975\pi$
$719$	44.7326	1.66824	0.834122	+	0.551581i	$0.185975\pi$
$720$	−29.7845	−1.11000
$721$	23.4422	0.873034
$722$	21.0864	0.784755
$723$	−45.1724	−1.67998
$724$	−28.7427	−1.06821
$725$	4.65898	0.173030
$726$	5.55388	0.206124
$727$	−29.7793	−1.10445	−0.552227	−	0.833694i	$-0.686222\pi$
$727$	−29.7793	−1.10445	−0.552227	+	0.833694i	$0.686222\pi$
$728$	−6.02754	−0.223396
$729$	−23.2270	−0.860260
$730$	1.83787	0.0680228
$731$	38.4854	1.42343
$732$	−15.7746	−0.583047
$733$	1.20460	0.0444928	0.0222464	−	0.999753i	$-0.492918\pi$
$733$	1.20460	0.0444928	0.0222464	+	0.999753i	$0.492918\pi$
$734$	−9.24238	−0.341143
$735$	−28.6709	−1.05754
$736$	2.85633	0.105286
$737$	9.87204	0.363641
$738$	−141.696	−5.21589
$739$	−37.5911	−1.38281	−0.691406	−	0.722467i	$-0.743008\pi$
$739$	−37.5911	−1.38281	−0.691406	+	0.722467i	$0.743008\pi$
$740$	−7.00567	−0.257534
$741$	10.7618	0.395345
$742$	−75.7353	−2.78033
$743$	29.8069	1.09351	0.546755	−	0.837293i	$-0.315863\pi$
$743$	29.8069	1.09351	0.546755	+	0.837293i	$0.315863\pi$
$744$	−23.8163	−0.873148
$745$	3.61988	0.132622
$746$	31.3409	1.14747
$747$	−73.3719	−2.68454
$748$	−4.50499	−0.164719
$749$	16.2785	0.594802
$750$	5.55388	0.202799
$751$	3.60940	0.131709	0.0658544	−	0.997829i	$-0.479023\pi$
$751$	3.60940	0.131709	0.0658544	+	0.997829i	$0.479023\pi$
$752$	24.9555	0.910032
$753$	58.7527	2.14107
$754$	11.1149	0.404782
$755$	14.9864	0.545410
$756$	−52.9482	−1.92571
$757$	46.7101	1.69771	0.848853	−	0.528629i	$-0.177294\pi$
$757$	46.7101	1.69771	0.848853	+	0.528629i	$0.177294\pi$
$758$	58.6948	2.13189
$759$	1.29994	0.0471850
$760$	3.13735	0.113804
$761$	−9.20578	−0.333709	−0.166855	−	0.985982i	$-0.553361\pi$
$761$	−9.20578	−0.333709	−0.166855	+	0.985982i	$0.553361\pi$
$762$	−26.1216	−0.946284
$763$	40.7684	1.47592
$764$	15.5796	0.563649
$765$	20.0498	0.724902
$766$	56.3594	2.03635
$767$	3.30058	0.119177
$768$	−63.3927	−2.28749
$769$	23.5365	0.848746	0.424373	−	0.905487i	$-0.360494\pi$
$769$	23.5365	0.848746	0.424373	+	0.905487i	$0.360494\pi$
$770$	7.46269	0.268937
$771$	−1.72389	−0.0620844
$772$	1.79386	0.0645624
$773$	49.2280	1.77061	0.885305	−	0.465011i	$-0.153950\pi$
$773$	49.2280	1.77061	0.885305	+	0.465011i	$0.153950\pi$
$774$	−132.646	−4.76787
$775$	6.89181	0.247561
$776$	−20.7529	−0.744986
$777$	62.3923	2.23831
$778$	−42.6351	−1.52854
$779$	34.4943	1.23589
$780$	5.40457	0.193515
$781$	−5.70174	−0.204024
$782$	−2.58507	−0.0924421
$783$	−44.0943	−1.57580
$784$	−46.0843	−1.64587
$785$	−3.99048	−0.142426
$786$	−78.3109	−2.79326
$787$	−40.8494	−1.45612	−0.728061	−	0.685512i	$-0.759578\pi$
$787$	−40.8494	−1.45612	−0.728061	+	0.685512i	$0.759578\pi$
$788$	−1.18758	−0.0423059
$789$	−28.2887	−1.00711
$790$	−9.54403	−0.339561
$791$	−0.536382	−0.0190715
$792$	−7.01223	−0.249169
$793$	−4.91812	−0.174648
$794$	−16.6648	−0.591410
$795$	−30.6679	−1.08768
$796$	−15.2573	−0.540779
$797$	−18.3707	−0.650725	−0.325362	−	0.945589i	$-0.605486\pi$
$797$	−18.3707	−0.650725	−0.325362	+	0.945589i	$0.605486\pi$
$798$	61.8700	2.19017
$799$	−16.7991	−0.594310
$800$	6.63995	0.234758
$801$	41.2043	1.45588
$802$	−6.48709	−0.229067
$803$	1.00000	0.0352892
$804$	41.1025	1.44957
$805$	1.74672	0.0615638
$806$	16.4418	0.579138
$807$	−31.8391	−1.12079
$808$	21.5038	0.756501
$809$	−15.7575	−0.554005	−0.277003	−	0.960869i	$-0.589341\pi$
$809$	−15.7575	−0.554005	−0.277003	+	0.960869i	$0.589341\pi$
$810$	−18.7549	−0.658981
$811$	38.3779	1.34763	0.673816	−	0.738900i	$-0.264654\pi$
$811$	38.3779	1.34763	0.673816	+	0.738900i	$0.264654\pi$
$812$	26.0646	0.914687
$813$	6.65336	0.233344
$814$	−9.34514	−0.327547
$815$	−17.0145	−0.595992
$816$	47.9941	1.68013
$817$	32.2913	1.12973
$818$	−40.7000	−1.42304
$819$	−32.3204	−1.12937
$820$	17.3230	0.604946
$821$	−16.5754	−0.578486	−0.289243	−	0.957256i	$-0.593404\pi$
$821$	−16.5754	−0.578486	−0.289243	+	0.957256i	$0.593404\pi$
$822$	−92.9149	−3.24078
$823$	−30.6181	−1.06728	−0.533640	−	0.845712i	$-0.679176\pi$
$823$	−30.6181	−1.06728	−0.533640	+	0.845712i	$0.679176\pi$
$824$	6.60206	0.229994
$825$	3.02191	0.105209
$826$	18.9752	0.660231
$827$	−49.3891	−1.71743	−0.858714	−	0.512455i	$-0.828736\pi$
$827$	−49.3891	−1.71743	−0.858714	+	0.512455i	$0.828736\pi$
$828$	3.63429	0.126300
$829$	21.9977	0.764011	0.382006	−	0.924160i	$-0.375233\pi$
$829$	21.9977	0.764011	0.382006	+	0.924160i	$0.375233\pi$
$830$	21.9912	0.763326
$831$	−16.6812	−0.578663
$832$	3.23068	0.112004
$833$	31.0223	1.07486
$834$	−42.5752	−1.47426
$835$	21.8127	0.754860
$836$	−3.77993	−0.130731
$837$	−65.2266	−2.25456
$838$	19.5681	0.675967
$839$	5.11758	0.176678	0.0883392	−	0.996090i	$-0.471844\pi$
$839$	5.11758	0.176678	0.0883392	+	0.996090i	$0.471844\pi$
$840$	−14.0320	−0.484151
$841$	−7.29388	−0.251513
$842$	15.4459	0.532301
$843$	−6.55273	−0.225688
$844$	−28.9136	−0.995246
$845$	−11.3150	−0.389248
$846$	57.9008	1.99067
$847$	4.06050	0.139521
$848$	−49.2942	−1.69277
$849$	−14.8136	−0.508401
$850$	−6.00938	−0.206120
$851$	−2.18733	−0.0749806
$852$	−23.7393	−0.813295
$853$	−20.6942	−0.708557	−0.354278	−	0.935140i	$-0.615273\pi$
$853$	−20.6942	−0.708557	−0.354278	+	0.935140i	$0.615273\pi$
$854$	−28.2744	−0.967531
$855$	16.8229	0.575330
$856$	4.58452	0.156696
$857$	−14.2311	−0.486124	−0.243062	−	0.970011i	$-0.578152\pi$
$857$	−14.2311	−0.486124	−0.243062	+	0.970011i	$0.578152\pi$
$858$	7.20937	0.246124
$859$	18.9367	0.646111	0.323056	−	0.946380i	$-0.395290\pi$
$859$	18.9367	0.646111	0.323056	+	0.946380i	$0.395290\pi$
$860$	16.2167	0.552985
$861$	−154.278	−5.25779
$862$	−48.1028	−1.63839
$863$	26.6157	0.906011	0.453005	−	0.891508i	$-0.350352\pi$
$863$	26.6157	0.906011	0.453005	+	0.891508i	$0.350352\pi$
$864$	−62.8429	−2.13796
$865$	2.55969	0.0870320
$866$	72.3017	2.45691
$867$	19.0645	0.647466
$868$	38.5561	1.30868
$869$	−5.19297	−0.176160
$870$	25.8754	0.877260
$871$	12.8147	0.434209
$872$	11.4816	0.388817
$873$	−111.280	−3.76624
$874$	−2.16902	−0.0733681
$875$	4.06050	0.137270
$876$	4.16352	0.140672
$877$	1.93430	0.0653167	0.0326584	−	0.999467i	$-0.489603\pi$
$877$	1.93430	0.0653167	0.0326584	+	0.999467i	$0.489603\pi$
$878$	18.2291	0.615201
$879$	−90.2871	−3.04531
$880$	4.85728	0.163739
$881$	−2.62189	−0.0883338	−0.0441669	−	0.999024i	$-0.514063\pi$
$881$	−2.62189	−0.0883338	−0.0441669	+	0.999024i	$0.514063\pi$
$882$	−106.923	−3.60029
$883$	−22.3795	−0.753129	−0.376564	−	0.926390i	$-0.622895\pi$
$883$	−22.3795	−0.753129	−0.376564	+	0.926390i	$0.622895\pi$
$884$	−5.84782	−0.196683
$885$	7.68372	0.258285
$886$	−27.6762	−0.929800
$887$	−4.97920	−0.167185	−0.0835926	−	0.996500i	$-0.526639\pi$
$887$	−4.97920	−0.167185	−0.0835926	+	0.996500i	$0.526639\pi$
$888$	17.5716	0.589664
$889$	−19.0978	−0.640518
$890$	−12.3498	−0.413968
$891$	−10.2047	−0.341870
$892$	25.7276	0.861423
$893$	−14.0953	−0.471683
$894$	20.1044	0.672391
$895$	0.528103	0.0176525
$896$	−35.3498	−1.18095
$897$	1.68743	0.0563416
$898$	−44.7656	−1.49385
$899$	32.1088	1.07089
$900$	8.44843	0.281614
$901$	33.1831	1.10549
$902$	23.1079	0.769408
$903$	−144.425	−4.80618
$904$	−0.151062	−0.00502423
$905$	−20.8616	−0.693464
$906$	83.2326	2.76522
$907$	4.77617	0.158590	0.0792950	−	0.996851i	$-0.474733\pi$
$907$	4.77617	0.158590	0.0792950	+	0.996851i	$0.474733\pi$
$908$	7.69770	0.255457
$909$	115.306	3.82446
$910$	9.68715	0.321126
$911$	4.98229	0.165071	0.0825353	−	0.996588i	$-0.473698\pi$
$911$	4.98229	0.165071	0.0825353	+	0.996588i	$0.473698\pi$
$912$	40.2697	1.33346
$913$	11.9656	0.396003
$914$	−2.93237	−0.0969940
$915$	−11.4493	−0.378503
$916$	−18.6475	−0.616130
$917$	−57.2539	−1.89069
$918$	56.8750	1.87715
$919$	−40.3651	−1.33152	−0.665762	−	0.746165i	$-0.731893\pi$
$919$	−40.3651	−1.33152	−0.665762	+	0.746165i	$0.731893\pi$
$920$	0.491930	0.0162185
$921$	49.5497	1.63272
$922$	44.3665	1.46113
$923$	−7.40129	−0.243617
$924$	16.9060	0.556166
$925$	−5.08475	−0.167186
$926$	2.44753	0.0804309
$927$	35.4010	1.16272
$928$	30.9354	1.01550
$929$	−13.1092	−0.430100	−0.215050	−	0.976603i	$-0.568991\pi$
$929$	−13.1092	−0.430100	−0.215050	+	0.976603i	$0.568991\pi$
$930$	38.2763	1.25513
$931$	26.0294	0.853078
$932$	−8.43759	−0.276382
$933$	−60.8256	−1.99134
$934$	29.8329	0.976164
$935$	−3.26974	−0.106932
$936$	−9.10242	−0.297522
$937$	−34.5199	−1.12772	−0.563858	−	0.825872i	$-0.690684\pi$
$937$	−34.5199	−1.12772	−0.563858	+	0.825872i	$0.690684\pi$
$938$	73.6720	2.40548
$939$	88.8945	2.90096
$940$	−7.07868	−0.230881
$941$	20.3390	0.663032	0.331516	−	0.943450i	$-0.392440\pi$
$941$	20.3390	0.663032	0.331516	+	0.943450i	$0.392440\pi$
$942$	−22.1627	−0.722099
$943$	5.40864	0.176129
$944$	12.3505	0.401974
$945$	−38.4301	−1.25013
$946$	21.6321	0.703320
$947$	−15.0278	−0.488339	−0.244169	−	0.969733i	$-0.578515\pi$
$947$	−15.0278	−0.488339	−0.244169	+	0.969733i	$0.578515\pi$
$948$	−21.6211	−0.702219
$949$	1.29808	0.0421374
$950$	−5.04219	−0.163590
$951$	75.4058	2.44520
$952$	15.1829	0.492079
$953$	13.5993	0.440526	0.220263	−	0.975441i	$-0.429308\pi$
$953$	13.5993	0.440526	0.220263	+	0.975441i	$0.429308\pi$
$954$	−114.371	−3.70289
$955$	11.3077	0.365910
$956$	−24.1306	−0.780438
$957$	14.0790	0.455110
$958$	4.30640	0.139133
$959$	−67.9311	−2.19361
$960$	7.52097	0.242738
$961$	16.4970	0.532162
$962$	−12.1307	−0.391110
$963$	24.5827	0.792168
$964$	20.5955	0.663336
$965$	1.30199	0.0419126
$966$	9.70108	0.312127
$967$	45.4041	1.46010	0.730049	−	0.683395i	$-0.239497\pi$
$967$	45.4041	1.46010	0.730049	+	0.683395i	$0.239497\pi$
$968$	1.14356	0.0367555
$969$	−27.1080	−0.870836
$970$	33.3530	1.07090
$971$	−2.44842	−0.0785735	−0.0392868	−	0.999228i	$-0.512509\pi$
$971$	−2.44842	−0.0785735	−0.0392868	+	0.999228i	$0.512509\pi$
$972$	−3.36797	−0.108028
$973$	−31.1272	−0.997892
$974$	69.0831	2.21357
$975$	3.92267	0.125626
$976$	−18.4031	−0.589070
$977$	13.7278	0.439191	0.219595	−	0.975591i	$-0.429526\pi$
$977$	13.7278	0.439191	0.219595	+	0.975591i	$0.429526\pi$
$978$	−94.4966	−3.02167
$979$	−6.71964	−0.214761
$980$	13.0719	0.417568
$981$	61.5659	1.96565
$982$	43.6035	1.39144
$983$	43.2081	1.37812	0.689062	−	0.724702i	$-0.258023\pi$
$983$	43.2081	1.37812	0.689062	+	0.724702i	$0.258023\pi$
$984$	−43.4495	−1.38512
$985$	−0.861954	−0.0274641
$986$	−27.9976	−0.891625
$987$	63.0425	2.00666
$988$	−4.90663	−0.156101
$989$	5.06321	0.161001
$990$	11.2697	0.358174
$991$	−34.7510	−1.10390	−0.551951	−	0.833876i	$-0.686117\pi$
$991$	−34.7510	−1.10390	−0.551951	+	0.833876i	$0.686117\pi$
$992$	45.7612	1.45292
$993$	37.8824	1.20216
$994$	−42.5503	−1.34961
$995$	−11.0738	−0.351063
$996$	49.8189	1.57857
$997$	−29.9773	−0.949390	−0.474695	−	0.880150i	$-0.657442\pi$
$997$	−29.9773	−0.949390	−0.474695	+	0.880150i	$0.657442\pi$
$998$	−5.62283	−0.177987
$999$	48.1240	1.52258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.i.1.7	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.i.1.7	✓	38	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)

\(f(q)\)	\(=\)	\(q-1.83787 q^{2} -3.02191 q^{3} +1.37778 q^{4} +1.00000 q^{5} +5.55388 q^{6} +4.06050 q^{7} +1.14356 q^{8} +6.13192 q^{9} +O(q^{10})\)	\(q-1.83787 q^{2} -3.02191 q^{3} +1.37778 q^{4} +1.00000 q^{5} +5.55388 q^{6} +4.06050 q^{7} +1.14356 q^{8} +6.13192 q^{9} -1.83787 q^{10} -1.00000 q^{11} -4.16352 q^{12} -1.29808 q^{13} -7.46269 q^{14} -3.02191 q^{15} -4.85728 q^{16} +3.26974 q^{17} -11.2697 q^{18} +2.74349 q^{19} +1.37778 q^{20} -12.2705 q^{21} +1.83787 q^{22} +0.430174 q^{23} -3.45574 q^{24} +1.00000 q^{25} +2.38570 q^{26} -9.46437 q^{27} +5.59448 q^{28} +4.65898 q^{29} +5.55388 q^{30} +6.89181 q^{31} +6.63995 q^{32} +3.02191 q^{33} -6.00938 q^{34} +4.06050 q^{35} +8.44843 q^{36} -5.08475 q^{37} -5.04219 q^{38} +3.92267 q^{39} +1.14356 q^{40} +12.5732 q^{41} +22.5516 q^{42} +11.7702 q^{43} -1.37778 q^{44} +6.13192 q^{45} -0.790605 q^{46} -5.13774 q^{47} +14.6783 q^{48} +9.48768 q^{49} -1.83787 q^{50} -9.88086 q^{51} -1.78846 q^{52} +10.1485 q^{53} +17.3943 q^{54} -1.00000 q^{55} +4.64344 q^{56} -8.29057 q^{57} -8.56262 q^{58} -2.54267 q^{59} -4.16352 q^{60} +3.78877 q^{61} -12.6663 q^{62} +24.8987 q^{63} -2.48882 q^{64} -1.29808 q^{65} -5.55388 q^{66} -9.87204 q^{67} +4.50499 q^{68} -1.29994 q^{69} -7.46269 q^{70} +5.70174 q^{71} +7.01223 q^{72} -1.00000 q^{73} +9.34514 q^{74} -3.02191 q^{75} +3.77993 q^{76} -4.06050 q^{77} -7.20937 q^{78} +5.19297 q^{79} -4.85728 q^{80} +10.2047 q^{81} -23.1079 q^{82} -11.9656 q^{83} -16.9060 q^{84} +3.26974 q^{85} -21.6321 q^{86} -14.0790 q^{87} -1.14356 q^{88} +6.71964 q^{89} -11.2697 q^{90} -5.27085 q^{91} +0.592684 q^{92} -20.8264 q^{93} +9.44252 q^{94} +2.74349 q^{95} -20.0653 q^{96} -18.1476 q^{97} -17.4372 q^{98} -6.13192 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9}+O(q^{10}) \) 38 * q + 4 * q^2 + 5 * q^3 + 50 * q^4 + 38 * q^5 + 11 * q^6 + 15 * q^8 + 63 * q^9	\( 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9} + 4 q^{10} - 38 q^{11} + 12 q^{12} - q^{13} + 23 q^{14} + 5 q^{15} + 74 q^{16} + 26 q^{17} + 16 q^{18} - 10 q^{19} + 50 q^{20} + 21 q^{21} - 4 q^{22} + 10 q^{23} + 41 q^{24} + 38 q^{25} + 25 q^{26} + 5 q^{27} + 2 q^{28} + 28 q^{29} + 11 q^{30} + 24 q^{31} + 39 q^{32} - 5 q^{33} + 38 q^{34} + 111 q^{36} + 12 q^{37} + 19 q^{38} - 18 q^{39} + 15 q^{40} + 62 q^{41} - 17 q^{42} - 32 q^{43} - 50 q^{44} + 63 q^{45} - 9 q^{46} + 31 q^{47} + 53 q^{48} + 88 q^{49} + 4 q^{50} - 3 q^{51} - 21 q^{52} + 30 q^{53} + 49 q^{54} - 38 q^{55} + 32 q^{56} + 49 q^{57} + 12 q^{58} + 31 q^{59} + 12 q^{60} + 25 q^{61} + 12 q^{62} + 15 q^{63} + 137 q^{64} - q^{65} - 11 q^{66} + 20 q^{67} + 75 q^{68} + 92 q^{69} + 23 q^{70} + 32 q^{71} + 6 q^{72} - 38 q^{73} + 55 q^{74} + 5 q^{75} - 57 q^{76} - 17 q^{78} - 2 q^{79} + 74 q^{80} + 118 q^{81} + 14 q^{82} + 4 q^{83} + 22 q^{84} + 26 q^{85} + 5 q^{86} + 24 q^{87} - 15 q^{88} + 143 q^{89} + 16 q^{90} + 66 q^{91} + 29 q^{92} - 8 q^{93} - 7 q^{94} - 10 q^{95} + 59 q^{96} + 41 q^{97} - 10 q^{98} - 63 q^{99}+O(q^{100}) \) 38 * q + 4 * q^2 + 5 * q^3 + 50 * q^4 + 38 * q^5 + 11 * q^6 + 15 * q^8 + 63 * q^9 + 4 * q^10 - 38 * q^11 + 12 * q^12 - q^13 + 23 * q^14 + 5 * q^15 + 74 * q^16 + 26 * q^17 + 16 * q^18 - 10 * q^19 + 50 * q^20 + 21 * q^21 - 4 * q^22 + 10 * q^23 + 41 * q^24 + 38 * q^25 + 25 * q^26 + 5 * q^27 + 2 * q^28 + 28 * q^29 + 11 * q^30 + 24 * q^31 + 39 * q^32 - 5 * q^33 + 38 * q^34 + 111 * q^36 + 12 * q^37 + 19 * q^38 - 18 * q^39 + 15 * q^40 + 62 * q^41 - 17 * q^42 - 32 * q^43 - 50 * q^44 + 63 * q^45 - 9 * q^46 + 31 * q^47 + 53 * q^48 + 88 * q^49 + 4 * q^50 - 3 * q^51 - 21 * q^52 + 30 * q^53 + 49 * q^54 - 38 * q^55 + 32 * q^56 + 49 * q^57 + 12 * q^58 + 31 * q^59 + 12 * q^60 + 25 * q^61 + 12 * q^62 + 15 * q^63 + 137 * q^64 - q^65 - 11 * q^66 + 20 * q^67 + 75 * q^68 + 92 * q^69 + 23 * q^70 + 32 * q^71 + 6 * q^72 - 38 * q^73 + 55 * q^74 + 5 * q^75 - 57 * q^76 - 17 * q^78 - 2 * q^79 + 74 * q^80 + 118 * q^81 + 14 * q^82 + 4 * q^83 + 22 * q^84 + 26 * q^85 + 5 * q^86 + 24 * q^87 - 15 * q^88 + 143 * q^89 + 16 * q^90 + 66 * q^91 + 29 * q^92 - 8 * q^93 - 7 * q^94 - 10 * q^95 + 59 * q^96 + 41 * q^97 - 10 * q^98 - 63 * q^99

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