LMFDB - Embedded newform 6035.2.a.h.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$0$
Dimension:	$59$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.25970 q^{2} +2.36319 q^{3} -0.413145 q^{4} +1.00000 q^{5} -2.97691 q^{6} +2.52906 q^{7} +3.03985 q^{8} +2.58464 q^{9} +O(q^{10})$	\(q-1.25970 q^{2} +2.36319 q^{3} -0.413145 q^{4} +1.00000 q^{5} -2.97691 q^{6} +2.52906 q^{7} +3.03985 q^{8} +2.58464 q^{9} -1.25970 q^{10} +4.41421 q^{11} -0.976339 q^{12} -1.16069 q^{13} -3.18587 q^{14} +2.36319 q^{15} -3.00302 q^{16} -1.00000 q^{17} -3.25589 q^{18} +0.0742195 q^{19} -0.413145 q^{20} +5.97665 q^{21} -5.56060 q^{22} +1.95922 q^{23} +7.18373 q^{24} +1.00000 q^{25} +1.46212 q^{26} -0.981562 q^{27} -1.04487 q^{28} +9.73215 q^{29} -2.97691 q^{30} +5.47750 q^{31} -2.29678 q^{32} +10.4316 q^{33} +1.25970 q^{34} +2.52906 q^{35} -1.06783 q^{36} -5.21744 q^{37} -0.0934946 q^{38} -2.74292 q^{39} +3.03985 q^{40} +4.71268 q^{41} -7.52881 q^{42} +3.70694 q^{43} -1.82371 q^{44} +2.58464 q^{45} -2.46804 q^{46} -5.30904 q^{47} -7.09669 q^{48} -0.603831 q^{49} -1.25970 q^{50} -2.36319 q^{51} +0.479533 q^{52} -4.55268 q^{53} +1.23648 q^{54} +4.41421 q^{55} +7.68798 q^{56} +0.175394 q^{57} -12.2596 q^{58} -0.00777003 q^{59} -0.976339 q^{60} +7.72713 q^{61} -6.90003 q^{62} +6.53673 q^{63} +8.89931 q^{64} -1.16069 q^{65} -13.1407 q^{66} +1.48443 q^{67} +0.413145 q^{68} +4.63000 q^{69} -3.18587 q^{70} -1.00000 q^{71} +7.85693 q^{72} -14.1502 q^{73} +6.57243 q^{74} +2.36319 q^{75} -0.0306634 q^{76} +11.1638 q^{77} +3.45527 q^{78} -4.58826 q^{79} -3.00302 q^{80} -10.0735 q^{81} -5.93658 q^{82} +4.97132 q^{83} -2.46922 q^{84} -1.00000 q^{85} -4.66965 q^{86} +22.9989 q^{87} +13.4185 q^{88} +9.32350 q^{89} -3.25589 q^{90} -2.93546 q^{91} -0.809443 q^{92} +12.9444 q^{93} +6.68782 q^{94} +0.0742195 q^{95} -5.42772 q^{96} -4.23539 q^{97} +0.760648 q^{98} +11.4092 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) $ 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9} + 2 q^{10} + 6 q^{11} + 16 q^{12} + 25 q^{13} + 8 q^{14} + 6 q^{15} + 114 q^{16} - 59 q^{17} + 3 q^{18} + 35 q^{19} + 76 q^{20} + 41 q^{21} + 13 q^{22} - 2 q^{23} + 35 q^{24} + 59 q^{25} + 10 q^{26} + 27 q^{27} + 28 q^{28} + 10 q^{29} + 14 q^{30} + 15 q^{31} + 19 q^{32} - 3 q^{33} - 2 q^{34} + 9 q^{35} + 160 q^{36} + 56 q^{37} + 17 q^{38} + 25 q^{39} + 6 q^{40} + 47 q^{41} + 46 q^{42} + 27 q^{43} + 39 q^{44} + 97 q^{45} + 4 q^{46} - 8 q^{47} + 58 q^{48} + 174 q^{49} + 2 q^{50} - 6 q^{51} + 13 q^{52} + 17 q^{53} + 48 q^{54} + 6 q^{55} + 33 q^{56} + 6 q^{57} + 32 q^{58} + 30 q^{59} + 16 q^{60} + 85 q^{61} - 3 q^{62} + 14 q^{63} + 168 q^{64} + 25 q^{65} + 87 q^{66} + 21 q^{67} - 76 q^{68} + 111 q^{69} + 8 q^{70} - 59 q^{71} - 52 q^{72} + 41 q^{73} + 11 q^{74} + 6 q^{75} + 118 q^{76} + 55 q^{77} - 54 q^{78} + 43 q^{79} + 114 q^{80} + 207 q^{81} + 45 q^{82} + 10 q^{83} + 62 q^{84} - 59 q^{85} + 19 q^{86} + 8 q^{87} + 35 q^{88} + 86 q^{89} + 3 q^{90} + 47 q^{91} - 98 q^{92} + 41 q^{93} + 30 q^{94} + 35 q^{95} + 69 q^{96} + 72 q^{97} + 14 q^{98} + 25 q^{99}+O(q^{100}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9 + 2 * q^10 + 6 * q^11 + 16 * q^12 + 25 * q^13 + 8 * q^14 + 6 * q^15 + 114 * q^16 - 59 * q^17 + 3 * q^18 + 35 * q^19 + 76 * q^20 + 41 * q^21 + 13 * q^22 - 2 * q^23 + 35 * q^24 + 59 * q^25 + 10 * q^26 + 27 * q^27 + 28 * q^28 + 10 * q^29 + 14 * q^30 + 15 * q^31 + 19 * q^32 - 3 * q^33 - 2 * q^34 + 9 * q^35 + 160 * q^36 + 56 * q^37 + 17 * q^38 + 25 * q^39 + 6 * q^40 + 47 * q^41 + 46 * q^42 + 27 * q^43 + 39 * q^44 + 97 * q^45 + 4 * q^46 - 8 * q^47 + 58 * q^48 + 174 * q^49 + 2 * q^50 - 6 * q^51 + 13 * q^52 + 17 * q^53 + 48 * q^54 + 6 * q^55 + 33 * q^56 + 6 * q^57 + 32 * q^58 + 30 * q^59 + 16 * q^60 + 85 * q^61 - 3 * q^62 + 14 * q^63 + 168 * q^64 + 25 * q^65 + 87 * q^66 + 21 * q^67 - 76 * q^68 + 111 * q^69 + 8 * q^70 - 59 * q^71 - 52 * q^72 + 41 * q^73 + 11 * q^74 + 6 * q^75 + 118 * q^76 + 55 * q^77 - 54 * q^78 + 43 * q^79 + 114 * q^80 + 207 * q^81 + 45 * q^82 + 10 * q^83 + 62 * q^84 - 59 * q^85 + 19 * q^86 + 8 * q^87 + 35 * q^88 + 86 * q^89 + 3 * q^90 + 47 * q^91 - 98 * q^92 + 41 * q^93 + 30 * q^94 + 35 * q^95 + 69 * q^96 + 72 * q^97 + 14 * q^98 + 25 * 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 $

$2$	−1.25970	−0.890745	−0.445373	−	0.895345i	$-0.646929\pi$
$2$	−1.25970	−0.890745	−0.445373	+	0.895345i	$0.646929\pi$
$3$	2.36319	1.36439	0.682193	−	0.731172i	$-0.261026\pi$
$3$	2.36319	1.36439	0.682193	+	0.731172i	$0.261026\pi$
$4$	−0.413145	−0.206573
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.97691	−1.21532
$7$	2.52906	0.955897	0.477948	−	0.878388i	$-0.341381\pi$
$7$	2.52906	0.955897	0.477948	+	0.878388i	$0.341381\pi$
$8$	3.03985	1.07475
$9$	2.58464	0.861548
$10$	−1.25970	−0.398353
$11$	4.41421	1.33093	0.665467	−	0.746427i	$-0.268232\pi$
$11$	4.41421	1.33093	0.665467	+	0.746427i	$0.268232\pi$
$12$	−0.976339	−0.281845
$13$	−1.16069	−0.321917	−0.160959	−	0.986961i	$-0.551459\pi$
$13$	−1.16069	−0.321917	−0.160959	+	0.986961i	$0.551459\pi$
$14$	−3.18587	−0.851461
$15$	2.36319	0.610172
$16$	−3.00302	−0.750755
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−3.25589	−0.767420
$19$	0.0742195	0.0170271	0.00851356	−	0.999964i	$-0.497290\pi$
$19$	0.0742195	0.0170271	0.00851356	+	0.999964i	$0.497290\pi$
$20$	−0.413145	−0.0923821
$21$	5.97665	1.30421
$22$	−5.56060	−1.18552
$23$	1.95922	0.408526	0.204263	−	0.978916i	$-0.434520\pi$
$23$	1.95922	0.408526	0.204263	+	0.978916i	$0.434520\pi$
$24$	7.18373	1.46637
$25$	1.00000	0.200000
$26$	1.46212	0.286746
$27$	−0.981562	−0.188902
$28$	−1.04487	−0.197462
$29$	9.73215	1.80721	0.903607	−	0.428362i	$-0.140909\pi$
$29$	9.73215	1.80721	0.903607	+	0.428362i	$0.140909\pi$
$30$	−2.97691	−0.543508
$31$	5.47750	0.983788	0.491894	−	0.870655i	$-0.336305\pi$
$31$	5.47750	0.983788	0.491894	+	0.870655i	$0.336305\pi$
$32$	−2.29678	−0.406017
$33$	10.4316	1.81591
$34$	1.25970	0.216037
$35$	2.52906	0.427490
$36$	−1.06783	−0.177972
$37$	−5.21744	−0.857742	−0.428871	−	0.903366i	$-0.641088\pi$
$37$	−5.21744	−0.857742	−0.428871	+	0.903366i	$0.641088\pi$
$38$	−0.0934946	−0.0151668
$39$	−2.74292	−0.439219
$40$	3.03985	0.480642
$41$	4.71268	0.735997	0.367999	−	0.929826i	$-0.380043\pi$
$41$	4.71268	0.735997	0.367999	+	0.929826i	$0.380043\pi$
$42$	−7.52881	−1.16172
$43$	3.70694	0.565304	0.282652	−	0.959223i	$-0.408786\pi$
$43$	3.70694	0.565304	0.282652	+	0.959223i	$0.408786\pi$
$44$	−1.82371	−0.274935
$45$	2.58464	0.385296
$46$	−2.46804	−0.363892
$47$	−5.30904	−0.774403	−0.387202	−	0.921995i	$-0.626558\pi$
$47$	−5.30904	−0.774403	−0.387202	+	0.921995i	$0.626558\pi$
$48$	−7.09669	−1.02432
$49$	−0.603831	−0.0862616
$50$	−1.25970	−0.178149
$51$	−2.36319	−0.330912
$52$	0.479533	0.0664992
$53$	−4.55268	−0.625359	−0.312679	−	0.949859i	$-0.601227\pi$
$53$	−4.55268	−0.625359	−0.312679	+	0.949859i	$0.601227\pi$
$54$	1.23648	0.168263
$55$	4.41421	0.595212
$56$	7.68798	1.02735
$57$	0.175394	0.0232315
$58$	−12.2596	−1.60977
$59$	−0.00777003	−0.00101157	−0.000505786	−	1.00000i	$-0.500161\pi$
$59$	−0.00777003	−0.00101157	−0.000505786		1.00000i	$0.500161\pi$
$60$	−0.976339	−0.126045
$61$	7.72713	0.989358	0.494679	−	0.869076i	$-0.335286\pi$
$61$	7.72713	0.989358	0.494679	+	0.869076i	$0.335286\pi$
$62$	−6.90003	−0.876305
$63$	6.53673	0.823551
$64$	8.89931	1.11241
$65$	−1.16069	−0.143966
$66$	−13.1407	−1.61751
$67$	1.48443	0.181352	0.0906760	−	0.995880i	$-0.471097\pi$
$67$	1.48443	0.181352	0.0906760	+	0.995880i	$0.471097\pi$
$68$	0.413145	0.0501012
$69$	4.63000	0.557387
$70$	−3.18587	−0.380785
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	7.85693	0.925948
$73$	−14.1502	−1.65616	−0.828079	−	0.560611i	$-0.810566\pi$
$73$	−14.1502	−1.65616	−0.828079	+	0.560611i	$0.810566\pi$
$74$	6.57243	0.764029
$75$	2.36319	0.272877
$76$	−0.0306634	−0.00351734
$77$	11.1638	1.27224
$78$	3.45527	0.391232
$79$	−4.58826	−0.516220	−0.258110	−	0.966116i	$-0.583100\pi$
$79$	−4.58826	−0.516220	−0.258110	+	0.966116i	$0.583100\pi$
$80$	−3.00302	−0.335748
$81$	−10.0735	−1.11928
$82$	−5.93658	−0.655586
$83$	4.97132	0.545673	0.272836	−	0.962060i	$-0.412038\pi$
$83$	4.97132	0.545673	0.272836	+	0.962060i	$0.412038\pi$
$84$	−2.46922	−0.269414
$85$	−1.00000	−0.108465
$86$	−4.66965	−0.503542
$87$	22.9989	2.46574
$88$	13.4185	1.43042
$89$	9.32350	0.988289	0.494144	−	0.869380i	$-0.335481\pi$
$89$	9.32350	0.988289	0.494144	+	0.869380i	$0.335481\pi$
$90$	−3.25589	−0.343201
$91$	−2.93546	−0.307719
$92$	−0.809443	−0.0843902
$93$	12.9444	1.34227
$94$	6.68782	0.689796
$95$	0.0742195	0.00761476
$96$	−5.42772	−0.553964
$97$	−4.23539	−0.430039	−0.215020	−	0.976610i	$-0.568982\pi$
$97$	−4.23539	−0.430039	−0.215020	+	0.976610i	$0.568982\pi$
$98$	0.760648	0.0768371
$99$	11.4092	1.14666
$100$	−0.413145	−0.0413145
$101$	11.0732	1.10182	0.550912	−	0.834563i	$-0.314280\pi$
$101$	11.0732	1.10182	0.550912	+	0.834563i	$0.314280\pi$
$102$	2.97691	0.294758
$103$	19.2257	1.89436	0.947180	−	0.320702i	$-0.103919\pi$
$103$	19.2257	1.89436	0.947180	+	0.320702i	$0.103919\pi$
$104$	−3.52832	−0.345980
$105$	5.97665	0.583261
$106$	5.73503	0.557035
$107$	−1.35981	−0.131458	−0.0657291	−	0.997838i	$-0.520937\pi$
$107$	−1.35981	−0.131458	−0.0657291	+	0.997838i	$0.520937\pi$
$108$	0.405528	0.0390219
$109$	1.60224	0.153467	0.0767335	−	0.997052i	$-0.475551\pi$
$109$	1.60224	0.153467	0.0767335	+	0.997052i	$0.475551\pi$
$110$	−5.56060	−0.530182
$111$	−12.3298	−1.17029
$112$	−7.59483	−0.717644
$113$	4.07312	0.383167	0.191584	−	0.981476i	$-0.438638\pi$
$113$	4.07312	0.383167	0.191584	+	0.981476i	$0.438638\pi$
$114$	−0.220945	−0.0206934
$115$	1.95922	0.182698
$116$	−4.02079	−0.373321
$117$	−2.99997	−0.277347
$118$	0.00978794	0.000901053 0
$119$	−2.52906	−0.231839
$120$	7.18373	0.655782
$121$	8.48526	0.771387
$122$	−9.73390	−0.881266
$123$	11.1369	1.00418
$124$	−2.26300	−0.203224
$125$	1.00000	0.0894427
$126$	−8.23435	−0.733574
$127$	−9.92186	−0.880422	−0.440211	−	0.897894i	$-0.645096\pi$
$127$	−9.92186	−0.880422	−0.440211	+	0.897894i	$0.645096\pi$
$128$	−6.61693	−0.584860
$129$	8.76020	0.771292
$130$	1.46212	0.128237
$131$	13.6960	1.19663	0.598314	−	0.801262i	$-0.295838\pi$
$131$	13.6960	1.19663	0.598314	+	0.801262i	$0.295838\pi$
$132$	−4.30977	−0.375117
$133$	0.187706	0.0162762
$134$	−1.86994	−0.161539
$135$	−0.981562	−0.0844794
$136$	−3.03985	−0.260665
$137$	5.55831	0.474878	0.237439	−	0.971402i	$-0.423692\pi$
$137$	5.55831	0.474878	0.237439	+	0.971402i	$0.423692\pi$
$138$	−5.83243	−0.496490
$139$	−0.982792	−0.0833593	−0.0416797	−	0.999131i	$-0.513271\pi$
$139$	−0.982792	−0.0833593	−0.0416797	+	0.999131i	$0.513271\pi$
$140$	−1.04487	−0.0883077
$141$	−12.5462	−1.05658
$142$	1.25970	0.105712
$143$	−5.12352	−0.428450
$144$	−7.76174	−0.646812
$145$	9.73215	0.808211
$146$	17.8251	1.47522
$147$	−1.42696	−0.117694
$148$	2.15556	0.177186
$149$	−7.46867	−0.611857	−0.305928	−	0.952054i	$-0.598967\pi$
$149$	−7.46867	−0.611857	−0.305928	+	0.952054i	$0.598967\pi$
$150$	−2.97691	−0.243064
$151$	−16.6907	−1.35827	−0.679135	−	0.734013i	$-0.737645\pi$
$151$	−16.6907	−1.35827	−0.679135	+	0.734013i	$0.737645\pi$
$152$	0.225616	0.0182999
$153$	−2.58464	−0.208956
$154$	−14.0631	−1.13324
$155$	5.47750	0.439964
$156$	1.13322	0.0907306
$157$	−12.0591	−0.962419	−0.481209	−	0.876606i	$-0.659802\pi$
$157$	−12.0591	−0.962419	−0.481209	+	0.876606i	$0.659802\pi$
$158$	5.77986	0.459821
$159$	−10.7588	−0.853230
$160$	−2.29678	−0.181576
$161$	4.95500	0.390508
$162$	12.6897	0.996996
$163$	−6.19944	−0.485578	−0.242789	−	0.970079i	$-0.578062\pi$
$163$	−6.19944	−0.485578	−0.242789	+	0.970079i	$0.578062\pi$
$164$	−1.94702	−0.152037
$165$	10.4316	0.812099
$166$	−6.26239	−0.486056
$167$	10.8983	0.843335	0.421667	−	0.906751i	$-0.361445\pi$
$167$	10.8983	0.843335	0.421667	+	0.906751i	$0.361445\pi$
$168$	18.1681	1.40170
$169$	−11.6528	−0.896369
$170$	1.25970	0.0966149
$171$	0.191831	0.0146697
$172$	−1.53151	−0.116776
$173$	−7.56130	−0.574875	−0.287438	−	0.957799i	$-0.592803\pi$
$173$	−7.56130	−0.574875	−0.287438	+	0.957799i	$0.592803\pi$
$174$	−28.9718	−2.19634
$175$	2.52906	0.191179
$176$	−13.2560	−0.999206
$177$	−0.0183620	−0.00138017
$178$	−11.7448	−0.880314
$179$	9.88258	0.738659	0.369329	−	0.929299i	$-0.379587\pi$
$179$	9.88258	0.738659	0.369329	+	0.929299i	$0.379587\pi$
$180$	−1.06783	−0.0795916
$181$	8.37136	0.622238	0.311119	−	0.950371i	$-0.399296\pi$
$181$	8.37136	0.622238	0.311119	+	0.950371i	$0.399296\pi$
$182$	3.69781	0.274100
$183$	18.2606	1.34987
$184$	5.95573	0.439063
$185$	−5.21744	−0.383594
$186$	−16.3061	−1.19562
$187$	−4.41421	−0.322799
$188$	2.19340	0.159970
$189$	−2.48244	−0.180571
$190$	−0.0934946	−0.00678281
$191$	−6.75666	−0.488895	−0.244447	−	0.969663i	$-0.578607\pi$
$191$	−6.75666	−0.488895	−0.244447	+	0.969663i	$0.578607\pi$
$192$	21.0307	1.51776
$193$	−12.5885	−0.906137	−0.453069	−	0.891476i	$-0.649671\pi$
$193$	−12.5885	−0.906137	−0.453069	+	0.891476i	$0.649671\pi$
$194$	5.33534	0.383055
$195$	−2.74292	−0.196425
$196$	0.249470	0.0178193
$197$	−11.0574	−0.787807	−0.393903	−	0.919152i	$-0.628876\pi$
$197$	−11.0574	−0.787807	−0.393903	+	0.919152i	$0.628876\pi$
$198$	−14.3722	−1.02139
$199$	−10.0522	−0.712579	−0.356289	−	0.934376i	$-0.615958\pi$
$199$	−10.0522	−0.712579	−0.356289	+	0.934376i	$0.615958\pi$
$200$	3.03985	0.214950
$201$	3.50798	0.247434
$202$	−13.9489	−0.981444
$203$	24.6132	1.72751
$204$	0.976339	0.0683574
$205$	4.71268	0.329148
$206$	−24.2186	−1.68739
$207$	5.06389	0.351965
$208$	3.48557	0.241681
$209$	0.327620	0.0226620
$210$	−7.52881	−0.519537
$211$	−1.93571	−0.133260	−0.0666298	−	0.997778i	$-0.521225\pi$
$211$	−1.93571	−0.133260	−0.0666298	+	0.997778i	$0.521225\pi$
$212$	1.88092	0.129182
$213$	−2.36319	−0.161923
$214$	1.71296	0.117096
$215$	3.70694	0.252812
$216$	−2.98380	−0.203022
$217$	13.8530	0.940400
$218$	−2.01835	−0.136700
$219$	−33.4396	−2.25964
$220$	−1.82371	−0.122955
$221$	1.16069	0.0780763
$222$	15.5319	1.04243
$223$	−5.87582	−0.393474	−0.196737	−	0.980456i	$-0.563035\pi$
$223$	−5.87582	−0.393474	−0.196737	+	0.980456i	$0.563035\pi$
$224$	−5.80871	−0.388111
$225$	2.58464	0.172310
$226$	−5.13093	−0.341305
$227$	−10.1643	−0.674631	−0.337316	−	0.941392i	$-0.609519\pi$
$227$	−10.1643	−0.674631	−0.337316	+	0.941392i	$0.609519\pi$
$228$	−0.0724633	−0.00479900
$229$	−19.1760	−1.26719	−0.633594	−	0.773665i	$-0.718421\pi$
$229$	−19.1760	−1.26719	−0.633594	+	0.773665i	$0.718421\pi$
$230$	−2.46804	−0.162738
$231$	26.3822	1.73582
$232$	29.5843	1.94230
$233$	20.6995	1.35607	0.678036	−	0.735029i	$-0.262832\pi$
$233$	20.6995	1.35607	0.678036	+	0.735029i	$0.262832\pi$
$234$	3.77907	0.247046
$235$	−5.30904	−0.346324
$236$	0.00321015	0.000208963 0
$237$	−10.8429	−0.704323
$238$	3.18587	0.206510
$239$	−5.68224	−0.367554	−0.183777	−	0.982968i	$-0.558832\pi$
$239$	−5.68224	−0.367554	−0.183777	+	0.982968i	$0.558832\pi$
$240$	−7.09669	−0.458090
$241$	16.5405	1.06546	0.532732	−	0.846284i	$-0.321165\pi$
$241$	16.5405	1.06546	0.532732	+	0.846284i	$0.321165\pi$
$242$	−10.6889	−0.687109
$243$	−20.8610	−1.33823
$244$	−3.19243	−0.204374
$245$	−0.603831	−0.0385773
$246$	−14.0292	−0.894472
$247$	−0.0861457	−0.00548132
$248$	16.6508	1.05733
$249$	11.7481	0.744508
$250$	−1.25970	−0.0796707
$251$	−29.9691	−1.89164	−0.945818	−	0.324698i	$-0.894737\pi$
$251$	−29.9691	−1.89164	−0.945818	+	0.324698i	$0.894737\pi$
$252$	−2.70062	−0.170123
$253$	8.64841	0.543721
$254$	12.4986	0.784232
$255$	−2.36319	−0.147988
$256$	−9.46324	−0.591452
$257$	12.2709	0.765439	0.382719	−	0.923865i	$-0.374988\pi$
$257$	12.2709	0.765439	0.382719	+	0.923865i	$0.374988\pi$
$258$	−11.0353	−0.687025
$259$	−13.1952	−0.819912
$260$	0.479533	0.0297394
$261$	25.1541	1.55700
$262$	−17.2529	−1.06589
$263$	−7.82454	−0.482482	−0.241241	−	0.970465i	$-0.577554\pi$
$263$	−7.82454	−0.482482	−0.241241	+	0.970465i	$0.577554\pi$
$264$	31.7105	1.95165
$265$	−4.55268	−0.279669
$266$	−0.236454	−0.0144979
$267$	22.0332	1.34841
$268$	−0.613285	−0.0374624
$269$	−12.6095	−0.768817	−0.384409	−	0.923163i	$-0.625595\pi$
$269$	−12.6095	−0.768817	−0.384409	+	0.923163i	$0.625595\pi$
$270$	1.23648	0.0752497
$271$	22.5878	1.37211	0.686056	−	0.727549i	$-0.259341\pi$
$271$	22.5878	1.37211	0.686056	+	0.727549i	$0.259341\pi$
$272$	3.00302	0.182085
$273$	−6.93703	−0.419848
$274$	−7.00182	−0.422996
$275$	4.41421	0.266187
$276$	−1.91286	−0.115141
$277$	15.7400	0.945722	0.472861	−	0.881137i	$-0.343221\pi$
$277$	15.7400	0.945722	0.472861	+	0.881137i	$0.343221\pi$
$278$	1.23803	0.0742519
$279$	14.1574	0.847581
$280$	7.68798	0.459444
$281$	9.08026	0.541683	0.270841	−	0.962624i	$-0.412698\pi$
$281$	9.08026	0.541683	0.270841	+	0.962624i	$0.412698\pi$
$282$	15.8046	0.941148
$283$	27.5752	1.63918	0.819589	−	0.572952i	$-0.194202\pi$
$283$	27.5752	1.63918	0.819589	+	0.572952i	$0.194202\pi$
$284$	0.413145	0.0245157
$285$	0.175394	0.0103895
$286$	6.45412	0.381640
$287$	11.9187	0.703537
$288$	−5.93636	−0.349803
$289$	1.00000	0.0588235
$290$	−12.2596	−0.719910
$291$	−10.0090	−0.586739
$292$	5.84610	0.342117
$293$	−22.7096	−1.32671	−0.663353	−	0.748306i	$-0.730867\pi$
$293$	−22.7096	−1.32671	−0.663353	+	0.748306i	$0.730867\pi$
$294$	1.79755	0.104835
$295$	−0.00777003	−0.000452389 0
$296$	−15.8602	−0.921857
$297$	−4.33282	−0.251416
$298$	9.40831	0.545009
$299$	−2.27404	−0.131511
$300$	−0.976339	−0.0563689
$301$	9.37510	0.540372
$302$	21.0254	1.20987
$303$	26.1680	1.50331
$304$	−0.222883	−0.0127832
$305$	7.72713	0.442454
$306$	3.25589	0.186127
$307$	−8.91575	−0.508849	−0.254424	−	0.967093i	$-0.581886\pi$
$307$	−8.91575	−0.508849	−0.254424	+	0.967093i	$0.581886\pi$
$308$	−4.61228	−0.262809
$309$	45.4338	2.58464
$310$	−6.90003	−0.391896
$311$	−19.5786	−1.11020	−0.555100	−	0.831784i	$-0.687320\pi$
$311$	−19.5786	−1.11020	−0.555100	+	0.831784i	$0.687320\pi$
$312$	−8.33807	−0.472050
$313$	15.2929	0.864406	0.432203	−	0.901776i	$-0.357736\pi$
$313$	15.2929	0.864406	0.432203	+	0.901776i	$0.357736\pi$
$314$	15.1909	0.857270
$315$	6.53673	0.368303
$316$	1.89562	0.106637
$317$	−25.5363	−1.43426	−0.717131	−	0.696939i	$-0.754545\pi$
$317$	−25.5363	−1.43426	−0.717131	+	0.696939i	$0.754545\pi$
$318$	13.5529	0.760011
$319$	42.9597	2.40528
$320$	8.89931	0.497486
$321$	−3.21349	−0.179360
$322$	−6.24183	−0.347844
$323$	−0.0742195	−0.00412968
$324$	4.16184	0.231213
$325$	−1.16069	−0.0643834
$326$	7.80946	0.432526
$327$	3.78639	0.209388
$328$	14.3258	0.791012
$329$	−13.4269	−0.740249
$330$	−13.1407	−0.723373
$331$	32.0411	1.76114	0.880569	−	0.473918i	$-0.157161\pi$
$331$	32.0411	1.76114	0.880569	+	0.473918i	$0.157161\pi$
$332$	−2.05388	−0.112721
$333$	−13.4852	−0.738986
$334$	−13.7286	−0.751197
$335$	1.48443	0.0811031
$336$	−17.9480	−0.979144
$337$	6.97814	0.380124	0.190062	−	0.981772i	$-0.439131\pi$
$337$	6.97814	0.380124	0.190062	+	0.981772i	$0.439131\pi$
$338$	14.6791	0.798437
$339$	9.62555	0.522788
$340$	0.413145	0.0224059
$341$	24.1788	1.30936
$342$	−0.241650	−0.0130669
$343$	−19.2306	−1.03835
$344$	11.2686	0.607560
$345$	4.63000	0.249271
$346$	9.52501	0.512068
$347$	3.40606	0.182847	0.0914233	−	0.995812i	$-0.470858\pi$
$347$	3.40606	0.182847	0.0914233	+	0.995812i	$0.470858\pi$
$348$	−9.50187	−0.509354
$349$	1.07410	0.0574951	0.0287476	−	0.999587i	$-0.490848\pi$
$349$	1.07410	0.0574951	0.0287476	+	0.999587i	$0.490848\pi$
$350$	−3.18587	−0.170292
$351$	1.13929	0.0608107
$352$	−10.1385	−0.540383
$353$	13.1211	0.698363	0.349182	−	0.937055i	$-0.386460\pi$
$353$	13.1211	0.698363	0.349182	+	0.937055i	$0.386460\pi$
$354$	0.0231307	0.00122938
$355$	−1.00000	−0.0530745
$356$	−3.85196	−0.204153
$357$	−5.97665	−0.316318
$358$	−12.4491	−0.657957
$359$	36.3541	1.91870	0.959348	−	0.282226i	$-0.0910729\pi$
$359$	36.3541	1.91870	0.959348	+	0.282226i	$0.0910729\pi$
$360$	7.85693	0.414097
$361$	−18.9945	−0.999710
$362$	−10.5454	−0.554256
$363$	20.0522	1.05247
$364$	1.21277	0.0635664
$365$	−14.1502	−0.740657
$366$	−23.0030	−1.20239
$367$	2.60290	0.135870	0.0679351	−	0.997690i	$-0.478359\pi$
$367$	2.60290	0.135870	0.0679351	+	0.997690i	$0.478359\pi$
$368$	−5.88358	−0.306703
$369$	12.1806	0.634097
$370$	6.57243	0.341684
$371$	−11.5140	−0.597778
$372$	−5.34790	−0.277276
$373$	9.97329	0.516397	0.258199	−	0.966092i	$-0.416871\pi$
$373$	9.97329	0.516397	0.258199	+	0.966092i	$0.416871\pi$
$374$	5.56060	0.287532
$375$	2.36319	0.122034
$376$	−16.1387	−0.832289
$377$	−11.2960	−0.581773
$378$	3.12713	0.160842
$379$	2.19049	0.112518	0.0562590	−	0.998416i	$-0.482083\pi$
$379$	2.19049	0.112518	0.0562590	+	0.998416i	$0.482083\pi$
$380$	−0.0306634	−0.00157300
$381$	−23.4472	−1.20124
$382$	8.51139	0.435481
$383$	25.4830	1.30212	0.651060	−	0.759027i	$-0.274325\pi$
$383$	25.4830	1.30212	0.651060	+	0.759027i	$0.274325\pi$
$384$	−15.6370	−0.797974
$385$	11.1638	0.568961
$386$	15.8577	0.807138
$387$	9.58113	0.487036
$388$	1.74983	0.0888343
$389$	18.1719	0.921354	0.460677	−	0.887568i	$-0.347607\pi$
$389$	18.1719	0.921354	0.460677	+	0.887568i	$0.347607\pi$
$390$	3.45527	0.174964
$391$	−1.95922	−0.0990820
$392$	−1.83556	−0.0927095
$393$	32.3662	1.63266
$394$	13.9290	0.701735
$395$	−4.58826	−0.230861
$396$	−4.71364	−0.236869
$397$	−36.8250	−1.84819	−0.924097	−	0.382158i	$-0.875181\pi$
$397$	−36.8250	−1.84819	−0.924097	+	0.382158i	$0.875181\pi$
$398$	12.6627	0.634726
$399$	0.443584	0.0222070
$400$	−3.00302	−0.150151
$401$	−5.90932	−0.295097	−0.147549	−	0.989055i	$-0.547138\pi$
$401$	−5.90932	−0.295097	−0.147549	+	0.989055i	$0.547138\pi$
$402$	−4.41902	−0.220401
$403$	−6.35767	−0.316698
$404$	−4.57484	−0.227607
$405$	−10.0735	−0.500559
$406$	−31.0054	−1.53877
$407$	−23.0309	−1.14160
$408$	−7.18373	−0.355647
$409$	−5.83738	−0.288640	−0.144320	−	0.989531i	$-0.546099\pi$
$409$	−5.83738	−0.288640	−0.144320	+	0.989531i	$0.546099\pi$
$410$	−5.93658	−0.293187
$411$	13.1353	0.647917
$412$	−7.94299	−0.391323
$413$	−0.0196509	−0.000966958 0
$414$	−6.37900	−0.313511
$415$	4.97132	0.244032
$416$	2.66585	0.130704
$417$	−2.32252	−0.113734
$418$	−0.412705	−0.0201860
$419$	−5.91932	−0.289178	−0.144589	−	0.989492i	$-0.546186\pi$
$419$	−5.91932	−0.289178	−0.144589	+	0.989492i	$0.546186\pi$
$420$	−2.46922	−0.120486
$421$	7.97769	0.388809	0.194405	−	0.980921i	$-0.437723\pi$
$421$	7.97769	0.388809	0.194405	+	0.980921i	$0.437723\pi$
$422$	2.43842	0.118700
$423$	−13.7220	−0.667186
$424$	−13.8395	−0.672104
$425$	−1.00000	−0.0485071
$426$	2.97691	0.144232
$427$	19.5424	0.945724
$428$	0.561801	0.0271557
$429$	−12.1078	−0.584572
$430$	−4.66965	−0.225191
$431$	−18.7461	−0.902968	−0.451484	−	0.892279i	$-0.649105\pi$
$431$	−18.7461	−0.902968	−0.451484	+	0.892279i	$0.649105\pi$
$432$	2.94765	0.141819
$433$	19.7187	0.947620	0.473810	−	0.880627i	$-0.342878\pi$
$433$	19.7187	0.947620	0.473810	+	0.880627i	$0.342878\pi$
$434$	−17.4506	−0.837657
$435$	22.9989	1.10271
$436$	−0.661959	−0.0317021
$437$	0.145412	0.00695601
$438$	42.1240	2.01276
$439$	26.9605	1.28675	0.643377	−	0.765549i	$-0.277533\pi$
$439$	26.9605	1.28675	0.643377	+	0.765549i	$0.277533\pi$
$440$	13.4185	0.639704
$441$	−1.56069	−0.0743185
$442$	−1.46212	−0.0695461
$443$	−1.47055	−0.0698681	−0.0349340	−	0.999390i	$-0.511122\pi$
$443$	−1.47055	−0.0698681	−0.0349340	+	0.999390i	$0.511122\pi$
$444$	5.09399	0.241750
$445$	9.32350	0.441976
$446$	7.40180	0.350485
$447$	−17.6498	−0.834809
$448$	22.5069	1.06335
$449$	−7.35281	−0.347001	−0.173500	−	0.984834i	$-0.555508\pi$
$449$	−7.35281	−0.347001	−0.173500	+	0.984834i	$0.555508\pi$
$450$	−3.25589	−0.153484
$451$	20.8028	0.979564
$452$	−1.68279	−0.0791519
$453$	−39.4432	−1.85321
$454$	12.8041	0.600925
$455$	−2.93546	−0.137616
$456$	0.533172	0.0249681
$457$	−28.6455	−1.33998	−0.669989	−	0.742371i	$-0.733701\pi$
$457$	−28.6455	−1.33998	−0.669989	+	0.742371i	$0.733701\pi$
$458$	24.1561	1.12874
$459$	0.981562	0.0458154
$460$	−0.809443	−0.0377405
$461$	17.8253	0.830206	0.415103	−	0.909774i	$-0.363746\pi$
$461$	17.8253	0.830206	0.415103	+	0.909774i	$0.363746\pi$
$462$	−33.2338	−1.54617
$463$	14.3079	0.664945	0.332473	−	0.943113i	$-0.392117\pi$
$463$	14.3079	0.664945	0.332473	+	0.943113i	$0.392117\pi$
$464$	−29.2258	−1.35678
$465$	12.9444	0.600280
$466$	−26.0753	−1.20791
$467$	−20.6754	−0.956743	−0.478372	−	0.878158i	$-0.658773\pi$
$467$	−20.6754	−0.956743	−0.478372	+	0.878158i	$0.658773\pi$
$468$	1.23942	0.0572923
$469$	3.75422	0.173354
$470$	6.68782	0.308486
$471$	−28.4978	−1.31311
$472$	−0.0236197	−0.00108719
$473$	16.3632	0.752382
$474$	13.6589	0.627373
$475$	0.0742195	0.00340542
$476$	1.04487	0.0478916
$477$	−11.7671	−0.538777
$478$	7.15794	0.327397
$479$	25.5653	1.16811	0.584054	−	0.811715i	$-0.301466\pi$
$479$	25.5653	1.16811	0.584054	+	0.811715i	$0.301466\pi$
$480$	−5.42772	−0.247740
$481$	6.05582	0.276122
$482$	−20.8361	−0.949057
$483$	11.7096	0.532804
$484$	−3.50564	−0.159347
$485$	−4.23539	−0.192319
$486$	26.2787	1.19202
$487$	24.8315	1.12522	0.562610	−	0.826722i	$-0.309797\pi$
$487$	24.8315	1.12522	0.562610	+	0.826722i	$0.309797\pi$
$488$	23.4893	1.06331
$489$	−14.6504	−0.662515
$490$	0.760648	0.0343626
$491$	−8.03370	−0.362556	−0.181278	−	0.983432i	$-0.558023\pi$
$491$	−8.03370	−0.362556	−0.181278	+	0.983432i	$0.558023\pi$
$492$	−4.60117	−0.207437
$493$	−9.73215	−0.438314
$494$	0.108518	0.00488246
$495$	11.4092	0.512804
$496$	−16.4491	−0.738584
$497$	−2.52906	−0.113444
$498$	−14.7992	−0.663167
$499$	14.1243	0.632291	0.316145	−	0.948711i	$-0.397611\pi$
$499$	14.1243	0.632291	0.316145	+	0.948711i	$0.397611\pi$
$500$	−0.413145	−0.0184764
$501$	25.7547	1.15063
$502$	37.7523	1.68497
$503$	11.1278	0.496164	0.248082	−	0.968739i	$-0.420200\pi$
$503$	11.1278	0.496164	0.248082	+	0.968739i	$0.420200\pi$
$504$	19.8707	0.885111
$505$	11.0732	0.492751
$506$	−10.8944	−0.484317
$507$	−27.5377	−1.22299
$508$	4.09917	0.181871
$509$	9.25264	0.410116	0.205058	−	0.978750i	$-0.434262\pi$
$509$	9.25264	0.410116	0.205058	+	0.978750i	$0.434262\pi$
$510$	2.97691	0.131820
$511$	−35.7868	−1.58312
$512$	25.1547	1.11169
$513$	−0.0728510	−0.00321645
$514$	−15.4577	−0.681811
$515$	19.2257	0.847184
$516$	−3.61923	−0.159328
$517$	−23.4352	−1.03068
$518$	16.6221	0.730333
$519$	−17.8688	−0.784352
$520$	−3.52832	−0.154727
$521$	−32.7637	−1.43541	−0.717703	−	0.696350i	$-0.754806\pi$
$521$	−32.7637	−1.43541	−0.717703	+	0.696350i	$0.754806\pi$
$522$	−31.6868	−1.38689
$523$	−11.1236	−0.486401	−0.243201	−	0.969976i	$-0.578197\pi$
$523$	−11.1236	−0.486401	−0.243201	+	0.969976i	$0.578197\pi$
$524$	−5.65845	−0.247190
$525$	5.97665	0.260842
$526$	9.85661	0.429769
$527$	−5.47750	−0.238604
$528$	−31.3263	−1.36330
$529$	−19.1615	−0.833107
$530$	5.73503	0.249114
$531$	−0.0200828	−0.000871518 0
$532$	−0.0775498	−0.00336221
$533$	−5.46995	−0.236930
$534$	−27.7553	−1.20109
$535$	−1.35981	−0.0587899
$536$	4.51244	0.194908
$537$	23.3544	1.00782
$538$	15.8843	0.684820
$539$	−2.66544	−0.114809
$540$	0.405528	0.0174511
$541$	−16.6823	−0.717226	−0.358613	−	0.933486i	$-0.616750\pi$
$541$	−16.6823	−0.717226	−0.358613	+	0.933486i	$0.616750\pi$
$542$	−28.4540	−1.22220
$543$	19.7831	0.848973
$544$	2.29678	0.0984737
$545$	1.60224	0.0686325
$546$	8.73860	0.373978
$547$	25.2299	1.07875	0.539377	−	0.842064i	$-0.318660\pi$
$547$	25.2299	1.07875	0.539377	+	0.842064i	$0.318660\pi$
$548$	−2.29639	−0.0980969
$549$	19.9719	0.852379
$550$	−5.56060	−0.237105
$551$	0.722315	0.0307716
$552$	14.0745	0.599051
$553$	−11.6040	−0.493453
$554$	−19.8277	−0.842398
$555$	−12.3298	−0.523370
$556$	0.406036	0.0172198
$557$	30.7593	1.30331	0.651656	−	0.758515i	$-0.274075\pi$
$557$	30.7593	1.30331	0.651656	+	0.758515i	$0.274075\pi$
$558$	−17.8341	−0.754979
$559$	−4.30261	−0.181981
$560$	−7.59483	−0.320940
$561$	−10.4316	−0.440422
$562$	−11.4384	−0.482501
$563$	3.48241	0.146766	0.0733829	−	0.997304i	$-0.476620\pi$
$563$	3.48241	0.146766	0.0733829	+	0.997304i	$0.476620\pi$
$564$	5.18342	0.218261
$565$	4.07312	0.171358
$566$	−34.7366	−1.46009
$567$	−25.4767	−1.06992
$568$	−3.03985	−0.127549
$569$	−14.5447	−0.609744	−0.304872	−	0.952393i	$-0.598614\pi$
$569$	−14.5447	−0.609744	−0.304872	+	0.952393i	$0.598614\pi$
$570$	−0.220945	−0.00925437
$571$	20.4140	0.854301	0.427150	−	0.904181i	$-0.359517\pi$
$571$	20.4140	0.854301	0.427150	+	0.904181i	$0.359517\pi$
$572$	2.11676	0.0885061
$573$	−15.9672	−0.667041
$574$	−15.0140	−0.626673
$575$	1.95922	0.0817051
$576$	23.0015	0.958397
$577$	11.5032	0.478885	0.239443	−	0.970911i	$-0.423035\pi$
$577$	11.5032	0.478885	0.239443	+	0.970911i	$0.423035\pi$
$578$	−1.25970	−0.0523968
$579$	−29.7489	−1.23632
$580$	−4.02079	−0.166954
$581$	12.5728	0.521607
$582$	12.6084	0.522635
$583$	−20.0965	−0.832311
$584$	−43.0145	−1.77995
$585$	−2.99997	−0.124033
$586$	28.6073	1.18176
$587$	−20.8211	−0.859379	−0.429689	−	0.902977i	$-0.641377\pi$
$587$	−20.8211	−0.859379	−0.429689	+	0.902977i	$0.641377\pi$
$588$	0.589544	0.0243124
$589$	0.406537	0.0167511
$590$	0.00978794	0.000402963 0
$591$	−26.1307	−1.07487
$592$	15.6681	0.643954
$593$	−8.19997	−0.336732	−0.168366	−	0.985725i	$-0.553849\pi$
$593$	−8.19997	−0.336732	−0.168366	+	0.985725i	$0.553849\pi$
$594$	5.45808	0.223948
$595$	−2.52906	−0.103682
$596$	3.08564	0.126393
$597$	−23.7551	−0.972232
$598$	2.86462	0.117143
$599$	7.35025	0.300323	0.150162	−	0.988661i	$-0.452021\pi$
$599$	7.35025	0.300323	0.150162	+	0.988661i	$0.452021\pi$
$600$	7.18373	0.293274
$601$	−4.48047	−0.182762	−0.0913811	−	0.995816i	$-0.529128\pi$
$601$	−4.48047	−0.182762	−0.0913811	+	0.995816i	$0.529128\pi$
$602$	−11.8099	−0.481334
$603$	3.83672	0.156244
$604$	6.89569	0.280582
$605$	8.48526	0.344975
$606$	−32.9639	−1.33907
$607$	31.9350	1.29620	0.648101	−	0.761554i	$-0.275563\pi$
$607$	31.9350	1.29620	0.648101	+	0.761554i	$0.275563\pi$
$608$	−0.170466	−0.00691330
$609$	58.1656	2.35699
$610$	−9.73390	−0.394114
$611$	6.16214	0.249294
$612$	1.06783	0.0431646
$613$	30.3408	1.22545	0.612726	−	0.790295i	$-0.290073\pi$
$613$	30.3408	1.22545	0.612726	+	0.790295i	$0.290073\pi$
$614$	11.2312	0.453255
$615$	11.1369	0.449085
$616$	33.9363	1.36733
$617$	−30.4732	−1.22680	−0.613402	−	0.789771i	$-0.710199\pi$
$617$	−30.4732	−1.22680	−0.613402	+	0.789771i	$0.710199\pi$
$618$	−57.2331	−2.30225
$619$	17.7421	0.713115	0.356558	−	0.934273i	$-0.383950\pi$
$619$	17.7421	0.713115	0.356558	+	0.934273i	$0.383950\pi$
$620$	−2.26300	−0.0908844
$621$	−1.92310	−0.0771712
$622$	24.6632	0.988905
$623$	23.5797	0.944702
$624$	8.23705	0.329746
$625$	1.00000	0.0400000
$626$	−19.2645	−0.769966
$627$	0.774228	0.0309197
$628$	4.98215	0.198809
$629$	5.21744	0.208033
$630$	−8.23435	−0.328064
$631$	−6.68998	−0.266324	−0.133162	−	0.991094i	$-0.542513\pi$
$631$	−6.68998	−0.266324	−0.133162	+	0.991094i	$0.542513\pi$
$632$	−13.9476	−0.554807
$633$	−4.57444	−0.181818
$634$	32.1682	1.27756
$635$	−9.92186	−0.393737
$636$	4.44496	0.176254
$637$	0.700860	0.0277691
$638$	−54.1166	−2.14250
$639$	−2.58464	−0.102247
$640$	−6.61693	−0.261557
$641$	−14.6928	−0.580331	−0.290165	−	0.956977i	$-0.593710\pi$
$641$	−14.6928	−0.580331	−0.290165	+	0.956977i	$0.593710\pi$
$642$	4.04805	0.159764
$643$	3.66261	0.144439	0.0722197	−	0.997389i	$-0.476992\pi$
$643$	3.66261	0.144439	0.0722197	+	0.997389i	$0.476992\pi$
$644$	−2.04713	−0.0806683
$645$	8.76020	0.344932
$646$	0.0934946	0.00367849
$647$	−17.7765	−0.698864	−0.349432	−	0.936962i	$-0.613626\pi$
$647$	−17.7765	−0.698864	−0.349432	+	0.936962i	$0.613626\pi$
$648$	−30.6221	−1.20295
$649$	−0.0342986	−0.00134634
$650$	1.46212	0.0573492
$651$	32.7371	1.28307
$652$	2.56127	0.100307
$653$	23.5759	0.922595	0.461298	−	0.887245i	$-0.347384\pi$
$653$	23.5759	0.922595	0.461298	+	0.887245i	$0.347384\pi$
$654$	−4.76974	−0.186511
$655$	13.6960	0.535148
$656$	−14.1523	−0.552554
$657$	−36.5733	−1.42686
$658$	16.9139	0.659374
$659$	33.6316	1.31010	0.655050	−	0.755586i	$-0.272648\pi$
$659$	33.6316	1.31010	0.655050	+	0.755586i	$0.272648\pi$
$660$	−4.30977	−0.167757
$661$	−13.1916	−0.513095	−0.256547	−	0.966532i	$-0.582585\pi$
$661$	−13.1916	−0.513095	−0.256547	+	0.966532i	$0.582585\pi$
$662$	−40.3623	−1.56873
$663$	2.74292	0.106526
$664$	15.1121	0.586461
$665$	0.187706	0.00727892
$666$	16.9874	0.658248
$667$	19.0674	0.738293
$668$	−4.50258	−0.174210
$669$	−13.8857	−0.536851
$670$	−1.86994	−0.0722422
$671$	34.1092	1.31677
$672$	−13.7271	−0.529533
$673$	−3.47161	−0.133821	−0.0669104	−	0.997759i	$-0.521314\pi$
$673$	−3.47161	−0.133821	−0.0669104	+	0.997759i	$0.521314\pi$
$674$	−8.79040	−0.338593
$675$	−0.981562	−0.0377804
$676$	4.81430	0.185165
$677$	−12.8926	−0.495501	−0.247751	−	0.968824i	$-0.579691\pi$
$677$	−12.8926	−0.495501	−0.247751	+	0.968824i	$0.579691\pi$
$678$	−12.1253	−0.465671
$679$	−10.7116	−0.411073
$680$	−3.03985	−0.116573
$681$	−24.0202	−0.920457
$682$	−30.4582	−1.16630
$683$	−45.3500	−1.73527	−0.867634	−	0.497204i	$-0.834360\pi$
$683$	−45.3500	−1.73527	−0.867634	+	0.497204i	$0.834360\pi$
$684$	−0.0792540	−0.00303035
$685$	5.55831	0.212372
$686$	24.2248	0.924909
$687$	−45.3166	−1.72893
$688$	−11.1320	−0.424405
$689$	5.28424	0.201314
$690$	−5.83243	−0.222037
$691$	25.0436	0.952704	0.476352	−	0.879255i	$-0.341959\pi$
$691$	25.0436	0.952704	0.476352	+	0.879255i	$0.341959\pi$
$692$	3.12392	0.118754
$693$	28.8545	1.09609
$694$	−4.29062	−0.162870
$695$	−0.982792	−0.0372794
$696$	69.9131	2.65005
$697$	−4.71268	−0.178506
$698$	−1.35305	−0.0512135
$699$	48.9168	1.85020
$700$	−1.04487	−0.0394924
$701$	−29.4965	−1.11407	−0.557035	−	0.830489i	$-0.688061\pi$
$701$	−29.4965	−1.11407	−0.557035	+	0.830489i	$0.688061\pi$
$702$	−1.43517	−0.0541668
$703$	−0.387236	−0.0146049
$704$	39.2834	1.48055
$705$	−12.5462	−0.472519
$706$	−16.5287	−0.622064
$707$	28.0048	1.05323
$708$	0.00758618	0.000285106 0
$709$	−1.13439	−0.0426031	−0.0213015	−	0.999773i	$-0.506781\pi$
$709$	−1.13439	−0.0426031	−0.0213015	+	0.999773i	$0.506781\pi$
$710$	1.25970	0.0472759
$711$	−11.8590	−0.444748
$712$	28.3420	1.06216
$713$	10.7316	0.401903
$714$	7.52881	0.281759
$715$	−5.12352	−0.191609
$716$	−4.08294	−0.152587
$717$	−13.4282	−0.501485
$718$	−45.7954	−1.70907
$719$	−33.8400	−1.26202	−0.631010	−	0.775774i	$-0.717359\pi$
$719$	−33.8400	−1.26202	−0.631010	+	0.775774i	$0.717359\pi$
$720$	−7.76174	−0.289263
$721$	48.6229	1.81081
$722$	23.9274	0.890487
$723$	39.0882	1.45370
$724$	−3.45859	−0.128537
$725$	9.73215	0.361443
$726$	−25.2599	−0.937482
$727$	−17.6891	−0.656051	−0.328025	−	0.944669i	$-0.606383\pi$
$727$	−17.6891	−0.656051	−0.328025	+	0.944669i	$0.606383\pi$
$728$	−8.92334	−0.330721
$729$	−19.0777	−0.706581
$730$	17.8251	0.659736
$731$	−3.70694	−0.137106
$732$	−7.54430	−0.278845
$733$	−28.8233	−1.06461	−0.532307	−	0.846551i	$-0.678675\pi$
$733$	−28.8233	−1.06461	−0.532307	+	0.846551i	$0.678675\pi$
$734$	−3.27888	−0.121026
$735$	−1.42696	−0.0526344
$736$	−4.49990	−0.165869
$737$	6.55259	0.241368
$738$	−15.3440	−0.564819
$739$	47.7566	1.75675	0.878377	−	0.477969i	$-0.158627\pi$
$739$	47.7566	1.75675	0.878377	+	0.477969i	$0.158627\pi$
$740$	2.15556	0.0792400
$741$	−0.203578	−0.00747863
$742$	14.5043	0.532468
$743$	27.9704	1.02614	0.513068	−	0.858348i	$-0.328509\pi$
$743$	27.9704	1.02614	0.513068	+	0.858348i	$0.328509\pi$
$744$	39.3489	1.44260
$745$	−7.46867	−0.273631
$746$	−12.5634	−0.459978
$747$	12.8491	0.470123
$748$	1.82371	0.0666815
$749$	−3.43906	−0.125661
$750$	−2.97691	−0.108702
$751$	45.5397	1.66177	0.830884	−	0.556445i	$-0.187835\pi$
$751$	45.5397	1.66177	0.830884	+	0.556445i	$0.187835\pi$
$752$	15.9432	0.581387
$753$	−70.8226	−2.58092
$754$	14.2296	0.518212
$755$	−16.6907	−0.607437
$756$	1.02561	0.0373009
$757$	−19.0429	−0.692124	−0.346062	−	0.938212i	$-0.612481\pi$
$757$	−19.0429	−0.692124	−0.346062	+	0.938212i	$0.612481\pi$
$758$	−2.75937	−0.100225
$759$	20.4378	0.741845
$760$	0.225616	0.00818395
$761$	−20.4327	−0.740683	−0.370342	−	0.928896i	$-0.620759\pi$
$761$	−20.4327	−0.740683	−0.370342	+	0.928896i	$0.620759\pi$
$762$	29.5365	1.07000
$763$	4.05217	0.146699
$764$	2.79148	0.100992
$765$	−2.58464	−0.0934480
$766$	−32.1010	−1.15986
$767$	0.00901858	0.000325642 0
$768$	−22.3634	−0.806969
$769$	−15.9044	−0.573528	−0.286764	−	0.958001i	$-0.592580\pi$
$769$	−15.9044	−0.573528	−0.286764	+	0.958001i	$0.592580\pi$
$770$	−14.0631	−0.506800
$771$	28.9984	1.04435
$772$	5.20086	0.187183
$773$	34.8703	1.25420	0.627098	−	0.778940i	$-0.284243\pi$
$773$	34.8703	1.25420	0.627098	+	0.778940i	$0.284243\pi$
$774$	−12.0694	−0.433825
$775$	5.47750	0.196758
$776$	−12.8750	−0.462184
$777$	−31.1828	−1.11868
$778$	−22.8913	−0.820692
$779$	0.349773	0.0125319
$780$	1.13322	0.0405760
$781$	−4.41421	−0.157953
$782$	2.46804	0.0882569
$783$	−9.55271	−0.341386
$784$	1.81332	0.0647613
$785$	−12.0591	−0.430407
$786$	−40.7719	−1.45429
$787$	−13.5217	−0.481996	−0.240998	−	0.970526i	$-0.577475\pi$
$787$	−13.5217	−0.481996	−0.240998	+	0.970526i	$0.577475\pi$
$788$	4.56831	0.162739
$789$	−18.4908	−0.658292
$790$	5.77986	0.205638
$791$	10.3012	0.366268
$792$	34.6821	1.23238
$793$	−8.96879	−0.318491
$794$	46.3886	1.64627
$795$	−10.7588	−0.381576
$796$	4.15300	0.147199
$797$	−53.9135	−1.90972	−0.954858	−	0.297064i	$-0.903993\pi$
$797$	−53.9135	−1.90972	−0.954858	+	0.297064i	$0.903993\pi$
$798$	−0.558784	−0.0197807
$799$	5.30904	0.187820
$800$	−2.29678	−0.0812035
$801$	24.0979	0.851458
$802$	7.44399	0.262856
$803$	−62.4621	−2.20424
$804$	−1.44931	−0.0511131
$805$	4.95500	0.174641
$806$	8.00879	0.282097
$807$	−29.7987	−1.04896
$808$	33.6608	1.18418
$809$	25.8649	0.909360	0.454680	−	0.890655i	$-0.349754\pi$
$809$	25.8649	0.909360	0.454680	+	0.890655i	$0.349754\pi$
$810$	12.6897	0.445870
$811$	−39.6438	−1.39208	−0.696042	−	0.718001i	$-0.745057\pi$
$811$	−39.6438	−1.39208	−0.696042	+	0.718001i	$0.745057\pi$
$812$	−10.1688	−0.356856
$813$	53.3792	1.87209
$814$	29.0121	1.01687
$815$	−6.19944	−0.217157
$816$	7.09669	0.248434
$817$	0.275127	0.00962549
$818$	7.35337	0.257105
$819$	−7.58711	−0.265115
$820$	−1.94702	−0.0679930
$821$	17.2858	0.603277	0.301639	−	0.953422i	$-0.402466\pi$
$821$	17.2858	0.603277	0.301639	+	0.953422i	$0.402466\pi$
$822$	−16.5466	−0.577129
$823$	27.2976	0.951534	0.475767	−	0.879571i	$-0.342171\pi$
$823$	27.2976	0.951534	0.475767	+	0.879571i	$0.342171\pi$
$824$	58.4431	2.03596
$825$	10.4316	0.363182
$826$	0.0247543	0.000861314 0
$827$	20.6571	0.718318	0.359159	−	0.933276i	$-0.383064\pi$
$827$	20.6571	0.718318	0.359159	+	0.933276i	$0.383064\pi$
$828$	−2.09212	−0.0727062
$829$	25.6406	0.890536	0.445268	−	0.895397i	$-0.353108\pi$
$829$	25.6406	0.890536	0.445268	+	0.895397i	$0.353108\pi$
$830$	−6.26239	−0.217371
$831$	37.1964	1.29033
$832$	−10.3293	−0.358105
$833$	0.603831	0.0209215
$834$	2.92569	0.101308
$835$	10.8983	0.377151
$836$	−0.135355	−0.00468134
$837$	−5.37651	−0.185839
$838$	7.45659	0.257584
$839$	−15.6957	−0.541877	−0.270939	−	0.962597i	$-0.587334\pi$
$839$	−15.6957	−0.541877	−0.270939	+	0.962597i	$0.587334\pi$
$840$	18.1681	0.626859
$841$	65.7146	2.26602
$842$	−10.0495	−0.346330
$843$	21.4583	0.739064
$844$	0.799728	0.0275278
$845$	−11.6528	−0.400869
$846$	17.2856	0.594292
$847$	21.4598	0.737366
$848$	13.6718	0.469491
$849$	65.1654	2.23647
$850$	1.25970	0.0432075
$851$	−10.2221	−0.350410
$852$	0.976339	0.0334488
$853$	−33.9324	−1.16182	−0.580911	−	0.813967i	$-0.697304\pi$
$853$	−33.9324	−1.16182	−0.580911	+	0.813967i	$0.697304\pi$
$854$	−24.6177	−0.842399
$855$	0.191831	0.00656048
$856$	−4.13363	−0.141285
$857$	−32.6757	−1.11618	−0.558090	−	0.829780i	$-0.688466\pi$
$857$	−32.6757	−1.11618	−0.558090	+	0.829780i	$0.688466\pi$
$858$	15.2523	0.520705
$859$	1.65262	0.0563865	0.0281933	−	0.999602i	$-0.491025\pi$
$859$	1.65262	0.0563865	0.0281933	+	0.999602i	$0.491025\pi$
$860$	−1.53151	−0.0522239
$861$	28.1660	0.959896
$862$	23.6146	0.804315
$863$	7.82762	0.266455	0.133228	−	0.991085i	$-0.457466\pi$
$863$	7.82762	0.266455	0.133228	+	0.991085i	$0.457466\pi$
$864$	2.25443	0.0766974
$865$	−7.56130	−0.257092
$866$	−24.8397	−0.844088
$867$	2.36319	0.0802580
$868$	−5.72328	−0.194261
$869$	−20.2536	−0.687055
$870$	−28.9718	−0.982235
$871$	−1.72296	−0.0583803
$872$	4.87057	0.164938
$873$	−10.9470	−0.370499
$874$	−0.183176	−0.00619604
$875$	2.52906	0.0854980
$876$	13.8154	0.466779
$877$	1.02540	0.0346252	0.0173126	−	0.999850i	$-0.494489\pi$
$877$	1.02540	0.0346252	0.0173126	+	0.999850i	$0.494489\pi$
$878$	−33.9622	−1.14617
$879$	−53.6669	−1.81014
$880$	−13.2560	−0.446859
$881$	−7.21126	−0.242954	−0.121477	−	0.992594i	$-0.538763\pi$
$881$	−7.21126	−0.242954	−0.121477	+	0.992594i	$0.538763\pi$
$882$	1.96601	0.0661989
$883$	−6.58100	−0.221468	−0.110734	−	0.993850i	$-0.535320\pi$
$883$	−6.58100	−0.221468	−0.110734	+	0.993850i	$0.535320\pi$
$884$	−0.479533	−0.0161284
$885$	−0.0183620	−0.000617233 0
$886$	1.85246	0.0622346
$887$	14.1614	0.475494	0.237747	−	0.971327i	$-0.423591\pi$
$887$	14.1614	0.475494	0.237747	+	0.971327i	$0.423591\pi$
$888$	−37.4807	−1.25777
$889$	−25.0930	−0.841593
$890$	−11.7448	−0.393688
$891$	−44.4668	−1.48969
$892$	2.42757	0.0812810
$893$	−0.394034	−0.0131858
$894$	22.2336	0.743602
$895$	9.88258	0.330338
$896$	−16.7346	−0.559065
$897$	−5.37399	−0.179432
$898$	9.26237	0.309089
$899$	53.3078	1.77792
$900$	−1.06783	−0.0355945
$901$	4.55268	0.151672
$902$	−26.2053	−0.872542
$903$	22.1551	0.737276
$904$	12.3817	0.411809
$905$	8.37136	0.278273
$906$	49.6868	1.65073
$907$	33.0380	1.09701	0.548505	−	0.836147i	$-0.315197\pi$
$907$	33.0380	1.09701	0.548505	+	0.836147i	$0.315197\pi$
$908$	4.19935	0.139360
$909$	28.6203	0.949274
$910$	3.69781	0.122581
$911$	−33.5925	−1.11297	−0.556484	−	0.830858i	$-0.687850\pi$
$911$	−33.5925	−1.11297	−0.556484	+	0.830858i	$0.687850\pi$
$912$	−0.526713	−0.0174412
$913$	21.9444	0.726255
$914$	36.0848	1.19358
$915$	18.2606	0.603678
$916$	7.92249	0.261767
$917$	34.6381	1.14385
$918$	−1.23648	−0.0408099
$919$	5.21483	0.172022	0.0860108	−	0.996294i	$-0.472588\pi$
$919$	5.21483	0.172022	0.0860108	+	0.996294i	$0.472588\pi$
$920$	5.95573	0.196355
$921$	−21.0696	−0.694266
$922$	−22.4546	−0.739502
$923$	1.16069	0.0382045
$924$	−10.8997	−0.358573
$925$	−5.21744	−0.171548
$926$	−18.0237	−0.592297
$927$	49.6915	1.63208
$928$	−22.3526	−0.733760
$929$	34.0302	1.11650	0.558248	−	0.829674i	$-0.311474\pi$
$929$	34.0302	1.11650	0.558248	+	0.829674i	$0.311474\pi$
$930$	−16.3061	−0.534697
$931$	−0.0448160	−0.00146879
$932$	−8.55191	−0.280127
$933$	−46.2678	−1.51474
$934$	26.0449	0.852214
$935$	−4.41421	−0.144360
$936$	−9.11945	−0.298078
$937$	−53.9053	−1.76101	−0.880504	−	0.474038i	$-0.842796\pi$
$937$	−53.9053	−1.76101	−0.880504	+	0.474038i	$0.842796\pi$
$938$	−4.72921	−0.154414
$939$	36.1400	1.17938
$940$	2.19340	0.0715410
$941$	−41.7936	−1.36243	−0.681216	−	0.732083i	$-0.738548\pi$
$941$	−41.7936	−1.36243	−0.681216	+	0.732083i	$0.738548\pi$
$942$	35.8988	1.16965
$943$	9.23318	0.300674
$944$	0.0233336	0.000759443 0
$945$	−2.48244	−0.0807536
$946$	−20.6128	−0.670181
$947$	38.3843	1.24732	0.623661	−	0.781695i	$-0.285645\pi$
$947$	38.3843	1.24732	0.623661	+	0.781695i	$0.285645\pi$
$948$	4.47970	0.145494
$949$	16.4240	0.533146
$950$	−0.0934946	−0.00303336
$951$	−60.3470	−1.95689
$952$	−7.68798	−0.249169
$953$	−52.2312	−1.69193	−0.845967	−	0.533236i	$-0.820976\pi$
$953$	−52.2312	−1.69193	−0.845967	+	0.533236i	$0.820976\pi$
$954$	14.8230	0.479913
$955$	−6.75666	−0.218640
$956$	2.34759	0.0759265
$957$	101.522	3.28173
$958$	−32.2047	−1.04049
$959$	14.0573	0.453935
$960$	21.0307	0.678763
$961$	−0.996972	−0.0321604
$962$	−7.62854	−0.245954
$963$	−3.51464	−0.113258
$964$	−6.83361	−0.220096
$965$	−12.5885	−0.405237
$966$	−14.7506	−0.474593
$967$	−10.0633	−0.323615	−0.161808	−	0.986822i	$-0.551732\pi$
$967$	−10.0633	−0.323615	−0.161808	+	0.986822i	$0.551732\pi$
$968$	25.7939	0.829047
$969$	−0.175394	−0.00563448
$970$	5.33534	0.171308
$971$	−31.2741	−1.00363	−0.501817	−	0.864974i	$-0.667335\pi$
$971$	−31.2741	−1.00363	−0.501817	+	0.864974i	$0.667335\pi$
$972$	8.61861	0.276442
$973$	−2.48554	−0.0796829
$974$	−31.2803	−1.00229
$975$	−2.74292	−0.0878438
$976$	−23.2047	−0.742765
$977$	−17.2635	−0.552307	−0.276153	−	0.961114i	$-0.589060\pi$
$977$	−17.2635	−0.552307	−0.276153	+	0.961114i	$0.589060\pi$
$978$	18.4552	0.590132
$979$	41.1559	1.31535
$980$	0.249470	0.00796902
$981$	4.14123	0.132219
$982$	10.1201	0.322945
$983$	−34.3981	−1.09713	−0.548564	−	0.836108i	$-0.684825\pi$
$983$	−34.3981	−1.09713	−0.548564	+	0.836108i	$0.684825\pi$
$984$	33.8546	1.07925
$985$	−11.0574	−0.352318
$986$	12.2596	0.390426
$987$	−31.7303	−1.00999
$988$	0.0355907	0.00113229
$989$	7.26272	0.230941
$990$	−14.3722	−0.456778
$991$	40.6925	1.29264	0.646320	−	0.763067i	$-0.276307\pi$
$991$	40.6925	1.29264	0.646320	+	0.763067i	$0.276307\pi$
$992$	−12.5806	−0.399435
$993$	75.7190	2.40287
$994$	3.18587	0.101050
$995$	−10.0522	−0.318675
$996$	−4.85369	−0.153795
$997$	−32.8038	−1.03891	−0.519453	−	0.854499i	$-0.673864\pi$
$997$	−32.8038	−1.03891	−0.519453	+	0.854499i	$0.673864\pi$
$998$	−17.7925	−0.563210
$999$	5.12124	0.162029

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.h.1.19	✓	59

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.h.1.19	✓	59	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-1.25970 q^{2} +2.36319 q^{3} -0.413145 q^{4} +1.00000 q^{5} -2.97691 q^{6} +2.52906 q^{7} +3.03985 q^{8} +2.58464 q^{9} +O(q^{10})\)	\(q-1.25970 q^{2} +2.36319 q^{3} -0.413145 q^{4} +1.00000 q^{5} -2.97691 q^{6} +2.52906 q^{7} +3.03985 q^{8} +2.58464 q^{9} -1.25970 q^{10} +4.41421 q^{11} -0.976339 q^{12} -1.16069 q^{13} -3.18587 q^{14} +2.36319 q^{15} -3.00302 q^{16} -1.00000 q^{17} -3.25589 q^{18} +0.0742195 q^{19} -0.413145 q^{20} +5.97665 q^{21} -5.56060 q^{22} +1.95922 q^{23} +7.18373 q^{24} +1.00000 q^{25} +1.46212 q^{26} -0.981562 q^{27} -1.04487 q^{28} +9.73215 q^{29} -2.97691 q^{30} +5.47750 q^{31} -2.29678 q^{32} +10.4316 q^{33} +1.25970 q^{34} +2.52906 q^{35} -1.06783 q^{36} -5.21744 q^{37} -0.0934946 q^{38} -2.74292 q^{39} +3.03985 q^{40} +4.71268 q^{41} -7.52881 q^{42} +3.70694 q^{43} -1.82371 q^{44} +2.58464 q^{45} -2.46804 q^{46} -5.30904 q^{47} -7.09669 q^{48} -0.603831 q^{49} -1.25970 q^{50} -2.36319 q^{51} +0.479533 q^{52} -4.55268 q^{53} +1.23648 q^{54} +4.41421 q^{55} +7.68798 q^{56} +0.175394 q^{57} -12.2596 q^{58} -0.00777003 q^{59} -0.976339 q^{60} +7.72713 q^{61} -6.90003 q^{62} +6.53673 q^{63} +8.89931 q^{64} -1.16069 q^{65} -13.1407 q^{66} +1.48443 q^{67} +0.413145 q^{68} +4.63000 q^{69} -3.18587 q^{70} -1.00000 q^{71} +7.85693 q^{72} -14.1502 q^{73} +6.57243 q^{74} +2.36319 q^{75} -0.0306634 q^{76} +11.1638 q^{77} +3.45527 q^{78} -4.58826 q^{79} -3.00302 q^{80} -10.0735 q^{81} -5.93658 q^{82} +4.97132 q^{83} -2.46922 q^{84} -1.00000 q^{85} -4.66965 q^{86} +22.9989 q^{87} +13.4185 q^{88} +9.32350 q^{89} -3.25589 q^{90} -2.93546 q^{91} -0.809443 q^{92} +12.9444 q^{93} +6.68782 q^{94} +0.0742195 q^{95} -5.42772 q^{96} -4.23539 q^{97} +0.760648 q^{98} +11.4092 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9} + 2 q^{10} + 6 q^{11} + 16 q^{12} + 25 q^{13} + 8 q^{14} + 6 q^{15} + 114 q^{16} - 59 q^{17} + 3 q^{18} + 35 q^{19} + 76 q^{20} + 41 q^{21} + 13 q^{22} - 2 q^{23} + 35 q^{24} + 59 q^{25} + 10 q^{26} + 27 q^{27} + 28 q^{28} + 10 q^{29} + 14 q^{30} + 15 q^{31} + 19 q^{32} - 3 q^{33} - 2 q^{34} + 9 q^{35} + 160 q^{36} + 56 q^{37} + 17 q^{38} + 25 q^{39} + 6 q^{40} + 47 q^{41} + 46 q^{42} + 27 q^{43} + 39 q^{44} + 97 q^{45} + 4 q^{46} - 8 q^{47} + 58 q^{48} + 174 q^{49} + 2 q^{50} - 6 q^{51} + 13 q^{52} + 17 q^{53} + 48 q^{54} + 6 q^{55} + 33 q^{56} + 6 q^{57} + 32 q^{58} + 30 q^{59} + 16 q^{60} + 85 q^{61} - 3 q^{62} + 14 q^{63} + 168 q^{64} + 25 q^{65} + 87 q^{66} + 21 q^{67} - 76 q^{68} + 111 q^{69} + 8 q^{70} - 59 q^{71} - 52 q^{72} + 41 q^{73} + 11 q^{74} + 6 q^{75} + 118 q^{76} + 55 q^{77} - 54 q^{78} + 43 q^{79} + 114 q^{80} + 207 q^{81} + 45 q^{82} + 10 q^{83} + 62 q^{84} - 59 q^{85} + 19 q^{86} + 8 q^{87} + 35 q^{88} + 86 q^{89} + 3 q^{90} + 47 q^{91} - 98 q^{92} + 41 q^{93} + 30 q^{94} + 35 q^{95} + 69 q^{96} + 72 q^{97} + 14 q^{98} + 25 q^{99}+O(q^{100}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9 + 2 * q^10 + 6 * q^11 + 16 * q^12 + 25 * q^13 + 8 * q^14 + 6 * q^15 + 114 * q^16 - 59 * q^17 + 3 * q^18 + 35 * q^19 + 76 * q^20 + 41 * q^21 + 13 * q^22 - 2 * q^23 + 35 * q^24 + 59 * q^25 + 10 * q^26 + 27 * q^27 + 28 * q^28 + 10 * q^29 + 14 * q^30 + 15 * q^31 + 19 * q^32 - 3 * q^33 - 2 * q^34 + 9 * q^35 + 160 * q^36 + 56 * q^37 + 17 * q^38 + 25 * q^39 + 6 * q^40 + 47 * q^41 + 46 * q^42 + 27 * q^43 + 39 * q^44 + 97 * q^45 + 4 * q^46 - 8 * q^47 + 58 * q^48 + 174 * q^49 + 2 * q^50 - 6 * q^51 + 13 * q^52 + 17 * q^53 + 48 * q^54 + 6 * q^55 + 33 * q^56 + 6 * q^57 + 32 * q^58 + 30 * q^59 + 16 * q^60 + 85 * q^61 - 3 * q^62 + 14 * q^63 + 168 * q^64 + 25 * q^65 + 87 * q^66 + 21 * q^67 - 76 * q^68 + 111 * q^69 + 8 * q^70 - 59 * q^71 - 52 * q^72 + 41 * q^73 + 11 * q^74 + 6 * q^75 + 118 * q^76 + 55 * q^77 - 54 * q^78 + 43 * q^79 + 114 * q^80 + 207 * q^81 + 45 * q^82 + 10 * q^83 + 62 * q^84 - 59 * q^85 + 19 * q^86 + 8 * q^87 + 35 * q^88 + 86 * q^89 + 3 * q^90 + 47 * q^91 - 98 * q^92 + 41 * q^93 + 30 * q^94 + 35 * q^95 + 69 * q^96 + 72 * q^97 + 14 * q^98 + 25 * q^99

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