LMFDB - Embedded newform 8015.2.a.k.1.16

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			1.16
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)

$f(q)$	$=$	$q-1.23019 q^{2} +2.26268 q^{3} -0.486637 q^{4} -1.00000 q^{5} -2.78352 q^{6} -1.00000 q^{7} +3.05903 q^{8} +2.11970 q^{9} +O(q^{10})$	\(q-1.23019 q^{2} +2.26268 q^{3} -0.486637 q^{4} -1.00000 q^{5} -2.78352 q^{6} -1.00000 q^{7} +3.05903 q^{8} +2.11970 q^{9} +1.23019 q^{10} +0.0423759 q^{11} -1.10110 q^{12} +2.92897 q^{13} +1.23019 q^{14} -2.26268 q^{15} -2.78991 q^{16} -2.56346 q^{17} -2.60763 q^{18} +3.83046 q^{19} +0.486637 q^{20} -2.26268 q^{21} -0.0521303 q^{22} -1.59025 q^{23} +6.92159 q^{24} +1.00000 q^{25} -3.60319 q^{26} -1.99184 q^{27} +0.486637 q^{28} -1.44039 q^{29} +2.78352 q^{30} -2.18695 q^{31} -2.68595 q^{32} +0.0958828 q^{33} +3.15354 q^{34} +1.00000 q^{35} -1.03152 q^{36} -0.287282 q^{37} -4.71218 q^{38} +6.62731 q^{39} -3.05903 q^{40} -0.141206 q^{41} +2.78352 q^{42} -8.41635 q^{43} -0.0206217 q^{44} -2.11970 q^{45} +1.95631 q^{46} +8.99476 q^{47} -6.31266 q^{48} +1.00000 q^{49} -1.23019 q^{50} -5.80028 q^{51} -1.42535 q^{52} -11.1203 q^{53} +2.45033 q^{54} -0.0423759 q^{55} -3.05903 q^{56} +8.66708 q^{57} +1.77195 q^{58} +9.00360 q^{59} +1.10110 q^{60} -6.11657 q^{61} +2.69036 q^{62} -2.11970 q^{63} +8.88404 q^{64} -2.92897 q^{65} -0.117954 q^{66} +5.12043 q^{67} +1.24748 q^{68} -3.59822 q^{69} -1.23019 q^{70} -9.43741 q^{71} +6.48422 q^{72} -4.32671 q^{73} +0.353411 q^{74} +2.26268 q^{75} -1.86404 q^{76} -0.0423759 q^{77} -8.15284 q^{78} -7.67866 q^{79} +2.78991 q^{80} -10.8660 q^{81} +0.173710 q^{82} +1.48971 q^{83} +1.10110 q^{84} +2.56346 q^{85} +10.3537 q^{86} -3.25914 q^{87} +0.129629 q^{88} +10.6293 q^{89} +2.60763 q^{90} -2.92897 q^{91} +0.773876 q^{92} -4.94836 q^{93} -11.0652 q^{94} -3.83046 q^{95} -6.07743 q^{96} -1.02717 q^{97} -1.23019 q^{98} +0.0898241 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.23019	−0.869874	−0.434937	−	0.900461i	$-0.643229\pi$
$2$	−1.23019	−0.869874	−0.434937	+	0.900461i	$0.643229\pi$
$3$	2.26268	1.30636	0.653178	−	0.757204i	$-0.273435\pi$
$3$	2.26268	1.30636	0.653178	+	0.757204i	$0.273435\pi$
$4$	−0.486637	−0.243319
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.78352	−1.13637
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.05903	1.08153
$9$	2.11970	0.706566
$10$	1.23019	0.389020
$11$	0.0423759	0.0127768	0.00638840	−	0.999980i	$-0.497966\pi$
$11$	0.0423759	0.0127768	0.00638840	+	0.999980i	$0.497966\pi$
$12$	−1.10110	−0.317861
$13$	2.92897	0.812351	0.406176	−	0.913795i	$-0.366862\pi$
$13$	2.92897	0.812351	0.406176	+	0.913795i	$0.366862\pi$
$14$	1.23019	0.328782
$15$	−2.26268	−0.584220
$16$	−2.78991	−0.697478
$17$	−2.56346	−0.621731	−0.310865	−	0.950454i	$-0.600619\pi$
$17$	−2.56346	−0.621731	−0.310865	+	0.950454i	$0.600619\pi$
$18$	−2.60763	−0.614624
$19$	3.83046	0.878767	0.439384	−	0.898299i	$-0.355197\pi$
$19$	3.83046	0.878767	0.439384	+	0.898299i	$0.355197\pi$
$20$	0.486637	0.108815
$21$	−2.26268	−0.493756
$22$	−0.0521303	−0.0111142
$23$	−1.59025	−0.331591	−0.165795	−	0.986160i	$-0.553019\pi$
$23$	−1.59025	−0.331591	−0.165795	+	0.986160i	$0.553019\pi$
$24$	6.92159	1.41286
$25$	1.00000	0.200000
$26$	−3.60319	−0.706643
$27$	−1.99184	−0.383329
$28$	0.486637	0.0919658
$29$	−1.44039	−0.267474	−0.133737	−	0.991017i	$-0.542698\pi$
$29$	−1.44039	−0.267474	−0.133737	+	0.991017i	$0.542698\pi$
$30$	2.78352	0.508198
$31$	−2.18695	−0.392788	−0.196394	−	0.980525i	$-0.562923\pi$
$31$	−2.18695	−0.392788	−0.196394	+	0.980525i	$0.562923\pi$
$32$	−2.68595	−0.474813
$33$	0.0958828	0.0166911
$34$	3.15354	0.540828
$35$	1.00000	0.169031
$36$	−1.03152	−0.171921
$37$	−0.287282	−0.0472288	−0.0236144	−	0.999721i	$-0.507517\pi$
$37$	−0.287282	−0.0472288	−0.0236144	+	0.999721i	$0.507517\pi$
$38$	−4.71218	−0.764417
$39$	6.62731	1.06122
$40$	−3.05903	−0.483675
$41$	−0.141206	−0.0220527	−0.0110263	−	0.999939i	$-0.503510\pi$
$41$	−0.141206	−0.0220527	−0.0110263	+	0.999939i	$0.503510\pi$
$42$	2.78352	0.429506
$43$	−8.41635	−1.28348	−0.641741	−	0.766921i	$-0.721788\pi$
$43$	−8.41635	−1.28348	−0.641741	+	0.766921i	$0.721788\pi$
$44$	−0.0206217	−0.00310883
$45$	−2.11970	−0.315986
$46$	1.95631	0.288442
$47$	8.99476	1.31202	0.656010	−	0.754752i	$-0.272243\pi$
$47$	8.99476	1.31202	0.656010	+	0.754752i	$0.272243\pi$
$48$	−6.31266	−0.911154
$49$	1.00000	0.142857
$50$	−1.23019	−0.173975
$51$	−5.80028	−0.812202
$52$	−1.42535	−0.197660
$53$	−11.1203	−1.52749	−0.763747	−	0.645516i	$-0.776642\pi$
$53$	−11.1203	−1.52749	−0.763747	+	0.645516i	$0.776642\pi$
$54$	2.45033	0.333448
$55$	−0.0423759	−0.00571396
$56$	−3.05903	−0.408780
$57$	8.66708	1.14798
$58$	1.77195	0.232669
$59$	9.00360	1.17217	0.586084	−	0.810250i	$-0.300669\pi$
$59$	9.00360	1.17217	0.586084	+	0.810250i	$0.300669\pi$
$60$	1.10110	0.142152
$61$	−6.11657	−0.783146	−0.391573	−	0.920147i	$-0.628069\pi$
$61$	−6.11657	−0.783146	−0.391573	+	0.920147i	$0.628069\pi$
$62$	2.69036	0.341677
$63$	−2.11970	−0.267057
$64$	8.88404	1.11051
$65$	−2.92897	−0.363294
$66$	−0.117954	−0.0145191
$67$	5.12043	0.625560	0.312780	−	0.949826i	$-0.398740\pi$
$67$	5.12043	0.625560	0.312780	+	0.949826i	$0.398740\pi$
$68$	1.24748	0.151279
$69$	−3.59822	−0.433175
$70$	−1.23019	−0.147036
$71$	−9.43741	−1.12001	−0.560007	−	0.828488i	$-0.689202\pi$
$71$	−9.43741	−1.12001	−0.560007	+	0.828488i	$0.689202\pi$
$72$	6.48422	0.764173
$73$	−4.32671	−0.506403	−0.253201	−	0.967414i	$-0.581483\pi$
$73$	−4.32671	−0.506403	−0.253201	+	0.967414i	$0.581483\pi$
$74$	0.353411	0.0410832
$75$	2.26268	0.261271
$76$	−1.86404	−0.213820
$77$	−0.0423759	−0.00482918
$78$	−8.15284	−0.923128
$79$	−7.67866	−0.863917	−0.431958	−	0.901894i	$-0.642177\pi$
$79$	−7.67866	−0.863917	−0.431958	+	0.901894i	$0.642177\pi$
$80$	2.78991	0.311921
$81$	−10.8660	−1.20733
$82$	0.173710	0.0191830
$83$	1.48971	0.163517	0.0817585	−	0.996652i	$-0.473946\pi$
$83$	1.48971	0.163517	0.0817585	+	0.996652i	$0.473946\pi$
$84$	1.10110	0.120140
$85$	2.56346	0.278047
$86$	10.3537	1.11647
$87$	−3.25914	−0.349416
$88$	0.129629	0.0138185
$89$	10.6293	1.12670	0.563349	−	0.826219i	$-0.309513\pi$
$89$	10.6293	1.12670	0.563349	+	0.826219i	$0.309513\pi$
$90$	2.60763	0.274868
$91$	−2.92897	−0.307040
$92$	0.773876	0.0806821
$93$	−4.94836	−0.513122
$94$	−11.0652	−1.14129
$95$	−3.83046	−0.392997
$96$	−6.07743	−0.620275
$97$	−1.02717	−0.104293	−0.0521467	−	0.998639i	$-0.516606\pi$
$97$	−1.02717	−0.104293	−0.0521467	+	0.998639i	$0.516606\pi$
$98$	−1.23019	−0.124268
$99$	0.0898241	0.00902766
$100$	−0.486637	−0.0486637
$101$	17.3183	1.72324	0.861619	−	0.507556i	$-0.169451\pi$
$101$	17.3183	1.72324	0.861619	+	0.507556i	$0.169451\pi$
$102$	7.13544	0.706514
$103$	−8.89350	−0.876303	−0.438151	−	0.898901i	$-0.644367\pi$
$103$	−8.89350	−0.876303	−0.438151	+	0.898901i	$0.644367\pi$
$104$	8.95982	0.878583
$105$	2.26268	0.220814
$106$	13.6801	1.32873
$107$	3.50197	0.338548	0.169274	−	0.985569i	$-0.445858\pi$
$107$	3.50197	0.338548	0.169274	+	0.985569i	$0.445858\pi$
$108$	0.969301	0.0932711
$109$	10.3381	0.990207	0.495104	−	0.868834i	$-0.335130\pi$
$109$	10.3381	0.990207	0.495104	+	0.868834i	$0.335130\pi$
$110$	0.0521303	0.00497043
$111$	−0.650025	−0.0616977
$112$	2.78991	0.263622
$113$	−0.726626	−0.0683552	−0.0341776	−	0.999416i	$-0.510881\pi$
$113$	−0.726626	−0.0683552	−0.0341776	+	0.999416i	$0.510881\pi$
$114$	−10.6621	−0.998601
$115$	1.59025	0.148292
$116$	0.700947	0.0650813
$117$	6.20854	0.573980
$118$	−11.0761	−1.01964
$119$	2.56346	0.234992
$120$	−6.92159	−0.631852
$121$	−10.9982	−0.999837
$122$	7.52453	0.681239
$123$	−0.319503	−0.0288086
$124$	1.06425	0.0955727
$125$	−1.00000	−0.0894427
$126$	2.60763	0.232306
$127$	−12.5342	−1.11223	−0.556114	−	0.831106i	$-0.687708\pi$
$127$	−12.5342	−1.11223	−0.556114	+	0.831106i	$0.687708\pi$
$128$	−5.55715	−0.491187
$129$	−19.0435	−1.67668
$130$	3.60319	0.316021
$131$	−0.422102	−0.0368793	−0.0184396	−	0.999830i	$-0.505870\pi$
$131$	−0.422102	−0.0368793	−0.0184396	+	0.999830i	$0.505870\pi$
$132$	−0.0466601	−0.00406124
$133$	−3.83046	−0.332143
$134$	−6.29909	−0.544158
$135$	1.99184	0.171430
$136$	−7.84171	−0.672421
$137$	−15.7795	−1.34814	−0.674068	−	0.738669i	$-0.735455\pi$
$137$	−15.7795	−1.34814	−0.674068	+	0.738669i	$0.735455\pi$
$138$	4.42649	0.376808
$139$	−12.5334	−1.06307	−0.531535	−	0.847036i	$-0.678385\pi$
$139$	−12.5334	−1.06307	−0.531535	+	0.847036i	$0.678385\pi$
$140$	−0.486637	−0.0411283
$141$	20.3522	1.71397
$142$	11.6098	0.974272
$143$	0.124118	0.0103792
$144$	−5.91377	−0.492814
$145$	1.44039	0.119618
$146$	5.32266	0.440507
$147$	2.26268	0.186622
$148$	0.139802	0.0114917
$149$	−17.7808	−1.45666	−0.728331	−	0.685225i	$-0.759704\pi$
$149$	−17.7808	−1.45666	−0.728331	+	0.685225i	$0.759704\pi$
$150$	−2.78352	−0.227273
$151$	19.7198	1.60478	0.802389	−	0.596802i	$-0.203562\pi$
$151$	19.7198	1.60478	0.802389	+	0.596802i	$0.203562\pi$
$152$	11.7175	0.950414
$153$	−5.43377	−0.439294
$154$	0.0521303	0.00420078
$155$	2.18695	0.175660
$156$	−3.22510	−0.258214
$157$	13.3172	1.06283	0.531413	−	0.847113i	$-0.321661\pi$
$157$	13.3172	1.06283	0.531413	+	0.847113i	$0.321661\pi$
$158$	9.44620	0.751499
$159$	−25.1617	−1.99545
$160$	2.68595	0.212343
$161$	1.59025	0.125329
$162$	13.3672	1.05023
$163$	−2.55483	−0.200110	−0.100055	−	0.994982i	$-0.531902\pi$
$163$	−2.55483	−0.200110	−0.100055	+	0.994982i	$0.531902\pi$
$164$	0.0687161	0.00536582
$165$	−0.0958828	−0.00746447
$166$	−1.83263	−0.142239
$167$	0.628984	0.0486723	0.0243361	−	0.999704i	$-0.492253\pi$
$167$	0.628984	0.0486723	0.0243361	+	0.999704i	$0.492253\pi$
$168$	−6.92159	−0.534013
$169$	−4.42112	−0.340086
$170$	−3.15354	−0.241866
$171$	8.11942	0.620907
$172$	4.09571	0.312295
$173$	24.4704	1.86045	0.930226	−	0.366987i	$-0.119611\pi$
$173$	24.4704	1.86045	0.930226	+	0.366987i	$0.119611\pi$
$174$	4.00935	0.303948
$175$	−1.00000	−0.0755929
$176$	−0.118225	−0.00891153
$177$	20.3722	1.53127
$178$	−13.0760	−0.980086
$179$	−25.1991	−1.88347	−0.941734	−	0.336359i	$-0.890804\pi$
$179$	−25.1991	−1.88347	−0.941734	+	0.336359i	$0.890804\pi$
$180$	1.03152	0.0768852
$181$	−8.95801	−0.665844	−0.332922	−	0.942954i	$-0.608035\pi$
$181$	−8.95801	−0.665844	−0.332922	+	0.942954i	$0.608035\pi$
$182$	3.60319	0.267086
$183$	−13.8398	−1.02307
$184$	−4.86463	−0.358625
$185$	0.287282	0.0211214
$186$	6.08742	0.446351
$187$	−0.108629	−0.00794373
$188$	−4.37718	−0.319239
$189$	1.99184	0.144885
$190$	4.71218	0.341858
$191$	7.07820	0.512161	0.256080	−	0.966655i	$-0.417569\pi$
$191$	7.07820	0.512161	0.256080	+	0.966655i	$0.417569\pi$
$192$	20.1017	1.45072
$193$	5.60284	0.403301	0.201650	−	0.979458i	$-0.435369\pi$
$193$	5.60284	0.403301	0.201650	+	0.979458i	$0.435369\pi$
$194$	1.26361	0.0907221
$195$	−6.62731	−0.474592
$196$	−0.486637	−0.0347598
$197$	0.780044	0.0555759	0.0277879	−	0.999614i	$-0.491154\pi$
$197$	0.780044	0.0555759	0.0277879	+	0.999614i	$0.491154\pi$
$198$	−0.110500	−0.00785293
$199$	15.7761	1.11834	0.559169	−	0.829053i	$-0.311120\pi$
$199$	15.7761	1.11834	0.559169	+	0.829053i	$0.311120\pi$
$200$	3.05903	0.216306
$201$	11.5859	0.817204
$202$	−21.3048	−1.49900
$203$	1.44039	0.101096
$204$	2.82263	0.197624
$205$	0.141206	0.00986225
$206$	10.9407	0.762273
$207$	−3.37086	−0.234291
$208$	−8.17157	−0.566597
$209$	0.162319	0.0112278
$210$	−2.78352	−0.192081
$211$	−12.3767	−0.852049	−0.426024	−	0.904712i	$-0.640086\pi$
$211$	−12.3767	−0.852049	−0.426024	+	0.904712i	$0.640086\pi$
$212$	5.41156	0.371667
$213$	−21.3538	−1.46314
$214$	−4.30808	−0.294494
$215$	8.41635	0.573991
$216$	−6.09309	−0.414582
$217$	2.18695	0.148460
$218$	−12.7178	−0.861356
$219$	−9.78993	−0.661542
$220$	0.0206217	0.00139031
$221$	−7.50831	−0.505064
$222$	0.799654	0.0536692
$223$	−4.66327	−0.312276	−0.156138	−	0.987735i	$-0.549904\pi$
$223$	−4.66327	−0.312276	−0.156138	+	0.987735i	$0.549904\pi$
$224$	2.68595	0.179462
$225$	2.11970	0.141313
$226$	0.893886	0.0594604
$227$	7.21663	0.478984	0.239492	−	0.970898i	$-0.423019\pi$
$227$	7.21663	0.478984	0.239492	+	0.970898i	$0.423019\pi$
$228$	−4.21772	−0.279326
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−1.95631	−0.128995
$231$	−0.0958828	−0.00630863
$232$	−4.40620	−0.289281
$233$	−18.6698	−1.22310	−0.611550	−	0.791206i	$-0.709453\pi$
$233$	−18.6698	−1.22310	−0.611550	+	0.791206i	$0.709453\pi$
$234$	−7.63767	−0.499290
$235$	−8.99476	−0.586753
$236$	−4.38148	−0.285210
$237$	−17.3743	−1.12858
$238$	−3.15354	−0.204414
$239$	0.0950559	0.00614865	0.00307433	−	0.999995i	$-0.499021\pi$
$239$	0.0950559	0.00614865	0.00307433	+	0.999995i	$0.499021\pi$
$240$	6.31266	0.407480
$241$	−17.9667	−1.15734	−0.578669	−	0.815562i	$-0.696428\pi$
$241$	−17.9667	−1.15734	−0.578669	+	0.815562i	$0.696428\pi$
$242$	13.5299	0.869732
$243$	−18.6107	−1.19387
$244$	2.97655	0.190554
$245$	−1.00000	−0.0638877
$246$	0.393049	0.0250599
$247$	11.2193	0.713868
$248$	−6.68996	−0.424813
$249$	3.37073	0.213612
$250$	1.23019	0.0778039
$251$	−18.3178	−1.15621	−0.578106	−	0.815962i	$-0.696208\pi$
$251$	−18.3178	−1.15621	−0.578106	+	0.815962i	$0.696208\pi$
$252$	1.03152	0.0649799
$253$	−0.0673883	−0.00423667
$254$	15.4194	0.967499
$255$	5.80028	0.363228
$256$	−10.9317	−0.683234
$257$	9.99123	0.623236	0.311618	−	0.950207i	$-0.399129\pi$
$257$	9.99123	0.623236	0.311618	+	0.950207i	$0.399129\pi$
$258$	23.4271	1.45851
$259$	0.287282	0.0178508
$260$	1.42535	0.0883963
$261$	−3.05319	−0.188988
$262$	0.519265	0.0320803
$263$	−6.90493	−0.425776	−0.212888	−	0.977077i	$-0.568287\pi$
$263$	−6.90493	−0.425776	−0.212888	+	0.977077i	$0.568287\pi$
$264$	0.293309	0.0180519
$265$	11.1203	0.683116
$266$	4.71218	0.288923
$267$	24.0505	1.47187
$268$	−2.49179	−0.152210
$269$	27.6560	1.68622	0.843109	−	0.537743i	$-0.180723\pi$
$269$	27.6560	1.68622	0.843109	+	0.537743i	$0.180723\pi$
$270$	−2.45033	−0.149123
$271$	17.2016	1.04492	0.522462	−	0.852662i	$-0.325013\pi$
$271$	17.2016	1.04492	0.522462	+	0.852662i	$0.325013\pi$
$272$	7.15183	0.433643
$273$	−6.62731	−0.401103
$274$	19.4118	1.17271
$275$	0.0423759	0.00255536
$276$	1.75103	0.105400
$277$	−10.7523	−0.646045	−0.323023	−	0.946391i	$-0.604699\pi$
$277$	−10.7523	−0.646045	−0.323023	+	0.946391i	$0.604699\pi$
$278$	15.4184	0.924737
$279$	−4.63568	−0.277531
$280$	3.05903	0.182812
$281$	10.4047	0.620693	0.310346	−	0.950624i	$-0.399555\pi$
$281$	10.4047	0.620693	0.310346	+	0.950624i	$0.399555\pi$
$282$	−25.0371	−1.49093
$283$	−2.64401	−0.157170	−0.0785851	−	0.996907i	$-0.525040\pi$
$283$	−2.64401	−0.157170	−0.0785851	+	0.996907i	$0.525040\pi$
$284$	4.59259	0.272520
$285$	−8.66708	−0.513394
$286$	−0.152688	−0.00902864
$287$	0.141206	0.00833512
$288$	−5.69340	−0.335487
$289$	−10.4287	−0.613451
$290$	−1.77195	−0.104053
$291$	−2.32415	−0.136244
$292$	2.10554	0.123217
$293$	−25.6919	−1.50094	−0.750468	−	0.660906i	$-0.770172\pi$
$293$	−25.6919	−1.50094	−0.750468	+	0.660906i	$0.770172\pi$
$294$	−2.78352	−0.162338
$295$	−9.00360	−0.524210
$296$	−0.878804	−0.0510794
$297$	−0.0844058	−0.00489772
$298$	21.8738	1.26711
$299$	−4.65781	−0.269368
$300$	−1.10110	−0.0635721
$301$	8.41635	0.485111
$302$	−24.2591	−1.39595
$303$	39.1857	2.25116
$304$	−10.6866	−0.612921
$305$	6.11657	0.350234
$306$	6.68456	0.382131
$307$	−2.75853	−0.157438	−0.0787189	−	0.996897i	$-0.525083\pi$
$307$	−2.75853	−0.157438	−0.0787189	+	0.996897i	$0.525083\pi$
$308$	0.0206217	0.00117503
$309$	−20.1231	−1.14476
$310$	−2.69036	−0.152802
$311$	−32.0945	−1.81991	−0.909955	−	0.414706i	$-0.863884\pi$
$311$	−32.0945	−1.81991	−0.909955	+	0.414706i	$0.863884\pi$
$312$	20.2732	1.14774
$313$	−22.3177	−1.26147	−0.630736	−	0.775998i	$-0.717247\pi$
$313$	−22.3177	−1.26147	−0.630736	+	0.775998i	$0.717247\pi$
$314$	−16.3826	−0.924525
$315$	2.11970	0.119431
$316$	3.73672	0.210207
$317$	−4.28972	−0.240934	−0.120467	−	0.992717i	$-0.538439\pi$
$317$	−4.28972	−0.240934	−0.120467	+	0.992717i	$0.538439\pi$
$318$	30.9536	1.73579
$319$	−0.0610378	−0.00341746
$320$	−8.88404	−0.496633
$321$	7.92381	0.442264
$322$	−1.95631	−0.109021
$323$	−9.81924	−0.546357
$324$	5.28779	0.293766
$325$	2.92897	0.162470
$326$	3.14292	0.174071
$327$	23.3917	1.29356
$328$	−0.431953	−0.0238506
$329$	−8.99476	−0.495897
$330$	0.117954	0.00649315
$331$	−18.4193	−1.01242	−0.506209	−	0.862411i	$-0.668953\pi$
$331$	−18.4193	−1.01242	−0.506209	+	0.862411i	$0.668953\pi$
$332$	−0.724949	−0.0397867
$333$	−0.608951	−0.0333703
$334$	−0.773769	−0.0423387
$335$	−5.12043	−0.279759
$336$	6.31266	0.344384
$337$	27.7659	1.51251	0.756253	−	0.654279i	$-0.227028\pi$
$337$	27.7659	1.51251	0.756253	+	0.654279i	$0.227028\pi$
$338$	5.43880	0.295832
$339$	−1.64412	−0.0892962
$340$	−1.24748	−0.0676539
$341$	−0.0926740	−0.00501858
$342$	−9.98841	−0.540111
$343$	−1.00000	−0.0539949
$344$	−25.7459	−1.38813
$345$	3.59822	0.193722
$346$	−30.1032	−1.61836
$347$	−0.140421	−0.00753820	−0.00376910	−	0.999993i	$-0.501200\pi$
$347$	−0.140421	−0.00753820	−0.00376910	+	0.999993i	$0.501200\pi$
$348$	1.58602	0.0850194
$349$	−35.4739	−1.89888	−0.949438	−	0.313953i	$-0.898346\pi$
$349$	−35.4739	−1.89888	−0.949438	+	0.313953i	$0.898346\pi$
$350$	1.23019	0.0657563
$351$	−5.83403	−0.311398
$352$	−0.113819	−0.00606659
$353$	31.5622	1.67988	0.839942	−	0.542676i	$-0.182589\pi$
$353$	31.5622	1.67988	0.839942	+	0.542676i	$0.182589\pi$
$354$	−25.0617	−1.33201
$355$	9.43741	0.500886
$356$	−5.17259	−0.274147
$357$	5.80028	0.306984
$358$	30.9996	1.63838
$359$	−16.3761	−0.864295	−0.432148	−	0.901803i	$-0.642244\pi$
$359$	−16.3761	−0.864295	−0.432148	+	0.901803i	$0.642244\pi$
$360$	−6.48422	−0.341749
$361$	−4.32759	−0.227768
$362$	11.0200	0.579201
$363$	−24.8854	−1.30614
$364$	1.42535	0.0747085
$365$	4.32671	0.226470
$366$	17.0256	0.889940
$367$	−13.0128	−0.679264	−0.339632	−	0.940558i	$-0.610302\pi$
$367$	−13.0128	−0.679264	−0.339632	+	0.940558i	$0.610302\pi$
$368$	4.43666	0.231277
$369$	−0.299314	−0.0155817
$370$	−0.353411	−0.0183729
$371$	11.1203	0.577338
$372$	2.40806	0.124852
$373$	−37.8763	−1.96116	−0.980580	−	0.196121i	$-0.937165\pi$
$373$	−37.8763	−1.96116	−0.980580	+	0.196121i	$0.937165\pi$
$374$	0.133634	0.00691005
$375$	−2.26268	−0.116844
$376$	27.5152	1.41899
$377$	−4.21886	−0.217283
$378$	−2.45033	−0.126032
$379$	−13.4119	−0.688922	−0.344461	−	0.938801i	$-0.611938\pi$
$379$	−13.4119	−0.688922	−0.344461	+	0.938801i	$0.611938\pi$
$380$	1.86404	0.0956234
$381$	−28.3608	−1.45297
$382$	−8.70752	−0.445516
$383$	0.500037	0.0255507	0.0127753	−	0.999918i	$-0.495933\pi$
$383$	0.500037	0.0255507	0.0127753	+	0.999918i	$0.495933\pi$
$384$	−12.5740	−0.641665
$385$	0.0423759	0.00215967
$386$	−6.89254	−0.350821
$387$	−17.8401	−0.906865
$388$	0.499859	0.0253765
$389$	−15.9593	−0.809170	−0.404585	−	0.914500i	$-0.632584\pi$
$389$	−15.9593	−0.809170	−0.404585	+	0.914500i	$0.632584\pi$
$390$	8.15284	0.412835
$391$	4.07655	0.206160
$392$	3.05903	0.154504
$393$	−0.955081	−0.0481774
$394$	−0.959601	−0.0483440
$395$	7.67866	0.386355
$396$	−0.0437117	−0.00219660
$397$	−6.18109	−0.310220	−0.155110	−	0.987897i	$-0.549573\pi$
$397$	−6.18109	−0.310220	−0.155110	+	0.987897i	$0.549573\pi$
$398$	−19.4076	−0.972814
$399$	−8.66708	−0.433897
$400$	−2.78991	−0.139496
$401$	−21.7906	−1.08817	−0.544086	−	0.839029i	$-0.683124\pi$
$401$	−21.7906	−1.08817	−0.544086	+	0.839029i	$0.683124\pi$
$402$	−14.2528	−0.710865
$403$	−6.40553	−0.319082
$404$	−8.42773	−0.419295
$405$	10.8660	0.539935
$406$	−1.77195	−0.0879405
$407$	−0.0121738	−0.000603434 0
$408$	−17.7432	−0.878422
$409$	15.3769	0.760337	0.380169	−	0.924917i	$-0.375866\pi$
$409$	15.3769	0.760337	0.380169	+	0.924917i	$0.375866\pi$
$410$	−0.173710	−0.00857892
$411$	−35.7040	−1.76115
$412$	4.32791	0.213221
$413$	−9.00360	−0.443038
$414$	4.14679	0.203803
$415$	−1.48971	−0.0731271
$416$	−7.86707	−0.385715
$417$	−28.3590	−1.38875
$418$	−0.199683	−0.00976681
$419$	1.59725	0.0780306	0.0390153	−	0.999239i	$-0.487578\pi$
$419$	1.59725	0.0780306	0.0390153	+	0.999239i	$0.487578\pi$
$420$	−1.10110	−0.0537283
$421$	16.6055	0.809300	0.404650	−	0.914472i	$-0.367393\pi$
$421$	16.6055	0.809300	0.404650	+	0.914472i	$0.367393\pi$
$422$	15.2257	0.741175
$423$	19.0662	0.927029
$424$	−34.0174	−1.65203
$425$	−2.56346	−0.124346
$426$	26.2692	1.27275
$427$	6.11657	0.296001
$428$	−1.70419	−0.0823749
$429$	0.280838	0.0135590
$430$	−10.3537	−0.499300
$431$	4.44947	0.214323	0.107162	−	0.994242i	$-0.465824\pi$
$431$	4.44947	0.214323	0.107162	+	0.994242i	$0.465824\pi$
$432$	5.55704	0.267363
$433$	−1.61172	−0.0774543	−0.0387272	−	0.999250i	$-0.512330\pi$
$433$	−1.61172	−0.0774543	−0.0387272	+	0.999250i	$0.512330\pi$
$434$	−2.69036	−0.129142
$435$	3.25914	0.156264
$436$	−5.03089	−0.240936
$437$	−6.09140	−0.291391
$438$	12.0435	0.575459
$439$	−2.59937	−0.124061	−0.0620307	−	0.998074i	$-0.519758\pi$
$439$	−2.59937	−0.124061	−0.0620307	+	0.998074i	$0.519758\pi$
$440$	−0.129629	−0.00617983
$441$	2.11970	0.100938
$442$	9.23664	0.439342
$443$	−21.8003	−1.03576	−0.517882	−	0.855452i	$-0.673279\pi$
$443$	−21.8003	−1.03576	−0.517882	+	0.855452i	$0.673279\pi$
$444$	0.316326	0.0150122
$445$	−10.6293	−0.503875
$446$	5.73670	0.271641
$447$	−40.2322	−1.90292
$448$	−8.88404	−0.419732
$449$	11.1151	0.524552	0.262276	−	0.964993i	$-0.415527\pi$
$449$	11.1151	0.524552	0.262276	+	0.964993i	$0.415527\pi$
$450$	−2.60763	−0.122925
$451$	−0.00598372	−0.000281763 0
$452$	0.353603	0.0166321
$453$	44.6196	2.09641
$454$	−8.87781	−0.416656
$455$	2.92897	0.137312
$456$	26.5129	1.24158
$457$	−25.7307	−1.20363	−0.601816	−	0.798635i	$-0.705556\pi$
$457$	−25.7307	−1.20363	−0.601816	+	0.798635i	$0.705556\pi$
$458$	1.23019	0.0574829
$459$	5.10600	0.238328
$460$	−0.773876	−0.0360821
$461$	−20.9661	−0.976488	−0.488244	−	0.872707i	$-0.662362\pi$
$461$	−20.9661	−0.976488	−0.488244	+	0.872707i	$0.662362\pi$
$462$	0.117954	0.00548771
$463$	11.5126	0.535034	0.267517	−	0.963553i	$-0.413797\pi$
$463$	11.5126	0.535034	0.267517	+	0.963553i	$0.413797\pi$
$464$	4.01856	0.186557
$465$	4.94836	0.229475
$466$	22.9674	1.06394
$467$	−27.6223	−1.27821	−0.639103	−	0.769121i	$-0.720694\pi$
$467$	−27.6223	−1.27821	−0.639103	+	0.769121i	$0.720694\pi$
$468$	−3.02131	−0.139660
$469$	−5.12043	−0.236439
$470$	11.0652	0.510402
$471$	30.1324	1.38843
$472$	27.5423	1.26774
$473$	−0.356650	−0.0163988
$474$	21.3737	0.981725
$475$	3.83046	0.175753
$476$	−1.24748	−0.0571780
$477$	−23.5717	−1.07928
$478$	−0.116937	−0.00534855
$479$	25.5313	1.16656	0.583278	−	0.812272i	$-0.301770\pi$
$479$	25.5313	1.16656	0.583278	+	0.812272i	$0.301770\pi$
$480$	6.07743	0.277395
$481$	−0.841441	−0.0383664
$482$	22.1024	1.00674
$483$	3.59822	0.163725
$484$	5.35213	0.243279
$485$	1.02717	0.0466414
$486$	22.8946	1.03852
$487$	40.7084	1.84468	0.922338	−	0.386385i	$-0.126276\pi$
$487$	40.7084	1.84468	0.922338	+	0.386385i	$0.126276\pi$
$488$	−18.7108	−0.846997
$489$	−5.78076	−0.261415
$490$	1.23019	0.0555742
$491$	−31.4955	−1.42137	−0.710687	−	0.703509i	$-0.751616\pi$
$491$	−31.4955	−1.42137	−0.710687	+	0.703509i	$0.751616\pi$
$492$	0.155482	0.00700967
$493$	3.69239	0.166297
$494$	−13.8019	−0.620975
$495$	−0.0898241	−0.00403729
$496$	6.10140	0.273961
$497$	9.43741	0.423326
$498$	−4.14664	−0.185815
$499$	32.5046	1.45510	0.727552	−	0.686053i	$-0.240658\pi$
$499$	32.5046	1.45510	0.727552	+	0.686053i	$0.240658\pi$
$500$	0.486637	0.0217631
$501$	1.42319	0.0635833
$502$	22.5344	1.00576
$503$	−38.8889	−1.73397	−0.866984	−	0.498335i	$-0.833945\pi$
$503$	−38.8889	−1.73397	−0.866984	+	0.498335i	$0.833945\pi$
$504$	−6.48422	−0.288830
$505$	−17.3183	−0.770655
$506$	0.0829003	0.00368537
$507$	−10.0035	−0.444273
$508$	6.09960	0.270626
$509$	−7.54237	−0.334310	−0.167155	−	0.985931i	$-0.553458\pi$
$509$	−7.54237	−0.334310	−0.167155	+	0.985931i	$0.553458\pi$
$510$	−7.13544	−0.315963
$511$	4.32671	0.191402
$512$	24.5624	1.08552
$513$	−7.62965	−0.336857
$514$	−12.2911	−0.542137
$515$	8.89350	0.391895
$516$	9.26726	0.407968
$517$	0.381161	0.0167634
$518$	−0.353411	−0.0155280
$519$	55.3686	2.43041
$520$	−8.95982	−0.392914
$521$	−30.4658	−1.33473	−0.667367	−	0.744729i	$-0.732579\pi$
$521$	−30.4658	−1.33473	−0.667367	+	0.744729i	$0.732579\pi$
$522$	3.75600	0.164396
$523$	−9.67683	−0.423138	−0.211569	−	0.977363i	$-0.567857\pi$
$523$	−9.67683	−0.423138	−0.211569	+	0.977363i	$0.567857\pi$
$524$	0.205411	0.00897341
$525$	−2.26268	−0.0987512
$526$	8.49436	0.370372
$527$	5.60617	0.244209
$528$	−0.267504	−0.0116416
$529$	−20.4711	−0.890048
$530$	−13.6801	−0.594225
$531$	19.0849	0.828214
$532$	1.86404	0.0808165
$533$	−0.413588	−0.0179145
$534$	−29.5867	−1.28034
$535$	−3.50197	−0.151403
$536$	15.6636	0.676562
$537$	−57.0173	−2.46048
$538$	−34.0221	−1.46680
$539$	0.0423759	0.00182526
$540$	−0.969301	−0.0417121
$541$	−21.5815	−0.927860	−0.463930	−	0.885872i	$-0.653561\pi$
$541$	−21.5815	−0.927860	−0.463930	+	0.885872i	$0.653561\pi$
$542$	−21.1612	−0.908953
$543$	−20.2691	−0.869829
$544$	6.88533	0.295206
$545$	−10.3381	−0.442834
$546$	8.15284	0.348910
$547$	−28.4280	−1.21549	−0.607746	−	0.794132i	$-0.707926\pi$
$547$	−28.4280	−1.21549	−0.607746	+	0.794132i	$0.707926\pi$
$548$	7.67890	0.328027
$549$	−12.9653	−0.553344
$550$	−0.0521303	−0.00222284
$551$	−5.51735	−0.235047
$552$	−11.0071	−0.468493
$553$	7.67866	0.326530
$554$	13.2274	0.561978
$555$	0.650025	0.0275920
$556$	6.09922	0.258665
$557$	−12.4037	−0.525560	−0.262780	−	0.964856i	$-0.584639\pi$
$557$	−12.4037	−0.525560	−0.262780	+	0.964856i	$0.584639\pi$
$558$	5.70276	0.241417
$559$	−24.6513	−1.04264
$560$	−2.78991	−0.117895
$561$	−0.245792	−0.0103773
$562$	−12.7997	−0.539925
$563$	33.9899	1.43250	0.716251	−	0.697843i	$-0.245857\pi$
$563$	33.9899	1.43250	0.716251	+	0.697843i	$0.245857\pi$
$564$	−9.90414	−0.417040
$565$	0.726626	0.0305694
$566$	3.25263	0.136718
$567$	10.8660	0.456328
$568$	−28.8693	−1.21133
$569$	14.0150	0.587539	0.293770	−	0.955876i	$-0.405090\pi$
$569$	14.0150	0.587539	0.293770	+	0.955876i	$0.405090\pi$
$570$	10.6621	0.446588
$571$	26.0144	1.08867	0.544335	−	0.838868i	$-0.316782\pi$
$571$	26.0144	1.08867	0.544335	+	0.838868i	$0.316782\pi$
$572$	−0.0604003	−0.00252546
$573$	16.0157	0.669064
$574$	−0.173710	−0.00725051
$575$	−1.59025	−0.0663181
$576$	18.8315	0.784645
$577$	2.84519	0.118447	0.0592234	−	0.998245i	$-0.481138\pi$
$577$	2.84519	0.118447	0.0592234	+	0.998245i	$0.481138\pi$
$578$	12.8292	0.533625
$579$	12.6774	0.526855
$580$	−0.700947	−0.0291052
$581$	−1.48971	−0.0618036
$582$	2.85914	0.118515
$583$	−0.471233	−0.0195165
$584$	−13.2355	−0.547690
$585$	−6.20854	−0.256692
$586$	31.6059	1.30563
$587$	−47.0746	−1.94297	−0.971487	−	0.237091i	$-0.923806\pi$
$587$	−47.0746	−1.94297	−0.971487	+	0.237091i	$0.923806\pi$
$588$	−1.10110	−0.0454087
$589$	−8.37703	−0.345170
$590$	11.0761	0.455997
$591$	1.76499	0.0726019
$592$	0.801490	0.0329411
$593$	−8.57754	−0.352237	−0.176119	−	0.984369i	$-0.556354\pi$
$593$	−8.57754	−0.352237	−0.176119	+	0.984369i	$0.556354\pi$
$594$	0.103835	0.00426040
$595$	−2.56346	−0.105092
$596$	8.65281	0.354433
$597$	35.6962	1.46095
$598$	5.72998	0.234316
$599$	−11.7455	−0.479908	−0.239954	−	0.970784i	$-0.577132\pi$
$599$	−11.7455	−0.479908	−0.239954	+	0.970784i	$0.577132\pi$
$600$	6.92159	0.282573
$601$	−17.2530	−0.703767	−0.351883	−	0.936044i	$-0.614459\pi$
$601$	−17.2530	−0.703767	−0.351883	+	0.936044i	$0.614459\pi$
$602$	−10.3537	−0.421985
$603$	10.8538	0.441999
$604$	−9.59640	−0.390472
$605$	10.9982	0.447141
$606$	−48.2058	−1.95823
$607$	−17.9947	−0.730381	−0.365190	−	0.930933i	$-0.618996\pi$
$607$	−17.9947	−0.730381	−0.365190	+	0.930933i	$0.618996\pi$
$608$	−10.2884	−0.417250
$609$	3.25914	0.132067
$610$	−7.52453	−0.304659
$611$	26.3454	1.06582
$612$	2.64427	0.106888
$613$	26.3473	1.06416	0.532079	−	0.846695i	$-0.321411\pi$
$613$	26.3473	1.06416	0.532079	+	0.846695i	$0.321411\pi$
$614$	3.39351	0.136951
$615$	0.319503	0.0128836
$616$	−0.129629	−0.00522291
$617$	28.9663	1.16614	0.583070	−	0.812422i	$-0.301851\pi$
$617$	28.9663	1.16614	0.583070	+	0.812422i	$0.301851\pi$
$618$	24.7552	0.995801
$619$	44.1095	1.77291	0.886456	−	0.462813i	$-0.153160\pi$
$619$	44.1095	1.77291	0.886456	+	0.462813i	$0.153160\pi$
$620$	−1.06425	−0.0427414
$621$	3.16752	0.127108
$622$	39.4822	1.58309
$623$	−10.6293	−0.425852
$624$	−18.4896	−0.740177
$625$	1.00000	0.0400000
$626$	27.4550	1.09732
$627$	0.367275	0.0146676
$628$	−6.48063	−0.258605
$629$	0.736436	0.0293636
$630$	−2.60763	−0.103890
$631$	−30.8506	−1.22814	−0.614071	−	0.789250i	$-0.710469\pi$
$631$	−30.8506	−1.22814	−0.614071	+	0.789250i	$0.710469\pi$
$632$	−23.4893	−0.934353
$633$	−28.0045	−1.11308
$634$	5.27716	0.209583
$635$	12.5342	0.497404
$636$	12.2446	0.485530
$637$	2.92897	0.116050
$638$	0.0750880	0.00297276
$639$	−20.0045	−0.791365
$640$	5.55715	0.219666
$641$	22.2536	0.878964	0.439482	−	0.898252i	$-0.355162\pi$
$641$	22.2536	0.878964	0.439482	+	0.898252i	$0.355162\pi$
$642$	−9.74778	−0.384714
$643$	−10.4393	−0.411687	−0.205843	−	0.978585i	$-0.565994\pi$
$643$	−10.4393	−0.411687	−0.205843	+	0.978585i	$0.565994\pi$
$644$	−0.773876	−0.0304950
$645$	19.0435	0.749836
$646$	12.0795	0.475262
$647$	32.6155	1.28225	0.641123	−	0.767438i	$-0.278469\pi$
$647$	32.6155	1.28225	0.641123	+	0.767438i	$0.278469\pi$
$648$	−33.2394	−1.30577
$649$	0.381535	0.0149766
$650$	−3.60319	−0.141329
$651$	4.94836	0.193942
$652$	1.24328	0.0486905
$653$	17.1477	0.671041	0.335520	−	0.942033i	$-0.391088\pi$
$653$	17.1477	0.671041	0.335520	+	0.942033i	$0.391088\pi$
$654$	−28.7762	−1.12524
$655$	0.422102	0.0164929
$656$	0.393952	0.0153812
$657$	−9.17131	−0.357807
$658$	11.0652	0.431368
$659$	46.3768	1.80658	0.903291	−	0.429028i	$-0.141144\pi$
$659$	46.3768	1.80658	0.903291	+	0.429028i	$0.141144\pi$
$660$	0.0466601	0.00181624
$661$	39.5429	1.53804	0.769020	−	0.639225i	$-0.220745\pi$
$661$	39.5429	1.53804	0.769020	+	0.639225i	$0.220745\pi$
$662$	22.6592	0.880676
$663$	−16.9889	−0.659793
$664$	4.55707	0.176849
$665$	3.83046	0.148539
$666$	0.749124	0.0290280
$667$	2.29058	0.0886918
$668$	−0.306087	−0.0118429
$669$	−10.5515	−0.407943
$670$	6.29909	0.243355
$671$	−0.259195	−0.0100061
$672$	6.07743	0.234442
$673$	−41.1596	−1.58659	−0.793294	−	0.608839i	$-0.791636\pi$
$673$	−41.1596	−1.58659	−0.793294	+	0.608839i	$0.791636\pi$
$674$	−34.1573	−1.31569
$675$	−1.99184	−0.0766658
$676$	2.15148	0.0827492
$677$	48.6301	1.86901	0.934504	−	0.355953i	$-0.115844\pi$
$677$	48.6301	1.86901	0.934504	+	0.355953i	$0.115844\pi$
$678$	2.02257	0.0776765
$679$	1.02717	0.0394192
$680$	7.84171	0.300716
$681$	16.3289	0.625724
$682$	0.114007	0.00436553
$683$	−13.6853	−0.523654	−0.261827	−	0.965115i	$-0.584325\pi$
$683$	−13.6853	−0.523654	−0.261827	+	0.965115i	$0.584325\pi$
$684$	−3.95121	−0.151078
$685$	15.7795	0.602905
$686$	1.23019	0.0469688
$687$	−2.26268	−0.0863264
$688$	23.4809	0.895200
$689$	−32.5711	−1.24086
$690$	−4.42649	−0.168514
$691$	−9.78594	−0.372275	−0.186137	−	0.982524i	$-0.559597\pi$
$691$	−9.78594	−0.372275	−0.186137	+	0.982524i	$0.559597\pi$
$692$	−11.9082	−0.452682
$693$	−0.0898241	−0.00341213
$694$	0.172744	0.00655729
$695$	12.5334	0.475419
$696$	−9.96980	−0.377904
$697$	0.361976	0.0137108
$698$	43.6396	1.65178
$699$	−42.2437	−1.59780
$700$	0.486637	0.0183932
$701$	32.3543	1.22201	0.611003	−	0.791628i	$-0.290766\pi$
$701$	32.3543	1.22201	0.611003	+	0.791628i	$0.290766\pi$
$702$	7.17696	0.270877
$703$	−1.10042	−0.0415032
$704$	0.376469	0.0141887
$705$	−20.3522	−0.766509
$706$	−38.8274	−1.46129
$707$	−17.3183	−0.651322
$708$	−9.91387	−0.372586
$709$	7.59869	0.285375	0.142687	−	0.989768i	$-0.454426\pi$
$709$	7.59869	0.285375	0.142687	+	0.989768i	$0.454426\pi$
$710$	−11.6098	−0.435708
$711$	−16.2764	−0.610414
$712$	32.5152	1.21856
$713$	3.47781	0.130245
$714$	−7.13544	−0.267037
$715$	−0.124118	−0.00464174
$716$	12.2628	0.458282
$717$	0.215081	0.00803233
$718$	20.1456	0.751828
$719$	38.3198	1.42909	0.714543	−	0.699591i	$-0.246635\pi$
$719$	38.3198	1.42909	0.714543	+	0.699591i	$0.246635\pi$
$720$	5.91377	0.220393
$721$	8.89350	0.331211
$722$	5.32375	0.198130
$723$	−40.6528	−1.51190
$724$	4.35930	0.162012
$725$	−1.44039	−0.0534947
$726$	30.6137	1.13618
$727$	−22.1251	−0.820573	−0.410287	−	0.911957i	$-0.634571\pi$
$727$	−22.1251	−0.820573	−0.410287	+	0.911957i	$0.634571\pi$
$728$	−8.95982	−0.332073
$729$	−9.51195	−0.352295
$730$	−5.32266	−0.197001
$731$	21.5750	0.797981
$732$	6.73496	0.248931
$733$	−10.3794	−0.383373	−0.191686	−	0.981456i	$-0.561396\pi$
$733$	−10.3794	−0.383373	−0.191686	+	0.981456i	$0.561396\pi$
$734$	16.0082	0.590874
$735$	−2.26268	−0.0834600
$736$	4.27134	0.157444
$737$	0.216983	0.00799266
$738$	0.368213	0.0135541
$739$	22.2147	0.817182	0.408591	−	0.912718i	$-0.366020\pi$
$739$	22.2147	0.817182	0.408591	+	0.912718i	$0.366020\pi$
$740$	−0.139802	−0.00513922
$741$	25.3857	0.932565
$742$	−13.6801	−0.502212
$743$	35.5787	1.30526	0.652628	−	0.757678i	$-0.273666\pi$
$743$	35.5787	1.30526	0.652628	+	0.757678i	$0.273666\pi$
$744$	−15.1372	−0.554957
$745$	17.7808	0.651439
$746$	46.5950	1.70596
$747$	3.15774	0.115536
$748$	0.0528629	0.00193286
$749$	−3.50197	−0.127959
$750$	2.78352	0.101640
$751$	3.59386	0.131142	0.0655709	−	0.997848i	$-0.479113\pi$
$751$	3.59386	0.131142	0.0655709	+	0.997848i	$0.479113\pi$
$752$	−25.0946	−0.915105
$753$	−41.4473	−1.51042
$754$	5.19000	0.189009
$755$	−19.7198	−0.717678
$756$	−0.969301	−0.0352531
$757$	−28.6023	−1.03957	−0.519783	−	0.854298i	$-0.673987\pi$
$757$	−28.6023	−1.03957	−0.519783	+	0.854298i	$0.673987\pi$
$758$	16.4991	0.599276
$759$	−0.152478	−0.00553460
$760$	−11.7175	−0.425038
$761$	−14.3001	−0.518379	−0.259189	−	0.965827i	$-0.583455\pi$
$761$	−14.3001	−0.518379	−0.259189	+	0.965827i	$0.583455\pi$
$762$	34.8891	1.26390
$763$	−10.3381	−0.374263
$764$	−3.44452	−0.124618
$765$	5.43377	0.196458
$766$	−0.615139	−0.0222259
$767$	26.3713	0.952212
$768$	−24.7350	−0.892547
$769$	19.6403	0.708248	0.354124	−	0.935198i	$-0.384779\pi$
$769$	19.6403	0.708248	0.354124	+	0.935198i	$0.384779\pi$
$770$	−0.0521303	−0.00187865
$771$	22.6069	0.814168
$772$	−2.72655	−0.0981306
$773$	42.8730	1.54203	0.771017	−	0.636815i	$-0.219749\pi$
$773$	42.8730	1.54203	0.771017	+	0.636815i	$0.219749\pi$
$774$	21.9467	0.788859
$775$	−2.18695	−0.0785577
$776$	−3.14215	−0.112796
$777$	0.650025	0.0233195
$778$	19.6330	0.703877
$779$	−0.540884	−0.0193792
$780$	3.22510	0.115477
$781$	−0.399918	−0.0143102
$782$	−5.01493	−0.179333
$783$	2.86902	0.102530
$784$	−2.78991	−0.0996397
$785$	−13.3172	−0.475310
$786$	1.17493	0.0419083
$787$	11.0619	0.394313	0.197157	−	0.980372i	$-0.436829\pi$
$787$	11.0619	0.394313	0.197157	+	0.980372i	$0.436829\pi$
$788$	−0.379599	−0.0135226
$789$	−15.6236	−0.556215
$790$	−9.44620	−0.336081
$791$	0.726626	0.0258358
$792$	0.274775	0.00976369
$793$	−17.9153	−0.636189
$794$	7.60390	0.269852
$795$	25.1617	0.892393
$796$	−7.67724	−0.272113
$797$	42.6826	1.51190	0.755948	−	0.654632i	$-0.227176\pi$
$797$	42.6826	1.51190	0.755948	+	0.654632i	$0.227176\pi$
$798$	10.6621	0.377436
$799$	−23.0577	−0.815724
$800$	−2.68595	−0.0949626
$801$	22.5308	0.796087
$802$	26.8066	0.946574
$803$	−0.183348	−0.00647021
$804$	−5.63811	−0.198841
$805$	−1.59025	−0.0560490
$806$	7.88000	0.277561
$807$	62.5766	2.20280
$808$	52.9773	1.86373
$809$	11.0088	0.387049	0.193524	−	0.981095i	$-0.438008\pi$
$809$	11.0088	0.387049	0.193524	+	0.981095i	$0.438008\pi$
$810$	−13.3672	−0.469675
$811$	−50.3998	−1.76978	−0.884889	−	0.465803i	$-0.845766\pi$
$811$	−50.3998	−1.76978	−0.884889	+	0.465803i	$0.845766\pi$
$812$	−0.700947	−0.0245984
$813$	38.9217	1.36504
$814$	0.0149761	0.000524911 0
$815$	2.55483	0.0894919
$816$	16.1823	0.566493
$817$	−32.2385	−1.12788
$818$	−18.9164	−0.661398
$819$	−6.20854	−0.216944
$820$	−0.0687161	−0.00239967
$821$	3.50393	0.122288	0.0611440	−	0.998129i	$-0.480525\pi$
$821$	3.50393	0.122288	0.0611440	+	0.998129i	$0.480525\pi$
$822$	43.9226	1.53198
$823$	−35.6073	−1.24119	−0.620597	−	0.784130i	$-0.713110\pi$
$823$	−35.6073	−1.24119	−0.620597	+	0.784130i	$0.713110\pi$
$824$	−27.2055	−0.947749
$825$	0.0958828	0.00333821
$826$	11.0761	0.385387
$827$	−48.2499	−1.67781	−0.838907	−	0.544275i	$-0.816805\pi$
$827$	−48.2499	−1.67781	−0.838907	+	0.544275i	$0.816805\pi$
$828$	1.64038	0.0570073
$829$	−24.7884	−0.860936	−0.430468	−	0.902606i	$-0.641651\pi$
$829$	−24.7884	−0.860936	−0.430468	+	0.902606i	$0.641651\pi$
$830$	1.83263	0.0636114
$831$	−24.3290	−0.843965
$832$	26.0211	0.902120
$833$	−2.56346	−0.0888187
$834$	34.8869	1.20804
$835$	−0.628984	−0.0217669
$836$	−0.0789904	−0.00273194
$837$	4.35605	0.150567
$838$	−1.96491	−0.0678768
$839$	21.1543	0.730328	0.365164	−	0.930943i	$-0.381013\pi$
$839$	21.1543	0.730328	0.365164	+	0.930943i	$0.381013\pi$
$840$	6.92159	0.238818
$841$	−26.9253	−0.928458
$842$	−20.4278	−0.703990
$843$	23.5425	0.810846
$844$	6.02297	0.207319
$845$	4.42112	0.152091
$846$	−23.4550	−0.806399
$847$	10.9982	0.377903
$848$	31.0247	1.06539
$849$	−5.98254	−0.205320
$850$	3.15354	0.108166
$851$	0.456851	0.0156606
$852$	10.3915	0.356009
$853$	−13.6690	−0.468019	−0.234009	−	0.972234i	$-0.575185\pi$
$853$	−13.6690	−0.468019	−0.234009	+	0.972234i	$0.575185\pi$
$854$	−7.52453	−0.257484
$855$	−8.11942	−0.277678
$856$	10.7126	0.366150
$857$	−35.6569	−1.21802	−0.609009	−	0.793163i	$-0.708433\pi$
$857$	−35.6569	−1.21802	−0.609009	+	0.793163i	$0.708433\pi$
$858$	−0.345484	−0.0117946
$859$	14.0990	0.481053	0.240527	−	0.970643i	$-0.422680\pi$
$859$	14.0990	0.481053	0.240527	+	0.970643i	$0.422680\pi$
$860$	−4.09571	−0.139663
$861$	0.319503	0.0108886
$862$	−5.47368	−0.186434
$863$	−15.1454	−0.515554	−0.257777	−	0.966204i	$-0.582990\pi$
$863$	−15.1454	−0.515554	−0.257777	+	0.966204i	$0.582990\pi$
$864$	5.34997	0.182010
$865$	−24.4704	−0.832019
$866$	1.98272	0.0673755
$867$	−23.5967	−0.801385
$868$	−1.06425	−0.0361231
$869$	−0.325390	−0.0110381
$870$	−4.00935	−0.135930
$871$	14.9976	0.508174
$872$	31.6245	1.07094
$873$	−2.17729	−0.0736901
$874$	7.49356	0.253474
$875$	1.00000	0.0338062
$876$	4.76414	0.160965
$877$	17.8464	0.602629	0.301314	−	0.953525i	$-0.402575\pi$
$877$	17.8464	0.602629	0.301314	+	0.953525i	$0.402575\pi$
$878$	3.19772	0.107918
$879$	−58.1324	−1.96076
$880$	0.118225	0.00398536
$881$	43.3623	1.46091	0.730457	−	0.682958i	$-0.239307\pi$
$881$	43.3623	1.46091	0.730457	+	0.682958i	$0.239307\pi$
$882$	−2.60763	−0.0878034
$883$	51.3262	1.72727	0.863633	−	0.504122i	$-0.168184\pi$
$883$	51.3262	1.72727	0.863633	+	0.504122i	$0.168184\pi$
$884$	3.65382	0.122891
$885$	−20.3722	−0.684804
$886$	26.8185	0.900985
$887$	−5.59698	−0.187928	−0.0939642	−	0.995576i	$-0.529954\pi$
$887$	−5.59698	−0.187928	−0.0939642	+	0.995576i	$0.529954\pi$
$888$	−1.98845	−0.0667279
$889$	12.5342	0.420383
$890$	13.0760	0.438308
$891$	−0.460455	−0.0154258
$892$	2.26932	0.0759825
$893$	34.4540	1.15296
$894$	49.4932	1.65530
$895$	25.1991	0.842312
$896$	5.55715	0.185651
$897$	−10.5391	−0.351890
$898$	−13.6736	−0.456295
$899$	3.15007	0.105061
$900$	−1.03152	−0.0343841
$901$	28.5065	0.949690
$902$	0.00736111	0.000245098 0
$903$	19.0435	0.633727
$904$	−2.22277	−0.0739283
$905$	8.95801	0.297774
$906$	−54.8905	−1.82361
$907$	35.6031	1.18218	0.591090	−	0.806605i	$-0.298698\pi$
$907$	35.6031	1.18218	0.591090	+	0.806605i	$0.298698\pi$
$908$	−3.51188	−0.116546
$909$	36.7096	1.21758
$910$	−3.60319	−0.119445
$911$	−17.4072	−0.576726	−0.288363	−	0.957521i	$-0.593111\pi$
$911$	−17.4072	−0.576726	−0.288363	+	0.957521i	$0.593111\pi$
$912$	−24.1804	−0.800692
$913$	0.0631278	0.00208923
$914$	31.6536	1.04701
$915$	13.8398	0.457530
$916$	0.486637	0.0160789
$917$	0.422102	0.0139390
$918$	−6.28134	−0.207315
$919$	−31.0651	−1.02474	−0.512372	−	0.858764i	$-0.671233\pi$
$919$	−31.0651	−1.02474	−0.512372	+	0.858764i	$0.671233\pi$
$920$	4.86463	0.160382
$921$	−6.24166	−0.205670
$922$	25.7922	0.849422
$923$	−27.6419	−0.909845
$924$	0.0466601	0.00153501
$925$	−0.287282	−0.00944577
$926$	−14.1626	−0.465412
$927$	−18.8515	−0.619166
$928$	3.86881	0.127000
$929$	−49.1487	−1.61252	−0.806259	−	0.591563i	$-0.798511\pi$
$929$	−49.1487	−1.61252	−0.806259	+	0.591563i	$0.798511\pi$
$930$	−6.08742	−0.199614
$931$	3.83046	0.125538
$932$	9.08541	0.297603
$933$	−72.6194	−2.37745
$934$	33.9806	1.11188
$935$	0.108629	0.00355255
$936$	18.9921	0.620777
$937$	−48.1883	−1.57424	−0.787122	−	0.616797i	$-0.788430\pi$
$937$	−48.1883	−1.57424	−0.787122	+	0.616797i	$0.788430\pi$
$938$	6.29909	0.205673
$939$	−50.4977	−1.64793
$940$	4.37718	0.142768
$941$	11.3600	0.370324	0.185162	−	0.982708i	$-0.440719\pi$
$941$	11.3600	0.370324	0.185162	+	0.982708i	$0.440719\pi$
$942$	−37.0686	−1.20776
$943$	0.224553	0.00731246
$944$	−25.1192	−0.817561
$945$	−1.99184	−0.0647944
$946$	0.438747	0.0142649
$947$	10.2313	0.332473	0.166237	−	0.986086i	$-0.446838\pi$
$947$	10.2313	0.332473	0.166237	+	0.986086i	$0.446838\pi$
$948$	8.45498	0.274605
$949$	−12.6728	−0.411377
$950$	−4.71218	−0.152883
$951$	−9.70623	−0.314746
$952$	7.84171	0.254151
$953$	−38.7361	−1.25479	−0.627393	−	0.778702i	$-0.715878\pi$
$953$	−38.7361	−1.25479	−0.627393	+	0.778702i	$0.715878\pi$
$954$	28.9977	0.938834
$955$	−7.07820	−0.229045
$956$	−0.0462577	−0.00149608
$957$	−0.138109	−0.00446442
$958$	−31.4084	−1.01476
$959$	15.7795	0.509548
$960$	−20.1017	−0.648780
$961$	−26.2172	−0.845717
$962$	1.03513	0.0333739
$963$	7.42311	0.239206
$964$	8.74327	0.281602
$965$	−5.60284	−0.180362
$966$	−4.42649	−0.142420
$967$	11.8635	0.381506	0.190753	−	0.981638i	$-0.438907\pi$
$967$	11.8635	0.381506	0.190753	+	0.981638i	$0.438907\pi$
$968$	−33.6439	−1.08135
$969$	−22.2177	−0.713737
$970$	−1.26361	−0.0405721
$971$	4.60640	0.147826	0.0739132	−	0.997265i	$-0.476451\pi$
$971$	4.60640	0.147826	0.0739132	+	0.997265i	$0.476451\pi$
$972$	9.05664	0.290492
$973$	12.5334	0.401803
$974$	−50.0790	−1.60464
$975$	6.62731	0.212244
$976$	17.0647	0.546227
$977$	43.3422	1.38664	0.693320	−	0.720630i	$-0.256147\pi$
$977$	43.3422	1.38664	0.693320	+	0.720630i	$0.256147\pi$
$978$	7.11142	0.227398
$979$	0.450424	0.0143956
$980$	0.486637	0.0155450
$981$	21.9136	0.699647
$982$	38.7454	1.23642
$983$	−51.9584	−1.65722	−0.828608	−	0.559829i	$-0.810867\pi$
$983$	−51.9584	−1.65722	−0.828608	+	0.559829i	$0.810867\pi$
$984$	−0.977370	−0.0311574
$985$	−0.780044	−0.0248543
$986$	−4.54233	−0.144657
$987$	−20.3522	−0.647818
$988$	−5.45973	−0.173697
$989$	13.3841	0.425591
$990$	0.110500	0.00351194
$991$	10.4217	0.331058	0.165529	−	0.986205i	$-0.447067\pi$
$991$	10.4217	0.331058	0.165529	+	0.986205i	$0.447067\pi$
$992$	5.87404	0.186501
$993$	−41.6769	−1.32258
$994$	−11.6098	−0.368240
$995$	−15.7761	−0.500136
$996$	−1.64032	−0.0519756
$997$	−38.1362	−1.20779	−0.603893	−	0.797065i	$-0.706385\pi$
$997$	−38.1362	−1.20779	−0.603893	+	0.797065i	$0.706385\pi$
$998$	−39.9867	−1.26576
$999$	0.572218	0.0181042

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.k.1.16	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.k.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-1.23019 q^{2} +2.26268 q^{3} -0.486637 q^{4} -1.00000 q^{5} -2.78352 q^{6} -1.00000 q^{7} +3.05903 q^{8} +2.11970 q^{9} +O(q^{10})\)	\(q-1.23019 q^{2} +2.26268 q^{3} -0.486637 q^{4} -1.00000 q^{5} -2.78352 q^{6} -1.00000 q^{7} +3.05903 q^{8} +2.11970 q^{9} +1.23019 q^{10} +0.0423759 q^{11} -1.10110 q^{12} +2.92897 q^{13} +1.23019 q^{14} -2.26268 q^{15} -2.78991 q^{16} -2.56346 q^{17} -2.60763 q^{18} +3.83046 q^{19} +0.486637 q^{20} -2.26268 q^{21} -0.0521303 q^{22} -1.59025 q^{23} +6.92159 q^{24} +1.00000 q^{25} -3.60319 q^{26} -1.99184 q^{27} +0.486637 q^{28} -1.44039 q^{29} +2.78352 q^{30} -2.18695 q^{31} -2.68595 q^{32} +0.0958828 q^{33} +3.15354 q^{34} +1.00000 q^{35} -1.03152 q^{36} -0.287282 q^{37} -4.71218 q^{38} +6.62731 q^{39} -3.05903 q^{40} -0.141206 q^{41} +2.78352 q^{42} -8.41635 q^{43} -0.0206217 q^{44} -2.11970 q^{45} +1.95631 q^{46} +8.99476 q^{47} -6.31266 q^{48} +1.00000 q^{49} -1.23019 q^{50} -5.80028 q^{51} -1.42535 q^{52} -11.1203 q^{53} +2.45033 q^{54} -0.0423759 q^{55} -3.05903 q^{56} +8.66708 q^{57} +1.77195 q^{58} +9.00360 q^{59} +1.10110 q^{60} -6.11657 q^{61} +2.69036 q^{62} -2.11970 q^{63} +8.88404 q^{64} -2.92897 q^{65} -0.117954 q^{66} +5.12043 q^{67} +1.24748 q^{68} -3.59822 q^{69} -1.23019 q^{70} -9.43741 q^{71} +6.48422 q^{72} -4.32671 q^{73} +0.353411 q^{74} +2.26268 q^{75} -1.86404 q^{76} -0.0423759 q^{77} -8.15284 q^{78} -7.67866 q^{79} +2.78991 q^{80} -10.8660 q^{81} +0.173710 q^{82} +1.48971 q^{83} +1.10110 q^{84} +2.56346 q^{85} +10.3537 q^{86} -3.25914 q^{87} +0.129629 q^{88} +10.6293 q^{89} +2.60763 q^{90} -2.92897 q^{91} +0.773876 q^{92} -4.94836 q^{93} -11.0652 q^{94} -3.83046 q^{95} -6.07743 q^{96} -1.02717 q^{97} -1.23019 q^{98} +0.0898241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) \) 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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