LMFDB - Embedded newform 1502.2.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} - 25 x^{14} + 59 x^{13} + 273 x^{12} - 443 x^{11} - 1620 x^{10} + 1595 x^{9} + \cdots + 864 $ x^16 - 3x^15 - 25x^14 + 59x^13 + 273x^12 - 443x^11 - 1620x^10 + 1595x^9 + 5490x^8 - 2787x^7 - 10540x^6 + 1919x^5 + 10822x^4 + 132x^3 - 5202x^2 - 408*x + 864
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.30501$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.305006 q^{3} +1.00000 q^{4} +2.67935 q^{5} -0.305006 q^{6} +2.41108 q^{7} +1.00000 q^{8} -2.90697 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.305006 q^{3} +1.00000 q^{4} +2.67935 q^{5} -0.305006 q^{6} +2.41108 q^{7} +1.00000 q^{8} -2.90697 q^{9} +2.67935 q^{10} -4.32689 q^{11} -0.305006 q^{12} +6.76346 q^{13} +2.41108 q^{14} -0.817217 q^{15} +1.00000 q^{16} -1.17614 q^{17} -2.90697 q^{18} -0.414369 q^{19} +2.67935 q^{20} -0.735392 q^{21} -4.32689 q^{22} +8.63243 q^{23} -0.305006 q^{24} +2.17892 q^{25} +6.76346 q^{26} +1.80166 q^{27} +2.41108 q^{28} -3.30975 q^{29} -0.817217 q^{30} +8.69603 q^{31} +1.00000 q^{32} +1.31973 q^{33} -1.17614 q^{34} +6.46012 q^{35} -2.90697 q^{36} +2.69205 q^{37} -0.414369 q^{38} -2.06289 q^{39} +2.67935 q^{40} -4.65927 q^{41} -0.735392 q^{42} +0.830651 q^{43} -4.32689 q^{44} -7.78879 q^{45} +8.63243 q^{46} -7.54908 q^{47} -0.305006 q^{48} -1.18671 q^{49} +2.17892 q^{50} +0.358729 q^{51} +6.76346 q^{52} -12.7799 q^{53} +1.80166 q^{54} -11.5933 q^{55} +2.41108 q^{56} +0.126385 q^{57} -3.30975 q^{58} +1.37476 q^{59} -0.817217 q^{60} +7.34207 q^{61} +8.69603 q^{62} -7.00893 q^{63} +1.00000 q^{64} +18.1217 q^{65} +1.31973 q^{66} +5.52915 q^{67} -1.17614 q^{68} -2.63294 q^{69} +6.46012 q^{70} +6.63252 q^{71} -2.90697 q^{72} -5.69241 q^{73} +2.69205 q^{74} -0.664582 q^{75} -0.414369 q^{76} -10.4325 q^{77} -2.06289 q^{78} +5.27433 q^{79} +2.67935 q^{80} +8.17140 q^{81} -4.65927 q^{82} -0.447396 q^{83} -0.735392 q^{84} -3.15129 q^{85} +0.830651 q^{86} +1.00949 q^{87} -4.32689 q^{88} -3.36588 q^{89} -7.78879 q^{90} +16.3072 q^{91} +8.63243 q^{92} -2.65234 q^{93} -7.54908 q^{94} -1.11024 q^{95} -0.305006 q^{96} -18.2599 q^{97} -1.18671 q^{98} +12.5782 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9	\( 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9} + 4 q^{10} + 4 q^{11} + 13 q^{12} + 17 q^{13} + 7 q^{14} + 8 q^{15} + 16 q^{16} - q^{17} + 21 q^{18} + 23 q^{19} + 4 q^{20} + 9 q^{21} + 4 q^{22} + 15 q^{23} + 13 q^{24} + 24 q^{25} + 17 q^{26} + 31 q^{27} + 7 q^{28} + 4 q^{29} + 8 q^{30} + 42 q^{31} + 16 q^{32} + 3 q^{33} - q^{34} - 13 q^{35} + 21 q^{36} + 31 q^{37} + 23 q^{38} - 2 q^{39} + 4 q^{40} - 9 q^{41} + 9 q^{42} + 13 q^{43} + 4 q^{44} - 2 q^{45} + 15 q^{46} + 18 q^{47} + 13 q^{48} - 9 q^{49} + 24 q^{50} - 2 q^{51} + 17 q^{52} - 14 q^{53} + 31 q^{54} - 2 q^{55} + 7 q^{56} - 18 q^{57} + 4 q^{58} + 4 q^{59} + 8 q^{60} + q^{61} + 42 q^{62} + 17 q^{63} + 16 q^{64} - 32 q^{65} + 3 q^{66} + 5 q^{67} - q^{68} + 6 q^{69} - 13 q^{70} + 9 q^{71} + 21 q^{72} + 28 q^{73} + 31 q^{74} + 16 q^{75} + 23 q^{76} - 30 q^{77} - 2 q^{78} + 10 q^{79} + 4 q^{80} + 12 q^{81} - 9 q^{82} + 3 q^{83} + 9 q^{84} - 7 q^{85} + 13 q^{86} - 22 q^{87} + 4 q^{88} - 17 q^{89} - 2 q^{90} + 12 q^{91} + 15 q^{92} - q^{93} + 18 q^{94} - 4 q^{95} + 13 q^{96} - 17 q^{97} - 9 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9 + 4 * q^10 + 4 * q^11 + 13 * q^12 + 17 * q^13 + 7 * q^14 + 8 * q^15 + 16 * q^16 - q^17 + 21 * q^18 + 23 * q^19 + 4 * q^20 + 9 * q^21 + 4 * q^22 + 15 * q^23 + 13 * q^24 + 24 * q^25 + 17 * q^26 + 31 * q^27 + 7 * q^28 + 4 * q^29 + 8 * q^30 + 42 * q^31 + 16 * q^32 + 3 * q^33 - q^34 - 13 * q^35 + 21 * q^36 + 31 * q^37 + 23 * q^38 - 2 * q^39 + 4 * q^40 - 9 * q^41 + 9 * q^42 + 13 * q^43 + 4 * q^44 - 2 * q^45 + 15 * q^46 + 18 * q^47 + 13 * q^48 - 9 * q^49 + 24 * q^50 - 2 * q^51 + 17 * q^52 - 14 * q^53 + 31 * q^54 - 2 * q^55 + 7 * q^56 - 18 * q^57 + 4 * q^58 + 4 * q^59 + 8 * q^60 + q^61 + 42 * q^62 + 17 * q^63 + 16 * q^64 - 32 * q^65 + 3 * q^66 + 5 * q^67 - q^68 + 6 * q^69 - 13 * q^70 + 9 * q^71 + 21 * q^72 + 28 * q^73 + 31 * q^74 + 16 * q^75 + 23 * q^76 - 30 * q^77 - 2 * q^78 + 10 * q^79 + 4 * q^80 + 12 * q^81 - 9 * q^82 + 3 * q^83 + 9 * q^84 - 7 * q^85 + 13 * q^86 - 22 * q^87 + 4 * q^88 - 17 * q^89 - 2 * q^90 + 12 * q^91 + 15 * q^92 - q^93 + 18 * q^94 - 4 * q^95 + 13 * q^96 - 17 * q^97 - 9 * q^98 - 10 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.305006	−0.176095	−0.0880476	−	0.996116i	$-0.528063\pi$
$3$	−0.305006	−0.176095	−0.0880476	+	0.996116i	$0.528063\pi$
$4$	1.00000	0.500000
$5$	2.67935	1.19824	0.599121	−	0.800659i	$-0.295517\pi$
$5$	2.67935	1.19824	0.599121	+	0.800659i	$0.295517\pi$
$6$	−0.305006	−0.124518
$7$	2.41108	0.911301	0.455650	−	0.890159i	$-0.349407\pi$
$7$	2.41108	0.911301	0.455650	+	0.890159i	$0.349407\pi$
$8$	1.00000	0.353553
$9$	−2.90697	−0.968991
$10$	2.67935	0.847285
$11$	−4.32689	−1.30461	−0.652304	−	0.757958i	$-0.726197\pi$
$11$	−4.32689	−1.30461	−0.652304	+	0.757958i	$0.726197\pi$
$12$	−0.305006	−0.0880476
$13$	6.76346	1.87585	0.937923	−	0.346843i	$-0.112746\pi$
$13$	6.76346	1.87585	0.937923	+	0.346843i	$0.112746\pi$
$14$	2.41108	0.644387
$15$	−0.817217	−0.211004
$16$	1.00000	0.250000
$17$	−1.17614	−0.285256	−0.142628	−	0.989776i	$-0.545555\pi$
$17$	−1.17614	−0.285256	−0.142628	+	0.989776i	$0.545555\pi$
$18$	−2.90697	−0.685180
$19$	−0.414369	−0.0950628	−0.0475314	−	0.998870i	$-0.515135\pi$
$19$	−0.414369	−0.0950628	−0.0475314	+	0.998870i	$0.515135\pi$
$20$	2.67935	0.599121
$21$	−0.735392	−0.160476
$22$	−4.32689	−0.922497
$23$	8.63243	1.79999	0.899993	−	0.435905i	$-0.143571\pi$
$23$	8.63243	1.79999	0.899993	+	0.435905i	$0.143571\pi$
$24$	−0.305006	−0.0622590
$25$	2.17892	0.435783
$26$	6.76346	1.32642
$27$	1.80166	0.346730
$28$	2.41108	0.455650
$29$	−3.30975	−0.614605	−0.307302	−	0.951612i	$-0.599426\pi$
$29$	−3.30975	−0.614605	−0.307302	+	0.951612i	$0.599426\pi$
$30$	−0.817217	−0.149203
$31$	8.69603	1.56185	0.780927	−	0.624623i	$-0.214747\pi$
$31$	8.69603	1.56185	0.780927	+	0.624623i	$0.214747\pi$
$32$	1.00000	0.176777
$33$	1.31973	0.229735
$34$	−1.17614	−0.201706
$35$	6.46012	1.09196
$36$	−2.90697	−0.484495
$37$	2.69205	0.442571	0.221285	−	0.975209i	$-0.428975\pi$
$37$	2.69205	0.442571	0.221285	+	0.975209i	$0.428975\pi$
$38$	−0.414369	−0.0672196
$39$	−2.06289	−0.330327
$40$	2.67935	0.423642
$41$	−4.65927	−0.727656	−0.363828	−	0.931466i	$-0.618530\pi$
$41$	−4.65927	−0.727656	−0.363828	+	0.931466i	$0.618530\pi$
$42$	−0.735392	−0.113473
$43$	0.830651	0.126673	0.0633365	−	0.997992i	$-0.479826\pi$
$43$	0.830651	0.126673	0.0633365	+	0.997992i	$0.479826\pi$
$44$	−4.32689	−0.652304
$45$	−7.78879	−1.16108
$46$	8.63243	1.27278
$47$	−7.54908	−1.10115	−0.550573	−	0.834787i	$-0.685591\pi$
$47$	−7.54908	−1.10115	−0.550573	+	0.834787i	$0.685591\pi$
$48$	−0.305006	−0.0440238
$49$	−1.18671	−0.169530
$50$	2.17892	0.308145
$51$	0.358729	0.0502322
$52$	6.76346	0.937923
$53$	−12.7799	−1.75545	−0.877726	−	0.479162i	$-0.840941\pi$
$53$	−12.7799	−1.75545	−0.877726	+	0.479162i	$0.840941\pi$
$54$	1.80166	0.245175
$55$	−11.5933	−1.56324
$56$	2.41108	0.322194
$57$	0.126385	0.0167401
$58$	−3.30975	−0.434591
$59$	1.37476	0.178979	0.0894895	−	0.995988i	$-0.471476\pi$
$59$	1.37476	0.178979	0.0894895	+	0.995988i	$0.471476\pi$
$60$	−0.817217	−0.105502
$61$	7.34207	0.940055	0.470028	−	0.882652i	$-0.344244\pi$
$61$	7.34207	0.940055	0.470028	+	0.882652i	$0.344244\pi$
$62$	8.69603	1.10440
$63$	−7.00893	−0.883042
$64$	1.00000	0.125000
$65$	18.1217	2.24772
$66$	1.31973	0.162447
$67$	5.52915	0.675494	0.337747	−	0.941237i	$-0.390335\pi$
$67$	5.52915	0.675494	0.337747	+	0.941237i	$0.390335\pi$
$68$	−1.17614	−0.142628
$69$	−2.63294	−0.316969
$70$	6.46012	0.772131
$71$	6.63252	0.787135	0.393567	−	0.919296i	$-0.371241\pi$
$71$	6.63252	0.787135	0.393567	+	0.919296i	$0.371241\pi$
$72$	−2.90697	−0.342590
$73$	−5.69241	−0.666247	−0.333123	−	0.942883i	$-0.608103\pi$
$73$	−5.69241	−0.666247	−0.333123	+	0.942883i	$0.608103\pi$
$74$	2.69205	0.312945
$75$	−0.664582	−0.0767393
$76$	−0.414369	−0.0475314
$77$	−10.4325	−1.18889
$78$	−2.06289	−0.233577
$79$	5.27433	0.593409	0.296704	−	0.954969i	$-0.404112\pi$
$79$	5.27433	0.593409	0.296704	+	0.954969i	$0.404112\pi$
$80$	2.67935	0.299560
$81$	8.17140	0.907933
$82$	−4.65927	−0.514531
$83$	−0.447396	−0.0491081	−0.0245540	−	0.999699i	$-0.507817\pi$
$83$	−0.447396	−0.0491081	−0.0245540	+	0.999699i	$0.507817\pi$
$84$	−0.735392	−0.0802378
$85$	−3.15129	−0.341805
$86$	0.830651	0.0895714
$87$	1.00949	0.108229
$88$	−4.32689	−0.461249
$89$	−3.36588	−0.356783	−0.178391	−	0.983960i	$-0.557089\pi$
$89$	−3.36588	−0.356783	−0.178391	+	0.983960i	$0.557089\pi$
$90$	−7.78879	−0.821011
$91$	16.3072	1.70946
$92$	8.63243	0.899993
$93$	−2.65234	−0.275035
$94$	−7.54908	−0.778628
$95$	−1.11024	−0.113908
$96$	−0.305006	−0.0311295
$97$	−18.2599	−1.85401	−0.927004	−	0.375051i	$-0.877625\pi$
$97$	−18.2599	−1.85401	−0.927004	+	0.375051i	$0.877625\pi$
$98$	−1.18671	−0.119876
$99$	12.5782	1.26415
$100$	2.17892	0.217892
$101$	−9.08940	−0.904430	−0.452215	−	0.891909i	$-0.649366\pi$
$101$	−9.08940	−0.904430	−0.452215	+	0.891909i	$0.649366\pi$
$102$	0.358729	0.0355195
$103$	3.71479	0.366029	0.183014	−	0.983110i	$-0.441415\pi$
$103$	3.71479	0.366029	0.183014	+	0.983110i	$0.441415\pi$
$104$	6.76346	0.663212
$105$	−1.97037	−0.192289
$106$	−12.7799	−1.24129
$107$	7.62976	0.737597	0.368798	−	0.929509i	$-0.379769\pi$
$107$	7.62976	0.737597	0.368798	+	0.929509i	$0.379769\pi$
$108$	1.80166	0.173365
$109$	15.1406	1.45020	0.725101	−	0.688642i	$-0.241793\pi$
$109$	15.1406	1.45020	0.725101	+	0.688642i	$0.241793\pi$
$110$	−11.5933	−1.10537
$111$	−0.821092	−0.0779346
$112$	2.41108	0.227825
$113$	−11.2960	−1.06264	−0.531321	−	0.847171i	$-0.678304\pi$
$113$	−11.2960	−1.06264	−0.531321	+	0.847171i	$0.678304\pi$
$114$	0.126385	0.0118370
$115$	23.1293	2.15682
$116$	−3.30975	−0.307302
$117$	−19.6612	−1.81768
$118$	1.37476	0.126557
$119$	−2.83576	−0.259954
$120$	−0.817217	−0.0746014
$121$	7.72202	0.702002
$122$	7.34207	0.664719
$123$	1.42111	0.128137
$124$	8.69603	0.780927
$125$	−7.55867	−0.676068
$126$	−7.00893	−0.624405
$127$	−10.8174	−0.959891	−0.479945	−	0.877298i	$-0.659344\pi$
$127$	−10.8174	−0.959891	−0.479945	+	0.877298i	$0.659344\pi$
$128$	1.00000	0.0883883
$129$	−0.253353	−0.0223065
$130$	18.1217	1.58938
$131$	11.8919	1.03900	0.519499	−	0.854471i	$-0.326118\pi$
$131$	11.8919	1.03900	0.519499	+	0.854471i	$0.326118\pi$
$132$	1.31973	0.114868
$133$	−0.999076	−0.0866309
$134$	5.52915	0.477646
$135$	4.82728	0.415466
$136$	−1.17614	−0.100853
$137$	6.40653	0.547347	0.273673	−	0.961823i	$-0.411761\pi$
$137$	6.40653	0.547347	0.273673	+	0.961823i	$0.411761\pi$
$138$	−2.63294	−0.224131
$139$	−16.1213	−1.36739	−0.683695	−	0.729768i	$-0.739628\pi$
$139$	−16.1213	−1.36739	−0.683695	+	0.729768i	$0.739628\pi$
$140$	6.46012	0.545979
$141$	2.30251	0.193907
$142$	6.63252	0.556588
$143$	−29.2648	−2.44724
$144$	−2.90697	−0.242248
$145$	−8.86797	−0.736445
$146$	−5.69241	−0.471108
$147$	0.361954	0.0298535
$148$	2.69205	0.221285
$149$	2.97469	0.243696	0.121848	−	0.992549i	$-0.461118\pi$
$149$	2.97469	0.243696	0.121848	+	0.992549i	$0.461118\pi$
$150$	−0.664582	−0.0542629
$151$	0.493137	0.0401309	0.0200655	−	0.999799i	$-0.493613\pi$
$151$	0.493137	0.0401309	0.0200655	+	0.999799i	$0.493613\pi$
$152$	−0.414369	−0.0336098
$153$	3.41901	0.276410
$154$	−10.4325	−0.840673
$155$	23.2997	1.87148
$156$	−2.06289	−0.165164
$157$	22.1544	1.76811	0.884056	−	0.467382i	$-0.154803\pi$
$157$	22.1544	1.76811	0.884056	+	0.467382i	$0.154803\pi$
$158$	5.27433	0.419603
$159$	3.89794	0.309127
$160$	2.67935	0.211821
$161$	20.8134	1.64033
$162$	8.17140	0.642006
$163$	−14.7793	−1.15760	−0.578802	−	0.815468i	$-0.696480\pi$
$163$	−14.7793	−1.15760	−0.578802	+	0.815468i	$0.696480\pi$
$164$	−4.65927	−0.363828
$165$	3.53601	0.275278
$166$	−0.447396	−0.0347247
$167$	−8.82366	−0.682795	−0.341398	−	0.939919i	$-0.610900\pi$
$167$	−8.82366	−0.682795	−0.341398	+	0.939919i	$0.610900\pi$
$168$	−0.735392	−0.0567367
$169$	32.7444	2.51880
$170$	−3.15129	−0.241693
$171$	1.20456	0.0921150
$172$	0.830651	0.0633365
$173$	−16.5297	−1.25673	−0.628364	−	0.777919i	$-0.716275\pi$
$173$	−16.5297	−1.25673	−0.628364	+	0.777919i	$0.716275\pi$
$174$	1.00949	0.0765294
$175$	5.25353	0.397130
$176$	−4.32689	−0.326152
$177$	−0.419311	−0.0315173
$178$	−3.36588	−0.252283
$179$	1.66766	0.124647	0.0623235	−	0.998056i	$-0.480149\pi$
$179$	1.66766	0.124647	0.0623235	+	0.998056i	$0.480149\pi$
$180$	−7.78879	−0.580542
$181$	−18.0058	−1.33836	−0.669179	−	0.743102i	$-0.733354\pi$
$181$	−18.0058	−1.33836	−0.669179	+	0.743102i	$0.733354\pi$
$182$	16.3072	1.20877
$183$	−2.23937	−0.165539
$184$	8.63243	0.636391
$185$	7.21295	0.530307
$186$	−2.65234	−0.194479
$187$	5.08903	0.372147
$188$	−7.54908	−0.550573
$189$	4.34394	0.315975
$190$	−1.11024	−0.0805453
$191$	−9.87703	−0.714677	−0.357338	−	0.933975i	$-0.616316\pi$
$191$	−9.87703	−0.714677	−0.357338	+	0.933975i	$0.616316\pi$
$192$	−0.305006	−0.0220119
$193$	13.8577	0.997500	0.498750	−	0.866746i	$-0.333793\pi$
$193$	13.8577	0.997500	0.498750	+	0.866746i	$0.333793\pi$
$194$	−18.2599	−1.31098
$195$	−5.52721	−0.395812
$196$	−1.18671	−0.0847652
$197$	−13.9844	−0.996346	−0.498173	−	0.867078i	$-0.665996\pi$
$197$	−13.9844	−0.996346	−0.498173	+	0.867078i	$0.665996\pi$
$198$	12.5782	0.893891
$199$	5.68579	0.403055	0.201527	−	0.979483i	$-0.435409\pi$
$199$	5.68579	0.403055	0.201527	+	0.979483i	$0.435409\pi$
$200$	2.17892	0.154073
$201$	−1.68642	−0.118951
$202$	−9.08940	−0.639528
$203$	−7.98005	−0.560090
$204$	0.358729	0.0251161
$205$	−12.4838	−0.871908
$206$	3.71479	0.258821
$207$	−25.0942	−1.74417
$208$	6.76346	0.468962
$209$	1.79293	0.124020
$210$	−1.97037	−0.135969
$211$	−24.7719	−1.70537	−0.852683	−	0.522429i	$-0.825026\pi$
$211$	−24.7719	−1.70537	−0.852683	+	0.522429i	$0.825026\pi$
$212$	−12.7799	−0.877726
$213$	−2.02296	−0.138611
$214$	7.62976	0.521560
$215$	2.22560	0.151785
$216$	1.80166	0.122587
$217$	20.9668	1.42332
$218$	15.1406	1.02545
$219$	1.73622	0.117323
$220$	−11.5933	−0.781618
$221$	−7.95478	−0.535096
$222$	−0.821092	−0.0551081
$223$	3.50433	0.234667	0.117334	−	0.993093i	$-0.462565\pi$
$223$	3.50433	0.234667	0.117334	+	0.993093i	$0.462565\pi$
$224$	2.41108	0.161097
$225$	−6.33405	−0.422270
$226$	−11.2960	−0.751401
$227$	−16.8860	−1.12076	−0.560380	−	0.828235i	$-0.689345\pi$
$227$	−16.8860	−1.12076	−0.560380	+	0.828235i	$0.689345\pi$
$228$	0.126385	0.00837005
$229$	−25.9482	−1.71470	−0.857352	−	0.514730i	$-0.827892\pi$
$229$	−25.9482	−1.71470	−0.857352	+	0.514730i	$0.827892\pi$
$230$	23.1293	1.52510
$231$	3.18196	0.209358
$232$	−3.30975	−0.217296
$233$	−2.32535	−0.152339	−0.0761695	−	0.997095i	$-0.524269\pi$
$233$	−2.32535	−0.152339	−0.0761695	+	0.997095i	$0.524269\pi$
$234$	−19.6612	−1.28529
$235$	−20.2266	−1.31944
$236$	1.37476	0.0894895
$237$	−1.60870	−0.104496
$238$	−2.83576	−0.183815
$239$	−3.62659	−0.234584	−0.117292	−	0.993097i	$-0.537421\pi$
$239$	−3.62659	−0.234584	−0.117292	+	0.993097i	$0.537421\pi$
$240$	−0.817217	−0.0527511
$241$	−16.8826	−1.08750	−0.543751	−	0.839246i	$-0.682997\pi$
$241$	−16.8826	−1.08750	−0.543751	+	0.839246i	$0.682997\pi$
$242$	7.72202	0.496390
$243$	−7.89730	−0.506612
$244$	7.34207	0.470028
$245$	−3.17962	−0.203138
$246$	1.42111	0.0906064
$247$	−2.80257	−0.178323
$248$	8.69603	0.552198
$249$	0.136458	0.00864769
$250$	−7.55867	−0.478052
$251$	29.3502	1.85257	0.926283	−	0.376829i	$-0.122985\pi$
$251$	29.3502	1.85257	0.926283	+	0.376829i	$0.122985\pi$
$252$	−7.00893	−0.441521
$253$	−37.3516	−2.34828
$254$	−10.8174	−0.678745
$255$	0.961162	0.0601903
$256$	1.00000	0.0625000
$257$	2.23849	0.139633	0.0698166	−	0.997560i	$-0.477759\pi$
$257$	2.23849	0.139633	0.0698166	+	0.997560i	$0.477759\pi$
$258$	−0.253353	−0.0157731
$259$	6.49075	0.403315
$260$	18.1217	1.12386
$261$	9.62134	0.595546
$262$	11.8919	0.734683
$263$	13.5386	0.834826	0.417413	−	0.908717i	$-0.362937\pi$
$263$	13.5386	0.834826	0.417413	+	0.908717i	$0.362937\pi$
$264$	1.31973	0.0812236
$265$	−34.2418	−2.10346
$266$	−0.999076	−0.0612573
$267$	1.02661	0.0628277
$268$	5.52915	0.337747
$269$	−12.7977	−0.780292	−0.390146	−	0.920753i	$-0.627575\pi$
$269$	−12.7977	−0.780292	−0.390146	+	0.920753i	$0.627575\pi$
$270$	4.82728	0.293779
$271$	−25.5859	−1.55423	−0.777115	−	0.629358i	$-0.783318\pi$
$271$	−25.5859	−1.55423	−0.777115	+	0.629358i	$0.783318\pi$
$272$	−1.17614	−0.0713140
$273$	−4.97379	−0.301028
$274$	6.40653	0.387033
$275$	−9.42794	−0.568526
$276$	−2.63294	−0.158484
$277$	−21.7902	−1.30924	−0.654622	−	0.755956i	$-0.727172\pi$
$277$	−21.7902	−1.30924	−0.654622	+	0.755956i	$0.727172\pi$
$278$	−16.1213	−0.966891
$279$	−25.2791	−1.51342
$280$	6.46012	0.386066
$281$	8.84539	0.527672	0.263836	−	0.964568i	$-0.415012\pi$
$281$	8.84539	0.527672	0.263836	+	0.964568i	$0.415012\pi$
$282$	2.30251	0.137113
$283$	10.8317	0.643876	0.321938	−	0.946761i	$-0.395666\pi$
$283$	10.8317	0.643876	0.321938	+	0.946761i	$0.395666\pi$
$284$	6.63252	0.393567
$285$	0.338630	0.0200587
$286$	−29.2648	−1.73046
$287$	−11.2339	−0.663114
$288$	−2.90697	−0.171295
$289$	−15.6167	−0.918629
$290$	−8.86797	−0.520745
$291$	5.56936	0.326482
$292$	−5.69241	−0.333123
$293$	17.4037	1.01673	0.508366	−	0.861141i	$-0.330250\pi$
$293$	17.4037	1.01673	0.508366	+	0.861141i	$0.330250\pi$
$294$	0.361954	0.0211096
$295$	3.68347	0.214460
$296$	2.69205	0.156472
$297$	−7.79559	−0.452346
$298$	2.97469	0.172319
$299$	58.3851	3.37650
$300$	−0.664582	−0.0383696
$301$	2.00276	0.115437
$302$	0.493137	0.0283769
$303$	2.77232	0.159266
$304$	−0.414369	−0.0237657
$305$	19.6720	1.12641
$306$	3.41901	0.195452
$307$	−13.3310	−0.760838	−0.380419	−	0.924814i	$-0.624220\pi$
$307$	−13.3310	−0.760838	−0.380419	+	0.924814i	$0.624220\pi$
$308$	−10.4325	−0.594445
$309$	−1.13303	−0.0644559
$310$	23.2997	1.32333
$311$	19.5654	1.10945	0.554726	−	0.832033i	$-0.312823\pi$
$311$	19.5654	1.10945	0.554726	+	0.832033i	$0.312823\pi$
$312$	−2.06289	−0.116788
$313$	27.5673	1.55820	0.779099	−	0.626901i	$-0.215677\pi$
$313$	27.5673	1.55820	0.779099	+	0.626901i	$0.215677\pi$
$314$	22.1544	1.25024
$315$	−18.7794	−1.05810
$316$	5.27433	0.296704
$317$	−4.06653	−0.228399	−0.114200	−	0.993458i	$-0.536430\pi$
$317$	−4.06653	−0.228399	−0.114200	+	0.993458i	$0.536430\pi$
$318$	3.89794	0.218586
$319$	14.3209	0.801818
$320$	2.67935	0.149780
$321$	−2.32712	−0.129887
$322$	20.8134	1.15989
$323$	0.487356	0.0271172
$324$	8.17140	0.453967
$325$	14.7370	0.817462
$326$	−14.7793	−0.818550
$327$	−4.61796	−0.255374
$328$	−4.65927	−0.257265
$329$	−18.2014	−1.00348
$330$	3.53601	0.194651
$331$	−1.37559	−0.0756091	−0.0378045	−	0.999285i	$-0.512036\pi$
$331$	−1.37559	−0.0756091	−0.0378045	+	0.999285i	$0.512036\pi$
$332$	−0.447396	−0.0245540
$333$	−7.82572	−0.428847
$334$	−8.82366	−0.482809
$335$	14.8145	0.809405
$336$	−0.735392	−0.0401189
$337$	−18.8476	−1.02670	−0.513348	−	0.858181i	$-0.671595\pi$
$337$	−18.8476	−1.02670	−0.513348	+	0.858181i	$0.671595\pi$
$338$	32.7444	1.78106
$339$	3.44536	0.187126
$340$	−3.15129	−0.170903
$341$	−37.6268	−2.03761
$342$	1.20456	0.0651351
$343$	−19.7388	−1.06579
$344$	0.830651	0.0447857
$345$	−7.05457	−0.379805
$346$	−16.5297	−0.888642
$347$	−5.36587	−0.288055	−0.144027	−	0.989574i	$-0.546005\pi$
$347$	−5.36587	−0.288055	−0.144027	+	0.989574i	$0.546005\pi$
$348$	1.00949	0.0541144
$349$	24.4608	1.30936	0.654678	−	0.755908i	$-0.272804\pi$
$349$	24.4608	1.30936	0.654678	+	0.755908i	$0.272804\pi$
$350$	5.25353	0.280813
$351$	12.1855	0.650411
$352$	−4.32689	−0.230624
$353$	24.3842	1.29784	0.648920	−	0.760856i	$-0.275221\pi$
$353$	24.3842	1.29784	0.648920	+	0.760856i	$0.275221\pi$
$354$	−0.419311	−0.0222861
$355$	17.7708	0.943178
$356$	−3.36588	−0.178391
$357$	0.864924	0.0457766
$358$	1.66766	0.0881387
$359$	−23.7649	−1.25426	−0.627131	−	0.778914i	$-0.715771\pi$
$359$	−23.7649	−1.25426	−0.627131	+	0.778914i	$0.715771\pi$
$360$	−7.78879	−0.410505
$361$	−18.8283	−0.990963
$362$	−18.0058	−0.946361
$363$	−2.35526	−0.123619
$364$	16.3072	0.854730
$365$	−15.2520	−0.798325
$366$	−2.23937	−0.117054
$367$	−3.60090	−0.187965	−0.0939827	−	0.995574i	$-0.529960\pi$
$367$	−3.60090	−0.187965	−0.0939827	+	0.995574i	$0.529960\pi$
$368$	8.63243	0.449996
$369$	13.5444	0.705092
$370$	7.21295	0.374984
$371$	−30.8133	−1.59975
$372$	−2.65234	−0.137517
$373$	32.9482	1.70599	0.852996	−	0.521918i	$-0.174783\pi$
$373$	32.9482	1.70599	0.852996	+	0.521918i	$0.174783\pi$
$374$	5.08903	0.263148
$375$	2.30544	0.119052
$376$	−7.54908	−0.389314
$377$	−22.3853	−1.15290
$378$	4.34394	0.223428
$379$	11.4688	0.589110	0.294555	−	0.955634i	$-0.404829\pi$
$379$	11.4688	0.589110	0.294555	+	0.955634i	$0.404829\pi$
$380$	−1.11024	−0.0569541
$381$	3.29937	0.169032
$382$	−9.87703	−0.505353
$383$	25.2266	1.28902	0.644510	−	0.764596i	$-0.277061\pi$
$383$	25.2266	1.28902	0.644510	+	0.764596i	$0.277061\pi$
$384$	−0.305006	−0.0155648
$385$	−27.9522	−1.42458
$386$	13.8577	0.705339
$387$	−2.41468	−0.122745
$388$	−18.2599	−0.927004
$389$	−26.4652	−1.34184	−0.670920	−	0.741530i	$-0.734101\pi$
$389$	−26.4652	−1.34184	−0.670920	+	0.741530i	$0.734101\pi$
$390$	−5.52721	−0.279881
$391$	−10.1529	−0.513456
$392$	−1.18671	−0.0599381
$393$	−3.62709	−0.182963
$394$	−13.9844	−0.704523
$395$	14.1318	0.711047
$396$	12.5782	0.632076
$397$	−35.4428	−1.77883	−0.889413	−	0.457105i	$-0.848886\pi$
$397$	−35.4428	−1.77883	−0.889413	+	0.457105i	$0.848886\pi$
$398$	5.68579	0.285003
$399$	0.304724	0.0152553
$400$	2.17892	0.108946
$401$	−13.1003	−0.654196	−0.327098	−	0.944990i	$-0.606071\pi$
$401$	−13.1003	−0.654196	−0.327098	+	0.944990i	$0.606071\pi$
$402$	−1.68642	−0.0841111
$403$	58.8153	2.92980
$404$	−9.08940	−0.452215
$405$	21.8940	1.08792
$406$	−7.98005	−0.396043
$407$	−11.6482	−0.577382
$408$	0.358729	0.0177598
$409$	8.11926	0.401472	0.200736	−	0.979645i	$-0.435667\pi$
$409$	8.11926	0.401472	0.200736	+	0.979645i	$0.435667\pi$
$410$	−12.4838	−0.616532
$411$	−1.95403	−0.0963851
$412$	3.71479	0.183014
$413$	3.31466	0.163104
$414$	−25.0942	−1.23331
$415$	−1.19873	−0.0588433
$416$	6.76346	0.331606
$417$	4.91708	0.240791
$418$	1.79293	0.0876952
$419$	−18.1707	−0.887697	−0.443849	−	0.896102i	$-0.646387\pi$
$419$	−18.1707	−0.887697	−0.443849	+	0.896102i	$0.646387\pi$
$420$	−1.97037	−0.0961443
$421$	16.1789	0.788510	0.394255	−	0.919001i	$-0.371003\pi$
$421$	16.1789	0.788510	0.394255	+	0.919001i	$0.371003\pi$
$422$	−24.7719	−1.20588
$423$	21.9450	1.06700
$424$	−12.7799	−0.620646
$425$	−2.56271	−0.124310
$426$	−2.02296	−0.0980125
$427$	17.7023	0.856673
$428$	7.62976	0.368798
$429$	8.92592	0.430948
$430$	2.22560	0.107328
$431$	31.9185	1.53746	0.768729	−	0.639574i	$-0.220889\pi$
$431$	31.9185	1.53746	0.768729	+	0.639574i	$0.220889\pi$
$432$	1.80166	0.0866824
$433$	−23.5949	−1.13390	−0.566950	−	0.823752i	$-0.691877\pi$
$433$	−23.5949	−1.13390	−0.566950	+	0.823752i	$0.691877\pi$
$434$	20.9668	1.00644
$435$	2.70478	0.129684
$436$	15.1406	0.725101
$437$	−3.57701	−0.171112
$438$	1.73622	0.0829597
$439$	−14.1776	−0.676661	−0.338330	−	0.941027i	$-0.609862\pi$
$439$	−14.1776	−0.676661	−0.338330	+	0.941027i	$0.609862\pi$
$440$	−11.5933	−0.552687
$441$	3.44974	0.164273
$442$	−7.95478	−0.378370
$443$	−14.4210	−0.685162	−0.342581	−	0.939488i	$-0.611301\pi$
$443$	−14.4210	−0.685162	−0.342581	+	0.939488i	$0.611301\pi$
$444$	−0.821092	−0.0389673
$445$	−9.01837	−0.427512
$446$	3.50433	0.165935
$447$	−0.907299	−0.0429138
$448$	2.41108	0.113913
$449$	−3.60563	−0.170160	−0.0850801	−	0.996374i	$-0.527115\pi$
$449$	−3.60563	−0.170160	−0.0850801	+	0.996374i	$0.527115\pi$
$450$	−6.33405	−0.298590
$451$	20.1602	0.949306
$452$	−11.2960	−0.531321
$453$	−0.150410	−0.00706686
$454$	−16.8860	−0.792497
$455$	43.6927	2.04835
$456$	0.126385	0.00591852
$457$	−18.4117	−0.861261	−0.430630	−	0.902528i	$-0.641709\pi$
$457$	−18.4117	−0.861261	−0.430630	+	0.902528i	$0.641709\pi$
$458$	−25.9482	−1.21248
$459$	−2.11900	−0.0989067
$460$	23.1293	1.07841
$461$	32.6736	1.52176	0.760880	−	0.648893i	$-0.224768\pi$
$461$	32.6736	1.52176	0.760880	+	0.648893i	$0.224768\pi$
$462$	3.18196	0.148038
$463$	6.96242	0.323571	0.161786	−	0.986826i	$-0.448275\pi$
$463$	6.96242	0.323571	0.161786	+	0.986826i	$0.448275\pi$
$464$	−3.30975	−0.153651
$465$	−7.10654	−0.329558
$466$	−2.32535	−0.107720
$467$	−30.9829	−1.43372	−0.716859	−	0.697219i	$-0.754421\pi$
$467$	−30.9829	−1.43372	−0.716859	+	0.697219i	$0.754421\pi$
$468$	−19.6612	−0.908839
$469$	13.3312	0.615578
$470$	−20.2266	−0.932985
$471$	−6.75721	−0.311356
$472$	1.37476	0.0632786
$473$	−3.59414	−0.165259
$474$	−1.60870	−0.0738901
$475$	−0.902876	−0.0414268
$476$	−2.83576	−0.129977
$477$	37.1508	1.70102
$478$	−3.62659	−0.165876
$479$	−1.01318	−0.0462935	−0.0231467	−	0.999732i	$-0.507368\pi$
$479$	−1.01318	−0.0462935	−0.0231467	+	0.999732i	$0.507368\pi$
$480$	−0.817217	−0.0373007
$481$	18.2076	0.830195
$482$	−16.8826	−0.768981
$483$	−6.34822	−0.288854
$484$	7.72202	0.351001
$485$	−48.9246	−2.22155
$486$	−7.89730	−0.358229
$487$	29.4840	1.33605	0.668024	−	0.744140i	$-0.267140\pi$
$487$	29.4840	1.33605	0.668024	+	0.744140i	$0.267140\pi$
$488$	7.34207	0.332360
$489$	4.50777	0.203849
$490$	−3.17962	−0.143641
$491$	−19.4899	−0.879568	−0.439784	−	0.898103i	$-0.644945\pi$
$491$	−19.4899	−0.879568	−0.439784	+	0.898103i	$0.644945\pi$
$492$	1.42111	0.0640684
$493$	3.89273	0.175320
$494$	−2.80257	−0.126094
$495$	33.7013	1.51476
$496$	8.69603	0.390463
$497$	15.9915	0.717317
$498$	0.136458	0.00611484
$499$	26.1130	1.16898	0.584489	−	0.811402i	$-0.301295\pi$
$499$	26.1130	1.16898	0.584489	+	0.811402i	$0.301295\pi$
$500$	−7.55867	−0.338034
$501$	2.69127	0.120237
$502$	29.3502	1.30996
$503$	32.1591	1.43390	0.716951	−	0.697124i	$-0.245537\pi$
$503$	32.1591	1.43390	0.716951	+	0.697124i	$0.245537\pi$
$504$	−7.00893	−0.312203
$505$	−24.3537	−1.08373
$506$	−37.3516	−1.66048
$507$	−9.98723	−0.443548
$508$	−10.8174	−0.479945
$509$	0.973757	0.0431610	0.0215805	−	0.999767i	$-0.493130\pi$
$509$	0.973757	0.0431610	0.0215805	+	0.999767i	$0.493130\pi$
$510$	0.961162	0.0425609
$511$	−13.7248	−0.607151
$512$	1.00000	0.0441942
$513$	−0.746553	−0.0329611
$514$	2.23849	0.0987356
$515$	9.95321	0.438591
$516$	−0.253353	−0.0111533
$517$	32.6641	1.43656
$518$	6.49075	0.285187
$519$	5.04165	0.221304
$520$	18.1217	0.794688
$521$	2.82829	0.123909	0.0619547	−	0.998079i	$-0.480267\pi$
$521$	2.82829	0.123909	0.0619547	+	0.998079i	$0.480267\pi$
$522$	9.62134	0.421115
$523$	1.24800	0.0545711	0.0272856	−	0.999628i	$-0.491314\pi$
$523$	1.24800	0.0545711	0.0272856	+	0.999628i	$0.491314\pi$
$524$	11.8919	0.519499
$525$	−1.60236	−0.0699326
$526$	13.5386	0.590311
$527$	−10.2277	−0.445528
$528$	1.31973	0.0574338
$529$	51.5188	2.23995
$530$	−34.2418	−1.48737
$531$	−3.99640	−0.173429
$532$	−0.999076	−0.0433154
$533$	−31.5128	−1.36497
$534$	1.02661	0.0444259
$535$	20.4428	0.883819
$536$	5.52915	0.238823
$537$	−0.508647	−0.0219497
$538$	−12.7977	−0.551750
$539$	5.13478	0.221171
$540$	4.82728	0.207733
$541$	9.47578	0.407396	0.203698	−	0.979034i	$-0.434704\pi$
$541$	9.47578	0.407396	0.203698	+	0.979034i	$0.434704\pi$
$542$	−25.5859	−1.09901
$543$	5.49186	0.235678
$544$	−1.17614	−0.0504266
$545$	40.5669	1.73769
$546$	−4.97379	−0.212859
$547$	34.9094	1.49262	0.746309	−	0.665600i	$-0.231824\pi$
$547$	34.9094	1.49262	0.746309	+	0.665600i	$0.231824\pi$
$548$	6.40653	0.273673
$549$	−21.3432	−0.910905
$550$	−9.42794	−0.402009
$551$	1.37146	0.0584261
$552$	−2.63294	−0.112065
$553$	12.7168	0.540774
$554$	−21.7902	−0.925776
$555$	−2.19999	−0.0933845
$556$	−16.1213	−0.683695
$557$	7.83956	0.332173	0.166086	−	0.986111i	$-0.446887\pi$
$557$	7.83956	0.332173	0.166086	+	0.986111i	$0.446887\pi$
$558$	−25.2791	−1.07015
$559$	5.61807	0.237619
$560$	6.46012	0.272990
$561$	−1.55218	−0.0655333
$562$	8.84539	0.373120
$563$	−9.51243	−0.400901	−0.200451	−	0.979704i	$-0.564241\pi$
$563$	−9.51243	−0.400901	−0.200451	+	0.979704i	$0.564241\pi$
$564$	2.30251	0.0969533
$565$	−30.2660	−1.27330
$566$	10.8317	0.455289
$567$	19.7019	0.827400
$568$	6.63252	0.278294
$569$	26.1746	1.09730	0.548649	−	0.836053i	$-0.315142\pi$
$569$	26.1746	1.09730	0.548649	+	0.836053i	$0.315142\pi$
$570$	0.338630	0.0141836
$571$	37.2218	1.55768	0.778842	−	0.627220i	$-0.215807\pi$
$571$	37.2218	1.55768	0.778842	+	0.627220i	$0.215807\pi$
$572$	−29.2648	−1.22362
$573$	3.01255	0.125851
$574$	−11.2339	−0.468892
$575$	18.8093	0.784403
$576$	−2.90697	−0.121124
$577$	20.3903	0.848860	0.424430	−	0.905461i	$-0.360475\pi$
$577$	20.3903	0.848860	0.424430	+	0.905461i	$0.360475\pi$
$578$	−15.6167	−0.649569
$579$	−4.22668	−0.175655
$580$	−8.86797	−0.368223
$581$	−1.07871	−0.0447522
$582$	5.56936	0.230858
$583$	55.2972	2.29018
$584$	−5.69241	−0.235554
$585$	−52.6792	−2.17802
$586$	17.4037	0.718939
$587$	14.1700	0.584857	0.292429	−	0.956287i	$-0.405537\pi$
$587$	14.1700	0.584857	0.292429	+	0.956287i	$0.405537\pi$
$588$	0.361954	0.0149267
$589$	−3.60337	−0.148474
$590$	3.68347	0.151646
$591$	4.26532	0.175452
$592$	2.69205	0.110643
$593$	−21.1708	−0.869382	−0.434691	−	0.900580i	$-0.643142\pi$
$593$	−21.1708	−0.869382	−0.434691	+	0.900580i	$0.643142\pi$
$594$	−7.79559	−0.319857
$595$	−7.59800	−0.311488
$596$	2.97469	0.121848
$597$	−1.73420	−0.0709760
$598$	58.3851	2.38754
$599$	−1.92867	−0.0788032	−0.0394016	−	0.999223i	$-0.512545\pi$
$599$	−1.92867	−0.0788032	−0.0394016	+	0.999223i	$0.512545\pi$
$600$	−0.664582	−0.0271314
$601$	−6.06412	−0.247360	−0.123680	−	0.992322i	$-0.539470\pi$
$601$	−6.06412	−0.247360	−0.123680	+	0.992322i	$0.539470\pi$
$602$	2.00276	0.0816265
$603$	−16.0731	−0.654547
$604$	0.493137	0.0200655
$605$	20.6900	0.841168
$606$	2.77232	0.112618
$607$	−1.11796	−0.0453767	−0.0226883	−	0.999743i	$-0.507223\pi$
$607$	−1.11796	−0.0453767	−0.0226883	+	0.999743i	$0.507223\pi$
$608$	−0.414369	−0.0168049
$609$	2.43396	0.0986291
$610$	19.6720	0.796495
$611$	−51.0579	−2.06558
$612$	3.41901	0.138205
$613$	−24.7295	−0.998814	−0.499407	−	0.866368i	$-0.666449\pi$
$613$	−24.7295	−0.998814	−0.499407	+	0.866368i	$0.666449\pi$
$614$	−13.3310	−0.537994
$615$	3.80764	0.153539
$616$	−10.4325	−0.420336
$617$	−23.4688	−0.944817	−0.472408	−	0.881380i	$-0.656615\pi$
$617$	−23.4688	−0.944817	−0.472408	+	0.881380i	$0.656615\pi$
$618$	−1.13303	−0.0455772
$619$	−10.8424	−0.435795	−0.217897	−	0.975972i	$-0.569920\pi$
$619$	−10.8424	−0.435795	−0.217897	+	0.975972i	$0.569920\pi$
$620$	23.2997	0.935739
$621$	15.5527	0.624108
$622$	19.5654	0.784501
$623$	−8.11540	−0.325136
$624$	−2.06289	−0.0825818
$625$	−31.1469	−1.24588
$626$	27.5673	1.10181
$627$	−0.546855	−0.0218393
$628$	22.1544	0.884056
$629$	−3.16623	−0.126246
$630$	−18.7794	−0.748188
$631$	−37.1024	−1.47702	−0.738511	−	0.674241i	$-0.764471\pi$
$631$	−37.1024	−1.47702	−0.738511	+	0.674241i	$0.764471\pi$
$632$	5.27433	0.209802
$633$	7.55556	0.300306
$634$	−4.06653	−0.161503
$635$	−28.9836	−1.15018
$636$	3.89794	0.154563
$637$	−8.02629	−0.318013
$638$	14.3209	0.566971
$639$	−19.2805	−0.762726
$640$	2.67935	0.105911
$641$	19.6987	0.778052	0.389026	−	0.921227i	$-0.372812\pi$
$641$	19.6987	0.778052	0.389026	+	0.921227i	$0.372812\pi$
$642$	−2.32712	−0.0918441
$643$	45.4007	1.79043	0.895215	−	0.445634i	$-0.147022\pi$
$643$	45.4007	1.79043	0.895215	+	0.445634i	$0.147022\pi$
$644$	20.8134	0.820164
$645$	−0.678822	−0.0267286
$646$	0.487356	0.0191748
$647$	−5.90609	−0.232192	−0.116096	−	0.993238i	$-0.537038\pi$
$647$	−5.90609	−0.232192	−0.116096	+	0.993238i	$0.537038\pi$
$648$	8.17140	0.321003
$649$	−5.94846	−0.233497
$650$	14.7370	0.578033
$651$	−6.39499	−0.250639
$652$	−14.7793	−0.578802
$653$	34.6853	1.35734	0.678671	−	0.734442i	$-0.262556\pi$
$653$	34.6853	1.35734	0.678671	+	0.734442i	$0.262556\pi$
$654$	−4.61796	−0.180576
$655$	31.8625	1.24497
$656$	−4.65927	−0.181914
$657$	16.5477	0.645587
$658$	−18.2014	−0.709565
$659$	−8.56904	−0.333802	−0.166901	−	0.985974i	$-0.553376\pi$
$659$	−8.56904	−0.333802	−0.166901	+	0.985974i	$0.553376\pi$
$660$	3.53601	0.137639
$661$	17.8322	0.693591	0.346795	−	0.937941i	$-0.387270\pi$
$661$	17.8322	0.693591	0.346795	+	0.937941i	$0.387270\pi$
$662$	−1.37559	−0.0534637
$663$	2.42625	0.0942278
$664$	−0.447396	−0.0173623
$665$	−2.67687	−0.103805
$666$	−7.82572	−0.303241
$667$	−28.5712	−1.10628
$668$	−8.82366	−0.341398
$669$	−1.06884	−0.0413238
$670$	14.8145	0.572335
$671$	−31.7683	−1.22640
$672$	−0.735392	−0.0283684
$673$	−40.6249	−1.56597	−0.782987	−	0.622038i	$-0.786305\pi$
$673$	−40.6249	−1.56597	−0.782987	+	0.622038i	$0.786305\pi$
$674$	−18.8476	−0.725983
$675$	3.92566	0.151099
$676$	32.7444	1.25940
$677$	36.7869	1.41384	0.706918	−	0.707296i	$-0.250085\pi$
$677$	36.7869	1.41384	0.706918	+	0.707296i	$0.250085\pi$
$678$	3.44536	0.132318
$679$	−44.0259	−1.68956
$680$	−3.15129	−0.120846
$681$	5.15031	0.197360
$682$	−37.6268	−1.44080
$683$	7.50412	0.287137	0.143569	−	0.989640i	$-0.454142\pi$
$683$	7.50412	0.287137	0.143569	+	0.989640i	$0.454142\pi$
$684$	1.20456	0.0460575
$685$	17.1653	0.655854
$686$	−19.7388	−0.753630
$687$	7.91434	0.301951
$688$	0.830651	0.0316683
$689$	−86.4363	−3.29296
$690$	−7.05457	−0.268563
$691$	35.0688	1.33408	0.667040	−	0.745022i	$-0.267561\pi$
$691$	35.0688	1.33408	0.667040	+	0.745022i	$0.267561\pi$
$692$	−16.5297	−0.628364
$693$	30.3269	1.15202
$694$	−5.36587	−0.203686
$695$	−43.1946	−1.63846
$696$	1.00949	0.0382647
$697$	5.47996	0.207568
$698$	24.4608	0.925855
$699$	0.709246	0.0268261
$700$	5.25353	0.198565
$701$	−9.91597	−0.374521	−0.187261	−	0.982310i	$-0.559961\pi$
$701$	−9.91597	−0.374521	−0.187261	+	0.982310i	$0.559961\pi$
$702$	12.1855	0.459910
$703$	−1.11550	−0.0420721
$704$	−4.32689	−0.163076
$705$	6.16924	0.232347
$706$	24.3842	0.917712
$707$	−21.9152	−0.824208
$708$	−0.419311	−0.0157587
$709$	−17.9747	−0.675054	−0.337527	−	0.941316i	$-0.609590\pi$
$709$	−17.9747	−0.675054	−0.337527	+	0.941316i	$0.609590\pi$
$710$	17.7708	0.666927
$711$	−15.3323	−0.575007
$712$	−3.36588	−0.126142
$713$	75.0679	2.81131
$714$	0.864924	0.0323690
$715$	−78.4106	−2.93239
$716$	1.66766	0.0623235
$717$	1.10613	0.0413092
$718$	−23.7649	−0.886897
$719$	9.76851	0.364304	0.182152	−	0.983270i	$-0.441694\pi$
$719$	9.76851	0.364304	0.182152	+	0.983270i	$0.441694\pi$
$720$	−7.78879	−0.290271
$721$	8.95663	0.333562
$722$	−18.8283	−0.700717
$723$	5.14928	0.191504
$724$	−18.0058	−0.669179
$725$	−7.21166	−0.267834
$726$	−2.35526	−0.0874119
$727$	2.87873	0.106766	0.0533830	−	0.998574i	$-0.483000\pi$
$727$	2.87873	0.106766	0.0533830	+	0.998574i	$0.483000\pi$
$728$	16.3072	0.604386
$729$	−22.1055	−0.818721
$730$	−15.2520	−0.564501
$731$	−0.976962	−0.0361342
$732$	−2.23937	−0.0827696
$733$	4.96029	0.183212	0.0916062	−	0.995795i	$-0.470800\pi$
$733$	4.96029	0.183212	0.0916062	+	0.995795i	$0.470800\pi$
$734$	−3.60090	−0.132912
$735$	0.969802	0.0357717
$736$	8.63243	0.318196
$737$	−23.9241	−0.881254
$738$	13.5444	0.498575
$739$	51.2264	1.88439	0.942197	−	0.335060i	$-0.108757\pi$
$739$	51.2264	1.88439	0.942197	+	0.335060i	$0.108757\pi$
$740$	7.21295	0.265153
$741$	0.854800	0.0314019
$742$	−30.8133	−1.13119
$743$	−29.7719	−1.09223	−0.546113	−	0.837711i	$-0.683893\pi$
$743$	−29.7719	−1.09223	−0.546113	+	0.837711i	$0.683893\pi$
$744$	−2.65234	−0.0972394
$745$	7.97025	0.292007
$746$	32.9482	1.20632
$747$	1.30057	0.0475853
$748$	5.08903	0.186074
$749$	18.3959	0.672173
$750$	2.30544	0.0841827
$751$	−1.00000	−0.0364905
$751$	−1.00000	−0.0364905
$752$	−7.54908	−0.275287
$753$	−8.95197	−0.326228
$754$	−22.3853	−0.815226
$755$	1.32129	0.0480865
$756$	4.34394	0.157988
$757$	2.50439	0.0910235	0.0455118	−	0.998964i	$-0.485508\pi$
$757$	2.50439	0.0910235	0.0455118	+	0.998964i	$0.485508\pi$
$758$	11.4688	0.416564
$759$	11.3925	0.413520
$760$	−1.11024	−0.0402727
$761$	−26.0103	−0.942873	−0.471437	−	0.881900i	$-0.656264\pi$
$761$	−26.0103	−0.942873	−0.471437	+	0.881900i	$0.656264\pi$
$762$	3.29937	0.119524
$763$	36.5050	1.32157
$764$	−9.87703	−0.357338
$765$	9.16071	0.331206
$766$	25.2266	0.911475
$767$	9.29816	0.335737
$768$	−0.305006	−0.0110059
$769$	13.6546	0.492396	0.246198	−	0.969220i	$-0.420819\pi$
$769$	13.6546	0.492396	0.246198	+	0.969220i	$0.420819\pi$
$770$	−27.9522	−1.00733
$771$	−0.682752	−0.0245887
$772$	13.8577	0.498750
$773$	−29.7146	−1.06876	−0.534380	−	0.845244i	$-0.679455\pi$
$773$	−29.7146	−1.06876	−0.534380	+	0.845244i	$0.679455\pi$
$774$	−2.41468	−0.0867938
$775$	18.9479	0.680629
$776$	−18.2599	−0.655491
$777$	−1.97971	−0.0710219
$778$	−26.4652	−0.948824
$779$	1.93066	0.0691731
$780$	−5.52721	−0.197906
$781$	−28.6982	−1.02690
$782$	−10.1529	−0.363069
$783$	−5.96304	−0.213102
$784$	−1.18671	−0.0423826
$785$	59.3593	2.11862
$786$	−3.62709	−0.129374
$787$	−19.3384	−0.689340	−0.344670	−	0.938724i	$-0.612009\pi$
$787$	−19.3384	−0.689340	−0.344670	+	0.938724i	$0.612009\pi$
$788$	−13.9844	−0.498173
$789$	−4.12935	−0.147009
$790$	14.1318	0.502786
$791$	−27.2356	−0.968387
$792$	12.5782	0.446945
$793$	49.6578	1.76340
$794$	−35.4428	−1.25782
$795$	10.4439	0.370408
$796$	5.68579	0.201527
$797$	−4.49184	−0.159109	−0.0795546	−	0.996831i	$-0.525350\pi$
$797$	−4.49184	−0.159109	−0.0795546	+	0.996831i	$0.525350\pi$
$798$	0.304724	0.0107871
$799$	8.87878	0.314109
$800$	2.17892	0.0770363
$801$	9.78452	0.345719
$802$	−13.1003	−0.462587
$803$	24.6305	0.869191
$804$	−1.68642	−0.0594756
$805$	55.7665	1.96551
$806$	58.8153	2.07168
$807$	3.90338	0.137406
$808$	−9.08940	−0.319764
$809$	23.0170	0.809235	0.404618	−	0.914486i	$-0.367405\pi$
$809$	23.0170	0.809235	0.404618	+	0.914486i	$0.367405\pi$
$810$	21.8940	0.769278
$811$	−11.7446	−0.412407	−0.206204	−	0.978509i	$-0.566111\pi$
$811$	−11.7446	−0.412407	−0.206204	+	0.978509i	$0.566111\pi$
$812$	−7.98005	−0.280045
$813$	7.80383	0.273692
$814$	−11.6482	−0.408270
$815$	−39.5989	−1.38709
$816$	0.358729	0.0125580
$817$	−0.344196	−0.0120419
$818$	8.11926	0.283883
$819$	−47.4046	−1.65645
$820$	−12.4838	−0.435954
$821$	10.6824	0.372819	0.186409	−	0.982472i	$-0.440315\pi$
$821$	10.6824	0.372819	0.186409	+	0.982472i	$0.440315\pi$
$822$	−1.95403	−0.0681546
$823$	42.5469	1.48309	0.741545	−	0.670903i	$-0.234093\pi$
$823$	42.5469	1.48309	0.741545	+	0.670903i	$0.234093\pi$
$824$	3.71479	0.129411
$825$	2.87557	0.100115
$826$	3.31466	0.115332
$827$	31.4506	1.09364	0.546822	−	0.837249i	$-0.315838\pi$
$827$	31.4506	1.09364	0.546822	+	0.837249i	$0.315838\pi$
$828$	−25.0942	−0.872085
$829$	33.2749	1.15569	0.577843	−	0.816148i	$-0.303894\pi$
$829$	33.2749	1.15569	0.577843	+	0.816148i	$0.303894\pi$
$830$	−1.19873	−0.0416085
$831$	6.64613	0.230552
$832$	6.76346	0.234481
$833$	1.39574	0.0483596
$834$	4.91708	0.170265
$835$	−23.6417	−0.818154
$836$	1.79293	0.0620099
$837$	15.6673	0.541541
$838$	−18.1707	−0.627697
$839$	−41.7828	−1.44250	−0.721251	−	0.692674i	$-0.756433\pi$
$839$	−41.7828	−1.44250	−0.721251	+	0.692674i	$0.756433\pi$
$840$	−1.97037	−0.0679843
$841$	−18.0456	−0.622261
$842$	16.1789	0.557561
$843$	−2.69789	−0.0929204
$844$	−24.7719	−0.852683
$845$	87.7337	3.01813
$846$	21.9450	0.754484
$847$	18.6184	0.639735
$848$	−12.7799	−0.438863
$849$	−3.30372	−0.113383
$850$	−2.56271	−0.0879002
$851$	23.2390	0.796621
$852$	−2.02296	−0.0693053
$853$	27.2270	0.932234	0.466117	−	0.884723i	$-0.345652\pi$
$853$	27.2270	0.932234	0.466117	+	0.884723i	$0.345652\pi$
$854$	17.7023	0.605760
$855$	3.22744	0.110376
$856$	7.62976	0.260780
$857$	−18.9883	−0.648630	−0.324315	−	0.945949i	$-0.605134\pi$
$857$	−18.9883	−0.648630	−0.324315	+	0.945949i	$0.605134\pi$
$858$	8.92592	0.304726
$859$	50.6363	1.72769	0.863844	−	0.503759i	$-0.168050\pi$
$859$	50.6363	1.72769	0.863844	+	0.503759i	$0.168050\pi$
$860$	2.22560	0.0758925
$861$	3.42639	0.116771
$862$	31.9185	1.08715
$863$	29.7146	1.01150	0.505748	−	0.862681i	$-0.331217\pi$
$863$	29.7146	1.01150	0.505748	+	0.862681i	$0.331217\pi$
$864$	1.80166	0.0612937
$865$	−44.2888	−1.50587
$866$	−23.5949	−0.801788
$867$	4.76318	0.161766
$868$	20.9668	0.711659
$869$	−22.8215	−0.774166
$870$	2.70478	0.0917007
$871$	37.3962	1.26712
$872$	15.1406	0.512724
$873$	53.0809	1.79652
$874$	−3.57701	−0.120994
$875$	−18.2245	−0.616102
$876$	1.73622	0.0586614
$877$	1.00355	0.0338875	0.0169437	−	0.999856i	$-0.494606\pi$
$877$	1.00355	0.0338875	0.0169437	+	0.999856i	$0.494606\pi$
$878$	−14.1776	−0.478471
$879$	−5.30822	−0.179042
$880$	−11.5933	−0.390809
$881$	−50.8567	−1.71341	−0.856704	−	0.515809i	$-0.827491\pi$
$881$	−50.8567	−1.71341	−0.856704	+	0.515809i	$0.827491\pi$
$882$	3.44974	0.116159
$883$	24.8089	0.834885	0.417443	−	0.908703i	$-0.362926\pi$
$883$	24.8089	0.834885	0.417443	+	0.908703i	$0.362926\pi$
$884$	−7.95478	−0.267548
$885$	−1.12348	−0.0377654
$886$	−14.4210	−0.484483
$887$	−23.6891	−0.795402	−0.397701	−	0.917515i	$-0.630192\pi$
$887$	−23.6891	−0.795402	−0.397701	+	0.917515i	$0.630192\pi$
$888$	−0.821092	−0.0275540
$889$	−26.0816	−0.874749
$890$	−9.01837	−0.302297
$891$	−35.3568	−1.18450
$892$	3.50433	0.117334
$893$	3.12811	0.104678
$894$	−0.907299	−0.0303446
$895$	4.46825	0.149357
$896$	2.41108	0.0805484
$897$	−17.8078	−0.594585
$898$	−3.60563	−0.120321
$899$	−28.7817	−0.959922
$900$	−6.33405	−0.211135
$901$	15.0309	0.500753
$902$	20.1602	0.671261
$903$	−0.610854	−0.0203279
$904$	−11.2960	−0.375701
$905$	−48.2437	−1.60368
$906$	−0.150410	−0.00499702
$907$	−18.6154	−0.618114	−0.309057	−	0.951044i	$-0.600013\pi$
$907$	−18.6154	−0.618114	−0.309057	+	0.951044i	$0.600013\pi$
$908$	−16.8860	−0.560380
$909$	26.4226	0.876384
$910$	43.6927	1.44840
$911$	−42.7452	−1.41621	−0.708106	−	0.706106i	$-0.750450\pi$
$911$	−42.7452	−1.41621	−0.708106	+	0.706106i	$0.750450\pi$
$912$	0.126385	0.00418503
$913$	1.93583	0.0640668
$914$	−18.4117	−0.609003
$915$	−6.00006	−0.198356
$916$	−25.9482	−0.857352
$917$	28.6722	0.946841
$918$	−2.11900	−0.0699376
$919$	25.6756	0.846961	0.423481	−	0.905905i	$-0.360808\pi$
$919$	25.6756	0.846961	0.423481	+	0.905905i	$0.360808\pi$
$920$	23.1293	0.762550
$921$	4.06602	0.133980
$922$	32.6736	1.07605
$923$	44.8588	1.47654
$924$	3.18196	0.104679
$925$	5.86576	0.192865
$926$	6.96242	0.228799
$927$	−10.7988	−0.354678
$928$	−3.30975	−0.108648
$929$	−23.4933	−0.770789	−0.385395	−	0.922752i	$-0.625935\pi$
$929$	−23.4933	−0.770789	−0.385395	+	0.922752i	$0.625935\pi$
$930$	−7.10654	−0.233033
$931$	0.491738	0.0161161
$932$	−2.32535	−0.0761695
$933$	−5.96756	−0.195369
$934$	−30.9829	−1.01379
$935$	13.6353	0.445922
$936$	−19.6612	−0.642646
$937$	54.4779	1.77972	0.889858	−	0.456237i	$-0.150803\pi$
$937$	54.4779	1.77972	0.889858	+	0.456237i	$0.150803\pi$
$938$	13.3312	0.435279
$939$	−8.40819	−0.274391
$940$	−20.2266	−0.659720
$941$	49.5290	1.61460	0.807300	−	0.590142i	$-0.200928\pi$
$941$	49.5290	1.61460	0.807300	+	0.590142i	$0.200928\pi$
$942$	−6.75721	−0.220162
$943$	−40.2209	−1.30977
$944$	1.37476	0.0447448
$945$	11.6389	0.378614
$946$	−3.59414	−0.116856
$947$	33.4073	1.08559	0.542796	−	0.839864i	$-0.317366\pi$
$947$	33.4073	1.08559	0.542796	+	0.839864i	$0.317366\pi$
$948$	−1.60870	−0.0522482
$949$	−38.5004	−1.24978
$950$	−0.902876	−0.0292932
$951$	1.24032	0.0402200
$952$	−2.83576	−0.0919076
$953$	−41.9544	−1.35904	−0.679518	−	0.733659i	$-0.737811\pi$
$953$	−41.9544	−1.35904	−0.679518	+	0.733659i	$0.737811\pi$
$954$	37.1508	1.20280
$955$	−26.4640	−0.856356
$956$	−3.62659	−0.117292
$957$	−4.36797	−0.141196
$958$	−1.01318	−0.0327344
$959$	15.4466	0.498798
$960$	−0.817217	−0.0263756
$961$	44.6209	1.43939
$962$	18.2076	0.587037
$963$	−22.1795	−0.714724
$964$	−16.8826	−0.543751
$965$	37.1297	1.19525
$966$	−6.34822	−0.204251
$967$	27.0862	0.871035	0.435517	−	0.900180i	$-0.356565\pi$
$967$	27.0862	0.871035	0.435517	+	0.900180i	$0.356565\pi$
$968$	7.72202	0.248195
$969$	−0.148646	−0.00477521
$970$	−48.9246	−1.57087
$971$	47.2399	1.51600	0.758000	−	0.652254i	$-0.226176\pi$
$971$	47.2399	1.51600	0.758000	+	0.652254i	$0.226176\pi$
$972$	−7.89730	−0.253306
$973$	−38.8697	−1.24610
$974$	29.4840	0.944729
$975$	−4.49487	−0.143951
$976$	7.34207	0.235014
$977$	26.6571	0.852837	0.426418	−	0.904526i	$-0.359775\pi$
$977$	26.6571	0.852837	0.426418	+	0.904526i	$0.359775\pi$
$978$	4.50777	0.144143
$979$	14.5638	0.465462
$980$	−3.17962	−0.101569
$981$	−44.0132	−1.40523
$982$	−19.4899	−0.621949
$983$	2.82254	0.0900249	0.0450125	−	0.998986i	$-0.485667\pi$
$983$	2.82254	0.0900249	0.0450125	+	0.998986i	$0.485667\pi$
$984$	1.42111	0.0453032
$985$	−37.4691	−1.19386
$986$	3.89273	0.123970
$987$	5.55153	0.176707
$988$	−2.80257	−0.0891616
$989$	7.17053	0.228010
$990$	33.7013	1.07110
$991$	14.7289	0.467879	0.233940	−	0.972251i	$-0.424838\pi$
$991$	14.7289	0.467879	0.233940	+	0.972251i	$0.424838\pi$
$992$	8.69603	0.276099
$993$	0.419562	0.0133144
$994$	15.9915	0.507220
$995$	15.2342	0.482957
$996$	0.136458	0.00432385
$997$	0.693393	0.0219600	0.0109800	−	0.999940i	$-0.496505\pi$
$997$	0.693393	0.0219600	0.0109800	+	0.999940i	$0.496505\pi$
$998$	26.1130	0.826592
$999$	4.85017	0.153452

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.g.1.6	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.g.1.6	✓	16	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:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.305006 q^{3} +1.00000 q^{4} +2.67935 q^{5} -0.305006 q^{6} +2.41108 q^{7} +1.00000 q^{8} -2.90697 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.305006 q^{3} +1.00000 q^{4} +2.67935 q^{5} -0.305006 q^{6} +2.41108 q^{7} +1.00000 q^{8} -2.90697 q^{9} +2.67935 q^{10} -4.32689 q^{11} -0.305006 q^{12} +6.76346 q^{13} +2.41108 q^{14} -0.817217 q^{15} +1.00000 q^{16} -1.17614 q^{17} -2.90697 q^{18} -0.414369 q^{19} +2.67935 q^{20} -0.735392 q^{21} -4.32689 q^{22} +8.63243 q^{23} -0.305006 q^{24} +2.17892 q^{25} +6.76346 q^{26} +1.80166 q^{27} +2.41108 q^{28} -3.30975 q^{29} -0.817217 q^{30} +8.69603 q^{31} +1.00000 q^{32} +1.31973 q^{33} -1.17614 q^{34} +6.46012 q^{35} -2.90697 q^{36} +2.69205 q^{37} -0.414369 q^{38} -2.06289 q^{39} +2.67935 q^{40} -4.65927 q^{41} -0.735392 q^{42} +0.830651 q^{43} -4.32689 q^{44} -7.78879 q^{45} +8.63243 q^{46} -7.54908 q^{47} -0.305006 q^{48} -1.18671 q^{49} +2.17892 q^{50} +0.358729 q^{51} +6.76346 q^{52} -12.7799 q^{53} +1.80166 q^{54} -11.5933 q^{55} +2.41108 q^{56} +0.126385 q^{57} -3.30975 q^{58} +1.37476 q^{59} -0.817217 q^{60} +7.34207 q^{61} +8.69603 q^{62} -7.00893 q^{63} +1.00000 q^{64} +18.1217 q^{65} +1.31973 q^{66} +5.52915 q^{67} -1.17614 q^{68} -2.63294 q^{69} +6.46012 q^{70} +6.63252 q^{71} -2.90697 q^{72} -5.69241 q^{73} +2.69205 q^{74} -0.664582 q^{75} -0.414369 q^{76} -10.4325 q^{77} -2.06289 q^{78} +5.27433 q^{79} +2.67935 q^{80} +8.17140 q^{81} -4.65927 q^{82} -0.447396 q^{83} -0.735392 q^{84} -3.15129 q^{85} +0.830651 q^{86} +1.00949 q^{87} -4.32689 q^{88} -3.36588 q^{89} -7.78879 q^{90} +16.3072 q^{91} +8.63243 q^{92} -2.65234 q^{93} -7.54908 q^{94} -1.11024 q^{95} -0.305006 q^{96} -18.2599 q^{97} -1.18671 q^{98} +12.5782 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9	\( 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9} + 4 q^{10} + 4 q^{11} + 13 q^{12} + 17 q^{13} + 7 q^{14} + 8 q^{15} + 16 q^{16} - q^{17} + 21 q^{18} + 23 q^{19} + 4 q^{20} + 9 q^{21} + 4 q^{22} + 15 q^{23} + 13 q^{24} + 24 q^{25} + 17 q^{26} + 31 q^{27} + 7 q^{28} + 4 q^{29} + 8 q^{30} + 42 q^{31} + 16 q^{32} + 3 q^{33} - q^{34} - 13 q^{35} + 21 q^{36} + 31 q^{37} + 23 q^{38} - 2 q^{39} + 4 q^{40} - 9 q^{41} + 9 q^{42} + 13 q^{43} + 4 q^{44} - 2 q^{45} + 15 q^{46} + 18 q^{47} + 13 q^{48} - 9 q^{49} + 24 q^{50} - 2 q^{51} + 17 q^{52} - 14 q^{53} + 31 q^{54} - 2 q^{55} + 7 q^{56} - 18 q^{57} + 4 q^{58} + 4 q^{59} + 8 q^{60} + q^{61} + 42 q^{62} + 17 q^{63} + 16 q^{64} - 32 q^{65} + 3 q^{66} + 5 q^{67} - q^{68} + 6 q^{69} - 13 q^{70} + 9 q^{71} + 21 q^{72} + 28 q^{73} + 31 q^{74} + 16 q^{75} + 23 q^{76} - 30 q^{77} - 2 q^{78} + 10 q^{79} + 4 q^{80} + 12 q^{81} - 9 q^{82} + 3 q^{83} + 9 q^{84} - 7 q^{85} + 13 q^{86} - 22 q^{87} + 4 q^{88} - 17 q^{89} - 2 q^{90} + 12 q^{91} + 15 q^{92} - q^{93} + 18 q^{94} - 4 q^{95} + 13 q^{96} - 17 q^{97} - 9 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9 + 4 * q^10 + 4 * q^11 + 13 * q^12 + 17 * q^13 + 7 * q^14 + 8 * q^15 + 16 * q^16 - q^17 + 21 * q^18 + 23 * q^19 + 4 * q^20 + 9 * q^21 + 4 * q^22 + 15 * q^23 + 13 * q^24 + 24 * q^25 + 17 * q^26 + 31 * q^27 + 7 * q^28 + 4 * q^29 + 8 * q^30 + 42 * q^31 + 16 * q^32 + 3 * q^33 - q^34 - 13 * q^35 + 21 * q^36 + 31 * q^37 + 23 * q^38 - 2 * q^39 + 4 * q^40 - 9 * q^41 + 9 * q^42 + 13 * q^43 + 4 * q^44 - 2 * q^45 + 15 * q^46 + 18 * q^47 + 13 * q^48 - 9 * q^49 + 24 * q^50 - 2 * q^51 + 17 * q^52 - 14 * q^53 + 31 * q^54 - 2 * q^55 + 7 * q^56 - 18 * q^57 + 4 * q^58 + 4 * q^59 + 8 * q^60 + q^61 + 42 * q^62 + 17 * q^63 + 16 * q^64 - 32 * q^65 + 3 * q^66 + 5 * q^67 - q^68 + 6 * q^69 - 13 * q^70 + 9 * q^71 + 21 * q^72 + 28 * q^73 + 31 * q^74 + 16 * q^75 + 23 * q^76 - 30 * q^77 - 2 * q^78 + 10 * q^79 + 4 * q^80 + 12 * q^81 - 9 * q^82 + 3 * q^83 + 9 * q^84 - 7 * q^85 + 13 * q^86 - 22 * q^87 + 4 * q^88 - 17 * q^89 - 2 * q^90 + 12 * q^91 + 15 * q^92 - q^93 + 18 * q^94 - 4 * q^95 + 13 * q^96 - 17 * q^97 - 9 * q^98 - 10 * q^99

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