LMFDB - Embedded newform 4034.2.a.d.1.19

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			1.19
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.570351 q^{3} +1.00000 q^{4} -1.34990 q^{5} -0.570351 q^{6} -5.21632 q^{7} +1.00000 q^{8} -2.67470 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.570351 q^{3} +1.00000 q^{4} -1.34990 q^{5} -0.570351 q^{6} -5.21632 q^{7} +1.00000 q^{8} -2.67470 q^{9} -1.34990 q^{10} +4.89676 q^{11} -0.570351 q^{12} -1.50729 q^{13} -5.21632 q^{14} +0.769917 q^{15} +1.00000 q^{16} +0.322117 q^{17} -2.67470 q^{18} -4.66258 q^{19} -1.34990 q^{20} +2.97514 q^{21} +4.89676 q^{22} -9.15574 q^{23} -0.570351 q^{24} -3.17777 q^{25} -1.50729 q^{26} +3.23657 q^{27} -5.21632 q^{28} +2.96884 q^{29} +0.769917 q^{30} +5.76322 q^{31} +1.00000 q^{32} -2.79288 q^{33} +0.322117 q^{34} +7.04151 q^{35} -2.67470 q^{36} +8.51683 q^{37} -4.66258 q^{38} +0.859688 q^{39} -1.34990 q^{40} +6.87743 q^{41} +2.97514 q^{42} -1.22389 q^{43} +4.89676 q^{44} +3.61058 q^{45} -9.15574 q^{46} -4.13339 q^{47} -0.570351 q^{48} +20.2100 q^{49} -3.17777 q^{50} -0.183720 q^{51} -1.50729 q^{52} +11.4389 q^{53} +3.23657 q^{54} -6.61014 q^{55} -5.21632 q^{56} +2.65931 q^{57} +2.96884 q^{58} +11.2413 q^{59} +0.769917 q^{60} -11.6601 q^{61} +5.76322 q^{62} +13.9521 q^{63} +1.00000 q^{64} +2.03470 q^{65} -2.79288 q^{66} -8.42595 q^{67} +0.322117 q^{68} +5.22199 q^{69} +7.04151 q^{70} +6.79327 q^{71} -2.67470 q^{72} -11.4400 q^{73} +8.51683 q^{74} +1.81245 q^{75} -4.66258 q^{76} -25.5431 q^{77} +0.859688 q^{78} -7.18568 q^{79} -1.34990 q^{80} +6.17811 q^{81} +6.87743 q^{82} +0.615951 q^{83} +2.97514 q^{84} -0.434825 q^{85} -1.22389 q^{86} -1.69328 q^{87} +4.89676 q^{88} +17.3622 q^{89} +3.61058 q^{90} +7.86253 q^{91} -9.15574 q^{92} -3.28706 q^{93} -4.13339 q^{94} +6.29402 q^{95} -0.570351 q^{96} +11.3356 q^{97} +20.2100 q^{98} -13.0974 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.570351	−0.329293	−0.164646	−	0.986353i	$-0.552648\pi$
$3$	−0.570351	−0.329293	−0.164646	+	0.986353i	$0.552648\pi$
$4$	1.00000	0.500000
$5$	−1.34990	−0.603694	−0.301847	−	0.953356i	$-0.597603\pi$
$5$	−1.34990	−0.603694	−0.301847	+	0.953356i	$0.597603\pi$
$6$	−0.570351	−0.232845
$7$	−5.21632	−1.97158	−0.985792	−	0.167971i	$-0.946279\pi$
$7$	−5.21632	−1.97158	−0.985792	+	0.167971i	$0.946279\pi$
$8$	1.00000	0.353553
$9$	−2.67470	−0.891566
$10$	−1.34990	−0.426876
$11$	4.89676	1.47643	0.738215	−	0.674566i	$-0.235669\pi$
$11$	4.89676	1.47643	0.738215	+	0.674566i	$0.235669\pi$
$12$	−0.570351	−0.164646
$13$	−1.50729	−0.418048	−0.209024	−	0.977910i	$-0.567029\pi$
$13$	−1.50729	−0.418048	−0.209024	+	0.977910i	$0.567029\pi$
$14$	−5.21632	−1.39412
$15$	0.769917	0.198792
$16$	1.00000	0.250000
$17$	0.322117	0.0781247	0.0390624	−	0.999237i	$-0.487563\pi$
$17$	0.322117	0.0781247	0.0390624	+	0.999237i	$0.487563\pi$
$18$	−2.67470	−0.630433
$19$	−4.66258	−1.06967	−0.534835	−	0.844956i	$-0.679626\pi$
$19$	−4.66258	−1.06967	−0.534835	+	0.844956i	$0.679626\pi$
$20$	−1.34990	−0.301847
$21$	2.97514	0.649228
$22$	4.89676	1.04399
$23$	−9.15574	−1.90910	−0.954551	−	0.298046i	$-0.903665\pi$
$23$	−9.15574	−1.90910	−0.954551	+	0.298046i	$0.903665\pi$
$24$	−0.570351	−0.116422
$25$	−3.17777	−0.635554
$26$	−1.50729	−0.295605
$27$	3.23657	0.622879
$28$	−5.21632	−0.985792
$29$	2.96884	0.551300	0.275650	−	0.961258i	$-0.411107\pi$
$29$	2.96884	0.551300	0.275650	+	0.961258i	$0.411107\pi$
$30$	0.769917	0.140567
$31$	5.76322	1.03510	0.517552	−	0.855651i	$-0.326843\pi$
$31$	5.76322	1.03510	0.517552	+	0.855651i	$0.326843\pi$
$32$	1.00000	0.176777
$33$	−2.79288	−0.486177
$34$	0.322117	0.0552425
$35$	7.04151	1.19023
$36$	−2.67470	−0.445783
$37$	8.51683	1.40016	0.700079	−	0.714065i	$-0.253148\pi$
$37$	8.51683	1.40016	0.700079	+	0.714065i	$0.253148\pi$
$38$	−4.66258	−0.756371
$39$	0.859688	0.137660
$40$	−1.34990	−0.213438
$41$	6.87743	1.07407	0.537037	−	0.843559i	$-0.319544\pi$
$41$	6.87743	1.07407	0.537037	+	0.843559i	$0.319544\pi$
$42$	2.97514	0.459073
$43$	−1.22389	−0.186641	−0.0933207	−	0.995636i	$-0.529748\pi$
$43$	−1.22389	−0.186641	−0.0933207	+	0.995636i	$0.529748\pi$
$44$	4.89676	0.738215
$45$	3.61058	0.538233
$46$	−9.15574	−1.34994
$47$	−4.13339	−0.602917	−0.301458	−	0.953479i	$-0.597473\pi$
$47$	−4.13339	−0.602917	−0.301458	+	0.953479i	$0.597473\pi$
$48$	−0.570351	−0.0823231
$49$	20.2100	2.88714
$50$	−3.17777	−0.449405
$51$	−0.183720	−0.0257259
$52$	−1.50729	−0.209024
$53$	11.4389	1.57126	0.785628	−	0.618699i	$-0.212340\pi$
$53$	11.4389	1.57126	0.785628	+	0.618699i	$0.212340\pi$
$54$	3.23657	0.440442
$55$	−6.61014	−0.891311
$56$	−5.21632	−0.697060
$57$	2.65931	0.352234
$58$	2.96884	0.389828
$59$	11.2413	1.46349	0.731747	−	0.681576i	$-0.238705\pi$
$59$	11.2413	1.46349	0.731747	+	0.681576i	$0.238705\pi$
$60$	0.769917	0.0993959
$61$	−11.6601	−1.49293	−0.746463	−	0.665427i	$-0.768250\pi$
$61$	−11.6601	−1.49293	−0.746463	+	0.665427i	$0.768250\pi$
$62$	5.76322	0.731930
$63$	13.9521	1.75780
$64$	1.00000	0.125000
$65$	2.03470	0.252373
$66$	−2.79288	−0.343779
$67$	−8.42595	−1.02939	−0.514697	−	0.857372i	$-0.672096\pi$
$67$	−8.42595	−1.02939	−0.514697	+	0.857372i	$0.672096\pi$
$68$	0.322117	0.0390624
$69$	5.22199	0.628653
$70$	7.04151	0.841622
$71$	6.79327	0.806212	0.403106	−	0.915153i	$-0.367931\pi$
$71$	6.79327	0.806212	0.403106	+	0.915153i	$0.367931\pi$
$72$	−2.67470	−0.315216
$73$	−11.4400	−1.33895	−0.669476	−	0.742834i	$-0.733481\pi$
$73$	−11.4400	−1.33895	−0.669476	+	0.742834i	$0.733481\pi$
$74$	8.51683	0.990062
$75$	1.81245	0.209283
$76$	−4.66258	−0.534835
$77$	−25.5431	−2.91091
$78$	0.859688	0.0973404
$79$	−7.18568	−0.808452	−0.404226	−	0.914659i	$-0.632459\pi$
$79$	−7.18568	−0.808452	−0.404226	+	0.914659i	$0.632459\pi$
$80$	−1.34990	−0.150923
$81$	6.17811	0.686457
$82$	6.87743	0.759485
$83$	0.615951	0.0676094	0.0338047	−	0.999428i	$-0.489238\pi$
$83$	0.615951	0.0676094	0.0338047	+	0.999428i	$0.489238\pi$
$84$	2.97514	0.324614
$85$	−0.434825	−0.0471634
$86$	−1.22389	−0.131975
$87$	−1.69328	−0.181539
$88$	4.89676	0.521997
$89$	17.3622	1.84039	0.920197	−	0.391456i	$-0.128028\pi$
$89$	17.3622	1.84039	0.920197	+	0.391456i	$0.128028\pi$
$90$	3.61058	0.380588
$91$	7.86253	0.824217
$92$	−9.15574	−0.954551
$93$	−3.28706	−0.340852
$94$	−4.13339	−0.426326
$95$	6.29402	0.645753
$96$	−0.570351	−0.0582112
$97$	11.3356	1.15096	0.575479	−	0.817817i	$-0.304816\pi$
$97$	11.3356	1.15096	0.575479	+	0.817817i	$0.304816\pi$
$98$	20.2100	2.04152
$99$	−13.0974	−1.31634
$100$	−3.17777	−0.317777
$101$	−8.87668	−0.883263	−0.441631	−	0.897197i	$-0.645600\pi$
$101$	−8.87668	−0.883263	−0.441631	+	0.897197i	$0.645600\pi$
$102$	−0.183720	−0.0181910
$103$	14.9086	1.46899	0.734496	−	0.678613i	$-0.237419\pi$
$103$	14.9086	1.46899	0.734496	+	0.678613i	$0.237419\pi$
$104$	−1.50729	−0.147802
$105$	−4.01614	−0.391935
$106$	11.4389	1.11105
$107$	4.02749	0.389352	0.194676	−	0.980868i	$-0.437634\pi$
$107$	4.02749	0.389352	0.194676	+	0.980868i	$0.437634\pi$
$108$	3.23657	0.311439
$109$	−12.4478	−1.19228	−0.596139	−	0.802881i	$-0.703299\pi$
$109$	−12.4478	−1.19228	−0.596139	+	0.802881i	$0.703299\pi$
$110$	−6.61014	−0.630252
$111$	−4.85759	−0.461062
$112$	−5.21632	−0.492896
$113$	−12.5797	−1.18340	−0.591701	−	0.806157i	$-0.701543\pi$
$113$	−12.5797	−1.18340	−0.591701	+	0.806157i	$0.701543\pi$
$114$	2.65931	0.249067
$115$	12.3593	1.15251
$116$	2.96884	0.275650
$117$	4.03156	0.372718
$118$	11.2413	1.03485
$119$	−1.68026	−0.154029
$120$	0.769917	0.0702835
$121$	12.9783	1.17985
$122$	−11.6601	−1.05566
$123$	−3.92255	−0.353684
$124$	5.76322	0.517552
$125$	11.0392	0.987374
$126$	13.9521	1.24295
$127$	−17.8995	−1.58832	−0.794161	−	0.607708i	$-0.792089\pi$
$127$	−17.8995	−1.58832	−0.794161	+	0.607708i	$0.792089\pi$
$128$	1.00000	0.0883883
$129$	0.698047	0.0614596
$130$	2.03470	0.178455
$131$	13.7807	1.20402	0.602012	−	0.798487i	$-0.294366\pi$
$131$	13.7807	1.20402	0.602012	+	0.798487i	$0.294366\pi$
$132$	−2.79288	−0.243089
$133$	24.3215	2.10894
$134$	−8.42595	−0.727892
$135$	−4.36905	−0.376028
$136$	0.322117	0.0276213
$137$	19.1060	1.63234	0.816169	−	0.577814i	$-0.196094\pi$
$137$	19.1060	1.63234	0.816169	+	0.577814i	$0.196094\pi$
$138$	5.22199	0.444525
$139$	8.94678	0.758856	0.379428	−	0.925221i	$-0.376121\pi$
$139$	8.94678	0.758856	0.379428	+	0.925221i	$0.376121\pi$
$140$	7.04151	0.595116
$141$	2.35748	0.198536
$142$	6.79327	0.570078
$143$	−7.38087	−0.617219
$144$	−2.67470	−0.222892
$145$	−4.00764	−0.332816
$146$	−11.4400	−0.946782
$147$	−11.5268	−0.950715
$148$	8.51683	0.700079
$149$	4.04808	0.331632	0.165816	−	0.986157i	$-0.446974\pi$
$149$	4.04808	0.331632	0.165816	+	0.986157i	$0.446974\pi$
$150$	1.81245	0.147986
$151$	6.54005	0.532221	0.266111	−	0.963942i	$-0.414261\pi$
$151$	6.54005	0.532221	0.266111	+	0.963942i	$0.414261\pi$
$152$	−4.66258	−0.378186
$153$	−0.861565	−0.0696534
$154$	−25.5431	−2.05832
$155$	−7.77977	−0.624886
$156$	0.859688	0.0688301
$157$	−5.48019	−0.437367	−0.218684	−	0.975796i	$-0.570176\pi$
$157$	−5.48019	−0.437367	−0.218684	+	0.975796i	$0.570176\pi$
$158$	−7.18568	−0.571662
$159$	−6.52420	−0.517403
$160$	−1.34990	−0.106719
$161$	47.7593	3.76396
$162$	6.17811	0.485399
$163$	−1.13211	−0.0886733	−0.0443367	−	0.999017i	$-0.514117\pi$
$163$	−1.13211	−0.0886733	−0.0443367	+	0.999017i	$0.514117\pi$
$164$	6.87743	0.537037
$165$	3.77010	0.293502
$166$	0.615951	0.0478071
$167$	5.63483	0.436036	0.218018	−	0.975945i	$-0.430041\pi$
$167$	5.63483	0.436036	0.218018	+	0.975945i	$0.430041\pi$
$168$	2.97514	0.229537
$169$	−10.7281	−0.825236
$170$	−0.434825	−0.0333496
$171$	12.4710	0.953682
$172$	−1.22389	−0.0933207
$173$	8.86807	0.674227	0.337113	−	0.941464i	$-0.390549\pi$
$173$	8.86807	0.674227	0.337113	+	0.941464i	$0.390549\pi$
$174$	−1.69328	−0.128367
$175$	16.5763	1.25305
$176$	4.89676	0.369107
$177$	−6.41150	−0.481918
$178$	17.3622	1.30136
$179$	−0.744506	−0.0556470	−0.0278235	−	0.999613i	$-0.508858\pi$
$179$	−0.744506	−0.0556470	−0.0278235	+	0.999613i	$0.508858\pi$
$180$	3.61058	0.269117
$181$	−9.27992	−0.689771	−0.344885	−	0.938645i	$-0.612082\pi$
$181$	−9.27992	−0.689771	−0.344885	+	0.938645i	$0.612082\pi$
$182$	7.86253	0.582810
$183$	6.65037	0.491609
$184$	−9.15574	−0.674970
$185$	−11.4969	−0.845267
$186$	−3.28706	−0.241019
$187$	1.57733	0.115346
$188$	−4.13339	−0.301458
$189$	−16.8830	−1.22806
$190$	6.29402	0.456616
$191$	11.8110	0.854613	0.427307	−	0.904107i	$-0.359463\pi$
$191$	11.8110	0.854613	0.427307	+	0.904107i	$0.359463\pi$
$192$	−0.570351	−0.0411616
$193$	−1.38758	−0.0998804	−0.0499402	−	0.998752i	$-0.515903\pi$
$193$	−1.38758	−0.0998804	−0.0499402	+	0.998752i	$0.515903\pi$
$194$	11.3356	0.813850
$195$	−1.16049	−0.0831046
$196$	20.2100	1.44357
$197$	−10.4728	−0.746156	−0.373078	−	0.927800i	$-0.621698\pi$
$197$	−10.4728	−0.746156	−0.373078	+	0.927800i	$0.621698\pi$
$198$	−13.0974	−0.930790
$199$	14.8353	1.05164	0.525822	−	0.850594i	$-0.323758\pi$
$199$	14.8353	1.05164	0.525822	+	0.850594i	$0.323758\pi$
$200$	−3.17777	−0.224702
$201$	4.80575	0.338972
$202$	−8.87668	−0.624561
$203$	−15.4864	−1.08693
$204$	−0.183720	−0.0128629
$205$	−9.28384	−0.648411
$206$	14.9086	1.03873
$207$	24.4888	1.70209
$208$	−1.50729	−0.104512
$209$	−22.8316	−1.57929
$210$	−4.01614	−0.277140
$211$	26.9035	1.85211	0.926057	−	0.377384i	$-0.123176\pi$
$211$	26.9035	1.85211	0.926057	+	0.377384i	$0.123176\pi$
$212$	11.4389	0.785628
$213$	−3.87455	−0.265480
$214$	4.02749	0.275314
$215$	1.65213	0.112674
$216$	3.23657	0.220221
$217$	−30.0628	−2.04080
$218$	−12.4478	−0.843068
$219$	6.52482	0.440907
$220$	−6.61014	−0.445656
$221$	−0.485525	−0.0326599
$222$	−4.85759	−0.326020
$223$	5.37965	0.360248	0.180124	−	0.983644i	$-0.442350\pi$
$223$	5.37965	0.360248	0.180124	+	0.983644i	$0.442350\pi$
$224$	−5.21632	−0.348530
$225$	8.49958	0.566639
$226$	−12.5797	−0.836792
$227$	17.7145	1.17576	0.587878	−	0.808950i	$-0.299964\pi$
$227$	17.7145	1.17576	0.587878	+	0.808950i	$0.299964\pi$
$228$	2.65931	0.176117
$229$	15.0714	0.995947	0.497974	−	0.867192i	$-0.334078\pi$
$229$	15.0714	0.995947	0.497974	+	0.867192i	$0.334078\pi$
$230$	12.3593	0.814950
$231$	14.5685	0.958539
$232$	2.96884	0.194914
$233$	2.85531	0.187057	0.0935287	−	0.995617i	$-0.470185\pi$
$233$	2.85531	0.187057	0.0935287	+	0.995617i	$0.470185\pi$
$234$	4.03156	0.263551
$235$	5.57966	0.363977
$236$	11.2413	0.731747
$237$	4.09836	0.266217
$238$	−1.68026	−0.108915
$239$	1.54106	0.0996831	0.0498415	−	0.998757i	$-0.484128\pi$
$239$	1.54106	0.0996831	0.0498415	+	0.998757i	$0.484128\pi$
$240$	0.769917	0.0496979
$241$	2.05203	0.132183	0.0660914	−	0.997814i	$-0.478947\pi$
$241$	2.05203	0.132183	0.0660914	+	0.997814i	$0.478947\pi$
$242$	12.9783	0.834277
$243$	−13.2334	−0.848924
$244$	−11.6601	−0.746463
$245$	−27.2815	−1.74295
$246$	−3.92255	−0.250093
$247$	7.02789	0.447174
$248$	5.76322	0.365965
$249$	−0.351308	−0.0222633
$250$	11.0392	0.698179
$251$	−21.3125	−1.34523	−0.672616	−	0.739992i	$-0.734829\pi$
$251$	−21.3125	−1.34523	−0.672616	+	0.739992i	$0.734829\pi$
$252$	13.9521	0.878899
$253$	−44.8335	−2.81866
$254$	−17.8995	−1.12311
$255$	0.248003	0.0155306
$256$	1.00000	0.0625000
$257$	1.74967	0.109142	0.0545708	−	0.998510i	$-0.482621\pi$
$257$	1.74967	0.109142	0.0545708	+	0.998510i	$0.482621\pi$
$258$	0.698047	0.0434585
$259$	−44.4265	−2.76053
$260$	2.03470	0.126187
$261$	−7.94075	−0.491520
$262$	13.7807	0.851374
$263$	−12.0852	−0.745204	−0.372602	−	0.927991i	$-0.621534\pi$
$263$	−12.0852	−0.745204	−0.372602	+	0.927991i	$0.621534\pi$
$264$	−2.79288	−0.171890
$265$	−15.4414	−0.948557
$266$	24.3215	1.49125
$267$	−9.90258	−0.606028
$268$	−8.42595	−0.514697
$269$	16.6643	1.01604	0.508020	−	0.861345i	$-0.330377\pi$
$269$	16.6643	1.01604	0.508020	+	0.861345i	$0.330377\pi$
$270$	−4.36905	−0.265892
$271$	−14.5424	−0.883387	−0.441694	−	0.897166i	$-0.645622\pi$
$271$	−14.5424	−0.883387	−0.441694	+	0.897166i	$0.645622\pi$
$272$	0.322117	0.0195312
$273$	−4.48441	−0.271409
$274$	19.1060	1.15424
$275$	−15.5608	−0.938351
$276$	5.22199	0.314327
$277$	−4.14787	−0.249221	−0.124611	−	0.992206i	$-0.539768\pi$
$277$	−4.14787	−0.249221	−0.124611	+	0.992206i	$0.539768\pi$
$278$	8.94678	0.536592
$279$	−15.4149	−0.922865
$280$	7.04151	0.420811
$281$	17.6806	1.05474	0.527368	−	0.849637i	$-0.323179\pi$
$281$	17.6806	1.05474	0.527368	+	0.849637i	$0.323179\pi$
$282$	2.35748	0.140386
$283$	−20.8410	−1.23887	−0.619436	−	0.785048i	$-0.712638\pi$
$283$	−20.8410	−1.23887	−0.619436	+	0.785048i	$0.712638\pi$
$284$	6.79327	0.403106
$285$	−3.58980	−0.212642
$286$	−7.38087	−0.436440
$287$	−35.8749	−2.11763
$288$	−2.67470	−0.157608
$289$	−16.8962	−0.993897
$290$	−4.00764	−0.235336
$291$	−6.46528	−0.379002
$292$	−11.4400	−0.669476
$293$	11.4157	0.666911	0.333455	−	0.942766i	$-0.391785\pi$
$293$	11.4157	0.666911	0.333455	+	0.942766i	$0.391785\pi$
$294$	−11.5268	−0.672257
$295$	−15.1747	−0.883503
$296$	8.51683	0.495031
$297$	15.8487	0.919637
$298$	4.04808	0.234499
$299$	13.8004	0.798097
$300$	1.81245	0.104642
$301$	6.38420	0.367979
$302$	6.54005	0.376337
$303$	5.06283	0.290852
$304$	−4.66258	−0.267418
$305$	15.7400	0.901270
$306$	−0.861565	−0.0492524
$307$	−1.95560	−0.111612	−0.0558059	−	0.998442i	$-0.517773\pi$
$307$	−1.95560	−0.111612	−0.0558059	+	0.998442i	$0.517773\pi$
$308$	−25.5431	−1.45545
$309$	−8.50316	−0.483728
$310$	−7.77977	−0.441861
$311$	20.7951	1.17918	0.589591	−	0.807702i	$-0.299289\pi$
$311$	20.7951	1.17918	0.589591	+	0.807702i	$0.299289\pi$
$312$	0.859688	0.0486702
$313$	9.78998	0.553363	0.276681	−	0.960962i	$-0.410765\pi$
$313$	9.78998	0.553363	0.276681	+	0.960962i	$0.410765\pi$
$314$	−5.48019	−0.309265
$315$	−18.8339	−1.06117
$316$	−7.18568	−0.404226
$317$	21.4136	1.20271	0.601355	−	0.798982i	$-0.294628\pi$
$317$	21.4136	1.20271	0.601355	+	0.798982i	$0.294628\pi$
$318$	−6.52420	−0.365859
$319$	14.5377	0.813955
$320$	−1.34990	−0.0754617
$321$	−2.29709	−0.128211
$322$	47.7593	2.66152
$323$	−1.50190	−0.0835677
$324$	6.17811	0.343229
$325$	4.78984	0.265692
$326$	−1.13211	−0.0627015
$327$	7.09959	0.392608
$328$	6.87743	0.379742
$329$	21.5611	1.18870
$330$	3.77010	0.207537
$331$	20.0123	1.09997	0.549986	−	0.835174i	$-0.314633\pi$
$331$	20.0123	1.09997	0.549986	+	0.835174i	$0.314633\pi$
$332$	0.615951	0.0338047
$333$	−22.7800	−1.24833
$334$	5.63483	0.308324
$335$	11.3742	0.621439
$336$	2.97514	0.162307
$337$	12.9771	0.706906	0.353453	−	0.935452i	$-0.385007\pi$
$337$	12.9771	0.706906	0.353453	+	0.935452i	$0.385007\pi$
$338$	−10.7281	−0.583530
$339$	7.17487	0.389685
$340$	−0.434825	−0.0235817
$341$	28.2211	1.52826
$342$	12.4710	0.674355
$343$	−68.9076	−3.72066
$344$	−1.22389	−0.0659877
$345$	−7.04916	−0.379514
$346$	8.86807	0.476750
$347$	−31.8177	−1.70806	−0.854031	−	0.520221i	$-0.825849\pi$
$347$	−31.8177	−1.70806	−0.854031	+	0.520221i	$0.825849\pi$
$348$	−1.69328	−0.0907694
$349$	−29.6834	−1.58892	−0.794459	−	0.607318i	$-0.792245\pi$
$349$	−29.6834	−1.58892	−0.794459	+	0.607318i	$0.792245\pi$
$350$	16.5763	0.886039
$351$	−4.87847	−0.260393
$352$	4.89676	0.260998
$353$	21.3908	1.13852	0.569258	−	0.822159i	$-0.307231\pi$
$353$	21.3908	1.13852	0.569258	+	0.822159i	$0.307231\pi$
$354$	−6.41150	−0.340767
$355$	−9.17023	−0.486705
$356$	17.3622	0.920197
$357$	0.958341	0.0507208
$358$	−0.744506	−0.0393483
$359$	−33.2527	−1.75501	−0.877504	−	0.479568i	$-0.840793\pi$
$359$	−33.2527	−1.75501	−0.877504	+	0.479568i	$0.840793\pi$
$360$	3.61058	0.190294
$361$	2.73969	0.144194
$362$	−9.27992	−0.487742
$363$	−7.40219	−0.388514
$364$	7.86253	0.412109
$365$	15.4429	0.808317
$366$	6.65037	0.347620
$367$	−9.57219	−0.499664	−0.249832	−	0.968289i	$-0.580375\pi$
$367$	−9.57219	−0.499664	−0.249832	+	0.968289i	$0.580375\pi$
$368$	−9.15574	−0.477276
$369$	−18.3950	−0.957608
$370$	−11.4969	−0.597694
$371$	−59.6691	−3.09786
$372$	−3.28706	−0.170426
$373$	−21.7305	−1.12516	−0.562582	−	0.826742i	$-0.690192\pi$
$373$	−21.7305	−1.12516	−0.562582	+	0.826742i	$0.690192\pi$
$374$	1.57733	0.0815617
$375$	−6.29621	−0.325135
$376$	−4.13339	−0.213163
$377$	−4.47492	−0.230470
$378$	−16.8830	−0.868368
$379$	−31.9976	−1.64361	−0.821803	−	0.569771i	$-0.807032\pi$
$379$	−31.9976	−1.64361	−0.821803	+	0.569771i	$0.807032\pi$
$380$	6.29402	0.322877
$381$	10.2090	0.523022
$382$	11.8110	0.604303
$383$	16.0904	0.822183	0.411091	−	0.911594i	$-0.365148\pi$
$383$	16.0904	0.822183	0.411091	+	0.911594i	$0.365148\pi$
$384$	−0.570351	−0.0291056
$385$	34.4806	1.75730
$386$	−1.38758	−0.0706261
$387$	3.27354	0.166403
$388$	11.3356	0.575479
$389$	12.6861	0.643213	0.321607	−	0.946873i	$-0.395777\pi$
$389$	12.6861	0.643213	0.321607	+	0.946873i	$0.395777\pi$
$390$	−1.16049	−0.0587638
$391$	−2.94921	−0.149148
$392$	20.2100	1.02076
$393$	−7.85983	−0.396476
$394$	−10.4728	−0.527612
$395$	9.69995	0.488057
$396$	−13.0974	−0.658168
$397$	−0.346410	−0.0173858	−0.00869291	−	0.999962i	$-0.502767\pi$
$397$	−0.346410	−0.0173858	−0.00869291	+	0.999962i	$0.502767\pi$
$398$	14.8353	0.743625
$399$	−13.8718	−0.694460
$400$	−3.17777	−0.158888
$401$	23.8455	1.19079	0.595394	−	0.803434i	$-0.296996\pi$
$401$	23.8455	1.19079	0.595394	+	0.803434i	$0.296996\pi$
$402$	4.80575	0.239689
$403$	−8.68687	−0.432724
$404$	−8.87668	−0.441631
$405$	−8.33984	−0.414410
$406$	−15.4864	−0.768578
$407$	41.7049	2.06724
$408$	−0.183720	−0.00909548
$409$	−1.11996	−0.0553783	−0.0276891	−	0.999617i	$-0.508815\pi$
$409$	−1.11996	−0.0553783	−0.0276891	+	0.999617i	$0.508815\pi$
$410$	−9.28384	−0.458496
$411$	−10.8971	−0.537516
$412$	14.9086	0.734496
$413$	−58.6383	−2.88540
$414$	24.4888	1.20356
$415$	−0.831472	−0.0408154
$416$	−1.50729	−0.0739012
$417$	−5.10281	−0.249885
$418$	−22.8316	−1.11673
$419$	−37.9806	−1.85547	−0.927737	−	0.373235i	$-0.878249\pi$
$419$	−37.9806	−1.85547	−0.927737	+	0.373235i	$0.878249\pi$
$420$	−4.01614	−0.195967
$421$	−3.97835	−0.193893	−0.0969464	−	0.995290i	$-0.530908\pi$
$421$	−3.97835	−0.193893	−0.0969464	+	0.995290i	$0.530908\pi$
$422$	26.9035	1.30964
$423$	11.0556	0.537540
$424$	11.4389	0.555523
$425$	−1.02361	−0.0496525
$426$	−3.87455	−0.187722
$427$	60.8230	2.94343
$428$	4.02749	0.194676
$429$	4.20969	0.203246
$430$	1.65213	0.0796727
$431$	20.1325	0.969748	0.484874	−	0.874584i	$-0.338865\pi$
$431$	20.1325	0.969748	0.484874	+	0.874584i	$0.338865\pi$
$432$	3.23657	0.155720
$433$	36.4879	1.75350	0.876748	−	0.480949i	$-0.159708\pi$
$433$	36.4879	1.75350	0.876748	+	0.480949i	$0.159708\pi$
$434$	−30.0628	−1.44306
$435$	2.28576	0.109594
$436$	−12.4478	−0.596139
$437$	42.6894	2.04211
$438$	6.52482	0.311768
$439$	−22.6093	−1.07908	−0.539541	−	0.841959i	$-0.681402\pi$
$439$	−22.6093	−1.07908	−0.539541	+	0.841959i	$0.681402\pi$
$440$	−6.61014	−0.315126
$441$	−54.0557	−2.57408
$442$	−0.485525	−0.0230940
$443$	−20.8098	−0.988705	−0.494352	−	0.869262i	$-0.664595\pi$
$443$	−20.8098	−0.988705	−0.494352	+	0.869262i	$0.664595\pi$
$444$	−4.85759	−0.230531
$445$	−23.4373	−1.11103
$446$	5.37965	0.254734
$447$	−2.30883	−0.109204
$448$	−5.21632	−0.246448
$449$	−38.4084	−1.81260	−0.906302	−	0.422630i	$-0.861107\pi$
$449$	−38.4084	−1.81260	−0.906302	+	0.422630i	$0.861107\pi$
$450$	8.49958	0.400674
$451$	33.6771	1.58579
$452$	−12.5797	−0.591701
$453$	−3.73012	−0.175257
$454$	17.7145	0.831385
$455$	−10.6136	−0.497575
$456$	2.65931	0.124534
$457$	22.2360	1.04016	0.520079	−	0.854118i	$-0.325903\pi$
$457$	22.2360	1.04016	0.520079	+	0.854118i	$0.325903\pi$
$458$	15.0714	0.704241
$459$	1.04255	0.0486622
$460$	12.3593	0.576257
$461$	8.26591	0.384982	0.192491	−	0.981299i	$-0.438343\pi$
$461$	8.26591	0.384982	0.192491	+	0.981299i	$0.438343\pi$
$462$	14.5685	0.677790
$463$	−27.2271	−1.26535	−0.632675	−	0.774417i	$-0.718043\pi$
$463$	−27.2271	−1.26535	−0.632675	+	0.774417i	$0.718043\pi$
$464$	2.96884	0.137825
$465$	4.43720	0.205770
$466$	2.85531	0.132270
$467$	−5.58987	−0.258668	−0.129334	−	0.991601i	$-0.541284\pi$
$467$	−5.58987	−0.258668	−0.129334	+	0.991601i	$0.541284\pi$
$468$	4.03156	0.186359
$469$	43.9525	2.02954
$470$	5.57966	0.257371
$471$	3.12564	0.144022
$472$	11.2413	0.517424
$473$	−5.99310	−0.275563
$474$	4.09836	0.188244
$475$	14.8166	0.679833
$476$	−1.68026	−0.0770147
$477$	−30.5957	−1.40088
$478$	1.54106	0.0704866
$479$	2.67407	0.122182	0.0610908	−	0.998132i	$-0.480542\pi$
$479$	2.67407	0.122182	0.0610908	+	0.998132i	$0.480542\pi$
$480$	0.769917	0.0351418
$481$	−12.8374	−0.585334
$482$	2.05203	0.0934673
$483$	−27.2396	−1.23944
$484$	12.9783	0.589923
$485$	−15.3019	−0.694826
$486$	−13.2334	−0.600280
$487$	40.4979	1.83513	0.917567	−	0.397581i	$-0.130150\pi$
$487$	40.4979	1.83513	0.917567	+	0.397581i	$0.130150\pi$
$488$	−11.6601	−0.527829
$489$	0.645698	0.0291995
$490$	−27.2815	−1.23245
$491$	18.4772	0.833865	0.416932	−	0.908938i	$-0.363105\pi$
$491$	18.4772	0.833865	0.416932	+	0.908938i	$0.363105\pi$
$492$	−3.92255	−0.176842
$493$	0.956312	0.0430701
$494$	7.02789	0.316200
$495$	17.6801	0.794663
$496$	5.76322	0.258776
$497$	−35.4359	−1.58952
$498$	−0.351308	−0.0157425
$499$	−29.2974	−1.31153	−0.655766	−	0.754964i	$-0.727654\pi$
$499$	−29.2974	−1.31153	−0.655766	+	0.754964i	$0.727654\pi$
$500$	11.0392	0.493687
$501$	−3.21383	−0.143583
$502$	−21.3125	−0.951222
$503$	−0.315857	−0.0140834	−0.00704169	−	0.999975i	$-0.502241\pi$
$503$	−0.315857	−0.0140834	−0.00704169	+	0.999975i	$0.502241\pi$
$504$	13.9521	0.621475
$505$	11.9826	0.533220
$506$	−44.8335	−1.99309
$507$	6.11877	0.271744
$508$	−17.8995	−0.794161
$509$	42.7339	1.89415	0.947074	−	0.321016i	$-0.104024\pi$
$509$	42.7339	1.89415	0.947074	+	0.321016i	$0.104024\pi$
$510$	0.248003	0.0109818
$511$	59.6747	2.63986
$512$	1.00000	0.0441942
$513$	−15.0908	−0.666275
$514$	1.74967	0.0771748
$515$	−20.1252	−0.886821
$516$	0.698047	0.0307298
$517$	−20.2402	−0.890164
$518$	−44.4265	−1.95199
$519$	−5.05792	−0.222018
$520$	2.03470	0.0892274
$521$	7.72520	0.338447	0.169224	−	0.985578i	$-0.445874\pi$
$521$	7.72520	0.338447	0.169224	+	0.985578i	$0.445874\pi$
$522$	−7.94075	−0.347557
$523$	−4.49738	−0.196657	−0.0983283	−	0.995154i	$-0.531350\pi$
$523$	−4.49738	−0.196657	−0.0983283	+	0.995154i	$0.531350\pi$
$524$	13.7807	0.602012
$525$	−9.45430	−0.412619
$526$	−12.0852	−0.526939
$527$	1.85643	0.0808673
$528$	−2.79288	−0.121544
$529$	60.8275	2.64467
$530$	−15.4414	−0.670731
$531$	−30.0671	−1.30480
$532$	24.3215	1.05447
$533$	−10.3663	−0.449015
$534$	−9.90258	−0.428526
$535$	−5.43671	−0.235050
$536$	−8.42595	−0.363946
$537$	0.424630	0.0183241
$538$	16.6643	0.718449
$539$	98.9636	4.26267
$540$	−4.36905	−0.188014
$541$	−23.9482	−1.02962	−0.514808	−	0.857306i	$-0.672137\pi$
$541$	−23.9482	−1.02962	−0.514808	+	0.857306i	$0.672137\pi$
$542$	−14.5424	−0.624649
$543$	5.29281	0.227136
$544$	0.322117	0.0138106
$545$	16.8032	0.719771
$546$	−4.48441	−0.191915
$547$	−28.8409	−1.23315	−0.616573	−	0.787298i	$-0.711480\pi$
$547$	−28.8409	−1.23315	−0.616573	+	0.787298i	$0.711480\pi$
$548$	19.1060	0.816169
$549$	31.1873	1.33104
$550$	−15.5608	−0.663514
$551$	−13.8425	−0.589709
$552$	5.22199	0.222262
$553$	37.4828	1.59393
$554$	−4.14787	−0.176226
$555$	6.55726	0.278340
$556$	8.94678	0.379428
$557$	−29.5672	−1.25280	−0.626402	−	0.779500i	$-0.715473\pi$
$557$	−29.5672	−1.25280	−0.626402	+	0.779500i	$0.715473\pi$
$558$	−15.4149	−0.652564
$559$	1.84476	0.0780251
$560$	7.04151	0.297558
$561$	−0.899632	−0.0379825
$562$	17.6806	0.745811
$563$	−25.6045	−1.07910	−0.539551	−	0.841953i	$-0.681406\pi$
$563$	−25.6045	−1.07910	−0.539551	+	0.841953i	$0.681406\pi$
$564$	2.35748	0.0992679
$565$	16.9814	0.714412
$566$	−20.8410	−0.876014
$567$	−32.2270	−1.35341
$568$	6.79327	0.285039
$569$	29.7372	1.24665	0.623325	−	0.781963i	$-0.285782\pi$
$569$	29.7372	1.24665	0.623325	+	0.781963i	$0.285782\pi$
$570$	−3.58980	−0.150360
$571$	28.3577	1.18673	0.593367	−	0.804932i	$-0.297798\pi$
$571$	28.3577	1.18673	0.593367	+	0.804932i	$0.297798\pi$
$572$	−7.38087	−0.308610
$573$	−6.73641	−0.281418
$574$	−35.8749	−1.49739
$575$	29.0948	1.21334
$576$	−2.67470	−0.111446
$577$	37.8697	1.57653	0.788267	−	0.615333i	$-0.210978\pi$
$577$	37.8697	1.57653	0.788267	+	0.615333i	$0.210978\pi$
$578$	−16.8962	−0.702791
$579$	0.791410	0.0328899
$580$	−4.00764	−0.166408
$581$	−3.21300	−0.133298
$582$	−6.46528	−0.267995
$583$	56.0137	2.31985
$584$	−11.4400	−0.473391
$585$	−5.44220	−0.225007
$586$	11.4157	0.471577
$587$	−15.5658	−0.642470	−0.321235	−	0.947000i	$-0.604098\pi$
$587$	−15.5658	−0.642470	−0.321235	+	0.947000i	$0.604098\pi$
$588$	−11.5268	−0.475357
$589$	−26.8715	−1.10722
$590$	−15.1747	−0.624731
$591$	5.97318	0.245704
$592$	8.51683	0.350040
$593$	33.2364	1.36486	0.682428	−	0.730953i	$-0.260924\pi$
$593$	33.2364	1.36486	0.682428	+	0.730953i	$0.260924\pi$
$594$	15.8487	0.650281
$595$	2.26819	0.0929866
$596$	4.04808	0.165816
$597$	−8.46132	−0.346299
$598$	13.8004	0.564340
$599$	−34.2324	−1.39870	−0.699349	−	0.714781i	$-0.746527\pi$
$599$	−34.2324	−1.39870	−0.699349	+	0.714781i	$0.746527\pi$
$600$	1.81245	0.0739928
$601$	−0.459329	−0.0187364	−0.00936821	−	0.999956i	$-0.502982\pi$
$601$	−0.459329	−0.0187364	−0.00936821	+	0.999956i	$0.502982\pi$
$602$	6.38420	0.260201
$603$	22.5369	0.917773
$604$	6.54005	0.266111
$605$	−17.5194	−0.712265
$606$	5.06283	0.205663
$607$	−39.7664	−1.61407	−0.807034	−	0.590506i	$-0.798928\pi$
$607$	−39.7664	−1.61407	−0.807034	+	0.590506i	$0.798928\pi$
$608$	−4.66258	−0.189093
$609$	8.83270	0.357919
$610$	15.7400	0.637294
$611$	6.23023	0.252048
$612$	−0.861565	−0.0348267
$613$	−24.6191	−0.994358	−0.497179	−	0.867648i	$-0.665631\pi$
$613$	−24.6191	−0.994358	−0.497179	+	0.867648i	$0.665631\pi$
$614$	−1.95560	−0.0789215
$615$	5.29505	0.213517
$616$	−25.5431	−1.02916
$617$	34.4311	1.38614	0.693071	−	0.720869i	$-0.256257\pi$
$617$	34.4311	1.38614	0.693071	+	0.720869i	$0.256257\pi$
$618$	−8.50316	−0.342047
$619$	10.0546	0.404128	0.202064	−	0.979372i	$-0.435235\pi$
$619$	10.0546	0.404128	0.202064	+	0.979372i	$0.435235\pi$
$620$	−7.77977	−0.312443
$621$	−29.6332	−1.18914
$622$	20.7951	0.833808
$623$	−90.5670	−3.62849
$624$	0.859688	0.0344150
$625$	0.987070	0.0394828
$626$	9.78998	0.391286
$627$	13.0220	0.520049
$628$	−5.48019	−0.218684
$629$	2.74341	0.109387
$630$	−18.8339	−0.750362
$631$	11.3772	0.452920	0.226460	−	0.974020i	$-0.427285\pi$
$631$	11.3772	0.452920	0.226460	+	0.974020i	$0.427285\pi$
$632$	−7.18568	−0.285831
$633$	−15.3444	−0.609887
$634$	21.4136	0.850444
$635$	24.1625	0.958859
$636$	−6.52420	−0.258701
$637$	−30.4624	−1.20697
$638$	14.5377	0.575553
$639$	−18.1699	−0.718792
$640$	−1.34990	−0.0533595
$641$	45.9301	1.81413	0.907065	−	0.420991i	$-0.138318\pi$
$641$	45.9301	1.81413	0.907065	+	0.420991i	$0.138318\pi$
$642$	−2.29709	−0.0906587
$643$	23.6098	0.931079	0.465540	−	0.885027i	$-0.345860\pi$
$643$	23.6098	0.931079	0.465540	+	0.885027i	$0.345860\pi$
$644$	47.7593	1.88198
$645$	−0.942293	−0.0371028
$646$	−1.50190	−0.0590913
$647$	14.5105	0.570468	0.285234	−	0.958458i	$-0.407929\pi$
$647$	14.5105	0.570468	0.285234	+	0.958458i	$0.407929\pi$
$648$	6.17811	0.242699
$649$	55.0461	2.16075
$650$	4.78984	0.187873
$651$	17.1464	0.672019
$652$	−1.13211	−0.0443367
$653$	32.5732	1.27469	0.637344	−	0.770579i	$-0.280033\pi$
$653$	32.5732	1.27469	0.637344	+	0.770579i	$0.280033\pi$
$654$	7.09959	0.277616
$655$	−18.6026	−0.726862
$656$	6.87743	0.268518
$657$	30.5986	1.19376
$658$	21.5611	0.840538
$659$	−9.88742	−0.385159	−0.192580	−	0.981281i	$-0.561685\pi$
$659$	−9.88742	−0.385159	−0.192580	+	0.981281i	$0.561685\pi$
$660$	3.77010	0.146751
$661$	35.1654	1.36777	0.683887	−	0.729588i	$-0.260288\pi$
$661$	35.1654	1.36777	0.683887	+	0.729588i	$0.260288\pi$
$662$	20.0123	0.777798
$663$	0.276920	0.0107547
$664$	0.615951	0.0239035
$665$	−32.8316	−1.27316
$666$	−22.7800	−0.882706
$667$	−27.1819	−1.05249
$668$	5.63483	0.218018
$669$	−3.06829	−0.118627
$670$	11.3742	0.439424
$671$	−57.0969	−2.20420
$672$	2.97514	0.114768
$673$	−23.4595	−0.904296	−0.452148	−	0.891943i	$-0.649342\pi$
$673$	−23.4595	−0.904296	−0.452148	+	0.891943i	$0.649342\pi$
$674$	12.9771	0.499858
$675$	−10.2851	−0.395873
$676$	−10.7281	−0.412618
$677$	22.5313	0.865947	0.432974	−	0.901407i	$-0.357464\pi$
$677$	22.5313	0.865947	0.432974	+	0.901407i	$0.357464\pi$
$678$	7.17487	0.275549
$679$	−59.1302	−2.26921
$680$	−0.434825	−0.0166748
$681$	−10.1035	−0.387167
$682$	28.2211	1.08064
$683$	35.8628	1.37225	0.686127	−	0.727482i	$-0.259310\pi$
$683$	35.8628	1.37225	0.686127	+	0.727482i	$0.259310\pi$
$684$	12.4710	0.476841
$685$	−25.7912	−0.985432
$686$	−68.9076	−2.63091
$687$	−8.59600	−0.327958
$688$	−1.22389	−0.0466603
$689$	−17.2418	−0.656861
$690$	−7.04916	−0.268357
$691$	−26.4427	−1.00593	−0.502964	−	0.864308i	$-0.667757\pi$
$691$	−26.4427	−1.00593	−0.502964	+	0.864308i	$0.667757\pi$
$692$	8.86807	0.337113
$693$	68.3201	2.59527
$694$	−31.8177	−1.20778
$695$	−12.0773	−0.458116
$696$	−1.69328	−0.0641837
$697$	2.21533	0.0839117
$698$	−29.6834	−1.12353
$699$	−1.62853	−0.0615966
$700$	16.5763	0.626524
$701$	1.80863	0.0683109	0.0341555	−	0.999417i	$-0.489126\pi$
$701$	1.80863	0.0683109	0.0341555	+	0.999417i	$0.489126\pi$
$702$	−4.87847	−0.184126
$703$	−39.7105	−1.49771
$704$	4.89676	0.184554
$705$	−3.18237	−0.119855
$706$	21.3908	0.805052
$707$	46.3036	1.74143
$708$	−6.41150	−0.240959
$709$	12.8308	0.481869	0.240935	−	0.970541i	$-0.422546\pi$
$709$	12.8308	0.481869	0.240935	+	0.970541i	$0.422546\pi$
$710$	−9.17023	−0.344153
$711$	19.2195	0.720789
$712$	17.3622	0.650678
$713$	−52.7665	−1.97612
$714$	0.958341	0.0358650
$715$	9.96343	0.372611
$716$	−0.744506	−0.0278235
$717$	−0.878947	−0.0328249
$718$	−33.2527	−1.24098
$719$	15.9441	0.594616	0.297308	−	0.954782i	$-0.403911\pi$
$719$	15.9441	0.594616	0.297308	+	0.954782i	$0.403911\pi$
$720$	3.61058	0.134558
$721$	−77.7683	−2.89624
$722$	2.73969	0.101961
$723$	−1.17038	−0.0435268
$724$	−9.27992	−0.344885
$725$	−9.43429	−0.350381
$726$	−7.40219	−0.274721
$727$	−42.8669	−1.58985	−0.794923	−	0.606710i	$-0.792489\pi$
$727$	−42.8669	−1.58985	−0.794923	+	0.606710i	$0.792489\pi$
$728$	7.86253	0.291405
$729$	−10.9866	−0.406913
$730$	15.4429	0.571566
$731$	−0.394235	−0.0145813
$732$	6.65037	0.245805
$733$	18.1886	0.671810	0.335905	−	0.941896i	$-0.390958\pi$
$733$	18.1886	0.671810	0.335905	+	0.941896i	$0.390958\pi$
$734$	−9.57219	−0.353316
$735$	15.5600	0.573940
$736$	−9.15574	−0.337485
$737$	−41.2599	−1.51983
$738$	−18.3950	−0.677131
$739$	−28.1395	−1.03513	−0.517565	−	0.855644i	$-0.673161\pi$
$739$	−28.1395	−1.03513	−0.517565	+	0.855644i	$0.673161\pi$
$740$	−11.4969	−0.422633
$741$	−4.00837	−0.147251
$742$	−59.6691	−2.19052
$743$	24.1449	0.885791	0.442895	−	0.896573i	$-0.353951\pi$
$743$	24.1449	0.885791	0.442895	+	0.896573i	$0.353951\pi$
$744$	−3.28706	−0.120509
$745$	−5.46451	−0.200204
$746$	−21.7305	−0.795611
$747$	−1.64748	−0.0602783
$748$	1.57733	0.0576729
$749$	−21.0087	−0.767641
$750$	−6.29621	−0.229905
$751$	−4.34927	−0.158707	−0.0793536	−	0.996847i	$-0.525286\pi$
$751$	−4.34927	−0.158707	−0.0793536	+	0.996847i	$0.525286\pi$
$752$	−4.13339	−0.150729
$753$	12.1556	0.442975
$754$	−4.47492	−0.162967
$755$	−8.82841	−0.321299
$756$	−16.8830	−0.614029
$757$	−29.4399	−1.07001	−0.535005	−	0.844849i	$-0.679690\pi$
$757$	−29.4399	−1.07001	−0.535005	+	0.844849i	$0.679690\pi$
$758$	−31.9976	−1.16221
$759$	25.5708	0.928163
$760$	6.29402	0.228308
$761$	−4.73746	−0.171733	−0.0858665	−	0.996307i	$-0.527366\pi$
$761$	−4.73746	−0.171733	−0.0858665	+	0.996307i	$0.527366\pi$
$762$	10.2090	0.369833
$763$	64.9315	2.35068
$764$	11.8110	0.427307
$765$	1.16303	0.0420493
$766$	16.0904	0.581371
$767$	−16.9440	−0.611812
$768$	−0.570351	−0.0205808
$769$	7.09119	0.255715	0.127857	−	0.991793i	$-0.459190\pi$
$769$	7.09119	0.255715	0.127857	+	0.991793i	$0.459190\pi$
$770$	34.4806	1.24260
$771$	−0.997929	−0.0359395
$772$	−1.38758	−0.0499402
$773$	−48.2015	−1.73369	−0.866844	−	0.498579i	$-0.833856\pi$
$773$	−48.2015	−1.73369	−0.866844	+	0.498579i	$0.833856\pi$
$774$	3.27354	0.117665
$775$	−18.3142	−0.657865
$776$	11.3356	0.406925
$777$	25.3387	0.909022
$778$	12.6861	0.454820
$779$	−32.0666	−1.14890
$780$	−1.16049	−0.0415523
$781$	33.2650	1.19032
$782$	−2.94921	−0.105464
$783$	9.60886	0.343393
$784$	20.2100	0.721786
$785$	7.39772	0.264036
$786$	−7.85983	−0.280351
$787$	42.7134	1.52257	0.761284	−	0.648419i	$-0.224569\pi$
$787$	42.7134	1.52257	0.761284	+	0.648419i	$0.224569\pi$
$788$	−10.4728	−0.373078
$789$	6.89280	0.245390
$790$	9.69995	0.345109
$791$	65.6199	2.33318
$792$	−13.0974	−0.465395
$793$	17.5752	0.624115
$794$	−0.346410	−0.0122936
$795$	8.80702	0.312353
$796$	14.8353	0.525822
$797$	33.1497	1.17422	0.587111	−	0.809506i	$-0.300265\pi$
$797$	33.1497	1.17422	0.587111	+	0.809506i	$0.300265\pi$
$798$	−13.8718	−0.491057
$799$	−1.33143	−0.0471027
$800$	−3.17777	−0.112351
$801$	−46.4388	−1.64083
$802$	23.8455	0.842015
$803$	−56.0190	−1.97687
$804$	4.80575	0.169486
$805$	−64.4702	−2.27228
$806$	−8.68687	−0.305982
$807$	−9.50451	−0.334575
$808$	−8.87668	−0.312280
$809$	−35.0877	−1.23362	−0.616810	−	0.787112i	$-0.711575\pi$
$809$	−35.0877	−1.23362	−0.616810	+	0.787112i	$0.711575\pi$
$810$	−8.33984	−0.293032
$811$	7.14130	0.250765	0.125382	−	0.992108i	$-0.459984\pi$
$811$	7.14130	0.250765	0.125382	+	0.992108i	$0.459984\pi$
$812$	−15.4864	−0.543467
$813$	8.29427	0.290893
$814$	41.7049	1.46176
$815$	1.52823	0.0535315
$816$	−0.183720	−0.00643147
$817$	5.70649	0.199645
$818$	−1.11996	−0.0391583
$819$	−21.0299	−0.734845
$820$	−9.28384	−0.324206
$821$	−12.4706	−0.435226	−0.217613	−	0.976035i	$-0.569827\pi$
$821$	−12.4706	−0.435226	−0.217613	+	0.976035i	$0.569827\pi$
$822$	−10.8971	−0.380082
$823$	7.16190	0.249648	0.124824	−	0.992179i	$-0.460163\pi$
$823$	7.16190	0.249648	0.124824	+	0.992179i	$0.460163\pi$
$824$	14.9086	0.519367
$825$	8.87512	0.308992
$826$	−58.6383	−2.04029
$827$	−51.1621	−1.77908	−0.889541	−	0.456856i	$-0.848976\pi$
$827$	−51.1621	−1.77908	−0.889541	+	0.456856i	$0.848976\pi$
$828$	24.4888	0.851046
$829$	40.4277	1.40411	0.702056	−	0.712122i	$-0.252266\pi$
$829$	40.4277	1.40411	0.702056	+	0.712122i	$0.252266\pi$
$830$	−0.831472	−0.0288608
$831$	2.36574	0.0820667
$832$	−1.50729	−0.0522560
$833$	6.50998	0.225557
$834$	−5.10281	−0.176696
$835$	−7.60646	−0.263232
$836$	−22.8316	−0.789647
$837$	18.6531	0.644745
$838$	−37.9806	−1.31202
$839$	−32.1188	−1.10887	−0.554433	−	0.832229i	$-0.687065\pi$
$839$	−32.1188	−1.10887	−0.554433	+	0.832229i	$0.687065\pi$
$840$	−4.01614	−0.138570
$841$	−20.1860	−0.696069
$842$	−3.97835	−0.137103
$843$	−10.0842	−0.347317
$844$	26.9035	0.926057
$845$	14.4818	0.498190
$846$	11.0556	0.380098
$847$	−67.6990	−2.32616
$848$	11.4389	0.392814
$849$	11.8867	0.407951
$850$	−1.02361	−0.0351096
$851$	−77.9779	−2.67305
$852$	−3.87455	−0.132740
$853$	29.8726	1.02282	0.511409	−	0.859337i	$-0.329124\pi$
$853$	29.8726	1.02282	0.511409	+	0.859337i	$0.329124\pi$
$854$	60.8230	2.08132
$855$	−16.8346	−0.575732
$856$	4.02749	0.137657
$857$	−36.3366	−1.24124	−0.620618	−	0.784113i	$-0.713118\pi$
$857$	−36.3366	−1.24124	−0.620618	+	0.784113i	$0.713118\pi$
$858$	4.20969	0.143716
$859$	16.2362	0.553973	0.276986	−	0.960874i	$-0.410664\pi$
$859$	16.2362	0.553973	0.276986	+	0.960874i	$0.410664\pi$
$860$	1.65213	0.0563371
$861$	20.4613	0.697318
$862$	20.1325	0.685715
$863$	21.2757	0.724233	0.362117	−	0.932133i	$-0.382054\pi$
$863$	21.2757	0.724233	0.362117	+	0.932133i	$0.382054\pi$
$864$	3.23657	0.110110
$865$	−11.9710	−0.407026
$866$	36.4879	1.23991
$867$	9.63679	0.327283
$868$	−30.0628	−1.02040
$869$	−35.1866	−1.19362
$870$	2.28576	0.0774945
$871$	12.7004	0.430336
$872$	−12.4478	−0.421534
$873$	−30.3194	−1.02615
$874$	42.6894	1.44399
$875$	−57.5839	−1.94669
$876$	6.52482	0.220453
$877$	34.6583	1.17033	0.585164	−	0.810915i	$-0.301030\pi$
$877$	34.6583	1.17033	0.585164	+	0.810915i	$0.301030\pi$
$878$	−22.6093	−0.763026
$879$	−6.51094	−0.219609
$880$	−6.61014	−0.222828
$881$	−35.0066	−1.17940	−0.589701	−	0.807622i	$-0.700754\pi$
$881$	−35.0066	−1.17940	−0.589701	+	0.807622i	$0.700754\pi$
$882$	−54.0557	−1.82015
$883$	23.4321	0.788553	0.394277	−	0.918992i	$-0.370995\pi$
$883$	23.4321	0.788553	0.394277	+	0.918992i	$0.370995\pi$
$884$	−0.485525	−0.0163300
$885$	8.65488	0.290931
$886$	−20.8098	−0.699120
$887$	−53.8044	−1.80658	−0.903288	−	0.429035i	$-0.858854\pi$
$887$	−53.8044	−1.80658	−0.903288	+	0.429035i	$0.858854\pi$
$888$	−4.85759	−0.163010
$889$	93.3694	3.13151
$890$	−23.4373	−0.785620
$891$	30.2528	1.01351
$892$	5.37965	0.180124
$893$	19.2723	0.644922
$894$	−2.30883	−0.0772188
$895$	1.00501	0.0335937
$896$	−5.21632	−0.174265
$897$	−7.87107	−0.262807
$898$	−38.4084	−1.28170
$899$	17.1101	0.570653
$900$	8.49958	0.283319
$901$	3.68466	0.122754
$902$	33.6771	1.12133
$903$	−3.64124	−0.121173
$904$	−12.5797	−0.418396
$905$	12.5270	0.416410
$906$	−3.73012	−0.123925
$907$	13.1054	0.435157	0.217578	−	0.976043i	$-0.430184\pi$
$907$	13.1054	0.435157	0.217578	+	0.976043i	$0.430184\pi$
$908$	17.7145	0.587878
$909$	23.7424	0.787487
$910$	−10.6136	−0.351839
$911$	−4.35027	−0.144131	−0.0720654	−	0.997400i	$-0.522959\pi$
$911$	−4.35027	−0.144131	−0.0720654	+	0.997400i	$0.522959\pi$
$912$	2.65931	0.0880586
$913$	3.01617	0.0998205
$914$	22.2360	0.735503
$915$	−8.97733	−0.296781
$916$	15.0714	0.497974
$917$	−71.8845	−2.37384
$918$	1.04255	0.0344094
$919$	51.8873	1.71160	0.855802	−	0.517303i	$-0.173064\pi$
$919$	51.8873	1.71160	0.855802	+	0.517303i	$0.173064\pi$
$920$	12.3593	0.407475
$921$	1.11538	0.0367529
$922$	8.26591	0.272223
$923$	−10.2395	−0.337036
$924$	14.5685	0.479270
$925$	−27.0645	−0.889876
$926$	−27.2271	−0.894738
$927$	−39.8761	−1.30970
$928$	2.96884	0.0974569
$929$	31.6185	1.03737	0.518684	−	0.854966i	$-0.326422\pi$
$929$	31.6185	1.03737	0.518684	+	0.854966i	$0.326422\pi$
$930$	4.43720	0.145502
$931$	−94.2309	−3.08829
$932$	2.85531	0.0935287
$933$	−11.8605	−0.388296
$934$	−5.58987	−0.182906
$935$	−2.12924	−0.0696335
$936$	4.03156	0.131776
$937$	29.0006	0.947407	0.473704	−	0.880684i	$-0.342917\pi$
$937$	29.0006	0.947407	0.473704	+	0.880684i	$0.342917\pi$
$938$	43.9525	1.43510
$939$	−5.58373	−0.182218
$940$	5.57966	0.181988
$941$	−1.22096	−0.0398021	−0.0199011	−	0.999802i	$-0.506335\pi$
$941$	−1.22096	−0.0398021	−0.0199011	+	0.999802i	$0.506335\pi$
$942$	3.12564	0.101839
$943$	−62.9679	−2.05052
$944$	11.2413	0.365874
$945$	22.7904	0.741371
$946$	−5.99310	−0.194852
$947$	45.0609	1.46428	0.732141	−	0.681154i	$-0.238521\pi$
$947$	45.0609	1.46428	0.732141	+	0.681154i	$0.238521\pi$
$948$	4.09836	0.133109
$949$	17.2435	0.559746
$950$	14.8166	0.480715
$951$	−12.2133	−0.396043
$952$	−1.68026	−0.0544576
$953$	−19.2424	−0.623323	−0.311661	−	0.950193i	$-0.600885\pi$
$953$	−19.2424	−0.623323	−0.311661	+	0.950193i	$0.600885\pi$
$954$	−30.5957	−0.990571
$955$	−15.9437	−0.515925
$956$	1.54106	0.0498415
$957$	−8.29160	−0.268029
$958$	2.67407	0.0863954
$959$	−99.6631	−3.21829
$960$	0.769917	0.0248490
$961$	2.21470	0.0714421
$962$	−12.8374	−0.413894
$963$	−10.7723	−0.347133
$964$	2.05203	0.0660914
$965$	1.87310	0.0602972
$966$	−27.2396	−0.876418
$967$	−5.11420	−0.164462	−0.0822309	−	0.996613i	$-0.526204\pi$
$967$	−5.11420	−0.164462	−0.0822309	+	0.996613i	$0.526204\pi$
$968$	12.9783	0.417138
$969$	0.856608	0.0275182
$970$	−15.3019	−0.491316
$971$	51.4507	1.65113	0.825566	−	0.564306i	$-0.190856\pi$
$971$	51.4507	1.65113	0.825566	+	0.564306i	$0.190856\pi$
$972$	−13.2334	−0.424462
$973$	−46.6693	−1.49615
$974$	40.4979	1.29764
$975$	−2.73189	−0.0874905
$976$	−11.6601	−0.373232
$977$	−16.9760	−0.543110	−0.271555	−	0.962423i	$-0.587538\pi$
$977$	−16.9760	−0.543110	−0.271555	+	0.962423i	$0.587538\pi$
$978$	0.645698	0.0206471
$979$	85.0188	2.71721
$980$	−27.2815	−0.871475
$981$	33.2940	1.06300
$982$	18.4772	0.589631
$983$	−0.922623	−0.0294271	−0.0147135	−	0.999892i	$-0.504684\pi$
$983$	−0.922623	−0.0294271	−0.0147135	+	0.999892i	$0.504684\pi$
$984$	−3.92255	−0.125046
$985$	14.1372	0.450450
$986$	0.956312	0.0304552
$987$	−12.2974	−0.391430
$988$	7.02789	0.223587
$989$	11.2056	0.356318
$990$	17.6801	0.561912
$991$	26.2547	0.834008	0.417004	−	0.908905i	$-0.363080\pi$
$991$	26.2547	0.834008	0.417004	+	0.908905i	$0.363080\pi$
$992$	5.76322	0.182982
$993$	−11.4140	−0.362213
$994$	−35.4359	−1.12396
$995$	−20.0261	−0.634871
$996$	−0.351308	−0.0111316
$997$	29.4017	0.931160	0.465580	−	0.885006i	$-0.345846\pi$
$997$	29.4017	0.931160	0.465580	+	0.885006i	$0.345846\pi$
$998$	−29.2974	−0.927393
$999$	27.5653	0.872129

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.d.1.19	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.d.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.570351 q^{3} +1.00000 q^{4} -1.34990 q^{5} -0.570351 q^{6} -5.21632 q^{7} +1.00000 q^{8} -2.67470 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.570351 q^{3} +1.00000 q^{4} -1.34990 q^{5} -0.570351 q^{6} -5.21632 q^{7} +1.00000 q^{8} -2.67470 q^{9} -1.34990 q^{10} +4.89676 q^{11} -0.570351 q^{12} -1.50729 q^{13} -5.21632 q^{14} +0.769917 q^{15} +1.00000 q^{16} +0.322117 q^{17} -2.67470 q^{18} -4.66258 q^{19} -1.34990 q^{20} +2.97514 q^{21} +4.89676 q^{22} -9.15574 q^{23} -0.570351 q^{24} -3.17777 q^{25} -1.50729 q^{26} +3.23657 q^{27} -5.21632 q^{28} +2.96884 q^{29} +0.769917 q^{30} +5.76322 q^{31} +1.00000 q^{32} -2.79288 q^{33} +0.322117 q^{34} +7.04151 q^{35} -2.67470 q^{36} +8.51683 q^{37} -4.66258 q^{38} +0.859688 q^{39} -1.34990 q^{40} +6.87743 q^{41} +2.97514 q^{42} -1.22389 q^{43} +4.89676 q^{44} +3.61058 q^{45} -9.15574 q^{46} -4.13339 q^{47} -0.570351 q^{48} +20.2100 q^{49} -3.17777 q^{50} -0.183720 q^{51} -1.50729 q^{52} +11.4389 q^{53} +3.23657 q^{54} -6.61014 q^{55} -5.21632 q^{56} +2.65931 q^{57} +2.96884 q^{58} +11.2413 q^{59} +0.769917 q^{60} -11.6601 q^{61} +5.76322 q^{62} +13.9521 q^{63} +1.00000 q^{64} +2.03470 q^{65} -2.79288 q^{66} -8.42595 q^{67} +0.322117 q^{68} +5.22199 q^{69} +7.04151 q^{70} +6.79327 q^{71} -2.67470 q^{72} -11.4400 q^{73} +8.51683 q^{74} +1.81245 q^{75} -4.66258 q^{76} -25.5431 q^{77} +0.859688 q^{78} -7.18568 q^{79} -1.34990 q^{80} +6.17811 q^{81} +6.87743 q^{82} +0.615951 q^{83} +2.97514 q^{84} -0.434825 q^{85} -1.22389 q^{86} -1.69328 q^{87} +4.89676 q^{88} +17.3622 q^{89} +3.61058 q^{90} +7.86253 q^{91} -9.15574 q^{92} -3.28706 q^{93} -4.13339 q^{94} +6.29402 q^{95} -0.570351 q^{96} +11.3356 q^{97} +20.2100 q^{98} -13.0974 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) \) 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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