LMFDB - Embedded newform 4034.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.33333 q^{3} +1.00000 q^{4} +2.98893 q^{5} +1.33333 q^{6} +1.91777 q^{7} -1.00000 q^{8} -1.22223 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.33333 q^{3} +1.00000 q^{4} +2.98893 q^{5} +1.33333 q^{6} +1.91777 q^{7} -1.00000 q^{8} -1.22223 q^{9} -2.98893 q^{10} +2.33413 q^{11} -1.33333 q^{12} -1.24369 q^{13} -1.91777 q^{14} -3.98523 q^{15} +1.00000 q^{16} +4.75205 q^{17} +1.22223 q^{18} -6.69664 q^{19} +2.98893 q^{20} -2.55702 q^{21} -2.33413 q^{22} +2.52597 q^{23} +1.33333 q^{24} +3.93370 q^{25} +1.24369 q^{26} +5.62963 q^{27} +1.91777 q^{28} -4.11267 q^{29} +3.98523 q^{30} +0.469368 q^{31} -1.00000 q^{32} -3.11216 q^{33} -4.75205 q^{34} +5.73207 q^{35} -1.22223 q^{36} -4.62422 q^{37} +6.69664 q^{38} +1.65825 q^{39} -2.98893 q^{40} +2.98791 q^{41} +2.55702 q^{42} +2.32394 q^{43} +2.33413 q^{44} -3.65316 q^{45} -2.52597 q^{46} +4.98057 q^{47} -1.33333 q^{48} -3.32217 q^{49} -3.93370 q^{50} -6.33605 q^{51} -1.24369 q^{52} +9.38381 q^{53} -5.62963 q^{54} +6.97654 q^{55} -1.91777 q^{56} +8.92883 q^{57} +4.11267 q^{58} +8.98826 q^{59} -3.98523 q^{60} +4.47226 q^{61} -0.469368 q^{62} -2.34395 q^{63} +1.00000 q^{64} -3.71729 q^{65} +3.11216 q^{66} +10.1840 q^{67} +4.75205 q^{68} -3.36795 q^{69} -5.73207 q^{70} +8.59830 q^{71} +1.22223 q^{72} +1.10340 q^{73} +4.62422 q^{74} -5.24492 q^{75} -6.69664 q^{76} +4.47631 q^{77} -1.65825 q^{78} -4.62998 q^{79} +2.98893 q^{80} -3.83946 q^{81} -2.98791 q^{82} -17.7455 q^{83} -2.55702 q^{84} +14.2036 q^{85} -2.32394 q^{86} +5.48354 q^{87} -2.33413 q^{88} +8.16173 q^{89} +3.65316 q^{90} -2.38510 q^{91} +2.52597 q^{92} -0.625823 q^{93} -4.98057 q^{94} -20.0158 q^{95} +1.33333 q^{96} +12.8159 q^{97} +3.32217 q^{98} -2.85284 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) $ 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * 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
$3$	−1.33333	−0.769798	−0.384899	−	0.922959i	$-0.625764\pi$
$3$	−1.33333	−0.769798	−0.384899	+	0.922959i	$0.625764\pi$
$4$	1.00000	0.500000
$5$	2.98893	1.33669	0.668345	−	0.743852i	$-0.267003\pi$
$5$	2.98893	1.33669	0.668345	+	0.743852i	$0.267003\pi$
$6$	1.33333	0.544330
$7$	1.91777	0.724847	0.362424	−	0.932013i	$-0.381949\pi$
$7$	1.91777	0.724847	0.362424	+	0.932013i	$0.381949\pi$
$8$	−1.00000	−0.353553
$9$	−1.22223	−0.407410
$10$	−2.98893	−0.945182
$11$	2.33413	0.703766	0.351883	−	0.936044i	$-0.385541\pi$
$11$	2.33413	0.703766	0.351883	+	0.936044i	$0.385541\pi$
$12$	−1.33333	−0.384899
$13$	−1.24369	−0.344937	−0.172468	−	0.985015i	$-0.555174\pi$
$13$	−1.24369	−0.344937	−0.172468	+	0.985015i	$0.555174\pi$
$14$	−1.91777	−0.512545
$15$	−3.98523	−1.02898
$16$	1.00000	0.250000
$17$	4.75205	1.15254	0.576271	−	0.817259i	$-0.304507\pi$
$17$	4.75205	1.15254	0.576271	+	0.817259i	$0.304507\pi$
$18$	1.22223	0.288083
$19$	−6.69664	−1.53631	−0.768157	−	0.640262i	$-0.778826\pi$
$19$	−6.69664	−1.53631	−0.768157	+	0.640262i	$0.778826\pi$
$20$	2.98893	0.668345
$21$	−2.55702	−0.557986
$22$	−2.33413	−0.497638
$23$	2.52597	0.526701	0.263351	−	0.964700i	$-0.415172\pi$
$23$	2.52597	0.526701	0.263351	+	0.964700i	$0.415172\pi$
$24$	1.33333	0.272165
$25$	3.93370	0.786739
$26$	1.24369	0.243907
$27$	5.62963	1.08342
$28$	1.91777	0.362424
$29$	−4.11267	−0.763703	−0.381852	−	0.924224i	$-0.624713\pi$
$29$	−4.11267	−0.763703	−0.381852	+	0.924224i	$0.624713\pi$
$30$	3.98523	0.727600
$31$	0.469368	0.0843010	0.0421505	−	0.999111i	$-0.486579\pi$
$31$	0.469368	0.0843010	0.0421505	+	0.999111i	$0.486579\pi$
$32$	−1.00000	−0.176777
$33$	−3.11216	−0.541758
$34$	−4.75205	−0.814970
$35$	5.73207	0.968896
$36$	−1.22223	−0.203705
$37$	−4.62422	−0.760217	−0.380109	−	0.924942i	$-0.624113\pi$
$37$	−4.62422	−0.760217	−0.380109	+	0.924942i	$0.624113\pi$
$38$	6.69664	1.08634
$39$	1.65825	0.265532
$40$	−2.98893	−0.472591
$41$	2.98791	0.466634	0.233317	−	0.972401i	$-0.425042\pi$
$41$	2.98791	0.466634	0.233317	+	0.972401i	$0.425042\pi$
$42$	2.55702	0.394556
$43$	2.32394	0.354397	0.177199	−	0.984175i	$-0.443297\pi$
$43$	2.32394	0.354397	0.177199	+	0.984175i	$0.443297\pi$
$44$	2.33413	0.351883
$45$	−3.65316	−0.544581
$46$	−2.52597	−0.372434
$47$	4.98057	0.726491	0.363245	−	0.931693i	$-0.381669\pi$
$47$	4.98057	0.726491	0.363245	+	0.931693i	$0.381669\pi$
$48$	−1.33333	−0.192450
$49$	−3.32217	−0.474596
$50$	−3.93370	−0.556309
$51$	−6.33605	−0.887225
$52$	−1.24369	−0.172468
$53$	9.38381	1.28897	0.644483	−	0.764619i	$-0.277073\pi$
$53$	9.38381	1.28897	0.644483	+	0.764619i	$0.277073\pi$
$54$	−5.62963	−0.766095
$55$	6.97654	0.940717
$56$	−1.91777	−0.256272
$57$	8.92883	1.18265
$58$	4.11267	0.540020
$59$	8.98826	1.17017	0.585086	−	0.810972i	$-0.301061\pi$
$59$	8.98826	1.17017	0.585086	+	0.810972i	$0.301061\pi$
$60$	−3.98523	−0.514491
$61$	4.47226	0.572614	0.286307	−	0.958138i	$-0.407572\pi$
$61$	4.47226	0.572614	0.286307	+	0.958138i	$0.407572\pi$
$62$	−0.469368	−0.0596098
$63$	−2.34395	−0.295310
$64$	1.00000	0.125000
$65$	−3.71729	−0.461074
$66$	3.11216	0.383081
$67$	10.1840	1.24418	0.622089	−	0.782947i	$-0.286284\pi$
$67$	10.1840	1.24418	0.622089	+	0.782947i	$0.286284\pi$
$68$	4.75205	0.576271
$69$	−3.36795	−0.405454
$70$	−5.73207	−0.685113
$71$	8.59830	1.02043	0.510215	−	0.860047i	$-0.329566\pi$
$71$	8.59830	1.02043	0.510215	+	0.860047i	$0.329566\pi$
$72$	1.22223	0.144041
$73$	1.10340	0.129143	0.0645714	−	0.997913i	$-0.479432\pi$
$73$	1.10340	0.129143	0.0645714	+	0.997913i	$0.479432\pi$
$74$	4.62422	0.537555
$75$	−5.24492	−0.605631
$76$	−6.69664	−0.768157
$77$	4.47631	0.510123
$78$	−1.65825	−0.187759
$79$	−4.62998	−0.520913	−0.260457	−	0.965486i	$-0.583873\pi$
$79$	−4.62998	−0.520913	−0.260457	+	0.965486i	$0.583873\pi$
$80$	2.98893	0.334172
$81$	−3.83946	−0.426606
$82$	−2.98791	−0.329960
$83$	−17.7455	−1.94782	−0.973912	−	0.226927i	$-0.927132\pi$
$83$	−17.7455	−1.94782	−0.973912	+	0.226927i	$0.927132\pi$
$84$	−2.55702	−0.278993
$85$	14.2036	1.54059
$86$	−2.32394	−0.250597
$87$	5.48354	0.587897
$88$	−2.33413	−0.248819
$89$	8.16173	0.865142	0.432571	−	0.901600i	$-0.357607\pi$
$89$	8.16173	0.865142	0.432571	+	0.901600i	$0.357607\pi$
$90$	3.65316	0.385077
$91$	−2.38510	−0.250027
$92$	2.52597	0.263351
$93$	−0.625823	−0.0648948
$94$	−4.98057	−0.513707
$95$	−20.0158	−2.05357
$96$	1.33333	0.136082
$97$	12.8159	1.30125	0.650627	−	0.759398i	$-0.274506\pi$
$97$	12.8159	1.30125	0.650627	+	0.759398i	$0.274506\pi$
$98$	3.32217	0.335590
$99$	−2.85284	−0.286722
$100$	3.93370	0.393370
$101$	7.41703	0.738022	0.369011	−	0.929425i	$-0.379696\pi$
$101$	7.41703	0.738022	0.369011	+	0.929425i	$0.379696\pi$
$102$	6.33605	0.627363
$103$	9.01476	0.888250	0.444125	−	0.895965i	$-0.353515\pi$
$103$	9.01476	0.888250	0.444125	+	0.895965i	$0.353515\pi$
$104$	1.24369	0.121954
$105$	−7.64274	−0.745855
$106$	−9.38381	−0.911436
$107$	5.10024	0.493059	0.246529	−	0.969135i	$-0.420710\pi$
$107$	5.10024	0.493059	0.246529	+	0.969135i	$0.420710\pi$
$108$	5.62963	0.541711
$109$	−4.60448	−0.441030	−0.220515	−	0.975384i	$-0.570774\pi$
$109$	−4.60448	−0.441030	−0.220515	+	0.975384i	$0.570774\pi$
$110$	−6.97654	−0.665187
$111$	6.16561	0.585214
$112$	1.91777	0.181212
$113$	19.0022	1.78758	0.893790	−	0.448487i	$-0.148037\pi$
$113$	19.0022	1.78758	0.893790	+	0.448487i	$0.148037\pi$
$114$	−8.92883	−0.836261
$115$	7.54995	0.704036
$116$	−4.11267	−0.381852
$117$	1.52007	0.140531
$118$	−8.98826	−0.827436
$119$	9.11333	0.835417
$120$	3.98523	0.363800
$121$	−5.55185	−0.504713
$122$	−4.47226	−0.404899
$123$	−3.98388	−0.359214
$124$	0.469368	0.0421505
$125$	−3.18710	−0.285063
$126$	2.34395	0.208816
$127$	−17.8145	−1.58079	−0.790393	−	0.612601i	$-0.790123\pi$
$127$	−17.8145	−1.58079	−0.790393	+	0.612601i	$0.790123\pi$
$128$	−1.00000	−0.0883883
$129$	−3.09857	−0.272814
$130$	3.71729	0.326028
$131$	−15.2437	−1.33185	−0.665923	−	0.746020i	$-0.731962\pi$
$131$	−15.2437	−1.33185	−0.665923	+	0.746020i	$0.731962\pi$
$132$	−3.11216	−0.270879
$133$	−12.8426	−1.11359
$134$	−10.1840	−0.879767
$135$	16.8266	1.44820
$136$	−4.75205	−0.407485
$137$	−19.6421	−1.67814	−0.839068	−	0.544026i	$-0.816899\pi$
$137$	−19.6421	−1.67814	−0.839068	+	0.544026i	$0.816899\pi$
$138$	3.36795	0.286699
$139$	1.71462	0.145432	0.0727162	−	0.997353i	$-0.476833\pi$
$139$	1.71462	0.145432	0.0727162	+	0.997353i	$0.476833\pi$
$140$	5.73207	0.484448
$141$	−6.64074	−0.559251
$142$	−8.59830	−0.721553
$143$	−2.90293	−0.242755
$144$	−1.22223	−0.101853
$145$	−12.2925	−1.02083
$146$	−1.10340	−0.0913178
$147$	4.42955	0.365343
$148$	−4.62422	−0.380109
$149$	−17.0292	−1.39509	−0.697543	−	0.716542i	$-0.745724\pi$
$149$	−17.0292	−1.39509	−0.697543	+	0.716542i	$0.745724\pi$
$150$	5.24492	0.428246
$151$	23.9792	1.95140	0.975698	−	0.219118i	$-0.0703181\pi$
$151$	23.9792	1.95140	0.975698	+	0.219118i	$0.0703181\pi$
$152$	6.69664	0.543169
$153$	−5.80811	−0.469558
$154$	−4.47631	−0.360711
$155$	1.40291	0.112684
$156$	1.65825	0.132766
$157$	−7.85769	−0.627112	−0.313556	−	0.949570i	$-0.601520\pi$
$157$	−7.85769	−0.627112	−0.313556	+	0.949570i	$0.601520\pi$
$158$	4.62998	0.368341
$159$	−12.5117	−0.992244
$160$	−2.98893	−0.236296
$161$	4.84422	0.381778
$162$	3.83946	0.301656
$163$	−12.6697	−0.992367	−0.496183	−	0.868218i	$-0.665266\pi$
$163$	−12.6697	−0.992367	−0.496183	+	0.868218i	$0.665266\pi$
$164$	2.98791	0.233317
$165$	−9.30203	−0.724162
$166$	17.7455	1.37732
$167$	10.8427	0.839031	0.419515	−	0.907748i	$-0.362200\pi$
$167$	10.8427	0.839031	0.419515	+	0.907748i	$0.362200\pi$
$168$	2.55702	0.197278
$169$	−11.4532	−0.881019
$170$	−14.2036	−1.08936
$171$	8.18484	0.625910
$172$	2.32394	0.177199
$173$	−15.9526	−1.21285	−0.606425	−	0.795141i	$-0.707397\pi$
$173$	−15.9526	−1.21285	−0.606425	+	0.795141i	$0.707397\pi$
$174$	−5.48354	−0.415706
$175$	7.54391	0.570266
$176$	2.33413	0.175941
$177$	−11.9843	−0.900796
$178$	−8.16173	−0.611748
$179$	19.9609	1.49195	0.745973	−	0.665976i	$-0.231985\pi$
$179$	19.9609	1.49195	0.745973	+	0.665976i	$0.231985\pi$
$180$	−3.65316	−0.272291
$181$	−14.5803	−1.08375	−0.541874	−	0.840460i	$-0.682285\pi$
$181$	−14.5803	−1.08375	−0.541874	+	0.840460i	$0.682285\pi$
$182$	2.38510	0.176796
$183$	−5.96300	−0.440798
$184$	−2.52597	−0.186217
$185$	−13.8215	−1.01617
$186$	0.625823	0.0458875
$187$	11.0919	0.811120
$188$	4.98057	0.363245
$189$	10.7963	0.785316
$190$	20.0158	1.45210
$191$	17.0309	1.23231	0.616157	−	0.787623i	$-0.288689\pi$
$191$	17.0309	1.23231	0.616157	+	0.787623i	$0.288689\pi$
$192$	−1.33333	−0.0962248
$193$	23.7253	1.70779	0.853893	−	0.520448i	$-0.174235\pi$
$193$	23.7253	1.70779	0.853893	+	0.520448i	$0.174235\pi$
$194$	−12.8159	−0.920125
$195$	4.95638	0.354934
$196$	−3.32217	−0.237298
$197$	22.1157	1.57568	0.787838	−	0.615882i	$-0.211200\pi$
$197$	22.1157	1.57568	0.787838	+	0.615882i	$0.211200\pi$
$198$	2.85284	0.202743
$199$	26.2679	1.86208	0.931041	−	0.364916i	$-0.118902\pi$
$199$	26.2679	1.86208	0.931041	+	0.364916i	$0.118902\pi$
$200$	−3.93370	−0.278154
$201$	−13.5787	−0.957766
$202$	−7.41703	−0.521860
$203$	−7.88713	−0.553568
$204$	−6.33605	−0.443613
$205$	8.93066	0.623745
$206$	−9.01476	−0.628088
$207$	−3.08732	−0.214584
$208$	−1.24369	−0.0862342
$209$	−15.6308	−1.08121
$210$	7.64274	0.527399
$211$	21.1043	1.45288	0.726439	−	0.687230i	$-0.241174\pi$
$211$	21.1043	1.45288	0.726439	+	0.687230i	$0.241174\pi$
$212$	9.38381	0.644483
$213$	−11.4644	−0.785525
$214$	−5.10024	−0.348645
$215$	6.94608	0.473719
$216$	−5.62963	−0.383048
$217$	0.900138	0.0611054
$218$	4.60448	0.311855
$219$	−1.47119	−0.0994140
$220$	6.97654	0.470358
$221$	−5.91007	−0.397554
$222$	−6.16561	−0.413809
$223$	12.5620	0.841213	0.420607	−	0.907243i	$-0.361817\pi$
$223$	12.5620	0.841213	0.420607	+	0.907243i	$0.361817\pi$
$224$	−1.91777	−0.128136
$225$	−4.80789	−0.320526
$226$	−19.0022	−1.26401
$227$	−0.728356	−0.0483427	−0.0241713	−	0.999708i	$-0.507695\pi$
$227$	−0.728356	−0.0483427	−0.0241713	+	0.999708i	$0.507695\pi$
$228$	8.92883	0.591326
$229$	3.37043	0.222724	0.111362	−	0.993780i	$-0.464479\pi$
$229$	3.37043	0.222724	0.111362	+	0.993780i	$0.464479\pi$
$230$	−7.54995	−0.497829
$231$	−5.96840	−0.392692
$232$	4.11267	0.270010
$233$	−4.65253	−0.304797	−0.152399	−	0.988319i	$-0.548700\pi$
$233$	−4.65253	−0.304797	−0.152399	+	0.988319i	$0.548700\pi$
$234$	−1.52007	−0.0993703
$235$	14.8866	0.971093
$236$	8.98826	0.585086
$237$	6.17329	0.400998
$238$	−9.11333	−0.590729
$239$	−11.4546	−0.740935	−0.370467	−	0.928845i	$-0.620802\pi$
$239$	−11.4546	−0.740935	−0.370467	+	0.928845i	$0.620802\pi$
$240$	−3.98523	−0.257245
$241$	−18.7577	−1.20829	−0.604145	−	0.796874i	$-0.706485\pi$
$241$	−18.7577	−1.20829	−0.604145	+	0.796874i	$0.706485\pi$
$242$	5.55185	0.356886
$243$	−11.7696	−0.755021
$244$	4.47226	0.286307
$245$	−9.92974	−0.634388
$246$	3.98388	0.254003
$247$	8.32852	0.529931
$248$	−0.469368	−0.0298049
$249$	23.6606	1.49943
$250$	3.18710	0.201570
$251$	15.4862	0.977480	0.488740	−	0.872429i	$-0.337457\pi$
$251$	15.4862	0.977480	0.488740	+	0.872429i	$0.337457\pi$
$252$	−2.34395	−0.147655
$253$	5.89594	0.370674
$254$	17.8145	1.11778
$255$	−18.9380	−1.18594
$256$	1.00000	0.0625000
$257$	−20.0194	−1.24878	−0.624389	−	0.781114i	$-0.714652\pi$
$257$	−20.0194	−1.24878	−0.624389	+	0.781114i	$0.714652\pi$
$258$	3.09857	0.192909
$259$	−8.86818	−0.551042
$260$	−3.71729	−0.230537
$261$	5.02663	0.311141
$262$	15.2437	0.941758
$263$	−17.1130	−1.05523	−0.527617	−	0.849483i	$-0.676914\pi$
$263$	−17.1130	−1.05523	−0.527617	+	0.849483i	$0.676914\pi$
$264$	3.11216	0.191540
$265$	28.0475	1.72295
$266$	12.8426	0.787429
$267$	−10.8823	−0.665985
$268$	10.1840	0.622089
$269$	−2.57418	−0.156950	−0.0784752	−	0.996916i	$-0.525005\pi$
$269$	−2.57418	−0.156950	−0.0784752	+	0.996916i	$0.525005\pi$
$270$	−16.8266	−1.02403
$271$	−1.71085	−0.103926	−0.0519632	−	0.998649i	$-0.516548\pi$
$271$	−1.71085	−0.103926	−0.0519632	+	0.998649i	$0.516548\pi$
$272$	4.75205	0.288136
$273$	3.18013	0.192470
$274$	19.6421	1.18662
$275$	9.18175	0.553680
$276$	−3.36795	−0.202727
$277$	20.8412	1.25222	0.626112	−	0.779733i	$-0.284645\pi$
$277$	20.8412	1.25222	0.626112	+	0.779733i	$0.284645\pi$
$278$	−1.71462	−0.102836
$279$	−0.573677	−0.0343451
$280$	−5.73207	−0.342557
$281$	12.3990	0.739665	0.369832	−	0.929098i	$-0.379415\pi$
$281$	12.3990	0.739665	0.369832	+	0.929098i	$0.379415\pi$
$282$	6.64074	0.395451
$283$	−13.2924	−0.790151	−0.395076	−	0.918649i	$-0.629282\pi$
$283$	−13.2924	−0.790151	−0.395076	+	0.918649i	$0.629282\pi$
$284$	8.59830	0.510215
$285$	26.6876	1.58084
$286$	2.90293	0.171654
$287$	5.73012	0.338238
$288$	1.22223	0.0720207
$289$	5.58201	0.328354
$290$	12.2925	0.721839
$291$	−17.0878	−1.00170
$292$	1.10340	0.0645714
$293$	−11.6140	−0.678498	−0.339249	−	0.940697i	$-0.610173\pi$
$293$	−11.6140	−0.678498	−0.339249	+	0.940697i	$0.610173\pi$
$294$	−4.42955	−0.258337
$295$	26.8653	1.56416
$296$	4.62422	0.268777
$297$	13.1403	0.762476
$298$	17.0292	0.986475
$299$	−3.14152	−0.181679
$300$	−5.24492	−0.302815
$301$	4.45677	0.256884
$302$	−23.9792	−1.37985
$303$	−9.88934	−0.568128
$304$	−6.69664	−0.384078
$305$	13.3673	0.765408
$306$	5.80811	0.332027
$307$	16.2335	0.926495	0.463247	−	0.886229i	$-0.346684\pi$
$307$	16.2335	0.926495	0.463247	+	0.886229i	$0.346684\pi$
$308$	4.47631	0.255061
$309$	−12.0196	−0.683774
$310$	−1.40291	−0.0796798
$311$	26.0622	1.47785	0.738925	−	0.673788i	$-0.235334\pi$
$311$	26.0622	1.47785	0.738925	+	0.673788i	$0.235334\pi$
$312$	−1.65825	−0.0938797
$313$	5.14258	0.290676	0.145338	−	0.989382i	$-0.453573\pi$
$313$	5.14258	0.290676	0.145338	+	0.989382i	$0.453573\pi$
$314$	7.85769	0.443435
$315$	−7.00591	−0.394738
$316$	−4.62998	−0.260457
$317$	9.06819	0.509321	0.254660	−	0.967031i	$-0.418036\pi$
$317$	9.06819	0.509321	0.254660	+	0.967031i	$0.418036\pi$
$318$	12.5117	0.701622
$319$	−9.59949	−0.537468
$320$	2.98893	0.167086
$321$	−6.80030	−0.379556
$322$	−4.84422	−0.269958
$323$	−31.8228	−1.77067
$324$	−3.83946	−0.213303
$325$	−4.89229	−0.271375
$326$	12.6697	0.701709
$327$	6.13930	0.339504
$328$	−2.98791	−0.164980
$329$	9.55157	0.526595
$330$	9.30203	0.512060
$331$	17.7206	0.974013	0.487006	−	0.873398i	$-0.338089\pi$
$331$	17.7206	0.974013	0.487006	+	0.873398i	$0.338089\pi$
$332$	−17.7455	−0.973912
$333$	5.65187	0.309720
$334$	−10.8427	−0.593284
$335$	30.4394	1.66308
$336$	−2.55702	−0.139497
$337$	−1.10289	−0.0600782	−0.0300391	−	0.999549i	$-0.509563\pi$
$337$	−1.10289	−0.0600782	−0.0300391	+	0.999549i	$0.509563\pi$
$338$	11.4532	0.622974
$339$	−25.3362	−1.37608
$340$	14.2036	0.770296
$341$	1.09557	0.0593282
$342$	−8.18484	−0.442585
$343$	−19.7955	−1.06886
$344$	−2.32394	−0.125298
$345$	−10.0666	−0.541966
$346$	15.9526	0.857615
$347$	18.1744	0.975654	0.487827	−	0.872940i	$-0.337790\pi$
$347$	18.1744	0.975654	0.487827	+	0.872940i	$0.337790\pi$
$348$	5.48354	0.293949
$349$	18.0704	0.967288	0.483644	−	0.875265i	$-0.339313\pi$
$349$	18.0704	0.967288	0.483644	+	0.875265i	$0.339313\pi$
$350$	−7.54391	−0.403239
$351$	−7.00150	−0.373712
$352$	−2.33413	−0.124409
$353$	−16.6377	−0.885536	−0.442768	−	0.896636i	$-0.646003\pi$
$353$	−16.6377	−0.885536	−0.442768	+	0.896636i	$0.646003\pi$
$354$	11.9843	0.636959
$355$	25.6997	1.36400
$356$	8.16173	0.432571
$357$	−12.1511	−0.643103
$358$	−19.9609	−1.05496
$359$	20.5853	1.08645	0.543226	−	0.839586i	$-0.317203\pi$
$359$	20.5853	1.08645	0.543226	+	0.839586i	$0.317203\pi$
$360$	3.65316	0.192539
$361$	25.8449	1.36026
$362$	14.5803	0.766326
$363$	7.40245	0.388528
$364$	−2.38510	−0.125013
$365$	3.29798	0.172624
$366$	5.96300	0.311691
$367$	5.46990	0.285526	0.142763	−	0.989757i	$-0.454401\pi$
$367$	5.46990	0.285526	0.142763	+	0.989757i	$0.454401\pi$
$368$	2.52597	0.131675
$369$	−3.65192	−0.190111
$370$	13.8215	0.718544
$371$	17.9960	0.934304
$372$	−0.625823	−0.0324474
$373$	−33.7563	−1.74784	−0.873918	−	0.486073i	$-0.838429\pi$
$373$	−33.7563	−1.74784	−0.873918	+	0.486073i	$0.838429\pi$
$374$	−11.0919	−0.573548
$375$	4.24946	0.219441
$376$	−4.98057	−0.256853
$377$	5.11487	0.263429
$378$	−10.7963	−0.555302
$379$	15.1793	0.779707	0.389854	−	0.920877i	$-0.372526\pi$
$379$	15.1793	0.779707	0.389854	+	0.920877i	$0.372526\pi$
$380$	−20.0158	−1.02679
$381$	23.7527	1.21689
$382$	−17.0309	−0.871378
$383$	17.7641	0.907705	0.453852	−	0.891077i	$-0.350049\pi$
$383$	17.7641	0.907705	0.453852	+	0.891077i	$0.350049\pi$
$384$	1.33333	0.0680412
$385$	13.3794	0.681876
$386$	−23.7253	−1.20759
$387$	−2.84039	−0.144385
$388$	12.8159	0.650627
$389$	15.3930	0.780456	0.390228	−	0.920718i	$-0.372396\pi$
$389$	15.3930	0.780456	0.390228	+	0.920718i	$0.372396\pi$
$390$	−4.95638	−0.250976
$391$	12.0035	0.607045
$392$	3.32217	0.167795
$393$	20.3249	1.02525
$394$	−22.1157	−1.11417
$395$	−13.8387	−0.696299
$396$	−2.85284	−0.143361
$397$	26.4279	1.32638	0.663189	−	0.748452i	$-0.269202\pi$
$397$	26.4279	1.32638	0.663189	+	0.748452i	$0.269202\pi$
$398$	−26.2679	−1.31669
$399$	17.1234	0.857242
$400$	3.93370	0.196685
$401$	−3.16838	−0.158221	−0.0791106	−	0.996866i	$-0.525208\pi$
$401$	−3.16838	−0.158221	−0.0791106	+	0.996866i	$0.525208\pi$
$402$	13.5787	0.677243
$403$	−0.583747	−0.0290785
$404$	7.41703	0.369011
$405$	−11.4759	−0.570240
$406$	7.88713	0.391432
$407$	−10.7935	−0.535015
$408$	6.33605	0.313681
$409$	−35.3341	−1.74716	−0.873579	−	0.486682i	$-0.838207\pi$
$409$	−35.3341	−1.74716	−0.873579	+	0.486682i	$0.838207\pi$
$410$	−8.93066	−0.441054
$411$	26.1894	1.29183
$412$	9.01476	0.444125
$413$	17.2374	0.848196
$414$	3.08732	0.151734
$415$	−53.0401	−2.60364
$416$	1.24369	0.0609768
$417$	−2.28616	−0.111954
$418$	15.6308	0.764528
$419$	−2.86936	−0.140177	−0.0700887	−	0.997541i	$-0.522328\pi$
$419$	−2.86936	−0.140177	−0.0700887	+	0.997541i	$0.522328\pi$
$420$	−7.64274	−0.372927
$421$	−4.13528	−0.201541	−0.100771	−	0.994910i	$-0.532131\pi$
$421$	−4.13528	−0.201541	−0.100771	+	0.994910i	$0.532131\pi$
$422$	−21.1043	−1.02734
$423$	−6.08741	−0.295980
$424$	−9.38381	−0.455718
$425$	18.6931	0.906750
$426$	11.4644	0.555450
$427$	8.57675	0.415058
$428$	5.10024	0.246529
$429$	3.87056	0.186872
$430$	−6.94608	−0.334970
$431$	−13.1289	−0.632398	−0.316199	−	0.948693i	$-0.602407\pi$
$431$	−13.1289	−0.632398	−0.316199	+	0.948693i	$0.602407\pi$
$432$	5.62963	0.270856
$433$	22.7745	1.09447	0.547236	−	0.836978i	$-0.315680\pi$
$433$	22.7745	1.09447	0.547236	+	0.836978i	$0.315680\pi$
$434$	−0.900138	−0.0432080
$435$	16.3899	0.785836
$436$	−4.60448	−0.220515
$437$	−16.9155	−0.809178
$438$	1.47119	0.0702963
$439$	33.3151	1.59004	0.795021	−	0.606583i	$-0.207460\pi$
$439$	33.3151	1.59004	0.795021	+	0.606583i	$0.207460\pi$
$440$	−6.97654	−0.332594
$441$	4.06046	0.193355
$442$	5.91007	0.281113
$443$	−30.4373	−1.44612	−0.723059	−	0.690786i	$-0.757265\pi$
$443$	−30.4373	−1.44612	−0.723059	+	0.690786i	$0.757265\pi$
$444$	6.16561	0.292607
$445$	24.3948	1.15643
$446$	−12.5620	−0.594828
$447$	22.7055	1.07394
$448$	1.91777	0.0906059
$449$	6.34738	0.299551	0.149776	−	0.988720i	$-0.452145\pi$
$449$	6.34738	0.299551	0.149776	+	0.988720i	$0.452145\pi$
$450$	4.80789	0.226646
$451$	6.97417	0.328401
$452$	19.0022	0.893790
$453$	−31.9721	−1.50218
$454$	0.728356	0.0341834
$455$	−7.12890	−0.334208
$456$	−8.92883	−0.418131
$457$	−1.55505	−0.0727423	−0.0363711	−	0.999338i	$-0.511580\pi$
$457$	−1.55505	−0.0727423	−0.0363711	+	0.999338i	$0.511580\pi$
$458$	−3.37043	−0.157490
$459$	26.7523	1.24869
$460$	7.54995	0.352018
$461$	30.9703	1.44243	0.721215	−	0.692712i	$-0.243584\pi$
$461$	30.9703	1.44243	0.721215	+	0.692712i	$0.243584\pi$
$462$	5.96840	0.277675
$463$	28.2842	1.31448	0.657239	−	0.753682i	$-0.271724\pi$
$463$	28.2842	1.31448	0.657239	+	0.753682i	$0.271724\pi$
$464$	−4.11267	−0.190926
$465$	−1.87054	−0.0867442
$466$	4.65253	0.215524
$467$	14.0223	0.648873	0.324436	−	0.945908i	$-0.394825\pi$
$467$	14.0223	0.648873	0.324436	+	0.945908i	$0.394825\pi$
$468$	1.52007	0.0702654
$469$	19.5306	0.901839
$470$	−14.8866	−0.686666
$471$	10.4769	0.482750
$472$	−8.98826	−0.413718
$473$	5.42437	0.249413
$474$	−6.17329	−0.283549
$475$	−26.3425	−1.20868
$476$	9.11333	0.417709
$477$	−11.4692	−0.525138
$478$	11.4546	0.523920
$479$	1.21117	0.0553400	0.0276700	−	0.999617i	$-0.491191\pi$
$479$	1.21117	0.0553400	0.0276700	+	0.999617i	$0.491191\pi$
$480$	3.98523	0.181900
$481$	5.75109	0.262227
$482$	18.7577	0.854390
$483$	−6.45894	−0.293892
$484$	−5.55185	−0.252357
$485$	38.3057	1.73937
$486$	11.7696	0.533881
$487$	4.85559	0.220028	0.110014	−	0.993930i	$-0.464910\pi$
$487$	4.85559	0.220028	0.110014	+	0.993930i	$0.464910\pi$
$488$	−4.47226	−0.202450
$489$	16.8929	0.763922
$490$	9.92974	0.448580
$491$	−2.42603	−0.109485	−0.0547425	−	0.998501i	$-0.517434\pi$
$491$	−2.42603	−0.109485	−0.0547425	+	0.998501i	$0.517434\pi$
$492$	−3.98388	−0.179607
$493$	−19.5436	−0.880200
$494$	−8.32852	−0.374718
$495$	−8.52695	−0.383258
$496$	0.469368	0.0210753
$497$	16.4895	0.739656
$498$	−23.6606	−1.06026
$499$	−8.45826	−0.378644	−0.189322	−	0.981915i	$-0.560629\pi$
$499$	−8.45826	−0.378644	−0.189322	+	0.981915i	$0.560629\pi$
$500$	−3.18710	−0.142532
$501$	−14.4569	−0.645885
$502$	−15.4862	−0.691183
$503$	−15.1942	−0.677476	−0.338738	−	0.940881i	$-0.610000\pi$
$503$	−15.1942	−0.677476	−0.338738	+	0.940881i	$0.610000\pi$
$504$	2.34395	0.104408
$505$	22.1690	0.986506
$506$	−5.89594	−0.262106
$507$	15.2709	0.678207
$508$	−17.8145	−0.790393
$509$	−36.3495	−1.61116	−0.805582	−	0.592485i	$-0.798147\pi$
$509$	−36.3495	−1.61116	−0.805582	+	0.592485i	$0.798147\pi$
$510$	18.9380	0.838590
$511$	2.11606	0.0936089
$512$	−1.00000	−0.0441942
$513$	−37.6996	−1.66448
$514$	20.0194	0.883019
$515$	26.9445	1.18732
$516$	−3.09857	−0.136407
$517$	11.6253	0.511280
$518$	8.86818	0.389645
$519$	21.2700	0.933650
$520$	3.71729	0.163014
$521$	10.5858	0.463773	0.231887	−	0.972743i	$-0.425510\pi$
$521$	10.5858	0.463773	0.231887	+	0.972743i	$0.425510\pi$
$522$	−5.02663	−0.220010
$523$	−1.45737	−0.0637263	−0.0318631	−	0.999492i	$-0.510144\pi$
$523$	−1.45737	−0.0637263	−0.0318631	+	0.999492i	$0.510144\pi$
$524$	−15.2437	−0.665923
$525$	−10.0585	−0.438990
$526$	17.1130	0.746163
$527$	2.23046	0.0971605
$528$	−3.11216	−0.135439
$529$	−16.6195	−0.722586
$530$	−28.0475	−1.21831
$531$	−10.9857	−0.476740
$532$	−12.8426	−0.556797
$533$	−3.71603	−0.160959
$534$	10.8823	0.470922
$535$	15.2443	0.659067
$536$	−10.1840	−0.439883
$537$	−26.6144	−1.14850
$538$	2.57418	0.110981
$539$	−7.75438	−0.334005
$540$	16.8266	0.724100
$541$	−28.1078	−1.20845	−0.604225	−	0.796814i	$-0.706517\pi$
$541$	−28.1078	−1.20845	−0.604225	+	0.796814i	$0.706517\pi$
$542$	1.71085	0.0734871
$543$	19.4404	0.834267
$544$	−4.75205	−0.203743
$545$	−13.7625	−0.589520
$546$	−3.18013	−0.136097
$547$	−32.4409	−1.38707	−0.693536	−	0.720422i	$-0.743948\pi$
$547$	−32.4409	−1.38707	−0.693536	+	0.720422i	$0.743948\pi$
$548$	−19.6421	−0.839068
$549$	−5.46614	−0.233289
$550$	−9.18175	−0.391511
$551$	27.5410	1.17329
$552$	3.36795	0.143350
$553$	−8.87922	−0.377583
$554$	−20.8412	−0.885456
$555$	18.4286	0.782250
$556$	1.71462	0.0727162
$557$	−39.2749	−1.66413	−0.832066	−	0.554677i	$-0.812842\pi$
$557$	−39.2749	−1.66413	−0.832066	+	0.554677i	$0.812842\pi$
$558$	0.573677	0.0242857
$559$	−2.89025	−0.122245
$560$	5.73207	0.242224
$561$	−14.7892	−0.624399
$562$	−12.3990	−0.523022
$563$	46.3256	1.95239	0.976195	−	0.216896i	$-0.0695931\pi$
$563$	46.3256	1.95239	0.976195	+	0.216896i	$0.0695931\pi$
$564$	−6.64074	−0.279626
$565$	56.7963	2.38944
$566$	13.2924	0.558721
$567$	−7.36318	−0.309224
$568$	−8.59830	−0.360777
$569$	−1.90580	−0.0798952	−0.0399476	−	0.999202i	$-0.512719\pi$
$569$	−1.90580	−0.0798952	−0.0399476	+	0.999202i	$0.512719\pi$
$570$	−26.6876	−1.11782
$571$	26.0415	1.08980	0.544901	−	0.838500i	$-0.316567\pi$
$571$	26.0415	1.08980	0.544901	+	0.838500i	$0.316567\pi$
$572$	−2.90293	−0.121377
$573$	−22.7078	−0.948634
$574$	−5.73012	−0.239171
$575$	9.93640	0.414377
$576$	−1.22223	−0.0509263
$577$	−10.5560	−0.439451	−0.219725	−	0.975562i	$-0.570516\pi$
$577$	−10.5560	−0.439451	−0.219725	+	0.975562i	$0.570516\pi$
$578$	−5.58201	−0.232181
$579$	−31.6337	−1.31465
$580$	−12.2925	−0.510417
$581$	−34.0318	−1.41188
$582$	17.0878	0.708311
$583$	21.9030	0.907130
$584$	−1.10340	−0.0456589
$585$	4.54339	0.187846
$586$	11.6140	0.479771
$587$	−31.2569	−1.29011	−0.645054	−	0.764137i	$-0.723165\pi$
$587$	−31.2569	−1.29011	−0.645054	+	0.764137i	$0.723165\pi$
$588$	4.42955	0.182672
$589$	−3.14319	−0.129513
$590$	−26.8653	−1.10603
$591$	−29.4875	−1.21295
$592$	−4.62422	−0.190054
$593$	−4.17751	−0.171550	−0.0857748	−	0.996315i	$-0.527337\pi$
$593$	−4.17751	−0.171550	−0.0857748	+	0.996315i	$0.527337\pi$
$594$	−13.1403	−0.539152
$595$	27.2391	1.11669
$596$	−17.0292	−0.697543
$597$	−35.0238	−1.43343
$598$	3.14152	0.128466
$599$	16.8143	0.687015	0.343507	−	0.939150i	$-0.388385\pi$
$599$	16.8143	0.687015	0.343507	+	0.939150i	$0.388385\pi$
$600$	5.24492	0.214123
$601$	31.8830	1.30053	0.650267	−	0.759706i	$-0.274657\pi$
$601$	31.8830	1.30053	0.650267	+	0.759706i	$0.274657\pi$
$602$	−4.45677	−0.181644
$603$	−12.4472	−0.506891
$604$	23.9792	0.975698
$605$	−16.5941	−0.674645
$606$	9.88934	0.401727
$607$	−32.0830	−1.30221	−0.651105	−	0.758988i	$-0.725694\pi$
$607$	−32.0830	−1.30221	−0.651105	+	0.758988i	$0.725694\pi$
$608$	6.69664	0.271584
$609$	10.5162	0.426136
$610$	−13.3673	−0.541225
$611$	−6.19427	−0.250593
$612$	−5.80811	−0.234779
$613$	26.5795	1.07354	0.536769	−	0.843729i	$-0.319645\pi$
$613$	26.5795	1.07354	0.536769	+	0.843729i	$0.319645\pi$
$614$	−16.2335	−0.655131
$615$	−11.9075	−0.480158
$616$	−4.47631	−0.180356
$617$	−15.9268	−0.641191	−0.320595	−	0.947216i	$-0.603883\pi$
$617$	−15.9268	−0.641191	−0.320595	+	0.947216i	$0.603883\pi$
$618$	12.0196	0.483501
$619$	−18.3398	−0.737138	−0.368569	−	0.929600i	$-0.620152\pi$
$619$	−18.3398	−0.737138	−0.368569	+	0.929600i	$0.620152\pi$
$620$	1.40291	0.0563422
$621$	14.2203	0.570640
$622$	−26.0622	−1.04500
$623$	15.6523	0.627096
$624$	1.65825	0.0663830
$625$	−29.1945	−1.16778
$626$	−5.14258	−0.205539
$627$	20.8410	0.832310
$628$	−7.85769	−0.313556
$629$	−21.9745	−0.876183
$630$	7.00591	0.279122
$631$	−42.4574	−1.69020	−0.845102	−	0.534605i	$-0.820460\pi$
$631$	−42.4574	−1.69020	−0.845102	+	0.534605i	$0.820460\pi$
$632$	4.62998	0.184171
$633$	−28.1390	−1.11842
$634$	−9.06819	−0.360144
$635$	−53.2464	−2.11302
$636$	−12.5117	−0.496122
$637$	4.13174	0.163706
$638$	9.59949	0.380047
$639$	−10.5091	−0.415734
$640$	−2.98893	−0.118148
$641$	20.3819	0.805035	0.402518	−	0.915412i	$-0.368135\pi$
$641$	20.3819	0.805035	0.402518	+	0.915412i	$0.368135\pi$
$642$	6.80030	0.268387
$643$	7.82337	0.308524	0.154262	−	0.988030i	$-0.450700\pi$
$643$	7.82337	0.308524	0.154262	+	0.988030i	$0.450700\pi$
$644$	4.84422	0.190889
$645$	−9.26142	−0.364668
$646$	31.8228	1.25205
$647$	−14.7223	−0.578793	−0.289397	−	0.957209i	$-0.593455\pi$
$647$	−14.7223	−0.578793	−0.289397	+	0.957209i	$0.593455\pi$
$648$	3.83946	0.150828
$649$	20.9797	0.823527
$650$	4.89229	0.191891
$651$	−1.20018	−0.0470388
$652$	−12.6697	−0.496183
$653$	−2.22868	−0.0872151	−0.0436075	−	0.999049i	$-0.513885\pi$
$653$	−2.22868	−0.0872151	−0.0436075	+	0.999049i	$0.513885\pi$
$654$	−6.13930	−0.240065
$655$	−45.5623	−1.78027
$656$	2.98791	0.116658
$657$	−1.34861	−0.0526142
$658$	−9.55157	−0.372359
$659$	−28.1050	−1.09481	−0.547407	−	0.836866i	$-0.684385\pi$
$659$	−28.1050	−1.09481	−0.547407	+	0.836866i	$0.684385\pi$
$660$	−9.30203	−0.362081
$661$	37.1058	1.44325	0.721625	−	0.692285i	$-0.243396\pi$
$661$	37.1058	1.44325	0.721625	+	0.692285i	$0.243396\pi$
$662$	−17.7206	−0.688731
$663$	7.88007	0.306037
$664$	17.7455	0.688660
$665$	−38.3856	−1.48853
$666$	−5.65187	−0.219005
$667$	−10.3885	−0.402243
$668$	10.8427	0.419515
$669$	−16.7493	−0.647565
$670$	−30.4394	−1.17598
$671$	10.4388	0.402986
$672$	2.55702	0.0986390
$673$	39.0990	1.50716	0.753579	−	0.657358i	$-0.228326\pi$
$673$	39.0990	1.50716	0.753579	+	0.657358i	$0.228326\pi$
$674$	1.10289	0.0424817
$675$	22.1452	0.852371
$676$	−11.4532	−0.440509
$677$	10.5775	0.406526	0.203263	−	0.979124i	$-0.434845\pi$
$677$	10.5775	0.406526	0.203263	+	0.979124i	$0.434845\pi$
$678$	25.3362	0.973032
$679$	24.5778	0.943210
$680$	−14.2036	−0.544681
$681$	0.971139	0.0372141
$682$	−1.09557	−0.0419514
$683$	15.0524	0.575965	0.287983	−	0.957636i	$-0.407015\pi$
$683$	15.0524	0.575965	0.287983	+	0.957636i	$0.407015\pi$
$684$	8.18484	0.312955
$685$	−58.7088	−2.24315
$686$	19.7955	0.755796
$687$	−4.49389	−0.171453
$688$	2.32394	0.0885993
$689$	−11.6705	−0.444612
$690$	10.0666	0.383228
$691$	13.8069	0.525238	0.262619	−	0.964900i	$-0.415414\pi$
$691$	13.8069	0.525238	0.262619	+	0.964900i	$0.415414\pi$
$692$	−15.9526	−0.606425
$693$	−5.47109	−0.207829
$694$	−18.1744	−0.689892
$695$	5.12488	0.194398
$696$	−5.48354	−0.207853
$697$	14.1987	0.537815
$698$	−18.0704	−0.683976
$699$	6.20335	0.234632
$700$	7.54391	0.285133
$701$	−46.0681	−1.73997	−0.869985	−	0.493079i	$-0.835871\pi$
$701$	−46.0681	−1.73997	−0.869985	+	0.493079i	$0.835871\pi$
$702$	7.00150	0.264254
$703$	30.9667	1.16793
$704$	2.33413	0.0879707
$705$	−19.8487	−0.747546
$706$	16.6377	0.626168
$707$	14.2241	0.534953
$708$	−11.9843	−0.450398
$709$	14.0797	0.528775	0.264387	−	0.964417i	$-0.414830\pi$
$709$	14.0797	0.528775	0.264387	+	0.964417i	$0.414830\pi$
$710$	−25.6997	−0.964493
$711$	5.65890	0.212225
$712$	−8.16173	−0.305874
$713$	1.18561	0.0444015
$714$	12.1511	0.454742
$715$	−8.67664	−0.324488
$716$	19.9609	0.745973
$717$	15.2727	0.570370
$718$	−20.5853	−0.768238
$719$	−43.8233	−1.63433	−0.817166	−	0.576402i	$-0.804456\pi$
$719$	−43.8233	−1.63433	−0.817166	+	0.576402i	$0.804456\pi$
$720$	−3.65316	−0.136145
$721$	17.2882	0.643846
$722$	−25.8449	−0.961849
$723$	25.0102	0.930140
$724$	−14.5803	−0.541874
$725$	−16.1780	−0.600835
$726$	−7.40245	−0.274731
$727$	24.3603	0.903475	0.451737	−	0.892151i	$-0.350804\pi$
$727$	24.3603	0.903475	0.451737	+	0.892151i	$0.350804\pi$
$728$	2.38510	0.0883978
$729$	27.2112	1.00782
$730$	−3.29798	−0.122064
$731$	11.0435	0.408458
$732$	−5.96300	−0.220399
$733$	−10.7654	−0.397630	−0.198815	−	0.980037i	$-0.563709\pi$
$733$	−10.7654	−0.397630	−0.198815	+	0.980037i	$0.563709\pi$
$734$	−5.46990	−0.201898
$735$	13.2396	0.488351
$736$	−2.52597	−0.0931085
$737$	23.7708	0.875610
$738$	3.65192	0.134429
$739$	−12.5874	−0.463034	−0.231517	−	0.972831i	$-0.574369\pi$
$739$	−12.5874	−0.463034	−0.231517	+	0.972831i	$0.574369\pi$
$740$	−13.8215	−0.508087
$741$	−11.1047	−0.407940
$742$	−17.9960	−0.660652
$743$	−35.8517	−1.31527	−0.657636	−	0.753335i	$-0.728444\pi$
$743$	−35.8517	−1.31527	−0.657636	+	0.753335i	$0.728444\pi$
$744$	0.625823	0.0229438
$745$	−50.8991	−1.86480
$746$	33.7563	1.23591
$747$	21.6891	0.793564
$748$	11.0919	0.405560
$749$	9.78107	0.357392
$750$	−4.24946	−0.155168
$751$	2.98977	0.109098	0.0545490	−	0.998511i	$-0.482628\pi$
$751$	2.98977	0.109098	0.0545490	+	0.998511i	$0.482628\pi$
$752$	4.98057	0.181623
$753$	−20.6482	−0.752463
$754$	−5.11487	−0.186273
$755$	71.6720	2.60841
$756$	10.7963	0.392658
$757$	4.15807	0.151127	0.0755637	−	0.997141i	$-0.475924\pi$
$757$	4.15807	0.151127	0.0755637	+	0.997141i	$0.475924\pi$
$758$	−15.1793	−0.551336
$759$	−7.86123	−0.285345
$760$	20.0158	0.726048
$761$	−5.23507	−0.189771	−0.0948856	−	0.995488i	$-0.530249\pi$
$761$	−5.23507	−0.189771	−0.0948856	+	0.995488i	$0.530249\pi$
$762$	−23.7527	−0.860468
$763$	−8.83032	−0.319679
$764$	17.0309	0.616157
$765$	−17.3600	−0.627653
$766$	−17.7641	−0.641844
$767$	−11.1786	−0.403635
$768$	−1.33333	−0.0481124
$769$	17.8240	0.642751	0.321376	−	0.946952i	$-0.395855\pi$
$769$	17.8240	0.642751	0.321376	+	0.946952i	$0.395855\pi$
$770$	−13.3794	−0.482159
$771$	26.6925	0.961307
$772$	23.7253	0.853893
$773$	−25.1551	−0.904767	−0.452384	−	0.891823i	$-0.649426\pi$
$773$	−25.1551	−0.904767	−0.452384	+	0.891823i	$0.649426\pi$
$774$	2.84039	0.102096
$775$	1.84635	0.0663229
$776$	−12.8159	−0.460063
$777$	11.8242	0.424191
$778$	−15.3930	−0.551866
$779$	−20.0090	−0.716896
$780$	4.95638	0.177467
$781$	20.0695	0.718144
$782$	−12.0035	−0.429246
$783$	−23.1528	−0.827413
$784$	−3.32217	−0.118649
$785$	−23.4861	−0.838254
$786$	−20.3249	−0.724964
$787$	−26.0504	−0.928596	−0.464298	−	0.885679i	$-0.653693\pi$
$787$	−26.0504	−0.928596	−0.464298	+	0.885679i	$0.653693\pi$
$788$	22.1157	0.787838
$789$	22.8173	0.812317
$790$	13.8387	0.492358
$791$	36.4418	1.29572
$792$	2.85284	0.101371
$793$	−5.56209	−0.197516
$794$	−26.4279	−0.937891
$795$	−37.3966	−1.32632
$796$	26.2679	0.931041
$797$	−8.88591	−0.314755	−0.157378	−	0.987539i	$-0.550304\pi$
$797$	−8.88591	−0.314755	−0.157378	+	0.987539i	$0.550304\pi$
$798$	−17.1234	−0.606162
$799$	23.6679	0.837311
$800$	−3.93370	−0.139077
$801$	−9.97552	−0.352468
$802$	3.16838	0.111879
$803$	2.57547	0.0908864
$804$	−13.5787	−0.478883
$805$	14.4790	0.510319
$806$	0.583747	0.0205616
$807$	3.43223	0.120820
$808$	−7.41703	−0.260930
$809$	46.2057	1.62451	0.812253	−	0.583305i	$-0.198241\pi$
$809$	46.2057	1.62451	0.812253	+	0.583305i	$0.198241\pi$
$810$	11.4759	0.403221
$811$	11.2100	0.393636	0.196818	−	0.980440i	$-0.436939\pi$
$811$	11.2100	0.393636	0.196818	+	0.980440i	$0.436939\pi$
$812$	−7.88713	−0.276784
$813$	2.28112	0.0800024
$814$	10.7935	0.378313
$815$	−37.8688	−1.32649
$816$	−6.33605	−0.221806
$817$	−15.5626	−0.544465
$818$	35.3341	1.23543
$819$	2.91515	0.101863
$820$	8.93066	0.311872
$821$	1.41021	0.0492165	0.0246083	−	0.999697i	$-0.492166\pi$
$821$	1.41021	0.0492165	0.0246083	+	0.999697i	$0.492166\pi$
$822$	−26.1894	−0.913460
$823$	−52.2846	−1.82253	−0.911263	−	0.411826i	$-0.864891\pi$
$823$	−52.2846	−1.82253	−0.911263	+	0.411826i	$0.864891\pi$
$824$	−9.01476	−0.314044
$825$	−12.2423	−0.426222
$826$	−17.2374	−0.599765
$827$	23.9394	0.832455	0.416228	−	0.909261i	$-0.363352\pi$
$827$	23.9394	0.832455	0.416228	+	0.909261i	$0.363352\pi$
$828$	−3.08732	−0.107292
$829$	−27.7631	−0.964254	−0.482127	−	0.876101i	$-0.660136\pi$
$829$	−27.7631	−0.964254	−0.482127	+	0.876101i	$0.660136\pi$
$830$	53.0401	1.84105
$831$	−27.7881	−0.963960
$832$	−1.24369	−0.0431171
$833$	−15.7871	−0.546992
$834$	2.28616	0.0791632
$835$	32.4080	1.12152
$836$	−15.6308	−0.540603
$837$	2.64237	0.0913336
$838$	2.86936	0.0991203
$839$	−43.7890	−1.51177	−0.755883	−	0.654707i	$-0.772792\pi$
$839$	−43.7890	−1.51177	−0.755883	+	0.654707i	$0.772792\pi$
$840$	7.64274	0.263699
$841$	−12.0860	−0.416758
$842$	4.13528	0.142511
$843$	−16.5320	−0.569393
$844$	21.1043	0.726439
$845$	−34.2329	−1.17765
$846$	6.08741	0.209289
$847$	−10.6471	−0.365840
$848$	9.38381	0.322241
$849$	17.7232	0.608257
$850$	−18.6931	−0.641169
$851$	−11.6806	−0.400407
$852$	−11.4644	−0.392763
$853$	−16.7815	−0.574587	−0.287293	−	0.957843i	$-0.592755\pi$
$853$	−16.7815	−0.574587	−0.287293	+	0.957843i	$0.592755\pi$
$854$	−8.57675	−0.293490
$855$	24.4639	0.836648
$856$	−5.10024	−0.174323
$857$	−26.6227	−0.909413	−0.454707	−	0.890641i	$-0.650256\pi$
$857$	−26.6227	−0.909413	−0.454707	+	0.890641i	$0.650256\pi$
$858$	−3.87056	−0.132139
$859$	24.4541	0.834364	0.417182	−	0.908823i	$-0.363018\pi$
$859$	24.4541	0.834364	0.417182	+	0.908823i	$0.363018\pi$
$860$	6.94608	0.236859
$861$	−7.64014	−0.260375
$862$	13.1289	0.447173
$863$	9.65292	0.328589	0.164295	−	0.986411i	$-0.447465\pi$
$863$	9.65292	0.328589	0.164295	+	0.986411i	$0.447465\pi$
$864$	−5.62963	−0.191524
$865$	−47.6810	−1.62120
$866$	−22.7745	−0.773909
$867$	−7.44266	−0.252766
$868$	0.900138	0.0305527
$869$	−10.8070	−0.366601
$870$	−16.3899	−0.555670
$871$	−12.6658	−0.429163
$872$	4.60448	0.155927
$873$	−15.6639	−0.530144
$874$	16.9155	0.572175
$875$	−6.11212	−0.206627
$876$	−1.47119	−0.0497070
$877$	−40.0819	−1.35347	−0.676736	−	0.736226i	$-0.736606\pi$
$877$	−40.0819	−1.35347	−0.676736	+	0.736226i	$0.736606\pi$
$878$	−33.3151	−1.12433
$879$	15.4853	0.522307
$880$	6.97654	0.235179
$881$	−33.4002	−1.12528	−0.562640	−	0.826702i	$-0.690214\pi$
$881$	−33.4002	−1.12528	−0.562640	+	0.826702i	$0.690214\pi$
$882$	−4.06046	−0.136723
$883$	24.7544	0.833052	0.416526	−	0.909124i	$-0.363247\pi$
$883$	24.7544	0.833052	0.416526	+	0.909124i	$0.363247\pi$
$884$	−5.91007	−0.198777
$885$	−35.8203	−1.20408
$886$	30.4373	1.02256
$887$	−4.02929	−0.135290	−0.0676452	−	0.997709i	$-0.521549\pi$
$887$	−4.02929	−0.135290	−0.0676452	+	0.997709i	$0.521549\pi$
$888$	−6.16561	−0.206904
$889$	−34.1641	−1.14583
$890$	−24.3948	−0.817717
$891$	−8.96178	−0.300231
$892$	12.5620	0.420607
$893$	−33.3531	−1.11612
$894$	−22.7055	−0.759387
$895$	59.6616	1.99427
$896$	−1.91777	−0.0640681
$897$	4.18868	0.139856
$898$	−6.34738	−0.211815
$899$	−1.93036	−0.0643810
$900$	−4.80789	−0.160263
$901$	44.5924	1.48559
$902$	−6.97417	−0.232215
$903$	−5.94234	−0.197749
$904$	−19.0022	−0.632005
$905$	−43.5796	−1.44863
$906$	31.9721	1.06220
$907$	12.2518	0.406815	0.203408	−	0.979094i	$-0.434798\pi$
$907$	12.2518	0.406815	0.203408	+	0.979094i	$0.434798\pi$
$908$	−0.728356	−0.0241713
$909$	−9.06532	−0.300678
$910$	7.12890	0.236321
$911$	35.7827	1.18553	0.592767	−	0.805374i	$-0.298036\pi$
$911$	35.7827	1.18553	0.592767	+	0.805374i	$0.298036\pi$
$912$	8.92883	0.295663
$913$	−41.4203	−1.37081
$914$	1.55505	0.0514366
$915$	−17.8230	−0.589210
$916$	3.37043	0.111362
$917$	−29.2338	−0.965386
$918$	−26.7523	−0.882957
$919$	41.3168	1.36292	0.681458	−	0.731857i	$-0.261346\pi$
$919$	41.3168	1.36292	0.681458	+	0.731857i	$0.261346\pi$
$920$	−7.54995	−0.248914
$921$	−21.6446	−0.713214
$922$	−30.9703	−1.01995
$923$	−10.6936	−0.351984
$924$	−5.96840	−0.196346
$925$	−18.1903	−0.598093
$926$	−28.2842	−0.929477
$927$	−11.0181	−0.361882
$928$	4.11267	0.135005
$929$	0.0160974	0.000528139 0	0.000264069	−	1.00000i	$-0.499916\pi$
$929$	0.0160974	0.000528139 0	0.000264069		1.00000i	$0.499916\pi$
$930$	1.87054	0.0613374
$931$	22.2474	0.729129
$932$	−4.65253	−0.152399
$933$	−34.7495	−1.13765
$934$	−14.0223	−0.458822
$935$	33.1529	1.08422
$936$	−1.52007	−0.0496852
$937$	−27.2636	−0.890664	−0.445332	−	0.895366i	$-0.646914\pi$
$937$	−27.2636	−0.890664	−0.445332	+	0.895366i	$0.646914\pi$
$938$	−19.5306	−0.637697
$939$	−6.85676	−0.223762
$940$	14.8866	0.485546
$941$	40.9371	1.33451	0.667256	−	0.744828i	$-0.267469\pi$
$941$	40.9371	1.33451	0.667256	+	0.744828i	$0.267469\pi$
$942$	−10.4769	−0.341356
$943$	7.54738	0.245777
$944$	8.98826	0.292543
$945$	32.2694	1.04972
$946$	−5.42437	−0.176361
$947$	48.2814	1.56894	0.784468	−	0.620170i	$-0.212936\pi$
$947$	48.2814	1.56894	0.784468	+	0.620170i	$0.212936\pi$
$948$	6.17329	0.200499
$949$	−1.37228	−0.0445461
$950$	26.3425	0.854665
$951$	−12.0909	−0.392074
$952$	−9.11333	−0.295365
$953$	38.4500	1.24552	0.622758	−	0.782414i	$-0.286012\pi$
$953$	38.4500	1.24552	0.622758	+	0.782414i	$0.286012\pi$
$954$	11.4692	0.371329
$955$	50.9042	1.64722
$956$	−11.4546	−0.370467
$957$	12.7993	0.413742
$958$	−1.21117	−0.0391313
$959$	−37.6689	−1.21639
$960$	−3.98523	−0.128623
$961$	−30.7797	−0.992893
$962$	−5.75109	−0.185422
$963$	−6.23367	−0.200877
$964$	−18.7577	−0.604145
$965$	70.9133	2.28278
$966$	6.45894	0.207813
$967$	−40.6779	−1.30811	−0.654057	−	0.756445i	$-0.726934\pi$
$967$	−40.6779	−1.30811	−0.654057	+	0.756445i	$0.726934\pi$
$968$	5.55185	0.178443
$969$	42.4303	1.36306
$970$	−38.3057	−1.22992
$971$	27.1185	0.870276	0.435138	−	0.900364i	$-0.356700\pi$
$971$	27.1185	0.870276	0.435138	+	0.900364i	$0.356700\pi$
$972$	−11.7696	−0.377511
$973$	3.28824	0.105416
$974$	−4.85559	−0.155583
$975$	6.52304	0.208904
$976$	4.47226	0.143154
$977$	−37.4524	−1.19821	−0.599104	−	0.800671i	$-0.704476\pi$
$977$	−37.4524	−1.19821	−0.599104	+	0.800671i	$0.704476\pi$
$978$	−16.8929	−0.540175
$979$	19.0505	0.608857
$980$	−9.92974	−0.317194
$981$	5.62774	0.179680
$982$	2.42603	0.0774176
$983$	−52.1576	−1.66357	−0.831785	−	0.555098i	$-0.812681\pi$
$983$	−52.1576	−1.66357	−0.831785	+	0.555098i	$0.812681\pi$
$984$	3.98388	0.127001
$985$	66.1022	2.10619
$986$	19.5436	0.622395
$987$	−12.7354	−0.405372
$988$	8.32852	0.264966
$989$	5.87020	0.186661
$990$	8.52695	0.271004
$991$	−1.42256	−0.0451892	−0.0225946	−	0.999745i	$-0.507193\pi$
$991$	−1.42256	−0.0451892	−0.0225946	+	0.999745i	$0.507193\pi$
$992$	−0.469368	−0.0149025
$993$	−23.6274	−0.749793
$994$	−16.4895	−0.523016
$995$	78.5128	2.48902
$996$	23.6606	0.749716
$997$	42.1691	1.33551	0.667755	−	0.744381i	$-0.267255\pi$
$997$	42.1691	1.33551	0.667755	+	0.744381i	$0.267255\pi$
$998$	8.45826	0.267742
$999$	−26.0326	−0.823636

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.c.1.15	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.c.1.15	✓	49	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.33333 q^{3} +1.00000 q^{4} +2.98893 q^{5} +1.33333 q^{6} +1.91777 q^{7} -1.00000 q^{8} -1.22223 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.33333 q^{3} +1.00000 q^{4} +2.98893 q^{5} +1.33333 q^{6} +1.91777 q^{7} -1.00000 q^{8} -1.22223 q^{9} -2.98893 q^{10} +2.33413 q^{11} -1.33333 q^{12} -1.24369 q^{13} -1.91777 q^{14} -3.98523 q^{15} +1.00000 q^{16} +4.75205 q^{17} +1.22223 q^{18} -6.69664 q^{19} +2.98893 q^{20} -2.55702 q^{21} -2.33413 q^{22} +2.52597 q^{23} +1.33333 q^{24} +3.93370 q^{25} +1.24369 q^{26} +5.62963 q^{27} +1.91777 q^{28} -4.11267 q^{29} +3.98523 q^{30} +0.469368 q^{31} -1.00000 q^{32} -3.11216 q^{33} -4.75205 q^{34} +5.73207 q^{35} -1.22223 q^{36} -4.62422 q^{37} +6.69664 q^{38} +1.65825 q^{39} -2.98893 q^{40} +2.98791 q^{41} +2.55702 q^{42} +2.32394 q^{43} +2.33413 q^{44} -3.65316 q^{45} -2.52597 q^{46} +4.98057 q^{47} -1.33333 q^{48} -3.32217 q^{49} -3.93370 q^{50} -6.33605 q^{51} -1.24369 q^{52} +9.38381 q^{53} -5.62963 q^{54} +6.97654 q^{55} -1.91777 q^{56} +8.92883 q^{57} +4.11267 q^{58} +8.98826 q^{59} -3.98523 q^{60} +4.47226 q^{61} -0.469368 q^{62} -2.34395 q^{63} +1.00000 q^{64} -3.71729 q^{65} +3.11216 q^{66} +10.1840 q^{67} +4.75205 q^{68} -3.36795 q^{69} -5.73207 q^{70} +8.59830 q^{71} +1.22223 q^{72} +1.10340 q^{73} +4.62422 q^{74} -5.24492 q^{75} -6.69664 q^{76} +4.47631 q^{77} -1.65825 q^{78} -4.62998 q^{79} +2.98893 q^{80} -3.83946 q^{81} -2.98791 q^{82} -17.7455 q^{83} -2.55702 q^{84} +14.2036 q^{85} -2.32394 q^{86} +5.48354 q^{87} -2.33413 q^{88} +8.16173 q^{89} +3.65316 q^{90} -2.38510 q^{91} +2.52597 q^{92} -0.625823 q^{93} -4.98057 q^{94} -20.0158 q^{95} +1.33333 q^{96} +12.8159 q^{97} +3.32217 q^{98} -2.85284 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * q^99

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