LMFDB - Embedded newform 8015.2.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66490 q^{2} +2.35676 q^{3} +5.10167 q^{4} -1.00000 q^{5} -6.28053 q^{6} -1.00000 q^{7} -8.26563 q^{8} +2.55434 q^{9} +O(q^{10})$	\(q-2.66490 q^{2} +2.35676 q^{3} +5.10167 q^{4} -1.00000 q^{5} -6.28053 q^{6} -1.00000 q^{7} -8.26563 q^{8} +2.55434 q^{9} +2.66490 q^{10} -2.82333 q^{11} +12.0234 q^{12} -4.49602 q^{13} +2.66490 q^{14} -2.35676 q^{15} +11.8237 q^{16} +3.23346 q^{17} -6.80704 q^{18} -0.770542 q^{19} -5.10167 q^{20} -2.35676 q^{21} +7.52388 q^{22} +3.86347 q^{23} -19.4801 q^{24} +1.00000 q^{25} +11.9814 q^{26} -1.05032 q^{27} -5.10167 q^{28} +4.50435 q^{29} +6.28053 q^{30} +0.581291 q^{31} -14.9777 q^{32} -6.65393 q^{33} -8.61684 q^{34} +1.00000 q^{35} +13.0314 q^{36} +1.54126 q^{37} +2.05342 q^{38} -10.5960 q^{39} +8.26563 q^{40} +5.28558 q^{41} +6.28053 q^{42} +8.74152 q^{43} -14.4037 q^{44} -2.55434 q^{45} -10.2958 q^{46} -1.70510 q^{47} +27.8657 q^{48} +1.00000 q^{49} -2.66490 q^{50} +7.62050 q^{51} -22.9372 q^{52} -2.20381 q^{53} +2.79900 q^{54} +2.82333 q^{55} +8.26563 q^{56} -1.81599 q^{57} -12.0036 q^{58} -3.45699 q^{59} -12.0234 q^{60} -2.89136 q^{61} -1.54908 q^{62} -2.55434 q^{63} +16.2666 q^{64} +4.49602 q^{65} +17.7320 q^{66} -12.9849 q^{67} +16.4961 q^{68} +9.10530 q^{69} -2.66490 q^{70} +0.478271 q^{71} -21.1132 q^{72} -3.51468 q^{73} -4.10731 q^{74} +2.35676 q^{75} -3.93105 q^{76} +2.82333 q^{77} +28.2374 q^{78} +2.56070 q^{79} -11.8237 q^{80} -10.1384 q^{81} -14.0855 q^{82} +14.5720 q^{83} -12.0234 q^{84} -3.23346 q^{85} -23.2952 q^{86} +10.6157 q^{87} +23.3366 q^{88} +6.59718 q^{89} +6.80704 q^{90} +4.49602 q^{91} +19.7102 q^{92} +1.36996 q^{93} +4.54391 q^{94} +0.770542 q^{95} -35.2989 q^{96} -14.9627 q^{97} -2.66490 q^{98} -7.21174 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) $ 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.66490	−1.88437	−0.942183	−	0.335099i	$-0.891230\pi$
$2$	−2.66490	−1.88437	−0.942183	+	0.335099i	$0.891230\pi$
$3$	2.35676	1.36068	0.680339	−	0.732897i	$-0.261832\pi$
$3$	2.35676	1.36068	0.680339	+	0.732897i	$0.261832\pi$
$4$	5.10167	2.55084
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−6.28053	−2.56402
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−8.26563	−2.92234
$9$	2.55434	0.851446
$10$	2.66490	0.842714
$11$	−2.82333	−0.851266	−0.425633	−	0.904896i	$-0.639949\pi$
$11$	−2.82333	−0.851266	−0.425633	+	0.904896i	$0.639949\pi$
$12$	12.0234	3.47087
$13$	−4.49602	−1.24697	−0.623485	−	0.781835i	$-0.714284\pi$
$13$	−4.49602	−1.24697	−0.623485	+	0.781835i	$0.714284\pi$
$14$	2.66490	0.712223
$15$	−2.35676	−0.608514
$16$	11.8237	2.95593
$17$	3.23346	0.784229	0.392115	−	0.919916i	$-0.371744\pi$
$17$	3.23346	0.784229	0.392115	+	0.919916i	$0.371744\pi$
$18$	−6.80704	−1.60444
$19$	−0.770542	−0.176775	−0.0883873	−	0.996086i	$-0.528171\pi$
$19$	−0.770542	−0.176775	−0.0883873	+	0.996086i	$0.528171\pi$
$20$	−5.10167	−1.14077
$21$	−2.35676	−0.514288
$22$	7.52388	1.60410
$23$	3.86347	0.805590	0.402795	−	0.915290i	$-0.368039\pi$
$23$	3.86347	0.805590	0.402795	+	0.915290i	$0.368039\pi$
$24$	−19.4801	−3.97637
$25$	1.00000	0.200000
$26$	11.9814	2.34975
$27$	−1.05032	−0.202135
$28$	−5.10167	−0.964125
$29$	4.50435	0.836437	0.418219	−	0.908346i	$-0.362655\pi$
$29$	4.50435	0.836437	0.418219	+	0.908346i	$0.362655\pi$
$30$	6.28053	1.14666
$31$	0.581291	0.104403	0.0522014	−	0.998637i	$-0.483376\pi$
$31$	0.581291	0.104403	0.0522014	+	0.998637i	$0.483376\pi$
$32$	−14.9777	−2.64771
$33$	−6.65393	−1.15830
$34$	−8.61684	−1.47778
$35$	1.00000	0.169031
$36$	13.0314	2.17190
$37$	1.54126	0.253382	0.126691	−	0.991942i	$-0.459564\pi$
$37$	1.54126	0.253382	0.126691	+	0.991942i	$0.459564\pi$
$38$	2.05342	0.333108
$39$	−10.5960	−1.69673
$40$	8.26563	1.30691
$41$	5.28558	0.825470	0.412735	−	0.910851i	$-0.364574\pi$
$41$	5.28558	0.825470	0.412735	+	0.910851i	$0.364574\pi$
$42$	6.28053	0.969107
$43$	8.74152	1.33307	0.666534	−	0.745474i	$-0.267777\pi$
$43$	8.74152	1.33307	0.666534	+	0.745474i	$0.267777\pi$
$44$	−14.4037	−2.17144
$45$	−2.55434	−0.380778
$46$	−10.2958	−1.51803
$47$	−1.70510	−0.248714	−0.124357	−	0.992238i	$-0.539687\pi$
$47$	−1.70510	−0.248714	−0.124357	+	0.992238i	$0.539687\pi$
$48$	27.8657	4.02207
$49$	1.00000	0.142857
$50$	−2.66490	−0.376873
$51$	7.62050	1.06708
$52$	−22.9372	−3.18082
$53$	−2.20381	−0.302717	−0.151358	−	0.988479i	$-0.548365\pi$
$53$	−2.20381	−0.302717	−0.151358	+	0.988479i	$0.548365\pi$
$54$	2.79900	0.380896
$55$	2.82333	0.380698
$56$	8.26563	1.10454
$57$	−1.81599	−0.240533
$58$	−12.0036	−1.57615
$59$	−3.45699	−0.450062	−0.225031	−	0.974352i	$-0.572248\pi$
$59$	−3.45699	−0.450062	−0.225031	+	0.974352i	$0.572248\pi$
$60$	−12.0234	−1.55222
$61$	−2.89136	−0.370201	−0.185101	−	0.982720i	$-0.559261\pi$
$61$	−2.89136	−0.370201	−0.185101	+	0.982720i	$0.559261\pi$
$62$	−1.54908	−0.196733
$63$	−2.55434	−0.321816
$64$	16.2666	2.03332
$65$	4.49602	0.557662
$66$	17.7320	2.18266
$67$	−12.9849	−1.58636	−0.793181	−	0.608986i	$-0.791577\pi$
$67$	−12.9849	−1.58636	−0.793181	+	0.608986i	$0.791577\pi$
$68$	16.4961	2.00044
$69$	9.10530	1.09615
$70$	−2.66490	−0.318516
$71$	0.478271	0.0567603	0.0283802	−	0.999597i	$-0.490965\pi$
$71$	0.478271	0.0567603	0.0283802	+	0.999597i	$0.490965\pi$
$72$	−21.1132	−2.48822
$73$	−3.51468	−0.411363	−0.205681	−	0.978619i	$-0.565941\pi$
$73$	−3.51468	−0.411363	−0.205681	+	0.978619i	$0.565941\pi$
$74$	−4.10731	−0.477465
$75$	2.35676	0.272136
$76$	−3.93105	−0.450923
$77$	2.82333	0.321748
$78$	28.2374	3.19725
$79$	2.56070	0.288101	0.144050	−	0.989570i	$-0.453987\pi$
$79$	2.56070	0.288101	0.144050	+	0.989570i	$0.453987\pi$
$80$	−11.8237	−1.32193
$81$	−10.1384	−1.12649
$82$	−14.0855	−1.55549
$83$	14.5720	1.59949	0.799744	−	0.600341i	$-0.204968\pi$
$83$	14.5720	1.59949	0.799744	+	0.600341i	$0.204968\pi$
$84$	−12.0234	−1.31186
$85$	−3.23346	−0.350718
$86$	−23.2952	−2.51199
$87$	10.6157	1.13812
$88$	23.3366	2.48769
$89$	6.59718	0.699300	0.349650	−	0.936880i	$-0.386301\pi$
$89$	6.59718	0.699300	0.349650	+	0.936880i	$0.386301\pi$
$90$	6.80704	0.717525
$91$	4.49602	0.471311
$92$	19.7102	2.05493
$93$	1.36996	0.142059
$94$	4.54391	0.468669
$95$	0.770542	0.0790560
$96$	−35.2989	−3.60268
$97$	−14.9627	−1.51923	−0.759617	−	0.650371i	$-0.774614\pi$
$97$	−14.9627	−1.51923	−0.759617	+	0.650371i	$0.774614\pi$
$98$	−2.66490	−0.269195
$99$	−7.21174	−0.724807
$100$	5.10167	0.510167
$101$	10.6832	1.06302	0.531511	−	0.847051i	$-0.321624\pi$
$101$	10.6832	1.06302	0.531511	+	0.847051i	$0.321624\pi$
$102$	−20.3079	−2.01078
$103$	−4.69456	−0.462569	−0.231284	−	0.972886i	$-0.574293\pi$
$103$	−4.69456	−0.462569	−0.231284	+	0.972886i	$0.574293\pi$
$104$	37.1624	3.64407
$105$	2.35676	0.229997
$106$	5.87293	0.570429
$107$	−12.5196	−1.21031	−0.605157	−	0.796106i	$-0.706890\pi$
$107$	−12.5196	−1.21031	−0.605157	+	0.796106i	$0.706890\pi$
$108$	−5.35840	−0.515612
$109$	−7.34095	−0.703135	−0.351568	−	0.936163i	$-0.614351\pi$
$109$	−7.34095	−0.703135	−0.351568	+	0.936163i	$0.614351\pi$
$110$	−7.52388	−0.717374
$111$	3.63240	0.344772
$112$	−11.8237	−1.11724
$113$	2.94082	0.276649	0.138325	−	0.990387i	$-0.455828\pi$
$113$	2.94082	0.276649	0.138325	+	0.990387i	$0.455828\pi$
$114$	4.83942	0.453253
$115$	−3.86347	−0.360271
$116$	22.9797	2.13361
$117$	−11.4843	−1.06173
$118$	9.21252	0.848082
$119$	−3.23346	−0.296411
$120$	19.4801	1.77829
$121$	−3.02880	−0.275345
$122$	7.70518	0.697595
$123$	12.4569	1.12320
$124$	2.96555	0.266315
$125$	−1.00000	−0.0894427
$126$	6.80704	0.606420
$127$	−3.09751	−0.274860	−0.137430	−	0.990512i	$-0.543884\pi$
$127$	−3.09751	−0.274860	−0.137430	+	0.990512i	$0.543884\pi$
$128$	−13.3934	−1.18382
$129$	20.6017	1.81388
$130$	−11.9814	−1.05084
$131$	−3.14201	−0.274519	−0.137260	−	0.990535i	$-0.543829\pi$
$131$	−3.14201	−0.274519	−0.137260	+	0.990535i	$0.543829\pi$
$132$	−33.9461	−2.95463
$133$	0.770542	0.0668145
$134$	34.6035	2.98929
$135$	1.05032	0.0903974
$136$	−26.7266	−2.29179
$137$	−2.85972	−0.244322	−0.122161	−	0.992510i	$-0.538982\pi$
$137$	−2.85972	−0.244322	−0.122161	+	0.992510i	$0.538982\pi$
$138$	−24.2647	−2.06555
$139$	5.80852	0.492672	0.246336	−	0.969184i	$-0.420773\pi$
$139$	5.80852	0.492672	0.246336	+	0.969184i	$0.420773\pi$
$140$	5.10167	0.431170
$141$	−4.01851	−0.338420
$142$	−1.27454	−0.106957
$143$	12.6937	1.06150
$144$	30.2017	2.51681
$145$	−4.50435	−0.374066
$146$	9.36627	0.775158
$147$	2.35676	0.194383
$148$	7.86302	0.646337
$149$	9.64595	0.790227	0.395113	−	0.918632i	$-0.370705\pi$
$149$	9.64595	0.790227	0.395113	+	0.918632i	$0.370705\pi$
$150$	−6.28053	−0.512803
$151$	5.79510	0.471599	0.235799	−	0.971802i	$-0.424229\pi$
$151$	5.79510	0.471599	0.235799	+	0.971802i	$0.424229\pi$
$152$	6.36902	0.516596
$153$	8.25935	0.667729
$154$	−7.52388	−0.606292
$155$	−0.581291	−0.0466904
$156$	−54.0576	−4.32807
$157$	−5.41567	−0.432218	−0.216109	−	0.976369i	$-0.569337\pi$
$157$	−5.41567	−0.432218	−0.216109	+	0.976369i	$0.569337\pi$
$158$	−6.82399	−0.542887
$159$	−5.19386	−0.411900
$160$	14.9777	1.18409
$161$	−3.86347	−0.304484
$162$	27.0177	2.12271
$163$	−2.68302	−0.210150	−0.105075	−	0.994464i	$-0.533508\pi$
$163$	−2.68302	−0.210150	−0.105075	+	0.994464i	$0.533508\pi$
$164$	26.9653	2.10564
$165$	6.65393	0.518007
$166$	−38.8330	−3.01402
$167$	−13.4843	−1.04344	−0.521722	−	0.853116i	$-0.674710\pi$
$167$	−13.4843	−1.04344	−0.521722	+	0.853116i	$0.674710\pi$
$168$	19.4801	1.50293
$169$	7.21416	0.554935
$170$	8.61684	0.660881
$171$	−1.96823	−0.150514
$172$	44.5963	3.40044
$173$	−1.71813	−0.130627	−0.0653133	−	0.997865i	$-0.520805\pi$
$173$	−1.71813	−0.130627	−0.0653133	+	0.997865i	$0.520805\pi$
$174$	−28.2897	−2.14464
$175$	−1.00000	−0.0755929
$176$	−33.3823	−2.51628
$177$	−8.14731	−0.612390
$178$	−17.5808	−1.31774
$179$	−13.0883	−0.978269	−0.489134	−	0.872208i	$-0.662687\pi$
$179$	−13.0883	−0.978269	−0.489134	+	0.872208i	$0.662687\pi$
$180$	−13.0314	−0.971302
$181$	13.4763	1.00169	0.500844	−	0.865537i	$-0.333023\pi$
$181$	13.4763	1.00169	0.500844	+	0.865537i	$0.333023\pi$
$182$	−11.9814	−0.888122
$183$	−6.81426	−0.503725
$184$	−31.9341	−2.35421
$185$	−1.54126	−0.113316
$186$	−3.65081	−0.267691
$187$	−9.12913	−0.667588
$188$	−8.69885	−0.634429
$189$	1.05032	0.0763997
$190$	−2.05342	−0.148970
$191$	13.4985	0.976716	0.488358	−	0.872643i	$-0.337596\pi$
$191$	13.4985	0.976716	0.488358	+	0.872643i	$0.337596\pi$
$192$	38.3365	2.76670
$193$	8.15672	0.587133	0.293567	−	0.955939i	$-0.405158\pi$
$193$	8.15672	0.587133	0.293567	+	0.955939i	$0.405158\pi$
$194$	39.8741	2.86279
$195$	10.5960	0.758799
$196$	5.10167	0.364405
$197$	−5.42577	−0.386570	−0.193285	−	0.981143i	$-0.561914\pi$
$197$	−5.42577	−0.386570	−0.193285	+	0.981143i	$0.561914\pi$
$198$	19.2185	1.36580
$199$	−11.7585	−0.833539	−0.416769	−	0.909012i	$-0.636838\pi$
$199$	−11.7585	−0.833539	−0.416769	+	0.909012i	$0.636838\pi$
$200$	−8.26563	−0.584469
$201$	−30.6024	−2.15853
$202$	−28.4697	−2.00312
$203$	−4.50435	−0.316143
$204$	38.8773	2.72196
$205$	−5.28558	−0.369161
$206$	12.5105	0.871649
$207$	9.86861	0.685916
$208$	−53.1596	−3.68595
$209$	2.17550	0.150482
$210$	−6.28053	−0.433398
$211$	−2.12190	−0.146078	−0.0730389	−	0.997329i	$-0.523270\pi$
$211$	−2.12190	−0.146078	−0.0730389	+	0.997329i	$0.523270\pi$
$212$	−11.2431	−0.772181
$213$	1.12717	0.0772326
$214$	33.3634	2.28067
$215$	−8.74152	−0.596166
$216$	8.68158	0.590707
$217$	−0.581291	−0.0394606
$218$	19.5629	1.32496
$219$	−8.28328	−0.559732
$220$	14.4037	0.971098
$221$	−14.5377	−0.977911
$222$	−9.67996	−0.649676
$223$	−23.0285	−1.54210	−0.771052	−	0.636772i	$-0.780269\pi$
$223$	−23.0285	−1.54210	−0.771052	+	0.636772i	$0.780269\pi$
$224$	14.9777	1.00074
$225$	2.55434	0.170289
$226$	−7.83698	−0.521308
$227$	−7.68972	−0.510385	−0.255192	−	0.966890i	$-0.582139\pi$
$227$	−7.68972	−0.510385	−0.255192	+	0.966890i	$0.582139\pi$
$228$	−9.26457	−0.613561
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	10.2958	0.678882
$231$	6.65393	0.437796
$232$	−37.2313	−2.44436
$233$	−15.6222	−1.02344	−0.511722	−	0.859151i	$-0.670992\pi$
$233$	−15.6222	−1.02344	−0.511722	+	0.859151i	$0.670992\pi$
$234$	30.6046	2.00068
$235$	1.70510	0.111228
$236$	−17.6364	−1.14803
$237$	6.03496	0.392012
$238$	8.61684	0.558547
$239$	−3.24570	−0.209947	−0.104973	−	0.994475i	$-0.533476\pi$
$239$	−3.24570	−0.209947	−0.104973	+	0.994475i	$0.533476\pi$
$240$	−27.8657	−1.79872
$241$	−15.3620	−0.989555	−0.494778	−	0.869020i	$-0.664750\pi$
$241$	−15.3620	−0.989555	−0.494778	+	0.869020i	$0.664750\pi$
$242$	8.07144	0.518852
$243$	−20.7428	−1.33065
$244$	−14.7508	−0.944323
$245$	−1.00000	−0.0638877
$246$	−33.1963	−2.11652
$247$	3.46437	0.220433
$248$	−4.80473	−0.305101
$249$	34.3428	2.17639
$250$	2.66490	0.168543
$251$	10.4889	0.662052	0.331026	−	0.943622i	$-0.392605\pi$
$251$	10.4889	0.662052	0.331026	+	0.943622i	$0.392605\pi$
$252$	−13.0314	−0.820900
$253$	−10.9079	−0.685772
$254$	8.25454	0.517936
$255$	−7.62050	−0.477215
$256$	3.15875	0.197422
$257$	−15.4423	−0.963263	−0.481631	−	0.876374i	$-0.659956\pi$
$257$	−15.4423	−0.963263	−0.481631	+	0.876374i	$0.659956\pi$
$258$	−54.9014	−3.41801
$259$	−1.54126	−0.0957695
$260$	22.9372	1.42250
$261$	11.5056	0.712181
$262$	8.37314	0.517294
$263$	21.0691	1.29917	0.649587	−	0.760288i	$-0.274942\pi$
$263$	21.0691	1.29917	0.649587	+	0.760288i	$0.274942\pi$
$264$	54.9989	3.38495
$265$	2.20381	0.135379
$266$	−2.05342	−0.125903
$267$	15.5480	0.951522
$268$	−66.2449	−4.04655
$269$	−5.74876	−0.350508	−0.175254	−	0.984523i	$-0.556075\pi$
$269$	−5.74876	−0.350508	−0.175254	+	0.984523i	$0.556075\pi$
$270$	−2.79900	−0.170342
$271$	−20.5909	−1.25081	−0.625405	−	0.780300i	$-0.715066\pi$
$271$	−20.5909	−1.25081	−0.625405	+	0.780300i	$0.715066\pi$
$272$	38.2315	2.31813
$273$	10.5960	0.641302
$274$	7.62085	0.460392
$275$	−2.82333	−0.170253
$276$	46.4522	2.79610
$277$	−8.13282	−0.488654	−0.244327	−	0.969693i	$-0.578567\pi$
$277$	−8.13282	−0.488654	−0.244327	+	0.969693i	$0.578567\pi$
$278$	−15.4791	−0.928375
$279$	1.48481	0.0888934
$280$	−8.26563	−0.493966
$281$	−17.8445	−1.06451	−0.532257	−	0.846583i	$-0.678656\pi$
$281$	−17.8445	−1.06451	−0.532257	+	0.846583i	$0.678656\pi$
$282$	10.7089	0.637707
$283$	−19.4703	−1.15739	−0.578693	−	0.815545i	$-0.696437\pi$
$283$	−19.4703	−1.15739	−0.578693	+	0.815545i	$0.696437\pi$
$284$	2.43998	0.144786
$285$	1.81599	0.107570
$286$	−33.8275	−2.00026
$287$	−5.28558	−0.311998
$288$	−38.2581	−2.25438
$289$	−6.54473	−0.384984
$290$	12.0036	0.704877
$291$	−35.2636	−2.06719
$292$	−17.9308	−1.04932
$293$	−15.5084	−0.906009	−0.453004	−	0.891508i	$-0.649648\pi$
$293$	−15.5084	−0.906009	−0.453004	+	0.891508i	$0.649648\pi$
$294$	−6.28053	−0.366288
$295$	3.45699	0.201274
$296$	−12.7395	−0.740470
$297$	2.96541	0.172070
$298$	−25.7055	−1.48908
$299$	−17.3702	−1.00455
$300$	12.0234	0.694173
$301$	−8.74152	−0.503853
$302$	−15.4433	−0.888664
$303$	25.1779	1.44643
$304$	−9.11067	−0.522533
$305$	2.89136	0.165559
$306$	−22.0103	−1.25825
$307$	9.72538	0.555057	0.277528	−	0.960717i	$-0.410485\pi$
$307$	9.72538	0.555057	0.277528	+	0.960717i	$0.410485\pi$
$308$	14.4037	0.820728
$309$	−11.0640	−0.629407
$310$	1.54908	0.0879818
$311$	3.42117	0.193997	0.0969984	−	0.995285i	$-0.469076\pi$
$311$	3.42117	0.193997	0.0969984	+	0.995285i	$0.469076\pi$
$312$	87.5831	4.95841
$313$	−28.0084	−1.58313	−0.791564	−	0.611086i	$-0.790733\pi$
$313$	−28.0084	−1.58313	−0.791564	+	0.611086i	$0.790733\pi$
$314$	14.4322	0.814456
$315$	2.55434	0.143921
$316$	13.0638	0.734898
$317$	−20.0614	−1.12676	−0.563381	−	0.826197i	$-0.690500\pi$
$317$	−20.0614	−1.12676	−0.563381	+	0.826197i	$0.690500\pi$
$318$	13.8411	0.776170
$319$	−12.7173	−0.712031
$320$	−16.2666	−0.909330
$321$	−29.5057	−1.64685
$322$	10.2958	0.573760
$323$	−2.49152	−0.138632
$324$	−51.7227	−2.87348
$325$	−4.49602	−0.249394
$326$	7.14996	0.396000
$327$	−17.3009	−0.956741
$328$	−43.6887	−2.41230
$329$	1.70510	0.0940051
$330$	−17.7320	−0.976116
$331$	−15.5311	−0.853665	−0.426832	−	0.904331i	$-0.640371\pi$
$331$	−15.5311	−0.853665	−0.426832	+	0.904331i	$0.640371\pi$
$332$	74.3417	4.08003
$333$	3.93691	0.215741
$334$	35.9342	1.96623
$335$	12.9849	0.709443
$336$	−27.8657	−1.52020
$337$	−10.6570	−0.580523	−0.290261	−	0.956947i	$-0.593742\pi$
$337$	−10.6570	−0.580523	−0.290261	+	0.956947i	$0.593742\pi$
$338$	−19.2250	−1.04570
$339$	6.93082	0.376431
$340$	−16.4961	−0.894624
$341$	−1.64118	−0.0888747
$342$	5.24512	0.283623
$343$	−1.00000	−0.0539949
$344$	−72.2542	−3.89568
$345$	−9.10530	−0.490213
$346$	4.57862	0.246148
$347$	22.1775	1.19055	0.595276	−	0.803522i	$-0.297043\pi$
$347$	22.1775	1.19055	0.595276	+	0.803522i	$0.297043\pi$
$348$	54.1578	2.90316
$349$	−13.5122	−0.723289	−0.361645	−	0.932316i	$-0.617785\pi$
$349$	−13.5122	−0.723289	−0.361645	+	0.932316i	$0.617785\pi$
$350$	2.66490	0.142445
$351$	4.72227	0.252056
$352$	42.2870	2.25390
$353$	−24.5701	−1.30773	−0.653867	−	0.756609i	$-0.726855\pi$
$353$	−24.5701	−1.30773	−0.653867	+	0.756609i	$0.726855\pi$
$354$	21.7117	1.15397
$355$	−0.478271	−0.0253840
$356$	33.6566	1.78380
$357$	−7.62050	−0.403320
$358$	34.8791	1.84342
$359$	−8.36648	−0.441566	−0.220783	−	0.975323i	$-0.570861\pi$
$359$	−8.36648	−0.441566	−0.220783	+	0.975323i	$0.570861\pi$
$360$	21.1132	1.11276
$361$	−18.4063	−0.968751
$362$	−35.9131	−1.88755
$363$	−7.13817	−0.374657
$364$	22.9372	1.20224
$365$	3.51468	0.183967
$366$	18.1593	0.949202
$367$	16.9504	0.884804	0.442402	−	0.896817i	$-0.354127\pi$
$367$	16.9504	0.884804	0.442402	+	0.896817i	$0.354127\pi$
$368$	45.6806	2.38127
$369$	13.5012	0.702842
$370$	4.10731	0.213529
$371$	2.20381	0.114416
$372$	6.98911	0.362368
$373$	15.5971	0.807587	0.403794	−	0.914850i	$-0.367691\pi$
$373$	15.5971	0.807587	0.403794	+	0.914850i	$0.367691\pi$
$374$	24.3282	1.25798
$375$	−2.35676	−0.121703
$376$	14.0937	0.726828
$377$	−20.2516	−1.04301
$378$	−2.79900	−0.143965
$379$	0.182177	0.00935779	0.00467889	−	0.999989i	$-0.498511\pi$
$379$	0.182177	0.00935779	0.00467889	+	0.999989i	$0.498511\pi$
$380$	3.93105	0.201659
$381$	−7.30010	−0.373995
$382$	−35.9721	−1.84049
$383$	−25.1874	−1.28701	−0.643507	−	0.765440i	$-0.722521\pi$
$383$	−25.1874	−1.28701	−0.643507	+	0.765440i	$0.722521\pi$
$384$	−31.5650	−1.61079
$385$	−2.82333	−0.143890
$386$	−21.7368	−1.10637
$387$	22.3288	1.13504
$388$	−76.3349	−3.87532
$389$	−3.49631	−0.177270	−0.0886350	−	0.996064i	$-0.528250\pi$
$389$	−3.49631	−0.177270	−0.0886350	+	0.996064i	$0.528250\pi$
$390$	−28.2374	−1.42985
$391$	12.4924	0.631767
$392$	−8.26563	−0.417478
$393$	−7.40499	−0.373532
$394$	14.4591	0.728440
$395$	−2.56070	−0.128843
$396$	−36.7919	−1.84886
$397$	−13.7137	−0.688271	−0.344136	−	0.938920i	$-0.611828\pi$
$397$	−13.7137	−0.688271	−0.344136	+	0.938920i	$0.611828\pi$
$398$	31.3352	1.57069
$399$	1.81599	0.0909131
$400$	11.8237	0.591186
$401$	−15.3130	−0.764693	−0.382347	−	0.924019i	$-0.624884\pi$
$401$	−15.3130	−0.764693	−0.382347	+	0.924019i	$0.624884\pi$
$402$	81.5523	4.06746
$403$	−2.61349	−0.130187
$404$	54.5024	2.71160
$405$	10.1384	0.503780
$406$	12.0036	0.595730
$407$	−4.35150	−0.215696
$408$	−62.9883	−3.11839
$409$	30.7319	1.51959	0.759797	−	0.650161i	$-0.225298\pi$
$409$	30.7319	1.51959	0.759797	+	0.650161i	$0.225298\pi$
$410$	14.0855	0.695635
$411$	−6.73968	−0.332444
$412$	−23.9501	−1.17994
$413$	3.45699	0.170107
$414$	−26.2988	−1.29252
$415$	−14.5720	−0.715313
$416$	67.3400	3.30161
$417$	13.6893	0.670368
$418$	−5.79747	−0.283564
$419$	8.70179	0.425110	0.212555	−	0.977149i	$-0.431821\pi$
$419$	8.70179	0.425110	0.212555	+	0.977149i	$0.431821\pi$
$420$	12.0234	0.586684
$421$	6.56121	0.319774	0.159887	−	0.987135i	$-0.448887\pi$
$421$	6.56121	0.319774	0.159887	+	0.987135i	$0.448887\pi$
$422$	5.65465	0.275264
$423$	−4.35540	−0.211767
$424$	18.2159	0.884642
$425$	3.23346	0.156846
$426$	−3.00380	−0.145534
$427$	2.89136	0.139923
$428$	−63.8708	−3.08731
$429$	29.9162	1.44437
$430$	23.2952	1.12340
$431$	18.0923	0.871474	0.435737	−	0.900074i	$-0.356488\pi$
$431$	18.0923	0.871474	0.435737	+	0.900074i	$0.356488\pi$
$432$	−12.4187	−0.597496
$433$	8.87023	0.426276	0.213138	−	0.977022i	$-0.431632\pi$
$433$	8.87023	0.426276	0.213138	+	0.977022i	$0.431632\pi$
$434$	1.54908	0.0743582
$435$	−10.6157	−0.508984
$436$	−37.4511	−1.79358
$437$	−2.97697	−0.142408
$438$	22.0741	1.05474
$439$	−8.50550	−0.405946	−0.202973	−	0.979184i	$-0.565060\pi$
$439$	−8.50550	−0.405946	−0.202973	+	0.979184i	$0.565060\pi$
$440$	−23.3366	−1.11253
$441$	2.55434	0.121635
$442$	38.7414	1.84274
$443$	−1.79835	−0.0854421	−0.0427211	−	0.999087i	$-0.513603\pi$
$443$	−1.79835	−0.0854421	−0.0427211	+	0.999087i	$0.513603\pi$
$444$	18.5313	0.879456
$445$	−6.59718	−0.312736
$446$	61.3686	2.90589
$447$	22.7332	1.07524
$448$	−16.2666	−0.768524
$449$	18.2483	0.861189	0.430594	−	0.902546i	$-0.358304\pi$
$449$	18.2483	0.861189	0.430594	+	0.902546i	$0.358304\pi$
$450$	−6.80704	−0.320887
$451$	−14.9230	−0.702694
$452$	15.0031	0.705687
$453$	13.6577	0.641694
$454$	20.4923	0.961751
$455$	−4.49602	−0.210776
$456$	15.0103	0.702921
$457$	−4.26448	−0.199484	−0.0997421	−	0.995013i	$-0.531802\pi$
$457$	−4.26448	−0.199484	−0.0997421	+	0.995013i	$0.531802\pi$
$458$	2.66490	0.124522
$459$	−3.39618	−0.158520
$460$	−19.7102	−0.918992
$461$	17.6732	0.823123	0.411562	−	0.911382i	$-0.364983\pi$
$461$	17.6732	0.823123	0.411562	+	0.911382i	$0.364983\pi$
$462$	−17.7320	−0.824968
$463$	19.7546	0.918075	0.459037	−	0.888417i	$-0.348194\pi$
$463$	19.7546	0.918075	0.459037	+	0.888417i	$0.348194\pi$
$464$	53.2581	2.47245
$465$	−1.36996	−0.0635306
$466$	41.6315	1.92854
$467$	−21.3635	−0.988583	−0.494292	−	0.869296i	$-0.664572\pi$
$467$	−21.3635	−0.988583	−0.494292	+	0.869296i	$0.664572\pi$
$468$	−58.5893	−2.70829
$469$	12.9849	0.599589
$470$	−4.54391	−0.209595
$471$	−12.7635	−0.588109
$472$	28.5742	1.31524
$473$	−24.6802	−1.13480
$474$	−16.0825	−0.738695
$475$	−0.770542	−0.0353549
$476$	−16.4961	−0.756095
$477$	−5.62927	−0.257747
$478$	8.64944	0.395616
$479$	30.4863	1.39296	0.696478	−	0.717578i	$-0.254749\pi$
$479$	30.4863	1.39296	0.696478	+	0.717578i	$0.254749\pi$
$480$	35.2989	1.61117
$481$	−6.92955	−0.315960
$482$	40.9382	1.86468
$483$	−9.10530	−0.414305
$484$	−15.4519	−0.702361
$485$	14.9627	0.679422
$486$	55.2774	2.50743
$487$	−3.89273	−0.176396	−0.0881982	−	0.996103i	$-0.528111\pi$
$487$	−3.89273	−0.176396	−0.0881982	+	0.996103i	$0.528111\pi$
$488$	23.8990	1.08185
$489$	−6.32324	−0.285947
$490$	2.66490	0.120388
$491$	33.4893	1.51135	0.755676	−	0.654946i	$-0.227308\pi$
$491$	33.4893	1.51135	0.755676	+	0.654946i	$0.227308\pi$
$492$	63.5509	2.86510
$493$	14.5646	0.655959
$494$	−9.23219	−0.415376
$495$	7.21174	0.324144
$496$	6.87301	0.308607
$497$	−0.478271	−0.0214534
$498$	−91.5201	−4.10112
$499$	2.48169	0.111096	0.0555479	−	0.998456i	$-0.482309\pi$
$499$	2.48169	0.111096	0.0555479	+	0.998456i	$0.482309\pi$
$500$	−5.10167	−0.228154
$501$	−31.7792	−1.41979
$502$	−27.9518	−1.24755
$503$	−11.8142	−0.526768	−0.263384	−	0.964691i	$-0.584839\pi$
$503$	−11.8142	−0.526768	−0.263384	+	0.964691i	$0.584839\pi$
$504$	21.1132	0.940457
$505$	−10.6832	−0.475398
$506$	29.0683	1.29225
$507$	17.0021	0.755089
$508$	−15.8025	−0.701122
$509$	12.8002	0.567357	0.283679	−	0.958919i	$-0.408445\pi$
$509$	12.8002	0.567357	0.283679	+	0.958919i	$0.408445\pi$
$510$	20.3079	0.899247
$511$	3.51468	0.155480
$512$	18.3690	0.811802
$513$	0.809318	0.0357323
$514$	41.1521	1.81514
$515$	4.69456	0.206867
$516$	105.103	4.62690
$517$	4.81406	0.211722
$518$	4.10731	0.180465
$519$	−4.04922	−0.177741
$520$	−37.1624	−1.62968
$521$	8.21903	0.360082	0.180041	−	0.983659i	$-0.442377\pi$
$521$	8.21903	0.360082	0.180041	+	0.983659i	$0.442377\pi$
$522$	−30.6613	−1.34201
$523$	−25.8248	−1.12924	−0.564619	−	0.825352i	$-0.690977\pi$
$523$	−25.8248	−1.12924	−0.564619	+	0.825352i	$0.690977\pi$
$524$	−16.0295	−0.700253
$525$	−2.35676	−0.102858
$526$	−56.1468	−2.44812
$527$	1.87958	0.0818758
$528$	−78.6741	−3.42385
$529$	−8.07357	−0.351025
$530$	−5.87293	−0.255104
$531$	−8.83032	−0.383203
$532$	3.93105	0.170433
$533$	−23.7641	−1.02934
$534$	−41.4338	−1.79302
$535$	12.5196	0.541269
$536$	107.329	4.63589
$537$	−30.8461	−1.33111
$538$	15.3199	0.660486
$539$	−2.82333	−0.121609
$540$	5.35840	0.230589
$541$	40.8995	1.75841	0.879204	−	0.476445i	$-0.158075\pi$
$541$	40.8995	1.75841	0.879204	+	0.476445i	$0.158075\pi$
$542$	54.8727	2.35698
$543$	31.7606	1.36298
$544$	−48.4298	−2.07641
$545$	7.34095	0.314452
$546$	−28.2374	−1.20845
$547$	−14.4655	−0.618498	−0.309249	−	0.950981i	$-0.600078\pi$
$547$	−14.4655	−0.618498	−0.309249	+	0.950981i	$0.600078\pi$
$548$	−14.5893	−0.623225
$549$	−7.38552	−0.315206
$550$	7.52388	0.320820
$551$	−3.47079	−0.147861
$552$	−75.2610	−3.20332
$553$	−2.56070	−0.108892
$554$	21.6731	0.920803
$555$	−3.63240	−0.154187
$556$	29.6332	1.25673
$557$	−38.9143	−1.64885	−0.824426	−	0.565970i	$-0.808502\pi$
$557$	−38.9143	−1.64885	−0.824426	+	0.565970i	$0.808502\pi$
$558$	−3.95687	−0.167508
$559$	−39.3020	−1.66230
$560$	11.8237	0.499643
$561$	−21.5152	−0.908373
$562$	47.5538	2.00593
$563$	−34.2875	−1.44505	−0.722523	−	0.691347i	$-0.757018\pi$
$563$	−34.2875	−1.44505	−0.722523	+	0.691347i	$0.757018\pi$
$564$	−20.5011	−0.863254
$565$	−2.94082	−0.123721
$566$	51.8862	2.18094
$567$	10.1384	0.425772
$568$	−3.95321	−0.165873
$569$	−0.0277513	−0.00116339	−0.000581697	−	1.00000i	$-0.500185\pi$
$569$	−0.0277513	−0.00116339	−0.000581697		1.00000i	$0.500185\pi$
$570$	−4.83942	−0.202701
$571$	−30.7607	−1.28730	−0.643648	−	0.765321i	$-0.722580\pi$
$571$	−30.7607	−1.28730	−0.643648	+	0.765321i	$0.722580\pi$
$572$	64.7593	2.70772
$573$	31.8127	1.32900
$574$	14.0855	0.587919
$575$	3.86347	0.161118
$576$	41.5503	1.73126
$577$	28.2718	1.17697	0.588486	−	0.808507i	$-0.299724\pi$
$577$	28.2718	1.17697	0.588486	+	0.808507i	$0.299724\pi$
$578$	17.4410	0.725451
$579$	19.2235	0.798900
$580$	−22.9797	−0.954181
$581$	−14.5720	−0.604550
$582$	93.9738	3.89534
$583$	6.22209	0.257693
$584$	29.0511	1.20214
$585$	11.4843	0.474819
$586$	41.3282	1.70725
$587$	30.9738	1.27842	0.639212	−	0.769030i	$-0.279260\pi$
$587$	30.9738	1.27842	0.639212	+	0.769030i	$0.279260\pi$
$588$	12.0234	0.495838
$589$	−0.447909	−0.0184558
$590$	−9.21252	−0.379274
$591$	−12.7873	−0.525998
$592$	18.2235	0.748980
$593$	1.01503	0.0416822	0.0208411	−	0.999783i	$-0.493366\pi$
$593$	1.01503	0.0416822	0.0208411	+	0.999783i	$0.493366\pi$
$594$	−7.90251	−0.324244
$595$	3.23346	0.132559
$596$	49.2105	2.01574
$597$	−27.7120	−1.13418
$598$	46.2899	1.89293
$599$	−27.3820	−1.11880	−0.559400	−	0.828898i	$-0.688968\pi$
$599$	−27.3820	−1.11880	−0.559400	+	0.828898i	$0.688968\pi$
$600$	−19.4801	−0.795274
$601$	27.1139	1.10600	0.553000	−	0.833181i	$-0.313483\pi$
$601$	27.1139	1.10600	0.553000	+	0.833181i	$0.313483\pi$
$602$	23.2952	0.949443
$603$	−33.1679	−1.35070
$604$	29.5647	1.20297
$605$	3.02880	0.123138
$606$	−67.0965	−2.72561
$607$	−20.6181	−0.836862	−0.418431	−	0.908249i	$-0.637420\pi$
$607$	−20.6181	−0.836862	−0.418431	+	0.908249i	$0.637420\pi$
$608$	11.5410	0.468047
$609$	−10.6157	−0.430170
$610$	−7.70518	−0.311974
$611$	7.66615	0.310139
$612$	42.1365	1.70327
$613$	0.350251	0.0141465	0.00707325	−	0.999975i	$-0.497748\pi$
$613$	0.350251	0.0141465	0.00707325	+	0.999975i	$0.497748\pi$
$614$	−25.9171	−1.04593
$615$	−12.4569	−0.502310
$616$	−23.3366	−0.940259
$617$	0.978393	0.0393886	0.0196943	−	0.999806i	$-0.493731\pi$
$617$	0.978393	0.0393886	0.0196943	+	0.999806i	$0.493731\pi$
$618$	29.4843	1.18603
$619$	−38.6053	−1.55168	−0.775839	−	0.630930i	$-0.782673\pi$
$619$	−38.6053	−1.55168	−0.775839	+	0.630930i	$0.782673\pi$
$620$	−2.96555	−0.119099
$621$	−4.05789	−0.162838
$622$	−9.11706	−0.365561
$623$	−6.59718	−0.264310
$624$	−125.285	−5.01540
$625$	1.00000	0.0400000
$626$	74.6395	2.98319
$627$	5.12713	0.204758
$628$	−27.6290	−1.10252
$629$	4.98362	0.198710
$630$	−6.80704	−0.271199
$631$	−26.8732	−1.06981	−0.534903	−	0.844913i	$-0.679652\pi$
$631$	−26.8732	−1.06981	−0.534903	+	0.844913i	$0.679652\pi$
$632$	−21.1658	−0.841929
$633$	−5.00082	−0.198765
$634$	53.4616	2.12323
$635$	3.09751	0.122921
$636$	−26.4974	−1.05069
$637$	−4.49602	−0.178139
$638$	33.8902	1.34173
$639$	1.22167	0.0483283
$640$	13.3934	0.529419
$641$	−12.0925	−0.477625	−0.238813	−	0.971066i	$-0.576758\pi$
$641$	−12.0925	−0.477625	−0.238813	+	0.971066i	$0.576758\pi$
$642$	78.6296	3.10326
$643$	26.7409	1.05456	0.527278	−	0.849693i	$-0.323213\pi$
$643$	26.7409	1.05456	0.527278	+	0.849693i	$0.323213\pi$
$644$	−19.7102	−0.776690
$645$	−20.6017	−0.811191
$646$	6.63964	0.261233
$647$	35.9992	1.41527	0.707636	−	0.706577i	$-0.249762\pi$
$647$	35.9992	1.41527	0.707636	+	0.706577i	$0.249762\pi$
$648$	83.8001	3.29198
$649$	9.76023	0.383123
$650$	11.9814	0.469950
$651$	−1.36996	−0.0536931
$652$	−13.6879	−0.536058
$653$	35.3892	1.38489	0.692443	−	0.721472i	$-0.256534\pi$
$653$	35.3892	1.38489	0.692443	+	0.721472i	$0.256534\pi$
$654$	46.1050	1.80285
$655$	3.14201	0.122769
$656$	62.4952	2.44003
$657$	−8.97769	−0.350253
$658$	−4.54391	−0.177140
$659$	34.0300	1.32562	0.662811	−	0.748787i	$-0.269363\pi$
$659$	34.0300	1.32562	0.662811	+	0.748787i	$0.269363\pi$
$660$	33.9461	1.32135
$661$	−1.14145	−0.0443974	−0.0221987	−	0.999754i	$-0.507067\pi$
$661$	−1.14145	−0.0443974	−0.0221987	+	0.999754i	$0.507067\pi$
$662$	41.3887	1.60862
$663$	−34.2619	−1.33062
$664$	−120.447	−4.67425
$665$	−0.770542	−0.0298804
$666$	−10.4915	−0.406535
$667$	17.4024	0.673825
$668$	−68.7923	−2.66165
$669$	−54.2728	−2.09831
$670$	−34.6035	−1.33685
$671$	8.16328	0.315140
$672$	35.2989	1.36168
$673$	−12.3975	−0.477888	−0.238944	−	0.971033i	$-0.576801\pi$
$673$	−12.3975	−0.477888	−0.238944	+	0.971033i	$0.576801\pi$
$674$	28.3998	1.09392
$675$	−1.05032	−0.0404269
$676$	36.8043	1.41555
$677$	11.0905	0.426241	0.213120	−	0.977026i	$-0.431637\pi$
$677$	11.0905	0.426241	0.213120	+	0.977026i	$0.431637\pi$
$678$	−18.4699	−0.709333
$679$	14.9627	0.574217
$680$	26.7266	1.02492
$681$	−18.1229	−0.694469
$682$	4.37356	0.167472
$683$	0.395581	0.0151365	0.00756825	−	0.999971i	$-0.497591\pi$
$683$	0.395581	0.0151365	0.00756825	+	0.999971i	$0.497591\pi$
$684$	−10.0412	−0.383936
$685$	2.85972	0.109264
$686$	2.66490	0.101746
$687$	−2.35676	−0.0899162
$688$	103.357	3.94045
$689$	9.90837	0.377479
$690$	24.2647	0.923740
$691$	−25.7838	−0.980864	−0.490432	−	0.871480i	$-0.663161\pi$
$691$	−25.7838	−0.980864	−0.490432	+	0.871480i	$0.663161\pi$
$692$	−8.76531	−0.333207
$693$	7.21174	0.273951
$694$	−59.1008	−2.24343
$695$	−5.80852	−0.220330
$696$	−87.7454	−3.32598
$697$	17.0907	0.647358
$698$	36.0085	1.36294
$699$	−36.8178	−1.39258
$700$	−5.10167	−0.192825
$701$	−0.930705	−0.0351522	−0.0175761	−	0.999846i	$-0.505595\pi$
$701$	−0.930705	−0.0351522	−0.0175761	+	0.999846i	$0.505595\pi$
$702$	−12.5844	−0.474966
$703$	−1.18761	−0.0447915
$704$	−45.9259	−1.73090
$705$	4.01851	0.151346
$706$	65.4768	2.46425
$707$	−10.6832	−0.401785
$708$	−41.5649	−1.56211
$709$	26.6670	1.00150	0.500749	−	0.865592i	$-0.333058\pi$
$709$	26.6670	1.00150	0.500749	+	0.865592i	$0.333058\pi$
$710$	1.27454	0.0478327
$711$	6.54088	0.245302
$712$	−54.5299	−2.04359
$713$	2.24580	0.0841059
$714$	20.3079	0.760002
$715$	−12.6937	−0.474719
$716$	−66.7724	−2.49540
$717$	−7.64934	−0.285670
$718$	22.2958	0.832072
$719$	50.2703	1.87476	0.937382	−	0.348302i	$-0.113242\pi$
$719$	50.2703	1.87476	0.937382	+	0.348302i	$0.113242\pi$
$720$	−30.2017	−1.12555
$721$	4.69456	0.174835
$722$	49.0508	1.82548
$723$	−36.2047	−1.34647
$724$	68.7519	2.55514
$725$	4.50435	0.167287
$726$	19.0225	0.705990
$727$	−31.0337	−1.15098	−0.575488	−	0.817811i	$-0.695188\pi$
$727$	−31.0337	−1.15098	−0.575488	+	0.817811i	$0.695188\pi$
$728$	−37.1624	−1.37733
$729$	−18.4707	−0.684101
$730$	−9.36627	−0.346661
$731$	28.2653	1.04543
$732$	−34.7641	−1.28492
$733$	26.9470	0.995309	0.497655	−	0.867375i	$-0.334195\pi$
$733$	26.9470	0.995309	0.497655	+	0.867375i	$0.334195\pi$
$734$	−45.1710	−1.66729
$735$	−2.35676	−0.0869306
$736$	−57.8659	−2.13297
$737$	36.6608	1.35042
$738$	−35.9792	−1.32441
$739$	−12.8061	−0.471080	−0.235540	−	0.971865i	$-0.575686\pi$
$739$	−12.8061	−0.471080	−0.235540	+	0.971865i	$0.575686\pi$
$740$	−7.86302	−0.289051
$741$	8.16471	0.299938
$742$	−5.87293	−0.215602
$743$	6.06154	0.222376	0.111188	−	0.993799i	$-0.464534\pi$
$743$	6.06154	0.222376	0.111188	+	0.993799i	$0.464534\pi$
$744$	−11.3236	−0.415144
$745$	−9.64595	−0.353400
$746$	−41.5646	−1.52179
$747$	37.2219	1.36188
$748$	−46.5738	−1.70291
$749$	12.5196	0.457455
$750$	6.28053	0.229333
$751$	9.20764	0.335991	0.167996	−	0.985788i	$-0.446271\pi$
$751$	9.20764	0.335991	0.167996	+	0.985788i	$0.446271\pi$
$752$	−20.1606	−0.735181
$753$	24.7198	0.900840
$754$	53.9685	1.96542
$755$	−5.79510	−0.210905
$756$	5.35840	0.194883
$757$	22.8360	0.829988	0.414994	−	0.909824i	$-0.363784\pi$
$757$	22.8360	0.829988	0.414994	+	0.909824i	$0.363784\pi$
$758$	−0.485482	−0.0176335
$759$	−25.7073	−0.933115
$760$	−6.36902	−0.231029
$761$	−5.41650	−0.196348	−0.0981740	−	0.995169i	$-0.531300\pi$
$761$	−5.41650	−0.196348	−0.0981740	+	0.995169i	$0.531300\pi$
$762$	19.4540	0.704744
$763$	7.34095	0.265760
$764$	68.8648	2.49144
$765$	−8.25935	−0.298617
$766$	67.1217	2.42521
$767$	15.5427	0.561214
$768$	7.44443	0.268628
$769$	18.7963	0.677812	0.338906	−	0.940820i	$-0.389943\pi$
$769$	18.7963	0.677812	0.338906	+	0.940820i	$0.389943\pi$
$770$	7.52388	0.271142
$771$	−36.3938	−1.31069
$772$	41.6129	1.49768
$773$	−47.4927	−1.70819	−0.854097	−	0.520114i	$-0.825889\pi$
$773$	−47.4927	−1.70819	−0.854097	+	0.520114i	$0.825889\pi$
$774$	−59.5039	−2.13882
$775$	0.581291	0.0208806
$776$	123.676	4.43972
$777$	−3.63240	−0.130311
$778$	9.31730	0.334041
$779$	−4.07277	−0.145922
$780$	54.0576	1.93557
$781$	−1.35032	−0.0483182
$782$	−33.2909	−1.19048
$783$	−4.73102	−0.169073
$784$	11.8237	0.422275
$785$	5.41567	0.193294
$786$	19.7335	0.703871
$787$	7.27762	0.259419	0.129709	−	0.991552i	$-0.458596\pi$
$787$	7.27762	0.259419	0.129709	+	0.991552i	$0.458596\pi$
$788$	−27.6805	−0.986077
$789$	49.6548	1.76776
$790$	6.82399	0.242787
$791$	−2.94082	−0.104564
$792$	59.6096	2.11813
$793$	12.9996	0.461630
$794$	36.5456	1.29696
$795$	5.19386	0.184207
$796$	−59.9881	−2.12622
$797$	6.38742	0.226254	0.113127	−	0.993581i	$-0.463913\pi$
$797$	6.38742	0.226254	0.113127	+	0.993581i	$0.463913\pi$
$798$	−4.83942	−0.171313
$799$	−5.51337	−0.195049
$800$	−14.9777	−0.529541
$801$	16.8514	0.595416
$802$	40.8075	1.44096
$803$	9.92312	0.350179
$804$	−156.124	−5.50605
$805$	3.86347	0.136170
$806$	6.96468	0.245321
$807$	−13.5485	−0.476929
$808$	−88.3038	−3.10652
$809$	18.6593	0.656027	0.328013	−	0.944673i	$-0.393621\pi$
$809$	18.6593	0.656027	0.328013	+	0.944673i	$0.393621\pi$
$810$	−27.0177	−0.949306
$811$	−10.6597	−0.374313	−0.187157	−	0.982330i	$-0.559927\pi$
$811$	−10.6597	−0.374313	−0.187157	+	0.982330i	$0.559927\pi$
$812$	−22.9797	−0.806430
$813$	−48.5280	−1.70195
$814$	11.5963	0.406450
$815$	2.68302	0.0939820
$816$	90.1026	3.15422
$817$	−6.73571	−0.235653
$818$	−81.8973	−2.86347
$819$	11.4843	0.401295
$820$	−26.9653	−0.941670
$821$	−22.4190	−0.782427	−0.391213	−	0.920300i	$-0.627945\pi$
$821$	−22.4190	−0.782427	−0.391213	+	0.920300i	$0.627945\pi$
$822$	17.9605	0.626446
$823$	−1.56657	−0.0546071	−0.0273035	−	0.999627i	$-0.508692\pi$
$823$	−1.56657	−0.0546071	−0.0273035	+	0.999627i	$0.508692\pi$
$824$	38.8035	1.35178
$825$	−6.65393	−0.231660
$826$	−9.21252	−0.320545
$827$	−11.7903	−0.409989	−0.204995	−	0.978763i	$-0.565718\pi$
$827$	−11.7903	−0.409989	−0.204995	+	0.978763i	$0.565718\pi$
$828$	50.3464	1.74966
$829$	−35.3247	−1.22688	−0.613439	−	0.789742i	$-0.710214\pi$
$829$	−35.3247	−1.22688	−0.613439	+	0.789742i	$0.710214\pi$
$830$	38.8330	1.34791
$831$	−19.1671	−0.664901
$832$	−73.1348	−2.53549
$833$	3.23346	0.112033
$834$	−36.4806	−1.26322
$835$	13.4843	0.466642
$836$	11.0987	0.383856
$837$	−0.610543	−0.0211034
$838$	−23.1894	−0.801064
$839$	−28.1421	−0.971574	−0.485787	−	0.874077i	$-0.661467\pi$
$839$	−28.1421	−0.971574	−0.485787	+	0.874077i	$0.661467\pi$
$840$	−19.4801	−0.672129
$841$	−8.71082	−0.300373
$842$	−17.4849	−0.602571
$843$	−42.0553	−1.44846
$844$	−10.8253	−0.372620
$845$	−7.21416	−0.248175
$846$	11.6067	0.399046
$847$	3.02880	0.104071
$848$	−26.0572	−0.894809
$849$	−45.8868	−1.57483
$850$	−8.61684	−0.295555
$851$	5.95463	0.204122
$852$	5.75046	0.197008
$853$	−45.1058	−1.54439	−0.772196	−	0.635384i	$-0.780842\pi$
$853$	−45.1058	−1.54439	−0.772196	+	0.635384i	$0.780842\pi$
$854$	−7.70518	−0.263666
$855$	1.96823	0.0673119
$856$	103.482	3.53695
$857$	−26.2004	−0.894988	−0.447494	−	0.894287i	$-0.647683\pi$
$857$	−26.2004	−0.894988	−0.447494	+	0.894287i	$0.647683\pi$
$858$	−79.7235	−2.72171
$859$	−3.37151	−0.115035	−0.0575173	−	0.998345i	$-0.518318\pi$
$859$	−3.37151	−0.115035	−0.0575173	+	0.998345i	$0.518318\pi$
$860$	−44.5963	−1.52072
$861$	−12.4569	−0.424529
$862$	−48.2140	−1.64218
$863$	34.5885	1.17741	0.588704	−	0.808349i	$-0.299638\pi$
$863$	34.5885	1.17741	0.588704	+	0.808349i	$0.299638\pi$
$864$	15.7314	0.535194
$865$	1.71813	0.0584180
$866$	−23.6382	−0.803260
$867$	−15.4244	−0.523840
$868$	−2.96555	−0.100657
$869$	−7.22969	−0.245251
$870$	28.2897	0.959111
$871$	58.3805	1.97815
$872$	60.6776	2.05480
$873$	−38.2198	−1.29355
$874$	7.93332	0.268348
$875$	1.00000	0.0338062
$876$	−42.2586	−1.42778
$877$	−39.6825	−1.33998	−0.669991	−	0.742369i	$-0.733702\pi$
$877$	−39.6825	−1.33998	−0.669991	+	0.742369i	$0.733702\pi$
$878$	22.6663	0.764950
$879$	−36.5496	−1.23279
$880$	33.3823	1.12532
$881$	−29.4725	−0.992952	−0.496476	−	0.868050i	$-0.665373\pi$
$881$	−29.4725	−0.992952	−0.496476	+	0.868050i	$0.665373\pi$
$882$	−6.80704	−0.229205
$883$	8.99101	0.302572	0.151286	−	0.988490i	$-0.451659\pi$
$883$	8.99101	0.302572	0.151286	+	0.988490i	$0.451659\pi$
$884$	−74.1665	−2.49449
$885$	8.14731	0.273869
$886$	4.79241	0.161004
$887$	46.1072	1.54813	0.774064	−	0.633108i	$-0.218221\pi$
$887$	46.1072	1.54813	0.774064	+	0.633108i	$0.218221\pi$
$888$	−30.0241	−1.00754
$889$	3.09751	0.103887
$890$	17.5808	0.589310
$891$	28.6240	0.958940
$892$	−117.484	−3.93365
$893$	1.31385	0.0439663
$894$	−60.5817	−2.02615
$895$	13.0883	0.437495
$896$	13.3934	0.447441
$897$	−40.9376	−1.36687
$898$	−48.6297	−1.62279
$899$	2.61834	0.0873264
$900$	13.0314	0.434380
$901$	−7.12594	−0.237399
$902$	39.7681	1.32413
$903$	−20.6017	−0.685581
$904$	−24.3077	−0.808464
$905$	−13.4763	−0.447969
$906$	−36.3963	−1.20919
$907$	−7.36434	−0.244529	−0.122264	−	0.992498i	$-0.539016\pi$
$907$	−7.36434	−0.244529	−0.122264	+	0.992498i	$0.539016\pi$
$908$	−39.2304	−1.30191
$909$	27.2886	0.905106
$910$	11.9814	0.397180
$911$	−55.5882	−1.84172	−0.920860	−	0.389892i	$-0.872512\pi$
$911$	−55.5882	−1.84172	−0.920860	+	0.389892i	$0.872512\pi$
$912$	−21.4717	−0.710999
$913$	−41.1417	−1.36159
$914$	11.3644	0.375901
$915$	6.81426	0.225273
$916$	−5.10167	−0.168564
$917$	3.14201	0.103758
$918$	9.05046	0.298710
$919$	22.2840	0.735082	0.367541	−	0.930007i	$-0.380200\pi$
$919$	22.2840	0.735082	0.367541	+	0.930007i	$0.380200\pi$
$920$	31.9341	1.05283
$921$	22.9204	0.755254
$922$	−47.0973	−1.55107
$923$	−2.15031	−0.0707785
$924$	33.9461	1.11675
$925$	1.54126	0.0506765
$926$	−52.6440	−1.72999
$927$	−11.9915	−0.393852
$928$	−67.4648	−2.21464
$929$	−28.9841	−0.950936	−0.475468	−	0.879733i	$-0.657721\pi$
$929$	−28.9841	−0.950936	−0.475468	+	0.879733i	$0.657721\pi$
$930$	3.65081	0.119715
$931$	−0.770542	−0.0252535
$932$	−79.6993	−2.61064
$933$	8.06289	0.263967
$934$	56.9314	1.86285
$935$	9.12913	0.298555
$936$	94.9253	3.10273
$937$	−54.5871	−1.78328	−0.891641	−	0.452743i	$-0.850445\pi$
$937$	−54.5871	−1.78328	−0.891641	+	0.452743i	$0.850445\pi$
$938$	−34.6035	−1.12984
$939$	−66.0092	−2.15413
$940$	8.69885	0.283725
$941$	49.7075	1.62042	0.810210	−	0.586140i	$-0.199353\pi$
$941$	49.7075	1.62042	0.810210	+	0.586140i	$0.199353\pi$
$942$	34.0133	1.10821
$943$	20.4207	0.664990
$944$	−40.8745	−1.33035
$945$	−1.05032	−0.0341670
$946$	65.7702	2.13837
$947$	−6.59679	−0.214367	−0.107183	−	0.994239i	$-0.534183\pi$
$947$	−6.59679	−0.214367	−0.107183	+	0.994239i	$0.534183\pi$
$948$	30.7884	0.999959
$949$	15.8021	0.512957
$950$	2.05342	0.0666216
$951$	−47.2800	−1.53316
$952$	26.7266	0.866214
$953$	−35.0771	−1.13626	−0.568129	−	0.822940i	$-0.692332\pi$
$953$	−35.0771	−1.13626	−0.568129	+	0.822940i	$0.692332\pi$
$954$	15.0014	0.485689
$955$	−13.4985	−0.436801
$956$	−16.5585	−0.535539
$957$	−29.9716	−0.968845
$958$	−81.2429	−2.62484
$959$	2.85972	0.0923451
$960$	−38.3365	−1.23731
$961$	−30.6621	−0.989100
$962$	18.4665	0.595385
$963$	−31.9792	−1.03052
$964$	−78.3720	−2.52419
$965$	−8.15672	−0.262574
$966$	24.2647	0.780703
$967$	32.7754	1.05398	0.526992	−	0.849870i	$-0.323320\pi$
$967$	32.7754	1.05398	0.526992	+	0.849870i	$0.323320\pi$
$968$	25.0350	0.804654
$969$	−5.87192	−0.188633
$970$	−39.8741	−1.28028
$971$	15.5370	0.498607	0.249303	−	0.968425i	$-0.419798\pi$
$971$	15.5370	0.498607	0.249303	+	0.968425i	$0.419798\pi$
$972$	−105.823	−3.39427
$973$	−5.80852	−0.186213
$974$	10.3737	0.332395
$975$	−10.5960	−0.339345
$976$	−34.1866	−1.09429
$977$	−32.4703	−1.03882	−0.519408	−	0.854526i	$-0.673847\pi$
$977$	−32.4703	−1.03882	−0.519408	+	0.854526i	$0.673847\pi$
$978$	16.8508	0.538828
$979$	−18.6260	−0.595290
$980$	−5.10167	−0.162967
$981$	−18.7513	−0.598681
$982$	−89.2456	−2.84794
$983$	−49.2992	−1.57240	−0.786201	−	0.617971i	$-0.787955\pi$
$983$	−49.2992	−1.57240	−0.786201	+	0.617971i	$0.787955\pi$
$984$	−102.964	−3.28237
$985$	5.42577	0.172879
$986$	−38.8133	−1.23607
$987$	4.01851	0.127911
$988$	17.6741	0.562288
$989$	33.7726	1.07391
$990$	−19.2185	−0.610805
$991$	−16.9985	−0.539975	−0.269988	−	0.962864i	$-0.587020\pi$
$991$	−16.9985	−0.539975	−0.269988	+	0.962864i	$0.587020\pi$
$992$	−8.70639	−0.276428
$993$	−36.6031	−1.16156
$994$	1.27454	0.0404260
$995$	11.7585	0.372770
$996$	175.206	5.55161
$997$	50.5389	1.60058	0.800291	−	0.599612i	$-0.204678\pi$
$997$	50.5389	1.60058	0.800291	+	0.599612i	$0.204678\pi$
$998$	−6.61345	−0.209345
$999$	−1.61882	−0.0512174

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.k.1.2	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.k.1.2	✓	49	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66490 q^{2} +2.35676 q^{3} +5.10167 q^{4} -1.00000 q^{5} -6.28053 q^{6} -1.00000 q^{7} -8.26563 q^{8} +2.55434 q^{9} +O(q^{10})\)	\(q-2.66490 q^{2} +2.35676 q^{3} +5.10167 q^{4} -1.00000 q^{5} -6.28053 q^{6} -1.00000 q^{7} -8.26563 q^{8} +2.55434 q^{9} +2.66490 q^{10} -2.82333 q^{11} +12.0234 q^{12} -4.49602 q^{13} +2.66490 q^{14} -2.35676 q^{15} +11.8237 q^{16} +3.23346 q^{17} -6.80704 q^{18} -0.770542 q^{19} -5.10167 q^{20} -2.35676 q^{21} +7.52388 q^{22} +3.86347 q^{23} -19.4801 q^{24} +1.00000 q^{25} +11.9814 q^{26} -1.05032 q^{27} -5.10167 q^{28} +4.50435 q^{29} +6.28053 q^{30} +0.581291 q^{31} -14.9777 q^{32} -6.65393 q^{33} -8.61684 q^{34} +1.00000 q^{35} +13.0314 q^{36} +1.54126 q^{37} +2.05342 q^{38} -10.5960 q^{39} +8.26563 q^{40} +5.28558 q^{41} +6.28053 q^{42} +8.74152 q^{43} -14.4037 q^{44} -2.55434 q^{45} -10.2958 q^{46} -1.70510 q^{47} +27.8657 q^{48} +1.00000 q^{49} -2.66490 q^{50} +7.62050 q^{51} -22.9372 q^{52} -2.20381 q^{53} +2.79900 q^{54} +2.82333 q^{55} +8.26563 q^{56} -1.81599 q^{57} -12.0036 q^{58} -3.45699 q^{59} -12.0234 q^{60} -2.89136 q^{61} -1.54908 q^{62} -2.55434 q^{63} +16.2666 q^{64} +4.49602 q^{65} +17.7320 q^{66} -12.9849 q^{67} +16.4961 q^{68} +9.10530 q^{69} -2.66490 q^{70} +0.478271 q^{71} -21.1132 q^{72} -3.51468 q^{73} -4.10731 q^{74} +2.35676 q^{75} -3.93105 q^{76} +2.82333 q^{77} +28.2374 q^{78} +2.56070 q^{79} -11.8237 q^{80} -10.1384 q^{81} -14.0855 q^{82} +14.5720 q^{83} -12.0234 q^{84} -3.23346 q^{85} -23.2952 q^{86} +10.6157 q^{87} +23.3366 q^{88} +6.59718 q^{89} +6.80704 q^{90} +4.49602 q^{91} +19.7102 q^{92} +1.36996 q^{93} +4.54391 q^{94} +0.770542 q^{95} -35.2989 q^{96} -14.9627 q^{97} -2.66490 q^{98} -7.21174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * q^99

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