LMFDB - Embedded newform 8035.2.a.d.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1597980241$
Analytic rank:	$1$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41030 q^{2} -2.44694 q^{3} +3.80955 q^{4} -1.00000 q^{5} +5.89785 q^{6} -4.60731 q^{7} -4.36157 q^{8} +2.98749 q^{9} +O(q^{10})$	\(q-2.41030 q^{2} -2.44694 q^{3} +3.80955 q^{4} -1.00000 q^{5} +5.89785 q^{6} -4.60731 q^{7} -4.36157 q^{8} +2.98749 q^{9} +2.41030 q^{10} +4.47378 q^{11} -9.32173 q^{12} -0.485248 q^{13} +11.1050 q^{14} +2.44694 q^{15} +2.89360 q^{16} -3.98574 q^{17} -7.20076 q^{18} -6.64741 q^{19} -3.80955 q^{20} +11.2738 q^{21} -10.7832 q^{22} +3.50686 q^{23} +10.6725 q^{24} +1.00000 q^{25} +1.16959 q^{26} +0.0306083 q^{27} -17.5518 q^{28} +0.845360 q^{29} -5.89785 q^{30} -1.93535 q^{31} +1.74870 q^{32} -10.9471 q^{33} +9.60683 q^{34} +4.60731 q^{35} +11.3810 q^{36} -6.85966 q^{37} +16.0223 q^{38} +1.18737 q^{39} +4.36157 q^{40} +3.43323 q^{41} -27.1732 q^{42} +0.478030 q^{43} +17.0431 q^{44} -2.98749 q^{45} -8.45258 q^{46} -0.505161 q^{47} -7.08045 q^{48} +14.2273 q^{49} -2.41030 q^{50} +9.75284 q^{51} -1.84858 q^{52} -10.4299 q^{53} -0.0737753 q^{54} -4.47378 q^{55} +20.0951 q^{56} +16.2658 q^{57} -2.03757 q^{58} +2.60496 q^{59} +9.32173 q^{60} -3.78316 q^{61} +4.66478 q^{62} -13.7643 q^{63} -10.0021 q^{64} +0.485248 q^{65} +26.3857 q^{66} -6.76282 q^{67} -15.1839 q^{68} -8.58105 q^{69} -11.1050 q^{70} +5.58804 q^{71} -13.0302 q^{72} +15.2480 q^{73} +16.5338 q^{74} -2.44694 q^{75} -25.3237 q^{76} -20.6121 q^{77} -2.86192 q^{78} -16.8661 q^{79} -2.89360 q^{80} -9.03737 q^{81} -8.27513 q^{82} -4.11606 q^{83} +42.9481 q^{84} +3.98574 q^{85} -1.15220 q^{86} -2.06854 q^{87} -19.5127 q^{88} +14.3344 q^{89} +7.20076 q^{90} +2.23569 q^{91} +13.3596 q^{92} +4.73568 q^{93} +1.21759 q^{94} +6.64741 q^{95} -4.27896 q^{96} -0.218512 q^{97} -34.2921 q^{98} +13.3654 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) $ 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.41030	−1.70434	−0.852170	−	0.523264i	$-0.824714\pi$
$2$	−2.41030	−1.70434	−0.852170	+	0.523264i	$0.824714\pi$
$3$	−2.44694	−1.41274	−0.706369	−	0.707843i	$-0.749668\pi$
$3$	−2.44694	−1.41274	−0.706369	+	0.707843i	$0.749668\pi$
$4$	3.80955	1.90478
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	5.89785	2.40779
$7$	−4.60731	−1.74140	−0.870700	−	0.491815i	$-0.836334\pi$
$7$	−4.60731	−1.74140	−0.870700	+	0.491815i	$0.836334\pi$
$8$	−4.36157	−1.54205
$9$	2.98749	0.995830
$10$	2.41030	0.762204
$11$	4.47378	1.34890	0.674448	−	0.738322i	$-0.264382\pi$
$11$	4.47378	1.34890	0.674448	+	0.738322i	$0.264382\pi$
$12$	−9.32173	−2.69095
$13$	−0.485248	−0.134584	−0.0672918	−	0.997733i	$-0.521436\pi$
$13$	−0.485248	−0.134584	−0.0672918	+	0.997733i	$0.521436\pi$
$14$	11.1050	2.96794
$15$	2.44694	0.631796
$16$	2.89360	0.723400
$17$	−3.98574	−0.966683	−0.483342	−	0.875432i	$-0.660577\pi$
$17$	−3.98574	−0.966683	−0.483342	+	0.875432i	$0.660577\pi$
$18$	−7.20076	−1.69723
$19$	−6.64741	−1.52502	−0.762510	−	0.646976i	$-0.776033\pi$
$19$	−6.64741	−1.52502	−0.762510	+	0.646976i	$0.776033\pi$
$20$	−3.80955	−0.851842
$21$	11.2738	2.46014
$22$	−10.7832	−2.29898
$23$	3.50686	0.731230	0.365615	−	0.930766i	$-0.380859\pi$
$23$	3.50686	0.731230	0.365615	+	0.930766i	$0.380859\pi$
$24$	10.6725	2.17851
$25$	1.00000	0.200000
$26$	1.16959	0.229376
$27$	0.0306083	0.00589057
$28$	−17.5518	−3.31698
$29$	0.845360	0.156979	0.0784897	−	0.996915i	$-0.474990\pi$
$29$	0.845360	0.156979	0.0784897	+	0.996915i	$0.474990\pi$
$30$	−5.89785	−1.07680
$31$	−1.93535	−0.347599	−0.173800	−	0.984781i	$-0.555605\pi$
$31$	−1.93535	−0.347599	−0.173800	+	0.984781i	$0.555605\pi$
$32$	1.74870	0.309129
$33$	−10.9471	−1.90564
$34$	9.60683	1.64756
$35$	4.60731	0.778778
$36$	11.3810	1.89684
$37$	−6.85966	−1.12772	−0.563860	−	0.825870i	$-0.690684\pi$
$37$	−6.85966	−1.12772	−0.563860	+	0.825870i	$0.690684\pi$
$38$	16.0223	2.59916
$39$	1.18737	0.190131
$40$	4.36157	0.689625
$41$	3.43323	0.536181	0.268091	−	0.963394i	$-0.413607\pi$
$41$	3.43323	0.536181	0.268091	+	0.963394i	$0.413607\pi$
$42$	−27.1732	−4.19292
$43$	0.478030	0.0728988	0.0364494	−	0.999335i	$-0.488395\pi$
$43$	0.478030	0.0728988	0.0364494	+	0.999335i	$0.488395\pi$
$44$	17.0431	2.56935
$45$	−2.98749	−0.445349
$46$	−8.45258	−1.24627
$47$	−0.505161	−0.0736852	−0.0368426	−	0.999321i	$-0.511730\pi$
$47$	−0.505161	−0.0736852	−0.0368426	+	0.999321i	$0.511730\pi$
$48$	−7.08045	−1.02197
$49$	14.2273	2.03247
$50$	−2.41030	−0.340868
$51$	9.75284	1.36567
$52$	−1.84858	−0.256352
$53$	−10.4299	−1.43265	−0.716327	−	0.697764i	$-0.754178\pi$
$53$	−10.4299	−1.43265	−0.716327	+	0.697764i	$0.754178\pi$
$54$	−0.0737753	−0.0100395
$55$	−4.47378	−0.603245
$56$	20.0951	2.68532
$57$	16.2658	2.15446
$58$	−2.03757	−0.267547
$59$	2.60496	0.339137	0.169568	−	0.985518i	$-0.445763\pi$
$59$	2.60496	0.339137	0.169568	+	0.985518i	$0.445763\pi$
$60$	9.32173	1.20343
$61$	−3.78316	−0.484384	−0.242192	−	0.970228i	$-0.577866\pi$
$61$	−3.78316	−0.484384	−0.242192	+	0.970228i	$0.577866\pi$
$62$	4.66478	0.592428
$63$	−13.7643	−1.73414
$64$	−10.0021	−1.25026
$65$	0.485248	0.0601876
$66$	26.3857	3.24786
$67$	−6.76282	−0.826210	−0.413105	−	0.910683i	$-0.635556\pi$
$67$	−6.76282	−0.826210	−0.413105	+	0.910683i	$0.635556\pi$
$68$	−15.1839	−1.84132
$69$	−8.58105	−1.03304
$70$	−11.1050	−1.32730
$71$	5.58804	0.663178	0.331589	−	0.943424i	$-0.392415\pi$
$71$	5.58804	0.663178	0.331589	+	0.943424i	$0.392415\pi$
$72$	−13.0302	−1.53562
$73$	15.2480	1.78465	0.892323	−	0.451398i	$-0.149075\pi$
$73$	15.2480	1.78465	0.892323	+	0.451398i	$0.149075\pi$
$74$	16.5338	1.92202
$75$	−2.44694	−0.282548
$76$	−25.3237	−2.90483
$77$	−20.6121	−2.34897
$78$	−2.86192	−0.324049
$79$	−16.8661	−1.89758	−0.948791	−	0.315905i	$-0.897692\pi$
$79$	−16.8661	−1.89758	−0.948791	+	0.315905i	$0.897692\pi$
$80$	−2.89360	−0.323514
$81$	−9.03737	−1.00415
$82$	−8.27513	−0.913835
$83$	−4.11606	−0.451796	−0.225898	−	0.974151i	$-0.572532\pi$
$83$	−4.11606	−0.451796	−0.225898	+	0.974151i	$0.572532\pi$
$84$	42.9481	4.68602
$85$	3.98574	0.432314
$86$	−1.15220	−0.124244
$87$	−2.06854	−0.221771
$88$	−19.5127	−2.08007
$89$	14.3344	1.51944	0.759721	−	0.650249i	$-0.225335\pi$
$89$	14.3344	1.51944	0.759721	+	0.650249i	$0.225335\pi$
$90$	7.20076	0.759026
$91$	2.23569	0.234364
$92$	13.3596	1.39283
$93$	4.73568	0.491067
$94$	1.21759	0.125585
$95$	6.64741	0.682010
$96$	−4.27896	−0.436719
$97$	−0.218512	−0.0221865	−0.0110933	−	0.999938i	$-0.503531\pi$
$97$	−0.218512	−0.0221865	−0.0110933	+	0.999938i	$0.503531\pi$
$98$	−34.2921	−3.46403
$99$	13.3654	1.34327
$100$	3.80955	0.380955
$101$	−17.1427	−1.70576	−0.852881	−	0.522106i	$-0.825147\pi$
$101$	−17.1427	−1.70576	−0.852881	+	0.522106i	$0.825147\pi$
$102$	−23.5073	−2.32757
$103$	19.6202	1.93324	0.966618	−	0.256222i	$-0.0824777\pi$
$103$	19.6202	1.93324	0.966618	+	0.256222i	$0.0824777\pi$
$104$	2.11645	0.207535
$105$	−11.2738	−1.10021
$106$	25.1392	2.44173
$107$	−6.60761	−0.638781	−0.319391	−	0.947623i	$-0.603478\pi$
$107$	−6.60761	−0.638781	−0.319391	+	0.947623i	$0.603478\pi$
$108$	0.116604	0.0112202
$109$	−7.24113	−0.693574	−0.346787	−	0.937944i	$-0.612727\pi$
$109$	−7.24113	−0.693574	−0.346787	+	0.937944i	$0.612727\pi$
$110$	10.7832	1.02813
$111$	16.7851	1.59317
$112$	−13.3317	−1.25973
$113$	−1.25121	−0.117704	−0.0588521	−	0.998267i	$-0.518744\pi$
$113$	−1.25121	−0.117704	−0.0588521	+	0.998267i	$0.518744\pi$
$114$	−39.2054	−3.67193
$115$	−3.50686	−0.327016
$116$	3.22045	0.299011
$117$	−1.44967	−0.134022
$118$	−6.27873	−0.578004
$119$	18.3635	1.68338
$120$	−10.6725	−0.974260
$121$	9.01475	0.819522
$122$	9.11855	0.825555
$123$	−8.40090	−0.757484
$124$	−7.37282	−0.662099
$125$	−1.00000	−0.0894427
$126$	33.1761	2.95556
$127$	1.59161	0.141232	0.0706161	−	0.997504i	$-0.477503\pi$
$127$	1.59161	0.141232	0.0706161	+	0.997504i	$0.477503\pi$
$128$	20.6107	1.82174
$129$	−1.16971	−0.102987
$130$	−1.16959	−0.102580
$131$	15.5999	1.36297	0.681484	−	0.731833i	$-0.261335\pi$
$131$	15.5999	1.36297	0.681484	+	0.731833i	$0.261335\pi$
$132$	−41.7034	−3.62982
$133$	30.6267	2.65567
$134$	16.3004	1.40814
$135$	−0.0306083	−0.00263434
$136$	17.3841	1.49067
$137$	6.88846	0.588521	0.294260	−	0.955725i	$-0.404927\pi$
$137$	6.88846	0.588521	0.294260	+	0.955725i	$0.404927\pi$
$138$	20.6829	1.76065
$139$	15.1145	1.28200	0.640998	−	0.767543i	$-0.278521\pi$
$139$	15.1145	1.28200	0.640998	+	0.767543i	$0.278521\pi$
$140$	17.5518	1.48340
$141$	1.23610	0.104098
$142$	−13.4689	−1.13028
$143$	−2.17090	−0.181539
$144$	8.64460	0.720384
$145$	−0.845360	−0.0702034
$146$	−36.7523	−3.04164
$147$	−34.8133	−2.87135
$148$	−26.1322	−2.14806
$149$	3.26814	0.267737	0.133868	−	0.990999i	$-0.457260\pi$
$149$	3.26814	0.267737	0.133868	+	0.990999i	$0.457260\pi$
$150$	5.89785	0.481558
$151$	−9.15734	−0.745214	−0.372607	−	0.927989i	$-0.621536\pi$
$151$	−9.15734	−0.745214	−0.372607	+	0.927989i	$0.621536\pi$
$152$	28.9932	2.35166
$153$	−11.9074	−0.962652
$154$	49.6814	4.00344
$155$	1.93535	0.155451
$156$	4.52335	0.362158
$157$	−0.346858	−0.0276823	−0.0138411	−	0.999904i	$-0.504406\pi$
$157$	−0.346858	−0.0276823	−0.0138411	+	0.999904i	$0.504406\pi$
$158$	40.6523	3.23413
$159$	25.5212	2.02397
$160$	−1.74870	−0.138247
$161$	−16.1572	−1.27336
$162$	21.7828	1.71142
$163$	−7.57253	−0.593127	−0.296563	−	0.955013i	$-0.595841\pi$
$163$	−7.57253	−0.593127	−0.296563	+	0.955013i	$0.595841\pi$
$164$	13.0791	1.02131
$165$	10.9471	0.852227
$166$	9.92094	0.770014
$167$	7.60001	0.588106	0.294053	−	0.955789i	$-0.404996\pi$
$167$	7.60001	0.588106	0.294053	+	0.955789i	$0.404996\pi$
$168$	−49.1715	−3.79366
$169$	−12.7645	−0.981887
$170$	−9.60683	−0.736810
$171$	−19.8591	−1.51866
$172$	1.82108	0.138856
$173$	−12.9027	−0.980977	−0.490488	−	0.871448i	$-0.663182\pi$
$173$	−12.9027	−0.980977	−0.490488	+	0.871448i	$0.663182\pi$
$174$	4.98581	0.377973
$175$	−4.60731	−0.348280
$176$	12.9453	0.975792
$177$	−6.37416	−0.479111
$178$	−34.5502	−2.58965
$179$	15.5177	1.15984	0.579922	−	0.814672i	$-0.303083\pi$
$179$	15.5177	1.15984	0.579922	+	0.814672i	$0.303083\pi$
$180$	−11.3810	−0.848291
$181$	21.7436	1.61619	0.808093	−	0.589055i	$-0.200500\pi$
$181$	21.7436	1.61619	0.808093	+	0.589055i	$0.200500\pi$
$182$	−5.38868	−0.399436
$183$	9.25714	0.684307
$184$	−15.2954	−1.12759
$185$	6.85966	0.504332
$186$	−11.4144	−0.836945
$187$	−17.8313	−1.30396
$188$	−1.92444	−0.140354
$189$	−0.141022	−0.0102578
$190$	−16.0223	−1.16238
$191$	−7.24591	−0.524296	−0.262148	−	0.965028i	$-0.584431\pi$
$191$	−7.24591	−0.524296	−0.262148	+	0.965028i	$0.584431\pi$
$192$	24.4745	1.76629
$193$	17.2334	1.24049	0.620243	−	0.784410i	$-0.287034\pi$
$193$	17.2334	1.24049	0.620243	+	0.784410i	$0.287034\pi$
$194$	0.526680	0.0378134
$195$	−1.18737	−0.0850294
$196$	54.1997	3.87141
$197$	−8.85068	−0.630585	−0.315292	−	0.948995i	$-0.602103\pi$
$197$	−8.85068	−0.630585	−0.315292	+	0.948995i	$0.602103\pi$
$198$	−32.2146	−2.28939
$199$	19.6138	1.39039	0.695193	−	0.718823i	$-0.255319\pi$
$199$	19.6138	1.39039	0.695193	+	0.718823i	$0.255319\pi$
$200$	−4.36157	−0.308410
$201$	16.5482	1.16722
$202$	41.3191	2.90720
$203$	−3.89484	−0.273364
$204$	37.1540	2.60130
$205$	−3.43323	−0.239788
$206$	−47.2906	−3.29489
$207$	10.4767	0.728181
$208$	−1.40411	−0.0973578
$209$	−29.7391	−2.05710
$210$	27.1732	1.87513
$211$	3.66728	0.252466	0.126233	−	0.992001i	$-0.459711\pi$
$211$	3.66728	0.252466	0.126233	+	0.992001i	$0.459711\pi$
$212$	−39.7332	−2.72889
$213$	−13.6736	−0.936897
$214$	15.9263	1.08870
$215$	−0.478030	−0.0326013
$216$	−0.133500	−0.00908355
$217$	8.91676	0.605309
$218$	17.4533	1.18209
$219$	−37.3109	−2.52124
$220$	−17.0431	−1.14905
$221$	1.93407	0.130100
$222$	−40.4572	−2.71531
$223$	26.9278	1.80322	0.901609	−	0.432553i	$-0.142387\pi$
$223$	26.9278	1.80322	0.901609	+	0.432553i	$0.142387\pi$
$224$	−8.05680	−0.538318
$225$	2.98749	0.199166
$226$	3.01580	0.200608
$227$	−21.2716	−1.41185	−0.705923	−	0.708289i	$-0.749467\pi$
$227$	−21.2716	−1.41185	−0.705923	+	0.708289i	$0.749467\pi$
$228$	61.9654	4.10376
$229$	3.64289	0.240729	0.120365	−	0.992730i	$-0.461594\pi$
$229$	3.64289	0.240729	0.120365	+	0.992730i	$0.461594\pi$
$230$	8.45258	0.557347
$231$	50.4365	3.31848
$232$	−3.68710	−0.242070
$233$	0.390371	0.0255741	0.0127870	−	0.999918i	$-0.495930\pi$
$233$	0.390371	0.0255741	0.0127870	+	0.999918i	$0.495930\pi$
$234$	3.49415	0.228420
$235$	0.505161	0.0329530
$236$	9.92373	0.645980
$237$	41.2702	2.68079
$238$	−44.2616	−2.86906
$239$	0.425843	0.0275455	0.0137727	−	0.999905i	$-0.495616\pi$
$239$	0.425843	0.0275455	0.0137727	+	0.999905i	$0.495616\pi$
$240$	7.08045	0.457041
$241$	−4.78867	−0.308466	−0.154233	−	0.988035i	$-0.549291\pi$
$241$	−4.78867	−0.308466	−0.154233	+	0.988035i	$0.549291\pi$
$242$	−21.7283	−1.39675
$243$	22.0220	1.41271
$244$	−14.4121	−0.922643
$245$	−14.2273	−0.908950
$246$	20.2487	1.29101
$247$	3.22564	0.205243
$248$	8.44117	0.536015
$249$	10.0717	0.638269
$250$	2.41030	0.152441
$251$	−7.32942	−0.462629	−0.231314	−	0.972879i	$-0.574303\pi$
$251$	−7.32942	−0.462629	−0.231314	+	0.972879i	$0.574303\pi$
$252$	−52.4359	−3.30315
$253$	15.6889	0.986354
$254$	−3.83625	−0.240708
$255$	−9.75284	−0.610746
$256$	−29.6737	−1.85461
$257$	−4.71710	−0.294245	−0.147122	−	0.989118i	$-0.547001\pi$
$257$	−4.71710	−0.294245	−0.147122	+	0.989118i	$0.547001\pi$
$258$	2.81935	0.175525
$259$	31.6046	1.96381
$260$	1.84858	0.114644
$261$	2.52551	0.156325
$262$	−37.6004	−2.32296
$263$	11.4304	0.704831	0.352415	−	0.935844i	$-0.385360\pi$
$263$	11.4304	0.704831	0.352415	+	0.935844i	$0.385360\pi$
$264$	47.7464	2.93859
$265$	10.4299	0.640703
$266$	−73.8196	−4.52617
$267$	−35.0753	−2.14658
$268$	−25.7633	−1.57375
$269$	−14.2622	−0.869581	−0.434791	−	0.900532i	$-0.643178\pi$
$269$	−14.2622	−0.869581	−0.434791	+	0.900532i	$0.643178\pi$
$270$	0.0737753	0.00448982
$271$	5.48846	0.333400	0.166700	−	0.986008i	$-0.446689\pi$
$271$	5.48846	0.333400	0.166700	+	0.986008i	$0.446689\pi$
$272$	−11.5331	−0.699298
$273$	−5.47058	−0.331095
$274$	−16.6033	−1.00304
$275$	4.47378	0.269779
$276$	−32.6900	−1.96771
$277$	13.2353	0.795233	0.397616	−	0.917552i	$-0.369837\pi$
$277$	13.2353	0.795233	0.397616	+	0.917552i	$0.369837\pi$
$278$	−36.4305	−2.18496
$279$	−5.78184	−0.346150
$280$	−20.0951	−1.20091
$281$	29.8179	1.77879	0.889395	−	0.457140i	$-0.151126\pi$
$281$	29.8179	1.77879	0.889395	+	0.457140i	$0.151126\pi$
$282$	−2.97936	−0.177418
$283$	−6.06422	−0.360480	−0.180240	−	0.983623i	$-0.557687\pi$
$283$	−6.06422	−0.360480	−0.180240	+	0.983623i	$0.557687\pi$
$284$	21.2879	1.26321
$285$	−16.2658	−0.963502
$286$	5.23251	0.309405
$287$	−15.8180	−0.933706
$288$	5.22423	0.307840
$289$	−1.11391	−0.0655239
$290$	2.03757	0.119650
$291$	0.534685	0.0313438
$292$	58.0881	3.39935
$293$	10.5266	0.614972	0.307486	−	0.951553i	$-0.400512\pi$
$293$	10.5266	0.614972	0.307486	+	0.951553i	$0.400512\pi$
$294$	83.9106	4.89376
$295$	−2.60496	−0.151666
$296$	29.9189	1.73900
$297$	0.136935	0.00794578
$298$	−7.87721	−0.456314
$299$	−1.70170	−0.0984116
$300$	−9.32173	−0.538191
$301$	−2.20243	−0.126946
$302$	22.0719	1.27010
$303$	41.9471	2.40980
$304$	−19.2349	−1.10320
$305$	3.78316	0.216623
$306$	28.7003	1.64069
$307$	29.8918	1.70602	0.853009	−	0.521897i	$-0.174775\pi$
$307$	29.8918	1.70602	0.853009	+	0.521897i	$0.174775\pi$
$308$	−78.5230	−4.47426
$309$	−48.0094	−2.73116
$310$	−4.66478	−0.264942
$311$	27.7911	1.57589	0.787943	−	0.615748i	$-0.211146\pi$
$311$	27.7911	1.57589	0.787943	+	0.615748i	$0.211146\pi$
$312$	−5.17880	−0.293192
$313$	20.1800	1.14064	0.570320	−	0.821423i	$-0.306819\pi$
$313$	20.1800	1.14064	0.570320	+	0.821423i	$0.306819\pi$
$314$	0.836032	0.0471800
$315$	13.7643	0.775530
$316$	−64.2522	−3.61447
$317$	4.57801	0.257127	0.128563	−	0.991701i	$-0.458963\pi$
$317$	4.57801	0.257127	0.128563	+	0.991701i	$0.458963\pi$
$318$	−61.5139	−3.44953
$319$	3.78196	0.211749
$320$	10.0021	0.559134
$321$	16.1684	0.902431
$322$	38.9437	2.17025
$323$	26.4948	1.47421
$324$	−34.4284	−1.91269
$325$	−0.485248	−0.0269167
$326$	18.2521	1.01089
$327$	17.7186	0.979839
$328$	−14.9743	−0.826818
$329$	2.32743	0.128315
$330$	−26.3857	−1.45249
$331$	−24.9009	−1.36868	−0.684339	−	0.729164i	$-0.739909\pi$
$331$	−24.9009	−1.36868	−0.684339	+	0.729164i	$0.739909\pi$
$332$	−15.6803	−0.860570
$333$	−20.4932	−1.12302
$334$	−18.3183	−1.00233
$335$	6.76282	0.369492
$336$	32.6218	1.77967
$337$	−6.96549	−0.379434	−0.189717	−	0.981839i	$-0.560757\pi$
$337$	−6.96549	−0.379434	−0.189717	+	0.981839i	$0.560757\pi$
$338$	30.7664	1.67347
$339$	3.06164	0.166285
$340$	15.1839	0.823462
$341$	−8.65834	−0.468875
$342$	47.8664	2.58832
$343$	−33.2985	−1.79795
$344$	−2.08496	−0.112414
$345$	8.58105	0.461988
$346$	31.0995	1.67192
$347$	35.1516	1.88704	0.943518	−	0.331320i	$-0.107494\pi$
$347$	35.1516	1.88704	0.943518	+	0.331320i	$0.107494\pi$
$348$	−7.88022	−0.422424
$349$	−12.4581	−0.666869	−0.333434	−	0.942773i	$-0.608208\pi$
$349$	−12.4581	−0.666869	−0.333434	+	0.942773i	$0.608208\pi$
$350$	11.1050	0.593588
$351$	−0.0148526	−0.000792775 0
$352$	7.82331	0.416984
$353$	−0.142500	−0.00758453	−0.00379227	−	0.999993i	$-0.501207\pi$
$353$	−0.142500	−0.00758453	−0.00379227	+	0.999993i	$0.501207\pi$
$354$	15.3637	0.816569
$355$	−5.58804	−0.296582
$356$	54.6077	2.89420
$357$	−44.9344	−2.37818
$358$	−37.4022	−1.97677
$359$	24.2477	1.27975	0.639874	−	0.768480i	$-0.278987\pi$
$359$	24.2477	1.27975	0.639874	+	0.768480i	$0.278987\pi$
$360$	13.0302	0.686750
$361$	25.1881	1.32569
$362$	−52.4085	−2.75453
$363$	−22.0585	−1.15777
$364$	8.51698	0.446411
$365$	−15.2480	−0.798118
$366$	−22.3125	−1.16629
$367$	−13.4942	−0.704389	−0.352195	−	0.935927i	$-0.614565\pi$
$367$	−13.4942	−0.704389	−0.352195	+	0.935927i	$0.614565\pi$
$368$	10.1474	0.528972
$369$	10.2568	0.533945
$370$	−16.5338	−0.859553
$371$	48.0537	2.49482
$372$	18.0408	0.935373
$373$	3.21463	0.166447	0.0832236	−	0.996531i	$-0.473478\pi$
$373$	3.21463	0.166447	0.0832236	+	0.996531i	$0.473478\pi$
$374$	42.9789	2.22238
$375$	2.44694	0.126359
$376$	2.20330	0.113626
$377$	−0.410209	−0.0211269
$378$	0.339906	0.0174829
$379$	19.0286	0.977431	0.488716	−	0.872443i	$-0.337466\pi$
$379$	19.0286	0.977431	0.488716	+	0.872443i	$0.337466\pi$
$380$	25.3237	1.29908
$381$	−3.89456	−0.199524
$382$	17.4648	0.893579
$383$	−2.58423	−0.132048	−0.0660239	−	0.997818i	$-0.521031\pi$
$383$	−2.58423	−0.132048	−0.0660239	+	0.997818i	$0.521031\pi$
$384$	−50.4330	−2.57365
$385$	20.6121	1.05049
$386$	−41.5376	−2.11421
$387$	1.42811	0.0725949
$388$	−0.832434	−0.0422604
$389$	11.0836	0.561962	0.280981	−	0.959713i	$-0.409340\pi$
$389$	11.0836	0.561962	0.280981	+	0.959713i	$0.409340\pi$
$390$	2.86192	0.144919
$391$	−13.9774	−0.706868
$392$	−62.0535	−3.13417
$393$	−38.1719	−1.92552
$394$	21.3328	1.07473
$395$	16.8661	0.848624
$396$	50.9162	2.55863
$397$	23.6608	1.18750	0.593751	−	0.804649i	$-0.297646\pi$
$397$	23.6608	1.18750	0.593751	+	0.804649i	$0.297646\pi$
$398$	−47.2752	−2.36969
$399$	−74.9415	−3.75177
$400$	2.89360	0.144680
$401$	−34.8688	−1.74126	−0.870632	−	0.491935i	$-0.836290\pi$
$401$	−34.8688	−1.74126	−0.870632	+	0.491935i	$0.836290\pi$
$402$	−39.8861	−1.98934
$403$	0.939125	0.0467812
$404$	−65.3060	−3.24910
$405$	9.03737	0.449071
$406$	9.38773	0.465905
$407$	−30.6886	−1.52118
$408$	−42.5377	−2.10593
$409$	−27.1832	−1.34412	−0.672060	−	0.740496i	$-0.734590\pi$
$409$	−27.1832	−1.34412	−0.672060	+	0.740496i	$0.734590\pi$
$410$	8.27513	0.408680
$411$	−16.8556	−0.831426
$412$	74.7442	3.68238
$413$	−12.0018	−0.590572
$414$	−25.2520	−1.24107
$415$	4.11606	0.202049
$416$	−0.848553	−0.0416037
$417$	−36.9842	−1.81112
$418$	71.6802	3.50599
$419$	34.2908	1.67522	0.837608	−	0.546272i	$-0.183953\pi$
$419$	34.2908	1.67522	0.837608	+	0.546272i	$0.183953\pi$
$420$	−42.9481	−2.09565
$421$	15.2554	0.743502	0.371751	−	0.928333i	$-0.378758\pi$
$421$	15.2554	0.743502	0.371751	+	0.928333i	$0.378758\pi$
$422$	−8.83924	−0.430288
$423$	−1.50916	−0.0733780
$424$	45.4907	2.20922
$425$	−3.98574	−0.193337
$426$	32.9574	1.59679
$427$	17.4302	0.843505
$428$	−25.1720	−1.21674
$429$	5.31204	0.256468
$430$	1.15220	0.0555638
$431$	−16.9383	−0.815891	−0.407946	−	0.913006i	$-0.633755\pi$
$431$	−16.9383	−0.815891	−0.407946	+	0.913006i	$0.633755\pi$
$432$	0.0885682	0.00426124
$433$	27.7406	1.33313	0.666563	−	0.745448i	$-0.267765\pi$
$433$	27.7406	1.33313	0.666563	+	0.745448i	$0.267765\pi$
$434$	−21.4921	−1.03165
$435$	2.06854	0.0991790
$436$	−27.5855	−1.32110
$437$	−23.3115	−1.11514
$438$	89.9305	4.29705
$439$	−27.3231	−1.30406	−0.652030	−	0.758193i	$-0.726083\pi$
$439$	−27.3231	−1.30406	−0.652030	+	0.758193i	$0.726083\pi$
$440$	19.5127	0.930233
$441$	42.5040	2.02400
$442$	−4.66169	−0.221734
$443$	−1.88337	−0.0894816	−0.0447408	−	0.998999i	$-0.514246\pi$
$443$	−1.88337	−0.0894816	−0.0447408	+	0.998999i	$0.514246\pi$
$444$	63.9439	3.03464
$445$	−14.3344	−0.679516
$446$	−64.9041	−3.07330
$447$	−7.99693	−0.378242
$448$	46.0828	2.17721
$449$	14.0161	0.661462	0.330731	−	0.943725i	$-0.392705\pi$
$449$	14.0161	0.661462	0.330731	+	0.943725i	$0.392705\pi$
$450$	−7.20076	−0.339447
$451$	15.3596	0.723253
$452$	−4.76657	−0.224200
$453$	22.4074	1.05279
$454$	51.2710	2.40627
$455$	−2.23569	−0.104811
$456$	−70.9444	−3.32228
$457$	0.488713	0.0228610	0.0114305	−	0.999935i	$-0.496361\pi$
$457$	0.488713	0.0228610	0.0114305	+	0.999935i	$0.496361\pi$
$458$	−8.78047	−0.410285
$459$	−0.121997	−0.00569432
$460$	−13.3596	−0.622893
$461$	−20.7391	−0.965914	−0.482957	−	0.875644i	$-0.660437\pi$
$461$	−20.7391	−0.965914	−0.482957	+	0.875644i	$0.660437\pi$
$462$	−121.567	−5.65582
$463$	31.5026	1.46405	0.732025	−	0.681278i	$-0.238576\pi$
$463$	31.5026	1.46405	0.732025	+	0.681278i	$0.238576\pi$
$464$	2.44613	0.113559
$465$	−4.73568	−0.219612
$466$	−0.940912	−0.0435869
$467$	0.621668	0.0287674	0.0143837	−	0.999897i	$-0.495421\pi$
$467$	0.621668	0.0287674	0.0143837	+	0.999897i	$0.495421\pi$
$468$	−5.52261	−0.255283
$469$	31.1584	1.43876
$470$	−1.21759	−0.0561632
$471$	0.848739	0.0391078
$472$	−11.3617	−0.522965
$473$	2.13860	0.0983330
$474$	−99.4736	−4.56897
$475$	−6.64741	−0.305004
$476$	69.9569	3.20647
$477$	−31.1592	−1.42668
$478$	−1.02641	−0.0469469
$479$	−29.0901	−1.32916	−0.664580	−	0.747218i	$-0.731389\pi$
$479$	−29.0901	−1.32916	−0.664580	+	0.747218i	$0.731389\pi$
$480$	4.27896	0.195307
$481$	3.32863	0.151773
$482$	11.5422	0.525731
$483$	39.5356	1.79893
$484$	34.3422	1.56101
$485$	0.218512	0.00992212
$486$	−53.0797	−2.40775
$487$	−24.5419	−1.11210	−0.556049	−	0.831149i	$-0.687683\pi$
$487$	−24.5419	−1.11210	−0.556049	+	0.831149i	$0.687683\pi$
$488$	16.5005	0.746943
$489$	18.5295	0.837933
$490$	34.2921	1.54916
$491$	29.0062	1.30903	0.654516	−	0.756048i	$-0.272872\pi$
$491$	29.0062	1.30903	0.654516	+	0.756048i	$0.272872\pi$
$492$	−32.0037	−1.44284
$493$	−3.36938	−0.151749
$494$	−7.77477	−0.349804
$495$	−13.3654	−0.600730
$496$	−5.60013	−0.251453
$497$	−25.7458	−1.15486
$498$	−24.2759	−1.08783
$499$	27.9067	1.24928	0.624639	−	0.780914i	$-0.285246\pi$
$499$	27.9067	1.24928	0.624639	+	0.780914i	$0.285246\pi$
$500$	−3.80955	−0.170368
$501$	−18.5967	−0.830840
$502$	17.6661	0.788477
$503$	−15.8439	−0.706444	−0.353222	−	0.935540i	$-0.614914\pi$
$503$	−15.8439	−0.706444	−0.353222	+	0.935540i	$0.614914\pi$
$504$	60.0340	2.67413
$505$	17.1427	0.762840
$506$	−37.8150	−1.68108
$507$	31.2340	1.38715
$508$	6.06331	0.269016
$509$	1.68083	0.0745015	0.0372507	−	0.999306i	$-0.488140\pi$
$509$	1.68083	0.0745015	0.0372507	+	0.999306i	$0.488140\pi$
$510$	23.5073	1.04092
$511$	−70.2523	−3.10778
$512$	30.3013	1.33914
$513$	−0.203466	−0.00898325
$514$	11.3696	0.501493
$515$	−19.6202	−0.864569
$516$	−4.45606	−0.196167
$517$	−2.25998	−0.0993938
$518$	−76.1765	−3.34701
$519$	31.5722	1.38586
$520$	−2.11645	−0.0928123
$521$	15.4209	0.675604	0.337802	−	0.941217i	$-0.390317\pi$
$521$	15.4209	0.675604	0.337802	+	0.941217i	$0.390317\pi$
$522$	−6.08723	−0.266431
$523$	20.3735	0.890872	0.445436	−	0.895314i	$-0.353049\pi$
$523$	20.3735	0.890872	0.445436	+	0.895314i	$0.353049\pi$
$524$	59.4286	2.59615
$525$	11.2738	0.492029
$526$	−27.5508	−1.20127
$527$	7.71380	0.336018
$528$	−31.6764	−1.37854
$529$	−10.7020	−0.465302
$530$	−25.1392	−1.09198
$531$	7.78229	0.337722
$532$	116.674	5.05846
$533$	−1.66597	−0.0721612
$534$	84.5421	3.65850
$535$	6.60761	0.285672
$536$	29.4965	1.27406
$537$	−37.9707	−1.63856
$538$	34.3762	1.48206
$539$	63.6499	2.74160
$540$	−0.116604	−0.00501784
$541$	−5.88074	−0.252833	−0.126416	−	0.991977i	$-0.540348\pi$
$541$	−5.88074	−0.252833	−0.126416	+	0.991977i	$0.540348\pi$
$542$	−13.2288	−0.568228
$543$	−53.2051	−2.28325
$544$	−6.96986	−0.298830
$545$	7.24113	0.310176
$546$	13.1858	0.564298
$547$	34.9958	1.49631	0.748156	−	0.663522i	$-0.230939\pi$
$547$	34.9958	1.49631	0.748156	+	0.663522i	$0.230939\pi$
$548$	26.2420	1.12100
$549$	−11.3021	−0.482364
$550$	−10.7832	−0.459796
$551$	−5.61946	−0.239397
$552$	37.4269	1.59299
$553$	77.7072	3.30445
$554$	−31.9011	−1.35535
$555$	−16.7851	−0.712489
$556$	57.5795	2.44192
$557$	8.12482	0.344260	0.172130	−	0.985074i	$-0.444935\pi$
$557$	8.12482	0.344260	0.172130	+	0.985074i	$0.444935\pi$
$558$	13.9360	0.589957
$559$	−0.231963	−0.00981099
$560$	13.3317	0.563368
$561$	43.6321	1.84215
$562$	−71.8702	−3.03166
$563$	−14.3560	−0.605035	−0.302517	−	0.953144i	$-0.597827\pi$
$563$	−14.3560	−0.605035	−0.302517	+	0.953144i	$0.597827\pi$
$564$	4.70897	0.198284
$565$	1.25121	0.0526390
$566$	14.6166	0.614381
$567$	41.6380	1.74863
$568$	−24.3726	−1.02265
$569$	−40.0198	−1.67772	−0.838858	−	0.544350i	$-0.816776\pi$
$569$	−40.0198	−1.67772	−0.838858	+	0.544350i	$0.816776\pi$
$570$	39.2054	1.64214
$571$	4.82240	0.201811	0.100906	−	0.994896i	$-0.467826\pi$
$571$	4.82240	0.201811	0.100906	+	0.994896i	$0.467826\pi$
$572$	−8.27014	−0.345792
$573$	17.7303	0.740693
$574$	38.1261	1.59135
$575$	3.50686	0.146246
$576$	−29.8812	−1.24505
$577$	−8.70886	−0.362554	−0.181277	−	0.983432i	$-0.558023\pi$
$577$	−8.70886	−0.362554	−0.181277	+	0.983432i	$0.558023\pi$
$578$	2.68485	0.111675
$579$	−42.1689	−1.75248
$580$	−3.22045	−0.133722
$581$	18.9639	0.786757
$582$	−1.28875	−0.0534205
$583$	−46.6610	−1.93250
$584$	−66.5053	−2.75201
$585$	1.44967	0.0599367
$586$	−25.3724	−1.04812
$587$	2.63702	0.108842	0.0544208	−	0.998518i	$-0.482669\pi$
$587$	2.63702	0.108842	0.0544208	+	0.998518i	$0.482669\pi$
$588$	−132.623	−5.46929
$589$	12.8651	0.530096
$590$	6.27873	0.258491
$591$	21.6570	0.890852
$592$	−19.8491	−0.815793
$593$	−42.9478	−1.76366	−0.881828	−	0.471571i	$-0.843687\pi$
$593$	−42.9478	−1.76366	−0.881828	+	0.471571i	$0.843687\pi$
$594$	−0.330055	−0.0135423
$595$	−18.3635	−0.752831
$596$	12.4502	0.509978
$597$	−47.9937	−1.96425
$598$	4.10160	0.167727
$599$	10.2124	0.417266	0.208633	−	0.977994i	$-0.433099\pi$
$599$	10.2124	0.417266	0.208633	+	0.977994i	$0.433099\pi$
$600$	10.6725	0.435702
$601$	22.7486	0.927935	0.463967	−	0.885852i	$-0.346425\pi$
$601$	22.7486	0.927935	0.463967	+	0.885852i	$0.346425\pi$
$602$	5.30852	0.216359
$603$	−20.2039	−0.822765
$604$	−34.8854	−1.41947
$605$	−9.01475	−0.366502
$606$	−101.105	−4.10711
$607$	14.1606	0.574761	0.287380	−	0.957817i	$-0.407216\pi$
$607$	14.1606	0.574761	0.287380	+	0.957817i	$0.407216\pi$
$608$	−11.6243	−0.471429
$609$	9.53041	0.386192
$610$	−9.11855	−0.369199
$611$	0.245128	0.00991683
$612$	−45.3617	−1.83364
$613$	3.99709	0.161441	0.0807205	−	0.996737i	$-0.474278\pi$
$613$	3.99709	0.161441	0.0807205	+	0.996737i	$0.474278\pi$
$614$	−72.0483	−2.90763
$615$	8.40090	0.338757
$616$	89.9013	3.62222
$617$	−2.41936	−0.0974000	−0.0487000	−	0.998813i	$-0.515508\pi$
$617$	−2.41936	−0.0974000	−0.0487000	+	0.998813i	$0.515508\pi$
$618$	115.717	4.65482
$619$	8.23130	0.330844	0.165422	−	0.986223i	$-0.447101\pi$
$619$	8.23130	0.330844	0.165422	+	0.986223i	$0.447101\pi$
$620$	7.37282	0.296100
$621$	0.107339	0.00430737
$622$	−66.9849	−2.68585
$623$	−66.0430	−2.64596
$624$	3.43577	0.137541
$625$	1.00000	0.0400000
$626$	−48.6399	−1.94404
$627$	72.7696	2.90614
$628$	−1.32137	−0.0527286
$629$	27.3408	1.09015
$630$	−33.1761	−1.32177
$631$	−31.9915	−1.27356	−0.636780	−	0.771046i	$-0.719734\pi$
$631$	−31.9915	−1.27356	−0.636780	+	0.771046i	$0.719734\pi$
$632$	73.5626	2.92616
$633$	−8.97359	−0.356668
$634$	−11.0344	−0.438232
$635$	−1.59161	−0.0631610
$636$	97.2246	3.85521
$637$	−6.90378	−0.273538
$638$	−9.11566	−0.360893
$639$	16.6942	0.660413
$640$	−20.6107	−0.814708
$641$	−35.0606	−1.38481	−0.692406	−	0.721508i	$-0.743449\pi$
$641$	−35.0606	−1.38481	−0.692406	+	0.721508i	$0.743449\pi$
$642$	−38.9707	−1.53805
$643$	8.65608	0.341362	0.170681	−	0.985326i	$-0.445403\pi$
$643$	8.65608	0.341362	0.170681	+	0.985326i	$0.445403\pi$
$644$	−61.5517	−2.42548
$645$	1.16971	0.0460572
$646$	−63.8605	−2.51256
$647$	−12.5222	−0.492298	−0.246149	−	0.969232i	$-0.579165\pi$
$647$	−12.5222	−0.492298	−0.246149	+	0.969232i	$0.579165\pi$
$648$	39.4172	1.54845
$649$	11.6540	0.457460
$650$	1.16959	0.0458753
$651$	−21.8187	−0.855144
$652$	−28.8480	−1.12977
$653$	3.28152	0.128416	0.0642080	−	0.997937i	$-0.479548\pi$
$653$	3.28152	0.128416	0.0642080	+	0.997937i	$0.479548\pi$
$654$	−42.7071	−1.66998
$655$	−15.5999	−0.609538
$656$	9.93441	0.387873
$657$	45.5533	1.77720
$658$	−5.60981	−0.218693
$659$	−44.0190	−1.71474	−0.857368	−	0.514703i	$-0.827902\pi$
$659$	−44.0190	−1.71474	−0.857368	+	0.514703i	$0.827902\pi$
$660$	41.7034	1.62330
$661$	−4.78607	−0.186156	−0.0930782	−	0.995659i	$-0.529671\pi$
$661$	−4.78607	−0.186156	−0.0930782	+	0.995659i	$0.529671\pi$
$662$	60.0187	2.33269
$663$	−4.73255	−0.183797
$664$	17.9525	0.696691
$665$	−30.6267	−1.18765
$666$	49.3947	1.91401
$667$	2.96456	0.114788
$668$	28.9526	1.12021
$669$	−65.8905	−2.54747
$670$	−16.3004	−0.629741
$671$	−16.9250	−0.653383
$672$	19.7145	0.760502
$673$	15.3913	0.593291	0.296646	−	0.954988i	$-0.404132\pi$
$673$	15.3913	0.593291	0.296646	+	0.954988i	$0.404132\pi$
$674$	16.7889	0.646686
$675$	0.0306083	0.00117811
$676$	−48.6272	−1.87028
$677$	−4.08819	−0.157122	−0.0785609	−	0.996909i	$-0.525033\pi$
$677$	−4.08819	−0.157122	−0.0785609	+	0.996909i	$0.525033\pi$
$678$	−7.37947	−0.283407
$679$	1.00675	0.0386356
$680$	−17.3841	−0.666649
$681$	52.0502	1.99457
$682$	20.8692	0.799124
$683$	−30.6231	−1.17176	−0.585880	−	0.810397i	$-0.699251\pi$
$683$	−30.6231	−1.17176	−0.585880	+	0.810397i	$0.699251\pi$
$684$	−75.6543	−2.89271
$685$	−6.88846	−0.263195
$686$	80.2594	3.06432
$687$	−8.91392	−0.340087
$688$	1.38323	0.0527350
$689$	5.06108	0.192812
$690$	−20.6829	−0.787386
$691$	47.3793	1.80239	0.901197	−	0.433410i	$-0.142690\pi$
$691$	47.3793	1.80239	0.901197	+	0.433410i	$0.142690\pi$
$692$	−49.1537	−1.86854
$693$	−61.5785	−2.33917
$694$	−84.7260	−3.21615
$695$	−15.1145	−0.573326
$696$	9.02210	0.341982
$697$	−13.6840	−0.518317
$698$	30.0279	1.13657
$699$	−0.955213	−0.0361295
$700$	−17.5518	−0.663396
$701$	11.1685	0.421827	0.210914	−	0.977505i	$-0.432356\pi$
$701$	11.1685	0.421827	0.210914	+	0.977505i	$0.432356\pi$
$702$	0.0357993	0.00135116
$703$	45.5990	1.71980
$704$	−44.7472	−1.68647
$705$	−1.23610	−0.0465540
$706$	0.343469	0.0129266
$707$	78.9817	2.97041
$708$	−24.2827	−0.912600
$709$	−50.0508	−1.87970	−0.939849	−	0.341590i	$-0.889034\pi$
$709$	−50.0508	−1.87970	−0.939849	+	0.341590i	$0.889034\pi$
$710$	13.4689	0.505477
$711$	−50.3872	−1.88967
$712$	−62.5205	−2.34306
$713$	−6.78700	−0.254175
$714$	108.305	4.05323
$715$	2.17090	0.0811869
$716$	59.1153	2.20924
$717$	−1.04201	−0.0389146
$718$	−58.4444	−2.18113
$719$	−51.8039	−1.93196	−0.965979	−	0.258619i	$-0.916733\pi$
$719$	−51.8039	−1.93196	−0.965979	+	0.258619i	$0.916733\pi$
$720$	−8.64460	−0.322165
$721$	−90.3964	−3.36654
$722$	−60.7109	−2.25942
$723$	11.7176	0.435781
$724$	82.8333	3.07848
$725$	0.845360	0.0313959
$726$	53.1676	1.97324
$727$	−38.7768	−1.43815	−0.719075	−	0.694932i	$-0.755434\pi$
$727$	−38.7768	−1.43815	−0.719075	+	0.694932i	$0.755434\pi$
$728$	−9.75112	−0.361401
$729$	−26.7744	−0.991643
$730$	36.7523	1.36026
$731$	−1.90530	−0.0704701
$732$	35.2656	1.30345
$733$	−43.4166	−1.60363	−0.801815	−	0.597573i	$-0.796132\pi$
$733$	−43.4166	−1.60363	−0.801815	+	0.597573i	$0.796132\pi$
$734$	32.5250	1.20052
$735$	34.8133	1.28411
$736$	6.13244	0.226045
$737$	−30.2554	−1.11447
$738$	−24.7219	−0.910025
$739$	−20.7229	−0.762304	−0.381152	−	0.924512i	$-0.624473\pi$
$739$	−20.7229	−0.762304	−0.381152	+	0.924512i	$0.624473\pi$
$740$	26.1322	0.960640
$741$	−7.89294	−0.289954
$742$	−115.824	−4.25203
$743$	−7.13496	−0.261756	−0.130878	−	0.991398i	$-0.541780\pi$
$743$	−7.13496	−0.261756	−0.130878	+	0.991398i	$0.541780\pi$
$744$	−20.6550	−0.757249
$745$	−3.26814	−0.119735
$746$	−7.74823	−0.283683
$747$	−12.2967	−0.449912
$748$	−67.9294	−2.48375
$749$	30.4433	1.11237
$750$	−5.89785	−0.215359
$751$	31.1560	1.13690	0.568449	−	0.822718i	$-0.307544\pi$
$751$	31.1560	1.13690	0.568449	+	0.822718i	$0.307544\pi$
$752$	−1.46173	−0.0533039
$753$	17.9346	0.653573
$754$	0.988729	0.0360074
$755$	9.15734	0.333270
$756$	−0.537231	−0.0195389
$757$	33.5544	1.21955	0.609777	−	0.792573i	$-0.291259\pi$
$757$	33.5544	1.21955	0.609777	+	0.792573i	$0.291259\pi$
$758$	−45.8646	−1.66588
$759$	−38.3898	−1.39346
$760$	−28.9932	−1.05169
$761$	18.3797	0.666265	0.333133	−	0.942880i	$-0.391894\pi$
$761$	18.3797	0.666265	0.333133	+	0.942880i	$0.391894\pi$
$762$	9.38706	0.340057
$763$	33.3621	1.20779
$764$	−27.6037	−0.998667
$765$	11.9074	0.430511
$766$	6.22876	0.225054
$767$	−1.26405	−0.0456422
$768$	72.6097	2.62008
$769$	12.2446	0.441552	0.220776	−	0.975325i	$-0.429141\pi$
$769$	12.2446	0.441552	0.220776	+	0.975325i	$0.429141\pi$
$770$	−49.6814	−1.79039
$771$	11.5424	0.415691
$772$	65.6515	2.36285
$773$	−25.6307	−0.921872	−0.460936	−	0.887433i	$-0.652486\pi$
$773$	−25.6307	−0.921872	−0.460936	+	0.887433i	$0.652486\pi$
$774$	−3.44217	−0.123726
$775$	−1.93535	−0.0695198
$776$	0.953056	0.0342127
$777$	−77.3343	−2.77435
$778$	−26.7149	−0.957775
$779$	−22.8221	−0.817687
$780$	−4.52335	−0.161962
$781$	24.9997	0.894558
$782$	33.6898	1.20474
$783$	0.0258751	0.000924699 0
$784$	41.1681	1.47029
$785$	0.346858	0.0123799
$786$	92.0058	3.28174
$787$	−14.7771	−0.526746	−0.263373	−	0.964694i	$-0.584835\pi$
$787$	−14.7771	−0.526746	−0.263373	+	0.964694i	$0.584835\pi$
$788$	−33.7172	−1.20112
$789$	−27.9695	−0.995742
$790$	−40.6523	−1.44634
$791$	5.76473	0.204970
$792$	−58.2941	−2.07139
$793$	1.83577	0.0651901
$794$	−57.0297	−2.02391
$795$	−25.5212	−0.905145
$796$	74.7199	2.64838
$797$	8.55047	0.302873	0.151437	−	0.988467i	$-0.451610\pi$
$797$	8.55047	0.302873	0.151437	+	0.988467i	$0.451610\pi$
$798$	180.632	6.39429
$799$	2.01344	0.0712303
$800$	1.74870	0.0618259
$801$	42.8239	1.51311
$802$	84.0443	2.96771
$803$	68.2163	2.40730
$804$	63.0412	2.22329
$805$	16.1572	0.569466
$806$	−2.26358	−0.0797310
$807$	34.8987	1.22849
$808$	74.7691	2.63037
$809$	44.2483	1.55569	0.777844	−	0.628458i	$-0.216313\pi$
$809$	44.2483	1.55569	0.777844	+	0.628458i	$0.216313\pi$
$810$	−21.7828	−0.765369
$811$	2.95300	0.103694	0.0518470	−	0.998655i	$-0.483489\pi$
$811$	2.95300	0.103694	0.0518470	+	0.998655i	$0.483489\pi$
$812$	−14.8376	−0.520698
$813$	−13.4299	−0.471007
$814$	73.9688	2.59261
$815$	7.57253	0.265254
$816$	28.2208	0.987926
$817$	−3.17766	−0.111172
$818$	65.5196	2.29084
$819$	6.67910	0.233387
$820$	−13.0791	−0.456742
$821$	−52.0629	−1.81701	−0.908505	−	0.417875i	$-0.862775\pi$
$821$	−52.0629	−1.81701	−0.908505	+	0.417875i	$0.862775\pi$
$822$	40.6271	1.41703
$823$	15.3091	0.533640	0.266820	−	0.963746i	$-0.414027\pi$
$823$	15.3091	0.533640	0.266820	+	0.963746i	$0.414027\pi$
$824$	−85.5750	−2.98115
$825$	−10.9471	−0.381128
$826$	28.9281	1.00654
$827$	0.485342	0.0168770	0.00843850	−	0.999964i	$-0.497314\pi$
$827$	0.485342	0.0168770	0.00843850	+	0.999964i	$0.497314\pi$
$828$	39.9116	1.38702
$829$	−50.2568	−1.74549	−0.872746	−	0.488174i	$-0.837663\pi$
$829$	−50.2568	−1.74549	−0.872746	+	0.488174i	$0.837663\pi$
$830$	−9.92094	−0.344361
$831$	−32.3859	−1.12346
$832$	4.85350	0.168265
$833$	−56.7063	−1.96476
$834$	89.1431	3.08677
$835$	−7.60001	−0.263009
$836$	−113.293	−3.91831
$837$	−0.0592378	−0.00204756
$838$	−82.6512	−2.85514
$839$	7.44939	0.257182	0.128591	−	0.991698i	$-0.458955\pi$
$839$	7.44939	0.257182	0.128591	+	0.991698i	$0.458955\pi$
$840$	49.1715	1.69658
$841$	−28.2854	−0.975357
$842$	−36.7701	−1.26718
$843$	−72.9626	−2.51296
$844$	13.9707	0.480891
$845$	12.7645	0.439113
$846$	3.63754	0.125061
$847$	−41.5337	−1.42712
$848$	−30.1799	−1.03638
$849$	14.8387	0.509264
$850$	9.60683	0.329511
$851$	−24.0558	−0.824623
$852$	−52.0902	−1.78458
$853$	−27.4518	−0.939931	−0.469965	−	0.882685i	$-0.655734\pi$
$853$	−27.4518	−0.939931	−0.469965	+	0.882685i	$0.655734\pi$
$854$	−42.0120	−1.43762
$855$	19.8591	0.679166
$856$	28.8196	0.985032
$857$	34.4180	1.17570	0.587849	−	0.808971i	$-0.299975\pi$
$857$	34.4180	1.17570	0.587849	+	0.808971i	$0.299975\pi$
$858$	−12.8036	−0.437108
$859$	0.802555	0.0273828	0.0136914	−	0.999906i	$-0.495642\pi$
$859$	0.802555	0.0273828	0.0136914	+	0.999906i	$0.495642\pi$
$860$	−1.82108	−0.0620983
$861$	38.7056	1.31908
$862$	40.8265	1.39056
$863$	33.0882	1.12633	0.563167	−	0.826343i	$-0.309583\pi$
$863$	33.0882	1.12633	0.563167	+	0.826343i	$0.309583\pi$
$864$	0.0535248	0.00182095
$865$	12.9027	0.438706
$866$	−66.8631	−2.27210
$867$	2.72566	0.0925682
$868$	33.9689	1.15298
$869$	−75.4552	−2.55964
$870$	−4.98581	−0.169035
$871$	3.28165	0.111194
$872$	31.5827	1.06953
$873$	−0.652803	−0.0220940
$874$	56.1878	1.90058
$875$	4.60731	0.155756
$876$	−142.138	−4.80240
$877$	−26.7956	−0.904824	−0.452412	−	0.891809i	$-0.649436\pi$
$877$	−26.7956	−0.904824	−0.452412	+	0.891809i	$0.649436\pi$
$878$	65.8569	2.22256
$879$	−25.7580	−0.868795
$880$	−12.9453	−0.436387
$881$	−35.5428	−1.19747	−0.598734	−	0.800948i	$-0.704329\pi$
$881$	−35.5428	−1.19747	−0.598734	+	0.800948i	$0.704329\pi$
$882$	−102.447	−3.44958
$883$	−21.8599	−0.735644	−0.367822	−	0.929896i	$-0.619896\pi$
$883$	−21.8599	−0.735644	−0.367822	+	0.929896i	$0.619896\pi$
$884$	7.36795	0.247811
$885$	6.37416	0.214265
$886$	4.53949	0.152507
$887$	24.2221	0.813298	0.406649	−	0.913585i	$-0.366697\pi$
$887$	24.2221	0.813298	0.406649	+	0.913585i	$0.366697\pi$
$888$	−73.2096	−2.45675
$889$	−7.33303	−0.245942
$890$	34.5502	1.15813
$891$	−40.4312	−1.35450
$892$	102.583	3.43473
$893$	3.35801	0.112372
$894$	19.2750	0.644653
$895$	−15.5177	−0.518698
$896$	−94.9597	−3.17238
$897$	4.16394	0.139030
$898$	−33.7831	−1.12736
$899$	−1.63607	−0.0545659
$900$	11.3810	0.379367
$901$	41.5708	1.38492
$902$	−37.0212	−1.23267
$903$	5.38921	0.179342
$904$	5.45726	0.181506
$905$	−21.7436	−0.722780
$906$	−54.0086	−1.79432
$907$	−19.8595	−0.659422	−0.329711	−	0.944082i	$-0.606951\pi$
$907$	−19.8595	−0.659422	−0.329711	+	0.944082i	$0.606951\pi$
$908$	−81.0353	−2.68925
$909$	−51.2136	−1.69865
$910$	5.38868	0.178633
$911$	−40.2172	−1.33245	−0.666227	−	0.745749i	$-0.732092\pi$
$911$	−40.2172	−1.33245	−0.666227	+	0.745749i	$0.732092\pi$
$912$	47.0667	1.55853
$913$	−18.4143	−0.609426
$914$	−1.17795	−0.0389630
$915$	−9.25714	−0.306032
$916$	13.8778	0.458536
$917$	−71.8735	−2.37347
$918$	0.294049	0.00970506
$919$	21.8396	0.720421	0.360211	−	0.932871i	$-0.382705\pi$
$919$	21.8396	0.720421	0.360211	+	0.932871i	$0.382705\pi$
$920$	15.2954	0.504275
$921$	−73.1434	−2.41016
$922$	49.9874	1.64625
$923$	−2.71158	−0.0892529
$924$	192.141	6.32096
$925$	−6.85966	−0.225544
$926$	−75.9307	−2.49524
$927$	58.6152	1.92518
$928$	1.47828	0.0485270
$929$	15.0859	0.494951	0.247476	−	0.968894i	$-0.420399\pi$
$929$	15.0859	0.494951	0.247476	+	0.968894i	$0.420399\pi$
$930$	11.4144	0.374293
$931$	−94.5748	−3.09956
$932$	1.48714	0.0487129
$933$	−68.0029	−2.22632
$934$	−1.49841	−0.0490294
$935$	17.8313	0.583147
$936$	6.32286	0.206669
$937$	−38.1307	−1.24567	−0.622837	−	0.782351i	$-0.714020\pi$
$937$	−38.1307	−1.24567	−0.622837	+	0.782351i	$0.714020\pi$
$938$	−75.1012	−2.45214
$939$	−49.3791	−1.61143
$940$	1.92444	0.0627682
$941$	4.19859	0.136870	0.0684350	−	0.997656i	$-0.478199\pi$
$941$	4.19859	0.136870	0.0684350	+	0.997656i	$0.478199\pi$
$942$	−2.04572	−0.0666531
$943$	12.0399	0.392072
$944$	7.53770	0.245331
$945$	0.141022	0.00458745
$946$	−5.15467	−0.167593
$947$	−46.8774	−1.52331	−0.761656	−	0.647982i	$-0.775613\pi$
$947$	−46.8774	−1.52331	−0.761656	+	0.647982i	$0.775613\pi$
$948$	157.221	5.10630
$949$	−7.39907	−0.240184
$950$	16.0223	0.519831
$951$	−11.2021	−0.363253
$952$	−80.0939	−2.59586
$953$	−43.9070	−1.42229	−0.711144	−	0.703047i	$-0.751822\pi$
$953$	−43.9070	−1.42229	−0.711144	+	0.703047i	$0.751822\pi$
$954$	75.1030	2.43155
$955$	7.24591	0.234472
$956$	1.62227	0.0524680
$957$	−9.25421	−0.299146
$958$	70.1158	2.26534
$959$	−31.7373	−1.02485
$960$	−24.4745	−0.789910
$961$	−27.2544	−0.879175
$962$	−8.02301	−0.258672
$963$	−19.7402	−0.636118
$964$	−18.2427	−0.587558
$965$	−17.2334	−0.554762
$966$	−95.2927	−3.06599
$967$	18.8346	0.605681	0.302840	−	0.953041i	$-0.402065\pi$
$967$	18.8346	0.605681	0.302840	+	0.953041i	$0.402065\pi$
$968$	−39.3185	−1.26374
$969$	−64.8311	−2.08268
$970$	−0.526680	−0.0169107
$971$	−3.00661	−0.0964867	−0.0482433	−	0.998836i	$-0.515362\pi$
$971$	−3.00661	−0.0964867	−0.0482433	+	0.998836i	$0.515362\pi$
$972$	83.8941	2.69091
$973$	−69.6372	−2.23247
$974$	59.1533	1.89539
$975$	1.18737	0.0380263
$976$	−10.9469	−0.350403
$977$	−1.53603	−0.0491420	−0.0245710	−	0.999698i	$-0.507822\pi$
$977$	−1.53603	−0.0491420	−0.0245710	+	0.999698i	$0.507822\pi$
$978$	−44.6617	−1.42812
$979$	64.1290	2.04957
$980$	−54.1997	−1.73135
$981$	−21.6328	−0.690682
$982$	−69.9137	−2.23104
$983$	41.7323	1.33105	0.665526	−	0.746374i	$-0.268207\pi$
$983$	41.7323	1.33105	0.665526	+	0.746374i	$0.268207\pi$
$984$	36.6412	1.16808
$985$	8.85068	0.282006
$986$	8.12123	0.258633
$987$	−5.69507	−0.181276
$988$	12.2883	0.390942
$989$	1.67638	0.0533058
$990$	32.2146	1.02385
$991$	−59.4508	−1.88852	−0.944258	−	0.329206i	$-0.893219\pi$
$991$	−59.4508	−1.88852	−0.944258	+	0.329206i	$0.893219\pi$
$992$	−3.38435	−0.107453
$993$	60.9309	1.93358
$994$	62.0552	1.96827
$995$	−19.6138	−0.621800
$996$	38.3688	1.21576
$997$	41.8313	1.32481	0.662405	−	0.749146i	$-0.269536\pi$
$997$	41.8313	1.32481	0.662405	+	0.749146i	$0.269536\pi$
$998$	−67.2637	−2.12919
$999$	−0.209963	−0.00664292

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.d.1.17	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.d.1.17	✓	140	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41030 q^{2} -2.44694 q^{3} +3.80955 q^{4} -1.00000 q^{5} +5.89785 q^{6} -4.60731 q^{7} -4.36157 q^{8} +2.98749 q^{9} +O(q^{10})\)	\(q-2.41030 q^{2} -2.44694 q^{3} +3.80955 q^{4} -1.00000 q^{5} +5.89785 q^{6} -4.60731 q^{7} -4.36157 q^{8} +2.98749 q^{9} +2.41030 q^{10} +4.47378 q^{11} -9.32173 q^{12} -0.485248 q^{13} +11.1050 q^{14} +2.44694 q^{15} +2.89360 q^{16} -3.98574 q^{17} -7.20076 q^{18} -6.64741 q^{19} -3.80955 q^{20} +11.2738 q^{21} -10.7832 q^{22} +3.50686 q^{23} +10.6725 q^{24} +1.00000 q^{25} +1.16959 q^{26} +0.0306083 q^{27} -17.5518 q^{28} +0.845360 q^{29} -5.89785 q^{30} -1.93535 q^{31} +1.74870 q^{32} -10.9471 q^{33} +9.60683 q^{34} +4.60731 q^{35} +11.3810 q^{36} -6.85966 q^{37} +16.0223 q^{38} +1.18737 q^{39} +4.36157 q^{40} +3.43323 q^{41} -27.1732 q^{42} +0.478030 q^{43} +17.0431 q^{44} -2.98749 q^{45} -8.45258 q^{46} -0.505161 q^{47} -7.08045 q^{48} +14.2273 q^{49} -2.41030 q^{50} +9.75284 q^{51} -1.84858 q^{52} -10.4299 q^{53} -0.0737753 q^{54} -4.47378 q^{55} +20.0951 q^{56} +16.2658 q^{57} -2.03757 q^{58} +2.60496 q^{59} +9.32173 q^{60} -3.78316 q^{61} +4.66478 q^{62} -13.7643 q^{63} -10.0021 q^{64} +0.485248 q^{65} +26.3857 q^{66} -6.76282 q^{67} -15.1839 q^{68} -8.58105 q^{69} -11.1050 q^{70} +5.58804 q^{71} -13.0302 q^{72} +15.2480 q^{73} +16.5338 q^{74} -2.44694 q^{75} -25.3237 q^{76} -20.6121 q^{77} -2.86192 q^{78} -16.8661 q^{79} -2.89360 q^{80} -9.03737 q^{81} -8.27513 q^{82} -4.11606 q^{83} +42.9481 q^{84} +3.98574 q^{85} -1.15220 q^{86} -2.06854 q^{87} -19.5127 q^{88} +14.3344 q^{89} +7.20076 q^{90} +2.23569 q^{91} +13.3596 q^{92} +4.73568 q^{93} +1.21759 q^{94} +6.64741 q^{95} -4.27896 q^{96} -0.218512 q^{97} -34.2921 q^{98} +13.3654 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * q^99

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