LMFDB - Embedded newform 6001.2.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53489 q^{2} +1.89170 q^{3} +4.42568 q^{4} -3.70427 q^{5} -4.79525 q^{6} +1.26299 q^{7} -6.14885 q^{8} +0.578524 q^{9} +O(q^{10})$	\(q-2.53489 q^{2} +1.89170 q^{3} +4.42568 q^{4} -3.70427 q^{5} -4.79525 q^{6} +1.26299 q^{7} -6.14885 q^{8} +0.578524 q^{9} +9.38992 q^{10} +2.05827 q^{11} +8.37206 q^{12} -4.01998 q^{13} -3.20155 q^{14} -7.00736 q^{15} +6.73530 q^{16} +1.00000 q^{17} -1.46650 q^{18} -7.14159 q^{19} -16.3939 q^{20} +2.38920 q^{21} -5.21750 q^{22} +5.87831 q^{23} -11.6318 q^{24} +8.72160 q^{25} +10.1902 q^{26} -4.58070 q^{27} +5.58960 q^{28} -7.52141 q^{29} +17.7629 q^{30} -9.88256 q^{31} -4.77558 q^{32} +3.89363 q^{33} -2.53489 q^{34} -4.67846 q^{35} +2.56036 q^{36} +5.71734 q^{37} +18.1032 q^{38} -7.60459 q^{39} +22.7770 q^{40} +2.81357 q^{41} -6.05637 q^{42} -11.9844 q^{43} +9.10926 q^{44} -2.14301 q^{45} -14.9009 q^{46} +12.0896 q^{47} +12.7412 q^{48} -5.40485 q^{49} -22.1083 q^{50} +1.89170 q^{51} -17.7912 q^{52} -5.95956 q^{53} +11.6116 q^{54} -7.62439 q^{55} -7.76594 q^{56} -13.5097 q^{57} +19.0660 q^{58} +4.96138 q^{59} -31.0123 q^{60} -1.33305 q^{61} +25.0512 q^{62} +0.730671 q^{63} -1.36503 q^{64} +14.8911 q^{65} -9.86994 q^{66} +9.10999 q^{67} +4.42568 q^{68} +11.1200 q^{69} +11.8594 q^{70} +11.8612 q^{71} -3.55726 q^{72} +12.7868 q^{73} -14.4928 q^{74} +16.4986 q^{75} -31.6064 q^{76} +2.59958 q^{77} +19.2768 q^{78} +3.67665 q^{79} -24.9494 q^{80} -10.4009 q^{81} -7.13211 q^{82} -11.3091 q^{83} +10.5738 q^{84} -3.70427 q^{85} +30.3792 q^{86} -14.2282 q^{87} -12.6560 q^{88} +2.88543 q^{89} +5.43230 q^{90} -5.07720 q^{91} +26.0156 q^{92} -18.6948 q^{93} -30.6460 q^{94} +26.4543 q^{95} -9.03395 q^{96} -10.6742 q^{97} +13.7007 q^{98} +1.19076 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * 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 $

$2$	−2.53489	−1.79244	−0.896220	−	0.443610i	$-0.853698\pi$
$2$	−2.53489	−1.79244	−0.896220	+	0.443610i	$0.853698\pi$
$3$	1.89170	1.09217	0.546086	−	0.837729i	$-0.316117\pi$
$3$	1.89170	1.09217	0.546086	+	0.837729i	$0.316117\pi$
$4$	4.42568	2.21284
$5$	−3.70427	−1.65660	−0.828300	−	0.560286i	$-0.810691\pi$
$5$	−3.70427	−1.65660	−0.828300	+	0.560286i	$0.810691\pi$
$6$	−4.79525	−1.95765
$7$	1.26299	0.477366	0.238683	−	0.971098i	$-0.423284\pi$
$7$	1.26299	0.477366	0.238683	+	0.971098i	$0.423284\pi$
$8$	−6.14885	−2.17395
$9$	0.578524	0.192841
$10$	9.38992	2.96935
$11$	2.05827	0.620592	0.310296	−	0.950640i	$-0.399572\pi$
$11$	2.05827	0.620592	0.310296	+	0.950640i	$0.399572\pi$
$12$	8.37206	2.41681
$13$	−4.01998	−1.11494	−0.557471	−	0.830196i	$-0.688228\pi$
$13$	−4.01998	−1.11494	−0.557471	+	0.830196i	$0.688228\pi$
$14$	−3.20155	−0.855650
$15$	−7.00736	−1.80929
$16$	6.73530	1.68383
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.46650	−0.345657
$19$	−7.14159	−1.63839	−0.819196	−	0.573514i	$-0.805580\pi$
$19$	−7.14159	−1.63839	−0.819196	+	0.573514i	$0.805580\pi$
$20$	−16.3939	−3.66579
$21$	2.38920	0.521366
$22$	−5.21750	−1.11237
$23$	5.87831	1.22571	0.612857	−	0.790194i	$-0.290020\pi$
$23$	5.87831	1.22571	0.612857	+	0.790194i	$0.290020\pi$
$24$	−11.6318	−2.37432
$25$	8.72160	1.74432
$26$	10.1902	1.99847
$27$	−4.58070	−0.881557
$28$	5.58960	1.05634
$29$	−7.52141	−1.39669	−0.698345	−	0.715761i	$-0.746080\pi$
$29$	−7.52141	−1.39669	−0.698345	+	0.715761i	$0.746080\pi$
$30$	17.7629	3.24305
$31$	−9.88256	−1.77496	−0.887480	−	0.460845i	$-0.847546\pi$
$31$	−9.88256	−1.77496	−0.887480	+	0.460845i	$0.847546\pi$
$32$	−4.77558	−0.844211
$33$	3.89363	0.677794
$34$	−2.53489	−0.434731
$35$	−4.67846	−0.790804
$36$	2.56036	0.426727
$37$	5.71734	0.939925	0.469962	−	0.882686i	$-0.344267\pi$
$37$	5.71734	0.939925	0.469962	+	0.882686i	$0.344267\pi$
$38$	18.1032	2.93672
$39$	−7.60459	−1.21771
$40$	22.7770	3.60136
$41$	2.81357	0.439406	0.219703	−	0.975567i	$-0.429491\pi$
$41$	2.81357	0.439406	0.219703	+	0.975567i	$0.429491\pi$
$42$	−6.05637	−0.934518
$43$	−11.9844	−1.82760	−0.913801	−	0.406161i	$-0.866867\pi$
$43$	−11.9844	−1.82760	−0.913801	+	0.406161i	$0.866867\pi$
$44$	9.10926	1.37327
$45$	−2.14301	−0.319461
$46$	−14.9009	−2.19702
$47$	12.0896	1.76346	0.881728	−	0.471758i	$-0.156380\pi$
$47$	12.0896	1.76346	0.881728	+	0.471758i	$0.156380\pi$
$48$	12.7412	1.83903
$49$	−5.40485	−0.772122
$50$	−22.1083	−3.12659
$51$	1.89170	0.264891
$52$	−17.7912	−2.46719
$53$	−5.95956	−0.818609	−0.409304	−	0.912398i	$-0.634229\pi$
$53$	−5.95956	−0.818609	−0.409304	+	0.912398i	$0.634229\pi$
$54$	11.6116	1.58014
$55$	−7.62439	−1.02807
$56$	−7.76594	−1.03777
$57$	−13.5097	−1.78941
$58$	19.0660	2.50348
$59$	4.96138	0.645916	0.322958	−	0.946413i	$-0.395323\pi$
$59$	4.96138	0.645916	0.322958	+	0.946413i	$0.395323\pi$
$60$	−31.0123	−4.00368
$61$	−1.33305	−0.170680	−0.0853398	−	0.996352i	$-0.527198\pi$
$61$	−1.33305	−0.170680	−0.0853398	+	0.996352i	$0.527198\pi$
$62$	25.0512	3.18151
$63$	0.730671	0.0920559
$64$	−1.36503	−0.170628
$65$	14.8911	1.84701
$66$	−9.86994	−1.21491
$67$	9.10999	1.11296	0.556481	−	0.830860i	$-0.312151\pi$
$67$	9.10999	1.11296	0.556481	+	0.830860i	$0.312151\pi$
$68$	4.42568	0.536693
$69$	11.1200	1.33869
$70$	11.8594	1.41747
$71$	11.8612	1.40767	0.703835	−	0.710363i	$-0.251469\pi$
$71$	11.8612	1.40767	0.703835	+	0.710363i	$0.251469\pi$
$72$	−3.55726	−0.419227
$73$	12.7868	1.49659	0.748293	−	0.663369i	$-0.230874\pi$
$73$	12.7868	1.49659	0.748293	+	0.663369i	$0.230874\pi$
$74$	−14.4928	−1.68476
$75$	16.4986	1.90510
$76$	−31.6064	−3.62550
$77$	2.59958	0.296250
$78$	19.2768	2.18267
$79$	3.67665	0.413655	0.206828	−	0.978377i	$-0.433686\pi$
$79$	3.67665	0.413655	0.206828	+	0.978377i	$0.433686\pi$
$80$	−24.9494	−2.78942
$81$	−10.4009	−1.15565
$82$	−7.13211	−0.787609
$83$	−11.3091	−1.24133	−0.620667	−	0.784074i	$-0.713138\pi$
$83$	−11.3091	−1.24133	−0.620667	+	0.784074i	$0.713138\pi$
$84$	10.5738	1.15370
$85$	−3.70427	−0.401784
$86$	30.3792	3.27587
$87$	−14.2282	−1.52543
$88$	−12.6560	−1.34913
$89$	2.88543	0.305855	0.152928	−	0.988237i	$-0.451130\pi$
$89$	2.88543	0.305855	0.152928	+	0.988237i	$0.451130\pi$
$90$	5.43230	0.572614
$91$	−5.07720	−0.532235
$92$	26.0156	2.71231
$93$	−18.6948	−1.93856
$94$	−30.6460	−3.16089
$95$	26.4543	2.71416
$96$	−9.03395	−0.922024
$97$	−10.6742	−1.08380	−0.541899	−	0.840444i	$-0.682294\pi$
$97$	−10.6742	−1.08380	−0.541899	+	0.840444i	$0.682294\pi$
$98$	13.7007	1.38398
$99$	1.19076	0.119676
$100$	38.5990	3.85990
$101$	12.6502	1.25874	0.629369	−	0.777107i	$-0.283314\pi$
$101$	12.6502	1.25874	0.629369	+	0.777107i	$0.283314\pi$
$102$	−4.79525	−0.474801
$103$	10.0135	0.986664	0.493332	−	0.869841i	$-0.335779\pi$
$103$	10.0135	0.986664	0.493332	+	0.869841i	$0.335779\pi$
$104$	24.7182	2.42382
$105$	−8.85024	−0.863695
$106$	15.1069	1.46731
$107$	8.88696	0.859135	0.429568	−	0.903035i	$-0.358666\pi$
$107$	8.88696	0.859135	0.429568	+	0.903035i	$0.358666\pi$
$108$	−20.2727	−1.95074
$109$	−8.67676	−0.831083	−0.415541	−	0.909574i	$-0.636408\pi$
$109$	−8.67676	−0.831083	−0.415541	+	0.909574i	$0.636408\pi$
$110$	19.3270	1.84276
$111$	10.8155	1.02656
$112$	8.50663	0.803801
$113$	1.02680	0.0965934	0.0482967	−	0.998833i	$-0.484621\pi$
$113$	1.02680	0.0965934	0.0482967	+	0.998833i	$0.484621\pi$
$114$	34.2457	3.20741
$115$	−21.7748	−2.03052
$116$	−33.2874	−3.09066
$117$	−2.32566	−0.215007
$118$	−12.5766	−1.15777
$119$	1.26299	0.115778
$120$	43.0872	3.93330
$121$	−6.76352	−0.614865
$122$	3.37914	0.305933
$123$	5.32243	0.479908
$124$	−43.7371	−3.92771
$125$	−13.7858	−1.23304
$126$	−1.85217	−0.165005
$127$	−7.10141	−0.630148	−0.315074	−	0.949067i	$-0.602029\pi$
$127$	−7.10141	−0.630148	−0.315074	+	0.949067i	$0.602029\pi$
$128$	13.0114	1.15005
$129$	−22.6709	−1.99606
$130$	−37.7473	−3.31066
$131$	−1.90149	−0.166134	−0.0830669	−	0.996544i	$-0.526472\pi$
$131$	−1.90149	−0.166134	−0.0830669	+	0.996544i	$0.526472\pi$
$132$	17.2320	1.49985
$133$	−9.01976	−0.782113
$134$	−23.0929	−1.99492
$135$	16.9682	1.46039
$136$	−6.14885	−0.527259
$137$	0.346599	0.0296120	0.0148060	−	0.999890i	$-0.495287\pi$
$137$	0.346599	0.0296120	0.0148060	+	0.999890i	$0.495287\pi$
$138$	−28.1880	−2.39952
$139$	−10.8123	−0.917083	−0.458542	−	0.888673i	$-0.651628\pi$
$139$	−10.8123	−0.917083	−0.458542	+	0.888673i	$0.651628\pi$
$140$	−20.7054	−1.74992
$141$	22.8700	1.92600
$142$	−30.0670	−2.52316
$143$	−8.27421	−0.691924
$144$	3.89653	0.324711
$145$	27.8613	2.31376
$146$	−32.4132	−2.68254
$147$	−10.2244	−0.843290
$148$	25.3031	2.07990
$149$	−20.9508	−1.71636	−0.858178	−	0.513353i	$-0.828403\pi$
$149$	−20.9508	−1.71636	−0.858178	+	0.513353i	$0.828403\pi$
$150$	−41.8223	−3.41478
$151$	8.98956	0.731560	0.365780	−	0.930701i	$-0.380802\pi$
$151$	8.98956	0.731560	0.365780	+	0.930701i	$0.380802\pi$
$152$	43.9125	3.56177
$153$	0.578524	0.0467709
$154$	−6.58966	−0.531010
$155$	36.6077	2.94040
$156$	−33.6555	−2.69460
$157$	14.2418	1.13662	0.568308	−	0.822816i	$-0.307598\pi$
$157$	14.2418	1.13662	0.568308	+	0.822816i	$0.307598\pi$
$158$	−9.31991	−0.741452
$159$	−11.2737	−0.894062
$160$	17.6900	1.39852
$161$	7.42426	0.585114
$162$	26.3651	2.07144
$163$	7.43863	0.582639	0.291319	−	0.956626i	$-0.405906\pi$
$163$	7.43863	0.582639	0.291319	+	0.956626i	$0.405906\pi$
$164$	12.4520	0.972336
$165$	−14.4230	−1.12283
$166$	28.6674	2.22502
$167$	−5.88825	−0.455646	−0.227823	−	0.973703i	$-0.573161\pi$
$167$	−5.88825	−0.455646	−0.227823	+	0.973703i	$0.573161\pi$
$168$	−14.6908	−1.13342
$169$	3.16025	0.243096
$170$	9.38992	0.720174
$171$	−4.13158	−0.315950
$172$	−53.0391	−4.04419
$173$	7.33461	0.557640	0.278820	−	0.960343i	$-0.410057\pi$
$173$	7.33461	0.557640	0.278820	+	0.960343i	$0.410057\pi$
$174$	36.0671	2.73424
$175$	11.0153	0.832679
$176$	13.8631	1.04497
$177$	9.38543	0.705452
$178$	−7.31426	−0.548227
$179$	16.6045	1.24108	0.620539	−	0.784175i	$-0.286914\pi$
$179$	16.6045	1.24108	0.620539	+	0.784175i	$0.286914\pi$
$180$	−9.48428	−0.706916
$181$	−17.8160	−1.32425	−0.662126	−	0.749392i	$-0.730346\pi$
$181$	−17.8160	−1.32425	−0.662126	+	0.749392i	$0.730346\pi$
$182$	12.8702	0.954000
$183$	−2.52173	−0.186412
$184$	−36.1448	−2.66463
$185$	−21.1786	−1.55708
$186$	47.3894	3.47476
$187$	2.05827	0.150516
$188$	53.5049	3.90225
$189$	−5.78539	−0.420825
$190$	−67.0589	−4.86497
$191$	−13.1314	−0.950154	−0.475077	−	0.879944i	$-0.657580\pi$
$191$	−13.1314	−0.950154	−0.475077	+	0.879944i	$0.657580\pi$
$192$	−2.58222	−0.186356
$193$	12.6791	0.912664	0.456332	−	0.889810i	$-0.349163\pi$
$193$	12.6791	0.912664	0.456332	+	0.889810i	$0.349163\pi$
$194$	27.0579	1.94264
$195$	28.1694	2.01726
$196$	−23.9202	−1.70858
$197$	−3.74763	−0.267007	−0.133504	−	0.991048i	$-0.542623\pi$
$197$	−3.74763	−0.267007	−0.133504	+	0.991048i	$0.542623\pi$
$198$	−3.01845	−0.214512
$199$	16.0413	1.13714	0.568568	−	0.822636i	$-0.307498\pi$
$199$	16.0413	1.13714	0.568568	+	0.822636i	$0.307498\pi$
$200$	−53.6278	−3.79206
$201$	17.2334	1.21555
$202$	−32.0668	−2.25621
$203$	−9.49948	−0.666733
$204$	8.37206	0.586161
$205$	−10.4222	−0.727920
$206$	−25.3833	−1.76854
$207$	3.40075	0.236368
$208$	−27.0758	−1.87737
$209$	−14.6993	−1.01677
$210$	22.4344	1.54812
$211$	9.74457	0.670844	0.335422	−	0.942068i	$-0.391121\pi$
$211$	9.74457	0.670844	0.335422	+	0.942068i	$0.391121\pi$
$212$	−26.3751	−1.81145
$213$	22.4379	1.53742
$214$	−22.5275	−1.53995
$215$	44.3934	3.02760
$216$	28.1660	1.91646
$217$	−12.4816	−0.847306
$218$	21.9947	1.48967
$219$	24.1888	1.63453
$220$	−33.7431	−2.27496
$221$	−4.01998	−0.270413
$222$	−27.4161	−1.84005
$223$	25.5681	1.71217	0.856084	−	0.516837i	$-0.172891\pi$
$223$	25.5681	1.71217	0.856084	+	0.516837i	$0.172891\pi$
$224$	−6.03151	−0.402997
$225$	5.04566	0.336377
$226$	−2.60283	−0.173138
$227$	−11.3696	−0.754628	−0.377314	−	0.926085i	$-0.623152\pi$
$227$	−11.3696	−0.754628	−0.377314	+	0.926085i	$0.623152\pi$
$228$	−59.7898	−3.95967
$229$	22.9864	1.51899	0.759493	−	0.650515i	$-0.225447\pi$
$229$	22.9864	1.51899	0.759493	+	0.650515i	$0.225447\pi$
$230$	55.1969	3.63958
$231$	4.91762	0.323556
$232$	46.2480	3.03633
$233$	−17.8690	−1.17064	−0.585319	−	0.810803i	$-0.699031\pi$
$233$	−17.8690	−1.17064	−0.585319	+	0.810803i	$0.699031\pi$
$234$	5.89529	0.385387
$235$	−44.7833	−2.92134
$236$	21.9575	1.42931
$237$	6.95511	0.451783
$238$	−3.20155	−0.207526
$239$	11.8831	0.768655	0.384328	−	0.923197i	$-0.374433\pi$
$239$	11.8831	0.768655	0.384328	+	0.923197i	$0.374433\pi$
$240$	−47.1967	−3.04653
$241$	10.9992	0.708519	0.354260	−	0.935147i	$-0.384733\pi$
$241$	10.9992	0.708519	0.354260	+	0.935147i	$0.384733\pi$
$242$	17.1448	1.10211
$243$	−5.93323	−0.380617
$244$	−5.89965	−0.377687
$245$	20.0210	1.27910
$246$	−13.4918	−0.860205
$247$	28.7090	1.82671
$248$	60.7664	3.85867
$249$	−21.3934	−1.35575
$250$	34.9456	2.21015
$251$	10.5157	0.663746	0.331873	−	0.943324i	$-0.392320\pi$
$251$	10.5157	0.663746	0.331873	+	0.943324i	$0.392320\pi$
$252$	3.23372	0.203705
$253$	12.0992	0.760668
$254$	18.0013	1.12950
$255$	−7.00736	−0.438818
$256$	−30.2523	−1.89077
$257$	10.7008	0.667498	0.333749	−	0.942662i	$-0.391686\pi$
$257$	10.7008	0.667498	0.333749	+	0.942662i	$0.391686\pi$
$258$	57.4682	3.57781
$259$	7.22095	0.448688
$260$	65.9032	4.08714
$261$	−4.35132	−0.269340
$262$	4.82007	0.297785
$263$	−15.5644	−0.959740	−0.479870	−	0.877340i	$-0.659316\pi$
$263$	−15.5644	−0.959740	−0.479870	+	0.877340i	$0.659316\pi$
$264$	−23.9413	−1.47349
$265$	22.0758	1.35611
$266$	22.8641	1.40189
$267$	5.45837	0.334047
$268$	40.3179	2.46281
$269$	11.2145	0.683762	0.341881	−	0.939743i	$-0.388936\pi$
$269$	11.2145	0.683762	0.341881	+	0.939743i	$0.388936\pi$
$270$	−43.0124	−2.61765
$271$	7.13795	0.433600	0.216800	−	0.976216i	$-0.430438\pi$
$271$	7.13795	0.433600	0.216800	+	0.976216i	$0.430438\pi$
$272$	6.73530	0.408388
$273$	−9.60454	−0.581293
$274$	−0.878592	−0.0530777
$275$	17.9514	1.08251
$276$	49.2136	2.96231
$277$	−18.9183	−1.13669	−0.568345	−	0.822791i	$-0.692416\pi$
$277$	−18.9183	−1.13669	−0.568345	+	0.822791i	$0.692416\pi$
$278$	27.4079	1.64382
$279$	−5.71730	−0.342286
$280$	28.7671	1.71916
$281$	30.2096	1.80216	0.901078	−	0.433658i	$-0.142777\pi$
$281$	30.2096	1.80216	0.901078	+	0.433658i	$0.142777\pi$
$282$	−57.9729	−3.45224
$283$	15.3575	0.912907	0.456454	−	0.889747i	$-0.349119\pi$
$283$	15.3575	0.912907	0.456454	+	0.889747i	$0.349119\pi$
$284$	52.4941	3.11495
$285$	50.0437	2.96433
$286$	20.9742	1.24023
$287$	3.55352	0.209758
$288$	−2.76279	−0.162799
$289$	1.00000	0.0588235
$290$	−70.6255	−4.14727
$291$	−20.1923	−1.18369
$292$	56.5905	3.31171
$293$	−5.51362	−0.322109	−0.161054	−	0.986946i	$-0.551489\pi$
$293$	−5.51362	−0.322109	−0.161054	+	0.986946i	$0.551489\pi$
$294$	25.9176	1.51155
$295$	−18.3783	−1.07002
$296$	−35.1550	−2.04334
$297$	−9.42833	−0.547087
$298$	53.1080	3.07646
$299$	−23.6307	−1.36660
$300$	73.0178	4.21568
$301$	−15.1362	−0.872435
$302$	−22.7876	−1.31128
$303$	23.9303	1.37476
$304$	−48.1007	−2.75877
$305$	4.93797	0.282748
$306$	−1.46650	−0.0838341
$307$	−26.8568	−1.53280	−0.766398	−	0.642366i	$-0.777953\pi$
$307$	−26.8568	−1.53280	−0.766398	+	0.642366i	$0.777953\pi$
$308$	11.5049	0.655553
$309$	18.9426	1.07761
$310$	−92.7965	−5.27049
$311$	16.8862	0.957530	0.478765	−	0.877943i	$-0.341085\pi$
$311$	16.8862	0.957530	0.478765	+	0.877943i	$0.341085\pi$
$312$	46.7595	2.64723
$313$	13.0636	0.738400	0.369200	−	0.929350i	$-0.379632\pi$
$313$	13.0636	0.738400	0.369200	+	0.929350i	$0.379632\pi$
$314$	−36.1013	−2.03732
$315$	−2.70660	−0.152500
$316$	16.2717	0.915354
$317$	−11.0945	−0.623131	−0.311565	−	0.950225i	$-0.600853\pi$
$317$	−11.0945	−0.623131	−0.311565	+	0.950225i	$0.600853\pi$
$318$	28.5776	1.60255
$319$	−15.4811	−0.866776
$320$	5.05643	0.282663
$321$	16.8115	0.938324
$322$	−18.8197	−1.04878
$323$	−7.14159	−0.397368
$324$	−46.0310	−2.55728
$325$	−35.0607	−1.94482
$326$	−18.8561	−1.04434
$327$	−16.4138	−0.907686
$328$	−17.3002	−0.955245
$329$	15.2691	0.841814
$330$	36.5609	2.01261
$331$	−7.61598	−0.418612	−0.209306	−	0.977850i	$-0.567120\pi$
$331$	−7.61598	−0.418612	−0.209306	+	0.977850i	$0.567120\pi$
$332$	−50.0505	−2.74688
$333$	3.30762	0.181256
$334$	14.9261	0.816718
$335$	−33.7459	−1.84373
$336$	16.0920	0.877889
$337$	−22.5953	−1.23084	−0.615422	−	0.788198i	$-0.711014\pi$
$337$	−22.5953	−1.23084	−0.615422	+	0.788198i	$0.711014\pi$
$338$	−8.01088	−0.435735
$339$	1.94240	0.105497
$340$	−16.3939	−0.889085
$341$	−20.3410	−1.10153
$342$	10.4731	0.566321
$343$	−15.6672	−0.845951
$344$	73.6902	3.97311
$345$	−41.1915	−2.21767
$346$	−18.5924	−0.999536
$347$	29.7595	1.59758	0.798788	−	0.601612i	$-0.205475\pi$
$347$	29.7595	1.59758	0.798788	+	0.601612i	$0.205475\pi$
$348$	−62.9697	−3.37553
$349$	33.1584	1.77493	0.887464	−	0.460877i	$-0.152465\pi$
$349$	33.1584	1.77493	0.887464	+	0.460877i	$0.152465\pi$
$350$	−27.9226	−1.49253
$351$	18.4143	0.982885
$352$	−9.82943	−0.523911
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	−23.7911	−1.26448
$355$	−43.9372	−2.33195
$356$	12.7700	0.676809
$357$	2.38920	0.126450
$358$	−42.0906	−2.22456
$359$	−16.5427	−0.873090	−0.436545	−	0.899682i	$-0.643798\pi$
$359$	−16.5427	−0.873090	−0.436545	+	0.899682i	$0.643798\pi$
$360$	13.1770	0.694490
$361$	32.0022	1.68433
$362$	45.1617	2.37364
$363$	−12.7945	−0.671539
$364$	−22.4701	−1.17775
$365$	−47.3658	−2.47924
$366$	6.39231	0.334131
$367$	7.99489	0.417330	0.208665	−	0.977987i	$-0.433088\pi$
$367$	7.99489	0.417330	0.208665	+	0.977987i	$0.433088\pi$
$368$	39.5922	2.06389
$369$	1.62772	0.0847357
$370$	53.6854	2.79097
$371$	−7.52688	−0.390776
$372$	−82.7374	−4.28973
$373$	12.6648	0.655759	0.327880	−	0.944720i	$-0.393666\pi$
$373$	12.6648	0.655759	0.327880	+	0.944720i	$0.393666\pi$
$374$	−5.21750	−0.269790
$375$	−26.0786	−1.34669
$376$	−74.3374	−3.83366
$377$	30.2359	1.55723
$378$	14.6653	0.754304
$379$	−19.2240	−0.987471	−0.493735	−	0.869612i	$-0.664369\pi$
$379$	−19.2240	−0.987471	−0.493735	+	0.869612i	$0.664369\pi$
$380$	117.079	6.00600
$381$	−13.4337	−0.688230
$382$	33.2867	1.70309
$383$	−13.0961	−0.669179	−0.334590	−	0.942364i	$-0.608598\pi$
$383$	−13.0961	−0.669179	−0.334590	+	0.942364i	$0.608598\pi$
$384$	24.6136	1.25606
$385$	−9.62954	−0.490767
$386$	−32.1403	−1.63590
$387$	−6.93326	−0.352437
$388$	−47.2405	−2.39827
$389$	−30.7458	−1.55887	−0.779436	−	0.626481i	$-0.784494\pi$
$389$	−30.7458	−1.55887	−0.779436	+	0.626481i	$0.784494\pi$
$390$	−71.4065	−3.61581
$391$	5.87831	0.297279
$392$	33.2336	1.67855
$393$	−3.59704	−0.181447
$394$	9.49984	0.478595
$395$	−13.6193	−0.685261
$396$	5.26993	0.264824
$397$	4.66852	0.234306	0.117153	−	0.993114i	$-0.462623\pi$
$397$	4.66852	0.234306	0.117153	+	0.993114i	$0.462623\pi$
$398$	−40.6629	−2.03825
$399$	−17.0627	−0.854202
$400$	58.7426	2.93713
$401$	−9.86032	−0.492401	−0.246200	−	0.969219i	$-0.579182\pi$
$401$	−9.86032	−0.492401	−0.246200	+	0.969219i	$0.579182\pi$
$402$	−43.6847	−2.17880
$403$	39.7277	1.97898
$404$	55.9856	2.78539
$405$	38.5277	1.91445
$406$	24.0802	1.19508
$407$	11.7678	0.583310
$408$	−11.6318	−0.575858
$409$	37.4412	1.85135	0.925674	−	0.378321i	$-0.123498\pi$
$409$	37.4412	1.85135	0.925674	+	0.378321i	$0.123498\pi$
$410$	26.4192	1.30475
$411$	0.655662	0.0323414
$412$	44.3168	2.18333
$413$	6.26618	0.308338
$414$	−8.62053	−0.423676
$415$	41.8919	2.05639
$416$	19.1977	0.941246
$417$	−20.4535	−1.00161
$418$	37.2612	1.82251
$419$	8.28899	0.404944	0.202472	−	0.979288i	$-0.435103\pi$
$419$	8.28899	0.404944	0.202472	+	0.979288i	$0.435103\pi$
$420$	−39.1683	−1.91122
$421$	−1.96341	−0.0956906	−0.0478453	−	0.998855i	$-0.515235\pi$
$421$	−1.96341	−0.0956906	−0.0478453	+	0.998855i	$0.515235\pi$
$422$	−24.7014	−1.20245
$423$	6.99415	0.340067
$424$	36.6444	1.77961
$425$	8.72160	0.423060
$426$	−56.8777	−2.75573
$427$	−1.68363	−0.0814766
$428$	39.3309	1.90113
$429$	−15.6523	−0.755701
$430$	−112.533	−5.42680
$431$	−7.65239	−0.368603	−0.184301	−	0.982870i	$-0.559002\pi$
$431$	−7.65239	−0.368603	−0.184301	+	0.982870i	$0.559002\pi$
$432$	−30.8524	−1.48439
$433$	1.88101	0.0903953	0.0451977	−	0.998978i	$-0.485608\pi$
$433$	1.88101	0.0903953	0.0451977	+	0.998978i	$0.485608\pi$
$434$	31.6395	1.51875
$435$	52.7052	2.52702
$436$	−38.4006	−1.83905
$437$	−41.9805	−2.00820
$438$	−61.3161	−2.92980
$439$	3.93308	0.187715	0.0938577	−	0.995586i	$-0.470080\pi$
$439$	3.93308	0.187715	0.0938577	+	0.995586i	$0.470080\pi$
$440$	46.8812	2.23497
$441$	−3.12684	−0.148897
$442$	10.1902	0.484699
$443$	−0.541180	−0.0257123	−0.0128561	−	0.999917i	$-0.504092\pi$
$443$	−0.541180	−0.0257123	−0.0128561	+	0.999917i	$0.504092\pi$
$444$	47.8659	2.27161
$445$	−10.6884	−0.506680
$446$	−64.8124	−3.06896
$447$	−39.6326	−1.87456
$448$	−1.72402	−0.0814522
$449$	−13.4213	−0.633391	−0.316696	−	0.948527i	$-0.602573\pi$
$449$	−13.4213	−0.633391	−0.316696	+	0.948527i	$0.602573\pi$
$450$	−12.7902	−0.602936
$451$	5.79110	0.272692
$452$	4.54430	0.213746
$453$	17.0055	0.798990
$454$	28.8208	1.35263
$455$	18.8073	0.881701
$456$	83.0692	3.89007
$457$	−20.2253	−0.946100	−0.473050	−	0.881035i	$-0.656847\pi$
$457$	−20.2253	−0.946100	−0.473050	+	0.881035i	$0.656847\pi$
$458$	−58.2682	−2.72269
$459$	−4.58070	−0.213809
$460$	−96.3686	−4.49321
$461$	34.6466	1.61365	0.806827	−	0.590787i	$-0.201183\pi$
$461$	34.6466	1.61365	0.806827	+	0.590787i	$0.201183\pi$
$462$	−12.4656	−0.579954
$463$	−9.18308	−0.426774	−0.213387	−	0.976968i	$-0.568449\pi$
$463$	−9.18308	−0.426774	−0.213387	+	0.976968i	$0.568449\pi$
$464$	−50.6590	−2.35178
$465$	69.2507	3.21142
$466$	45.2960	2.09830
$467$	0.159268	0.00737004	0.00368502	−	0.999993i	$-0.498827\pi$
$467$	0.159268	0.00737004	0.00368502	+	0.999993i	$0.498827\pi$
$468$	−10.2926	−0.475776
$469$	11.5058	0.531291
$470$	113.521	5.23633
$471$	26.9411	1.24138
$472$	−30.5067	−1.40419
$473$	−24.6671	−1.13420
$474$	−17.6305	−0.809794
$475$	−62.2861	−2.85788
$476$	5.58960	0.256199
$477$	−3.44775	−0.157862
$478$	−30.1224	−1.37777
$479$	14.3314	0.654818	0.327409	−	0.944883i	$-0.393825\pi$
$479$	14.3314	0.654818	0.327409	+	0.944883i	$0.393825\pi$
$480$	33.4642	1.52742
$481$	−22.9836	−1.04796
$482$	−27.8817	−1.26998
$483$	14.0445	0.639045
$484$	−29.9332	−1.36060
$485$	39.5400	1.79542
$486$	15.0401	0.682233
$487$	0.835205	0.0378468	0.0189234	−	0.999821i	$-0.493976\pi$
$487$	0.835205	0.0378468	0.0189234	+	0.999821i	$0.493976\pi$
$488$	8.19672	0.371048
$489$	14.0717	0.636342
$490$	−50.7511	−2.29270
$491$	−8.07830	−0.364568	−0.182284	−	0.983246i	$-0.558349\pi$
$491$	−8.07830	−0.364568	−0.182284	+	0.983246i	$0.558349\pi$
$492$	23.5554	1.06196
$493$	−7.52141	−0.338747
$494$	−72.7743	−3.27427
$495$	−4.41089	−0.198255
$496$	−66.5620	−2.98872
$497$	14.9806	0.671974
$498$	54.2300	2.43010
$499$	8.76958	0.392580	0.196290	−	0.980546i	$-0.437111\pi$
$499$	8.76958	0.392580	0.196290	+	0.980546i	$0.437111\pi$
$500$	−61.0116	−2.72852
$501$	−11.1388	−0.497644
$502$	−26.6562	−1.18972
$503$	27.6402	1.23242	0.616208	−	0.787583i	$-0.288668\pi$
$503$	27.6402	1.23242	0.616208	+	0.787583i	$0.288668\pi$
$504$	−4.49278	−0.200125
$505$	−46.8596	−2.08522
$506$	−30.6701	−1.36345
$507$	5.97823	0.265503
$508$	−31.4286	−1.39442
$509$	10.2374	0.453763	0.226881	−	0.973922i	$-0.427147\pi$
$509$	10.2374	0.453763	0.226881	+	0.973922i	$0.427147\pi$
$510$	17.7629	0.786555
$511$	16.1497	0.714419
$512$	50.6637	2.23904
$513$	32.7135	1.44434
$514$	−27.1254	−1.19645
$515$	−37.0928	−1.63451
$516$	−100.334	−4.41696
$517$	24.8838	1.09439
$518$	−18.3043	−0.804247
$519$	13.8749	0.609039
$520$	−91.5630	−4.01530
$521$	30.7483	1.34711	0.673554	−	0.739138i	$-0.264767\pi$
$521$	30.7483	1.34711	0.673554	+	0.739138i	$0.264767\pi$
$522$	11.0301	0.482775
$523$	−35.6191	−1.55751	−0.778756	−	0.627327i	$-0.784149\pi$
$523$	−35.6191	−1.55751	−0.778756	+	0.627327i	$0.784149\pi$
$524$	−8.41538	−0.367628
$525$	20.8376	0.909430
$526$	39.4540	1.72028
$527$	−9.88256	−0.430491
$528$	26.2248	1.14129
$529$	11.5546	0.502373
$530$	−55.9598	−2.43074
$531$	2.87028	0.124559
$532$	−39.9186	−1.73069
$533$	−11.3105	−0.489912
$534$	−13.8364	−0.598759
$535$	−32.9197	−1.42324
$536$	−56.0159	−2.41952
$537$	31.4107	1.35547
$538$	−28.4276	−1.22560
$539$	−11.1247	−0.479173
$540$	75.0956	3.23160
$541$	25.4079	1.09237	0.546186	−	0.837664i	$-0.316079\pi$
$541$	25.4079	1.09237	0.546186	+	0.837664i	$0.316079\pi$
$542$	−18.0940	−0.777202
$543$	−33.7025	−1.44631
$544$	−4.77558	−0.204751
$545$	32.1410	1.37677
$546$	24.3465	1.04193
$547$	−7.19318	−0.307558	−0.153779	−	0.988105i	$-0.549144\pi$
$547$	−7.19318	−0.307558	−0.153779	+	0.988105i	$0.549144\pi$
$548$	1.53394	0.0655266
$549$	−0.771201	−0.0329141
$550$	−45.5049	−1.94034
$551$	53.7148	2.28833
$552$	−68.3752	−2.91024
$553$	4.64358	0.197465
$554$	47.9558	2.03745
$555$	−40.0634	−1.70060
$556$	−47.8516	−2.02936
$557$	12.9529	0.548832	0.274416	−	0.961611i	$-0.411516\pi$
$557$	12.9529	0.548832	0.274416	+	0.961611i	$0.411516\pi$
$558$	14.4928	0.613527
$559$	48.1770	2.03767
$560$	−31.5108	−1.33158
$561$	3.89363	0.164389
$562$	−76.5782	−3.23026
$563$	24.0665	1.01428	0.507140	−	0.861864i	$-0.330703\pi$
$563$	24.0665	1.01428	0.507140	+	0.861864i	$0.330703\pi$
$564$	101.215	4.26193
$565$	−3.80355	−0.160016
$566$	−38.9296	−1.63633
$567$	−13.1362	−0.551670
$568$	−72.9329	−3.06020
$569$	18.9215	0.793231	0.396615	−	0.917985i	$-0.370185\pi$
$569$	18.9215	0.793231	0.396615	+	0.917985i	$0.370185\pi$
$570$	−126.855	−5.31338
$571$	17.0666	0.714214	0.357107	−	0.934063i	$-0.383763\pi$
$571$	17.0666	0.714214	0.357107	+	0.934063i	$0.383763\pi$
$572$	−36.6190	−1.53112
$573$	−24.8406	−1.03773
$574$	−9.00779	−0.375978
$575$	51.2683	2.13804
$576$	−0.789702	−0.0329042
$577$	20.5748	0.856541	0.428271	−	0.903650i	$-0.359123\pi$
$577$	20.5748	0.856541	0.428271	+	0.903650i	$0.359123\pi$
$578$	−2.53489	−0.105438
$579$	23.9851	0.996787
$580$	123.305	5.11998
$581$	−14.2833	−0.592571
$582$	51.1853	2.12170
$583$	−12.2664	−0.508022
$584$	−78.6243	−3.25349
$585$	8.61485	0.356180
$586$	13.9764	0.577361
$587$	45.1252	1.86252	0.931258	−	0.364360i	$-0.118712\pi$
$587$	45.1252	1.86252	0.931258	+	0.364360i	$0.118712\pi$
$588$	−45.2497	−1.86607
$589$	70.5772	2.90808
$590$	46.5869	1.91795
$591$	−7.08938	−0.291618
$592$	38.5080	1.58267
$593$	−36.2490	−1.48857	−0.744283	−	0.667864i	$-0.767209\pi$
$593$	−36.2490	−1.48857	−0.744283	+	0.667864i	$0.767209\pi$
$594$	23.8998	0.980621
$595$	−4.67846	−0.191798
$596$	−92.7215	−3.79802
$597$	30.3452	1.24195
$598$	59.9013	2.44955
$599$	36.6703	1.49831	0.749155	−	0.662395i	$-0.230460\pi$
$599$	36.6703	1.49831	0.749155	+	0.662395i	$0.230460\pi$
$600$	−101.448	−4.14158
$601$	−41.3365	−1.68615	−0.843075	−	0.537795i	$-0.819257\pi$
$601$	−41.3365	−1.68615	−0.843075	+	0.537795i	$0.819257\pi$
$602$	38.3686	1.56379
$603$	5.27035	0.214625
$604$	39.7849	1.61883
$605$	25.0539	1.01859
$606$	−60.6607	−2.46417
$607$	−46.8989	−1.90357	−0.951783	−	0.306771i	$-0.900751\pi$
$607$	−46.8989	−1.90357	−0.951783	+	0.306771i	$0.900751\pi$
$608$	34.1052	1.38315
$609$	−17.9702	−0.728187
$610$	−12.5172	−0.506808
$611$	−48.6001	−1.96615
$612$	2.56036	0.103497
$613$	40.5133	1.63632	0.818159	−	0.574992i	$-0.194995\pi$
$613$	40.5133	1.63632	0.818159	+	0.574992i	$0.194995\pi$
$614$	68.0790	2.74745
$615$	−19.7157	−0.795014
$616$	−15.9844	−0.644030
$617$	37.2429	1.49934	0.749672	−	0.661810i	$-0.230211\pi$
$617$	37.2429	1.49934	0.749672	+	0.661810i	$0.230211\pi$
$618$	−48.0175	−1.93155
$619$	−44.6149	−1.79322	−0.896611	−	0.442818i	$-0.853979\pi$
$619$	−44.6149	−1.79322	−0.896611	+	0.442818i	$0.853979\pi$
$620$	162.014	6.50664
$621$	−26.9268	−1.08054
$622$	−42.8048	−1.71632
$623$	3.64428	0.146005
$624$	−51.2192	−2.05041
$625$	7.45832	0.298333
$626$	−33.1149	−1.32354
$627$	−27.8067	−1.11049
$628$	63.0295	2.51515
$629$	5.71734	0.227965
$630$	6.86095	0.273347
$631$	35.5835	1.41656	0.708279	−	0.705933i	$-0.249472\pi$
$631$	35.5835	1.41656	0.708279	+	0.705933i	$0.249472\pi$
$632$	−22.6071	−0.899264
$633$	18.4338	0.732677
$634$	28.1234	1.11692
$635$	26.3055	1.04390
$636$	−49.8938	−1.97842
$637$	21.7274	0.860871
$638$	39.2429	1.55364
$639$	6.86202	0.271457
$640$	−48.1975	−1.90517
$641$	−18.1886	−0.718405	−0.359203	−	0.933260i	$-0.616951\pi$
$641$	−18.1886	−0.718405	−0.359203	+	0.933260i	$0.616951\pi$
$642$	−42.6152	−1.68189
$643$	−37.5065	−1.47911	−0.739557	−	0.673094i	$-0.764965\pi$
$643$	−37.5065	−1.47911	−0.739557	+	0.673094i	$0.764965\pi$
$644$	32.8574	1.29476
$645$	83.9789	3.30667
$646$	18.1032	0.712259
$647$	−11.2084	−0.440649	−0.220325	−	0.975427i	$-0.570712\pi$
$647$	−11.2084	−0.440649	−0.220325	+	0.975427i	$0.570712\pi$
$648$	63.9534	2.51233
$649$	10.2119	0.400851
$650$	88.8750	3.48597
$651$	−23.6114	−0.925405
$652$	32.9210	1.28929
$653$	−13.1738	−0.515532	−0.257766	−	0.966207i	$-0.582986\pi$
$653$	−13.1738	−0.515532	−0.257766	+	0.966207i	$0.582986\pi$
$654$	41.6073	1.62697
$655$	7.04362	0.275217
$656$	18.9503	0.739883
$657$	7.39749	0.288604
$658$	−38.7056	−1.50890
$659$	−1.27800	−0.0497840	−0.0248920	−	0.999690i	$-0.507924\pi$
$659$	−1.27800	−0.0497840	−0.0248920	+	0.999690i	$0.507924\pi$
$660$	−63.8318	−2.48465
$661$	29.0887	1.13142	0.565709	−	0.824605i	$-0.308602\pi$
$661$	29.0887	1.13142	0.565709	+	0.824605i	$0.308602\pi$
$662$	19.3057	0.750337
$663$	−7.60459	−0.295338
$664$	69.5379	2.69859
$665$	33.4116	1.29565
$666$	−8.38446	−0.324891
$667$	−44.2132	−1.71194
$668$	−26.0595	−1.00827
$669$	48.3672	1.86998
$670$	85.5421	3.30478
$671$	−2.74378	−0.105922
$672$	−11.4098	−0.440143
$673$	29.8126	1.14919	0.574595	−	0.818438i	$-0.305159\pi$
$673$	29.8126	1.14919	0.574595	+	0.818438i	$0.305159\pi$
$674$	57.2766	2.20621
$675$	−39.9511	−1.53772
$676$	13.9862	0.537932
$677$	31.6439	1.21617	0.608087	−	0.793870i	$-0.291937\pi$
$677$	31.6439	1.21617	0.608087	+	0.793870i	$0.291937\pi$
$678$	−4.92377	−0.189096
$679$	−13.4814	−0.517368
$680$	22.7770	0.873457
$681$	−21.5079	−0.824184
$682$	51.5623	1.97442
$683$	−24.8039	−0.949096	−0.474548	−	0.880230i	$-0.657389\pi$
$683$	−24.8039	−0.949096	−0.474548	+	0.880230i	$0.657389\pi$
$684$	−18.2851	−0.699147
$685$	−1.28390	−0.0490552
$686$	39.7147	1.51632
$687$	43.4834	1.65900
$688$	−80.7185	−3.07736
$689$	23.9573	0.912702
$690$	104.416	3.97505
$691$	−1.91205	−0.0727380	−0.0363690	−	0.999338i	$-0.511579\pi$
$691$	−1.91205	−0.0727380	−0.0363690	+	0.999338i	$0.511579\pi$
$692$	32.4606	1.23397
$693$	1.50392	0.0571292
$694$	−75.4373	−2.86356
$695$	40.0515	1.51924
$696$	87.4873	3.31620
$697$	2.81357	0.106572
$698$	−84.0530	−3.18145
$699$	−33.8028	−1.27854
$700$	48.7503	1.84259
$701$	−14.7393	−0.556695	−0.278347	−	0.960480i	$-0.589787\pi$
$701$	−14.7393	−0.556695	−0.278347	+	0.960480i	$0.589787\pi$
$702$	−46.6784	−1.76176
$703$	−40.8309	−1.53997
$704$	−2.80960	−0.105891
$705$	−84.7165	−3.19061
$706$	2.53489	0.0954020
$707$	15.9770	0.600878
$708$	41.5369	1.56105
$709$	29.6627	1.11401	0.557003	−	0.830510i	$-0.311951\pi$
$709$	29.6627	1.11401	0.557003	+	0.830510i	$0.311951\pi$
$710$	111.376	4.17987
$711$	2.12703	0.0797699
$712$	−17.7421	−0.664913
$713$	−58.0928	−2.17559
$714$	−6.05637	−0.226654
$715$	30.6499	1.14624
$716$	73.4862	2.74631
$717$	22.4793	0.839504
$718$	41.9340	1.56496
$719$	−39.0871	−1.45770	−0.728851	−	0.684672i	$-0.759946\pi$
$719$	−39.0871	−1.45770	−0.728851	+	0.684672i	$0.759946\pi$
$720$	−14.4338	−0.537916
$721$	12.6470	0.471000
$722$	−81.1223	−3.01906
$723$	20.8071	0.773825
$724$	−78.8480	−2.93036
$725$	−65.5987	−2.43628
$726$	32.4328	1.20369
$727$	1.92745	0.0714850	0.0357425	−	0.999361i	$-0.488620\pi$
$727$	1.92745	0.0714850	0.0357425	+	0.999361i	$0.488620\pi$
$728$	31.2189	1.15705
$729$	19.9788	0.739954
$730$	120.067	4.44389
$731$	−11.9844	−0.443259
$732$	−11.1604	−0.412499
$733$	25.9978	0.960250	0.480125	−	0.877200i	$-0.340591\pi$
$733$	25.9978	0.960250	0.480125	+	0.877200i	$0.340591\pi$
$734$	−20.2662	−0.748039
$735$	37.8737	1.39699
$736$	−28.0723	−1.03476
$737$	18.7508	0.690696
$738$	−4.12610	−0.151884
$739$	4.19370	0.154268	0.0771338	−	0.997021i	$-0.475423\pi$
$739$	4.19370	0.154268	0.0771338	+	0.997021i	$0.475423\pi$
$740$	−93.7296	−3.44557
$741$	54.3089	1.99509
$742$	19.0798	0.700443
$743$	42.1031	1.54461	0.772307	−	0.635250i	$-0.219103\pi$
$743$	42.1031	1.54461	0.772307	+	0.635250i	$0.219103\pi$
$744$	114.952	4.21433
$745$	77.6073	2.84331
$746$	−32.1039	−1.17541
$747$	−6.54259	−0.239381
$748$	9.10926	0.333067
$749$	11.2242	0.410122
$750$	66.1065	2.41387
$751$	23.8813	0.871441	0.435720	−	0.900082i	$-0.356494\pi$
$751$	23.8813	0.871441	0.435720	+	0.900082i	$0.356494\pi$
$752$	81.4274	2.96935
$753$	19.8926	0.724925
$754$	−76.6448	−2.79124
$755$	−33.2997	−1.21190
$756$	−25.6043	−0.931219
$757$	−38.9490	−1.41562	−0.707812	−	0.706401i	$-0.750318\pi$
$757$	−38.9490	−1.41562	−0.707812	+	0.706401i	$0.750318\pi$
$758$	48.7308	1.76998
$759$	22.8880	0.830781
$760$	−162.664	−5.90043
$761$	10.5514	0.382486	0.191243	−	0.981543i	$-0.438748\pi$
$761$	10.5514	0.382486	0.191243	+	0.981543i	$0.438748\pi$
$762$	34.0530	1.23361
$763$	−10.9587	−0.396731
$764$	−58.1154	−2.10254
$765$	−2.14301	−0.0774806
$766$	33.1972	1.19946
$767$	−19.9446	−0.720159
$768$	−57.2283	−2.06505
$769$	32.8447	1.18441	0.592205	−	0.805787i	$-0.298257\pi$
$769$	32.8447	1.18441	0.592205	+	0.805787i	$0.298257\pi$
$770$	24.4099	0.879670
$771$	20.2427	0.729024
$772$	56.1138	2.01958
$773$	9.91906	0.356764	0.178382	−	0.983961i	$-0.442914\pi$
$773$	9.91906	0.356764	0.178382	+	0.983961i	$0.442914\pi$
$774$	17.5751	0.631723
$775$	−86.1918	−3.09610
$776$	65.6338	2.35612
$777$	13.6599	0.490045
$778$	77.9373	2.79419
$779$	−20.0934	−0.719920
$780$	124.669	4.46387
$781$	24.4137	0.873589
$782$	−14.9009	−0.532855
$783$	34.4533	1.23126
$784$	−36.4033	−1.30012
$785$	−52.7553	−1.88292
$786$	9.11811	0.325232
$787$	33.7039	1.20142	0.600708	−	0.799469i	$-0.294886\pi$
$787$	33.7039	1.20142	0.600708	+	0.799469i	$0.294886\pi$
$788$	−16.5858	−0.590845
$789$	−29.4431	−1.04820
$790$	34.5234	1.22829
$791$	1.29684	0.0461104
$792$	−7.32180	−0.260169
$793$	5.35883	0.190298
$794$	−11.8342	−0.419980
$795$	41.7608	1.48110
$796$	70.9936	2.51630
$797$	−3.67313	−0.130109	−0.0650544	−	0.997882i	$-0.520722\pi$
$797$	−3.67313	−0.130109	−0.0650544	+	0.997882i	$0.520722\pi$
$798$	43.2521	1.53111
$799$	12.0896	0.427701
$800$	−41.6507	−1.47257
$801$	1.66929	0.0589816
$802$	24.9948	0.882599
$803$	26.3188	0.928769
$804$	76.2694	2.68981
$805$	−27.5015	−0.969299
$806$	−100.706	−3.54720
$807$	21.2145	0.746786
$808$	−77.7838	−2.73643
$809$	3.30616	0.116239	0.0581193	−	0.998310i	$-0.481490\pi$
$809$	3.30616	0.116239	0.0581193	+	0.998310i	$0.481490\pi$
$810$	−97.6635	−3.43155
$811$	16.5693	0.581828	0.290914	−	0.956749i	$-0.406041\pi$
$811$	16.5693	0.581828	0.290914	+	0.956749i	$0.406041\pi$
$812$	−42.0417	−1.47537
$813$	13.5029	0.473566
$814$	−29.8302	−1.04555
$815$	−27.5547	−0.965199
$816$	12.7412	0.446030
$817$	85.5876	2.99433
$818$	−94.9095	−3.31843
$819$	−2.93728	−0.102637
$820$	−46.1255	−1.61077
$821$	43.1270	1.50514	0.752571	−	0.658511i	$-0.228813\pi$
$821$	43.1270	1.50514	0.752571	+	0.658511i	$0.228813\pi$
$822$	−1.66203	−0.0579700
$823$	2.77092	0.0965881	0.0482940	−	0.998833i	$-0.484622\pi$
$823$	2.77092	0.0965881	0.0482940	+	0.998833i	$0.484622\pi$
$824$	−61.5717	−2.14495
$825$	33.9587	1.18229
$826$	−15.8841	−0.552678
$827$	−46.0538	−1.60145	−0.800723	−	0.599034i	$-0.795551\pi$
$827$	−46.0538	−1.60145	−0.800723	+	0.599034i	$0.795551\pi$
$828$	15.0506	0.523045
$829$	7.48886	0.260099	0.130049	−	0.991508i	$-0.458486\pi$
$829$	7.48886	0.260099	0.130049	+	0.991508i	$0.458486\pi$
$830$	−106.192	−3.68596
$831$	−35.7877	−1.24146
$832$	5.48739	0.190241
$833$	−5.40485	−0.187267
$834$	51.8475	1.79533
$835$	21.8116	0.754823
$836$	−65.0545	−2.24996
$837$	45.2691	1.56473
$838$	−21.0117	−0.725837
$839$	4.79257	0.165458	0.0827290	−	0.996572i	$-0.473636\pi$
$839$	4.79257	0.165458	0.0827290	+	0.996572i	$0.473636\pi$
$840$	54.4187	1.87762
$841$	27.5716	0.950745
$842$	4.97703	0.171520
$843$	57.1475	1.96826
$844$	43.1264	1.48447
$845$	−11.7064	−0.402712
$846$	−17.7294	−0.609550
$847$	−8.54227	−0.293516
$848$	−40.1395	−1.37839
$849$	29.0517	0.997052
$850$	−22.1083	−0.758309
$851$	33.6083	1.15208
$852$	99.3030	3.40206
$853$	−1.55519	−0.0532489	−0.0266244	−	0.999646i	$-0.508476\pi$
$853$	−1.55519	−0.0532489	−0.0266244	+	0.999646i	$0.508476\pi$
$854$	4.26782	0.146042
$855$	15.3045	0.523402
$856$	−54.6446	−1.86771
$857$	2.16560	0.0739754	0.0369877	−	0.999316i	$-0.488224\pi$
$857$	2.16560	0.0739754	0.0369877	+	0.999316i	$0.488224\pi$
$858$	39.6770	1.35455
$859$	3.08914	0.105400	0.0527000	−	0.998610i	$-0.483217\pi$
$859$	3.08914	0.105400	0.0527000	+	0.998610i	$0.483217\pi$
$860$	196.471	6.69961
$861$	6.72219	0.229092
$862$	19.3980	0.660698
$863$	28.3208	0.964052	0.482026	−	0.876157i	$-0.339901\pi$
$863$	28.3208	0.964052	0.482026	+	0.876157i	$0.339901\pi$
$864$	21.8755	0.744219
$865$	−27.1693	−0.923786
$866$	−4.76815	−0.162028
$867$	1.89170	0.0642455
$868$	−55.2396	−1.87495
$869$	7.56754	0.256711
$870$	−133.602	−4.52954
$871$	−36.6220	−1.24089
$872$	53.3520	1.80673
$873$	−6.17526	−0.209001
$874$	106.416	3.59958
$875$	−17.4114	−0.588611
$876$	107.052	3.61696
$877$	13.1320	0.443436	0.221718	−	0.975111i	$-0.428834\pi$
$877$	13.1320	0.443436	0.221718	+	0.975111i	$0.428834\pi$
$878$	−9.96993	−0.336469
$879$	−10.4301	−0.351799
$880$	−51.3526	−1.73109
$881$	−11.8407	−0.398923	−0.199461	−	0.979906i	$-0.563919\pi$
$881$	−11.8407	−0.398923	−0.199461	+	0.979906i	$0.563919\pi$
$882$	7.92620	0.266889
$883$	−32.7068	−1.10067	−0.550336	−	0.834943i	$-0.685501\pi$
$883$	−32.7068	−1.10067	−0.550336	+	0.834943i	$0.685501\pi$
$884$	−17.7912	−0.598381
$885$	−34.7661	−1.16865
$886$	1.37183	0.0460877
$887$	56.3390	1.89168	0.945839	−	0.324636i	$-0.105242\pi$
$887$	56.3390	1.89168	0.945839	+	0.324636i	$0.105242\pi$
$888$	−66.5027	−2.23169
$889$	−8.96902	−0.300811
$890$	27.0940	0.908193
$891$	−21.4078	−0.717190
$892$	113.156	3.78875
$893$	−86.3392	−2.88923
$894$	100.464	3.36003
$895$	−61.5075	−2.05597
$896$	16.4332	0.548996
$897$	−44.7022	−1.49256
$898$	34.0216	1.13532
$899$	74.3308	2.47907
$900$	22.3305	0.744349
$901$	−5.95956	−0.198542
$902$	−14.6798	−0.488784
$903$	−28.6331	−0.952850
$904$	−6.31364	−0.209989
$905$	65.9952	2.19376
$906$	−43.1072	−1.43214
$907$	12.0674	0.400691	0.200346	−	0.979725i	$-0.435793\pi$
$907$	12.0674	0.400691	0.200346	+	0.979725i	$0.435793\pi$
$908$	−50.3183	−1.66987
$909$	7.31842	0.242737
$910$	−47.6745	−1.58040
$911$	−34.9689	−1.15857	−0.579286	−	0.815124i	$-0.696669\pi$
$911$	−34.9689	−1.15857	−0.579286	+	0.815124i	$0.696669\pi$
$912$	−90.9921	−3.01305
$913$	−23.2772	−0.770363
$914$	51.2690	1.69583
$915$	9.34116	0.308809
$916$	101.731	3.36128
$917$	−2.40156	−0.0793066
$918$	11.6116	0.383240
$919$	−12.2329	−0.403527	−0.201764	−	0.979434i	$-0.564667\pi$
$919$	−12.2329	−0.403527	−0.201764	+	0.979434i	$0.564667\pi$
$920$	133.890	4.41423
$921$	−50.8049	−1.67408
$922$	−87.8255	−2.89238
$923$	−47.6820	−1.56947
$924$	21.7638	0.715978
$925$	49.8644	1.63953
$926$	23.2781	0.764966
$927$	5.79308	0.190270
$928$	35.9191	1.17910
$929$	33.2595	1.09121	0.545605	−	0.838043i	$-0.316300\pi$
$929$	33.2595	1.09121	0.545605	+	0.838043i	$0.316300\pi$
$930$	−175.543	−5.75628
$931$	38.5992	1.26504
$932$	−79.0826	−2.59044
$933$	31.9437	1.04579
$934$	−0.403727	−0.0132104
$935$	−7.62439	−0.249344
$936$	14.3001	0.467413
$937$	−46.9777	−1.53470	−0.767348	−	0.641231i	$-0.778424\pi$
$937$	−46.9777	−1.53470	−0.767348	+	0.641231i	$0.778424\pi$
$938$	−29.1661	−0.952306
$939$	24.7124	0.806460
$940$	−198.197	−6.46446
$941$	51.3962	1.67547	0.837734	−	0.546078i	$-0.183880\pi$
$941$	51.3962	1.67547	0.837734	+	0.546078i	$0.183880\pi$
$942$	−68.2928	−2.22510
$943$	16.5391	0.538586
$944$	33.4164	1.08761
$945$	21.4306	0.697139
$946$	62.5285	2.03298
$947$	−22.9063	−0.744354	−0.372177	−	0.928162i	$-0.621389\pi$
$947$	−22.9063	−0.744354	−0.372177	+	0.928162i	$0.621389\pi$
$948$	30.7811	0.999724
$949$	−51.4028	−1.66861
$950$	157.889	5.12258
$951$	−20.9875	−0.680567
$952$	−7.76594	−0.251696
$953$	1.22177	0.0395771	0.0197885	−	0.999804i	$-0.493701\pi$
$953$	1.22177	0.0395771	0.0197885	+	0.999804i	$0.493701\pi$
$954$	8.73968	0.282958
$955$	48.6422	1.57402
$956$	52.5909	1.70091
$957$	−29.2856	−0.946669
$958$	−36.3285	−1.17372
$959$	0.437752	0.0141358
$960$	9.56524	0.308717
$961$	66.6651	2.15049
$962$	58.2609	1.87841
$963$	5.14132	0.165677
$964$	48.6789	1.56784
$965$	−46.9669	−1.51192
$966$	−35.6012	−1.14545
$967$	9.85707	0.316982	0.158491	−	0.987360i	$-0.449337\pi$
$967$	9.85707	0.316982	0.158491	+	0.987360i	$0.449337\pi$
$968$	41.5878	1.33668
$969$	−13.5097	−0.433995
$970$	−100.230	−3.21818
$971$	−10.2777	−0.329828	−0.164914	−	0.986308i	$-0.552735\pi$
$971$	−10.2777	−0.329828	−0.164914	+	0.986308i	$0.552735\pi$
$972$	−26.2586	−0.842244
$973$	−13.6558	−0.437784
$974$	−2.11716	−0.0678381
$975$	−66.3242	−2.12408
$976$	−8.97849	−0.287394
$977$	55.0147	1.76008	0.880039	−	0.474902i	$-0.157516\pi$
$977$	55.0147	1.76008	0.880039	+	0.474902i	$0.157516\pi$
$978$	−35.6701	−1.14061
$979$	5.93901	0.189811
$980$	88.6067	2.83044
$981$	−5.01971	−0.160267
$982$	20.4776	0.653467
$983$	52.4702	1.67354	0.836769	−	0.547556i	$-0.184442\pi$
$983$	52.4702	1.67354	0.836769	+	0.547556i	$0.184442\pi$
$984$	−32.7268	−1.04329
$985$	13.8822	0.442324
$986$	19.0660	0.607184
$987$	28.8846	0.919406
$988$	127.057	4.04222
$989$	−70.4480	−2.24012
$990$	11.1811	0.355360
$991$	44.9375	1.42749	0.713743	−	0.700407i	$-0.246998\pi$
$991$	44.9375	1.42749	0.713743	+	0.700407i	$0.246998\pi$
$992$	47.1949	1.49844
$993$	−14.4071	−0.457197
$994$	−37.9743	−1.20447
$995$	−59.4212	−1.88378
$996$	−94.6804	−3.00006
$997$	−14.0423	−0.444725	−0.222363	−	0.974964i	$-0.571377\pi$
$997$	−14.0423	−0.444725	−0.222363	+	0.974964i	$0.571377\pi$
$998$	−22.2300	−0.703677
$999$	−26.1894	−0.828597

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.d.1.7	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.d.1.7	✓	121	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53489 q^{2} +1.89170 q^{3} +4.42568 q^{4} -3.70427 q^{5} -4.79525 q^{6} +1.26299 q^{7} -6.14885 q^{8} +0.578524 q^{9} +O(q^{10})\)	\(q-2.53489 q^{2} +1.89170 q^{3} +4.42568 q^{4} -3.70427 q^{5} -4.79525 q^{6} +1.26299 q^{7} -6.14885 q^{8} +0.578524 q^{9} +9.38992 q^{10} +2.05827 q^{11} +8.37206 q^{12} -4.01998 q^{13} -3.20155 q^{14} -7.00736 q^{15} +6.73530 q^{16} +1.00000 q^{17} -1.46650 q^{18} -7.14159 q^{19} -16.3939 q^{20} +2.38920 q^{21} -5.21750 q^{22} +5.87831 q^{23} -11.6318 q^{24} +8.72160 q^{25} +10.1902 q^{26} -4.58070 q^{27} +5.58960 q^{28} -7.52141 q^{29} +17.7629 q^{30} -9.88256 q^{31} -4.77558 q^{32} +3.89363 q^{33} -2.53489 q^{34} -4.67846 q^{35} +2.56036 q^{36} +5.71734 q^{37} +18.1032 q^{38} -7.60459 q^{39} +22.7770 q^{40} +2.81357 q^{41} -6.05637 q^{42} -11.9844 q^{43} +9.10926 q^{44} -2.14301 q^{45} -14.9009 q^{46} +12.0896 q^{47} +12.7412 q^{48} -5.40485 q^{49} -22.1083 q^{50} +1.89170 q^{51} -17.7912 q^{52} -5.95956 q^{53} +11.6116 q^{54} -7.62439 q^{55} -7.76594 q^{56} -13.5097 q^{57} +19.0660 q^{58} +4.96138 q^{59} -31.0123 q^{60} -1.33305 q^{61} +25.0512 q^{62} +0.730671 q^{63} -1.36503 q^{64} +14.8911 q^{65} -9.86994 q^{66} +9.10999 q^{67} +4.42568 q^{68} +11.1200 q^{69} +11.8594 q^{70} +11.8612 q^{71} -3.55726 q^{72} +12.7868 q^{73} -14.4928 q^{74} +16.4986 q^{75} -31.6064 q^{76} +2.59958 q^{77} +19.2768 q^{78} +3.67665 q^{79} -24.9494 q^{80} -10.4009 q^{81} -7.13211 q^{82} -11.3091 q^{83} +10.5738 q^{84} -3.70427 q^{85} +30.3792 q^{86} -14.2282 q^{87} -12.6560 q^{88} +2.88543 q^{89} +5.43230 q^{90} -5.07720 q^{91} +26.0156 q^{92} -18.6948 q^{93} -30.6460 q^{94} +26.4543 q^{95} -9.03395 q^{96} -10.6742 q^{97} +13.7007 q^{98} +1.19076 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * q^99

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