LMFDB - Embedded newform 4034.2.a.d.1.16

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:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.04358 q^{3} +1.00000 q^{4} +1.25349 q^{5} -1.04358 q^{6} +0.828851 q^{7} +1.00000 q^{8} -1.91094 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.04358 q^{3} +1.00000 q^{4} +1.25349 q^{5} -1.04358 q^{6} +0.828851 q^{7} +1.00000 q^{8} -1.91094 q^{9} +1.25349 q^{10} +6.21529 q^{11} -1.04358 q^{12} +0.865537 q^{13} +0.828851 q^{14} -1.30811 q^{15} +1.00000 q^{16} -6.80039 q^{17} -1.91094 q^{18} +6.14782 q^{19} +1.25349 q^{20} -0.864972 q^{21} +6.21529 q^{22} +5.96113 q^{23} -1.04358 q^{24} -3.42877 q^{25} +0.865537 q^{26} +5.12496 q^{27} +0.828851 q^{28} -3.08253 q^{29} -1.30811 q^{30} +1.21145 q^{31} +1.00000 q^{32} -6.48615 q^{33} -6.80039 q^{34} +1.03896 q^{35} -1.91094 q^{36} -2.09272 q^{37} +6.14782 q^{38} -0.903257 q^{39} +1.25349 q^{40} +10.4877 q^{41} -0.864972 q^{42} +6.70944 q^{43} +6.21529 q^{44} -2.39534 q^{45} +5.96113 q^{46} -3.80558 q^{47} -1.04358 q^{48} -6.31301 q^{49} -3.42877 q^{50} +7.09675 q^{51} +0.865537 q^{52} -13.0641 q^{53} +5.12496 q^{54} +7.79080 q^{55} +0.828851 q^{56} -6.41574 q^{57} -3.08253 q^{58} -2.61789 q^{59} -1.30811 q^{60} +15.2222 q^{61} +1.21145 q^{62} -1.58389 q^{63} +1.00000 q^{64} +1.08494 q^{65} -6.48615 q^{66} +10.1005 q^{67} -6.80039 q^{68} -6.22091 q^{69} +1.03896 q^{70} +11.9824 q^{71} -1.91094 q^{72} -10.2155 q^{73} -2.09272 q^{74} +3.57819 q^{75} +6.14782 q^{76} +5.15155 q^{77} -0.903257 q^{78} -13.2547 q^{79} +1.25349 q^{80} +0.384529 q^{81} +10.4877 q^{82} -7.59965 q^{83} -0.864972 q^{84} -8.52421 q^{85} +6.70944 q^{86} +3.21687 q^{87} +6.21529 q^{88} +14.7901 q^{89} -2.39534 q^{90} +0.717402 q^{91} +5.96113 q^{92} -1.26424 q^{93} -3.80558 q^{94} +7.70622 q^{95} -1.04358 q^{96} +12.8202 q^{97} -6.31301 q^{98} -11.8771 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) $ 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * 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
$3$	−1.04358	−0.602511	−0.301255	−	0.953544i	$-0.597406\pi$
$3$	−1.04358	−0.602511	−0.301255	+	0.953544i	$0.597406\pi$
$4$	1.00000	0.500000
$5$	1.25349	0.560577	0.280288	−	0.959916i	$-0.409570\pi$
$5$	1.25349	0.560577	0.280288	+	0.959916i	$0.409570\pi$
$6$	−1.04358	−0.426039
$7$	0.828851	0.313276	0.156638	−	0.987656i	$-0.449934\pi$
$7$	0.828851	0.313276	0.156638	+	0.987656i	$0.449934\pi$
$8$	1.00000	0.353553
$9$	−1.91094	−0.636981
$10$	1.25349	0.396388
$11$	6.21529	1.87398	0.936991	−	0.349354i	$-0.113599\pi$
$11$	6.21529	1.87398	0.936991	+	0.349354i	$0.113599\pi$
$12$	−1.04358	−0.301255
$13$	0.865537	0.240057	0.120028	−	0.992770i	$-0.461701\pi$
$13$	0.865537	0.240057	0.120028	+	0.992770i	$0.461701\pi$
$14$	0.828851	0.221520
$15$	−1.30811	−0.337754
$16$	1.00000	0.250000
$17$	−6.80039	−1.64934	−0.824669	−	0.565616i	$-0.808639\pi$
$17$	−6.80039	−1.64934	−0.824669	+	0.565616i	$0.808639\pi$
$18$	−1.91094	−0.450413
$19$	6.14782	1.41041	0.705203	−	0.709005i	$-0.250856\pi$
$19$	6.14782	1.41041	0.705203	+	0.709005i	$0.250856\pi$
$20$	1.25349	0.280288
$21$	−0.864972	−0.188752
$22$	6.21529	1.32510
$23$	5.96113	1.24298	0.621491	−	0.783421i	$-0.286527\pi$
$23$	5.96113	1.24298	0.621491	+	0.783421i	$0.286527\pi$
$24$	−1.04358	−0.213020
$25$	−3.42877	−0.685753
$26$	0.865537	0.169746
$27$	5.12496	0.986298
$28$	0.828851	0.156638
$29$	−3.08253	−0.572412	−0.286206	−	0.958168i	$-0.592394\pi$
$29$	−3.08253	−0.572412	−0.286206	+	0.958168i	$0.592394\pi$
$30$	−1.30811	−0.238828
$31$	1.21145	0.217583	0.108791	−	0.994065i	$-0.465302\pi$
$31$	1.21145	0.217583	0.108791	+	0.994065i	$0.465302\pi$
$32$	1.00000	0.176777
$33$	−6.48615	−1.12909
$34$	−6.80039	−1.16626
$35$	1.03896	0.175616
$36$	−1.91094	−0.318490
$37$	−2.09272	−0.344042	−0.172021	−	0.985093i	$-0.555030\pi$
$37$	−2.09272	−0.344042	−0.172021	+	0.985093i	$0.555030\pi$
$38$	6.14782	0.997308
$39$	−0.903257	−0.144637
$40$	1.25349	0.198194
$41$	10.4877	1.63790	0.818952	−	0.573862i	$-0.194555\pi$
$41$	10.4877	1.63790	0.818952	+	0.573862i	$0.194555\pi$
$42$	−0.864972	−0.133468
$43$	6.70944	1.02318	0.511590	−	0.859230i	$-0.329057\pi$
$43$	6.70944	1.02318	0.511590	+	0.859230i	$0.329057\pi$
$44$	6.21529	0.936991
$45$	−2.39534	−0.357077
$46$	5.96113	0.878921
$47$	−3.80558	−0.555101	−0.277551	−	0.960711i	$-0.589523\pi$
$47$	−3.80558	−0.555101	−0.277551	+	0.960711i	$0.589523\pi$
$48$	−1.04358	−0.150628
$49$	−6.31301	−0.901858
$50$	−3.42877	−0.484901
$51$	7.09675	0.993744
$52$	0.865537	0.120028
$53$	−13.0641	−1.79449	−0.897244	−	0.441535i	$-0.854434\pi$
$53$	−13.0641	−1.79449	−0.897244	+	0.441535i	$0.854434\pi$
$54$	5.12496	0.697418
$55$	7.79080	1.05051
$56$	0.828851	0.110760
$57$	−6.41574	−0.849785
$58$	−3.08253	−0.404756
$59$	−2.61789	−0.340820	−0.170410	−	0.985373i	$-0.554509\pi$
$59$	−2.61789	−0.340820	−0.170410	+	0.985373i	$0.554509\pi$
$60$	−1.30811	−0.168877
$61$	15.2222	1.94900	0.974499	−	0.224394i	$-0.0720402\pi$
$61$	15.2222	1.94900	0.974499	+	0.224394i	$0.0720402\pi$
$62$	1.21145	0.153854
$63$	−1.58389	−0.199551
$64$	1.00000	0.125000
$65$	1.08494	0.134570
$66$	−6.48615	−0.798390
$67$	10.1005	1.23398	0.616988	−	0.786973i	$-0.288353\pi$
$67$	10.1005	1.23398	0.616988	+	0.786973i	$0.288353\pi$
$68$	−6.80039	−0.824669
$69$	−6.22091	−0.748910
$70$	1.03896	0.124179
$71$	11.9824	1.42205	0.711024	−	0.703167i	$-0.248231\pi$
$71$	11.9824	1.42205	0.711024	+	0.703167i	$0.248231\pi$
$72$	−1.91094	−0.225207
$73$	−10.2155	−1.19564	−0.597818	−	0.801632i	$-0.703965\pi$
$73$	−10.2155	−1.19564	−0.597818	+	0.801632i	$0.703965\pi$
$74$	−2.09272	−0.243274
$75$	3.57819	0.413174
$76$	6.14782	0.705203
$77$	5.15155	0.587074
$78$	−0.903257	−0.102274
$79$	−13.2547	−1.49127	−0.745633	−	0.666357i	$-0.767853\pi$
$79$	−13.2547	−1.49127	−0.745633	+	0.666357i	$0.767853\pi$
$80$	1.25349	0.140144
$81$	0.384529	0.0427254
$82$	10.4877	1.15817
$83$	−7.59965	−0.834170	−0.417085	−	0.908867i	$-0.636948\pi$
$83$	−7.59965	−0.834170	−0.417085	+	0.908867i	$0.636948\pi$
$84$	−0.864972	−0.0943762
$85$	−8.52421	−0.924581
$86$	6.70944	0.723497
$87$	3.21687	0.344884
$88$	6.21529	0.662552
$89$	14.7901	1.56774	0.783872	−	0.620922i	$-0.213242\pi$
$89$	14.7901	1.56774	0.783872	+	0.620922i	$0.213242\pi$
$90$	−2.39534	−0.252491
$91$	0.717402	0.0752041
$92$	5.96113	0.621491
$93$	−1.26424	−0.131096
$94$	−3.80558	−0.392516
$95$	7.70622	0.790642
$96$	−1.04358	−0.106510
$97$	12.8202	1.30169	0.650846	−	0.759210i	$-0.274414\pi$
$97$	12.8202	1.30169	0.650846	+	0.759210i	$0.274414\pi$
$98$	−6.31301	−0.637710
$99$	−11.8771	−1.19369
$100$	−3.42877	−0.342877
$101$	−11.4101	−1.13535	−0.567675	−	0.823253i	$-0.692157\pi$
$101$	−11.4101	−1.13535	−0.567675	+	0.823253i	$0.692157\pi$
$102$	7.09675	0.702683
$103$	7.64058	0.752849	0.376425	−	0.926447i	$-0.377153\pi$
$103$	7.64058	0.752849	0.376425	+	0.926447i	$0.377153\pi$
$104$	0.865537	0.0848729
$105$	−1.08423	−0.105810
$106$	−13.0641	−1.26889
$107$	4.91583	0.475231	0.237615	−	0.971359i	$-0.423634\pi$
$107$	4.91583	0.475231	0.237615	+	0.971359i	$0.423634\pi$
$108$	5.12496	0.493149
$109$	−11.3104	−1.08334	−0.541668	−	0.840592i	$-0.682207\pi$
$109$	−11.3104	−1.08334	−0.541668	+	0.840592i	$0.682207\pi$
$110$	7.79080	0.742823
$111$	2.18392	0.207289
$112$	0.828851	0.0783191
$113$	5.23842	0.492789	0.246395	−	0.969170i	$-0.420754\pi$
$113$	5.23842	0.492789	0.246395	+	0.969170i	$0.420754\pi$
$114$	−6.41574	−0.600889
$115$	7.47221	0.696787
$116$	−3.08253	−0.286206
$117$	−1.65399	−0.152912
$118$	−2.61789	−0.240996
$119$	−5.63652	−0.516699
$120$	−1.30811	−0.119414
$121$	27.6299	2.51181
$122$	15.2222	1.37815
$123$	−10.9448	−0.986855
$124$	1.21145	0.108791
$125$	−10.5654	−0.944995
$126$	−1.58389	−0.141104
$127$	3.45432	0.306521	0.153261	−	0.988186i	$-0.451023\pi$
$127$	3.45432	0.306521	0.153261	+	0.988186i	$0.451023\pi$
$128$	1.00000	0.0883883
$129$	−7.00183	−0.616477
$130$	1.08494	0.0951556
$131$	1.25780	0.109894	0.0549471	−	0.998489i	$-0.482501\pi$
$131$	1.25780	0.109894	0.0549471	+	0.998489i	$0.482501\pi$
$132$	−6.48615	−0.564547
$133$	5.09563	0.441847
$134$	10.1005	0.872552
$135$	6.42407	0.552896
$136$	−6.80039	−0.583129
$137$	16.0337	1.36985	0.684926	−	0.728612i	$-0.259834\pi$
$137$	16.0337	1.36985	0.684926	+	0.728612i	$0.259834\pi$
$138$	−6.22091	−0.529559
$139$	1.20032	0.101810	0.0509048	−	0.998704i	$-0.483789\pi$
$139$	1.20032	0.101810	0.0509048	+	0.998704i	$0.483789\pi$
$140$	1.03896	0.0878078
$141$	3.97143	0.334454
$142$	11.9824	1.00554
$143$	5.37957	0.449862
$144$	−1.91094	−0.159245
$145$	−3.86392	−0.320881
$146$	−10.2155	−0.845442
$147$	6.58812	0.543379
$148$	−2.09272	−0.172021
$149$	9.79280	0.802257	0.401129	−	0.916022i	$-0.368618\pi$
$149$	9.79280	0.802257	0.401129	+	0.916022i	$0.368618\pi$
$150$	3.57819	0.292158
$151$	−10.8680	−0.884426	−0.442213	−	0.896910i	$-0.645807\pi$
$151$	−10.8680	−0.884426	−0.442213	+	0.896910i	$0.645807\pi$
$152$	6.14782	0.498654
$153$	12.9952	1.05060
$154$	5.15155	0.415124
$155$	1.51854	0.121972
$156$	−0.903257	−0.0723184
$157$	−13.6618	−1.09033	−0.545167	−	0.838327i	$-0.683534\pi$
$157$	−13.6618	−1.09033	−0.545167	+	0.838327i	$0.683534\pi$
$158$	−13.2547	−1.05448
$159$	13.6334	1.08120
$160$	1.25349	0.0990969
$161$	4.94089	0.389397
$162$	0.384529	0.0302115
$163$	3.22517	0.252614	0.126307	−	0.991991i	$-0.459687\pi$
$163$	3.22517	0.252614	0.126307	+	0.991991i	$0.459687\pi$
$164$	10.4877	0.818952
$165$	−8.13031	−0.632944
$166$	−7.59965	−0.589847
$167$	−9.12706	−0.706273	−0.353136	−	0.935572i	$-0.614885\pi$
$167$	−9.12706	−0.706273	−0.353136	+	0.935572i	$0.614885\pi$
$168$	−0.864972	−0.0667340
$169$	−12.2508	−0.942373
$170$	−8.52421	−0.653777
$171$	−11.7481	−0.898402
$172$	6.70944	0.511590
$173$	−4.78033	−0.363441	−0.181721	−	0.983350i	$-0.558167\pi$
$173$	−4.78033	−0.363441	−0.181721	+	0.983350i	$0.558167\pi$
$174$	3.21687	0.243870
$175$	−2.84194	−0.214830
$176$	6.21529	0.468495
$177$	2.73198	0.205348
$178$	14.7901	1.10856
$179$	−8.25300	−0.616858	−0.308429	−	0.951247i	$-0.599803\pi$
$179$	−8.25300	−0.616858	−0.308429	+	0.951247i	$0.599803\pi$
$180$	−2.39534	−0.178538
$181$	22.4047	1.66533	0.832663	−	0.553780i	$-0.186815\pi$
$181$	22.4047	1.66533	0.832663	+	0.553780i	$0.186815\pi$
$182$	0.717402	0.0531773
$183$	−15.8855	−1.17429
$184$	5.96113	0.439460
$185$	−2.62320	−0.192862
$186$	−1.26424	−0.0926989
$187$	−42.2664	−3.09083
$188$	−3.80558	−0.277551
$189$	4.24783	0.308984
$190$	7.70622	0.559068
$191$	20.7592	1.50209	0.751043	−	0.660253i	$-0.229551\pi$
$191$	20.7592	1.50209	0.751043	+	0.660253i	$0.229551\pi$
$192$	−1.04358	−0.0753138
$193$	11.7359	0.844771	0.422385	−	0.906416i	$-0.361193\pi$
$193$	11.7359	0.844771	0.422385	+	0.906416i	$0.361193\pi$
$194$	12.8202	0.920435
$195$	−1.13222	−0.0810801
$196$	−6.31301	−0.450929
$197$	−10.7241	−0.764058	−0.382029	−	0.924150i	$-0.624775\pi$
$197$	−10.7241	−0.764058	−0.382029	+	0.924150i	$0.624775\pi$
$198$	−11.8771	−0.844066
$199$	8.16835	0.579039	0.289520	−	0.957172i	$-0.406504\pi$
$199$	8.16835	0.579039	0.289520	+	0.957172i	$0.406504\pi$
$200$	−3.42877	−0.242450
$201$	−10.5407	−0.743483
$202$	−11.4101	−0.802813
$203$	−2.55496	−0.179323
$204$	7.09675	0.496872
$205$	13.1462	0.918172
$206$	7.64058	0.532345
$207$	−11.3914	−0.791755
$208$	0.865537	0.0600142
$209$	38.2105	2.64308
$210$	−1.08423	−0.0748191
$211$	26.6914	1.83751	0.918757	−	0.394823i	$-0.129194\pi$
$211$	26.6914	1.83751	0.918757	+	0.394823i	$0.129194\pi$
$212$	−13.0641	−0.897244
$213$	−12.5046	−0.856800
$214$	4.91583	0.336039
$215$	8.41020	0.573571
$216$	5.12496	0.348709
$217$	1.00411	0.0681636
$218$	−11.3104	−0.766034
$219$	10.6607	0.720383
$220$	7.79080	0.525255
$221$	−5.88599	−0.395935
$222$	2.18392	0.146575
$223$	15.0713	1.00925	0.504625	−	0.863338i	$-0.331631\pi$
$223$	15.0713	1.00925	0.504625	+	0.863338i	$0.331631\pi$
$224$	0.828851	0.0553800
$225$	6.55218	0.436812
$226$	5.23842	0.348455
$227$	−25.6143	−1.70008	−0.850039	−	0.526720i	$-0.823422\pi$
$227$	−25.6143	−1.70008	−0.850039	+	0.526720i	$0.823422\pi$
$228$	−6.41574	−0.424893
$229$	−3.02832	−0.200117	−0.100059	−	0.994982i	$-0.531903\pi$
$229$	−3.02832	−0.200117	−0.100059	+	0.994982i	$0.531903\pi$
$230$	7.47221	0.492703
$231$	−5.37605	−0.353718
$232$	−3.08253	−0.202378
$233$	−16.3038	−1.06810	−0.534049	−	0.845453i	$-0.679330\pi$
$233$	−16.3038	−1.06810	−0.534049	+	0.845453i	$0.679330\pi$
$234$	−1.65399	−0.108125
$235$	−4.77025	−0.311177
$236$	−2.61789	−0.170410
$237$	13.8323	0.898504
$238$	−5.63652	−0.365361
$239$	28.0855	1.81670	0.908350	−	0.418211i	$-0.137343\pi$
$239$	28.0855	1.81670	0.908350	+	0.418211i	$0.137343\pi$
$240$	−1.30811	−0.0844384
$241$	−19.7801	−1.27415	−0.637073	−	0.770804i	$-0.719855\pi$
$241$	−19.7801	−1.27415	−0.637073	+	0.770804i	$0.719855\pi$
$242$	27.6299	1.77612
$243$	−15.7762	−1.01204
$244$	15.2222	0.974499
$245$	−7.91328	−0.505561
$246$	−10.9448	−0.697812
$247$	5.32117	0.338578
$248$	1.21145	0.0769272
$249$	7.93084	0.502596
$250$	−10.5654	−0.668212
$251$	28.5753	1.80365	0.901827	−	0.432096i	$-0.142226\pi$
$251$	28.5753	1.80365	0.901827	+	0.432096i	$0.142226\pi$
$252$	−1.58389	−0.0997755
$253$	37.0502	2.32932
$254$	3.45432	0.216743
$255$	8.89569	0.557070
$256$	1.00000	0.0625000
$257$	7.77246	0.484833	0.242417	−	0.970172i	$-0.422060\pi$
$257$	7.77246	0.484833	0.242417	+	0.970172i	$0.422060\pi$
$258$	−7.00183	−0.435915
$259$	−1.73456	−0.107780
$260$	1.08494	0.0672852
$261$	5.89054	0.364615
$262$	1.25780	0.0777070
$263$	0.0139729	0.000861606 0	0.000430803	−	1.00000i	$-0.499863\pi$
$263$	0.0139729	0.000861606 0	0.000430803		1.00000i	$0.499863\pi$
$264$	−6.48615	−0.399195
$265$	−16.3757	−1.00595
$266$	5.09563	0.312433
$267$	−15.4346	−0.944583
$268$	10.1005	0.616988
$269$	29.5427	1.80125	0.900625	−	0.434597i	$-0.143109\pi$
$269$	29.5427	1.80125	0.900625	+	0.434597i	$0.143109\pi$
$270$	6.42407	0.390957
$271$	−4.31315	−0.262005	−0.131003	−	0.991382i	$-0.541820\pi$
$271$	−4.31315	−0.262005	−0.131003	+	0.991382i	$0.541820\pi$
$272$	−6.80039	−0.412334
$273$	−0.748665	−0.0453113
$274$	16.0337	0.968632
$275$	−21.3108	−1.28509
$276$	−6.22091	−0.374455
$277$	−3.14142	−0.188749	−0.0943747	−	0.995537i	$-0.530085\pi$
$277$	−3.14142	−0.188749	−0.0943747	+	0.995537i	$0.530085\pi$
$278$	1.20032	0.0719903
$279$	−2.31501	−0.138596
$280$	1.03896	0.0620895
$281$	−14.3643	−0.856901	−0.428451	−	0.903565i	$-0.640940\pi$
$281$	−14.3643	−0.856901	−0.428451	+	0.903565i	$0.640940\pi$
$282$	3.97143	0.236495
$283$	−13.0024	−0.772913	−0.386456	−	0.922308i	$-0.626301\pi$
$283$	−13.0024	−0.772913	−0.386456	+	0.922308i	$0.626301\pi$
$284$	11.9824	0.711024
$285$	−8.04205	−0.476370
$286$	5.37957	0.318100
$287$	8.69275	0.513117
$288$	−1.91094	−0.112603
$289$	29.2454	1.72032
$290$	−3.86392	−0.226897
$291$	−13.3789	−0.784283
$292$	−10.2155	−0.597818
$293$	0.623583	0.0364301	0.0182150	−	0.999834i	$-0.494202\pi$
$293$	0.623583	0.0364301	0.0182150	+	0.999834i	$0.494202\pi$
$294$	6.58812	0.384227
$295$	−3.28150	−0.191056
$296$	−2.09272	−0.121637
$297$	31.8531	1.84831
$298$	9.79280	0.567281
$299$	5.15958	0.298386
$300$	3.57819	0.206587
$301$	5.56112	0.320538
$302$	−10.8680	−0.625384
$303$	11.9074	0.684060
$304$	6.14782	0.352602
$305$	19.0808	1.09256
$306$	12.9952	0.742884
$307$	10.1719	0.580542	0.290271	−	0.956944i	$-0.406255\pi$
$307$	10.1719	0.580542	0.290271	+	0.956944i	$0.406255\pi$
$308$	5.15155	0.293537
$309$	−7.97355	−0.453600
$310$	1.51854	0.0862472
$311$	−26.4309	−1.49876	−0.749378	−	0.662142i	$-0.769648\pi$
$311$	−26.4309	−1.49876	−0.749378	+	0.662142i	$0.769648\pi$
$312$	−0.903257	−0.0511368
$313$	33.5439	1.89601	0.948005	−	0.318254i	$-0.103097\pi$
$313$	33.5439	1.89601	0.948005	+	0.318254i	$0.103097\pi$
$314$	−13.6618	−0.770983
$315$	−1.98538	−0.111864
$316$	−13.2547	−0.745633
$317$	−19.8086	−1.11256	−0.556282	−	0.830993i	$-0.687773\pi$
$317$	−19.8086	−1.11256	−0.556282	+	0.830993i	$0.687773\pi$
$318$	13.6334	0.764523
$319$	−19.1588	−1.07269
$320$	1.25349	0.0700721
$321$	−5.13005	−0.286332
$322$	4.94089	0.275345
$323$	−41.8076	−2.32624
$324$	0.384529	0.0213627
$325$	−2.96773	−0.164620
$326$	3.22517	0.178625
$327$	11.8033	0.652722
$328$	10.4877	0.579087
$329$	−3.15426	−0.173900
$330$	−8.13031	−0.447559
$331$	−26.7987	−1.47299	−0.736494	−	0.676444i	$-0.763520\pi$
$331$	−26.7987	−1.47299	−0.736494	+	0.676444i	$0.763520\pi$
$332$	−7.59965	−0.417085
$333$	3.99907	0.219148
$334$	−9.12706	−0.499410
$335$	12.6609	0.691738
$336$	−0.864972	−0.0471881
$337$	−24.9822	−1.36086	−0.680432	−	0.732811i	$-0.738208\pi$
$337$	−24.9822	−1.36086	−0.680432	+	0.732811i	$0.738208\pi$
$338$	−12.2508	−0.666358
$339$	−5.46671	−0.296911
$340$	−8.52421	−0.462290
$341$	7.52952	0.407746
$342$	−11.7481	−0.635266
$343$	−11.0345	−0.595807
$344$	6.70944	0.361749
$345$	−7.79784	−0.419822
$346$	−4.78033	−0.256992
$347$	8.83481	0.474277	0.237139	−	0.971476i	$-0.423790\pi$
$347$	8.83481	0.474277	0.237139	+	0.971476i	$0.423790\pi$
$348$	3.21687	0.172442
$349$	6.49505	0.347672	0.173836	−	0.984775i	$-0.444384\pi$
$349$	6.49505	0.347672	0.173836	+	0.984775i	$0.444384\pi$
$350$	−2.84194	−0.151908
$351$	4.43584	0.236768
$352$	6.21529	0.331276
$353$	4.24613	0.225999	0.112999	−	0.993595i	$-0.463954\pi$
$353$	4.24613	0.225999	0.112999	+	0.993595i	$0.463954\pi$
$354$	2.73198	0.145203
$355$	15.0198	0.797168
$356$	14.7901	0.783872
$357$	5.88215	0.311316
$358$	−8.25300	−0.436184
$359$	−5.56784	−0.293860	−0.146930	−	0.989147i	$-0.546939\pi$
$359$	−5.56784	−0.293860	−0.146930	+	0.989147i	$0.546939\pi$
$360$	−2.39534	−0.126246
$361$	18.7957	0.989248
$362$	22.4047	1.17756
$363$	−28.8340	−1.51339
$364$	0.717402	0.0376021
$365$	−12.8050	−0.670245
$366$	−15.8855	−0.830350
$367$	10.3769	0.541671	0.270836	−	0.962626i	$-0.412700\pi$
$367$	10.3769	0.541671	0.270836	+	0.962626i	$0.412700\pi$
$368$	5.96113	0.310745
$369$	−20.0414	−1.04331
$370$	−2.62320	−0.136374
$371$	−10.8282	−0.562171
$372$	−1.26424	−0.0655480
$373$	−15.1138	−0.782562	−0.391281	−	0.920271i	$-0.627968\pi$
$373$	−15.1138	−0.782562	−0.391281	+	0.920271i	$0.627968\pi$
$374$	−42.2664	−2.18555
$375$	11.0258	0.569369
$376$	−3.80558	−0.196258
$377$	−2.66805	−0.137411
$378$	4.24783	0.218485
$379$	−20.1927	−1.03723	−0.518615	−	0.855008i	$-0.673552\pi$
$379$	−20.1927	−1.03723	−0.518615	+	0.855008i	$0.673552\pi$
$380$	7.70622	0.395321
$381$	−3.60486	−0.184682
$382$	20.7592	1.06214
$383$	−2.49821	−0.127653	−0.0638263	−	0.997961i	$-0.520330\pi$
$383$	−2.49821	−0.127653	−0.0638263	+	0.997961i	$0.520330\pi$
$384$	−1.04358	−0.0532549
$385$	6.45741	0.329100
$386$	11.7359	0.597343
$387$	−12.8213	−0.651746
$388$	12.8202	0.650846
$389$	−35.4660	−1.79820	−0.899099	−	0.437746i	$-0.855777\pi$
$389$	−35.4660	−1.79820	−0.899099	+	0.437746i	$0.855777\pi$
$390$	−1.13222	−0.0573323
$391$	−40.5380	−2.05010
$392$	−6.31301	−0.318855
$393$	−1.31261	−0.0662125
$394$	−10.7241	−0.540270
$395$	−16.6146	−0.835969
$396$	−11.8771	−0.596845
$397$	−21.4444	−1.07626	−0.538131	−	0.842861i	$-0.680870\pi$
$397$	−21.4444	−1.07626	−0.538131	+	0.842861i	$0.680870\pi$
$398$	8.16835	0.409443
$399$	−5.31769	−0.266218
$400$	−3.42877	−0.171438
$401$	−0.576737	−0.0288009	−0.0144004	−	0.999896i	$-0.504584\pi$
$401$	−0.576737	−0.0288009	−0.0144004	+	0.999896i	$0.504584\pi$
$402$	−10.5407	−0.525722
$403$	1.04856	0.0522323
$404$	−11.4101	−0.567675
$405$	0.482003	0.0239509
$406$	−2.55496	−0.126801
$407$	−13.0069	−0.644728
$408$	7.09675	0.351341
$409$	−15.9873	−0.790522	−0.395261	−	0.918569i	$-0.629346\pi$
$409$	−15.9873	−0.790522	−0.395261	+	0.918569i	$0.629346\pi$
$410$	13.1462	0.649245
$411$	−16.7325	−0.825351
$412$	7.64058	0.376425
$413$	−2.16984	−0.106771
$414$	−11.3914	−0.559856
$415$	−9.52607	−0.467617
$416$	0.865537	0.0424365
$417$	−1.25263	−0.0613414
$418$	38.2105	1.86894
$419$	8.90380	0.434979	0.217490	−	0.976063i	$-0.430213\pi$
$419$	8.90380	0.434979	0.217490	+	0.976063i	$0.430213\pi$
$420$	−1.08423	−0.0529051
$421$	−28.5443	−1.39116	−0.695581	−	0.718448i	$-0.744853\pi$
$421$	−28.5443	−1.39116	−0.695581	+	0.718448i	$0.744853\pi$
$422$	26.6914	1.29932
$423$	7.27225	0.353589
$424$	−13.0641	−0.634447
$425$	23.3170	1.13104
$426$	−12.5046	−0.605849
$427$	12.6169	0.610575
$428$	4.91583	0.237615
$429$	−5.61400	−0.271047
$430$	8.41020	0.405576
$431$	9.60792	0.462797	0.231399	−	0.972859i	$-0.425670\pi$
$431$	9.60792	0.462797	0.231399	+	0.972859i	$0.425670\pi$
$432$	5.12496	0.246575
$433$	−5.66799	−0.272386	−0.136193	−	0.990682i	$-0.543487\pi$
$433$	−5.66799	−0.272386	−0.136193	+	0.990682i	$0.543487\pi$
$434$	1.00411	0.0481989
$435$	4.03230	0.193334
$436$	−11.3104	−0.541668
$437$	36.6480	1.75311
$438$	10.6607	0.509388
$439$	−2.24501	−0.107148	−0.0535742	−	0.998564i	$-0.517061\pi$
$439$	−2.24501	−0.107148	−0.0535742	+	0.998564i	$0.517061\pi$
$440$	7.79080	0.371412
$441$	12.0638	0.574466
$442$	−5.88599	−0.279968
$443$	−6.40432	−0.304279	−0.152139	−	0.988359i	$-0.548616\pi$
$443$	−6.40432	−0.304279	−0.152139	+	0.988359i	$0.548616\pi$
$444$	2.18392	0.103644
$445$	18.5392	0.878842
$446$	15.0713	0.713648
$447$	−10.2196	−0.483368
$448$	0.828851	0.0391595
$449$	−12.0705	−0.569642	−0.284821	−	0.958581i	$-0.591934\pi$
$449$	−12.0705	−0.569642	−0.284821	+	0.958581i	$0.591934\pi$
$450$	6.55218	0.308873
$451$	65.1842	3.06940
$452$	5.23842	0.246395
$453$	11.3416	0.532876
$454$	−25.6143	−1.20214
$455$	0.899254	0.0421577
$456$	−6.41574	−0.300444
$457$	14.1848	0.663535	0.331768	−	0.943361i	$-0.392355\pi$
$457$	14.1848	0.663535	0.331768	+	0.943361i	$0.392355\pi$
$458$	−3.02832	−0.141504
$459$	−34.8517	−1.62674
$460$	7.47221	0.348393
$461$	−1.76534	−0.0822199	−0.0411099	−	0.999155i	$-0.513089\pi$
$461$	−1.76534	−0.0822199	−0.0411099	+	0.999155i	$0.513089\pi$
$462$	−5.37605	−0.250117
$463$	−24.0956	−1.11982	−0.559908	−	0.828555i	$-0.689164\pi$
$463$	−24.0956	−1.11982	−0.559908	+	0.828555i	$0.689164\pi$
$464$	−3.08253	−0.143103
$465$	−1.58472	−0.0734894
$466$	−16.3038	−0.755260
$467$	−5.03203	−0.232855	−0.116427	−	0.993199i	$-0.537144\pi$
$467$	−5.03203	−0.232855	−0.116427	+	0.993199i	$0.537144\pi$
$468$	−1.65399	−0.0764558
$469$	8.37183	0.386575
$470$	−4.77025	−0.220035
$471$	14.2572	0.656938
$472$	−2.61789	−0.120498
$473$	41.7011	1.91742
$474$	13.8323	0.635338
$475$	−21.0794	−0.967191
$476$	−5.63652	−0.258349
$477$	24.9647	1.14305
$478$	28.0855	1.28460
$479$	14.5764	0.666011	0.333005	−	0.942925i	$-0.391937\pi$
$479$	14.5764	0.666011	0.333005	+	0.942925i	$0.391937\pi$
$480$	−1.30811	−0.0597070
$481$	−1.81133	−0.0825895
$482$	−19.7801	−0.900957
$483$	−5.15621	−0.234616
$484$	27.6299	1.25590
$485$	16.0699	0.729698
$486$	−15.7762	−0.715621
$487$	−13.1104	−0.594089	−0.297045	−	0.954864i	$-0.596001\pi$
$487$	−13.1104	−0.594089	−0.297045	+	0.954864i	$0.596001\pi$
$488$	15.2222	0.689075
$489$	−3.36572	−0.152203
$490$	−7.91328	−0.357485
$491$	15.5892	0.703530	0.351765	−	0.936088i	$-0.385582\pi$
$491$	15.5892	0.703530	0.351765	+	0.936088i	$0.385582\pi$
$492$	−10.9448	−0.493428
$493$	20.9624	0.944100
$494$	5.32117	0.239411
$495$	−14.8878	−0.669155
$496$	1.21145	0.0543957
$497$	9.93163	0.445494
$498$	7.93084	0.355389
$499$	22.8412	1.02251	0.511255	−	0.859429i	$-0.329181\pi$
$499$	22.8412	1.02251	0.511255	+	0.859429i	$0.329181\pi$
$500$	−10.5654	−0.472497
$501$	9.52481	0.425537
$502$	28.5753	1.27538
$503$	−38.0256	−1.69548	−0.847739	−	0.530414i	$-0.822037\pi$
$503$	−38.0256	−1.69548	−0.847739	+	0.530414i	$0.822037\pi$
$504$	−1.58389	−0.0705519
$505$	−14.3025	−0.636451
$506$	37.0502	1.64708
$507$	12.7847	0.567790
$508$	3.45432	0.153261
$509$	36.4654	1.61630	0.808149	−	0.588978i	$-0.200469\pi$
$509$	36.4654	1.61630	0.808149	+	0.588978i	$0.200469\pi$
$510$	8.89569	0.393908
$511$	−8.46714	−0.374564
$512$	1.00000	0.0441942
$513$	31.5073	1.39108
$514$	7.77246	0.342829
$515$	9.57738	0.422030
$516$	−7.00183	−0.308238
$517$	−23.6528	−1.04025
$518$	−1.73456	−0.0762120
$519$	4.98865	0.218977
$520$	1.08494	0.0475778
$521$	1.40002	0.0613361	0.0306681	−	0.999530i	$-0.490237\pi$
$521$	1.40002	0.0613361	0.0306681	+	0.999530i	$0.490237\pi$
$522$	5.89054	0.257822
$523$	3.98865	0.174412	0.0872058	−	0.996190i	$-0.472206\pi$
$523$	3.98865	0.174412	0.0872058	+	0.996190i	$0.472206\pi$
$524$	1.25780	0.0549471
$525$	2.96579	0.129438
$526$	0.0139729	0.000609247 0
$527$	−8.23834	−0.358868
$528$	−6.48615	−0.282273
$529$	12.5351	0.545003
$530$	−16.3757	−0.711313
$531$	5.00264	0.217096
$532$	5.09563	0.220924
$533$	9.07750	0.393190
$534$	−15.4346	−0.667921
$535$	6.16193	0.266404
$536$	10.1005	0.436276
$537$	8.61266	0.371664
$538$	29.5427	1.27368
$539$	−39.2372	−1.69006
$540$	6.42407	0.276448
$541$	−21.2376	−0.913077	−0.456539	−	0.889704i	$-0.650911\pi$
$541$	−21.2376	−0.913077	−0.456539	+	0.889704i	$0.650911\pi$
$542$	−4.31315	−0.185266
$543$	−23.3810	−1.00338
$544$	−6.80039	−0.291565
$545$	−14.1774	−0.607293
$546$	−0.748665	−0.0320399
$547$	−23.0288	−0.984641	−0.492320	−	0.870414i	$-0.663851\pi$
$547$	−23.0288	−0.984641	−0.492320	+	0.870414i	$0.663851\pi$
$548$	16.0337	0.684926
$549$	−29.0887	−1.24147
$550$	−21.3108	−0.908695
$551$	−18.9508	−0.807333
$552$	−6.22091	−0.264780
$553$	−10.9861	−0.467178
$554$	−3.14142	−0.133466
$555$	2.73752	0.116201
$556$	1.20032	0.0509048
$557$	5.12218	0.217034	0.108517	−	0.994095i	$-0.465390\pi$
$557$	5.12218	0.217034	0.108517	+	0.994095i	$0.465390\pi$
$558$	−2.31501	−0.0980023
$559$	5.80727	0.245621
$560$	1.03896	0.0439039
$561$	44.1084	1.86226
$562$	−14.3643	−0.605921
$563$	33.9207	1.42959	0.714794	−	0.699335i	$-0.246521\pi$
$563$	33.9207	1.42959	0.714794	+	0.699335i	$0.246521\pi$
$564$	3.97143	0.167227
$565$	6.56630	0.276246
$566$	−13.0024	−0.546532
$567$	0.318717	0.0133849
$568$	11.9824	0.502770
$569$	−41.5207	−1.74064	−0.870318	−	0.492490i	$-0.836087\pi$
$569$	−41.5207	−1.74064	−0.870318	+	0.492490i	$0.836087\pi$
$570$	−8.04205	−0.336845
$571$	−35.1012	−1.46894	−0.734469	−	0.678642i	$-0.762569\pi$
$571$	−35.1012	−1.46894	−0.734469	+	0.678642i	$0.762569\pi$
$572$	5.37957	0.224931
$573$	−21.6639	−0.905023
$574$	8.69275	0.362828
$575$	−20.4393	−0.852379
$576$	−1.91094	−0.0796226
$577$	−5.38586	−0.224216	−0.112108	−	0.993696i	$-0.535760\pi$
$577$	−5.38586	−0.224216	−0.112108	+	0.993696i	$0.535760\pi$
$578$	29.2454	1.21645
$579$	−12.2474	−0.508983
$580$	−3.86392	−0.160440
$581$	−6.29898	−0.261326
$582$	−13.3789	−0.554572
$583$	−81.1970	−3.36284
$584$	−10.2155	−0.422721
$585$	−2.07326	−0.0857187
$586$	0.623583	0.0257600
$587$	8.69627	0.358934	0.179467	−	0.983764i	$-0.442563\pi$
$587$	8.69627	0.358934	0.179467	+	0.983764i	$0.442563\pi$
$588$	6.58812	0.271690
$589$	7.44778	0.306881
$590$	−3.28150	−0.135097
$591$	11.1914	0.460353
$592$	−2.09272	−0.0860104
$593$	−7.42580	−0.304941	−0.152471	−	0.988308i	$-0.548723\pi$
$593$	−7.42580	−0.304941	−0.152471	+	0.988308i	$0.548723\pi$
$594$	31.8531	1.30695
$595$	−7.06531	−0.289649
$596$	9.79280	0.401129
$597$	−8.52432	−0.348877
$598$	5.15958	0.210991
$599$	−6.23895	−0.254917	−0.127458	−	0.991844i	$-0.540682\pi$
$599$	−6.23895	−0.254917	−0.127458	+	0.991844i	$0.540682\pi$
$600$	3.57819	0.146079
$601$	−0.218630	−0.00891811	−0.00445905	−	0.999990i	$-0.501419\pi$
$601$	−0.218630	−0.00891811	−0.00445905	+	0.999990i	$0.501419\pi$
$602$	5.56112	0.226655
$603$	−19.3015	−0.786019
$604$	−10.8680	−0.442213
$605$	34.6337	1.40806
$606$	11.9074	0.483704
$607$	25.9579	1.05360	0.526798	−	0.849990i	$-0.323392\pi$
$607$	25.9579	1.05360	0.526798	+	0.849990i	$0.323392\pi$
$608$	6.14782	0.249327
$609$	2.66630	0.108044
$610$	19.0808	0.772559
$611$	−3.29387	−0.133256
$612$	12.9952	0.525298
$613$	−4.72664	−0.190907	−0.0954537	−	0.995434i	$-0.530430\pi$
$613$	−4.72664	−0.190907	−0.0954537	+	0.995434i	$0.530430\pi$
$614$	10.1719	0.410505
$615$	−13.7191	−0.553208
$616$	5.15155	0.207562
$617$	−13.1225	−0.528292	−0.264146	−	0.964483i	$-0.585090\pi$
$617$	−13.1225	−0.528292	−0.264146	+	0.964483i	$0.585090\pi$
$618$	−7.97355	−0.320743
$619$	35.1344	1.41217	0.706086	−	0.708126i	$-0.250459\pi$
$619$	35.1344	1.41217	0.706086	+	0.708126i	$0.250459\pi$
$620$	1.51854	0.0609860
$621$	30.5505	1.22595
$622$	−26.4309	−1.05978
$623$	12.2588	0.491137
$624$	−0.903257	−0.0361592
$625$	3.90028	0.156011
$626$	33.5439	1.34068
$627$	−39.8757	−1.59248
$628$	−13.6618	−0.545167
$629$	14.2313	0.567441
$630$	−1.98538	−0.0790996
$631$	−1.26963	−0.0505432	−0.0252716	−	0.999681i	$-0.508045\pi$
$631$	−1.26963	−0.0505432	−0.0252716	+	0.999681i	$0.508045\pi$
$632$	−13.2547	−0.527242
$633$	−27.8546	−1.10712
$634$	−19.8086	−0.786702
$635$	4.32995	0.171829
$636$	13.6334	0.540599
$637$	−5.46414	−0.216497
$638$	−19.1588	−0.758505
$639$	−22.8977	−0.905818
$640$	1.25349	0.0495485
$641$	−35.6042	−1.40628	−0.703141	−	0.711051i	$-0.748220\pi$
$641$	−35.6042	−1.40628	−0.703141	+	0.711051i	$0.748220\pi$
$642$	−5.13005	−0.202467
$643$	49.6708	1.95882	0.979412	−	0.201873i	$-0.0647028\pi$
$643$	49.6708	1.95882	0.979412	+	0.201873i	$0.0647028\pi$
$644$	4.94089	0.194698
$645$	−8.77671	−0.345583
$646$	−41.8076	−1.64490
$647$	−4.33400	−0.170387	−0.0851936	−	0.996364i	$-0.527151\pi$
$647$	−4.33400	−0.170387	−0.0851936	+	0.996364i	$0.527151\pi$
$648$	0.384529	0.0151057
$649$	−16.2710	−0.638691
$650$	−2.96773	−0.116404
$651$	−1.04787	−0.0410693
$652$	3.22517	0.126307
$653$	9.19447	0.359807	0.179904	−	0.983684i	$-0.442421\pi$
$653$	9.19447	0.359807	0.179904	+	0.983684i	$0.442421\pi$
$654$	11.8033	0.461544
$655$	1.57663	0.0616042
$656$	10.4877	0.409476
$657$	19.5213	0.761597
$658$	−3.15426	−0.122966
$659$	−38.2912	−1.49161	−0.745806	−	0.666163i	$-0.767935\pi$
$659$	−38.2912	−1.49161	−0.745806	+	0.666163i	$0.767935\pi$
$660$	−8.13031	−0.316472
$661$	−25.3806	−0.987189	−0.493595	−	0.869692i	$-0.664317\pi$
$661$	−25.3806	−0.987189	−0.493595	+	0.869692i	$0.664317\pi$
$662$	−26.7987	−1.04156
$663$	6.14250	0.238555
$664$	−7.59965	−0.294924
$665$	6.38731	0.247689
$666$	3.99907	0.154961
$667$	−18.3754	−0.711497
$668$	−9.12706	−0.353136
$669$	−15.7281	−0.608084
$670$	12.6609	0.489133
$671$	94.6101	3.65238
$672$	−0.864972	−0.0333670
$673$	−34.9171	−1.34595	−0.672977	−	0.739663i	$-0.734985\pi$
$673$	−34.9171	−1.34595	−0.672977	+	0.739663i	$0.734985\pi$
$674$	−24.9822	−0.962277
$675$	−17.5723	−0.676358
$676$	−12.2508	−0.471186
$677$	−34.3084	−1.31858	−0.659290	−	0.751888i	$-0.729143\pi$
$677$	−34.3084	−1.31858	−0.659290	+	0.751888i	$0.729143\pi$
$678$	−5.46671	−0.209948
$679$	10.6260	0.407789
$680$	−8.52421	−0.326889
$681$	26.7305	1.02432
$682$	7.52952	0.288320
$683$	−43.6101	−1.66869	−0.834347	−	0.551240i	$-0.814155\pi$
$683$	−43.6101	−1.66869	−0.834347	+	0.551240i	$0.814155\pi$
$684$	−11.7481	−0.449201
$685$	20.0981	0.767908
$686$	−11.0345	−0.421299
$687$	3.16029	0.120573
$688$	6.70944	0.255795
$689$	−11.3074	−0.430779
$690$	−7.79784	−0.296859
$691$	19.5554	0.743921	0.371961	−	0.928248i	$-0.378686\pi$
$691$	19.5554	0.743921	0.371961	+	0.928248i	$0.378686\pi$
$692$	−4.78033	−0.181721
$693$	−9.84432	−0.373955
$694$	8.83481	0.335365
$695$	1.50458	0.0570721
$696$	3.21687	0.121935
$697$	−71.3205	−2.70146
$698$	6.49505	0.245841
$699$	17.0143	0.643541
$700$	−2.84194	−0.107415
$701$	42.8634	1.61893	0.809464	−	0.587170i	$-0.199758\pi$
$701$	42.8634	1.61893	0.809464	+	0.587170i	$0.199758\pi$
$702$	4.43584	0.167420
$703$	−12.8657	−0.485239
$704$	6.21529	0.234248
$705$	4.97814	0.187487
$706$	4.24613	0.159805
$707$	−9.45729	−0.355678
$708$	2.73198	0.102674
$709$	−27.6891	−1.03989	−0.519943	−	0.854201i	$-0.674047\pi$
$709$	−27.6891	−1.03989	−0.519943	+	0.854201i	$0.674047\pi$
$710$	15.0198	0.563683
$711$	25.3289	0.949908
$712$	14.7901	0.554282
$713$	7.22162	0.270452
$714$	5.88215	0.220134
$715$	6.74322	0.252182
$716$	−8.25300	−0.308429
$717$	−29.3094	−1.09458
$718$	−5.56784	−0.207790
$719$	−23.4596	−0.874896	−0.437448	−	0.899244i	$-0.644118\pi$
$719$	−23.4596	−0.874896	−0.437448	+	0.899244i	$0.644118\pi$
$720$	−2.39534	−0.0892692
$721$	6.33291	0.235850
$722$	18.7957	0.699504
$723$	20.6421	0.767686
$724$	22.4047	0.832663
$725$	10.5693	0.392533
$726$	−28.8340	−1.07013
$727$	−17.0209	−0.631271	−0.315635	−	0.948881i	$-0.602218\pi$
$727$	−17.0209	−0.631271	−0.315635	+	0.948881i	$0.602218\pi$
$728$	0.717402	0.0265887
$729$	15.3101	0.567040
$730$	−12.8050	−0.473935
$731$	−45.6268	−1.68757
$732$	−15.8855	−0.587146
$733$	−31.6475	−1.16893	−0.584463	−	0.811420i	$-0.698695\pi$
$733$	−31.6475	−1.16893	−0.584463	+	0.811420i	$0.698695\pi$
$734$	10.3769	0.383020
$735$	8.25813	0.304606
$736$	5.96113	0.219730
$737$	62.7777	2.31245
$738$	−20.0414	−0.737734
$739$	22.6632	0.833678	0.416839	−	0.908980i	$-0.363138\pi$
$739$	22.6632	0.833678	0.416839	+	0.908980i	$0.363138\pi$
$740$	−2.62320	−0.0964309
$741$	−5.55306	−0.203997
$742$	−10.8282	−0.397515
$743$	−20.2456	−0.742739	−0.371370	−	0.928485i	$-0.621112\pi$
$743$	−20.2456	−0.742739	−0.371370	+	0.928485i	$0.621112\pi$
$744$	−1.26424	−0.0463495
$745$	12.2752	0.449727
$746$	−15.1138	−0.553355
$747$	14.5225	0.531350
$748$	−42.2664	−1.54541
$749$	4.07449	0.148879
$750$	11.0258	0.402605
$751$	−26.1416	−0.953922	−0.476961	−	0.878924i	$-0.658262\pi$
$751$	−26.1416	−0.953922	−0.476961	+	0.878924i	$0.658262\pi$
$752$	−3.80558	−0.138775
$753$	−29.8206	−1.08672
$754$	−2.66805	−0.0971645
$755$	−13.6229	−0.495789
$756$	4.24783	0.154492
$757$	44.4605	1.61594	0.807972	−	0.589220i	$-0.200565\pi$
$757$	44.4605	1.61594	0.807972	+	0.589220i	$0.200565\pi$
$758$	−20.1927	−0.733433
$759$	−38.6648	−1.40344
$760$	7.70622	0.279534
$761$	−21.0301	−0.762339	−0.381170	−	0.924505i	$-0.624479\pi$
$761$	−21.0301	−0.762339	−0.381170	+	0.924505i	$0.624479\pi$
$762$	−3.60486	−0.130590
$763$	−9.37461	−0.339384
$764$	20.7592	0.751043
$765$	16.2893	0.588940
$766$	−2.49821	−0.0902640
$767$	−2.26588	−0.0818163
$768$	−1.04358	−0.0376569
$769$	8.28771	0.298862	0.149431	−	0.988772i	$-0.452256\pi$
$769$	8.28771	0.298862	0.149431	+	0.988772i	$0.452256\pi$
$770$	6.45741	0.232709
$771$	−8.11118	−0.292117
$772$	11.7359	0.422385
$773$	−21.4183	−0.770361	−0.385181	−	0.922841i	$-0.625861\pi$
$773$	−21.4183	−0.770361	−0.385181	+	0.922841i	$0.625861\pi$
$774$	−12.8213	−0.460854
$775$	−4.15378	−0.149208
$776$	12.8202	0.460217
$777$	1.81015	0.0649387
$778$	−35.4660	−1.27152
$779$	64.4766	2.31011
$780$	−1.13222	−0.0405400
$781$	74.4741	2.66489
$782$	−40.5380	−1.44964
$783$	−15.7978	−0.564569
$784$	−6.31301	−0.225464
$785$	−17.1250	−0.611216
$786$	−1.31261	−0.0468193
$787$	27.4987	0.980222	0.490111	−	0.871660i	$-0.336956\pi$
$787$	27.4987	0.980222	0.490111	+	0.871660i	$0.336956\pi$
$788$	−10.7241	−0.382029
$789$	−0.0145818	−0.000519127 0
$790$	−16.6146	−0.591120
$791$	4.34187	0.154379
$792$	−11.8771	−0.422033
$793$	13.1753	0.467870
$794$	−21.4444	−0.761033
$795$	17.0893	0.606095
$796$	8.16835	0.289520
$797$	−37.3363	−1.32252	−0.661259	−	0.750158i	$-0.729978\pi$
$797$	−37.3363	−1.32252	−0.661259	+	0.750158i	$0.729978\pi$
$798$	−5.31769	−0.188244
$799$	25.8795	0.915549
$800$	−3.42877	−0.121225
$801$	−28.2630	−0.998623
$802$	−0.576737	−0.0203653
$803$	−63.4924	−2.24060
$804$	−10.5407	−0.371742
$805$	6.19335	0.218287
$806$	1.04856	0.0369338
$807$	−30.8301	−1.08527
$808$	−11.4101	−0.401407
$809$	−47.8295	−1.68159	−0.840797	−	0.541350i	$-0.817913\pi$
$809$	−47.8295	−1.68159	−0.840797	+	0.541350i	$0.817913\pi$
$810$	0.482003	0.0169358
$811$	29.1721	1.02437	0.512185	−	0.858875i	$-0.328836\pi$
$811$	29.1721	1.02437	0.512185	+	0.858875i	$0.328836\pi$
$812$	−2.55496	−0.0896615
$813$	4.50111	0.157861
$814$	−13.0069	−0.455891
$815$	4.04271	0.141610
$816$	7.09675	0.248436
$817$	41.2484	1.44310
$818$	−15.9873	−0.558983
$819$	−1.37091	−0.0479036
$820$	13.1462	0.459086
$821$	−24.0734	−0.840167	−0.420084	−	0.907485i	$-0.637999\pi$
$821$	−24.0734	−0.840167	−0.420084	+	0.907485i	$0.637999\pi$
$822$	−16.7325	−0.583611
$823$	3.51481	0.122518	0.0612592	−	0.998122i	$-0.480488\pi$
$823$	3.51481	0.122518	0.0612592	+	0.998122i	$0.480488\pi$
$824$	7.64058	0.266172
$825$	22.2395	0.774280
$826$	−2.16984	−0.0754985
$827$	−33.4872	−1.16446	−0.582232	−	0.813022i	$-0.697821\pi$
$827$	−33.4872	−1.16446	−0.582232	+	0.813022i	$0.697821\pi$
$828$	−11.3914	−0.395878
$829$	−33.1847	−1.15255	−0.576276	−	0.817255i	$-0.695495\pi$
$829$	−33.1847	−1.15255	−0.576276	+	0.817255i	$0.695495\pi$
$830$	−9.52607	−0.330655
$831$	3.27832	0.113724
$832$	0.865537	0.0300071
$833$	42.9309	1.48747
$834$	−1.25263	−0.0433749
$835$	−11.4407	−0.395920
$836$	38.2105	1.32154
$837$	6.20863	0.214602
$838$	8.90380	0.307577
$839$	6.80617	0.234975	0.117488	−	0.993074i	$-0.462516\pi$
$839$	6.80617	0.234975	0.117488	+	0.993074i	$0.462516\pi$
$840$	−1.08423	−0.0374096
$841$	−19.4980	−0.672345
$842$	−28.5443	−0.983700
$843$	14.9903	0.516292
$844$	26.6914	0.918757
$845$	−15.3563	−0.528272
$846$	7.27225	0.250025
$847$	22.9011	0.786889
$848$	−13.0641	−0.448622
$849$	13.5690	0.465688
$850$	23.3170	0.799765
$851$	−12.4750	−0.427637
$852$	−12.5046	−0.428400
$853$	−5.72853	−0.196141	−0.0980705	−	0.995179i	$-0.531267\pi$
$853$	−5.72853	−0.196141	−0.0980705	+	0.995179i	$0.531267\pi$
$854$	12.6169	0.431742
$855$	−14.7261	−0.503624
$856$	4.91583	0.168019
$857$	−26.4618	−0.903917	−0.451958	−	0.892039i	$-0.649274\pi$
$857$	−26.4618	−0.903917	−0.451958	+	0.892039i	$0.649274\pi$
$858$	−5.61400	−0.191659
$859$	−50.4440	−1.72113	−0.860564	−	0.509343i	$-0.829889\pi$
$859$	−50.4440	−1.72113	−0.860564	+	0.509343i	$0.829889\pi$
$860$	8.41020	0.286785
$861$	−9.07157	−0.309158
$862$	9.60792	0.327247
$863$	21.5663	0.734124	0.367062	−	0.930196i	$-0.380364\pi$
$863$	21.5663	0.734124	0.367062	+	0.930196i	$0.380364\pi$
$864$	5.12496	0.174355
$865$	−5.99208	−0.203737
$866$	−5.66799	−0.192606
$867$	−30.5199	−1.03651
$868$	1.00411	0.0340818
$869$	−82.3816	−2.79460
$870$	4.03230	0.136708
$871$	8.74238	0.296224
$872$	−11.3104	−0.383017
$873$	−24.4986	−0.829153
$874$	36.6480	1.23964
$875$	−8.75711	−0.296044
$876$	10.6607	0.360191
$877$	−0.648721	−0.0219057	−0.0109529	−	0.999940i	$-0.503486\pi$
$877$	−0.648721	−0.0219057	−0.0109529	+	0.999940i	$0.503486\pi$
$878$	−2.24501	−0.0757653
$879$	−0.650758	−0.0219495
$880$	7.79080	0.262628
$881$	−16.6564	−0.561167	−0.280583	−	0.959830i	$-0.590528\pi$
$881$	−16.6564	−0.561167	−0.280583	+	0.959830i	$0.590528\pi$
$882$	12.0638	0.406209
$883$	−29.0335	−0.977055	−0.488528	−	0.872548i	$-0.662466\pi$
$883$	−29.0335	−0.977055	−0.488528	+	0.872548i	$0.662466\pi$
$884$	−5.88599	−0.197967
$885$	3.42450	0.115113
$886$	−6.40432	−0.215157
$887$	−23.6703	−0.794770	−0.397385	−	0.917652i	$-0.630082\pi$
$887$	−23.6703	−0.794770	−0.397385	+	0.917652i	$0.630082\pi$
$888$	2.18392	0.0732876
$889$	2.86312	0.0960259
$890$	18.5392	0.621435
$891$	2.38996	0.0800667
$892$	15.0713	0.504625
$893$	−23.3960	−0.782918
$894$	−10.2196	−0.341793
$895$	−10.3450	−0.345796
$896$	0.828851	0.0276900
$897$	−5.38443	−0.179781
$898$	−12.0705	−0.402798
$899$	−3.73433	−0.124547
$900$	6.55218	0.218406
$901$	88.8408	2.95972
$902$	65.1842	2.17040
$903$	−5.80347	−0.193128
$904$	5.23842	0.174227
$905$	28.0840	0.933543
$906$	11.3416	0.376800
$907$	−1.13307	−0.0376230	−0.0188115	−	0.999823i	$-0.505988\pi$
$907$	−1.13307	−0.0376230	−0.0188115	+	0.999823i	$0.505988\pi$
$908$	−25.6143	−0.850039
$909$	21.8041	0.723196
$910$	0.899254	0.0298100
$911$	16.7688	0.555574	0.277787	−	0.960643i	$-0.410399\pi$
$911$	16.7688	0.555574	0.277787	+	0.960643i	$0.410399\pi$
$912$	−6.41574	−0.212446
$913$	−47.2341	−1.56322
$914$	14.1848	0.469190
$915$	−19.9123	−0.658281
$916$	−3.02832	−0.100059
$917$	1.04253	0.0344273
$918$	−34.8517	−1.15028
$919$	53.0530	1.75006	0.875028	−	0.484072i	$-0.160843\pi$
$919$	53.0530	1.75006	0.875028	+	0.484072i	$0.160843\pi$
$920$	7.47221	0.246351
$921$	−10.6152	−0.349783
$922$	−1.76534	−0.0581382
$923$	10.3712	0.341373
$924$	−5.37605	−0.176859
$925$	7.17546	0.235928
$926$	−24.0956	−0.791829
$927$	−14.6007	−0.479550
$928$	−3.08253	−0.101189
$929$	−39.7600	−1.30448	−0.652241	−	0.758012i	$-0.726171\pi$
$929$	−39.7600	−1.30448	−0.652241	+	0.758012i	$0.726171\pi$
$930$	−1.58472	−0.0519649
$931$	−38.8112	−1.27199
$932$	−16.3038	−0.534049
$933$	27.5827	0.903017
$934$	−5.03203	−0.164653
$935$	−52.9805	−1.73265
$936$	−1.65399	−0.0540624
$937$	31.3165	1.02307	0.511533	−	0.859264i	$-0.329078\pi$
$937$	31.3165	1.02307	0.511533	+	0.859264i	$0.329078\pi$
$938$	8.37183	0.273350
$939$	−35.0057	−1.14237
$940$	−4.77025	−0.155588
$941$	−28.4497	−0.927434	−0.463717	−	0.885983i	$-0.653485\pi$
$941$	−28.4497	−0.927434	−0.463717	+	0.885983i	$0.653485\pi$
$942$	14.2572	0.464525
$943$	62.5186	2.03589
$944$	−2.61789	−0.0852051
$945$	5.32460	0.173209
$946$	41.7011	1.35582
$947$	−38.1676	−1.24028	−0.620140	−	0.784491i	$-0.712924\pi$
$947$	−38.1676	−1.24028	−0.620140	+	0.784491i	$0.712924\pi$
$948$	13.8323	0.449252
$949$	−8.84190	−0.287020
$950$	−21.0794	−0.683908
$951$	20.6719	0.670332
$952$	−5.63652	−0.182681
$953$	13.3366	0.432013	0.216007	−	0.976392i	$-0.430697\pi$
$953$	13.3366	0.432013	0.216007	+	0.976392i	$0.430697\pi$
$954$	24.9647	0.808262
$955$	26.0215	0.842035
$956$	28.0855	0.908350
$957$	19.9938	0.646306
$958$	14.5764	0.470941
$959$	13.2896	0.429142
$960$	−1.30811	−0.0422192
$961$	−29.5324	−0.952658
$962$	−1.81133	−0.0583996
$963$	−9.39386	−0.302713
$964$	−19.7801	−0.637073
$965$	14.7109	0.473559
$966$	−5.15621	−0.165898
$967$	46.1912	1.48541	0.742705	−	0.669619i	$-0.233543\pi$
$967$	46.1912	1.48541	0.742705	+	0.669619i	$0.233543\pi$
$968$	27.6299	0.888058
$969$	43.6296	1.40158
$970$	16.0699	0.515975
$971$	−45.7609	−1.46854	−0.734268	−	0.678860i	$-0.762474\pi$
$971$	−45.7609	−1.46854	−0.734268	+	0.678860i	$0.762474\pi$
$972$	−15.7762	−0.506021
$973$	0.994885	0.0318946
$974$	−13.1104	−0.420085
$975$	3.09706	0.0991852
$976$	15.2222	0.487249
$977$	14.7173	0.470848	0.235424	−	0.971893i	$-0.424352\pi$
$977$	14.7173	0.470848	0.235424	+	0.971893i	$0.424352\pi$
$978$	−3.36572	−0.107624
$979$	91.9247	2.93792
$980$	−7.91328	−0.252780
$981$	21.6135	0.690064
$982$	15.5892	0.497471
$983$	−23.0020	−0.733651	−0.366825	−	0.930290i	$-0.619555\pi$
$983$	−23.0020	−0.733651	−0.366825	+	0.930290i	$0.619555\pi$
$984$	−10.9448	−0.348906
$985$	−13.4425	−0.428313
$986$	20.9624	0.667580
$987$	3.29172	0.104777
$988$	5.32117	0.169289
$989$	39.9958	1.27179
$990$	−14.8878	−0.473164
$991$	54.8488	1.74233	0.871165	−	0.490991i	$-0.163365\pi$
$991$	54.8488	1.74233	0.871165	+	0.490991i	$0.163365\pi$
$992$	1.21145	0.0384636
$993$	27.9665	0.887491
$994$	9.93163	0.315012
$995$	10.2389	0.324596
$996$	7.93084	0.251298
$997$	−22.3014	−0.706293	−0.353147	−	0.935568i	$-0.614888\pi$
$997$	−22.3014	−0.706293	−0.353147	+	0.935568i	$0.614888\pi$
$998$	22.8412	0.723024
$999$	−10.7251	−0.339328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.d.1.16	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.d.1.16	✓	52	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.04358 q^{3} +1.00000 q^{4} +1.25349 q^{5} -1.04358 q^{6} +0.828851 q^{7} +1.00000 q^{8} -1.91094 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.04358 q^{3} +1.00000 q^{4} +1.25349 q^{5} -1.04358 q^{6} +0.828851 q^{7} +1.00000 q^{8} -1.91094 q^{9} +1.25349 q^{10} +6.21529 q^{11} -1.04358 q^{12} +0.865537 q^{13} +0.828851 q^{14} -1.30811 q^{15} +1.00000 q^{16} -6.80039 q^{17} -1.91094 q^{18} +6.14782 q^{19} +1.25349 q^{20} -0.864972 q^{21} +6.21529 q^{22} +5.96113 q^{23} -1.04358 q^{24} -3.42877 q^{25} +0.865537 q^{26} +5.12496 q^{27} +0.828851 q^{28} -3.08253 q^{29} -1.30811 q^{30} +1.21145 q^{31} +1.00000 q^{32} -6.48615 q^{33} -6.80039 q^{34} +1.03896 q^{35} -1.91094 q^{36} -2.09272 q^{37} +6.14782 q^{38} -0.903257 q^{39} +1.25349 q^{40} +10.4877 q^{41} -0.864972 q^{42} +6.70944 q^{43} +6.21529 q^{44} -2.39534 q^{45} +5.96113 q^{46} -3.80558 q^{47} -1.04358 q^{48} -6.31301 q^{49} -3.42877 q^{50} +7.09675 q^{51} +0.865537 q^{52} -13.0641 q^{53} +5.12496 q^{54} +7.79080 q^{55} +0.828851 q^{56} -6.41574 q^{57} -3.08253 q^{58} -2.61789 q^{59} -1.30811 q^{60} +15.2222 q^{61} +1.21145 q^{62} -1.58389 q^{63} +1.00000 q^{64} +1.08494 q^{65} -6.48615 q^{66} +10.1005 q^{67} -6.80039 q^{68} -6.22091 q^{69} +1.03896 q^{70} +11.9824 q^{71} -1.91094 q^{72} -10.2155 q^{73} -2.09272 q^{74} +3.57819 q^{75} +6.14782 q^{76} +5.15155 q^{77} -0.903257 q^{78} -13.2547 q^{79} +1.25349 q^{80} +0.384529 q^{81} +10.4877 q^{82} -7.59965 q^{83} -0.864972 q^{84} -8.52421 q^{85} +6.70944 q^{86} +3.21687 q^{87} +6.21529 q^{88} +14.7901 q^{89} -2.39534 q^{90} +0.717402 q^{91} +5.96113 q^{92} -1.26424 q^{93} -3.80558 q^{94} +7.70622 q^{95} -1.04358 q^{96} +12.8202 q^{97} -6.31301 q^{98} -11.8771 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * q^99

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