LMFDB - Embedded newform 4015.2.a.h.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-1.86942 q^{2} -2.63227 q^{3} +1.49473 q^{4} +1.00000 q^{5} +4.92082 q^{6} -2.31866 q^{7} +0.944554 q^{8} +3.92884 q^{9} +O(q^{10})$	\(q-1.86942 q^{2} -2.63227 q^{3} +1.49473 q^{4} +1.00000 q^{5} +4.92082 q^{6} -2.31866 q^{7} +0.944554 q^{8} +3.92884 q^{9} -1.86942 q^{10} +1.00000 q^{11} -3.93454 q^{12} -2.05468 q^{13} +4.33454 q^{14} -2.63227 q^{15} -4.75524 q^{16} -5.64494 q^{17} -7.34466 q^{18} -4.69534 q^{19} +1.49473 q^{20} +6.10333 q^{21} -1.86942 q^{22} -7.33488 q^{23} -2.48632 q^{24} +1.00000 q^{25} +3.84106 q^{26} -2.44496 q^{27} -3.46577 q^{28} -5.39768 q^{29} +4.92082 q^{30} +2.07630 q^{31} +7.00043 q^{32} -2.63227 q^{33} +10.5528 q^{34} -2.31866 q^{35} +5.87257 q^{36} +2.42502 q^{37} +8.77757 q^{38} +5.40846 q^{39} +0.944554 q^{40} +10.2948 q^{41} -11.4097 q^{42} +0.817099 q^{43} +1.49473 q^{44} +3.92884 q^{45} +13.7120 q^{46} -2.17927 q^{47} +12.5171 q^{48} -1.62384 q^{49} -1.86942 q^{50} +14.8590 q^{51} -3.07120 q^{52} -8.22789 q^{53} +4.57066 q^{54} +1.00000 q^{55} -2.19010 q^{56} +12.3594 q^{57} +10.0905 q^{58} -0.531662 q^{59} -3.93454 q^{60} -6.90212 q^{61} -3.88148 q^{62} -9.10963 q^{63} -3.57628 q^{64} -2.05468 q^{65} +4.92082 q^{66} -6.19999 q^{67} -8.43768 q^{68} +19.3074 q^{69} +4.33454 q^{70} -8.72428 q^{71} +3.71100 q^{72} +1.00000 q^{73} -4.53339 q^{74} -2.63227 q^{75} -7.01829 q^{76} -2.31866 q^{77} -10.1107 q^{78} +2.92720 q^{79} -4.75524 q^{80} -5.35073 q^{81} -19.2453 q^{82} -7.28519 q^{83} +9.12285 q^{84} -5.64494 q^{85} -1.52750 q^{86} +14.2082 q^{87} +0.944554 q^{88} -2.65720 q^{89} -7.34466 q^{90} +4.76409 q^{91} -10.9637 q^{92} -5.46538 q^{93} +4.07397 q^{94} -4.69534 q^{95} -18.4270 q^{96} -15.5081 q^{97} +3.03563 q^{98} +3.92884 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.86942	−1.32188	−0.660940	−	0.750439i	$-0.729842\pi$
$2$	−1.86942	−1.32188	−0.660940	+	0.750439i	$0.729842\pi$
$3$	−2.63227	−1.51974	−0.759871	−	0.650074i	$-0.774738\pi$
$3$	−2.63227	−1.51974	−0.759871	+	0.650074i	$0.774738\pi$
$4$	1.49473	0.747367
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.92082	2.00892
$7$	−2.31866	−0.876369	−0.438185	−	0.898885i	$-0.644378\pi$
$7$	−2.31866	−0.876369	−0.438185	+	0.898885i	$0.644378\pi$
$8$	0.944554	0.333950
$9$	3.92884	1.30961
$10$	−1.86942	−0.591163
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.93454	−1.13580
$13$	−2.05468	−0.569865	−0.284932	−	0.958548i	$-0.591971\pi$
$13$	−2.05468	−0.569865	−0.284932	+	0.958548i	$0.591971\pi$
$14$	4.33454	1.15846
$15$	−2.63227	−0.679649
$16$	−4.75524	−1.18881
$17$	−5.64494	−1.36910	−0.684549	−	0.728967i	$-0.740001\pi$
$17$	−5.64494	−1.36910	−0.684549	+	0.728967i	$0.740001\pi$
$18$	−7.34466	−1.73115
$19$	−4.69534	−1.07719	−0.538593	−	0.842566i	$-0.681044\pi$
$19$	−4.69534	−1.07719	−0.538593	+	0.842566i	$0.681044\pi$
$20$	1.49473	0.334233
$21$	6.10333	1.33185
$22$	−1.86942	−0.398562
$23$	−7.33488	−1.52943	−0.764715	−	0.644369i	$-0.777120\pi$
$23$	−7.33488	−1.52943	−0.764715	+	0.644369i	$0.777120\pi$
$24$	−2.48632	−0.507518
$25$	1.00000	0.200000
$26$	3.84106	0.753293
$27$	−2.44496	−0.470533
$28$	−3.46577	−0.654970
$29$	−5.39768	−1.00232	−0.501162	−	0.865353i	$-0.667094\pi$
$29$	−5.39768	−1.00232	−0.501162	+	0.865353i	$0.667094\pi$
$30$	4.92082	0.898415
$31$	2.07630	0.372915	0.186457	−	0.982463i	$-0.440299\pi$
$31$	2.07630	0.372915	0.186457	+	0.982463i	$0.440299\pi$
$32$	7.00043	1.23751
$33$	−2.63227	−0.458219
$34$	10.5528	1.80978
$35$	−2.31866	−0.391924
$36$	5.87257	0.978762
$37$	2.42502	0.398671	0.199336	−	0.979931i	$-0.436122\pi$
$37$	2.42502	0.398671	0.199336	+	0.979931i	$0.436122\pi$
$38$	8.77757	1.42391
$39$	5.40846	0.866047
$40$	0.944554	0.149347
$41$	10.2948	1.60778	0.803890	−	0.594778i	$-0.202760\pi$
$41$	10.2948	1.60778	0.803890	+	0.594778i	$0.202760\pi$
$42$	−11.4097	−1.76055
$43$	0.817099	0.124606	0.0623032	−	0.998057i	$-0.480155\pi$
$43$	0.817099	0.124606	0.0623032	+	0.998057i	$0.480155\pi$
$44$	1.49473	0.225340
$45$	3.92884	0.585677
$46$	13.7120	2.02172
$47$	−2.17927	−0.317879	−0.158940	−	0.987288i	$-0.550808\pi$
$47$	−2.17927	−0.317879	−0.158940	+	0.987288i	$0.550808\pi$
$48$	12.5171	1.80668
$49$	−1.62384	−0.231977
$50$	−1.86942	−0.264376
$51$	14.8590	2.08068
$52$	−3.07120	−0.425898
$53$	−8.22789	−1.13019	−0.565094	−	0.825026i	$-0.691160\pi$
$53$	−8.22789	−1.13019	−0.565094	+	0.825026i	$0.691160\pi$
$54$	4.57066	0.621988
$55$	1.00000	0.134840
$56$	−2.19010	−0.292664
$57$	12.3594	1.63704
$58$	10.0905	1.32495
$59$	−0.531662	−0.0692164	−0.0346082	−	0.999401i	$-0.511018\pi$
$59$	−0.531662	−0.0692164	−0.0346082	+	0.999401i	$0.511018\pi$
$60$	−3.93454	−0.507947
$61$	−6.90212	−0.883726	−0.441863	−	0.897082i	$-0.645682\pi$
$61$	−6.90212	−0.883726	−0.441863	+	0.897082i	$0.645682\pi$
$62$	−3.88148	−0.492948
$63$	−9.10963	−1.14771
$64$	−3.57628	−0.447035
$65$	−2.05468	−0.254851
$66$	4.92082	0.605711
$67$	−6.19999	−0.757449	−0.378725	−	0.925509i	$-0.623637\pi$
$67$	−6.19999	−0.757449	−0.378725	+	0.925509i	$0.623637\pi$
$68$	−8.43768	−1.02322
$69$	19.3074	2.32434
$70$	4.33454	0.518077
$71$	−8.72428	−1.03538	−0.517691	−	0.855568i	$-0.673208\pi$
$71$	−8.72428	−1.03538	−0.517691	+	0.855568i	$0.673208\pi$
$72$	3.71100	0.437346
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−4.53339	−0.526996
$75$	−2.63227	−0.303948
$76$	−7.01829	−0.805053
$77$	−2.31866	−0.264235
$78$	−10.1107	−1.14481
$79$	2.92720	0.329335	0.164668	−	0.986349i	$-0.447345\pi$
$79$	2.92720	0.329335	0.164668	+	0.986349i	$0.447345\pi$
$80$	−4.75524	−0.531652
$81$	−5.35073	−0.594526
$82$	−19.2453	−2.12529
$83$	−7.28519	−0.799654	−0.399827	−	0.916591i	$-0.630930\pi$
$83$	−7.28519	−0.799654	−0.399827	+	0.916591i	$0.630930\pi$
$84$	9.12285	0.995385
$85$	−5.64494	−0.612279
$86$	−1.52750	−0.164715
$87$	14.2082	1.52327
$88$	0.944554	0.100690
$89$	−2.65720	−0.281662	−0.140831	−	0.990034i	$-0.544977\pi$
$89$	−2.65720	−0.281662	−0.140831	+	0.990034i	$0.544977\pi$
$90$	−7.34466	−0.774195
$91$	4.76409	0.499412
$92$	−10.9637	−1.14305
$93$	−5.46538	−0.566734
$94$	4.07397	0.420198
$95$	−4.69534	−0.481732
$96$	−18.4270	−1.88070
$97$	−15.5081	−1.57461	−0.787307	−	0.616561i	$-0.788525\pi$
$97$	−15.5081	−1.57461	−0.787307	+	0.616561i	$0.788525\pi$
$98$	3.03563	0.306645
$99$	3.92884	0.394863
$100$	1.49473	0.149473
$101$	19.9313	1.98323	0.991617	−	0.129210i	$-0.0412442\pi$
$101$	19.9313	1.98323	0.991617	+	0.129210i	$0.0412442\pi$
$102$	−27.7777	−2.75040
$103$	−8.67756	−0.855026	−0.427513	−	0.904009i	$-0.640610\pi$
$103$	−8.67756	−0.855026	−0.427513	+	0.904009i	$0.640610\pi$
$104$	−1.94075	−0.190306
$105$	6.10333	0.595624
$106$	15.3814	1.49397
$107$	−15.3399	−1.48296	−0.741480	−	0.670975i	$-0.765876\pi$
$107$	−15.3399	−1.48296	−0.741480	+	0.670975i	$0.765876\pi$
$108$	−3.65457	−0.351661
$109$	3.80535	0.364487	0.182243	−	0.983253i	$-0.441664\pi$
$109$	3.80535	0.364487	0.182243	+	0.983253i	$0.441664\pi$
$110$	−1.86942	−0.178242
$111$	−6.38331	−0.605877
$112$	11.0258	1.04184
$113$	−7.99314	−0.751931	−0.375966	−	0.926634i	$-0.622689\pi$
$113$	−7.99314	−0.751931	−0.375966	+	0.926634i	$0.622689\pi$
$114$	−23.1049	−2.16398
$115$	−7.33488	−0.683982
$116$	−8.06810	−0.749104
$117$	−8.07250	−0.746303
$118$	0.993899	0.0914958
$119$	13.0887	1.19984
$120$	−2.48632	−0.226969
$121$	1.00000	0.0909091
$122$	12.9030	1.16818
$123$	−27.0987	−2.44341
$124$	3.10352	0.278704
$125$	1.00000	0.0894427
$126$	17.0297	1.51713
$127$	17.1056	1.51787	0.758937	−	0.651164i	$-0.225719\pi$
$127$	17.1056	1.51787	0.758937	+	0.651164i	$0.225719\pi$
$128$	−7.31529	−0.646587
$129$	−2.15082	−0.189370
$130$	3.84106	0.336883
$131$	−5.97264	−0.521832	−0.260916	−	0.965362i	$-0.584024\pi$
$131$	−5.97264	−0.521832	−0.260916	+	0.965362i	$0.584024\pi$
$132$	−3.93454	−0.342458
$133$	10.8869	0.944013
$134$	11.5904	1.00126
$135$	−2.44496	−0.210429
$136$	−5.33195	−0.457211
$137$	1.16619	0.0996345	0.0498173	−	0.998758i	$-0.484136\pi$
$137$	1.16619	0.0996345	0.0498173	+	0.998758i	$0.484136\pi$
$138$	−36.0936	−3.07249
$139$	−2.46233	−0.208852	−0.104426	−	0.994533i	$-0.533301\pi$
$139$	−2.46233	−0.208852	−0.104426	+	0.994533i	$0.533301\pi$
$140$	−3.46577	−0.292911
$141$	5.73642	0.483094
$142$	16.3093	1.36865
$143$	−2.05468	−0.171821
$144$	−18.6826	−1.55688
$145$	−5.39768	−0.448253
$146$	−1.86942	−0.154714
$147$	4.27437	0.352544
$148$	3.62477	0.297954
$149$	13.9210	1.14045	0.570225	−	0.821489i	$-0.306856\pi$
$149$	13.9210	1.14045	0.570225	+	0.821489i	$0.306856\pi$
$150$	4.92082	0.401783
$151$	−22.0184	−1.79183	−0.895915	−	0.444226i	$-0.853479\pi$
$151$	−22.0184	−1.79183	−0.895915	+	0.444226i	$0.853479\pi$
$152$	−4.43501	−0.359726
$153$	−22.1781	−1.79299
$154$	4.33454	0.349287
$155$	2.07630	0.166772
$156$	8.08421	0.647255
$157$	4.30608	0.343663	0.171831	−	0.985126i	$-0.445032\pi$
$157$	4.30608	0.343663	0.171831	+	0.985126i	$0.445032\pi$
$158$	−5.47216	−0.435342
$159$	21.6580	1.71759
$160$	7.00043	0.553433
$161$	17.0071	1.34034
$162$	10.0028	0.785892
$163$	5.31470	0.416279	0.208140	−	0.978099i	$-0.433259\pi$
$163$	5.31470	0.416279	0.208140	+	0.978099i	$0.433259\pi$
$164$	15.3880	1.20160
$165$	−2.63227	−0.204922
$166$	13.6191	1.05705
$167$	5.28842	0.409230	0.204615	−	0.978843i	$-0.434406\pi$
$167$	5.28842	0.409230	0.204615	+	0.978843i	$0.434406\pi$
$168$	5.76492	0.444773
$169$	−8.77830	−0.675254
$170$	10.5528	0.809360
$171$	−18.4473	−1.41070
$172$	1.22135	0.0931267
$173$	−22.8886	−1.74018	−0.870092	−	0.492889i	$-0.835941\pi$
$173$	−22.8886	−1.74018	−0.870092	+	0.492889i	$0.835941\pi$
$174$	−26.5610	−2.01359
$175$	−2.31866	−0.175274
$176$	−4.75524	−0.358440
$177$	1.39948	0.105191
$178$	4.96742	0.372324
$179$	−20.5054	−1.53264	−0.766321	−	0.642458i	$-0.777915\pi$
$179$	−20.5054	−1.53264	−0.766321	+	0.642458i	$0.777915\pi$
$180$	5.87257	0.437716
$181$	13.7138	1.01934	0.509671	−	0.860369i	$-0.329767\pi$
$181$	13.7138	1.01934	0.509671	+	0.860369i	$0.329767\pi$
$182$	−8.90608	−0.660163
$183$	18.1682	1.34304
$184$	−6.92819	−0.510753
$185$	2.42502	0.178291
$186$	10.2171	0.749154
$187$	−5.64494	−0.412799
$188$	−3.25743	−0.237572
$189$	5.66902	0.412360
$190$	8.77757	0.636792
$191$	−23.6805	−1.71346	−0.856730	−	0.515765i	$-0.827508\pi$
$191$	−23.6805	−1.71346	−0.856730	+	0.515765i	$0.827508\pi$
$192$	9.41373	0.679378
$193$	22.3771	1.61074	0.805370	−	0.592772i	$-0.201966\pi$
$193$	22.3771	1.61074	0.805370	+	0.592772i	$0.201966\pi$
$194$	28.9913	2.08145
$195$	5.40846	0.387308
$196$	−2.42720	−0.173372
$197$	12.2767	0.874680	0.437340	−	0.899296i	$-0.355921\pi$
$197$	12.2767	0.874680	0.437340	+	0.899296i	$0.355921\pi$
$198$	−7.34466	−0.521962
$199$	−10.9920	−0.779203	−0.389602	−	0.920984i	$-0.627387\pi$
$199$	−10.9920	−0.779203	−0.389602	+	0.920984i	$0.627387\pi$
$200$	0.944554	0.0667901
$201$	16.3200	1.15113
$202$	−37.2599	−2.62160
$203$	12.5154	0.878406
$204$	22.2102	1.55503
$205$	10.2948	0.719021
$206$	16.2220	1.13024
$207$	−28.8176	−2.00296
$208$	9.77048	0.677461
$209$	−4.69534	−0.324784
$210$	−11.4097	−0.787343
$211$	−5.05261	−0.347836	−0.173918	−	0.984760i	$-0.555643\pi$
$211$	−5.05261	−0.347836	−0.173918	+	0.984760i	$0.555643\pi$
$212$	−12.2985	−0.844666
$213$	22.9646	1.57351
$214$	28.6766	1.96029
$215$	0.817099	0.0557257
$216$	−2.30940	−0.157135
$217$	−4.81423	−0.326811
$218$	−7.11381	−0.481808
$219$	−2.63227	−0.177872
$220$	1.49473	0.100775
$221$	11.5985	0.780201
$222$	11.9331	0.800897
$223$	−24.7199	−1.65537	−0.827684	−	0.561194i	$-0.810342\pi$
$223$	−24.7199	−1.65537	−0.827684	+	0.561194i	$0.810342\pi$
$224$	−16.2316	−1.08452
$225$	3.92884	0.261923
$226$	14.9425	0.993963
$227$	−3.44484	−0.228642	−0.114321	−	0.993444i	$-0.536469\pi$
$227$	−3.44484	−0.228642	−0.114321	+	0.993444i	$0.536469\pi$
$228$	18.4740	1.22347
$229$	−12.1093	−0.800206	−0.400103	−	0.916470i	$-0.631026\pi$
$229$	−12.1093	−0.800206	−0.400103	+	0.916470i	$0.631026\pi$
$230$	13.7120	0.904142
$231$	6.10333	0.401569
$232$	−5.09840	−0.334726
$233$	2.23168	0.146202	0.0731011	−	0.997325i	$-0.476710\pi$
$233$	2.23168	0.146202	0.0731011	+	0.997325i	$0.476710\pi$
$234$	15.0909	0.986523
$235$	−2.17927	−0.142160
$236$	−0.794693	−0.0517301
$237$	−7.70517	−0.500504
$238$	−24.4682	−1.58604
$239$	−4.32984	−0.280074	−0.140037	−	0.990146i	$-0.544722\pi$
$239$	−4.32984	−0.280074	−0.140037	+	0.990146i	$0.544722\pi$
$240$	12.5171	0.807973
$241$	10.1902	0.656410	0.328205	−	0.944607i	$-0.393556\pi$
$241$	10.1902	0.656410	0.328205	+	0.944607i	$0.393556\pi$
$242$	−1.86942	−0.120171
$243$	21.4194	1.37406
$244$	−10.3168	−0.660468
$245$	−1.62384	−0.103743
$246$	50.6589	3.22989
$247$	9.64741	0.613850
$248$	1.96118	0.124535
$249$	19.1766	1.21527
$250$	−1.86942	−0.118233
$251$	20.3922	1.28714	0.643572	−	0.765386i	$-0.277452\pi$
$251$	20.3922	1.28714	0.643572	+	0.765386i	$0.277452\pi$
$252$	−13.6165	−0.857757
$253$	−7.33488	−0.461140
$254$	−31.9775	−2.00645
$255$	14.8590	0.930506
$256$	20.8279	1.30175
$257$	8.69505	0.542382	0.271191	−	0.962526i	$-0.412582\pi$
$257$	8.69505	0.542382	0.271191	+	0.962526i	$0.412582\pi$
$258$	4.02080	0.250324
$259$	−5.62279	−0.349383
$260$	−3.07120	−0.190467
$261$	−21.2066	−1.31266
$262$	11.1654	0.689799
$263$	22.1826	1.36784	0.683918	−	0.729559i	$-0.260275\pi$
$263$	22.1826	1.36784	0.683918	+	0.729559i	$0.260275\pi$
$264$	−2.48632	−0.153022
$265$	−8.22789	−0.505436
$266$	−20.3522	−1.24787
$267$	6.99446	0.428054
$268$	−9.26734	−0.566093
$269$	−10.3880	−0.633370	−0.316685	−	0.948531i	$-0.602570\pi$
$269$	−10.3880	−0.633370	−0.316685	+	0.948531i	$0.602570\pi$
$270$	4.57066	0.278161
$271$	−3.19327	−0.193977	−0.0969886	−	0.995285i	$-0.530921\pi$
$271$	−3.19327	−0.193977	−0.0969886	+	0.995285i	$0.530921\pi$
$272$	26.8430	1.62760
$273$	−12.5404	−0.758977
$274$	−2.18010	−0.131705
$275$	1.00000	0.0603023
$276$	28.8594	1.73713
$277$	25.1949	1.51381	0.756907	−	0.653522i	$-0.226709\pi$
$277$	25.1949	1.51381	0.756907	+	0.653522i	$0.226709\pi$
$278$	4.60314	0.276078
$279$	8.15745	0.488374
$280$	−2.19010	−0.130883
$281$	−6.41999	−0.382985	−0.191492	−	0.981494i	$-0.561333\pi$
$281$	−6.41999	−0.382985	−0.191492	+	0.981494i	$0.561333\pi$
$282$	−10.7238	−0.638593
$283$	−22.1267	−1.31529	−0.657647	−	0.753326i	$-0.728448\pi$
$283$	−22.1267	−1.31529	−0.657647	+	0.753326i	$0.728448\pi$
$284$	−13.0405	−0.773810
$285$	12.3594	0.732108
$286$	3.84106	0.227126
$287$	−23.8701	−1.40901
$288$	27.5036	1.62066
$289$	14.8653	0.874430
$290$	10.0905	0.592537
$291$	40.8216	2.39301
$292$	1.49473	0.0874727
$293$	−10.6042	−0.619504	−0.309752	−	0.950817i	$-0.600246\pi$
$293$	−10.6042	−0.619504	−0.309752	+	0.950817i	$0.600246\pi$
$294$	−7.99060	−0.466021
$295$	−0.531662	−0.0309545
$296$	2.29057	0.133136
$297$	−2.44496	−0.141871
$298$	−26.0241	−1.50754
$299$	15.0708	0.871568
$300$	−3.93454	−0.227161
$301$	−1.89457	−0.109201
$302$	41.1616	2.36858
$303$	−52.4644	−3.01400
$304$	22.3275	1.28057
$305$	−6.90212	−0.395214
$306$	41.4601	2.37012
$307$	−15.5305	−0.886370	−0.443185	−	0.896430i	$-0.646151\pi$
$307$	−15.5305	−0.886370	−0.443185	+	0.896430i	$0.646151\pi$
$308$	−3.46577	−0.197481
$309$	22.8417	1.29942
$310$	−3.88148	−0.220453
$311$	26.0257	1.47578	0.737891	−	0.674920i	$-0.235822\pi$
$311$	26.0257	1.47578	0.737891	+	0.674920i	$0.235822\pi$
$312$	5.10858	0.289217
$313$	8.77516	0.496002	0.248001	−	0.968760i	$-0.420226\pi$
$313$	8.77516	0.496002	0.248001	+	0.968760i	$0.420226\pi$
$314$	−8.04988	−0.454281
$315$	−9.10963	−0.513269
$316$	4.37538	0.246134
$317$	14.8784	0.835654	0.417827	−	0.908527i	$-0.362792\pi$
$317$	14.8784	0.835654	0.417827	+	0.908527i	$0.362792\pi$
$318$	−40.4880	−2.27045
$319$	−5.39768	−0.302212
$320$	−3.57628	−0.199920
$321$	40.3786	2.25371
$322$	−31.7934	−1.77178
$323$	26.5049	1.47477
$324$	−7.99792	−0.444329
$325$	−2.05468	−0.113973
$326$	−9.93540	−0.550271
$327$	−10.0167	−0.553926
$328$	9.72401	0.536918
$329$	5.05298	0.278580
$330$	4.92082	0.270882
$331$	−15.9860	−0.878673	−0.439336	−	0.898323i	$-0.644786\pi$
$331$	−15.9860	−0.878673	−0.439336	+	0.898323i	$0.644786\pi$
$332$	−10.8894	−0.597635
$333$	9.52753	0.522105
$334$	−9.88627	−0.540953
$335$	−6.19999	−0.338742
$336$	−29.0228	−1.58332
$337$	10.6872	0.582166	0.291083	−	0.956698i	$-0.405984\pi$
$337$	10.6872	0.582166	0.291083	+	0.956698i	$0.405984\pi$
$338$	16.4103	0.892605
$339$	21.0401	1.14274
$340$	−8.43768	−0.457597
$341$	2.07630	0.112438
$342$	34.4857	1.86477
$343$	19.9957	1.07967
$344$	0.771794	0.0416123
$345$	19.3074	1.03947
$346$	42.7883	2.30032
$347$	−12.8687	−0.690827	−0.345413	−	0.938451i	$-0.612261\pi$
$347$	−12.8687	−0.690827	−0.345413	+	0.938451i	$0.612261\pi$
$348$	21.2374	1.13844
$349$	−23.7664	−1.27219	−0.636093	−	0.771612i	$-0.719451\pi$
$349$	−23.7664	−1.27219	−0.636093	+	0.771612i	$0.719451\pi$
$350$	4.33454	0.231691
$351$	5.02360	0.268140
$352$	7.00043	0.373124
$353$	34.5154	1.83707	0.918535	−	0.395339i	$-0.129373\pi$
$353$	34.5154	1.83707	0.918535	+	0.395339i	$0.129373\pi$
$354$	−2.61621	−0.139050
$355$	−8.72428	−0.463037
$356$	−3.97181	−0.210505
$357$	−34.4529	−1.82344
$358$	38.3331	2.02597
$359$	17.0673	0.900780	0.450390	−	0.892832i	$-0.351285\pi$
$359$	17.0673	0.900780	0.450390	+	0.892832i	$0.351285\pi$
$360$	3.71100	0.195587
$361$	3.04625	0.160329
$362$	−25.6369	−1.34745
$363$	−2.63227	−0.138158
$364$	7.12105	0.373244
$365$	1.00000	0.0523424
$366$	−33.9641	−1.77533
$367$	−36.0794	−1.88333	−0.941666	−	0.336550i	$-0.890740\pi$
$367$	−36.0794	−1.88333	−0.941666	+	0.336550i	$0.890740\pi$
$368$	34.8791	1.81820
$369$	40.4467	2.10557
$370$	−4.53339	−0.235680
$371$	19.0777	0.990462
$372$	−8.16929	−0.423558
$373$	−17.8517	−0.924328	−0.462164	−	0.886794i	$-0.652927\pi$
$373$	−17.8517	−0.924328	−0.462164	+	0.886794i	$0.652927\pi$
$374$	10.5528	0.545670
$375$	−2.63227	−0.135930
$376$	−2.05844	−0.106156
$377$	11.0905	0.571189
$378$	−10.5978	−0.545091
$379$	−9.76239	−0.501460	−0.250730	−	0.968057i	$-0.580671\pi$
$379$	−9.76239	−0.501460	−0.250730	+	0.968057i	$0.580671\pi$
$380$	−7.01829	−0.360031
$381$	−45.0265	−2.30678
$382$	44.2688	2.26499
$383$	32.6905	1.67041	0.835203	−	0.549942i	$-0.185350\pi$
$383$	32.6905	1.67041	0.835203	+	0.549942i	$0.185350\pi$
$384$	19.2558	0.982645
$385$	−2.31866	−0.118170
$386$	−41.8323	−2.12921
$387$	3.21025	0.163186
$388$	−23.1806	−1.17681
$389$	15.3291	0.777214	0.388607	−	0.921404i	$-0.372956\pi$
$389$	15.3291	0.777214	0.388607	+	0.921404i	$0.372956\pi$
$390$	−10.1107	−0.511975
$391$	41.4050	2.09394
$392$	−1.53380	−0.0774686
$393$	15.7216	0.793049
$394$	−22.9504	−1.15622
$395$	2.92720	0.147283
$396$	5.87257	0.295108
$397$	−1.20870	−0.0606629	−0.0303315	−	0.999540i	$-0.509656\pi$
$397$	−1.20870	−0.0606629	−0.0303315	+	0.999540i	$0.509656\pi$
$398$	20.5487	1.03001
$399$	−28.6572	−1.43466
$400$	−4.75524	−0.237762
$401$	−19.0629	−0.951956	−0.475978	−	0.879457i	$-0.657906\pi$
$401$	−19.0629	−0.951956	−0.475978	+	0.879457i	$0.657906\pi$
$402$	−30.5090	−1.52165
$403$	−4.26613	−0.212511
$404$	29.7919	1.48220
$405$	−5.35073	−0.265880
$406$	−23.3965	−1.16115
$407$	2.42502	0.120204
$408$	14.0351	0.694842
$409$	−4.81050	−0.237864	−0.118932	−	0.992902i	$-0.537947\pi$
$409$	−4.81050	−0.237864	−0.118932	+	0.992902i	$0.537947\pi$
$410$	−19.2453	−0.950459
$411$	−3.06973	−0.151419
$412$	−12.9707	−0.639018
$413$	1.23274	0.0606592
$414$	53.8722	2.64767
$415$	−7.28519	−0.357616
$416$	−14.3836	−0.705215
$417$	6.48152	0.317401
$418$	8.77757	0.429325
$419$	−5.31371	−0.259592	−0.129796	−	0.991541i	$-0.541432\pi$
$419$	−5.31371	−0.259592	−0.129796	+	0.991541i	$0.541432\pi$
$420$	9.12285	0.445150
$421$	37.0089	1.80371	0.901853	−	0.432044i	$-0.142207\pi$
$421$	37.0089	1.80371	0.901853	+	0.432044i	$0.142207\pi$
$422$	9.44546	0.459798
$423$	−8.56200	−0.416299
$424$	−7.77169	−0.377427
$425$	−5.64494	−0.273820
$426$	−42.9306	−2.07999
$427$	16.0036	0.774471
$428$	−22.9290	−1.10832
$429$	5.40846	0.261123
$430$	−1.52750	−0.0736627
$431$	27.7183	1.33514	0.667572	−	0.744545i	$-0.267334\pi$
$431$	27.7183	1.33514	0.667572	+	0.744545i	$0.267334\pi$
$432$	11.6264	0.559374
$433$	5.52240	0.265390	0.132695	−	0.991157i	$-0.457637\pi$
$433$	5.52240	0.265390	0.132695	+	0.991157i	$0.457637\pi$
$434$	8.99981	0.432005
$435$	14.2082	0.681229
$436$	5.68799	0.272406
$437$	34.4398	1.64748
$438$	4.92082	0.235126
$439$	−29.8825	−1.42621	−0.713106	−	0.701056i	$-0.752712\pi$
$439$	−29.8825	−1.42621	−0.713106	+	0.701056i	$0.752712\pi$
$440$	0.944554	0.0450298
$441$	−6.37979	−0.303800
$442$	−21.6825	−1.03133
$443$	1.22325	0.0581185	0.0290592	−	0.999578i	$-0.490749\pi$
$443$	1.22325	0.0581185	0.0290592	+	0.999578i	$0.490749\pi$
$444$	−9.54136	−0.452813
$445$	−2.65720	−0.125963
$446$	46.2119	2.18820
$447$	−36.6437	−1.73319
$448$	8.29216	0.391768
$449$	2.24760	0.106071	0.0530354	−	0.998593i	$-0.483110\pi$
$449$	2.24760	0.106071	0.0530354	+	0.998593i	$0.483110\pi$
$450$	−7.34466	−0.346230
$451$	10.2948	0.484764
$452$	−11.9476	−0.561969
$453$	57.9583	2.72312
$454$	6.43986	0.302238
$455$	4.76409	0.223344
$456$	11.6741	0.546691
$457$	16.8453	0.787988	0.393994	−	0.919113i	$-0.371093\pi$
$457$	16.8453	0.787988	0.393994	+	0.919113i	$0.371093\pi$
$458$	22.6374	1.05778
$459$	13.8016	0.644205
$460$	−10.9637	−0.511185
$461$	17.3722	0.809103	0.404552	−	0.914515i	$-0.367428\pi$
$461$	17.3722	0.809103	0.404552	+	0.914515i	$0.367428\pi$
$462$	−11.4097	−0.530827
$463$	14.1392	0.657103	0.328552	−	0.944486i	$-0.393439\pi$
$463$	14.1392	0.657103	0.328552	+	0.944486i	$0.393439\pi$
$464$	25.6673	1.19157
$465$	−5.46538	−0.253451
$466$	−4.17195	−0.193262
$467$	−0.111111	−0.00514160	−0.00257080	−	0.999997i	$-0.500818\pi$
$467$	−0.111111	−0.00514160	−0.00257080	+	0.999997i	$0.500818\pi$
$468$	−12.0662	−0.557762
$469$	14.3756	0.663806
$470$	4.07397	0.187918
$471$	−11.3348	−0.522278
$472$	−0.502183	−0.0231148
$473$	0.817099	0.0375702
$474$	14.4042	0.661607
$475$	−4.69534	−0.215437
$476$	19.5641	0.896718
$477$	−32.3261	−1.48011
$478$	8.09429	0.370224
$479$	0.0129715	0.000592681 0	0.000296341	−	1.00000i	$-0.499906\pi$
$479$	0.0129715	0.000592681 0	0.000296341		1.00000i	$0.499906\pi$
$480$	−18.4270	−0.841075
$481$	−4.98264	−0.227189
$482$	−19.0498	−0.867695
$483$	−44.7672	−2.03698
$484$	1.49473	0.0679425
$485$	−15.5081	−0.704189
$486$	−40.0420	−1.81634
$487$	−36.8567	−1.67014	−0.835069	−	0.550145i	$-0.814572\pi$
$487$	−36.8567	−1.67014	−0.835069	+	0.550145i	$0.814572\pi$
$488$	−6.51943	−0.295121
$489$	−13.9897	−0.632637
$490$	3.03563	0.137136
$491$	41.3508	1.86614	0.933068	−	0.359701i	$-0.117121\pi$
$491$	41.3508	1.86614	0.933068	+	0.359701i	$0.117121\pi$
$492$	−40.5054	−1.82612
$493$	30.4696	1.37228
$494$	−18.0351	−0.811436
$495$	3.92884	0.176588
$496$	−9.87330	−0.443324
$497$	20.2286	0.907377
$498$	−35.8491	−1.60644
$499$	−29.2254	−1.30831	−0.654153	−	0.756362i	$-0.726975\pi$
$499$	−29.2254	−1.30831	−0.654153	+	0.756362i	$0.726975\pi$
$500$	1.49473	0.0668466
$501$	−13.9205	−0.621924
$502$	−38.1216	−1.70145
$503$	−10.5576	−0.470738	−0.235369	−	0.971906i	$-0.575630\pi$
$503$	−10.5576	−0.470738	−0.235369	+	0.971906i	$0.575630\pi$
$504$	−8.60454	−0.383277
$505$	19.9313	0.886929
$506$	13.7120	0.609572
$507$	23.1069	1.02621
$508$	25.5683	1.13441
$509$	19.5917	0.868389	0.434194	−	0.900819i	$-0.357033\pi$
$509$	19.5917	0.868389	0.434194	+	0.900819i	$0.357033\pi$
$510$	−27.7777	−1.23002
$511$	−2.31866	−0.102571
$512$	−24.3056	−1.07416
$513$	11.4799	0.506851
$514$	−16.2547	−0.716964
$515$	−8.67756	−0.382379
$516$	−3.21491	−0.141529
$517$	−2.17927	−0.0958442
$518$	10.5114	0.461843
$519$	60.2488	2.64463
$520$	−1.94075	−0.0851076
$521$	26.7569	1.17224	0.586120	−	0.810224i	$-0.300655\pi$
$521$	26.7569	1.17224	0.586120	+	0.810224i	$0.300655\pi$
$522$	39.6441	1.73518
$523$	33.2544	1.45412	0.727058	−	0.686576i	$-0.240887\pi$
$523$	33.2544	1.45412	0.727058	+	0.686576i	$0.240887\pi$
$524$	−8.92750	−0.390000
$525$	6.10333	0.266371
$526$	−41.4685	−1.80811
$527$	−11.7206	−0.510557
$528$	12.5171	0.544735
$529$	30.8005	1.33915
$530$	15.3814	0.668125
$531$	−2.08881	−0.0906468
$532$	16.2730	0.705524
$533$	−21.1525	−0.916217
$534$	−13.0756	−0.565836
$535$	−15.3399	−0.663200
$536$	−5.85623	−0.252950
$537$	53.9756	2.32922
$538$	19.4196	0.837240
$539$	−1.62384	−0.0699436
$540$	−3.65457	−0.157267
$541$	−23.7282	−1.02015	−0.510077	−	0.860129i	$-0.670383\pi$
$541$	−23.7282	−1.02015	−0.510077	+	0.860129i	$0.670383\pi$
$542$	5.96956	0.256415
$543$	−36.0985	−1.54914
$544$	−39.5170	−1.69428
$545$	3.80535	0.163003
$546$	23.4432	1.00328
$547$	23.2207	0.992844	0.496422	−	0.868081i	$-0.334647\pi$
$547$	23.2207	0.992844	0.496422	+	0.868081i	$0.334647\pi$
$548$	1.74315	0.0744636
$549$	−27.1173	−1.15734
$550$	−1.86942	−0.0797124
$551$	25.3440	1.07969
$552$	18.2369	0.776213
$553$	−6.78716	−0.288619
$554$	−47.0999	−2.00108
$555$	−6.38331	−0.270957
$556$	−3.68053	−0.156089
$557$	6.21306	0.263256	0.131628	−	0.991299i	$-0.457980\pi$
$557$	6.21306	0.263256	0.131628	+	0.991299i	$0.457980\pi$
$558$	−15.2497	−0.645572
$559$	−1.67887	−0.0710088
$560$	11.0258	0.465923
$561$	14.8590	0.627347
$562$	12.0017	0.506260
$563$	43.4457	1.83102	0.915509	−	0.402297i	$-0.131788\pi$
$563$	43.4457	1.83102	0.915509	+	0.402297i	$0.131788\pi$
$564$	8.57443	0.361049
$565$	−7.99314	−0.336274
$566$	41.3641	1.73866
$567$	12.4065	0.521024
$568$	−8.24055	−0.345766
$569$	16.6658	0.698666	0.349333	−	0.936999i	$-0.386408\pi$
$569$	16.6658	0.698666	0.349333	+	0.936999i	$0.386408\pi$
$570$	−23.1049	−0.967759
$571$	33.6730	1.40917	0.704585	−	0.709619i	$-0.251133\pi$
$571$	33.6730	1.40917	0.704585	+	0.709619i	$0.251133\pi$
$572$	−3.07120	−0.128413
$573$	62.3334	2.60402
$574$	44.6233	1.86254
$575$	−7.33488	−0.305886
$576$	−14.0506	−0.585443
$577$	19.8551	0.826580	0.413290	−	0.910599i	$-0.364380\pi$
$577$	19.8551	0.826580	0.413290	+	0.910599i	$0.364380\pi$
$578$	−27.7895	−1.15589
$579$	−58.9026	−2.44791
$580$	−8.06810	−0.335010
$581$	16.8919	0.700792
$582$	−76.3128	−3.16327
$583$	−8.22789	−0.340765
$584$	0.944554	0.0390859
$585$	−8.07250	−0.333757
$586$	19.8237	0.818911
$587$	29.4398	1.21511	0.607556	−	0.794277i	$-0.292150\pi$
$587$	29.4398	1.21511	0.607556	+	0.794277i	$0.292150\pi$
$588$	6.38905	0.263480
$589$	−9.74894	−0.401698
$590$	0.993899	0.0409182
$591$	−32.3156	−1.32929
$592$	−11.5316	−0.473944
$593$	−27.4004	−1.12520	−0.562600	−	0.826729i	$-0.690199\pi$
$593$	−27.4004	−1.12520	−0.562600	+	0.826729i	$0.690199\pi$
$594$	4.57066	0.187536
$595$	13.0887	0.536583
$596$	20.8081	0.852335
$597$	28.9339	1.18419
$598$	−28.1737	−1.15211
$599$	34.7195	1.41860	0.709299	−	0.704907i	$-0.249012\pi$
$599$	34.7195	1.41860	0.709299	+	0.704907i	$0.249012\pi$
$600$	−2.48632	−0.101504
$601$	−3.41657	−0.139365	−0.0696825	−	0.997569i	$-0.522199\pi$
$601$	−3.41657	−0.139365	−0.0696825	+	0.997569i	$0.522199\pi$
$602$	3.54175	0.144351
$603$	−24.3588	−0.991966
$604$	−32.9116	−1.33915
$605$	1.00000	0.0406558
$606$	98.0781	3.98415
$607$	39.0259	1.58401	0.792006	−	0.610513i	$-0.209037\pi$
$607$	39.0259	1.58401	0.792006	+	0.610513i	$0.209037\pi$
$608$	−32.8694	−1.33303
$609$	−32.9438	−1.33495
$610$	12.9030	0.522426
$611$	4.47769	0.181148
$612$	−33.1503	−1.34002
$613$	−29.4630	−1.19000	−0.594999	−	0.803726i	$-0.702848\pi$
$613$	−29.4630	−1.19000	−0.594999	+	0.803726i	$0.702848\pi$
$614$	29.0330	1.17167
$615$	−27.0987	−1.09273
$616$	−2.19010	−0.0882415
$617$	−36.0242	−1.45028	−0.725139	−	0.688603i	$-0.758224\pi$
$617$	−36.0242	−1.45028	−0.725139	+	0.688603i	$0.758224\pi$
$618$	−42.7007	−1.71767
$619$	−35.9962	−1.44681	−0.723405	−	0.690424i	$-0.757424\pi$
$619$	−35.9962	−1.44681	−0.723405	+	0.690424i	$0.757424\pi$
$620$	3.10352	0.124640
$621$	17.9335	0.719646
$622$	−48.6530	−1.95081
$623$	6.16113	0.246840
$624$	−25.7185	−1.02956
$625$	1.00000	0.0400000
$626$	−16.4045	−0.655655
$627$	12.3594	0.493587
$628$	6.43645	0.256842
$629$	−13.6891	−0.545820
$630$	17.0297	0.678481
$631$	−31.6079	−1.25829	−0.629146	−	0.777288i	$-0.716595\pi$
$631$	−31.6079	−1.25829	−0.629146	+	0.777288i	$0.716595\pi$
$632$	2.76489	0.109982
$633$	13.2998	0.528621
$634$	−27.8140	−1.10463
$635$	17.1056	0.678814
$636$	32.3730	1.28367
$637$	3.33646	0.132195
$638$	10.0905	0.399488
$639$	−34.2763	−1.35595
$640$	−7.31529	−0.289162
$641$	20.5015	0.809761	0.404881	−	0.914370i	$-0.367313\pi$
$641$	20.5015	0.809761	0.404881	+	0.914370i	$0.367313\pi$
$642$	−75.4846	−2.97914
$643$	−27.5515	−1.08652	−0.543262	−	0.839563i	$-0.682811\pi$
$643$	−27.5515	−1.08652	−0.543262	+	0.839563i	$0.682811\pi$
$644$	25.4211	1.00173
$645$	−2.15082	−0.0846886
$646$	−49.5488	−1.94947
$647$	−16.6039	−0.652765	−0.326382	−	0.945238i	$-0.605830\pi$
$647$	−16.6039	−0.652765	−0.326382	+	0.945238i	$0.605830\pi$
$648$	−5.05405	−0.198542
$649$	−0.531662	−0.0208695
$650$	3.84106	0.150659
$651$	12.6723	0.496668
$652$	7.94406	0.311113
$653$	−7.21202	−0.282228	−0.141114	−	0.989993i	$-0.545068\pi$
$653$	−7.21202	−0.282228	−0.141114	+	0.989993i	$0.545068\pi$
$654$	18.7255	0.732223
$655$	−5.97264	−0.233370
$656$	−48.9543	−1.91134
$657$	3.92884	0.153279
$658$	−9.44614	−0.368249
$659$	−27.2223	−1.06043	−0.530214	−	0.847864i	$-0.677889\pi$
$659$	−27.2223	−1.06043	−0.530214	+	0.847864i	$0.677889\pi$
$660$	−3.93454	−0.153152
$661$	5.53570	0.215314	0.107657	−	0.994188i	$-0.465665\pi$
$661$	5.53570	0.215314	0.107657	+	0.994188i	$0.465665\pi$
$662$	29.8847	1.16150
$663$	−30.5304	−1.18570
$664$	−6.88126	−0.267045
$665$	10.8869	0.422175
$666$	−17.8110	−0.690161
$667$	39.5914	1.53298
$668$	7.90478	0.305845
$669$	65.0695	2.51573
$670$	11.5904	0.447776
$671$	−6.90212	−0.266454
$672$	42.7259	1.64819
$673$	−17.7571	−0.684487	−0.342243	−	0.939611i	$-0.611187\pi$
$673$	−17.7571	−0.684487	−0.342243	+	0.939611i	$0.611187\pi$
$674$	−19.9788	−0.769554
$675$	−2.44496	−0.0941065
$676$	−13.1212	−0.504663
$677$	−31.9759	−1.22893	−0.614467	−	0.788942i	$-0.710629\pi$
$677$	−31.9759	−1.22893	−0.614467	+	0.788942i	$0.710629\pi$
$678$	−39.3328	−1.51057
$679$	35.9581	1.37994
$680$	−5.33195	−0.204471
$681$	9.06775	0.347477
$682$	−3.88148	−0.148630
$683$	−9.38423	−0.359077	−0.179539	−	0.983751i	$-0.557461\pi$
$683$	−9.38423	−0.359077	−0.179539	+	0.983751i	$0.557461\pi$
$684$	−27.5738	−1.05431
$685$	1.16619	0.0445579
$686$	−37.3804	−1.42719
$687$	31.8750	1.21611
$688$	−3.88550	−0.148133
$689$	16.9057	0.644054
$690$	−36.0936	−1.37406
$691$	20.1558	0.766765	0.383382	−	0.923590i	$-0.374759\pi$
$691$	20.1558	0.766765	0.383382	+	0.923590i	$0.374759\pi$
$692$	−34.2123	−1.30056
$693$	−9.10963	−0.346046
$694$	24.0570	0.913190
$695$	−2.46233	−0.0934016
$696$	13.4204	0.508698
$697$	−58.1136	−2.20121
$698$	44.4294	1.68168
$699$	−5.87438	−0.222189
$700$	−3.46577	−0.130994
$701$	−4.28717	−0.161924	−0.0809621	−	0.996717i	$-0.525799\pi$
$701$	−4.28717	−0.161924	−0.0809621	+	0.996717i	$0.525799\pi$
$702$	−9.39122	−0.354449
$703$	−11.3863	−0.429443
$704$	−3.57628	−0.134786
$705$	5.73642	0.216046
$706$	−64.5238	−2.42839
$707$	−46.2137	−1.73805
$708$	2.09185	0.0786164
$709$	−39.7722	−1.49367	−0.746837	−	0.665007i	$-0.768429\pi$
$709$	−39.7722	−1.49367	−0.746837	+	0.665007i	$0.768429\pi$
$710$	16.3093	0.612079
$711$	11.5005	0.431302
$712$	−2.50987	−0.0940612
$713$	−15.2294	−0.570346
$714$	64.4069	2.41037
$715$	−2.05468	−0.0768405
$716$	−30.6501	−1.14545
$717$	11.3973	0.425640
$718$	−31.9061	−1.19072
$719$	−11.1836	−0.417076	−0.208538	−	0.978014i	$-0.566871\pi$
$719$	−11.1836	−0.417076	−0.208538	+	0.978014i	$0.566871\pi$
$720$	−18.6826	−0.696258
$721$	20.1203	0.749318
$722$	−5.69473	−0.211936
$723$	−26.8234	−0.997573
$724$	20.4986	0.761823
$725$	−5.39768	−0.200465
$726$	4.92082	0.182629
$727$	5.24603	0.194565	0.0972823	−	0.995257i	$-0.468985\pi$
$727$	5.24603	0.194565	0.0972823	+	0.995257i	$0.468985\pi$
$728$	4.49994	0.166779
$729$	−40.3295	−1.49369
$730$	−1.86942	−0.0691904
$731$	−4.61247	−0.170598
$732$	27.1567	1.00374
$733$	−47.8133	−1.76602	−0.883012	−	0.469351i	$-0.844488\pi$
$733$	−47.8133	−1.76602	−0.883012	+	0.469351i	$0.844488\pi$
$734$	67.4476	2.48954
$735$	4.27437	0.157663
$736$	−51.3474	−1.89269
$737$	−6.19999	−0.228380
$738$	−75.6119	−2.78331
$739$	−16.5685	−0.609483	−0.304742	−	0.952435i	$-0.598570\pi$
$739$	−16.5685	−0.609483	−0.304742	+	0.952435i	$0.598570\pi$
$740$	3.62477	0.133249
$741$	−25.3946	−0.932893
$742$	−35.6642	−1.30927
$743$	0.360507	0.0132257	0.00661285	−	0.999978i	$-0.497895\pi$
$743$	0.360507	0.0132257	0.00661285	+	0.999978i	$0.497895\pi$
$744$	−5.16235	−0.189261
$745$	13.9210	0.510025
$746$	33.3724	1.22185
$747$	−28.6224	−1.04724
$748$	−8.43768	−0.308512
$749$	35.5678	1.29962
$750$	4.92082	0.179683
$751$	−8.54101	−0.311666	−0.155833	−	0.987783i	$-0.549806\pi$
$751$	−8.54101	−0.311666	−0.155833	+	0.987783i	$0.549806\pi$
$752$	10.3629	0.377898
$753$	−53.6777	−1.95613
$754$	−20.7328	−0.755044
$755$	−22.0184	−0.801331
$756$	8.47368	0.308185
$757$	4.95859	0.180223	0.0901115	−	0.995932i	$-0.471278\pi$
$757$	4.95859	0.180223	0.0901115	+	0.995932i	$0.471278\pi$
$758$	18.2500	0.662871
$759$	19.3074	0.700814
$760$	−4.43501	−0.160875
$761$	27.9433	1.01294	0.506471	−	0.862257i	$-0.330950\pi$
$761$	27.9433	1.01294	0.506471	+	0.862257i	$0.330950\pi$
$762$	84.1734	3.04928
$763$	−8.82331	−0.319425
$764$	−35.3961	−1.28058
$765$	−22.1781	−0.801849
$766$	−61.1123	−2.20808
$767$	1.09239	0.0394440
$768$	−54.8247	−1.97832
$769$	−37.1776	−1.34066	−0.670330	−	0.742064i	$-0.733847\pi$
$769$	−37.1776	−1.34066	−0.670330	+	0.742064i	$0.733847\pi$
$770$	4.33454	0.156206
$771$	−22.8877	−0.824281
$772$	33.4479	1.20381
$773$	31.5644	1.13529	0.567645	−	0.823273i	$-0.307854\pi$
$773$	31.5644	1.13529	0.567645	+	0.823273i	$0.307854\pi$
$774$	−6.00131	−0.215713
$775$	2.07630	0.0745829
$776$	−14.6483	−0.525843
$777$	14.8007	0.530972
$778$	−28.6565	−1.02738
$779$	−48.3377	−1.73188
$780$	8.08421	0.289461
$781$	−8.72428	−0.312179
$782$	−77.4033	−2.76794
$783$	13.1971	0.471626
$784$	7.72173	0.275776
$785$	4.30608	0.153691
$786$	−29.3903	−1.04832
$787$	14.1531	0.504503	0.252251	−	0.967662i	$-0.418829\pi$
$787$	14.1531	0.504503	0.252251	+	0.967662i	$0.418829\pi$
$788$	18.3504	0.653707
$789$	−58.3905	−2.07876
$790$	−5.47216	−0.194691
$791$	18.5333	0.658970
$792$	3.71100	0.131865
$793$	14.1816	0.503604
$794$	2.25957	0.0801891
$795$	21.6580	0.768131
$796$	−16.4301	−0.582351
$797$	21.1224	0.748194	0.374097	−	0.927389i	$-0.377953\pi$
$797$	21.1224	0.748194	0.374097	+	0.927389i	$0.377953\pi$
$798$	53.5724	1.89644
$799$	12.3018	0.435208
$800$	7.00043	0.247503
$801$	−10.4397	−0.368869
$802$	35.6366	1.25837
$803$	1.00000	0.0352892
$804$	24.3941	0.860315
$805$	17.0071	0.599420
$806$	7.97518	0.280914
$807$	27.3441	0.962559
$808$	18.8262	0.662302
$809$	−13.9789	−0.491473	−0.245736	−	0.969337i	$-0.579030\pi$
$809$	−13.9789	−0.491473	−0.245736	+	0.969337i	$0.579030\pi$
$810$	10.0028	0.351461
$811$	47.0796	1.65319	0.826593	−	0.562800i	$-0.190276\pi$
$811$	47.0796	1.65319	0.826593	+	0.562800i	$0.190276\pi$
$812$	18.7071	0.656492
$813$	8.40554	0.294795
$814$	−4.53339	−0.158895
$815$	5.31470	0.186166
$816$	−70.6580	−2.47353
$817$	−3.83656	−0.134224
$818$	8.99284	0.314427
$819$	18.7173	0.654037
$820$	15.3880	0.537373
$821$	5.52178	0.192711	0.0963557	−	0.995347i	$-0.469281\pi$
$821$	5.52178	0.192711	0.0963557	+	0.995347i	$0.469281\pi$
$822$	5.73862	0.200157
$823$	16.2460	0.566301	0.283150	−	0.959076i	$-0.408620\pi$
$823$	16.2460	0.566301	0.283150	+	0.959076i	$0.408620\pi$
$824$	−8.19643	−0.285536
$825$	−2.63227	−0.0916438
$826$	−2.30451	−0.0801842
$827$	28.5272	0.991989	0.495995	−	0.868326i	$-0.334804\pi$
$827$	28.5272	0.991989	0.495995	+	0.868326i	$0.334804\pi$
$828$	−43.0747	−1.49695
$829$	14.1575	0.491711	0.245855	−	0.969307i	$-0.420931\pi$
$829$	14.1575	0.491711	0.245855	+	0.969307i	$0.420931\pi$
$830$	13.6191	0.472726
$831$	−66.3198	−2.30061
$832$	7.34810	0.254749
$833$	9.16645	0.317599
$834$	−12.1167	−0.419567
$835$	5.28842	0.183013
$836$	−7.01829	−0.242733
$837$	−5.07647	−0.175468
$838$	9.93356	0.343149
$839$	12.0464	0.415887	0.207943	−	0.978141i	$-0.433323\pi$
$839$	12.0464	0.415887	0.207943	+	0.978141i	$0.433323\pi$
$840$	5.76492	0.198909
$841$	0.134966	0.00465399
$842$	−69.1853	−2.38428
$843$	16.8991	0.582037
$844$	−7.55232	−0.259961
$845$	−8.77830	−0.301983
$846$	16.0060	0.550297
$847$	−2.31866	−0.0796699
$848$	39.1256	1.34358
$849$	58.2434	1.99891
$850$	10.5528	0.361957
$851$	−17.7873	−0.609740
$852$	34.3261	1.17599
$853$	11.8617	0.406136	0.203068	−	0.979165i	$-0.434909\pi$
$853$	11.8617	0.406136	0.203068	+	0.979165i	$0.434909\pi$
$854$	−29.9176	−1.02376
$855$	−18.4473	−0.630883
$856$	−14.4893	−0.495235
$857$	51.0560	1.74404	0.872020	−	0.489470i	$-0.162810\pi$
$857$	51.0560	1.74404	0.872020	+	0.489470i	$0.162810\pi$
$858$	−10.1107	−0.345173
$859$	−25.0448	−0.854518	−0.427259	−	0.904129i	$-0.640521\pi$
$859$	−25.0448	−0.854518	−0.427259	+	0.904129i	$0.640521\pi$
$860$	1.22135	0.0416475
$861$	62.8326	2.14133
$862$	−51.8172	−1.76490
$863$	−11.2661	−0.383503	−0.191751	−	0.981444i	$-0.561417\pi$
$863$	−11.2661	−0.383503	−0.191751	+	0.981444i	$0.561417\pi$
$864$	−17.1158	−0.582290
$865$	−22.8886	−0.778234
$866$	−10.3237	−0.350813
$867$	−39.1295	−1.32891
$868$	−7.19599	−0.244248
$869$	2.92720	0.0992983
$870$	−26.5610	−0.900503
$871$	12.7390	0.431644
$872$	3.59436	0.121720
$873$	−60.9290	−2.06214
$874$	−64.3825	−2.17777
$875$	−2.31866	−0.0783849
$876$	−3.93454	−0.132936
$877$	17.7317	0.598756	0.299378	−	0.954135i	$-0.403221\pi$
$877$	17.7317	0.598756	0.299378	+	0.954135i	$0.403221\pi$
$878$	55.8629	1.88528
$879$	27.9131	0.941486
$880$	−4.75524	−0.160299
$881$	27.1891	0.916024	0.458012	−	0.888946i	$-0.348562\pi$
$881$	27.1891	0.916024	0.458012	+	0.888946i	$0.348562\pi$
$882$	11.9265	0.401587
$883$	20.0274	0.673974	0.336987	−	0.941509i	$-0.390592\pi$
$883$	20.0274	0.673974	0.336987	+	0.941509i	$0.390592\pi$
$884$	17.3367	0.583096
$885$	1.39948	0.0470429
$886$	−2.28677	−0.0768257
$887$	−1.46978	−0.0493504	−0.0246752	−	0.999696i	$-0.507855\pi$
$887$	−1.46978	−0.0493504	−0.0246752	+	0.999696i	$0.507855\pi$
$888$	−6.02938	−0.202333
$889$	−39.6619	−1.33022
$890$	4.96742	0.166508
$891$	−5.35073	−0.179256
$892$	−36.9497	−1.23717
$893$	10.2324	0.342415
$894$	68.5026	2.29107
$895$	−20.5054	−0.685419
$896$	16.9616	0.566649
$897$	−39.6704	−1.32456
$898$	−4.20171	−0.140213
$899$	−11.2072	−0.373781
$900$	5.87257	0.195752
$901$	46.4459	1.54734
$902$	−19.2453	−0.640800
$903$	4.98702	0.165958
$904$	−7.54995	−0.251108
$905$	13.7138	0.455864
$906$	−108.348	−3.59964
$907$	7.40490	0.245876	0.122938	−	0.992414i	$-0.460768\pi$
$907$	7.40490	0.245876	0.122938	+	0.992414i	$0.460768\pi$
$908$	−5.14913	−0.170880
$909$	78.3068	2.59727
$910$	−8.90608	−0.295234
$911$	−10.3475	−0.342828	−0.171414	−	0.985199i	$-0.554834\pi$
$911$	−10.3475	−0.342828	−0.171414	+	0.985199i	$0.554834\pi$
$912$	−58.7719	−1.94613
$913$	−7.28519	−0.241105
$914$	−31.4909	−1.04163
$915$	18.1682	0.600624
$916$	−18.1002	−0.598048
$917$	13.8485	0.457317
$918$	−25.8011	−0.851562
$919$	20.6624	0.681588	0.340794	−	0.940138i	$-0.389304\pi$
$919$	20.6624	0.681588	0.340794	+	0.940138i	$0.389304\pi$
$920$	−6.92819	−0.228416
$921$	40.8803	1.34705
$922$	−32.4759	−1.06954
$923$	17.9256	0.590027
$924$	9.12285	0.300120
$925$	2.42502	0.0797343
$926$	−26.4321	−0.868612
$927$	−34.0928	−1.11975
$928$	−37.7861	−1.24039
$929$	−2.16663	−0.0710848	−0.0355424	−	0.999368i	$-0.511316\pi$
$929$	−2.16663	−0.0710848	−0.0355424	+	0.999368i	$0.511316\pi$
$930$	10.2171	0.335032
$931$	7.62447	0.249882
$932$	3.33577	0.109267
$933$	−68.5067	−2.24281
$934$	0.207713	0.00679657
$935$	−5.64494	−0.184609
$936$	−7.62491	−0.249228
$937$	−1.18997	−0.0388745	−0.0194373	−	0.999811i	$-0.506187\pi$
$937$	−1.18997	−0.0388745	−0.0194373	+	0.999811i	$0.506187\pi$
$938$	−26.8741	−0.877471
$939$	−23.0986	−0.753794
$940$	−3.25743	−0.106246
$941$	17.5590	0.572406	0.286203	−	0.958169i	$-0.407607\pi$
$941$	17.5590	0.572406	0.286203	+	0.958169i	$0.407607\pi$
$942$	21.1894	0.690390
$943$	−75.5113	−2.45899
$944$	2.52818	0.0822852
$945$	5.66902	0.184413
$946$	−1.52750	−0.0496634
$947$	44.0792	1.43238	0.716191	−	0.697904i	$-0.245884\pi$
$947$	44.0792	1.43238	0.716191	+	0.697904i	$0.245884\pi$
$948$	−11.5172	−0.374061
$949$	−2.05468	−0.0666976
$950$	8.77757	0.284782
$951$	−39.1640	−1.26998
$952$	12.3629	0.400685
$953$	−6.83843	−0.221519	−0.110759	−	0.993847i	$-0.535328\pi$
$953$	−6.83843	−0.221519	−0.110759	+	0.993847i	$0.535328\pi$
$954$	60.4311	1.95653
$955$	−23.6805	−0.766283
$956$	−6.47196	−0.209318
$957$	14.2082	0.459284
$958$	−0.0242491	−0.000783454 0
$959$	−2.70400	−0.0873167
$960$	9.41373	0.303827
$961$	−26.6890	−0.860935
$962$	9.31465	0.300316
$963$	−60.2678	−1.94210
$964$	15.2317	0.490579
$965$	22.3771	0.720345
$966$	83.6887	2.69264
$967$	51.7397	1.66384	0.831918	−	0.554899i	$-0.187243\pi$
$967$	51.7397	1.66384	0.831918	+	0.554899i	$0.187243\pi$
$968$	0.944554	0.0303591
$969$	−69.7681	−2.24127
$970$	28.9913	0.930853
$971$	12.1075	0.388547	0.194274	−	0.980947i	$-0.437765\pi$
$971$	12.1075	0.388547	0.194274	+	0.980947i	$0.437765\pi$
$972$	32.0164	1.02693
$973$	5.70930	0.183032
$974$	68.9008	2.20772
$975$	5.40846	0.173209
$976$	32.8212	1.05058
$977$	13.2742	0.424679	0.212339	−	0.977196i	$-0.431892\pi$
$977$	13.2742	0.424679	0.212339	+	0.977196i	$0.431892\pi$
$978$	26.1527	0.836270
$979$	−2.65720	−0.0849244
$980$	−2.42720	−0.0775342
$981$	14.9506	0.477337
$982$	−77.3020	−2.46681
$983$	41.2776	1.31655	0.658275	−	0.752777i	$-0.271286\pi$
$983$	41.2776	1.31655	0.658275	+	0.752777i	$0.271286\pi$
$984$	−25.5962	−0.815977
$985$	12.2767	0.391169
$986$	−56.9604	−1.81399
$987$	−13.3008	−0.423369
$988$	14.4203	0.458771
$989$	−5.99333	−0.190577
$990$	−7.34466	−0.233429
$991$	−38.0590	−1.20899	−0.604493	−	0.796611i	$-0.706624\pi$
$991$	−38.0590	−1.20899	−0.604493	+	0.796611i	$0.706624\pi$
$992$	14.5350	0.461487
$993$	42.0796	1.33536
$994$	−37.8158	−1.19944
$995$	−10.9920	−0.348470
$996$	28.6639	0.908251
$997$	7.56988	0.239741	0.119870	−	0.992790i	$-0.461752\pi$
$997$	7.56988	0.239741	0.119870	+	0.992790i	$0.461752\pi$
$998$	54.6345	1.72942
$999$	−5.92908	−0.187588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.8	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.8	✓	37	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.86942 q^{2} -2.63227 q^{3} +1.49473 q^{4} +1.00000 q^{5} +4.92082 q^{6} -2.31866 q^{7} +0.944554 q^{8} +3.92884 q^{9} +O(q^{10})\)	\(q-1.86942 q^{2} -2.63227 q^{3} +1.49473 q^{4} +1.00000 q^{5} +4.92082 q^{6} -2.31866 q^{7} +0.944554 q^{8} +3.92884 q^{9} -1.86942 q^{10} +1.00000 q^{11} -3.93454 q^{12} -2.05468 q^{13} +4.33454 q^{14} -2.63227 q^{15} -4.75524 q^{16} -5.64494 q^{17} -7.34466 q^{18} -4.69534 q^{19} +1.49473 q^{20} +6.10333 q^{21} -1.86942 q^{22} -7.33488 q^{23} -2.48632 q^{24} +1.00000 q^{25} +3.84106 q^{26} -2.44496 q^{27} -3.46577 q^{28} -5.39768 q^{29} +4.92082 q^{30} +2.07630 q^{31} +7.00043 q^{32} -2.63227 q^{33} +10.5528 q^{34} -2.31866 q^{35} +5.87257 q^{36} +2.42502 q^{37} +8.77757 q^{38} +5.40846 q^{39} +0.944554 q^{40} +10.2948 q^{41} -11.4097 q^{42} +0.817099 q^{43} +1.49473 q^{44} +3.92884 q^{45} +13.7120 q^{46} -2.17927 q^{47} +12.5171 q^{48} -1.62384 q^{49} -1.86942 q^{50} +14.8590 q^{51} -3.07120 q^{52} -8.22789 q^{53} +4.57066 q^{54} +1.00000 q^{55} -2.19010 q^{56} +12.3594 q^{57} +10.0905 q^{58} -0.531662 q^{59} -3.93454 q^{60} -6.90212 q^{61} -3.88148 q^{62} -9.10963 q^{63} -3.57628 q^{64} -2.05468 q^{65} +4.92082 q^{66} -6.19999 q^{67} -8.43768 q^{68} +19.3074 q^{69} +4.33454 q^{70} -8.72428 q^{71} +3.71100 q^{72} +1.00000 q^{73} -4.53339 q^{74} -2.63227 q^{75} -7.01829 q^{76} -2.31866 q^{77} -10.1107 q^{78} +2.92720 q^{79} -4.75524 q^{80} -5.35073 q^{81} -19.2453 q^{82} -7.28519 q^{83} +9.12285 q^{84} -5.64494 q^{85} -1.52750 q^{86} +14.2082 q^{87} +0.944554 q^{88} -2.65720 q^{89} -7.34466 q^{90} +4.76409 q^{91} -10.9637 q^{92} -5.46538 q^{93} +4.07397 q^{94} -4.69534 q^{95} -18.4270 q^{96} -15.5081 q^{97} +3.03563 q^{98} +3.92884 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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