LMFDB - Embedded newform 6035.2.a.a.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:	$1$
Dimension:	$36$
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)

$f(q)$	$=$	$q+0.0925953 q^{2} +0.181897 q^{3} -1.99143 q^{4} +1.00000 q^{5} +0.0168428 q^{6} -0.294707 q^{7} -0.369587 q^{8} -2.96691 q^{9} +O(q^{10})$	\(q+0.0925953 q^{2} +0.181897 q^{3} -1.99143 q^{4} +1.00000 q^{5} +0.0168428 q^{6} -0.294707 q^{7} -0.369587 q^{8} -2.96691 q^{9} +0.0925953 q^{10} +3.76230 q^{11} -0.362234 q^{12} -0.924570 q^{13} -0.0272885 q^{14} +0.181897 q^{15} +3.94863 q^{16} +1.00000 q^{17} -0.274722 q^{18} -4.03388 q^{19} -1.99143 q^{20} -0.0536063 q^{21} +0.348371 q^{22} +2.83718 q^{23} -0.0672268 q^{24} +1.00000 q^{25} -0.0856108 q^{26} -1.08536 q^{27} +0.586888 q^{28} +4.98610 q^{29} +0.0168428 q^{30} -6.65037 q^{31} +1.10480 q^{32} +0.684350 q^{33} +0.0925953 q^{34} -0.294707 q^{35} +5.90839 q^{36} -5.06401 q^{37} -0.373518 q^{38} -0.168176 q^{39} -0.369587 q^{40} -3.20671 q^{41} -0.00496369 q^{42} +0.706777 q^{43} -7.49233 q^{44} -2.96691 q^{45} +0.262709 q^{46} -5.14474 q^{47} +0.718244 q^{48} -6.91315 q^{49} +0.0925953 q^{50} +0.181897 q^{51} +1.84121 q^{52} -2.87422 q^{53} -0.100500 q^{54} +3.76230 q^{55} +0.108920 q^{56} -0.733750 q^{57} +0.461689 q^{58} +8.74553 q^{59} -0.362234 q^{60} +14.4979 q^{61} -0.615793 q^{62} +0.874371 q^{63} -7.79496 q^{64} -0.924570 q^{65} +0.0633676 q^{66} +3.45160 q^{67} -1.99143 q^{68} +0.516074 q^{69} -0.0272885 q^{70} -1.00000 q^{71} +1.09653 q^{72} +11.5132 q^{73} -0.468904 q^{74} +0.181897 q^{75} +8.03317 q^{76} -1.10878 q^{77} -0.0155723 q^{78} +0.139482 q^{79} +3.94863 q^{80} +8.70332 q^{81} -0.296926 q^{82} +0.334644 q^{83} +0.106753 q^{84} +1.00000 q^{85} +0.0654443 q^{86} +0.906956 q^{87} -1.39050 q^{88} -6.33966 q^{89} -0.274722 q^{90} +0.272477 q^{91} -5.65003 q^{92} -1.20968 q^{93} -0.476379 q^{94} -4.03388 q^{95} +0.200960 q^{96} -2.96072 q^{97} -0.640125 q^{98} -11.1624 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * 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 $

$2$	0.0925953	0.0654748	0.0327374	−	0.999464i	$-0.489578\pi$
$2$	0.0925953	0.0654748	0.0327374	+	0.999464i	$0.489578\pi$
$3$	0.181897	0.105018	0.0525091	−	0.998620i	$-0.483278\pi$
$3$	0.181897	0.105018	0.0525091	+	0.998620i	$0.483278\pi$
$4$	−1.99143	−0.995713
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.0168428	0.00687604
$7$	−0.294707	−0.111389	−0.0556944	−	0.998448i	$-0.517737\pi$
$7$	−0.294707	−0.111389	−0.0556944	+	0.998448i	$0.517737\pi$
$8$	−0.369587	−0.130669
$9$	−2.96691	−0.988971
$10$	0.0925953	0.0292812
$11$	3.76230	1.13437	0.567187	−	0.823589i	$-0.308032\pi$
$11$	3.76230	1.13437	0.567187	+	0.823589i	$0.308032\pi$
$12$	−0.362234	−0.104568
$13$	−0.924570	−0.256430	−0.128215	−	0.991746i	$-0.540925\pi$
$13$	−0.924570	−0.256430	−0.128215	+	0.991746i	$0.540925\pi$
$14$	−0.0272885	−0.00729316
$15$	0.181897	0.0469656
$16$	3.94863	0.987158
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.274722	−0.0647527
$19$	−4.03388	−0.925435	−0.462717	−	0.886506i	$-0.653126\pi$
$19$	−4.03388	−0.925435	−0.462717	+	0.886506i	$0.653126\pi$
$20$	−1.99143	−0.445296
$21$	−0.0536063	−0.0116979
$22$	0.348371	0.0742729
$23$	2.83718	0.591592	0.295796	−	0.955251i	$-0.404415\pi$
$23$	2.83718	0.591592	0.295796	+	0.955251i	$0.404415\pi$
$24$	−0.0672268	−0.0137226
$25$	1.00000	0.200000
$26$	−0.0856108	−0.0167897
$27$	−1.08536	−0.208878
$28$	0.586888	0.110911
$29$	4.98610	0.925896	0.462948	−	0.886386i	$-0.346792\pi$
$29$	4.98610	0.925896	0.462948	+	0.886386i	$0.346792\pi$
$30$	0.0168428	0.00307506
$31$	−6.65037	−1.19444	−0.597221	−	0.802077i	$-0.703728\pi$
$31$	−6.65037	−1.19444	−0.597221	+	0.802077i	$0.703728\pi$
$32$	1.10480	0.195303
$33$	0.684350	0.119130
$34$	0.0925953	0.0158800
$35$	−0.294707	−0.0498146
$36$	5.90839	0.984732
$37$	−5.06401	−0.832519	−0.416259	−	0.909246i	$-0.636659\pi$
$37$	−5.06401	−0.832519	−0.416259	+	0.909246i	$0.636659\pi$
$38$	−0.373518	−0.0605926
$39$	−0.168176	−0.0269298
$40$	−0.369587	−0.0584369
$41$	−3.20671	−0.500804	−0.250402	−	0.968142i	$-0.580563\pi$
$41$	−3.20671	−0.500804	−0.250402	+	0.968142i	$0.580563\pi$
$42$	−0.00496369	−0.000765915 0
$43$	0.706777	0.107783	0.0538913	−	0.998547i	$-0.482838\pi$
$43$	0.706777	0.107783	0.0538913	+	0.998547i	$0.482838\pi$
$44$	−7.49233	−1.12951
$45$	−2.96691	−0.442281
$46$	0.262709	0.0387344
$47$	−5.14474	−0.750437	−0.375219	−	0.926936i	$-0.622432\pi$
$47$	−5.14474	−0.750437	−0.375219	+	0.926936i	$0.622432\pi$
$48$	0.718244	0.103670
$49$	−6.91315	−0.987593
$50$	0.0925953	0.0130950
$51$	0.181897	0.0254707
$52$	1.84121	0.255330
$53$	−2.87422	−0.394805	−0.197403	−	0.980323i	$-0.563251\pi$
$53$	−2.87422	−0.394805	−0.197403	+	0.980323i	$0.563251\pi$
$54$	−0.100500	−0.0136763
$55$	3.76230	0.507308
$56$	0.108920	0.0145551
$57$	−0.733750	−0.0971875
$58$	0.461689	0.0606228
$59$	8.74553	1.13857	0.569286	−	0.822140i	$-0.307220\pi$
$59$	8.74553	1.13857	0.569286	+	0.822140i	$0.307220\pi$
$60$	−0.362234	−0.0467642
$61$	14.4979	1.85626	0.928131	−	0.372255i	$-0.121415\pi$
$61$	14.4979	1.85626	0.928131	+	0.372255i	$0.121415\pi$
$62$	−0.615793	−0.0782058
$63$	0.874371	0.110160
$64$	−7.79496	−0.974370
$65$	−0.924570	−0.114679
$66$	0.0633676	0.00780001
$67$	3.45160	0.421679	0.210840	−	0.977521i	$-0.432380\pi$
$67$	3.45160	0.421679	0.210840	+	0.977521i	$0.432380\pi$
$68$	−1.99143	−0.241496
$69$	0.516074	0.0621280
$70$	−0.0272885	−0.00326160
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	1.09653	0.129228
$73$	11.5132	1.34752	0.673761	−	0.738949i	$-0.264678\pi$
$73$	11.5132	1.34752	0.673761	+	0.738949i	$0.264678\pi$
$74$	−0.468904	−0.0545090
$75$	0.181897	0.0210036
$76$	8.03317	0.921468
$77$	−1.10878	−0.126357
$78$	−0.0155723	−0.00176322
$79$	0.139482	0.0156929	0.00784647	−	0.999969i	$-0.497502\pi$
$79$	0.139482	0.0156929	0.00784647	+	0.999969i	$0.497502\pi$
$80$	3.94863	0.441470
$81$	8.70332	0.967035
$82$	−0.296926	−0.0327900
$83$	0.334644	0.0367320	0.0183660	−	0.999831i	$-0.494154\pi$
$83$	0.334644	0.0367320	0.0183660	+	0.999831i	$0.494154\pi$
$84$	0.106753	0.0116477
$85$	1.00000	0.108465
$86$	0.0654443	0.00705704
$87$	0.906956	0.0972359
$88$	−1.39050	−0.148227
$89$	−6.33966	−0.672003	−0.336001	−	0.941861i	$-0.609075\pi$
$89$	−6.33966	−0.672003	−0.336001	+	0.941861i	$0.609075\pi$
$90$	−0.274722	−0.0289583
$91$	0.272477	0.0285634
$92$	−5.65003	−0.589056
$93$	−1.20968	−0.125438
$94$	−0.476379	−0.0491347
$95$	−4.03388	−0.413867
$96$	0.200960	0.0205104
$97$	−2.96072	−0.300616	−0.150308	−	0.988639i	$-0.548027\pi$
$97$	−2.96072	−0.300616	−0.150308	+	0.988639i	$0.548027\pi$
$98$	−0.640125	−0.0646624
$99$	−11.1624	−1.12186
$100$	−1.99143	−0.199143
$101$	−6.02457	−0.599467	−0.299734	−	0.954023i	$-0.596898\pi$
$101$	−6.02457	−0.599467	−0.299734	+	0.954023i	$0.596898\pi$
$102$	0.0168428	0.00166769
$103$	9.26385	0.912794	0.456397	−	0.889776i	$-0.349140\pi$
$103$	9.26385	0.912794	0.456397	+	0.889776i	$0.349140\pi$
$104$	0.341709	0.0335074
$105$	−0.0536063	−0.00523144
$106$	−0.266140	−0.0258498
$107$	5.82098	0.562735	0.281368	−	0.959600i	$-0.409212\pi$
$107$	5.82098	0.562735	0.281368	+	0.959600i	$0.409212\pi$
$108$	2.16142	0.207983
$109$	−7.72150	−0.739585	−0.369793	−	0.929114i	$-0.620571\pi$
$109$	−7.72150	−0.739585	−0.369793	+	0.929114i	$0.620571\pi$
$110$	0.348371	0.0332159
$111$	−0.921129	−0.0874297
$112$	−1.16369	−0.109958
$113$	−14.7455	−1.38714	−0.693570	−	0.720389i	$-0.743963\pi$
$113$	−14.7455	−1.38714	−0.693570	+	0.720389i	$0.743963\pi$
$114$	−0.0679418	−0.00636333
$115$	2.83718	0.264568
$116$	−9.92945	−0.921926
$117$	2.74312	0.253601
$118$	0.809795	0.0745477
$119$	−0.294707	−0.0270158
$120$	−0.0672268	−0.00613694
$121$	3.15487	0.286806
$122$	1.34243	0.121538
$123$	−0.583291	−0.0525936
$124$	13.2437	1.18932
$125$	1.00000	0.0894427
$126$	0.0809626	0.00721272
$127$	−10.3322	−0.916834	−0.458417	−	0.888737i	$-0.651583\pi$
$127$	−10.3322	−0.916834	−0.458417	+	0.888737i	$0.651583\pi$
$128$	−2.93138	−0.259099
$129$	0.128561	0.0113191
$130$	−0.0856108	−0.00750857
$131$	−12.7925	−1.11768	−0.558842	−	0.829274i	$-0.688754\pi$
$131$	−12.7925	−1.11768	−0.558842	+	0.829274i	$0.688754\pi$
$132$	−1.36283	−0.118619
$133$	1.18881	0.103083
$134$	0.319601	0.0276094
$135$	−1.08536	−0.0934132
$136$	−0.369587	−0.0316918
$137$	−17.7194	−1.51387	−0.756937	−	0.653488i	$-0.773305\pi$
$137$	−17.7194	−1.51387	−0.756937	+	0.653488i	$0.773305\pi$
$138$	0.0477860	0.00406781
$139$	−0.0550266	−0.00466729	−0.00233365	−	0.999997i	$-0.500743\pi$
$139$	−0.0550266	−0.00466729	−0.00233365	+	0.999997i	$0.500743\pi$
$140$	0.586888	0.0496011
$141$	−0.935812	−0.0788096
$142$	−0.0925953	−0.00777042
$143$	−3.47850	−0.290887
$144$	−11.7152	−0.976270
$145$	4.98610	0.414073
$146$	1.06607	0.0882287
$147$	−1.25748	−0.103715
$148$	10.0846	0.828950
$149$	−3.51969	−0.288344	−0.144172	−	0.989553i	$-0.546052\pi$
$149$	−3.51969	−0.288344	−0.144172	+	0.989553i	$0.546052\pi$
$150$	0.0168428	0.00137521
$151$	−11.4425	−0.931180	−0.465590	−	0.885001i	$-0.654158\pi$
$151$	−11.4425	−0.931180	−0.465590	+	0.885001i	$0.654158\pi$
$152$	1.49087	0.120926
$153$	−2.96691	−0.239861
$154$	−0.102667	−0.00827317
$155$	−6.65037	−0.534170
$156$	0.334911	0.0268143
$157$	−6.72066	−0.536367	−0.268184	−	0.963368i	$-0.586423\pi$
$157$	−6.72066	−0.536367	−0.268184	+	0.963368i	$0.586423\pi$
$158$	0.0129154	0.00102749
$159$	−0.522813	−0.0414617
$160$	1.10480	0.0873420
$161$	−0.836136	−0.0658968
$162$	0.805886	0.0633164
$163$	−11.9581	−0.936629	−0.468314	−	0.883562i	$-0.655139\pi$
$163$	−11.9581	−0.936629	−0.468314	+	0.883562i	$0.655139\pi$
$164$	6.38593	0.498657
$165$	0.684350	0.0532766
$166$	0.0309865	0.00240502
$167$	−23.5460	−1.82205	−0.911023	−	0.412356i	$-0.864706\pi$
$167$	−23.5460	−1.82205	−0.911023	+	0.412356i	$0.864706\pi$
$168$	0.0198122	0.00152855
$169$	−12.1452	−0.934244
$170$	0.0925953	0.00710173
$171$	11.9682	0.915228
$172$	−1.40750	−0.107320
$173$	7.28792	0.554091	0.277045	−	0.960857i	$-0.410645\pi$
$173$	7.28792	0.554091	0.277045	+	0.960857i	$0.410645\pi$
$174$	0.0839799	0.00636650
$175$	−0.294707	−0.0222778
$176$	14.8559	1.11981
$177$	1.59079	0.119571
$178$	−0.587023	−0.0439992
$179$	−7.74663	−0.579011	−0.289505	−	0.957176i	$-0.593491\pi$
$179$	−7.74663	−0.579011	−0.289505	+	0.957176i	$0.593491\pi$
$180$	5.90839	0.440385
$181$	23.8271	1.77106	0.885528	−	0.464586i	$-0.153797\pi$
$181$	23.8271	1.77106	0.885528	+	0.464586i	$0.153797\pi$
$182$	0.0252301	0.00187018
$183$	2.63712	0.194941
$184$	−1.04858	−0.0773027
$185$	−5.06401	−0.372314
$186$	−0.112011	−0.00821303
$187$	3.76230	0.275126
$188$	10.2454	0.747220
$189$	0.319864	0.0232667
$190$	−0.373518	−0.0270978
$191$	4.25324	0.307753	0.153877	−	0.988090i	$-0.450824\pi$
$191$	4.25324	0.307753	0.153877	+	0.988090i	$0.450824\pi$
$192$	−1.41788	−0.102327
$193$	6.68923	0.481501	0.240750	−	0.970587i	$-0.422606\pi$
$193$	6.68923	0.481501	0.240750	+	0.970587i	$0.422606\pi$
$194$	−0.274149	−0.0196828
$195$	−0.168176	−0.0120434
$196$	13.7670	0.983359
$197$	2.13141	0.151857	0.0759284	−	0.997113i	$-0.475808\pi$
$197$	2.13141	0.151857	0.0759284	+	0.997113i	$0.475808\pi$
$198$	−1.03359	−0.0734538
$199$	−10.3390	−0.732912	−0.366456	−	0.930435i	$-0.619429\pi$
$199$	−10.3390	−0.732912	−0.366456	+	0.930435i	$0.619429\pi$
$200$	−0.369587	−0.0261338
$201$	0.627835	0.0442840
$202$	−0.557847	−0.0392500
$203$	−1.46944	−0.103134
$204$	−0.362234	−0.0253615
$205$	−3.20671	−0.223966
$206$	0.857789	0.0597650
$207$	−8.41766	−0.585068
$208$	−3.65078	−0.253136
$209$	−15.1766	−1.04979
$210$	−0.00496369	−0.000342527 0
$211$	10.2599	0.706318	0.353159	−	0.935563i	$-0.385107\pi$
$211$	10.2599	0.706318	0.353159	+	0.935563i	$0.385107\pi$
$212$	5.72380	0.393113
$213$	−0.181897	−0.0124634
$214$	0.538995	0.0368449
$215$	0.706777	0.0482018
$216$	0.401136	0.0272939
$217$	1.95991	0.133047
$218$	−0.714974	−0.0484242
$219$	2.09422	0.141514
$220$	−7.49233	−0.505133
$221$	−0.924570	−0.0621933
$222$	−0.0852922	−0.00572444
$223$	2.09529	0.140311	0.0701553	−	0.997536i	$-0.477650\pi$
$223$	2.09529	0.140311	0.0701553	+	0.997536i	$0.477650\pi$
$224$	−0.325592	−0.0217545
$225$	−2.96691	−0.197794
$226$	−1.36536	−0.0908227
$227$	−12.3038	−0.816630	−0.408315	−	0.912841i	$-0.633884\pi$
$227$	−12.3038	−0.816630	−0.408315	+	0.912841i	$0.633884\pi$
$228$	1.46121	0.0967709
$229$	−21.0262	−1.38945	−0.694724	−	0.719276i	$-0.744473\pi$
$229$	−21.0262	−1.38945	−0.694724	+	0.719276i	$0.744473\pi$
$230$	0.262709	0.0173225
$231$	−0.201683	−0.0132698
$232$	−1.84280	−0.120986
$233$	25.0080	1.63833	0.819163	−	0.573561i	$-0.194438\pi$
$233$	25.0080	1.63833	0.819163	+	0.573561i	$0.194438\pi$
$234$	0.254000	0.0166045
$235$	−5.14474	−0.335606
$236$	−17.4161	−1.13369
$237$	0.0253713	0.00164804
$238$	−0.0272885	−0.00176885
$239$	−26.5414	−1.71682	−0.858410	−	0.512964i	$-0.828547\pi$
$239$	−26.5414	−1.71682	−0.858410	+	0.512964i	$0.828547\pi$
$240$	0.718244	0.0463624
$241$	−11.6005	−0.747254	−0.373627	−	0.927579i	$-0.621886\pi$
$241$	−11.6005	−0.747254	−0.373627	+	0.927579i	$0.621886\pi$
$242$	0.292126	0.0187785
$243$	4.83920	0.310435
$244$	−28.8714	−1.84830
$245$	−6.91315	−0.441665
$246$	−0.0540100	−0.00344355
$247$	3.72960	0.237309
$248$	2.45789	0.156076
$249$	0.0608707	0.00385753
$250$	0.0925953	0.00585624
$251$	24.6252	1.55433	0.777164	−	0.629298i	$-0.216657\pi$
$251$	24.6252	1.55433	0.777164	+	0.629298i	$0.216657\pi$
$252$	−1.74124	−0.109688
$253$	10.6743	0.671087
$254$	−0.956713	−0.0600295
$255$	0.181897	0.0113908
$256$	15.3185	0.957406
$257$	−27.8145	−1.73502	−0.867510	−	0.497420i	$-0.834281\pi$
$257$	−27.8145	−1.73502	−0.867510	+	0.497420i	$0.834281\pi$
$258$	0.0119041	0.000741118 0
$259$	1.49240	0.0927333
$260$	1.84121	0.114187
$261$	−14.7933	−0.915684
$262$	−1.18452	−0.0731801
$263$	−25.5431	−1.57506	−0.787529	−	0.616278i	$-0.788640\pi$
$263$	−25.5431	−1.57506	−0.787529	+	0.616278i	$0.788640\pi$
$264$	−0.252927	−0.0155666
$265$	−2.87422	−0.176562
$266$	0.110078	0.00674934
$267$	−1.15316	−0.0705726
$268$	−6.87360	−0.419872
$269$	−4.29893	−0.262110	−0.131055	−	0.991375i	$-0.541836\pi$
$269$	−4.29893	−0.262110	−0.131055	+	0.991375i	$0.541836\pi$
$270$	−0.100500	−0.00611621
$271$	3.34310	0.203079	0.101539	−	0.994832i	$-0.467623\pi$
$271$	3.34310	0.203079	0.101539	+	0.994832i	$0.467623\pi$
$272$	3.94863	0.239421
$273$	0.0495628	0.00299968
$274$	−1.64074	−0.0991205
$275$	3.76230	0.226875
$276$	−1.02772	−0.0618616
$277$	−6.28703	−0.377751	−0.188876	−	0.982001i	$-0.560484\pi$
$277$	−6.28703	−0.377751	−0.188876	+	0.982001i	$0.560484\pi$
$278$	−0.00509520	−0.000305590 0
$279$	19.7311	1.18127
$280$	0.108920	0.00650922
$281$	−17.1491	−1.02303	−0.511514	−	0.859275i	$-0.670915\pi$
$281$	−17.1491	−1.02303	−0.511514	+	0.859275i	$0.670915\pi$
$282$	−0.0866518	−0.00516004
$283$	−7.70993	−0.458308	−0.229154	−	0.973390i	$-0.573596\pi$
$283$	−7.70993	−0.458308	−0.229154	+	0.973390i	$0.573596\pi$
$284$	1.99143	0.118169
$285$	−0.733750	−0.0434636
$286$	−0.322093	−0.0190458
$287$	0.945041	0.0557840
$288$	−3.27784	−0.193149
$289$	1.00000	0.0588235
$290$	0.461689	0.0271113
$291$	−0.538546	−0.0315702
$292$	−22.9278	−1.34175
$293$	−1.34703	−0.0786943	−0.0393471	−	0.999226i	$-0.512528\pi$
$293$	−1.34703	−0.0786943	−0.0393471	+	0.999226i	$0.512528\pi$
$294$	−0.116437	−0.00679073
$295$	8.74553	0.509185
$296$	1.87159	0.108784
$297$	−4.08346	−0.236946
$298$	−0.325907	−0.0188793
$299$	−2.62317	−0.151702
$300$	−0.362234	−0.0209136
$301$	−0.208292	−0.0120058
$302$	−1.05952	−0.0609688
$303$	−1.09585	−0.0629550
$304$	−15.9283	−0.913550
$305$	14.4979	0.830145
$306$	−0.274722	−0.0157048
$307$	22.9270	1.30851	0.654257	−	0.756272i	$-0.272981\pi$
$307$	22.9270	1.30851	0.654257	+	0.756272i	$0.272981\pi$
$308$	2.20804	0.125815
$309$	1.68507	0.0958601
$310$	−0.615793	−0.0349747
$311$	3.05116	0.173015	0.0865076	−	0.996251i	$-0.472429\pi$
$311$	3.05116	0.173015	0.0865076	+	0.996251i	$0.472429\pi$
$312$	0.0621559	0.00351888
$313$	−12.8463	−0.726114	−0.363057	−	0.931767i	$-0.618267\pi$
$313$	−12.8463	−0.726114	−0.363057	+	0.931767i	$0.618267\pi$
$314$	−0.622302	−0.0351185
$315$	0.874371	0.0492652
$316$	−0.277768	−0.0156257
$317$	14.6415	0.822349	0.411174	−	0.911557i	$-0.365119\pi$
$317$	14.6415	0.822349	0.411174	+	0.911557i	$0.365119\pi$
$318$	−0.0484100	−0.00271470
$319$	18.7592	1.05031
$320$	−7.79496	−0.435752
$321$	1.05882	0.0590974
$322$	−0.0774223	−0.00431457
$323$	−4.03388	−0.224451
$324$	−17.3320	−0.962890
$325$	−0.924570	−0.0512859
$326$	−1.10726	−0.0613256
$327$	−1.40452	−0.0776699
$328$	1.18516	0.0654395
$329$	1.51619	0.0835903
$330$	0.0633676	0.00348827
$331$	−28.4810	−1.56546	−0.782728	−	0.622363i	$-0.786173\pi$
$331$	−28.4810	−1.56546	−0.782728	+	0.622363i	$0.786173\pi$
$332$	−0.666419	−0.0365745
$333$	15.0245	0.823337
$334$	−2.18025	−0.119298
$335$	3.45160	0.188581
$336$	−0.211672	−0.0115476
$337$	7.85439	0.427856	0.213928	−	0.976849i	$-0.431374\pi$
$337$	7.85439	0.427856	0.213928	+	0.976849i	$0.431374\pi$
$338$	−1.12459	−0.0611694
$339$	−2.68216	−0.145675
$340$	−1.99143	−0.108000
$341$	−25.0206	−1.35494
$342$	1.10820	0.0599244
$343$	4.10030	0.221396
$344$	−0.261216	−0.0140838
$345$	0.516074	0.0277845
$346$	0.674827	0.0362790
$347$	−13.9906	−0.751056	−0.375528	−	0.926811i	$-0.622539\pi$
$347$	−13.9906	−0.751056	−0.375528	+	0.926811i	$0.622539\pi$
$348$	−1.80614	−0.0968191
$349$	−35.6879	−1.91033	−0.955166	−	0.296071i	$-0.904324\pi$
$349$	−35.6879	−1.91033	−0.955166	+	0.296071i	$0.904324\pi$
$350$	−0.0272885	−0.00145863
$351$	1.00349	0.0535626
$352$	4.15658	0.221546
$353$	−7.25982	−0.386401	−0.193201	−	0.981159i	$-0.561887\pi$
$353$	−7.25982	−0.386401	−0.193201	+	0.981159i	$0.561887\pi$
$354$	0.147299	0.00782887
$355$	−1.00000	−0.0530745
$356$	12.6250	0.669122
$357$	−0.0536063	−0.00283715
$358$	−0.717302	−0.0379106
$359$	14.2249	0.750762	0.375381	−	0.926871i	$-0.377512\pi$
$359$	14.2249	0.750762	0.375381	+	0.926871i	$0.377512\pi$
$360$	1.09653	0.0577924
$361$	−2.72783	−0.143570
$362$	2.20628	0.115959
$363$	0.573860	0.0301199
$364$	−0.542619	−0.0284409
$365$	11.5132	0.602630
$366$	0.244185	0.0127637
$367$	8.15524	0.425700	0.212850	−	0.977085i	$-0.431725\pi$
$367$	8.15524	0.425700	0.212850	+	0.977085i	$0.431725\pi$
$368$	11.2030	0.583995
$369$	9.51404	0.495281
$370$	−0.468904	−0.0243771
$371$	0.847055	0.0439769
$372$	2.40899	0.124900
$373$	−35.7265	−1.84985	−0.924925	−	0.380149i	$-0.875873\pi$
$373$	−35.7265	−1.84985	−0.924925	+	0.380149i	$0.875873\pi$
$374$	0.348371	0.0180138
$375$	0.181897	0.00939312
$376$	1.90143	0.0980588
$377$	−4.61000	−0.237427
$378$	0.0296179	0.00152338
$379$	18.5558	0.953146	0.476573	−	0.879135i	$-0.341879\pi$
$379$	18.5558	0.953146	0.476573	+	0.879135i	$0.341879\pi$
$380$	8.03317	0.412093
$381$	−1.87940	−0.0962843
$382$	0.393830	0.0201501
$383$	−26.6470	−1.36160	−0.680798	−	0.732471i	$-0.738367\pi$
$383$	−26.6470	−1.36160	−0.680798	+	0.732471i	$0.738367\pi$
$384$	−0.533208	−0.0272102
$385$	−1.10878	−0.0565084
$386$	0.619391	0.0315262
$387$	−2.09695	−0.106594
$388$	5.89606	0.299327
$389$	29.3607	1.48865	0.744324	−	0.667819i	$-0.232772\pi$
$389$	29.3607	1.48865	0.744324	+	0.667819i	$0.232772\pi$
$390$	−0.0155723	−0.000788536 0
$391$	2.83718	0.143482
$392$	2.55501	0.129048
$393$	−2.32691	−0.117377
$394$	0.197359	0.00994279
$395$	0.139482	0.00701810
$396$	22.2291	1.11705
$397$	11.1972	0.561973	0.280986	−	0.959712i	$-0.409338\pi$
$397$	11.1972	0.561973	0.280986	+	0.959712i	$0.409338\pi$
$398$	−0.957343	−0.0479873
$399$	0.216241	0.0108256
$400$	3.94863	0.197432
$401$	−11.9587	−0.597188	−0.298594	−	0.954380i	$-0.596518\pi$
$401$	−11.9587	−0.597188	−0.298594	+	0.954380i	$0.596518\pi$
$402$	0.0581345	0.00289949
$403$	6.14873	0.306290
$404$	11.9975	0.596897
$405$	8.70332	0.432471
$406$	−0.136063	−0.00675270
$407$	−19.0523	−0.944388
$408$	−0.0672268	−0.00332822
$409$	2.86569	0.141699	0.0708496	−	0.997487i	$-0.477429\pi$
$409$	2.86569	0.141699	0.0708496	+	0.997487i	$0.477429\pi$
$410$	−0.296926	−0.0146642
$411$	−3.22311	−0.158984
$412$	−18.4483	−0.908881
$413$	−2.57737	−0.126824
$414$	−0.779435	−0.0383072
$415$	0.334644	0.0164270
$416$	−1.02146	−0.0500814
$417$	−0.0100092	−0.000490151 0
$418$	−1.40529	−0.0687347
$419$	−6.71166	−0.327886	−0.163943	−	0.986470i	$-0.552421\pi$
$419$	−6.71166	−0.327886	−0.163943	+	0.986470i	$0.552421\pi$
$420$	0.106753	0.00520902
$421$	12.8116	0.624398	0.312199	−	0.950017i	$-0.398934\pi$
$421$	12.8116	0.624398	0.312199	+	0.950017i	$0.398934\pi$
$422$	0.950015	0.0462460
$423$	15.2640	0.742161
$424$	1.06228	0.0515887
$425$	1.00000	0.0485071
$426$	−0.0168428	−0.000816036 0
$427$	−4.27262	−0.206767
$428$	−11.5920	−0.560323
$429$	−0.632729	−0.0305485
$430$	0.0654443	0.00315600
$431$	−9.37957	−0.451798	−0.225899	−	0.974151i	$-0.572532\pi$
$431$	−9.37957	−0.451798	−0.225899	+	0.974151i	$0.572532\pi$
$432$	−4.28570	−0.206196
$433$	33.9259	1.63037	0.815187	−	0.579198i	$-0.196634\pi$
$433$	33.9259	1.63037	0.815187	+	0.579198i	$0.196634\pi$
$434$	0.181479	0.00871125
$435$	0.906956	0.0434852
$436$	15.3768	0.736415
$437$	−11.4448	−0.547480
$438$	0.193915	0.00926562
$439$	−16.1160	−0.769175	−0.384587	−	0.923089i	$-0.625656\pi$
$439$	−16.1160	−0.769175	−0.384587	+	0.923089i	$0.625656\pi$
$440$	−1.39050	−0.0662893
$441$	20.5107	0.976701
$442$	−0.0856108	−0.00407209
$443$	−40.1607	−1.90809	−0.954047	−	0.299659i	$-0.903127\pi$
$443$	−40.1607	−1.90809	−0.954047	+	0.299659i	$0.903127\pi$
$444$	1.83436	0.0870548
$445$	−6.33966	−0.300529
$446$	0.194014	0.00918681
$447$	−0.640221	−0.0302814
$448$	2.29723	0.108534
$449$	20.5622	0.970392	0.485196	−	0.874405i	$-0.338748\pi$
$449$	20.5622	0.970392	0.485196	+	0.874405i	$0.338748\pi$
$450$	−0.274722	−0.0129505
$451$	−12.0646	−0.568100
$452$	29.3646	1.38119
$453$	−2.08136	−0.0977908
$454$	−1.13927	−0.0534687
$455$	0.272477	0.0127739
$456$	0.271185	0.0126994
$457$	−28.5907	−1.33742	−0.668708	−	0.743526i	$-0.733152\pi$
$457$	−28.5907	−1.33742	−0.668708	+	0.743526i	$0.733152\pi$
$458$	−1.94692	−0.0909738
$459$	−1.08536	−0.0506604
$460$	−5.65003	−0.263434
$461$	27.9865	1.30346	0.651731	−	0.758450i	$-0.274043\pi$
$461$	27.9865	1.30346	0.651731	+	0.758450i	$0.274043\pi$
$462$	−0.0186749	−0.000868834 0
$463$	2.08208	0.0967623	0.0483811	−	0.998829i	$-0.484594\pi$
$463$	2.08208	0.0967623	0.0483811	+	0.998829i	$0.484594\pi$
$464$	19.6883	0.914005
$465$	−1.20968	−0.0560976
$466$	2.31562	0.107269
$467$	5.71386	0.264406	0.132203	−	0.991223i	$-0.457795\pi$
$467$	5.71386	0.264406	0.132203	+	0.991223i	$0.457795\pi$
$468$	−5.46272	−0.252514
$469$	−1.01721	−0.0469704
$470$	−0.476379	−0.0219737
$471$	−1.22247	−0.0563283
$472$	−3.23224	−0.148776
$473$	2.65911	0.122266
$474$	0.00234927	0.000107905 0
$475$	−4.03388	−0.185087
$476$	0.586888	0.0268999
$477$	8.52757	0.390451
$478$	−2.45761	−0.112408
$479$	−6.24795	−0.285476	−0.142738	−	0.989761i	$-0.545591\pi$
$479$	−6.24795	−0.285476	−0.142738	+	0.989761i	$0.545591\pi$
$480$	0.200960	0.00917251
$481$	4.68203	0.213482
$482$	−1.07415	−0.0489263
$483$	−0.152091	−0.00692036
$484$	−6.28268	−0.285576
$485$	−2.96072	−0.134440
$486$	0.448087	0.0203256
$487$	39.1904	1.77589	0.887944	−	0.459952i	$-0.152133\pi$
$487$	39.1904	1.77589	0.887944	+	0.459952i	$0.152133\pi$
$488$	−5.35823	−0.242555
$489$	−2.17514	−0.0983631
$490$	−0.640125	−0.0289179
$491$	−5.42447	−0.244803	−0.122401	−	0.992481i	$-0.539060\pi$
$491$	−5.42447	−0.244803	−0.122401	+	0.992481i	$0.539060\pi$
$492$	1.16158	0.0523681
$493$	4.98610	0.224563
$494$	0.345344	0.0155377
$495$	−11.1624	−0.501713
$496$	−26.2598	−1.17910
$497$	0.294707	0.0132194
$498$	0.00563634	0.000252571 0
$499$	16.1051	0.720965	0.360482	−	0.932766i	$-0.382612\pi$
$499$	16.1051	0.720965	0.360482	+	0.932766i	$0.382612\pi$
$500$	−1.99143	−0.0890593
$501$	−4.28295	−0.191348
$502$	2.28018	0.101769
$503$	−18.6884	−0.833277	−0.416638	−	0.909072i	$-0.636792\pi$
$503$	−18.6884	−0.833277	−0.416638	+	0.909072i	$0.636792\pi$
$504$	−0.323156	−0.0143945
$505$	−6.02457	−0.268090
$506$	0.988389	0.0439393
$507$	−2.20917	−0.0981127
$508$	20.5758	0.912904
$509$	−26.5158	−1.17529	−0.587645	−	0.809119i	$-0.699945\pi$
$509$	−26.5158	−1.17529	−0.587645	+	0.809119i	$0.699945\pi$
$510$	0.0168428	0.000745812 0
$511$	−3.39303	−0.150099
$512$	7.28117	0.321785
$513$	4.37822	0.193303
$514$	−2.57549	−0.113600
$515$	9.26385	0.408214
$516$	−0.256019	−0.0112706
$517$	−19.3560	−0.851277
$518$	0.138189	0.00607169
$519$	1.32565	0.0581896
$520$	0.341709	0.0149849
$521$	8.88031	0.389053	0.194527	−	0.980897i	$-0.437683\pi$
$521$	8.88031	0.389053	0.194527	+	0.980897i	$0.437683\pi$
$522$	−1.36979	−0.0599542
$523$	5.76069	0.251898	0.125949	−	0.992037i	$-0.459803\pi$
$523$	5.76069	0.251898	0.125949	+	0.992037i	$0.459803\pi$
$524$	25.4753	1.11289
$525$	−0.0536063	−0.00233957
$526$	−2.36517	−0.103127
$527$	−6.65037	−0.289695
$528$	2.70224	0.117600
$529$	−14.9504	−0.650019
$530$	−0.266140	−0.0115604
$531$	−25.9472	−1.12601
$532$	−2.36743	−0.102641
$533$	2.96483	0.128421
$534$	−0.106778	−0.00462072
$535$	5.82098	0.251663
$536$	−1.27567	−0.0551004
$537$	−1.40909	−0.0608067
$538$	−0.398060	−0.0171616
$539$	−26.0093	−1.12030
$540$	2.16142	0.0930127
$541$	−11.5530	−0.496703	−0.248351	−	0.968670i	$-0.579889\pi$
$541$	−11.5530	−0.496703	−0.248351	+	0.968670i	$0.579889\pi$
$542$	0.309556	0.0132965
$543$	4.33408	0.185993
$544$	1.10480	0.0473679
$545$	−7.72150	−0.330753
$546$	0.00458928	0.000196403 0
$547$	−12.3681	−0.528822	−0.264411	−	0.964410i	$-0.585178\pi$
$547$	−12.3681	−0.528822	−0.264411	+	0.964410i	$0.585178\pi$
$548$	35.2870	1.50738
$549$	−43.0139	−1.83579
$550$	0.348371	0.0148546
$551$	−20.1133	−0.856856
$552$	−0.190734	−0.00811819
$553$	−0.0411063	−0.00174802
$554$	−0.582150	−0.0247332
$555$	−0.921129	−0.0390997
$556$	0.109581	0.00464729
$557$	44.2516	1.87500	0.937500	−	0.347987i	$-0.113135\pi$
$557$	44.2516	1.87500	0.937500	+	0.347987i	$0.113135\pi$
$558$	1.82700	0.0773432
$559$	−0.653465	−0.0276386
$560$	−1.16369	−0.0491749
$561$	0.684350	0.0288933
$562$	−1.58792	−0.0669825
$563$	−36.5060	−1.53854	−0.769272	−	0.638921i	$-0.779381\pi$
$563$	−36.5060	−1.53854	−0.769272	+	0.638921i	$0.779381\pi$
$564$	1.86360	0.0784718
$565$	−14.7455	−0.620348
$566$	−0.713904	−0.0300076
$567$	−2.56493	−0.107717
$568$	0.369587	0.0155075
$569$	−20.1991	−0.846789	−0.423395	−	0.905945i	$-0.639162\pi$
$569$	−20.1991	−0.846789	−0.423395	+	0.905945i	$0.639162\pi$
$570$	−0.0679418	−0.00284577
$571$	13.4364	0.562296	0.281148	−	0.959664i	$-0.409285\pi$
$571$	13.4364	0.562296	0.281148	+	0.959664i	$0.409285\pi$
$572$	6.92719	0.289640
$573$	0.773651	0.0323197
$574$	0.0875064	0.00365244
$575$	2.83718	0.118318
$576$	23.1270	0.963624
$577$	20.4229	0.850217	0.425109	−	0.905142i	$-0.360236\pi$
$577$	20.4229	0.850217	0.425109	+	0.905142i	$0.360236\pi$
$578$	0.0925953	0.00385146
$579$	1.21675	0.0505664
$580$	−9.92945	−0.412298
$581$	−0.0986220	−0.00409153
$582$	−0.0498669	−0.00206705
$583$	−10.8137	−0.447857
$584$	−4.25514	−0.176079
$585$	2.74312	0.113414
$586$	−0.124729	−0.00515249
$587$	13.6554	0.563620	0.281810	−	0.959470i	$-0.409065\pi$
$587$	13.6554	0.563620	0.281810	+	0.959470i	$0.409065\pi$
$588$	2.50418	0.103271
$589$	26.8268	1.10538
$590$	0.809795	0.0333387
$591$	0.387697	0.0159477
$592$	−19.9959	−0.821827
$593$	−28.0093	−1.15020	−0.575101	−	0.818082i	$-0.695037\pi$
$593$	−28.0093	−1.15020	−0.575101	+	0.818082i	$0.695037\pi$
$594$	−0.378109	−0.0155140
$595$	−0.294707	−0.0120818
$596$	7.00920	0.287108
$597$	−1.88063	−0.0769692
$598$	−0.242893	−0.00993263
$599$	−18.9623	−0.774779	−0.387389	−	0.921916i	$-0.626623\pi$
$599$	−18.9623	−0.774779	−0.387389	+	0.921916i	$0.626623\pi$
$600$	−0.0672268	−0.00274452
$601$	−6.59726	−0.269108	−0.134554	−	0.990906i	$-0.542960\pi$
$601$	−6.59726	−0.269108	−0.134554	+	0.990906i	$0.542960\pi$
$602$	−0.0192869	−0.000786075 0
$603$	−10.2406	−0.417029
$604$	22.7869	0.927188
$605$	3.15487	0.128264
$606$	−0.101471	−0.00412196
$607$	−26.8055	−1.08800	−0.544001	−	0.839085i	$-0.683091\pi$
$607$	−26.8055	−1.08800	−0.544001	+	0.839085i	$0.683091\pi$
$608$	−4.45662	−0.180740
$609$	−0.267287	−0.0108310
$610$	1.34243	0.0543536
$611$	4.75667	0.192434
$612$	5.90839	0.238832
$613$	−39.2317	−1.58455	−0.792277	−	0.610162i	$-0.791104\pi$
$613$	−39.2317	−1.58455	−0.792277	+	0.610162i	$0.791104\pi$
$614$	2.12293	0.0856747
$615$	−0.583291	−0.0235206
$616$	0.409789	0.0165109
$617$	30.9301	1.24520	0.622599	−	0.782541i	$-0.286077\pi$
$617$	30.9301	1.24520	0.622599	+	0.782541i	$0.286077\pi$
$618$	0.156029	0.00627642
$619$	37.7817	1.51858	0.759288	−	0.650755i	$-0.225547\pi$
$619$	37.7817	1.51858	0.759288	+	0.650755i	$0.225547\pi$
$620$	13.2437	0.531880
$621$	−3.07937	−0.123571
$622$	0.282523	0.0113281
$623$	1.86834	0.0748536
$624$	−0.664067	−0.0265839
$625$	1.00000	0.0400000
$626$	−1.18950	−0.0475421
$627$	−2.76058	−0.110247
$628$	13.3837	0.534068
$629$	−5.06401	−0.201915
$630$	0.0809626	0.00322563
$631$	−6.79427	−0.270476	−0.135238	−	0.990813i	$-0.543180\pi$
$631$	−6.79427	−0.270476	−0.135238	+	0.990813i	$0.543180\pi$
$632$	−0.0515507	−0.00205058
$633$	1.86624	0.0741763
$634$	1.35573	0.0538431
$635$	−10.3322	−0.410021
$636$	1.04114	0.0412840
$637$	6.39169	0.253248
$638$	1.73701	0.0687690
$639$	2.96691	0.117369
$640$	−2.93138	−0.115873
$641$	8.00682	0.316250	0.158125	−	0.987419i	$-0.449455\pi$
$641$	8.00682	0.316250	0.158125	+	0.987419i	$0.449455\pi$
$642$	0.0980415	0.00386939
$643$	−38.1796	−1.50566	−0.752829	−	0.658216i	$-0.771311\pi$
$643$	−38.1796	−1.50566	−0.752829	+	0.658216i	$0.771311\pi$
$644$	1.66510	0.0656143
$645$	0.128561	0.00506207
$646$	−0.373518	−0.0146959
$647$	−16.8626	−0.662935	−0.331468	−	0.943467i	$-0.607544\pi$
$647$	−16.8626	−0.662935	−0.331468	+	0.943467i	$0.607544\pi$
$648$	−3.21663	−0.126361
$649$	32.9033	1.29157
$650$	−0.0856108	−0.00335793
$651$	0.356502	0.0139724
$652$	23.8136	0.932614
$653$	34.3974	1.34607	0.673037	−	0.739608i	$-0.264989\pi$
$653$	34.3974	1.34607	0.673037	+	0.739608i	$0.264989\pi$
$654$	−0.130052	−0.00508542
$655$	−12.7925	−0.499844
$656$	−12.6621	−0.494373
$657$	−34.1588	−1.33266
$658$	0.140392	0.00547306
$659$	25.1484	0.979644	0.489822	−	0.871822i	$-0.337062\pi$
$659$	25.1484	0.979644	0.489822	+	0.871822i	$0.337062\pi$
$660$	−1.36283	−0.0530482
$661$	−8.89951	−0.346151	−0.173075	−	0.984909i	$-0.555370\pi$
$661$	−8.89951	−0.346151	−0.173075	+	0.984909i	$0.555370\pi$
$662$	−2.63721	−0.102498
$663$	−0.168176	−0.00653143
$664$	−0.123680	−0.00479972
$665$	1.18881	0.0461002
$666$	1.39120	0.0539078
$667$	14.1464	0.547753
$668$	46.8901	1.81423
$669$	0.381126	0.0147352
$670$	0.319601	0.0123473
$671$	54.5452	2.10570
$672$	−0.0592242	−0.00228462
$673$	4.51598	0.174078	0.0870390	−	0.996205i	$-0.472260\pi$
$673$	4.51598	0.174078	0.0870390	+	0.996205i	$0.472260\pi$
$674$	0.727280	0.0280138
$675$	−1.08536	−0.0417757
$676$	24.1862	0.930239
$677$	23.8113	0.915144	0.457572	−	0.889173i	$-0.348719\pi$
$677$	23.8113	0.915144	0.457572	+	0.889173i	$0.348719\pi$
$678$	−0.248356	−0.00953804
$679$	0.872546	0.0334853
$680$	−0.369587	−0.0141730
$681$	−2.23802	−0.0857611
$682$	−2.31679	−0.0887146
$683$	18.3283	0.701311	0.350656	−	0.936504i	$-0.385959\pi$
$683$	18.3283	0.701311	0.350656	+	0.936504i	$0.385959\pi$
$684$	−23.8337	−0.911305
$685$	−17.7194	−0.677025
$686$	0.379669	0.0144958
$687$	−3.82459	−0.145917
$688$	2.79080	0.106398
$689$	2.65742	0.101240
$690$	0.0477860	0.00181918
$691$	−24.7209	−0.940429	−0.470214	−	0.882552i	$-0.655823\pi$
$691$	−24.7209	−0.940429	−0.470214	+	0.882552i	$0.655823\pi$
$692$	−14.5134	−0.551715
$693$	3.28964	0.124963
$694$	−1.29547	−0.0491752
$695$	−0.0550266	−0.00208728
$696$	−0.335200	−0.0127057
$697$	−3.20671	−0.121463
$698$	−3.30454	−0.125079
$699$	4.54887	0.172054
$700$	0.586888	0.0221823
$701$	−46.7296	−1.76495	−0.882476	−	0.470358i	$-0.844125\pi$
$701$	−46.7296	−1.76495	−0.882476	+	0.470358i	$0.844125\pi$
$702$	0.0929188	0.00350700
$703$	20.4276	0.770442
$704$	−29.3269	−1.10530
$705$	−0.935812	−0.0352447
$706$	−0.672225	−0.0252995
$707$	1.77548	0.0667739
$708$	−3.16793	−0.119058
$709$	51.0727	1.91807	0.959037	−	0.283280i	$-0.0914226\pi$
$709$	51.0727	1.91807	0.959037	+	0.283280i	$0.0914226\pi$
$710$	−0.0925953	−0.00347504
$711$	−0.413831	−0.0155199
$712$	2.34306	0.0878098
$713$	−18.8683	−0.706622
$714$	−0.00496369	−0.000185762 0
$715$	−3.47850	−0.130089
$716$	15.4268	0.576528
$717$	−4.82780	−0.180297
$718$	1.31716	0.0491559
$719$	−8.65620	−0.322822	−0.161411	−	0.986887i	$-0.551604\pi$
$719$	−8.65620	−0.322822	−0.161411	+	0.986887i	$0.551604\pi$
$720$	−11.7152	−0.436601
$721$	−2.73012	−0.101675
$722$	−0.252585	−0.00940023
$723$	−2.11009	−0.0784753
$724$	−47.4500	−1.76346
$725$	4.98610	0.185179
$726$	0.0531368	0.00197209
$727$	20.9713	0.777784	0.388892	−	0.921283i	$-0.372858\pi$
$727$	20.9713	0.777784	0.388892	+	0.921283i	$0.372858\pi$
$728$	−0.100704	−0.00373235
$729$	−25.2297	−0.934434
$730$	1.06607	0.0394571
$731$	0.706777	0.0261411
$732$	−5.25162	−0.194106
$733$	24.0644	0.888838	0.444419	−	0.895819i	$-0.353410\pi$
$733$	24.0644	0.888838	0.444419	+	0.895819i	$0.353410\pi$
$734$	0.755137	0.0278726
$735$	−1.25748	−0.0463829
$736$	3.13451	0.115540
$737$	12.9859	0.478343
$738$	0.880955	0.0324284
$739$	31.4109	1.15547	0.577734	−	0.816225i	$-0.303937\pi$
$739$	31.4109	1.15547	0.577734	+	0.816225i	$0.303937\pi$
$740$	10.0846	0.370718
$741$	0.678403	0.0249218
$742$	0.0784333	0.00287938
$743$	−4.98142	−0.182751	−0.0913753	−	0.995817i	$-0.529126\pi$
$743$	−4.98142	−0.182751	−0.0913753	+	0.995817i	$0.529126\pi$
$744$	0.447083	0.0163909
$745$	−3.51969	−0.128951
$746$	−3.30811	−0.121119
$747$	−0.992860	−0.0363268
$748$	−7.49233	−0.273947
$749$	−1.71548	−0.0626824
$750$	0.0168428	0.000615012 0
$751$	6.52970	0.238272	0.119136	−	0.992878i	$-0.461988\pi$
$751$	6.52970	0.238272	0.119136	+	0.992878i	$0.461988\pi$
$752$	−20.3147	−0.740800
$753$	4.47925	0.163233
$754$	−0.426864	−0.0155455
$755$	−11.4425	−0.416436
$756$	−0.636986	−0.0231670
$757$	−24.6648	−0.896459	−0.448230	−	0.893918i	$-0.647945\pi$
$757$	−24.6648	−0.896459	−0.448230	+	0.893918i	$0.647945\pi$
$758$	1.71818	0.0624070
$759$	1.94162	0.0704764
$760$	1.49087	0.0540795
$761$	−35.1459	−1.27404	−0.637018	−	0.770849i	$-0.719833\pi$
$761$	−35.1459	−1.27404	−0.637018	+	0.770849i	$0.719833\pi$
$762$	−0.174023	−0.00630419
$763$	2.27558	0.0823815
$764$	−8.47001	−0.306434
$765$	−2.96691	−0.107269
$766$	−2.46738	−0.0891502
$767$	−8.08586	−0.291963
$768$	2.78639	0.100545
$769$	−18.0140	−0.649602	−0.324801	−	0.945782i	$-0.605297\pi$
$769$	−18.0140	−0.649602	−0.324801	+	0.945782i	$0.605297\pi$
$770$	−0.102667	−0.00369988
$771$	−5.05937	−0.182209
$772$	−13.3211	−0.479437
$773$	−4.81631	−0.173231	−0.0866153	−	0.996242i	$-0.527605\pi$
$773$	−4.81631	−0.173231	−0.0866153	+	0.996242i	$0.527605\pi$
$774$	−0.194167	−0.00697921
$775$	−6.65037	−0.238888
$776$	1.09425	0.0392811
$777$	0.271463	0.00973869
$778$	2.71866	0.0974689
$779$	12.9355	0.463462
$780$	0.334911	0.0119917
$781$	−3.76230	−0.134626
$782$	0.262709	0.00939446
$783$	−5.41173	−0.193399
$784$	−27.2975	−0.974909
$785$	−6.72066	−0.239871
$786$	−0.215461	−0.00768525
$787$	38.2585	1.36377	0.681883	−	0.731461i	$-0.261161\pi$
$787$	38.2585	1.36377	0.681883	+	0.731461i	$0.261161\pi$
$788$	−4.24455	−0.151206
$789$	−4.64622	−0.165410
$790$	0.0129154	0.000459508 0
$791$	4.34561	0.154512
$792$	4.12548	0.146593
$793$	−13.4043	−0.476000
$794$	1.03681	0.0367950
$795$	−0.522813	−0.0185423
$796$	20.5894	0.729770
$797$	−31.7193	−1.12356	−0.561778	−	0.827288i	$-0.689882\pi$
$797$	−31.7193	−1.12356	−0.561778	+	0.827288i	$0.689882\pi$
$798$	0.0200229	0.000708804 0
$799$	−5.14474	−0.182008
$800$	1.10480	0.0390605
$801$	18.8092	0.664591
$802$	−1.10732	−0.0391007
$803$	43.3162	1.52859
$804$	−1.25029	−0.0440942
$805$	−0.836136	−0.0294699
$806$	0.569343	0.0200543
$807$	−0.781962	−0.0275264
$808$	2.22660	0.0783317
$809$	45.7337	1.60791	0.803955	−	0.594690i	$-0.202725\pi$
$809$	45.7337	1.60791	0.803955	+	0.594690i	$0.202725\pi$
$810$	0.805886	0.0283160
$811$	7.67304	0.269437	0.134719	−	0.990884i	$-0.456987\pi$
$811$	7.67304	0.269437	0.134719	+	0.990884i	$0.456987\pi$
$812$	2.92628	0.102692
$813$	0.608100	0.0213270
$814$	−1.76415	−0.0618336
$815$	−11.9581	−0.418873
$816$	0.718244	0.0251436
$817$	−2.85105	−0.0997457
$818$	0.265349	0.00927772
$819$	−0.808417	−0.0282484
$820$	6.38593	0.223006
$821$	−8.76983	−0.306069	−0.153035	−	0.988221i	$-0.548905\pi$
$821$	−8.76983	−0.306069	−0.153035	+	0.988221i	$0.548905\pi$
$822$	−0.298445	−0.0104095
$823$	44.7639	1.56037	0.780186	−	0.625548i	$-0.215125\pi$
$823$	44.7639	1.56037	0.780186	+	0.625548i	$0.215125\pi$
$824$	−3.42380	−0.119274
$825$	0.684350	0.0238260
$826$	−0.238652	−0.00830378
$827$	31.2064	1.08515	0.542577	−	0.840006i	$-0.317449\pi$
$827$	31.2064	1.08515	0.542577	+	0.840006i	$0.317449\pi$
$828$	16.7631	0.582559
$829$	17.9941	0.624960	0.312480	−	0.949924i	$-0.398840\pi$
$829$	17.9941	0.624960	0.312480	+	0.949924i	$0.398840\pi$
$830$	0.0309865	0.00107556
$831$	−1.14359	−0.0396708
$832$	7.20699	0.249857
$833$	−6.91315	−0.239526
$834$	−0.000926802 0	−3.20925e−5 0
$835$	−23.5460	−0.814843
$836$	30.2232	1.04529
$837$	7.21806	0.249493
$838$	−0.621468	−0.0214683
$839$	−23.6223	−0.815532	−0.407766	−	0.913086i	$-0.633692\pi$
$839$	−23.6223	−0.815532	−0.407766	+	0.913086i	$0.633692\pi$
$840$	0.0198122	0.000683587 0
$841$	−4.13880	−0.142717
$842$	1.18629	0.0408823
$843$	−3.11936	−0.107437
$844$	−20.4318	−0.703290
$845$	−12.1452	−0.417807
$846$	1.41337	0.0485928
$847$	−0.929761	−0.0319470
$848$	−11.3492	−0.389735
$849$	−1.40241	−0.0481307
$850$	0.0925953	0.00317599
$851$	−14.3675	−0.492511
$852$	0.362234	0.0124099
$853$	49.4042	1.69157	0.845783	−	0.533527i	$-0.179134\pi$
$853$	49.4042	1.69157	0.845783	+	0.533527i	$0.179134\pi$
$854$	−0.395625	−0.0135380
$855$	11.9682	0.409303
$856$	−2.15136	−0.0735319
$857$	−2.49944	−0.0853792	−0.0426896	−	0.999088i	$-0.513593\pi$
$857$	−2.49944	−0.0853792	−0.0426896	+	0.999088i	$0.513593\pi$
$858$	−0.0585878	−0.00200015
$859$	−48.3637	−1.65015	−0.825074	−	0.565024i	$-0.808867\pi$
$859$	−48.3637	−1.65015	−0.825074	+	0.565024i	$0.808867\pi$
$860$	−1.40750	−0.0479952
$861$	0.171900	0.00585834
$862$	−0.868504	−0.0295814
$863$	17.8740	0.608437	0.304219	−	0.952602i	$-0.401605\pi$
$863$	17.8740	0.608437	0.304219	+	0.952602i	$0.401605\pi$
$864$	−1.19911	−0.0407945
$865$	7.28792	0.247797
$866$	3.14138	0.106748
$867$	0.181897	0.00617754
$868$	−3.90302	−0.132477
$869$	0.524772	0.0178017
$870$	0.0839799	0.00284719
$871$	−3.19124	−0.108131
$872$	2.85377	0.0966407
$873$	8.78421	0.297300
$874$	−1.05974	−0.0358461
$875$	−0.294707	−0.00996292
$876$	−4.17049	−0.140908
$877$	41.4562	1.39988	0.699938	−	0.714203i	$-0.253211\pi$
$877$	41.4562	1.39988	0.699938	+	0.714203i	$0.253211\pi$
$878$	−1.49227	−0.0503615
$879$	−0.245020	−0.00826433
$880$	14.8559	0.500793
$881$	−14.0235	−0.472463	−0.236231	−	0.971697i	$-0.575912\pi$
$881$	−14.0235	−0.472463	−0.236231	+	0.971697i	$0.575912\pi$
$882$	1.89920	0.0639492
$883$	44.3564	1.49271	0.746356	−	0.665547i	$-0.231802\pi$
$883$	44.3564	1.49271	0.746356	+	0.665547i	$0.231802\pi$
$884$	1.84121	0.0619267
$885$	1.59079	0.0534737
$886$	−3.71869	−0.124932
$887$	−38.4014	−1.28939	−0.644697	−	0.764438i	$-0.723016\pi$
$887$	−38.4014	−1.28939	−0.644697	+	0.764438i	$0.723016\pi$
$888$	0.340437	0.0114243
$889$	3.04497	0.102125
$890$	−0.587023	−0.0196770
$891$	32.7444	1.09698
$892$	−4.17261	−0.139709
$893$	20.7532	0.694481
$894$	−0.0592814	−0.00198267
$895$	−7.74663	−0.258941
$896$	0.863897	0.0288608
$897$	−0.477146	−0.0159314
$898$	1.90397	0.0635362
$899$	−33.1594	−1.10593
$900$	5.90839	0.196946
$901$	−2.87422	−0.0957543
$902$	−1.11712	−0.0371962
$903$	−0.0378877	−0.00126083
$904$	5.44975	0.181256
$905$	23.8271	0.792040
$906$	−0.192724	−0.00640283
$907$	22.2812	0.739836	0.369918	−	0.929064i	$-0.379386\pi$
$907$	22.2812	0.739836	0.369918	+	0.929064i	$0.379386\pi$
$908$	24.5021	0.813129
$909$	17.8744	0.592856
$910$	0.0252301	0.000836371 0
$911$	5.92125	0.196180	0.0980898	−	0.995178i	$-0.468727\pi$
$911$	5.92125	0.196180	0.0980898	+	0.995178i	$0.468727\pi$
$912$	−2.89731	−0.0959394
$913$	1.25903	0.0416678
$914$	−2.64736	−0.0875669
$915$	2.63712	0.0871804
$916$	41.8721	1.38349
$917$	3.77004	0.124498
$918$	−0.100500	−0.00331698
$919$	−1.49097	−0.0491825	−0.0245912	−	0.999698i	$-0.507828\pi$
$919$	−1.49097	−0.0491825	−0.0245912	+	0.999698i	$0.507828\pi$
$920$	−1.04858	−0.0345708
$921$	4.17036	0.137418
$922$	2.59142	0.0853439
$923$	0.924570	0.0304326
$924$	0.401637	0.0132129
$925$	−5.06401	−0.166504
$926$	0.192790	0.00633549
$927$	−27.4850	−0.902727
$928$	5.50864	0.180830
$929$	19.2783	0.632502	0.316251	−	0.948676i	$-0.397576\pi$
$929$	19.2783	0.632502	0.316251	+	0.948676i	$0.397576\pi$
$930$	−0.112011	−0.00367298
$931$	27.8868	0.913953
$932$	−49.8015	−1.63130
$933$	0.554996	0.0181698
$934$	0.529076	0.0173119
$935$	3.76230	0.123040
$936$	−1.01382	−0.0331378
$937$	−15.3484	−0.501409	−0.250705	−	0.968064i	$-0.580662\pi$
$937$	−15.3484	−0.501409	−0.250705	+	0.968064i	$0.580662\pi$
$938$	−0.0941889	−0.00307538
$939$	−2.33670	−0.0762552
$940$	10.2454	0.334167
$941$	47.8865	1.56106	0.780528	−	0.625121i	$-0.214950\pi$
$941$	47.8865	1.56106	0.780528	+	0.625121i	$0.214950\pi$
$942$	−0.113195	−0.00368808
$943$	−9.09801	−0.296272
$944$	34.5329	1.12395
$945$	0.319864	0.0104052
$946$	0.246221	0.00800532
$947$	36.6501	1.19097	0.595483	−	0.803368i	$-0.296961\pi$
$947$	36.6501	1.19097	0.595483	+	0.803368i	$0.296961\pi$
$948$	−0.0505251	−0.00164098
$949$	−10.6448	−0.345544
$950$	−0.373518	−0.0121185
$951$	2.66324	0.0863616
$952$	0.108920	0.00353012
$953$	−44.7039	−1.44810	−0.724050	−	0.689747i	$-0.757722\pi$
$953$	−44.7039	−1.44810	−0.724050	+	0.689747i	$0.757722\pi$
$954$	0.789613	0.0255647
$955$	4.25324	0.137632
$956$	52.8552	1.70946
$957$	3.41224	0.110302
$958$	−0.578530	−0.0186915
$959$	5.22205	0.168629
$960$	−1.41788	−0.0457619
$961$	13.2274	0.426690
$962$	0.433534	0.0139777
$963$	−17.2703	−0.556529
$964$	23.1015	0.744050
$965$	6.68923	0.215334
$966$	−0.0140829	−0.000453109 0
$967$	14.1991	0.456612	0.228306	−	0.973589i	$-0.426681\pi$
$967$	14.1991	0.456612	0.228306	+	0.973589i	$0.426681\pi$
$968$	−1.16600	−0.0374766
$969$	−0.733750	−0.0235714
$970$	−0.274149	−0.00880239
$971$	40.4476	1.29803	0.649013	−	0.760777i	$-0.275182\pi$
$971$	40.4476	1.29803	0.649013	+	0.760777i	$0.275182\pi$
$972$	−9.63690	−0.309104
$973$	0.0162167	0.000519884 0
$974$	3.62885	0.116276
$975$	−0.168176	−0.00538596
$976$	57.2467	1.83242
$977$	21.1254	0.675861	0.337931	−	0.941171i	$-0.390273\pi$
$977$	21.1254	0.675861	0.337931	+	0.941171i	$0.390273\pi$
$978$	−0.201408	−0.00644030
$979$	−23.8517	−0.762303
$980$	13.7670	0.439771
$981$	22.9090	0.731428
$982$	−0.502280	−0.0160284
$983$	39.9264	1.27345	0.636727	−	0.771089i	$-0.280288\pi$
$983$	39.9264	1.27345	0.636727	+	0.771089i	$0.280288\pi$
$984$	0.215577	0.00687234
$985$	2.13141	0.0679124
$986$	0.461689	0.0147032
$987$	0.275791	0.00877851
$988$	−7.42723	−0.236292
$989$	2.00525	0.0637633
$990$	−1.03359	−0.0328495
$991$	0.795914	0.0252830	0.0126415	−	0.999920i	$-0.495976\pi$
$991$	0.795914	0.0252830	0.0126415	+	0.999920i	$0.495976\pi$
$992$	−7.34732	−0.233278
$993$	−5.18061	−0.164402
$994$	0.0272885	0.000865539 0
$995$	−10.3390	−0.327768
$996$	−0.121220	−0.00384099
$997$	8.27112	0.261949	0.130974	−	0.991386i	$-0.458189\pi$
$997$	8.27112	0.261949	0.130974	+	0.991386i	$0.458189\pi$
$998$	1.49126	0.0472050
$999$	5.49629	0.173895

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.a.1.19	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.a.1.19	✓	36	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)

\(f(q)\)	\(=\)	\(q+0.0925953 q^{2} +0.181897 q^{3} -1.99143 q^{4} +1.00000 q^{5} +0.0168428 q^{6} -0.294707 q^{7} -0.369587 q^{8} -2.96691 q^{9} +O(q^{10})\)	\(q+0.0925953 q^{2} +0.181897 q^{3} -1.99143 q^{4} +1.00000 q^{5} +0.0168428 q^{6} -0.294707 q^{7} -0.369587 q^{8} -2.96691 q^{9} +0.0925953 q^{10} +3.76230 q^{11} -0.362234 q^{12} -0.924570 q^{13} -0.0272885 q^{14} +0.181897 q^{15} +3.94863 q^{16} +1.00000 q^{17} -0.274722 q^{18} -4.03388 q^{19} -1.99143 q^{20} -0.0536063 q^{21} +0.348371 q^{22} +2.83718 q^{23} -0.0672268 q^{24} +1.00000 q^{25} -0.0856108 q^{26} -1.08536 q^{27} +0.586888 q^{28} +4.98610 q^{29} +0.0168428 q^{30} -6.65037 q^{31} +1.10480 q^{32} +0.684350 q^{33} +0.0925953 q^{34} -0.294707 q^{35} +5.90839 q^{36} -5.06401 q^{37} -0.373518 q^{38} -0.168176 q^{39} -0.369587 q^{40} -3.20671 q^{41} -0.00496369 q^{42} +0.706777 q^{43} -7.49233 q^{44} -2.96691 q^{45} +0.262709 q^{46} -5.14474 q^{47} +0.718244 q^{48} -6.91315 q^{49} +0.0925953 q^{50} +0.181897 q^{51} +1.84121 q^{52} -2.87422 q^{53} -0.100500 q^{54} +3.76230 q^{55} +0.108920 q^{56} -0.733750 q^{57} +0.461689 q^{58} +8.74553 q^{59} -0.362234 q^{60} +14.4979 q^{61} -0.615793 q^{62} +0.874371 q^{63} -7.79496 q^{64} -0.924570 q^{65} +0.0633676 q^{66} +3.45160 q^{67} -1.99143 q^{68} +0.516074 q^{69} -0.0272885 q^{70} -1.00000 q^{71} +1.09653 q^{72} +11.5132 q^{73} -0.468904 q^{74} +0.181897 q^{75} +8.03317 q^{76} -1.10878 q^{77} -0.0155723 q^{78} +0.139482 q^{79} +3.94863 q^{80} +8.70332 q^{81} -0.296926 q^{82} +0.334644 q^{83} +0.106753 q^{84} +1.00000 q^{85} +0.0654443 q^{86} +0.906956 q^{87} -1.39050 q^{88} -6.33966 q^{89} -0.274722 q^{90} +0.272477 q^{91} -5.65003 q^{92} -1.20968 q^{93} -0.476379 q^{94} -4.03388 q^{95} +0.200960 q^{96} -2.96072 q^{97} -0.640125 q^{98} -11.1624 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

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