LMFDB - Embedded newform 8018.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.09428 q^{3} +1.00000 q^{4} +2.68879 q^{5} -3.09428 q^{6} +2.69798 q^{7} +1.00000 q^{8} +6.57455 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.09428 q^{3} +1.00000 q^{4} +2.68879 q^{5} -3.09428 q^{6} +2.69798 q^{7} +1.00000 q^{8} +6.57455 q^{9} +2.68879 q^{10} -5.80467 q^{11} -3.09428 q^{12} -1.02008 q^{13} +2.69798 q^{14} -8.31986 q^{15} +1.00000 q^{16} -5.21133 q^{17} +6.57455 q^{18} +1.00000 q^{19} +2.68879 q^{20} -8.34831 q^{21} -5.80467 q^{22} +4.91566 q^{23} -3.09428 q^{24} +2.22960 q^{25} -1.02008 q^{26} -11.0607 q^{27} +2.69798 q^{28} +3.23208 q^{29} -8.31986 q^{30} +6.99206 q^{31} +1.00000 q^{32} +17.9613 q^{33} -5.21133 q^{34} +7.25432 q^{35} +6.57455 q^{36} -9.62772 q^{37} +1.00000 q^{38} +3.15640 q^{39} +2.68879 q^{40} -5.63748 q^{41} -8.34831 q^{42} -4.61898 q^{43} -5.80467 q^{44} +17.6776 q^{45} +4.91566 q^{46} -2.14466 q^{47} -3.09428 q^{48} +0.279119 q^{49} +2.22960 q^{50} +16.1253 q^{51} -1.02008 q^{52} -10.0456 q^{53} -11.0607 q^{54} -15.6075 q^{55} +2.69798 q^{56} -3.09428 q^{57} +3.23208 q^{58} +5.68410 q^{59} -8.31986 q^{60} -8.48789 q^{61} +6.99206 q^{62} +17.7380 q^{63} +1.00000 q^{64} -2.74277 q^{65} +17.9613 q^{66} -4.70299 q^{67} -5.21133 q^{68} -15.2104 q^{69} +7.25432 q^{70} +6.37379 q^{71} +6.57455 q^{72} -12.3353 q^{73} -9.62772 q^{74} -6.89899 q^{75} +1.00000 q^{76} -15.6609 q^{77} +3.15640 q^{78} +2.49251 q^{79} +2.68879 q^{80} +14.5011 q^{81} -5.63748 q^{82} -6.10451 q^{83} -8.34831 q^{84} -14.0122 q^{85} -4.61898 q^{86} -10.0009 q^{87} -5.80467 q^{88} -2.99680 q^{89} +17.6776 q^{90} -2.75215 q^{91} +4.91566 q^{92} -21.6354 q^{93} -2.14466 q^{94} +2.68879 q^{95} -3.09428 q^{96} +4.49014 q^{97} +0.279119 q^{98} -38.1631 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) $ 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.09428	−1.78648	−0.893241	−	0.449578i	$-0.851574\pi$
$3$	−3.09428	−1.78648	−0.893241	+	0.449578i	$0.851574\pi$
$4$	1.00000	0.500000
$5$	2.68879	1.20246	0.601232	−	0.799075i	$-0.294677\pi$
$5$	2.68879	1.20246	0.601232	+	0.799075i	$0.294677\pi$
$6$	−3.09428	−1.26323
$7$	2.69798	1.01974	0.509871	−	0.860251i	$-0.329693\pi$
$7$	2.69798	1.01974	0.509871	+	0.860251i	$0.329693\pi$
$8$	1.00000	0.353553
$9$	6.57455	2.19152
$10$	2.68879	0.850270
$11$	−5.80467	−1.75017	−0.875087	−	0.483965i	$-0.839196\pi$
$11$	−5.80467	−1.75017	−0.875087	+	0.483965i	$0.839196\pi$
$12$	−3.09428	−0.893241
$13$	−1.02008	−0.282918	−0.141459	−	0.989944i	$-0.545179\pi$
$13$	−1.02008	−0.282918	−0.141459	+	0.989944i	$0.545179\pi$
$14$	2.69798	0.721067
$15$	−8.31986	−2.14818
$16$	1.00000	0.250000
$17$	−5.21133	−1.26393	−0.631967	−	0.774996i	$-0.717752\pi$
$17$	−5.21133	−1.26393	−0.631967	+	0.774996i	$0.717752\pi$
$18$	6.57455	1.54964
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.68879	0.601232
$21$	−8.34831	−1.82175
$22$	−5.80467	−1.23756
$23$	4.91566	1.02499	0.512493	−	0.858691i	$-0.328722\pi$
$23$	4.91566	1.02499	0.512493	+	0.858691i	$0.328722\pi$
$24$	−3.09428	−0.631617
$25$	2.22960	0.445919
$26$	−1.02008	−0.200054
$27$	−11.0607	−2.12862
$28$	2.69798	0.509871
$29$	3.23208	0.600182	0.300091	−	0.953911i	$-0.402983\pi$
$29$	3.23208	0.600182	0.300091	+	0.953911i	$0.402983\pi$
$30$	−8.31986	−1.51899
$31$	6.99206	1.25581	0.627905	−	0.778290i	$-0.283913\pi$
$31$	6.99206	1.25581	0.627905	+	0.778290i	$0.283913\pi$
$32$	1.00000	0.176777
$33$	17.9613	3.12666
$34$	−5.21133	−0.893736
$35$	7.25432	1.22620
$36$	6.57455	1.09576
$37$	−9.62772	−1.58279	−0.791394	−	0.611307i	$-0.790644\pi$
$37$	−9.62772	−1.58279	−0.791394	+	0.611307i	$0.790644\pi$
$38$	1.00000	0.162221
$39$	3.15640	0.505429
$40$	2.68879	0.425135
$41$	−5.63748	−0.880427	−0.440214	−	0.897893i	$-0.645097\pi$
$41$	−5.63748	−0.880427	−0.440214	+	0.897893i	$0.645097\pi$
$42$	−8.34831	−1.28817
$43$	−4.61898	−0.704388	−0.352194	−	0.935927i	$-0.614564\pi$
$43$	−4.61898	−0.704388	−0.352194	+	0.935927i	$0.614564\pi$
$44$	−5.80467	−0.875087
$45$	17.6776	2.63522
$46$	4.91566	0.724775
$47$	−2.14466	−0.312831	−0.156416	−	0.987691i	$-0.549994\pi$
$47$	−2.14466	−0.312831	−0.156416	+	0.987691i	$0.549994\pi$
$48$	−3.09428	−0.446620
$49$	0.279119	0.0398741
$50$	2.22960	0.315312
$51$	16.1253	2.25799
$52$	−1.02008	−0.141459
$53$	−10.0456	−1.37986	−0.689932	−	0.723874i	$-0.742360\pi$
$53$	−10.0456	−1.37986	−0.689932	+	0.723874i	$0.742360\pi$
$54$	−11.0607	−1.50516
$55$	−15.6075	−2.10452
$56$	2.69798	0.360533
$57$	−3.09428	−0.409847
$58$	3.23208	0.424393
$59$	5.68410	0.740007	0.370003	−	0.929030i	$-0.379357\pi$
$59$	5.68410	0.740007	0.370003	+	0.929030i	$0.379357\pi$
$60$	−8.31986	−1.07409
$61$	−8.48789	−1.08676	−0.543381	−	0.839486i	$-0.682856\pi$
$61$	−8.48789	−1.08676	−0.543381	+	0.839486i	$0.682856\pi$
$62$	6.99206	0.887992
$63$	17.7380	2.23478
$64$	1.00000	0.125000
$65$	−2.74277	−0.340199
$66$	17.9613	2.21088
$67$	−4.70299	−0.574562	−0.287281	−	0.957846i	$-0.592751\pi$
$67$	−4.70299	−0.574562	−0.287281	+	0.957846i	$0.592751\pi$
$68$	−5.21133	−0.631967
$69$	−15.2104	−1.83112
$70$	7.25432	0.867056
$71$	6.37379	0.756430	0.378215	−	0.925718i	$-0.376538\pi$
$71$	6.37379	0.756430	0.378215	+	0.925718i	$0.376538\pi$
$72$	6.57455	0.774818
$73$	−12.3353	−1.44374	−0.721868	−	0.692031i	$-0.756716\pi$
$73$	−12.3353	−1.44374	−0.721868	+	0.692031i	$0.756716\pi$
$74$	−9.62772	−1.11920
$75$	−6.89899	−0.796627
$76$	1.00000	0.114708
$77$	−15.6609	−1.78473
$78$	3.15640	0.357392
$79$	2.49251	0.280429	0.140214	−	0.990121i	$-0.455221\pi$
$79$	2.49251	0.280429	0.140214	+	0.990121i	$0.455221\pi$
$80$	2.68879	0.300616
$81$	14.5011	1.61123
$82$	−5.63748	−0.622556
$83$	−6.10451	−0.670057	−0.335028	−	0.942208i	$-0.608746\pi$
$83$	−6.10451	−0.670057	−0.335028	+	0.942208i	$0.608746\pi$
$84$	−8.34831	−0.910875
$85$	−14.0122	−1.51983
$86$	−4.61898	−0.498078
$87$	−10.0009	−1.07221
$88$	−5.80467	−0.618780
$89$	−2.99680	−0.317660	−0.158830	−	0.987306i	$-0.550772\pi$
$89$	−2.99680	−0.317660	−0.158830	+	0.987306i	$0.550772\pi$
$90$	17.6776	1.86338
$91$	−2.75215	−0.288504
$92$	4.91566	0.512493
$93$	−21.6354	−2.24348
$94$	−2.14466	−0.221205
$95$	2.68879	0.275864
$96$	−3.09428	−0.315808
$97$	4.49014	0.455904	0.227952	−	0.973672i	$-0.426797\pi$
$97$	4.49014	0.455904	0.227952	+	0.973672i	$0.426797\pi$
$98$	0.279119	0.0281953
$99$	−38.1631	−3.83554
$100$	2.22960	0.222960
$101$	6.09662	0.606637	0.303318	−	0.952889i	$-0.401905\pi$
$101$	6.09662	0.606637	0.303318	+	0.952889i	$0.401905\pi$
$102$	16.1253	1.59664
$103$	2.01258	0.198306	0.0991529	−	0.995072i	$-0.468387\pi$
$103$	2.01258	0.198306	0.0991529	+	0.995072i	$0.468387\pi$
$104$	−1.02008	−0.100027
$105$	−22.4469	−2.19059
$106$	−10.0456	−0.975711
$107$	2.95811	0.285971	0.142985	−	0.989725i	$-0.454330\pi$
$107$	2.95811	0.285971	0.142985	+	0.989725i	$0.454330\pi$
$108$	−11.0607	−1.06431
$109$	12.9724	1.24253	0.621264	−	0.783601i	$-0.286619\pi$
$109$	12.9724	1.24253	0.621264	+	0.783601i	$0.286619\pi$
$110$	−15.6075	−1.48812
$111$	29.7908	2.82762
$112$	2.69798	0.254936
$113$	−11.0538	−1.03985	−0.519927	−	0.854211i	$-0.674041\pi$
$113$	−11.0538	−1.03985	−0.519927	+	0.854211i	$0.674041\pi$
$114$	−3.09428	−0.289806
$115$	13.2172	1.23251
$116$	3.23208	0.300091
$117$	−6.70655	−0.620021
$118$	5.68410	0.523264
$119$	−14.0601	−1.28889
$120$	−8.31986	−0.759496
$121$	22.6942	2.06311
$122$	−8.48789	−0.768457
$123$	17.4439	1.57287
$124$	6.99206	0.627905
$125$	−7.44904	−0.666262
$126$	17.7380	1.58023
$127$	−6.99251	−0.620485	−0.310243	−	0.950657i	$-0.600410\pi$
$127$	−6.99251	−0.620485	−0.310243	+	0.950657i	$0.600410\pi$
$128$	1.00000	0.0883883
$129$	14.2924	1.25838
$130$	−2.74277	−0.240557
$131$	−21.2407	−1.85581	−0.927903	−	0.372821i	$-0.878391\pi$
$131$	−21.2407	−1.85581	−0.927903	+	0.372821i	$0.878391\pi$
$132$	17.9613	1.56333
$133$	2.69798	0.233945
$134$	−4.70299	−0.406277
$135$	−29.7398	−2.55959
$136$	−5.21133	−0.446868
$137$	16.9283	1.44629	0.723143	−	0.690699i	$-0.242697\pi$
$137$	16.9283	1.44629	0.723143	+	0.690699i	$0.242697\pi$
$138$	−15.2104	−1.29480
$139$	0.538672	0.0456896	0.0228448	−	0.999739i	$-0.492728\pi$
$139$	0.538672	0.0456896	0.0228448	+	0.999739i	$0.492728\pi$
$140$	7.25432	0.613102
$141$	6.63618	0.558867
$142$	6.37379	0.534877
$143$	5.92121	0.495157
$144$	6.57455	0.547879
$145$	8.69038	0.721697
$146$	−12.3353	−1.02088
$147$	−0.863671	−0.0712344
$148$	−9.62772	−0.791394
$149$	−22.0651	−1.80764	−0.903821	−	0.427910i	$-0.859250\pi$
$149$	−22.0651	−1.80764	−0.903821	+	0.427910i	$0.859250\pi$
$150$	−6.89899	−0.563300
$151$	11.2101	0.912263	0.456131	−	0.889912i	$-0.349235\pi$
$151$	11.2101	0.912263	0.456131	+	0.889912i	$0.349235\pi$
$152$	1.00000	0.0811107
$153$	−34.2622	−2.76993
$154$	−15.6609	−1.26199
$155$	18.8002	1.51007
$156$	3.15640	0.252714
$157$	−3.27420	−0.261309	−0.130655	−	0.991428i	$-0.541708\pi$
$157$	−3.27420	−0.261309	−0.130655	+	0.991428i	$0.541708\pi$
$158$	2.49251	0.198293
$159$	31.0838	2.46510
$160$	2.68879	0.212568
$161$	13.2624	1.04522
$162$	14.5011	1.13931
$163$	−21.6594	−1.69649	−0.848247	−	0.529601i	$-0.822342\pi$
$163$	−21.6594	−1.69649	−0.848247	+	0.529601i	$0.822342\pi$
$164$	−5.63748	−0.440214
$165$	48.2941	3.75969
$166$	−6.10451	−0.473802
$167$	18.4021	1.42400	0.711998	−	0.702181i	$-0.247790\pi$
$167$	18.4021	1.42400	0.711998	+	0.702181i	$0.247790\pi$
$168$	−8.34831	−0.644086
$169$	−11.9594	−0.919957
$170$	−14.0122	−1.07468
$171$	6.57455	0.502769
$172$	−4.61898	−0.352194
$173$	24.7440	1.88125	0.940625	−	0.339448i	$-0.110240\pi$
$173$	24.7440	1.88125	0.940625	+	0.339448i	$0.110240\pi$
$174$	−10.0009	−0.758170
$175$	6.01541	0.454723
$176$	−5.80467	−0.437544
$177$	−17.5882	−1.32201
$178$	−2.99680	−0.224620
$179$	−23.0901	−1.72584	−0.862918	−	0.505343i	$-0.831366\pi$
$179$	−23.0901	−1.72584	−0.862918	+	0.505343i	$0.831366\pi$
$180$	17.6776	1.31761
$181$	5.37021	0.399165	0.199582	−	0.979881i	$-0.436041\pi$
$181$	5.37021	0.399165	0.199582	+	0.979881i	$0.436041\pi$
$182$	−2.75215	−0.204003
$183$	26.2639	1.94148
$184$	4.91566	0.362387
$185$	−25.8869	−1.90324
$186$	−21.6354	−1.58638
$187$	30.2501	2.21210
$188$	−2.14466	−0.156416
$189$	−29.8415	−2.17065
$190$	2.68879	0.195065
$191$	3.26272	0.236082	0.118041	−	0.993009i	$-0.462339\pi$
$191$	3.26272	0.236082	0.118041	+	0.993009i	$0.462339\pi$
$192$	−3.09428	−0.223310
$193$	5.16392	0.371707	0.185853	−	0.982577i	$-0.440495\pi$
$193$	5.16392	0.371707	0.185853	+	0.982577i	$0.440495\pi$
$194$	4.49014	0.322373
$195$	8.48690	0.607760
$196$	0.279119	0.0199371
$197$	−1.77258	−0.126291	−0.0631455	−	0.998004i	$-0.520113\pi$
$197$	−1.77258	−0.126291	−0.0631455	+	0.998004i	$0.520113\pi$
$198$	−38.1631	−2.71213
$199$	3.95646	0.280466	0.140233	−	0.990119i	$-0.455215\pi$
$199$	3.95646	0.280466	0.140233	+	0.990119i	$0.455215\pi$
$200$	2.22960	0.157656
$201$	14.5524	1.02644
$202$	6.09662	0.428957
$203$	8.72009	0.612031
$204$	16.1253	1.12900
$205$	−15.1580	−1.05868
$206$	2.01258	0.140223
$207$	32.3183	2.24627
$208$	−1.02008	−0.0707296
$209$	−5.80467	−0.401518
$210$	−22.4469	−1.54898
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−10.0456	−0.689932
$213$	−19.7223	−1.35135
$214$	2.95811	0.202212
$215$	−12.4195	−0.847001
$216$	−11.0607	−0.752582
$217$	18.8645	1.28060
$218$	12.9724	0.878600
$219$	38.1688	2.57921
$220$	−15.6075	−1.05226
$221$	5.31596	0.357590
$222$	29.7908	1.99943
$223$	−11.7745	−0.788478	−0.394239	−	0.919008i	$-0.628992\pi$
$223$	−11.7745	−0.788478	−0.394239	+	0.919008i	$0.628992\pi$
$224$	2.69798	0.180267
$225$	14.6586	0.977240
$226$	−11.0538	−0.735287
$227$	20.7359	1.37629	0.688145	−	0.725573i	$-0.258425\pi$
$227$	20.7359	1.37629	0.688145	+	0.725573i	$0.258425\pi$
$228$	−3.09428	−0.204924
$229$	−7.70226	−0.508979	−0.254490	−	0.967075i	$-0.581907\pi$
$229$	−7.70226	−0.508979	−0.254490	+	0.967075i	$0.581907\pi$
$230$	13.2172	0.871515
$231$	48.4592	3.18838
$232$	3.23208	0.212196
$233$	−13.0991	−0.858148	−0.429074	−	0.903269i	$-0.641160\pi$
$233$	−13.0991	−0.858148	−0.429074	+	0.903269i	$0.641160\pi$
$234$	−6.70655	−0.438421
$235$	−5.76655	−0.376168
$236$	5.68410	0.370003
$237$	−7.71250	−0.500981
$238$	−14.0601	−0.911380
$239$	3.58986	0.232209	0.116104	−	0.993237i	$-0.462959\pi$
$239$	3.58986	0.232209	0.116104	+	0.993237i	$0.462959\pi$
$240$	−8.31986	−0.537045
$241$	−20.7327	−1.33551	−0.667756	−	0.744380i	$-0.732745\pi$
$241$	−20.7327	−1.33551	−0.667756	+	0.744380i	$0.732745\pi$
$242$	22.6942	1.45884
$243$	−11.6884	−0.749811
$244$	−8.48789	−0.543381
$245$	0.750492	0.0479472
$246$	17.4439	1.11219
$247$	−1.02008	−0.0649059
$248$	6.99206	0.443996
$249$	18.8890	1.19704
$250$	−7.44904	−0.471118
$251$	20.0261	1.26404	0.632018	−	0.774953i	$-0.282227\pi$
$251$	20.0261	1.26404	0.632018	+	0.774953i	$0.282227\pi$
$252$	17.7380	1.11739
$253$	−28.5338	−1.79390
$254$	−6.99251	−0.438749
$255$	43.3576	2.71516
$256$	1.00000	0.0625000
$257$	−20.5611	−1.28257	−0.641283	−	0.767304i	$-0.721598\pi$
$257$	−20.5611	−1.28257	−0.641283	+	0.767304i	$0.721598\pi$
$258$	14.2924	0.889807
$259$	−25.9754	−1.61403
$260$	−2.74277	−0.170100
$261$	21.2495	1.31531
$262$	−21.2407	−1.31225
$263$	18.8516	1.16244	0.581219	−	0.813747i	$-0.302576\pi$
$263$	18.8516	1.16244	0.581219	+	0.813747i	$0.302576\pi$
$264$	17.9613	1.10544
$265$	−27.0104	−1.65924
$266$	2.69798	0.165424
$267$	9.27294	0.567495
$268$	−4.70299	−0.287281
$269$	12.3597	0.753585	0.376792	−	0.926298i	$-0.377027\pi$
$269$	12.3597	0.753585	0.376792	+	0.926298i	$0.377027\pi$
$270$	−29.7398	−1.80991
$271$	−9.97986	−0.606233	−0.303117	−	0.952953i	$-0.598027\pi$
$271$	−9.97986	−0.606233	−0.303117	+	0.952953i	$0.598027\pi$
$272$	−5.21133	−0.315983
$273$	8.51592	0.515407
$274$	16.9283	1.02268
$275$	−12.9421	−0.780436
$276$	−15.2104	−0.915560
$277$	−16.2948	−0.979059	−0.489530	−	0.871987i	$-0.662832\pi$
$277$	−16.2948	−0.979059	−0.489530	+	0.871987i	$0.662832\pi$
$278$	0.538672	0.0323074
$279$	45.9696	2.75213
$280$	7.25432	0.433528
$281$	7.82076	0.466547	0.233274	−	0.972411i	$-0.425056\pi$
$281$	7.82076	0.466547	0.233274	+	0.972411i	$0.425056\pi$
$282$	6.63618	0.395179
$283$	−16.2700	−0.967153	−0.483577	−	0.875302i	$-0.660663\pi$
$283$	−16.2700	−0.967153	−0.483577	+	0.875302i	$0.660663\pi$
$284$	6.37379	0.378215
$285$	−8.31986	−0.492826
$286$	5.92121	0.350129
$287$	−15.2098	−0.897809
$288$	6.57455	0.387409
$289$	10.1580	0.597527
$290$	8.69038	0.510317
$291$	−13.8937	−0.814465
$292$	−12.3353	−0.721868
$293$	4.48833	0.262211	0.131106	−	0.991368i	$-0.458147\pi$
$293$	4.48833	0.262211	0.131106	+	0.991368i	$0.458147\pi$
$294$	−0.863671	−0.0503703
$295$	15.2834	0.889831
$296$	−9.62772	−0.559600
$297$	64.2035	3.72546
$298$	−22.0651	−1.27820
$299$	−5.01435	−0.289987
$300$	−6.89899	−0.398313
$301$	−12.4619	−0.718294
$302$	11.2101	0.645067
$303$	−18.8646	−1.08375
$304$	1.00000	0.0573539
$305$	−22.8222	−1.30679
$306$	−34.2622	−1.95864
$307$	11.5583	0.659666	0.329833	−	0.944039i	$-0.393008\pi$
$307$	11.5583	0.659666	0.329833	+	0.944039i	$0.393008\pi$
$308$	−15.6609	−0.892363
$309$	−6.22749	−0.354270
$310$	18.8002	1.06778
$311$	11.3152	0.641629	0.320814	−	0.947142i	$-0.396043\pi$
$311$	11.3152	0.641629	0.320814	+	0.947142i	$0.396043\pi$
$312$	3.15640	0.178696
$313$	−22.1917	−1.25435	−0.627174	−	0.778879i	$-0.715789\pi$
$313$	−22.1917	−1.25435	−0.627174	+	0.778879i	$0.715789\pi$
$314$	−3.27420	−0.184774
$315$	47.6939	2.68725
$316$	2.49251	0.140214
$317$	10.0320	0.563453	0.281726	−	0.959495i	$-0.409093\pi$
$317$	10.0320	0.563453	0.281726	+	0.959495i	$0.409093\pi$
$318$	31.0838	1.74309
$319$	−18.7612	−1.05042
$320$	2.68879	0.150308
$321$	−9.15320	−0.510882
$322$	13.2624	0.739083
$323$	−5.21133	−0.289966
$324$	14.5011	0.805616
$325$	−2.27436	−0.126159
$326$	−21.6594	−1.19960
$327$	−40.1401	−2.21975
$328$	−5.63748	−0.311278
$329$	−5.78627	−0.319007
$330$	48.2941	2.65850
$331$	6.12083	0.336431	0.168216	−	0.985750i	$-0.446200\pi$
$331$	6.12083	0.336431	0.168216	+	0.985750i	$0.446200\pi$
$332$	−6.10451	−0.335028
$333$	−63.2979	−3.46871
$334$	18.4021	1.00692
$335$	−12.6454	−0.690890
$336$	−8.34831	−0.455438
$337$	−30.1681	−1.64336	−0.821681	−	0.569948i	$-0.806963\pi$
$337$	−30.1681	−1.64336	−0.821681	+	0.569948i	$0.806963\pi$
$338$	−11.9594	−0.650508
$339$	34.2035	1.85768
$340$	−14.0122	−0.759917
$341$	−40.5866	−2.19789
$342$	6.57455	0.355511
$343$	−18.1328	−0.979081
$344$	−4.61898	−0.249039
$345$	−40.8976	−2.20185
$346$	24.7440	1.33024
$347$	−6.59271	−0.353915	−0.176958	−	0.984218i	$-0.556626\pi$
$347$	−6.59271	−0.353915	−0.176958	+	0.984218i	$0.556626\pi$
$348$	−10.0009	−0.536107
$349$	−8.52462	−0.456312	−0.228156	−	0.973625i	$-0.573270\pi$
$349$	−8.52462	−0.456312	−0.228156	+	0.973625i	$0.573270\pi$
$350$	6.01541	0.321537
$351$	11.2827	0.602227
$352$	−5.80467	−0.309390
$353$	−10.3889	−0.552947	−0.276474	−	0.961021i	$-0.589166\pi$
$353$	−10.3889	−0.552947	−0.276474	+	0.961021i	$0.589166\pi$
$354$	−17.5882	−0.934801
$355$	17.1378	0.909579
$356$	−2.99680	−0.158830
$357$	43.5058	2.30257
$358$	−23.0901	−1.22035
$359$	25.3768	1.33933	0.669667	−	0.742661i	$-0.266437\pi$
$359$	25.3768	1.33933	0.669667	+	0.742661i	$0.266437\pi$
$360$	17.6776	0.931691
$361$	1.00000	0.0526316
$362$	5.37021	0.282252
$363$	−70.2222	−3.68571
$364$	−2.75215	−0.144252
$365$	−33.1670	−1.73604
$366$	26.2639	1.37283
$367$	14.9400	0.779864	0.389932	−	0.920844i	$-0.372499\pi$
$367$	14.9400	0.779864	0.389932	+	0.920844i	$0.372499\pi$
$368$	4.91566	0.256247
$369$	−37.0639	−1.92947
$370$	−25.8869	−1.34580
$371$	−27.1028	−1.40711
$372$	−21.6354	−1.12174
$373$	−18.2635	−0.945650	−0.472825	−	0.881156i	$-0.656766\pi$
$373$	−18.2635	−0.945650	−0.472825	+	0.881156i	$0.656766\pi$
$374$	30.2501	1.56419
$375$	23.0494	1.19027
$376$	−2.14466	−0.110603
$377$	−3.29697	−0.169802
$378$	−29.8415	−1.53488
$379$	−15.4863	−0.795477	−0.397738	−	0.917499i	$-0.630205\pi$
$379$	−15.4863	−0.795477	−0.397738	+	0.917499i	$0.630205\pi$
$380$	2.68879	0.137932
$381$	21.6368	1.10849
$382$	3.26272	0.166935
$383$	8.99696	0.459723	0.229862	−	0.973223i	$-0.426173\pi$
$383$	8.99696	0.459723	0.229862	+	0.973223i	$0.426173\pi$
$384$	−3.09428	−0.157904
$385$	−42.1089	−2.14607
$386$	5.16392	0.262836
$387$	−30.3677	−1.54368
$388$	4.49014	0.227952
$389$	22.4887	1.14022	0.570112	−	0.821567i	$-0.306900\pi$
$389$	22.4887	1.14022	0.570112	+	0.821567i	$0.306900\pi$
$390$	8.48690	0.429751
$391$	−25.6171	−1.29551
$392$	0.279119	0.0140976
$393$	65.7246	3.31537
$394$	−1.77258	−0.0893013
$395$	6.70183	0.337205
$396$	−38.1631	−1.91777
$397$	13.8583	0.695526	0.347763	−	0.937582i	$-0.386941\pi$
$397$	13.8583	0.695526	0.347763	+	0.937582i	$0.386941\pi$
$398$	3.95646	0.198319
$399$	−8.34831	−0.417938
$400$	2.22960	0.111480
$401$	−16.8575	−0.841824	−0.420912	−	0.907101i	$-0.638290\pi$
$401$	−16.8575	−0.841824	−0.420912	+	0.907101i	$0.638290\pi$
$402$	14.5524	0.725806
$403$	−7.13243	−0.355292
$404$	6.09662	0.303318
$405$	38.9904	1.93745
$406$	8.72009	0.432771
$407$	55.8858	2.77015
$408$	16.1253	0.798321
$409$	10.9497	0.541430	0.270715	−	0.962660i	$-0.412740\pi$
$409$	10.9497	0.541430	0.270715	+	0.962660i	$0.412740\pi$
$410$	−15.1580	−0.748601
$411$	−52.3810	−2.58376
$412$	2.01258	0.0991529
$413$	15.3356	0.754616
$414$	32.3183	1.58836
$415$	−16.4137	−0.805719
$416$	−1.02008	−0.0500134
$417$	−1.66680	−0.0816236
$418$	−5.80467	−0.283916
$419$	10.0233	0.489668	0.244834	−	0.969565i	$-0.421266\pi$
$419$	10.0233	0.489668	0.244834	+	0.969565i	$0.421266\pi$
$420$	−22.4469	−1.09529
$421$	10.6602	0.519548	0.259774	−	0.965669i	$-0.416352\pi$
$421$	10.6602	0.519548	0.259774	+	0.965669i	$0.416352\pi$
$422$	−1.00000	−0.0486792
$423$	−14.1002	−0.685575
$424$	−10.0456	−0.487856
$425$	−11.6192	−0.563612
$426$	−19.7223	−0.955547
$427$	−22.9002	−1.10822
$428$	2.95811	0.142985
$429$	−18.3219	−0.884588
$430$	−12.4195	−0.598920
$431$	29.9005	1.44025	0.720127	−	0.693842i	$-0.244084\pi$
$431$	29.9005	1.44025	0.720127	+	0.693842i	$0.244084\pi$
$432$	−11.0607	−0.532156
$433$	−2.10175	−0.101004	−0.0505018	−	0.998724i	$-0.516082\pi$
$433$	−2.10175	−0.101004	−0.0505018	+	0.998724i	$0.516082\pi$
$434$	18.8645	0.905523
$435$	−26.8904	−1.28930
$436$	12.9724	0.621264
$437$	4.91566	0.235148
$438$	38.1688	1.82377
$439$	−29.7140	−1.41817	−0.709086	−	0.705122i	$-0.750892\pi$
$439$	−29.7140	−1.41817	−0.709086	+	0.705122i	$0.750892\pi$
$440$	−15.6075	−0.744061
$441$	1.83508	0.0873848
$442$	5.31596	0.252854
$443$	−29.1694	−1.38588	−0.692941	−	0.720994i	$-0.743685\pi$
$443$	−29.1694	−1.38588	−0.692941	+	0.720994i	$0.743685\pi$
$444$	29.7908	1.41381
$445$	−8.05778	−0.381975
$446$	−11.7745	−0.557538
$447$	68.2755	3.22932
$448$	2.69798	0.127468
$449$	−21.3994	−1.00990	−0.504950	−	0.863148i	$-0.668489\pi$
$449$	−21.3994	−1.00990	−0.504950	+	0.863148i	$0.668489\pi$
$450$	14.6586	0.691013
$451$	32.7238	1.54090
$452$	−11.0538	−0.519927
$453$	−34.6871	−1.62974
$454$	20.7359	0.973184
$455$	−7.39996	−0.346915
$456$	−3.09428	−0.144903
$457$	25.2187	1.17968	0.589841	−	0.807519i	$-0.299190\pi$
$457$	25.2187	1.17968	0.589841	+	0.807519i	$0.299190\pi$
$458$	−7.70226	−0.359903
$459$	57.6407	2.69044
$460$	13.2172	0.616254
$461$	−18.4586	−0.859703	−0.429852	−	0.902900i	$-0.641434\pi$
$461$	−18.4586	−0.859703	−0.429852	+	0.902900i	$0.641434\pi$
$462$	48.4592	2.25453
$463$	−30.6189	−1.42298	−0.711491	−	0.702695i	$-0.751980\pi$
$463$	−30.6189	−1.42298	−0.711491	+	0.702695i	$0.751980\pi$
$464$	3.23208	0.150045
$465$	−58.1730	−2.69771
$466$	−13.0991	−0.606803
$467$	−20.9490	−0.969403	−0.484701	−	0.874680i	$-0.661072\pi$
$467$	−20.9490	−0.969403	−0.484701	+	0.874680i	$0.661072\pi$
$468$	−6.70655	−0.310010
$469$	−12.6886	−0.585905
$470$	−5.76655	−0.265991
$471$	10.1313	0.466824
$472$	5.68410	0.261632
$473$	26.8117	1.23280
$474$	−7.71250	−0.354247
$475$	2.22960	0.102301
$476$	−14.0601	−0.644443
$477$	−66.0451	−3.02400
$478$	3.58986	0.164196
$479$	−18.1492	−0.829258	−0.414629	−	0.909990i	$-0.636089\pi$
$479$	−18.1492	−0.829258	−0.414629	+	0.909990i	$0.636089\pi$
$480$	−8.31986	−0.379748
$481$	9.82101	0.447800
$482$	−20.7327	−0.944350
$483$	−41.0375	−1.86727
$484$	22.6942	1.03156
$485$	12.0730	0.548208
$486$	−11.6884	−0.530196
$487$	−12.2598	−0.555546	−0.277773	−	0.960647i	$-0.589596\pi$
$487$	−12.2598	−0.555546	−0.277773	+	0.960647i	$0.589596\pi$
$488$	−8.48789	−0.384229
$489$	67.0201	3.03076
$490$	0.750492	0.0339038
$491$	0.409512	0.0184810	0.00924052	−	0.999957i	$-0.497059\pi$
$491$	0.409512	0.0184810	0.00924052	+	0.999957i	$0.497059\pi$
$492$	17.4439	0.786434
$493$	−16.8434	−0.758590
$494$	−1.02008	−0.0458954
$495$	−102.613	−4.61210
$496$	6.99206	0.313953
$497$	17.1964	0.771363
$498$	18.8890	0.846438
$499$	19.8019	0.886453	0.443227	−	0.896410i	$-0.353834\pi$
$499$	19.8019	0.886453	0.443227	+	0.896410i	$0.353834\pi$
$500$	−7.44904	−0.333131
$501$	−56.9412	−2.54394
$502$	20.0261	0.893809
$503$	−8.25561	−0.368100	−0.184050	−	0.982917i	$-0.558921\pi$
$503$	−8.25561	−0.368100	−0.184050	+	0.982917i	$0.558921\pi$
$504$	17.7380	0.790115
$505$	16.3925	0.729459
$506$	−28.5338	−1.26848
$507$	37.0058	1.64349
$508$	−6.99251	−0.310243
$509$	−15.8574	−0.702867	−0.351433	−	0.936213i	$-0.614306\pi$
$509$	−15.8574	−0.702867	−0.351433	+	0.936213i	$0.614306\pi$
$510$	43.3576	1.91990
$511$	−33.2804	−1.47224
$512$	1.00000	0.0441942
$513$	−11.0607	−0.488340
$514$	−20.5611	−0.906911
$515$	5.41142	0.238456
$516$	14.2924	0.629188
$517$	12.4491	0.547509
$518$	−25.9754	−1.14129
$519$	−76.5647	−3.36082
$520$	−2.74277	−0.120279
$521$	15.9390	0.698302	0.349151	−	0.937067i	$-0.386470\pi$
$521$	15.9390	0.698302	0.349151	+	0.937067i	$0.386470\pi$
$522$	21.2495	0.930064
$523$	4.73045	0.206848	0.103424	−	0.994637i	$-0.467020\pi$
$523$	4.73045	0.206848	0.103424	+	0.994637i	$0.467020\pi$
$524$	−21.2407	−0.927903
$525$	−18.6134	−0.812354
$526$	18.8516	0.821968
$527$	−36.4379	−1.58726
$528$	17.9613	0.781664
$529$	1.16372	0.0505965
$530$	−27.0104	−1.17326
$531$	37.3704	1.62174
$532$	2.69798	0.116972
$533$	5.75067	0.249089
$534$	9.27294	0.401279
$535$	7.95373	0.343870
$536$	−4.70299	−0.203138
$537$	71.4472	3.08318
$538$	12.3597	0.532865
$539$	−1.62019	−0.0697867
$540$	−29.7398	−1.27980
$541$	−28.9967	−1.24666	−0.623332	−	0.781957i	$-0.714221\pi$
$541$	−28.9967	−1.24666	−0.623332	+	0.781957i	$0.714221\pi$
$542$	−9.97986	−0.428672
$543$	−16.6169	−0.713100
$544$	−5.21133	−0.223434
$545$	34.8800	1.49410
$546$	8.51592	0.364448
$547$	−28.4124	−1.21483	−0.607414	−	0.794385i	$-0.707793\pi$
$547$	−28.4124	−1.21483	−0.607414	+	0.794385i	$0.707793\pi$
$548$	16.9283	0.723143
$549$	−55.8040	−2.38166
$550$	−12.9421	−0.551852
$551$	3.23208	0.137691
$552$	−15.2104	−0.647398
$553$	6.72474	0.285965
$554$	−16.2948	−0.692300
$555$	80.1013	3.40011
$556$	0.538672	0.0228448
$557$	34.4257	1.45866	0.729331	−	0.684161i	$-0.239831\pi$
$557$	34.4257	1.45866	0.729331	+	0.684161i	$0.239831\pi$
$558$	45.9696	1.94605
$559$	4.71172	0.199284
$560$	7.25432	0.306551
$561$	−93.6021	−3.95188
$562$	7.82076	0.329899
$563$	−6.20147	−0.261361	−0.130680	−	0.991425i	$-0.541716\pi$
$563$	−6.20147	−0.261361	−0.130680	+	0.991425i	$0.541716\pi$
$564$	6.63618	0.279434
$565$	−29.7213	−1.25039
$566$	−16.2700	−0.683881
$567$	39.1237	1.64304
$568$	6.37379	0.267438
$569$	−42.3188	−1.77410	−0.887049	−	0.461675i	$-0.847248\pi$
$569$	−42.3188	−1.77410	−0.887049	+	0.461675i	$0.847248\pi$
$570$	−8.31986	−0.348481
$571$	−6.92442	−0.289778	−0.144889	−	0.989448i	$-0.546282\pi$
$571$	−6.92442	−0.289778	−0.144889	+	0.989448i	$0.546282\pi$
$572$	5.92121	0.247578
$573$	−10.0958	−0.421756
$574$	−15.2098	−0.634847
$575$	10.9599	0.457061
$576$	6.57455	0.273940
$577$	−11.0193	−0.458741	−0.229370	−	0.973339i	$-0.573667\pi$
$577$	−11.0193	−0.458741	−0.229370	+	0.973339i	$0.573667\pi$
$578$	10.1580	0.422515
$579$	−15.9786	−0.664048
$580$	8.69038	0.360848
$581$	−16.4699	−0.683285
$582$	−13.8937	−0.575913
$583$	58.3112	2.41500
$584$	−12.3353	−0.510438
$585$	−18.0325	−0.745552
$586$	4.48833	0.185411
$587$	−28.6989	−1.18453	−0.592265	−	0.805743i	$-0.701766\pi$
$587$	−28.6989	−1.18453	−0.592265	+	0.805743i	$0.701766\pi$
$588$	−0.863671	−0.0356172
$589$	6.99206	0.288103
$590$	15.2834	0.629206
$591$	5.48485	0.225617
$592$	−9.62772	−0.395697
$593$	−47.1414	−1.93586	−0.967932	−	0.251211i	$-0.919171\pi$
$593$	−47.1414	−1.93586	−0.967932	+	0.251211i	$0.919171\pi$
$594$	64.2035	2.63430
$595$	−37.8046	−1.54984
$596$	−22.0651	−0.903821
$597$	−12.2424	−0.501047
$598$	−5.01435	−0.205052
$599$	−12.8321	−0.524304	−0.262152	−	0.965027i	$-0.584432\pi$
$599$	−12.8321	−0.524304	−0.262152	+	0.965027i	$0.584432\pi$
$600$	−6.89899	−0.281650
$601$	30.4272	1.24115	0.620577	−	0.784146i	$-0.286899\pi$
$601$	30.4272	1.24115	0.620577	+	0.784146i	$0.286899\pi$
$602$	−12.4619	−0.507911
$603$	−30.9201	−1.25916
$604$	11.2101	0.456131
$605$	61.0200	2.48082
$606$	−18.8646	−0.766324
$607$	−3.64491	−0.147942	−0.0739712	−	0.997260i	$-0.523567\pi$
$607$	−3.64491	−0.147942	−0.0739712	+	0.997260i	$0.523567\pi$
$608$	1.00000	0.0405554
$609$	−26.9824	−1.09338
$610$	−22.8222	−0.924042
$611$	2.18772	0.0885057
$612$	−34.2622	−1.38497
$613$	18.6551	0.753473	0.376736	−	0.926321i	$-0.377046\pi$
$613$	18.6551	0.753473	0.376736	+	0.926321i	$0.377046\pi$
$614$	11.5583	0.466455
$615$	46.9031	1.89132
$616$	−15.6609	−0.630996
$617$	14.6266	0.588843	0.294422	−	0.955676i	$-0.404873\pi$
$617$	14.6266	0.588843	0.294422	+	0.955676i	$0.404873\pi$
$618$	−6.22749	−0.250507
$619$	1.44896	0.0582387	0.0291194	−	0.999576i	$-0.490730\pi$
$619$	1.44896	0.0582387	0.0291194	+	0.999576i	$0.490730\pi$
$620$	18.8002	0.755033
$621$	−54.3704	−2.18181
$622$	11.3152	0.453700
$623$	−8.08533	−0.323932
$624$	3.15640	0.126357
$625$	−31.1769	−1.24708
$626$	−22.1917	−0.886958
$627$	17.9613	0.717304
$628$	−3.27420	−0.130655
$629$	50.1732	2.00054
$630$	47.6939	1.90017
$631$	−17.2479	−0.686629	−0.343315	−	0.939220i	$-0.611550\pi$
$631$	−17.2479	−0.686629	−0.343315	+	0.939220i	$0.611550\pi$
$632$	2.49251	0.0991465
$633$	3.09428	0.122986
$634$	10.0320	0.398421
$635$	−18.8014	−0.746111
$636$	31.0838	1.23255
$637$	−0.284723	−0.0112811
$638$	−18.7612	−0.742761
$639$	41.9048	1.65773
$640$	2.68879	0.106284
$641$	23.3046	0.920477	0.460238	−	0.887795i	$-0.347764\pi$
$641$	23.3046	0.920477	0.460238	+	0.887795i	$0.347764\pi$
$642$	−9.15320	−0.361248
$643$	−29.2777	−1.15460	−0.577300	−	0.816532i	$-0.695894\pi$
$643$	−29.2777	−1.15460	−0.577300	+	0.816532i	$0.695894\pi$
$644$	13.2624	0.522611
$645$	38.4293	1.51315
$646$	−5.21133	−0.205037
$647$	24.3443	0.957074	0.478537	−	0.878067i	$-0.341167\pi$
$647$	24.3443	0.957074	0.478537	+	0.878067i	$0.341167\pi$
$648$	14.5011	0.569656
$649$	−32.9943	−1.29514
$650$	−2.27436	−0.0892077
$651$	−58.3719	−2.28777
$652$	−21.6594	−0.848247
$653$	−20.2614	−0.792891	−0.396445	−	0.918058i	$-0.629756\pi$
$653$	−20.2614	−0.792891	−0.396445	+	0.918058i	$0.629756\pi$
$654$	−40.1401	−1.56960
$655$	−57.1117	−2.23154
$656$	−5.63748	−0.220107
$657$	−81.0989	−3.16397
$658$	−5.78627	−0.225572
$659$	−46.0440	−1.79362	−0.896809	−	0.442418i	$-0.854121\pi$
$659$	−46.0440	−1.79362	−0.896809	+	0.442418i	$0.854121\pi$
$660$	48.2941	1.87984
$661$	0.200679	0.00780551	0.00390276	−	0.999992i	$-0.498758\pi$
$661$	0.200679	0.00780551	0.00390276	+	0.999992i	$0.498758\pi$
$662$	6.12083	0.237893
$663$	−16.4490	−0.638828
$664$	−6.10451	−0.236901
$665$	7.25432	0.281310
$666$	−63.2979	−2.45275
$667$	15.8878	0.615178
$668$	18.4021	0.711998
$669$	36.4335	1.40860
$670$	−12.6454	−0.488533
$671$	49.2694	1.90202
$672$	−8.34831	−0.322043
$673$	−10.8814	−0.419448	−0.209724	−	0.977761i	$-0.567257\pi$
$673$	−10.8814	−0.419448	−0.209724	+	0.977761i	$0.567257\pi$
$674$	−30.1681	−1.16203
$675$	−24.6608	−0.949194
$676$	−11.9594	−0.459979
$677$	−16.8531	−0.647718	−0.323859	−	0.946105i	$-0.604980\pi$
$677$	−16.8531	−0.647718	−0.323859	+	0.946105i	$0.604980\pi$
$678$	34.2035	1.31358
$679$	12.1143	0.464905
$680$	−14.0122	−0.537342
$681$	−64.1626	−2.45872
$682$	−40.5866	−1.55414
$683$	3.36580	0.128789	0.0643944	−	0.997925i	$-0.479488\pi$
$683$	3.36580	0.128789	0.0643944	+	0.997925i	$0.479488\pi$
$684$	6.57455	0.251384
$685$	45.5168	1.73911
$686$	−18.1328	−0.692315
$687$	23.8329	0.909282
$688$	−4.61898	−0.176097
$689$	10.2472	0.390389
$690$	−40.8976	−1.55695
$691$	13.1189	0.499068	0.249534	−	0.968366i	$-0.419723\pi$
$691$	13.1189	0.499068	0.249534	+	0.968366i	$0.419723\pi$
$692$	24.7440	0.940625
$693$	−102.963	−3.91126
$694$	−6.59271	−0.250256
$695$	1.44838	0.0549401
$696$	−10.0009	−0.379085
$697$	29.3788	1.11280
$698$	−8.52462	−0.322662
$699$	40.5322	1.53307
$700$	6.01541	0.227361
$701$	−15.8741	−0.599557	−0.299779	−	0.954009i	$-0.596913\pi$
$701$	−15.8741	−0.599557	−0.299779	+	0.954009i	$0.596913\pi$
$702$	11.2827	0.425839
$703$	−9.62772	−0.363116
$704$	−5.80467	−0.218772
$705$	17.8433	0.672018
$706$	−10.3889	−0.390993
$707$	16.4486	0.618613
$708$	−17.5882	−0.661004
$709$	−1.40514	−0.0527710	−0.0263855	−	0.999652i	$-0.508400\pi$
$709$	−1.40514	−0.0527710	−0.0263855	+	0.999652i	$0.508400\pi$
$710$	17.1378	0.643170
$711$	16.3871	0.614565
$712$	−2.99680	−0.112310
$713$	34.3706	1.28719
$714$	43.5058	1.62816
$715$	15.9209	0.595408
$716$	−23.0901	−0.862918
$717$	−11.1080	−0.414836
$718$	25.3768	0.947052
$719$	50.1743	1.87119	0.935593	−	0.353081i	$-0.114866\pi$
$719$	50.1743	1.87119	0.935593	+	0.353081i	$0.114866\pi$
$720$	17.6776	0.658805
$721$	5.42992	0.202221
$722$	1.00000	0.0372161
$723$	64.1528	2.38587
$724$	5.37021	0.199582
$725$	7.20623	0.267633
$726$	−70.2222	−2.60619
$727$	−7.84044	−0.290786	−0.145393	−	0.989374i	$-0.546445\pi$
$727$	−7.84044	−0.290786	−0.145393	+	0.989374i	$0.546445\pi$
$728$	−2.75215	−0.102001
$729$	−7.33610	−0.271708
$730$	−33.1670	−1.22757
$731$	24.0710	0.890299
$732$	26.2639	0.970741
$733$	−19.6031	−0.724056	−0.362028	−	0.932167i	$-0.617916\pi$
$733$	−19.6031	−0.724056	−0.362028	+	0.932167i	$0.617916\pi$
$734$	14.9400	0.551447
$735$	−2.32223	−0.0856568
$736$	4.91566	0.181194
$737$	27.2993	1.00558
$738$	−37.0639	−1.36434
$739$	38.6814	1.42292	0.711459	−	0.702728i	$-0.248035\pi$
$739$	38.6814	1.42292	0.711459	+	0.702728i	$0.248035\pi$
$740$	−25.8869	−0.951622
$741$	3.15640	0.115953
$742$	−27.1028	−0.994974
$743$	35.4939	1.30214	0.651072	−	0.759016i	$-0.274320\pi$
$743$	35.4939	1.30214	0.651072	+	0.759016i	$0.274320\pi$
$744$	−21.6354	−0.793191
$745$	−59.3284	−2.17362
$746$	−18.2635	−0.668676
$747$	−40.1344	−1.46844
$748$	30.2501	1.10605
$749$	7.98092	0.291617
$750$	23.0494	0.841645
$751$	3.42607	0.125019	0.0625095	−	0.998044i	$-0.480090\pi$
$751$	3.42607	0.125019	0.0625095	+	0.998044i	$0.480090\pi$
$752$	−2.14466	−0.0782078
$753$	−61.9663	−2.25818
$754$	−3.29697	−0.120068
$755$	30.1415	1.09696
$756$	−29.8415	−1.08532
$757$	47.2149	1.71605	0.858027	−	0.513604i	$-0.171690\pi$
$757$	47.2149	1.71605	0.858027	+	0.513604i	$0.171690\pi$
$758$	−15.4863	−0.562487
$759$	88.2915	3.20478
$760$	2.68879	0.0975327
$761$	18.0283	0.653524	0.326762	−	0.945107i	$-0.394042\pi$
$761$	18.0283	0.653524	0.326762	+	0.945107i	$0.394042\pi$
$762$	21.6368	0.783818
$763$	34.9993	1.26706
$764$	3.26272	0.118041
$765$	−92.1238	−3.33074
$766$	8.99696	0.325073
$767$	−5.79822	−0.209361
$768$	−3.09428	−0.111655
$769$	12.5508	0.452595	0.226298	−	0.974058i	$-0.427338\pi$
$769$	12.5508	0.452595	0.226298	+	0.974058i	$0.427338\pi$
$770$	−42.1089	−1.51750
$771$	63.6218	2.29128
$772$	5.16392	0.185853
$773$	−17.9794	−0.646676	−0.323338	−	0.946284i	$-0.604805\pi$
$773$	−17.9794	−0.646676	−0.323338	+	0.946284i	$0.604805\pi$
$774$	−30.3677	−1.09155
$775$	15.5895	0.559990
$776$	4.49014	0.161186
$777$	80.3752	2.88344
$778$	22.4887	0.806261
$779$	−5.63748	−0.201984
$780$	8.48690	0.303880
$781$	−36.9978	−1.32388
$782$	−25.6171	−0.916067
$783$	−35.7489	−1.27756
$784$	0.279119	0.00996853
$785$	−8.80363	−0.314215
$786$	65.7246	2.34432
$787$	−48.5559	−1.73083	−0.865416	−	0.501054i	$-0.832946\pi$
$787$	−48.5559	−1.73083	−0.865416	+	0.501054i	$0.832946\pi$
$788$	−1.77258	−0.0631455
$789$	−58.3320	−2.07668
$790$	6.70183	0.238440
$791$	−29.8230	−1.06038
$792$	−38.1631	−1.35607
$793$	8.65829	0.307465
$794$	13.8583	0.491811
$795$	83.5777	2.96420
$796$	3.95646	0.140233
$797$	48.3845	1.71387	0.856934	−	0.515426i	$-0.172366\pi$
$797$	48.3845	1.71387	0.856934	+	0.515426i	$0.172366\pi$
$798$	−8.34831	−0.295527
$799$	11.1765	0.395398
$800$	2.22960	0.0788281
$801$	−19.7026	−0.696158
$802$	−16.8575	−0.595260
$803$	71.6023	2.52679
$804$	14.5524	0.513222
$805$	35.6598	1.25684
$806$	−7.13243	−0.251229
$807$	−38.2444	−1.34627
$808$	6.09662	0.214479
$809$	−2.93682	−0.103253	−0.0516266	−	0.998666i	$-0.516441\pi$
$809$	−2.93682	−0.103253	−0.0516266	+	0.998666i	$0.516441\pi$
$810$	38.9904	1.36998
$811$	30.0317	1.05456	0.527278	−	0.849693i	$-0.323213\pi$
$811$	30.0317	1.05456	0.527278	+	0.849693i	$0.323213\pi$
$812$	8.72009	0.306015
$813$	30.8804	1.08302
$814$	55.8858	1.95879
$815$	−58.2376	−2.03997
$816$	16.1253	0.564498
$817$	−4.61898	−0.161598
$818$	10.9497	0.382849
$819$	−18.0942	−0.632261
$820$	−15.1580	−0.529341
$821$	−46.8286	−1.63433	−0.817164	−	0.576405i	$-0.804455\pi$
$821$	−46.8286	−1.63433	−0.817164	+	0.576405i	$0.804455\pi$
$822$	−52.3810	−1.82700
$823$	−40.0217	−1.39507	−0.697535	−	0.716551i	$-0.745720\pi$
$823$	−40.0217	−1.39507	−0.697535	+	0.716551i	$0.745720\pi$
$824$	2.01258	0.0701117
$825$	40.0464	1.39424
$826$	15.3356	0.533594
$827$	31.9683	1.11165	0.555823	−	0.831301i	$-0.312403\pi$
$827$	31.9683	1.11165	0.555823	+	0.831301i	$0.312403\pi$
$828$	32.3183	1.12314
$829$	28.3019	0.982965	0.491482	−	0.870887i	$-0.336455\pi$
$829$	28.3019	0.982965	0.491482	+	0.870887i	$0.336455\pi$
$830$	−16.4137	−0.569729
$831$	50.4206	1.74907
$832$	−1.02008	−0.0353648
$833$	−1.45458	−0.0503982
$834$	−1.66680	−0.0577166
$835$	49.4794	1.71230
$836$	−5.80467	−0.200759
$837$	−77.3367	−2.67315
$838$	10.0233	0.346248
$839$	−18.3322	−0.632897	−0.316448	−	0.948610i	$-0.602490\pi$
$839$	−18.3322	−0.632897	−0.316448	+	0.948610i	$0.602490\pi$
$840$	−22.4469	−0.774490
$841$	−18.5537	−0.639782
$842$	10.6602	0.367376
$843$	−24.1996	−0.833478
$844$	−1.00000	−0.0344214
$845$	−32.1564	−1.10622
$846$	−14.1002	−0.484775
$847$	61.2287	2.10384
$848$	−10.0456	−0.344966
$849$	50.3440	1.72780
$850$	−11.6192	−0.398534
$851$	−47.3266	−1.62233
$852$	−19.7223	−0.675674
$853$	2.64013	0.0903964	0.0451982	−	0.998978i	$-0.485608\pi$
$853$	2.64013	0.0903964	0.0451982	+	0.998978i	$0.485608\pi$
$854$	−22.9002	−0.783628
$855$	17.6776	0.604561
$856$	2.95811	0.101106
$857$	51.8234	1.77025	0.885127	−	0.465349i	$-0.154071\pi$
$857$	51.8234	1.77025	0.885127	+	0.465349i	$0.154071\pi$
$858$	−18.3219	−0.625498
$859$	−10.1640	−0.346790	−0.173395	−	0.984852i	$-0.555474\pi$
$859$	−10.1640	−0.346790	−0.173395	+	0.984852i	$0.555474\pi$
$860$	−12.4195	−0.423501
$861$	47.0635	1.60392
$862$	29.9005	1.01841
$863$	5.69497	0.193859	0.0969296	−	0.995291i	$-0.469098\pi$
$863$	5.69497	0.193859	0.0969296	+	0.995291i	$0.469098\pi$
$864$	−11.0607	−0.376291
$865$	66.5314	2.26213
$866$	−2.10175	−0.0714204
$867$	−31.4315	−1.06747
$868$	18.8645	0.640302
$869$	−14.4682	−0.490799
$870$	−26.8904	−0.911672
$871$	4.79741	0.162554
$872$	12.9724	0.439300
$873$	29.5206	0.999122
$874$	4.91566	0.166275
$875$	−20.0974	−0.679416
$876$	38.1688	1.28960
$877$	33.4559	1.12973	0.564863	−	0.825185i	$-0.308929\pi$
$877$	33.4559	1.12973	0.564863	+	0.825185i	$0.308929\pi$
$878$	−29.7140	−1.00280
$879$	−13.8881	−0.468436
$880$	−15.6075	−0.526130
$881$	−10.5076	−0.354009	−0.177004	−	0.984210i	$-0.556641\pi$
$881$	−10.5076	−0.354009	−0.177004	+	0.984210i	$0.556641\pi$
$882$	1.83508	0.0617904
$883$	8.18920	0.275589	0.137794	−	0.990461i	$-0.455999\pi$
$883$	8.18920	0.275589	0.137794	+	0.990461i	$0.455999\pi$
$884$	5.31596	0.178795
$885$	−47.2909	−1.58967
$886$	−29.1694	−0.979966
$887$	0.0122459	0.000411177 0	0.000205589	−	1.00000i	$-0.499935\pi$
$887$	0.0122459	0.000411177 0	0.000205589		1.00000i	$0.499935\pi$
$888$	29.7908	0.999715
$889$	−18.8657	−0.632735
$890$	−8.05778	−0.270097
$891$	−84.1740	−2.81994
$892$	−11.7745	−0.394239
$893$	−2.14466	−0.0717684
$894$	68.2755	2.28347
$895$	−62.0845	−2.07526
$896$	2.69798	0.0901333
$897$	15.5158	0.518057
$898$	−21.3994	−0.714107
$899$	22.5989	0.753715
$900$	14.6586	0.488620
$901$	52.3507	1.74406
$902$	32.7238	1.08958
$903$	38.5607	1.28322
$904$	−11.0538	−0.367644
$905$	14.4394	0.479981
$906$	−34.6871	−1.15240
$907$	−39.5002	−1.31158	−0.655791	−	0.754943i	$-0.727665\pi$
$907$	−39.5002	−1.31158	−0.655791	+	0.754943i	$0.727665\pi$
$908$	20.7359	0.688145
$909$	40.0826	1.32946
$910$	−7.39996	−0.245306
$911$	−7.57559	−0.250991	−0.125495	−	0.992094i	$-0.540052\pi$
$911$	−7.57559	−0.250991	−0.125495	+	0.992094i	$0.540052\pi$
$912$	−3.09428	−0.102462
$913$	35.4347	1.17272
$914$	25.2187	0.834161
$915$	70.6181	2.33456
$916$	−7.70226	−0.254490
$917$	−57.3070	−1.89244
$918$	57.6407	1.90243
$919$	58.2143	1.92031	0.960157	−	0.279463i	$-0.0901563\pi$
$919$	58.2143	1.92031	0.960157	+	0.279463i	$0.0901563\pi$
$920$	13.2172	0.435758
$921$	−35.7645	−1.17848
$922$	−18.4586	−0.607902
$923$	−6.50175	−0.214008
$924$	48.4592	1.59419
$925$	−21.4659	−0.705795
$926$	−30.6189	−1.00620
$927$	13.2318	0.434591
$928$	3.23208	0.106098
$929$	51.2285	1.68075	0.840376	−	0.542004i	$-0.182334\pi$
$929$	51.2285	1.68075	0.840376	+	0.542004i	$0.182334\pi$
$930$	−58.1730	−1.90757
$931$	0.279119	0.00914775
$932$	−13.0991	−0.429074
$933$	−35.0125	−1.14626
$934$	−20.9490	−0.685471
$935$	81.3361	2.65997
$936$	−6.70655	−0.219210
$937$	10.3375	0.337712	0.168856	−	0.985641i	$-0.445993\pi$
$937$	10.3375	0.337712	0.168856	+	0.985641i	$0.445993\pi$
$938$	−12.6886	−0.414298
$939$	68.6673	2.24087
$940$	−5.76655	−0.188084
$941$	35.7453	1.16526	0.582632	−	0.812736i	$-0.302023\pi$
$941$	35.7453	1.16526	0.582632	+	0.812736i	$0.302023\pi$
$942$	10.1313	0.330095
$943$	−27.7120	−0.902426
$944$	5.68410	0.185002
$945$	−80.2375	−2.61013
$946$	26.8117	0.871723
$947$	−6.11275	−0.198638	−0.0993189	−	0.995056i	$-0.531666\pi$
$947$	−6.11275	−0.198638	−0.0993189	+	0.995056i	$0.531666\pi$
$948$	−7.71250	−0.250490
$949$	12.5829	0.408459
$950$	2.22960	0.0723376
$951$	−31.0418	−1.00660
$952$	−14.0601	−0.455690
$953$	6.85567	0.222077	0.111038	−	0.993816i	$-0.464582\pi$
$953$	6.85567	0.222077	0.111038	+	0.993816i	$0.464582\pi$
$954$	−66.0451	−2.13829
$955$	8.77277	0.283880
$956$	3.58986	0.116104
$957$	58.0522	1.87656
$958$	−18.1492	−0.586374
$959$	45.6724	1.47484
$960$	−8.31986	−0.268522
$961$	17.8889	0.577060
$962$	9.82101	0.316642
$963$	19.4482	0.626710
$964$	−20.7327	−0.667756
$965$	13.8847	0.446964
$966$	−41.0375	−1.32036
$967$	49.1958	1.58203	0.791015	−	0.611796i	$-0.209553\pi$
$967$	49.1958	1.58203	0.791015	+	0.611796i	$0.209553\pi$
$968$	22.6942	0.729420
$969$	16.1253	0.518019
$970$	12.0730	0.387642
$971$	22.2753	0.714850	0.357425	−	0.933942i	$-0.383655\pi$
$971$	22.2753	0.714850	0.357425	+	0.933942i	$0.383655\pi$
$972$	−11.6884	−0.374905
$973$	1.45333	0.0465916
$974$	−12.2598	−0.392830
$975$	7.03750	0.225380
$976$	−8.48789	−0.271691
$977$	54.6672	1.74896	0.874479	−	0.485063i	$-0.161204\pi$
$977$	54.6672	1.74896	0.874479	+	0.485063i	$0.161204\pi$
$978$	67.0201	2.14307
$979$	17.3955	0.555961
$980$	0.750492	0.0239736
$981$	85.2876	2.72302
$982$	0.409512	0.0130681
$983$	−20.5308	−0.654832	−0.327416	−	0.944880i	$-0.606178\pi$
$983$	−20.5308	−0.654832	−0.327416	+	0.944880i	$0.606178\pi$
$984$	17.4439	0.556093
$985$	−4.76610	−0.151860
$986$	−16.8434	−0.536404
$987$	17.9043	0.569901
$988$	−1.02008	−0.0324530
$989$	−22.7053	−0.721988
$990$	−102.613	−3.26124
$991$	−33.6003	−1.06735	−0.533675	−	0.845690i	$-0.679189\pi$
$991$	−33.6003	−1.06735	−0.533675	+	0.845690i	$0.679189\pi$
$992$	6.99206	0.221998
$993$	−18.9395	−0.601028
$994$	17.1964	0.545436
$995$	10.6381	0.337250
$996$	18.8890	0.598522
$997$	33.3144	1.05508	0.527538	−	0.849531i	$-0.323115\pi$
$997$	33.3144	1.05508	0.527538	+	0.849531i	$0.323115\pi$
$998$	19.8019	0.626817
$999$	106.489	3.36916

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.2	✓	30	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.09428 q^{3} +1.00000 q^{4} +2.68879 q^{5} -3.09428 q^{6} +2.69798 q^{7} +1.00000 q^{8} +6.57455 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.09428 q^{3} +1.00000 q^{4} +2.68879 q^{5} -3.09428 q^{6} +2.69798 q^{7} +1.00000 q^{8} +6.57455 q^{9} +2.68879 q^{10} -5.80467 q^{11} -3.09428 q^{12} -1.02008 q^{13} +2.69798 q^{14} -8.31986 q^{15} +1.00000 q^{16} -5.21133 q^{17} +6.57455 q^{18} +1.00000 q^{19} +2.68879 q^{20} -8.34831 q^{21} -5.80467 q^{22} +4.91566 q^{23} -3.09428 q^{24} +2.22960 q^{25} -1.02008 q^{26} -11.0607 q^{27} +2.69798 q^{28} +3.23208 q^{29} -8.31986 q^{30} +6.99206 q^{31} +1.00000 q^{32} +17.9613 q^{33} -5.21133 q^{34} +7.25432 q^{35} +6.57455 q^{36} -9.62772 q^{37} +1.00000 q^{38} +3.15640 q^{39} +2.68879 q^{40} -5.63748 q^{41} -8.34831 q^{42} -4.61898 q^{43} -5.80467 q^{44} +17.6776 q^{45} +4.91566 q^{46} -2.14466 q^{47} -3.09428 q^{48} +0.279119 q^{49} +2.22960 q^{50} +16.1253 q^{51} -1.02008 q^{52} -10.0456 q^{53} -11.0607 q^{54} -15.6075 q^{55} +2.69798 q^{56} -3.09428 q^{57} +3.23208 q^{58} +5.68410 q^{59} -8.31986 q^{60} -8.48789 q^{61} +6.99206 q^{62} +17.7380 q^{63} +1.00000 q^{64} -2.74277 q^{65} +17.9613 q^{66} -4.70299 q^{67} -5.21133 q^{68} -15.2104 q^{69} +7.25432 q^{70} +6.37379 q^{71} +6.57455 q^{72} -12.3353 q^{73} -9.62772 q^{74} -6.89899 q^{75} +1.00000 q^{76} -15.6609 q^{77} +3.15640 q^{78} +2.49251 q^{79} +2.68879 q^{80} +14.5011 q^{81} -5.63748 q^{82} -6.10451 q^{83} -8.34831 q^{84} -14.0122 q^{85} -4.61898 q^{86} -10.0009 q^{87} -5.80467 q^{88} -2.99680 q^{89} +17.6776 q^{90} -2.75215 q^{91} +4.91566 q^{92} -21.6354 q^{93} -2.14466 q^{94} +2.68879 q^{95} -3.09428 q^{96} +4.49014 q^{97} +0.279119 q^{98} -38.1631 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

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