LMFDB - Embedded newform 8043.2.a.r.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.54493 q^{2} -1.00000 q^{3} +4.47665 q^{4} +0.653154 q^{5} +2.54493 q^{6} -1.00000 q^{7} -6.30289 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.54493 q^{2} -1.00000 q^{3} +4.47665 q^{4} +0.653154 q^{5} +2.54493 q^{6} -1.00000 q^{7} -6.30289 q^{8} +1.00000 q^{9} -1.66223 q^{10} +1.19393 q^{11} -4.47665 q^{12} -6.03807 q^{13} +2.54493 q^{14} -0.653154 q^{15} +7.08708 q^{16} -2.30025 q^{17} -2.54493 q^{18} +5.19533 q^{19} +2.92394 q^{20} +1.00000 q^{21} -3.03845 q^{22} -1.76702 q^{23} +6.30289 q^{24} -4.57339 q^{25} +15.3664 q^{26} -1.00000 q^{27} -4.47665 q^{28} +0.998454 q^{29} +1.66223 q^{30} -0.532726 q^{31} -5.43033 q^{32} -1.19393 q^{33} +5.85396 q^{34} -0.653154 q^{35} +4.47665 q^{36} +3.77194 q^{37} -13.2217 q^{38} +6.03807 q^{39} -4.11675 q^{40} -7.36403 q^{41} -2.54493 q^{42} -1.47714 q^{43} +5.34478 q^{44} +0.653154 q^{45} +4.49693 q^{46} +1.89201 q^{47} -7.08708 q^{48} +1.00000 q^{49} +11.6389 q^{50} +2.30025 q^{51} -27.0303 q^{52} +9.51992 q^{53} +2.54493 q^{54} +0.779817 q^{55} +6.30289 q^{56} -5.19533 q^{57} -2.54099 q^{58} +13.9296 q^{59} -2.92394 q^{60} +11.8014 q^{61} +1.35575 q^{62} -1.00000 q^{63} -0.354383 q^{64} -3.94379 q^{65} +3.03845 q^{66} -5.22028 q^{67} -10.2974 q^{68} +1.76702 q^{69} +1.66223 q^{70} -3.73726 q^{71} -6.30289 q^{72} +7.15594 q^{73} -9.59931 q^{74} +4.57339 q^{75} +23.2577 q^{76} -1.19393 q^{77} -15.3664 q^{78} -11.2861 q^{79} +4.62895 q^{80} +1.00000 q^{81} +18.7409 q^{82} -1.39987 q^{83} +4.47665 q^{84} -1.50242 q^{85} +3.75922 q^{86} -0.998454 q^{87} -7.52517 q^{88} +16.8126 q^{89} -1.66223 q^{90} +6.03807 q^{91} -7.91031 q^{92} +0.532726 q^{93} -4.81502 q^{94} +3.39335 q^{95} +5.43033 q^{96} -3.96788 q^{97} -2.54493 q^{98} +1.19393 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9} - 10 q^{10} + 31 q^{11} - 45 q^{12} - 32 q^{13} - 3 q^{14} + 9 q^{15} + 43 q^{16} - 36 q^{17} + 3 q^{18} - 13 q^{19} - 19 q^{20} + 46 q^{21} - 13 q^{22} + 24 q^{23} - 6 q^{24} + 35 q^{25} - 11 q^{26} - 46 q^{27} - 45 q^{28} + 11 q^{29} + 10 q^{30} - 23 q^{31} + 5 q^{32} - 31 q^{33} - 35 q^{34} + 9 q^{35} + 45 q^{36} - 37 q^{37} - 32 q^{38} + 32 q^{39} - 28 q^{40} - 27 q^{41} + 3 q^{42} - 7 q^{43} + 46 q^{44} - 9 q^{45} + 16 q^{46} - 18 q^{47} - 43 q^{48} + 46 q^{49} + 10 q^{50} + 36 q^{51} - 62 q^{52} - 62 q^{53} - 3 q^{54} - 28 q^{55} - 6 q^{56} + 13 q^{57} - 36 q^{58} - 3 q^{59} + 19 q^{60} - 31 q^{61} - 41 q^{62} - 46 q^{63} + 42 q^{64} + 2 q^{65} + 13 q^{66} - 9 q^{67} - 70 q^{68} - 24 q^{69} + 10 q^{70} + 77 q^{71} + 6 q^{72} - 38 q^{73} + 14 q^{74} - 35 q^{75} - 41 q^{76} - 31 q^{77} + 11 q^{78} + 8 q^{79} - 59 q^{80} + 46 q^{81} - 53 q^{82} - 38 q^{83} + 45 q^{84} - 26 q^{85} + 37 q^{86} - 11 q^{87} - 26 q^{88} - 39 q^{89} - 10 q^{90} + 32 q^{91} + 2 q^{92} + 23 q^{93} - 55 q^{94} + 35 q^{95} - 5 q^{96} - 61 q^{97} + 3 q^{98} + 31 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9 - 10 * q^10 + 31 * q^11 - 45 * q^12 - 32 * q^13 - 3 * q^14 + 9 * q^15 + 43 * q^16 - 36 * q^17 + 3 * q^18 - 13 * q^19 - 19 * q^20 + 46 * q^21 - 13 * q^22 + 24 * q^23 - 6 * q^24 + 35 * q^25 - 11 * q^26 - 46 * q^27 - 45 * q^28 + 11 * q^29 + 10 * q^30 - 23 * q^31 + 5 * q^32 - 31 * q^33 - 35 * q^34 + 9 * q^35 + 45 * q^36 - 37 * q^37 - 32 * q^38 + 32 * q^39 - 28 * q^40 - 27 * q^41 + 3 * q^42 - 7 * q^43 + 46 * q^44 - 9 * q^45 + 16 * q^46 - 18 * q^47 - 43 * q^48 + 46 * q^49 + 10 * q^50 + 36 * q^51 - 62 * q^52 - 62 * q^53 - 3 * q^54 - 28 * q^55 - 6 * q^56 + 13 * q^57 - 36 * q^58 - 3 * q^59 + 19 * q^60 - 31 * q^61 - 41 * q^62 - 46 * q^63 + 42 * q^64 + 2 * q^65 + 13 * q^66 - 9 * q^67 - 70 * q^68 - 24 * q^69 + 10 * q^70 + 77 * q^71 + 6 * q^72 - 38 * q^73 + 14 * q^74 - 35 * q^75 - 41 * q^76 - 31 * q^77 + 11 * q^78 + 8 * q^79 - 59 * q^80 + 46 * q^81 - 53 * q^82 - 38 * q^83 + 45 * q^84 - 26 * q^85 + 37 * q^86 - 11 * q^87 - 26 * q^88 - 39 * q^89 - 10 * q^90 + 32 * q^91 + 2 * q^92 + 23 * q^93 - 55 * q^94 + 35 * q^95 - 5 * q^96 - 61 * q^97 + 3 * q^98 + 31 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.54493	−1.79953	−0.899767	−	0.436370i	$-0.856264\pi$
$2$	−2.54493	−1.79953	−0.899767	+	0.436370i	$0.856264\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.47665	2.23832
$5$	0.653154	0.292099	0.146050	−	0.989277i	$-0.453344\pi$
$5$	0.653154	0.292099	0.146050	+	0.989277i	$0.453344\pi$
$6$	2.54493	1.03896
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−6.30289	−2.22841
$9$	1.00000	0.333333
$10$	−1.66223	−0.525643
$11$	1.19393	0.359982	0.179991	−	0.983668i	$-0.442393\pi$
$11$	1.19393	0.359982	0.179991	+	0.983668i	$0.442393\pi$
$12$	−4.47665	−1.29230
$13$	−6.03807	−1.67466	−0.837329	−	0.546699i	$-0.815884\pi$
$13$	−6.03807	−1.67466	−0.837329	+	0.546699i	$0.815884\pi$
$14$	2.54493	0.680160
$15$	−0.653154	−0.168644
$16$	7.08708	1.77177
$17$	−2.30025	−0.557892	−0.278946	−	0.960307i	$-0.589985\pi$
$17$	−2.30025	−0.557892	−0.278946	+	0.960307i	$0.589985\pi$
$18$	−2.54493	−0.599845
$19$	5.19533	1.19189	0.595945	−	0.803025i	$-0.296777\pi$
$19$	5.19533	1.19189	0.595945	+	0.803025i	$0.296777\pi$
$20$	2.92394	0.653813
$21$	1.00000	0.218218
$22$	−3.03845	−0.647800
$23$	−1.76702	−0.368448	−0.184224	−	0.982884i	$-0.558977\pi$
$23$	−1.76702	−0.368448	−0.184224	+	0.982884i	$0.558977\pi$
$24$	6.30289	1.28657
$25$	−4.57339	−0.914678
$26$	15.3664	3.01361
$27$	−1.00000	−0.192450
$28$	−4.47665	−0.846007
$29$	0.998454	0.185408	0.0927041	−	0.995694i	$-0.470449\pi$
$29$	0.998454	0.185408	0.0927041	+	0.995694i	$0.470449\pi$
$30$	1.66223	0.303480
$31$	−0.532726	−0.0956804	−0.0478402	−	0.998855i	$-0.515234\pi$
$31$	−0.532726	−0.0956804	−0.0478402	+	0.998855i	$0.515234\pi$
$32$	−5.43033	−0.959955
$33$	−1.19393	−0.207836
$34$	5.85396	1.00395
$35$	−0.653154	−0.110403
$36$	4.47665	0.746108
$37$	3.77194	0.620103	0.310052	−	0.950720i	$-0.399654\pi$
$37$	3.77194	0.620103	0.310052	+	0.950720i	$0.399654\pi$
$38$	−13.2217	−2.14485
$39$	6.03807	0.966865
$40$	−4.11675	−0.650916
$41$	−7.36403	−1.15007	−0.575034	−	0.818129i	$-0.695011\pi$
$41$	−7.36403	−1.15007	−0.575034	+	0.818129i	$0.695011\pi$
$42$	−2.54493	−0.392691
$43$	−1.47714	−0.225262	−0.112631	−	0.993637i	$-0.535928\pi$
$43$	−1.47714	−0.225262	−0.112631	+	0.993637i	$0.535928\pi$
$44$	5.34478	0.805756
$45$	0.653154	0.0973664
$46$	4.49693	0.663036
$47$	1.89201	0.275978	0.137989	−	0.990434i	$-0.455936\pi$
$47$	1.89201	0.275978	0.137989	+	0.990434i	$0.455936\pi$
$48$	−7.08708	−1.02293
$49$	1.00000	0.142857
$50$	11.6389	1.64599
$51$	2.30025	0.322099
$52$	−27.0303	−3.74843
$53$	9.51992	1.30766	0.653830	−	0.756641i	$-0.273161\pi$
$53$	9.51992	1.30766	0.653830	+	0.756641i	$0.273161\pi$
$54$	2.54493	0.346321
$55$	0.779817	0.105150
$56$	6.30289	0.842259
$57$	−5.19533	−0.688139
$58$	−2.54099	−0.333649
$59$	13.9296	1.81348	0.906738	−	0.421694i	$-0.138564\pi$
$59$	13.9296	1.81348	0.906738	+	0.421694i	$0.138564\pi$
$60$	−2.92394	−0.377479
$61$	11.8014	1.51102	0.755508	−	0.655140i	$-0.227390\pi$
$61$	11.8014	1.51102	0.755508	+	0.655140i	$0.227390\pi$
$62$	1.35575	0.172180
$63$	−1.00000	−0.125988
$64$	−0.354383	−0.0442979
$65$	−3.94379	−0.489167
$66$	3.03845	0.374007
$67$	−5.22028	−0.637759	−0.318880	−	0.947795i	$-0.603307\pi$
$67$	−5.22028	−0.637759	−0.318880	+	0.947795i	$0.603307\pi$
$68$	−10.2974	−1.24874
$69$	1.76702	0.212724
$70$	1.66223	0.198674
$71$	−3.73726	−0.443531	−0.221765	−	0.975100i	$-0.571182\pi$
$71$	−3.73726	−0.443531	−0.221765	+	0.975100i	$0.571182\pi$
$72$	−6.30289	−0.742802
$73$	7.15594	0.837539	0.418770	−	0.908093i	$-0.362461\pi$
$73$	7.15594	0.837539	0.418770	+	0.908093i	$0.362461\pi$
$74$	−9.59931	−1.11590
$75$	4.57339	0.528090
$76$	23.2577	2.66784
$77$	−1.19393	−0.136060
$78$	−15.3664	−1.73991
$79$	−11.2861	−1.26979	−0.634893	−	0.772600i	$-0.718956\pi$
$79$	−11.2861	−1.26979	−0.634893	+	0.772600i	$0.718956\pi$
$80$	4.62895	0.517533
$81$	1.00000	0.111111
$82$	18.7409	2.06959
$83$	−1.39987	−0.153655	−0.0768276	−	0.997044i	$-0.524479\pi$
$83$	−1.39987	−0.153655	−0.0768276	+	0.997044i	$0.524479\pi$
$84$	4.47665	0.488442
$85$	−1.50242	−0.162960
$86$	3.75922	0.405367
$87$	−0.998454	−0.107046
$88$	−7.52517	−0.802186
$89$	16.8126	1.78213	0.891067	−	0.453871i	$-0.149957\pi$
$89$	16.8126	1.78213	0.891067	+	0.453871i	$0.149957\pi$
$90$	−1.66223	−0.175214
$91$	6.03807	0.632962
$92$	−7.91031	−0.824707
$93$	0.532726	0.0552411
$94$	−4.81502	−0.496631
$95$	3.39335	0.348150
$96$	5.43033	0.554230
$97$	−3.96788	−0.402877	−0.201439	−	0.979501i	$-0.564562\pi$
$97$	−3.96788	−0.402877	−0.201439	+	0.979501i	$0.564562\pi$
$98$	−2.54493	−0.257076
$99$	1.19393	0.119994
$100$	−20.4735	−2.04735
$101$	15.5441	1.54670	0.773349	−	0.633981i	$-0.218580\pi$
$101$	15.5441	1.54670	0.773349	+	0.633981i	$0.218580\pi$
$102$	−5.85396	−0.579629
$103$	−8.67908	−0.855175	−0.427588	−	0.903974i	$-0.640636\pi$
$103$	−8.67908	−0.855175	−0.427588	+	0.903974i	$0.640636\pi$
$104$	38.0573	3.73182
$105$	0.653154	0.0637413
$106$	−24.2275	−2.35318
$107$	4.46605	0.431750	0.215875	−	0.976421i	$-0.430740\pi$
$107$	4.46605	0.431750	0.215875	+	0.976421i	$0.430740\pi$
$108$	−4.47665	−0.430766
$109$	−1.08114	−0.103554	−0.0517772	−	0.998659i	$-0.516489\pi$
$109$	−1.08114	−0.103554	−0.0517772	+	0.998659i	$0.516489\pi$
$110$	−1.98458	−0.189222
$111$	−3.77194	−0.358017
$112$	−7.08708	−0.669666
$113$	5.77733	0.543486	0.271743	−	0.962370i	$-0.412400\pi$
$113$	5.77733	0.543486	0.271743	+	0.962370i	$0.412400\pi$
$114$	13.2217	1.23833
$115$	−1.15413	−0.107623
$116$	4.46973	0.415004
$117$	−6.03807	−0.558220
$118$	−35.4497	−3.26341
$119$	2.30025	0.210863
$120$	4.11675	0.375806
$121$	−9.57454	−0.870413
$122$	−30.0337	−2.71912
$123$	7.36403	0.663992
$124$	−2.38483	−0.214164
$125$	−6.25290	−0.559276
$126$	2.54493	0.226720
$127$	14.5272	1.28908	0.644541	−	0.764570i	$-0.277048\pi$
$127$	14.5272	1.28908	0.644541	+	0.764570i	$0.277048\pi$
$128$	11.7625	1.03967
$129$	1.47714	0.130055
$130$	10.0366	0.880272
$131$	3.34258	0.292043	0.146021	−	0.989281i	$-0.453353\pi$
$131$	3.34258	0.292043	0.146021	+	0.989281i	$0.453353\pi$
$132$	−5.34478	−0.465204
$133$	−5.19533	−0.450492
$134$	13.2852	1.14767
$135$	−0.653154	−0.0562145
$136$	14.4982	1.24321
$137$	−6.91912	−0.591140	−0.295570	−	0.955321i	$-0.595510\pi$
$137$	−6.91912	−0.591140	−0.295570	+	0.955321i	$0.595510\pi$
$138$	−4.49693	−0.382804
$139$	3.49706	0.296617	0.148309	−	0.988941i	$-0.452617\pi$
$139$	3.49706	0.296617	0.148309	+	0.988941i	$0.452617\pi$
$140$	−2.92394	−0.247118
$141$	−1.89201	−0.159336
$142$	9.51104	0.798149
$143$	−7.20900	−0.602847
$144$	7.08708	0.590590
$145$	0.652144	0.0541576
$146$	−18.2113	−1.50718
$147$	−1.00000	−0.0824786
$148$	16.8857	1.38799
$149$	1.53642	0.125868	0.0629342	−	0.998018i	$-0.479954\pi$
$149$	1.53642	0.125868	0.0629342	+	0.998018i	$0.479954\pi$
$150$	−11.6389	−0.950315
$151$	−18.2109	−1.48198	−0.740992	−	0.671514i	$-0.765644\pi$
$151$	−18.2109	−1.48198	−0.740992	+	0.671514i	$0.765644\pi$
$152$	−32.7456	−2.65602
$153$	−2.30025	−0.185964
$154$	3.03845	0.244845
$155$	−0.347952	−0.0279482
$156$	27.0303	2.16416
$157$	−10.4170	−0.831368	−0.415684	−	0.909509i	$-0.636458\pi$
$157$	−10.4170	−0.831368	−0.415684	+	0.909509i	$0.636458\pi$
$158$	28.7223	2.28502
$159$	−9.51992	−0.754978
$160$	−3.54684	−0.280402
$161$	1.76702	0.139260
$162$	−2.54493	−0.199948
$163$	−4.66172	−0.365134	−0.182567	−	0.983193i	$-0.558441\pi$
$163$	−4.66172	−0.365134	−0.182567	+	0.983193i	$0.558441\pi$
$164$	−32.9662	−2.57423
$165$	−0.779817	−0.0607086
$166$	3.56256	0.276508
$167$	−22.8303	−1.76666	−0.883329	−	0.468753i	$-0.844703\pi$
$167$	−22.8303	−1.76666	−0.883329	+	0.468753i	$0.844703\pi$
$168$	−6.30289	−0.486278
$169$	23.4583	1.80448
$170$	3.82354	0.293252
$171$	5.19533	0.397297
$172$	−6.61266	−0.504210
$173$	3.15917	0.240187	0.120094	−	0.992763i	$-0.461681\pi$
$173$	3.15917	0.240187	0.120094	+	0.992763i	$0.461681\pi$
$174$	2.54099	0.192632
$175$	4.57339	0.345716
$176$	8.46145	0.637805
$177$	−13.9296	−1.04701
$178$	−42.7869	−3.20701
$179$	−20.5253	−1.53413	−0.767065	−	0.641570i	$-0.778284\pi$
$179$	−20.5253	−1.53413	−0.767065	+	0.641570i	$0.778284\pi$
$180$	2.92394	0.217938
$181$	−3.91699	−0.291147	−0.145574	−	0.989347i	$-0.546503\pi$
$181$	−3.91699	−0.291147	−0.145574	+	0.989347i	$0.546503\pi$
$182$	−15.3664	−1.13904
$183$	−11.8014	−0.872385
$184$	11.1373	0.821053
$185$	2.46366	0.181132
$186$	−1.35575	−0.0994083
$187$	−2.74632	−0.200831
$188$	8.46985	0.617728
$189$	1.00000	0.0727393
$190$	−8.63583	−0.626509
$191$	2.65349	0.192000	0.0960000	−	0.995381i	$-0.469395\pi$
$191$	2.65349	0.192000	0.0960000	+	0.995381i	$0.469395\pi$
$192$	0.354383	0.0255754
$193$	−0.652868	−0.0469944	−0.0234972	−	0.999724i	$-0.507480\pi$
$193$	−0.652868	−0.0469944	−0.0234972	+	0.999724i	$0.507480\pi$
$194$	10.0980	0.724992
$195$	3.94379	0.282420
$196$	4.47665	0.319761
$197$	8.23478	0.586703	0.293352	−	0.956005i	$-0.405229\pi$
$197$	8.23478	0.586703	0.293352	+	0.956005i	$0.405229\pi$
$198$	−3.03845	−0.215933
$199$	−14.3628	−1.01815	−0.509075	−	0.860722i	$-0.670013\pi$
$199$	−14.3628	−1.01815	−0.509075	+	0.860722i	$0.670013\pi$
$200$	28.8256	2.03827
$201$	5.22028	0.368210
$202$	−39.5586	−2.78334
$203$	−0.998454	−0.0700777
$204$	10.2974	0.720963
$205$	−4.80985	−0.335934
$206$	22.0876	1.53892
$207$	−1.76702	−0.122816
$208$	−42.7923	−2.96711
$209$	6.20284	0.429059
$210$	−1.66223	−0.114705
$211$	12.2832	0.845614	0.422807	−	0.906220i	$-0.361045\pi$
$211$	12.2832	0.845614	0.422807	+	0.906220i	$0.361045\pi$
$212$	42.6173	2.92697
$213$	3.73726	0.256073
$214$	−11.3658	−0.776948
$215$	−0.964802	−0.0657990
$216$	6.30289	0.428857
$217$	0.532726	0.0361638
$218$	2.75142	0.186350
$219$	−7.15594	−0.483553
$220$	3.49096	0.235361
$221$	13.8891	0.934279
$222$	9.59931	0.644264
$223$	−28.3992	−1.90175	−0.950876	−	0.309573i	$-0.899814\pi$
$223$	−28.3992	−1.90175	−0.950876	+	0.309573i	$0.899814\pi$
$224$	5.43033	0.362829
$225$	−4.57339	−0.304893
$226$	−14.7029	−0.978022
$227$	−11.9645	−0.794115	−0.397057	−	0.917794i	$-0.629969\pi$
$227$	−11.9645	−0.794115	−0.397057	+	0.917794i	$0.629969\pi$
$228$	−23.2577	−1.54028
$229$	−18.4185	−1.21713	−0.608566	−	0.793503i	$-0.708255\pi$
$229$	−18.4185	−1.21713	−0.608566	+	0.793503i	$0.708255\pi$
$230$	2.93718	0.193672
$231$	1.19393	0.0785545
$232$	−6.29314	−0.413165
$233$	0.572087	0.0374786	0.0187393	−	0.999824i	$-0.494035\pi$
$233$	0.572087	0.0374786	0.0187393	+	0.999824i	$0.494035\pi$
$234$	15.3664	1.00454
$235$	1.23577	0.0806129
$236$	62.3578	4.05915
$237$	11.2861	0.733111
$238$	−5.85396	−0.379456
$239$	21.8421	1.41285	0.706424	−	0.707789i	$-0.250307\pi$
$239$	21.8421	1.41285	0.706424	+	0.707789i	$0.250307\pi$
$240$	−4.62895	−0.298798
$241$	−8.65469	−0.557497	−0.278749	−	0.960364i	$-0.589920\pi$
$241$	−8.65469	−0.557497	−0.278749	+	0.960364i	$0.589920\pi$
$242$	24.3665	1.56634
$243$	−1.00000	−0.0641500
$244$	52.8308	3.38214
$245$	0.653154	0.0417285
$246$	−18.7409	−1.19488
$247$	−31.3698	−1.99601
$248$	3.35771	0.213215
$249$	1.39987	0.0887129
$250$	15.9132	1.00644
$251$	22.4681	1.41817	0.709087	−	0.705121i	$-0.249107\pi$
$251$	22.4681	1.41817	0.709087	+	0.705121i	$0.249107\pi$
$252$	−4.47665	−0.282002
$253$	−2.10969	−0.132635
$254$	−36.9707	−2.31975
$255$	1.50242	0.0940849
$256$	−29.2260	−1.82663
$257$	−18.3958	−1.14750	−0.573749	−	0.819031i	$-0.694512\pi$
$257$	−18.3958	−1.14750	−0.573749	+	0.819031i	$0.694512\pi$
$258$	−3.75922	−0.234039
$259$	−3.77194	−0.234377
$260$	−17.6549	−1.09491
$261$	0.998454	0.0618028
$262$	−8.50663	−0.525541
$263$	25.7004	1.58475	0.792376	−	0.610033i	$-0.208844\pi$
$263$	25.7004	1.58475	0.792376	+	0.610033i	$0.208844\pi$
$264$	7.52517	0.463142
$265$	6.21797	0.381967
$266$	13.2217	0.810677
$267$	−16.8126	−1.02892
$268$	−23.3694	−1.42751
$269$	−8.97219	−0.547044	−0.273522	−	0.961866i	$-0.588189\pi$
$269$	−8.97219	−0.547044	−0.273522	+	0.961866i	$0.588189\pi$
$270$	1.66223	0.101160
$271$	−7.59837	−0.461568	−0.230784	−	0.973005i	$-0.574129\pi$
$271$	−7.59837	−0.461568	−0.230784	+	0.973005i	$0.574129\pi$
$272$	−16.3021	−0.988457
$273$	−6.03807	−0.365441
$274$	17.6087	1.06378
$275$	−5.46029	−0.329268
$276$	7.91031	0.476145
$277$	−8.65277	−0.519895	−0.259947	−	0.965623i	$-0.583705\pi$
$277$	−8.65277	−0.519895	−0.259947	+	0.965623i	$0.583705\pi$
$278$	−8.89977	−0.533773
$279$	−0.532726	−0.0318935
$280$	4.11675	0.246023
$281$	25.8249	1.54058	0.770292	−	0.637692i	$-0.220111\pi$
$281$	25.8249	1.54058	0.770292	+	0.637692i	$0.220111\pi$
$282$	4.81502	0.286730
$283$	30.6401	1.82136	0.910682	−	0.413107i	$-0.135557\pi$
$283$	30.6401	1.82136	0.910682	+	0.413107i	$0.135557\pi$
$284$	−16.7304	−0.992766
$285$	−3.39335	−0.201005
$286$	18.3464	1.08484
$287$	7.36403	0.434685
$288$	−5.43033	−0.319985
$289$	−11.7089	−0.688756
$290$	−1.65966	−0.0974585
$291$	3.96788	0.232601
$292$	32.0346	1.87468
$293$	−3.53796	−0.206690	−0.103345	−	0.994646i	$-0.532955\pi$
$293$	−3.53796	−0.206690	−0.103345	+	0.994646i	$0.532955\pi$
$294$	2.54493	0.148423
$295$	9.09815	0.529715
$296$	−23.7741	−1.38184
$297$	−1.19393	−0.0692786
$298$	−3.91007	−0.226505
$299$	10.6694	0.617025
$300$	20.4735	1.18204
$301$	1.47714	0.0851412
$302$	46.3454	2.66688
$303$	−15.5441	−0.892986
$304$	36.8197	2.11176
$305$	7.70813	0.441367
$306$	5.85396	0.334649
$307$	10.0032	0.570914	0.285457	−	0.958392i	$-0.407855\pi$
$307$	10.0032	0.570914	0.285457	+	0.958392i	$0.407855\pi$
$308$	−5.34478	−0.304547
$309$	8.67908	0.493736
$310$	0.885512	0.0502937
$311$	−26.3258	−1.49280	−0.746400	−	0.665497i	$-0.768219\pi$
$311$	−26.3258	−1.49280	−0.746400	+	0.665497i	$0.768219\pi$
$312$	−38.0573	−2.15457
$313$	3.31813	0.187552	0.0937760	−	0.995593i	$-0.470106\pi$
$313$	3.31813	0.187552	0.0937760	+	0.995593i	$0.470106\pi$
$314$	26.5105	1.49608
$315$	−0.653154	−0.0368010
$316$	−50.5239	−2.84219
$317$	9.07897	0.509926	0.254963	−	0.966951i	$-0.417937\pi$
$317$	9.07897	0.509926	0.254963	+	0.966951i	$0.417937\pi$
$318$	24.2275	1.35861
$319$	1.19208	0.0667436
$320$	−0.231467	−0.0129394
$321$	−4.46605	−0.249271
$322$	−4.49693	−0.250604
$323$	−11.9506	−0.664947
$324$	4.47665	0.248703
$325$	27.6144	1.53177
$326$	11.8637	0.657071
$327$	1.08114	0.0597871
$328$	46.4147	2.56282
$329$	−1.89201	−0.104310
$330$	1.98458	0.109247
$331$	−15.8431	−0.870817	−0.435409	−	0.900233i	$-0.643396\pi$
$331$	−15.8431	−0.870817	−0.435409	+	0.900233i	$0.643396\pi$
$332$	−6.26671	−0.343930
$333$	3.77194	0.206701
$334$	58.1013	3.17916
$335$	−3.40965	−0.186289
$336$	7.08708	0.386632
$337$	−17.4833	−0.952378	−0.476189	−	0.879343i	$-0.657982\pi$
$337$	−17.4833	−0.952378	−0.476189	+	0.879343i	$0.657982\pi$
$338$	−59.6996	−3.24723
$339$	−5.77733	−0.313782
$340$	−6.72579	−0.364757
$341$	−0.636035	−0.0344432
$342$	−13.2217	−0.714950
$343$	−1.00000	−0.0539949
$344$	9.31027	0.501976
$345$	1.15413	0.0621365
$346$	−8.03986	−0.432225
$347$	31.6932	1.70138	0.850689	−	0.525669i	$-0.176185\pi$
$347$	31.6932	1.70138	0.850689	+	0.525669i	$0.176185\pi$
$348$	−4.46973	−0.239603
$349$	30.9001	1.65405	0.827023	−	0.562168i	$-0.190033\pi$
$349$	30.9001	1.65405	0.827023	+	0.562168i	$0.190033\pi$
$350$	−11.6389	−0.622127
$351$	6.03807	0.322288
$352$	−6.48340	−0.345567
$353$	1.01319	0.0539267	0.0269633	−	0.999636i	$-0.491416\pi$
$353$	1.01319	0.0539267	0.0269633	+	0.999636i	$0.491416\pi$
$354$	35.4497	1.88413
$355$	−2.44100	−0.129555
$356$	75.2642	3.98899
$357$	−2.30025	−0.121742
$358$	52.2353	2.76072
$359$	−0.190730	−0.0100663	−0.00503316	−	0.999987i	$-0.501602\pi$
$359$	−0.190730	−0.0100663	−0.00503316	+	0.999987i	$0.501602\pi$
$360$	−4.11675	−0.216972
$361$	7.99148	0.420604
$362$	9.96844	0.523930
$363$	9.57454	0.502533
$364$	27.0303	1.41677
$365$	4.67393	0.244645
$366$	30.0337	1.56989
$367$	8.56403	0.447039	0.223519	−	0.974699i	$-0.428245\pi$
$367$	8.56403	0.447039	0.223519	+	0.974699i	$0.428245\pi$
$368$	−12.5230	−0.652806
$369$	−7.36403	−0.383356
$370$	−6.26983	−0.325953
$371$	−9.51992	−0.494249
$372$	2.38483	0.123648
$373$	−13.8203	−0.715585	−0.357793	−	0.933801i	$-0.616471\pi$
$373$	−13.8203	−0.715585	−0.357793	+	0.933801i	$0.616471\pi$
$374$	6.98919	0.361403
$375$	6.25290	0.322898
$376$	−11.9251	−0.614991
$377$	−6.02873	−0.310496
$378$	−2.54493	−0.130897
$379$	−0.688074	−0.0353440	−0.0176720	−	0.999844i	$-0.505625\pi$
$379$	−0.688074	−0.0353440	−0.0176720	+	0.999844i	$0.505625\pi$
$380$	15.1908	0.779273
$381$	−14.5272	−0.744252
$382$	−6.75294	−0.345511
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	−11.7625	−0.600254
$385$	−0.779817	−0.0397431
$386$	1.66150	0.0845681
$387$	−1.47714	−0.0750875
$388$	−17.7628	−0.901770
$389$	7.00207	0.355019	0.177509	−	0.984119i	$-0.443196\pi$
$389$	7.00207	0.355019	0.177509	+	0.984119i	$0.443196\pi$
$390$	−10.0366	−0.508225
$391$	4.06458	0.205555
$392$	−6.30289	−0.318344
$393$	−3.34258	−0.168611
$394$	−20.9569	−1.05579
$395$	−7.37156	−0.370903
$396$	5.34478	0.268585
$397$	−30.3976	−1.52561	−0.762806	−	0.646627i	$-0.776179\pi$
$397$	−30.3976	−1.52561	−0.762806	+	0.646627i	$0.776179\pi$
$398$	36.5522	1.83220
$399$	5.19533	0.260092
$400$	−32.4120	−1.62060
$401$	−28.9454	−1.44546	−0.722731	−	0.691129i	$-0.757113\pi$
$401$	−28.9454	−1.44546	−0.722731	+	0.691129i	$0.757113\pi$
$402$	−13.2852	−0.662607
$403$	3.21664	0.160232
$404$	69.5856	3.46201
$405$	0.653154	0.0324555
$406$	2.54099	0.126107
$407$	4.50342	0.223226
$408$	−14.4982	−0.717768
$409$	7.58066	0.374839	0.187420	−	0.982280i	$-0.439988\pi$
$409$	7.58066	0.374839	0.187420	+	0.982280i	$0.439988\pi$
$410$	12.2407	0.604525
$411$	6.91912	0.341295
$412$	−38.8532	−1.91416
$413$	−13.9296	−0.685430
$414$	4.49693	0.221012
$415$	−0.914328	−0.0448826
$416$	32.7887	1.60760
$417$	−3.49706	−0.171252
$418$	−15.7858	−0.772107
$419$	−13.0014	−0.635158	−0.317579	−	0.948232i	$-0.602870\pi$
$419$	−13.0014	−0.635158	−0.317579	+	0.948232i	$0.602870\pi$
$420$	2.92394	0.142674
$421$	25.4042	1.23813	0.619063	−	0.785342i	$-0.287513\pi$
$421$	25.4042	1.23813	0.619063	+	0.785342i	$0.287513\pi$
$422$	−31.2600	−1.52171
$423$	1.89201	0.0919926
$424$	−60.0029	−2.91400
$425$	10.5199	0.510292
$426$	−9.51104	−0.460812
$427$	−11.8014	−0.571110
$428$	19.9930	0.966396
$429$	7.20900	0.348054
$430$	2.45535	0.118407
$431$	11.9791	0.577015	0.288508	−	0.957478i	$-0.406841\pi$
$431$	11.9791	0.577015	0.288508	+	0.957478i	$0.406841\pi$
$432$	−7.08708	−0.340977
$433$	6.48753	0.311771	0.155885	−	0.987775i	$-0.450177\pi$
$433$	6.48753	0.311771	0.155885	+	0.987775i	$0.450177\pi$
$434$	−1.35575	−0.0650780
$435$	−0.652144	−0.0312679
$436$	−4.83988	−0.231788
$437$	−9.18024	−0.439150
$438$	18.2113	0.870171
$439$	−3.11823	−0.148825	−0.0744124	−	0.997228i	$-0.523708\pi$
$439$	−3.11823	−0.148825	−0.0744124	+	0.997228i	$0.523708\pi$
$440$	−4.91510	−0.234318
$441$	1.00000	0.0476190
$442$	−35.3466	−1.68127
$443$	25.3407	1.20397	0.601986	−	0.798506i	$-0.294376\pi$
$443$	25.3407	1.20397	0.601986	+	0.798506i	$0.294376\pi$
$444$	−16.8857	−0.801358
$445$	10.9812	0.520560
$446$	72.2739	3.42227
$447$	−1.53642	−0.0726702
$448$	0.354383	0.0167430
$449$	−1.25808	−0.0593726	−0.0296863	−	0.999559i	$-0.509451\pi$
$449$	−1.25808	−0.0593726	−0.0296863	+	0.999559i	$0.509451\pi$
$450$	11.6389	0.548665
$451$	−8.79210	−0.414004
$452$	25.8631	1.21650
$453$	18.2109	0.855623
$454$	30.4489	1.42904
$455$	3.94379	0.184888
$456$	32.7456	1.53345
$457$	−7.98212	−0.373388	−0.186694	−	0.982418i	$-0.559777\pi$
$457$	−7.98212	−0.373388	−0.186694	+	0.982418i	$0.559777\pi$
$458$	46.8738	2.19027
$459$	2.30025	0.107366
$460$	−5.16665	−0.240896
$461$	−1.45292	−0.0676690	−0.0338345	−	0.999427i	$-0.510772\pi$
$461$	−1.45292	−0.0676690	−0.0338345	+	0.999427i	$0.510772\pi$
$462$	−3.03845	−0.141362
$463$	−2.56945	−0.119412	−0.0597062	−	0.998216i	$-0.519016\pi$
$463$	−2.56945	−0.119412	−0.0597062	+	0.998216i	$0.519016\pi$
$464$	7.07613	0.328501
$465$	0.347952	0.0161359
$466$	−1.45592	−0.0674441
$467$	−21.7817	−1.00794	−0.503969	−	0.863722i	$-0.668128\pi$
$467$	−21.7817	−1.00794	−0.503969	+	0.863722i	$0.668128\pi$
$468$	−27.0303	−1.24948
$469$	5.22028	0.241050
$470$	−3.14495	−0.145066
$471$	10.4170	0.479990
$472$	−87.7965	−4.04116
$473$	−1.76360	−0.0810904
$474$	−28.7223	−1.31926
$475$	−23.7603	−1.09020
$476$	10.2974	0.471981
$477$	9.51992	0.435887
$478$	−55.5865	−2.54247
$479$	−15.2197	−0.695404	−0.347702	−	0.937605i	$-0.613038\pi$
$479$	−15.2197	−0.695404	−0.347702	+	0.937605i	$0.613038\pi$
$480$	3.54684	0.161890
$481$	−22.7752	−1.03846
$482$	22.0255	1.00324
$483$	−1.76702	−0.0804020
$484$	−42.8619	−1.94827
$485$	−2.59164	−0.117680
$486$	2.54493	0.115440
$487$	12.3727	0.560662	0.280331	−	0.959903i	$-0.409556\pi$
$487$	12.3727	0.560662	0.280331	+	0.959903i	$0.409556\pi$
$488$	−74.3829	−3.36716
$489$	4.66172	0.210810
$490$	−1.66223	−0.0750918
$491$	18.7686	0.847013	0.423507	−	0.905893i	$-0.360799\pi$
$491$	18.7686	0.847013	0.423507	+	0.905893i	$0.360799\pi$
$492$	32.9662	1.48623
$493$	−2.29669	−0.103438
$494$	79.8338	3.59189
$495$	0.779817	0.0350501
$496$	−3.77547	−0.169524
$497$	3.73726	0.167639
$498$	−3.56256	−0.159642
$499$	−19.4462	−0.870532	−0.435266	−	0.900302i	$-0.643346\pi$
$499$	−19.4462	−0.870532	−0.435266	+	0.900302i	$0.643346\pi$
$500$	−27.9920	−1.25184
$501$	22.8303	1.01998
$502$	−57.1797	−2.55205
$503$	−11.2344	−0.500917	−0.250458	−	0.968127i	$-0.580581\pi$
$503$	−11.2344	−0.500917	−0.250458	+	0.968127i	$0.580581\pi$
$504$	6.30289	0.280753
$505$	10.1527	0.451789
$506$	5.36899	0.238681
$507$	−23.4583	−1.04182
$508$	65.0333	2.88538
$509$	−28.2408	−1.25175	−0.625876	−	0.779922i	$-0.715259\pi$
$509$	−28.2408	−1.25175	−0.625876	+	0.779922i	$0.715259\pi$
$510$	−3.82354	−0.169309
$511$	−7.15594	−0.316560
$512$	50.8530	2.24740
$513$	−5.19533	−0.229380
$514$	46.8160	2.06496
$515$	−5.66877	−0.249796
$516$	6.61266	0.291106
$517$	2.25892	0.0993470
$518$	9.59931	0.421770
$519$	−3.15917	−0.138672
$520$	24.8572	1.09006
$521$	−39.7535	−1.74163	−0.870817	−	0.491608i	$-0.836409\pi$
$521$	−39.7535	−1.74163	−0.870817	+	0.491608i	$0.836409\pi$
$522$	−2.54099	−0.111216
$523$	10.4490	0.456905	0.228452	−	0.973555i	$-0.426633\pi$
$523$	10.4490	0.456905	0.228452	+	0.973555i	$0.426633\pi$
$524$	14.9636	0.653687
$525$	−4.57339	−0.199599
$526$	−65.4055	−2.85182
$527$	1.22540	0.0533794
$528$	−8.46145	−0.368237
$529$	−19.8777	−0.864246
$530$	−15.8243	−0.687362
$531$	13.9296	0.604492
$532$	−23.2577	−1.00835
$533$	44.4645	1.92597
$534$	42.7869	1.85157
$535$	2.91702	0.126114
$536$	32.9028	1.42119
$537$	20.5253	0.885730
$538$	22.8336	0.984425
$539$	1.19393	0.0514260
$540$	−2.92394	−0.125826
$541$	22.8104	0.980697	0.490348	−	0.871527i	$-0.336870\pi$
$541$	22.8104	0.980697	0.490348	+	0.871527i	$0.336870\pi$
$542$	19.3373	0.830608
$543$	3.91699	0.168094
$544$	12.4911	0.535552
$545$	−0.706150	−0.0302481
$546$	15.3664	0.657623
$547$	2.27882	0.0974355	0.0487178	−	0.998813i	$-0.484487\pi$
$547$	2.27882	0.0974355	0.0487178	+	0.998813i	$0.484487\pi$
$548$	−30.9745	−1.32316
$549$	11.8014	0.503672
$550$	13.8960	0.592528
$551$	5.18730	0.220986
$552$	−11.1373	−0.474035
$553$	11.2861	0.479934
$554$	22.0207	0.935568
$555$	−2.46366	−0.104576
$556$	15.6551	0.663925
$557$	3.84320	0.162842	0.0814209	−	0.996680i	$-0.474054\pi$
$557$	3.84320	0.162842	0.0814209	+	0.996680i	$0.474054\pi$
$558$	1.35575	0.0573934
$559$	8.91910	0.377238
$560$	−4.62895	−0.195609
$561$	2.74632	0.115950
$562$	−65.7224	−2.77233
$563$	−17.2426	−0.726689	−0.363344	−	0.931655i	$-0.618365\pi$
$563$	−17.2426	−0.726689	−0.363344	+	0.931655i	$0.618365\pi$
$564$	−8.46985	−0.356645
$565$	3.77349	0.158752
$566$	−77.9768	−3.27761
$567$	−1.00000	−0.0419961
$568$	23.5555	0.988367
$569$	9.57793	0.401528	0.200764	−	0.979640i	$-0.435658\pi$
$569$	9.57793	0.401528	0.200764	+	0.979640i	$0.435658\pi$
$570$	8.63583	0.361715
$571$	37.5764	1.57252	0.786262	−	0.617893i	$-0.212013\pi$
$571$	37.5764	1.57252	0.786262	+	0.617893i	$0.212013\pi$
$572$	−32.2722	−1.34937
$573$	−2.65349	−0.110851
$574$	−18.7409	−0.782231
$575$	8.08126	0.337012
$576$	−0.354383	−0.0147660
$577$	−1.29582	−0.0539456	−0.0269728	−	0.999636i	$-0.508587\pi$
$577$	−1.29582	−0.0539456	−0.0269728	+	0.999636i	$0.508587\pi$
$578$	29.7982	1.23944
$579$	0.652868	0.0271322
$580$	2.91942	0.121222
$581$	1.39987	0.0580762
$582$	−10.0980	−0.418574
$583$	11.3661	0.470734
$584$	−45.1031	−1.86638
$585$	−3.94379	−0.163056
$586$	9.00385	0.371946
$587$	−39.1695	−1.61670	−0.808349	−	0.588704i	$-0.799638\pi$
$587$	−39.1695	−1.61670	−0.808349	+	0.588704i	$0.799638\pi$
$588$	−4.47665	−0.184614
$589$	−2.76769	−0.114041
$590$	−23.1541	−0.953240
$591$	−8.23478	−0.338733
$592$	26.7321	1.09868
$593$	−37.8633	−1.55486	−0.777429	−	0.628971i	$-0.783477\pi$
$593$	−37.8633	−1.55486	−0.777429	+	0.628971i	$0.783477\pi$
$594$	3.03845	0.124669
$595$	1.50242	0.0615931
$596$	6.87801	0.281734
$597$	14.3628	0.587830
$598$	−27.1527	−1.11036
$599$	1.30766	0.0534295	0.0267148	−	0.999643i	$-0.491495\pi$
$599$	1.30766	0.0534295	0.0267148	+	0.999643i	$0.491495\pi$
$600$	−28.8256	−1.17680
$601$	33.8183	1.37948	0.689739	−	0.724058i	$-0.257725\pi$
$601$	33.8183	1.37948	0.689739	+	0.724058i	$0.257725\pi$
$602$	−3.75922	−0.153214
$603$	−5.22028	−0.212586
$604$	−81.5239	−3.31716
$605$	−6.25365	−0.254247
$606$	39.5586	1.60696
$607$	−26.8457	−1.08964	−0.544818	−	0.838555i	$-0.683401\pi$
$607$	−26.8457	−1.08964	−0.544818	+	0.838555i	$0.683401\pi$
$608$	−28.2124	−1.14416
$609$	0.998454	0.0404594
$610$	−19.6166	−0.794254
$611$	−11.4241	−0.462169
$612$	−10.2974	−0.416248
$613$	−32.8829	−1.32813	−0.664064	−	0.747676i	$-0.731170\pi$
$613$	−32.8829	−1.32813	−0.664064	+	0.747676i	$0.731170\pi$
$614$	−25.4575	−1.02738
$615$	4.80985	0.193952
$616$	7.52517	0.303198
$617$	−16.8598	−0.678751	−0.339375	−	0.940651i	$-0.610216\pi$
$617$	−16.8598	−0.678751	−0.339375	+	0.940651i	$0.610216\pi$
$618$	−22.0876	−0.888494
$619$	12.9501	0.520510	0.260255	−	0.965540i	$-0.416193\pi$
$619$	12.9501	0.520510	0.260255	+	0.965540i	$0.416193\pi$
$620$	−1.55766	−0.0625571
$621$	1.76702	0.0709079
$622$	66.9973	2.68635
$623$	−16.8126	−0.673584
$624$	42.7923	1.71306
$625$	18.7828	0.751314
$626$	−8.44440	−0.337506
$627$	−6.20284	−0.247717
$628$	−46.6333	−1.86087
$629$	−8.67640	−0.345951
$630$	1.66223	0.0662247
$631$	18.4310	0.733726	0.366863	−	0.930275i	$-0.380432\pi$
$631$	18.4310	0.733726	0.366863	+	0.930275i	$0.380432\pi$
$632$	71.1350	2.82960
$633$	−12.2832	−0.488215
$634$	−23.1053	−0.917629
$635$	9.48851	0.376540
$636$	−42.6173	−1.68989
$637$	−6.03807	−0.239237
$638$	−3.03375	−0.120107
$639$	−3.73726	−0.147844
$640$	7.68274	0.303687
$641$	−23.5493	−0.930143	−0.465072	−	0.885273i	$-0.653971\pi$
$641$	−23.5493	−0.930143	−0.465072	+	0.885273i	$0.653971\pi$
$642$	11.3658	0.448571
$643$	16.8622	0.664980	0.332490	−	0.943107i	$-0.392111\pi$
$643$	16.8622	0.664980	0.332490	+	0.943107i	$0.392111\pi$
$644$	7.91031	0.311710
$645$	0.964802	0.0379890
$646$	30.4133	1.19659
$647$	−24.9387	−0.980440	−0.490220	−	0.871599i	$-0.663084\pi$
$647$	−24.9387	−0.980440	−0.490220	+	0.871599i	$0.663084\pi$
$648$	−6.30289	−0.247601
$649$	16.6309	0.652819
$650$	−70.2767	−2.75648
$651$	−0.532726	−0.0208792
$652$	−20.8689	−0.817288
$653$	−9.04005	−0.353764	−0.176882	−	0.984232i	$-0.556601\pi$
$653$	−9.04005	−0.353764	−0.176882	+	0.984232i	$0.556601\pi$
$654$	−2.75142	−0.107589
$655$	2.18322	0.0853055
$656$	−52.1895	−2.03766
$657$	7.15594	0.279180
$658$	4.81502	0.187709
$659$	−0.105993	−0.00412890	−0.00206445	−	0.999998i	$-0.500657\pi$
$659$	−0.105993	−0.00412890	−0.00206445	+	0.999998i	$0.500657\pi$
$660$	−3.49096	−0.135886
$661$	−5.71796	−0.222403	−0.111201	−	0.993798i	$-0.535470\pi$
$661$	−5.71796	−0.222403	−0.111201	+	0.993798i	$0.535470\pi$
$662$	40.3196	1.56707
$663$	−13.8891	−0.539406
$664$	8.82320	0.342406
$665$	−3.39335	−0.131588
$666$	−9.59931	−0.371966
$667$	−1.76428	−0.0683134
$668$	−102.203	−3.95435
$669$	28.3992	1.09798
$670$	8.67730	0.335233
$671$	14.0900	0.543938
$672$	−5.43033	−0.209479
$673$	−2.53355	−0.0976610	−0.0488305	−	0.998807i	$-0.515549\pi$
$673$	−2.53355	−0.0976610	−0.0488305	+	0.998807i	$0.515549\pi$
$674$	44.4938	1.71384
$675$	4.57339	0.176030
$676$	105.014	4.03902
$677$	39.8846	1.53289	0.766445	−	0.642310i	$-0.222024\pi$
$677$	39.8846	1.53289	0.766445	+	0.642310i	$0.222024\pi$
$678$	14.7029	0.564661
$679$	3.96788	0.152273
$680$	9.46956	0.363141
$681$	11.9645	0.458482
$682$	1.61866	0.0619818
$683$	35.3133	1.35123	0.675613	−	0.737257i	$-0.263879\pi$
$683$	35.3133	1.35123	0.675613	+	0.737257i	$0.263879\pi$
$684$	23.2577	0.889279
$685$	−4.51925	−0.172672
$686$	2.54493	0.0971657
$687$	18.4185	0.702711
$688$	−10.4686	−0.399113
$689$	−57.4819	−2.18989
$690$	−2.93718	−0.111817
$691$	−21.0769	−0.801805	−0.400902	−	0.916121i	$-0.631303\pi$
$691$	−21.0769	−0.801805	−0.400902	+	0.916121i	$0.631303\pi$
$692$	14.1425	0.537617
$693$	−1.19393	−0.0453535
$694$	−80.6568	−3.06169
$695$	2.28412	0.0866416
$696$	6.29314	0.238541
$697$	16.9391	0.641614
$698$	−78.6385	−2.97651
$699$	−0.572087	−0.0216383
$700$	20.4735	0.773824
$701$	2.94436	0.111207	0.0556035	−	0.998453i	$-0.482292\pi$
$701$	2.94436	0.111207	0.0556035	+	0.998453i	$0.482292\pi$
$702$	−15.3664	−0.579969
$703$	19.5965	0.739096
$704$	−0.423107	−0.0159464
$705$	−1.23577	−0.0465419
$706$	−2.57849	−0.0970429
$707$	−15.5441	−0.584597
$708$	−62.3578	−2.34355
$709$	−10.5517	−0.396278	−0.198139	−	0.980174i	$-0.563490\pi$
$709$	−10.5517	−0.396278	−0.198139	+	0.980174i	$0.563490\pi$
$710$	6.21217	0.233139
$711$	−11.2861	−0.423262
$712$	−105.968	−3.97132
$713$	0.941336	0.0352533
$714$	5.85396	0.219079
$715$	−4.70859	−0.176091
$716$	−91.8844	−3.43388
$717$	−21.8421	−0.815708
$718$	0.485393	0.0181147
$719$	40.0706	1.49438	0.747190	−	0.664611i	$-0.231403\pi$
$719$	40.0706	1.49438	0.747190	+	0.664611i	$0.231403\pi$
$720$	4.62895	0.172511
$721$	8.67908	0.323226
$722$	−20.3377	−0.756891
$723$	8.65469	0.321871
$724$	−17.5350	−0.651682
$725$	−4.56632	−0.169589
$726$	−24.3665	−0.904326
$727$	0.0865511	0.00321000	0.00160500	−	0.999999i	$-0.499489\pi$
$727$	0.0865511	0.00321000	0.00160500	+	0.999999i	$0.499489\pi$
$728$	−38.0573	−1.41050
$729$	1.00000	0.0370370
$730$	−11.8948	−0.440246
$731$	3.39780	0.125672
$732$	−52.8308	−1.95268
$733$	−26.8082	−0.990183	−0.495092	−	0.868841i	$-0.664865\pi$
$733$	−26.8082	−0.990183	−0.495092	+	0.868841i	$0.664865\pi$
$734$	−21.7948	−0.804462
$735$	−0.653154	−0.0240919
$736$	9.59548	0.353694
$737$	−6.23263	−0.229582
$738$	18.7409	0.689863
$739$	35.9316	1.32177	0.660883	−	0.750489i	$-0.270182\pi$
$739$	35.9316	1.32177	0.660883	+	0.750489i	$0.270182\pi$
$740$	11.0289	0.405431
$741$	31.3698	1.15240
$742$	24.2275	0.889419
$743$	18.0399	0.661820	0.330910	−	0.943662i	$-0.392644\pi$
$743$	18.0399	0.661820	0.330910	+	0.943662i	$0.392644\pi$
$744$	−3.35771	−0.123100
$745$	1.00352	0.0367661
$746$	35.1715	1.28772
$747$	−1.39987	−0.0512184
$748$	−12.2943	−0.449525
$749$	−4.46605	−0.163186
$750$	−15.9132	−0.581066
$751$	−12.8246	−0.467975	−0.233987	−	0.972240i	$-0.575177\pi$
$751$	−12.8246	−0.467975	−0.233987	+	0.972240i	$0.575177\pi$
$752$	13.4088	0.488969
$753$	−22.4681	−0.818783
$754$	15.3427	0.558748
$755$	−11.8945	−0.432886
$756$	4.47665	0.162814
$757$	−0.141466	−0.00514166	−0.00257083	−	0.999997i	$-0.500818\pi$
$757$	−0.141466	−0.00514166	−0.00257083	+	0.999997i	$0.500818\pi$
$758$	1.75110	0.0636027
$759$	2.10969	0.0765767
$760$	−21.3879	−0.775821
$761$	−4.87013	−0.176542	−0.0882711	−	0.996096i	$-0.528134\pi$
$761$	−4.87013	−0.176542	−0.0882711	+	0.996096i	$0.528134\pi$
$762$	36.9707	1.33931
$763$	1.08114	0.0391399
$764$	11.8788	0.429758
$765$	−1.50242	−0.0543200
$766$	2.54493	0.0919519
$767$	−84.1077	−3.03695
$768$	29.2260	1.05460
$769$	−38.2323	−1.37869	−0.689345	−	0.724433i	$-0.742102\pi$
$769$	−38.2323	−1.37869	−0.689345	+	0.724433i	$0.742102\pi$
$770$	1.98458	0.0715191
$771$	18.3958	0.662509
$772$	−2.92266	−0.105189
$773$	−38.7462	−1.39360	−0.696802	−	0.717263i	$-0.745394\pi$
$773$	−38.7462	−1.39360	−0.696802	+	0.717263i	$0.745394\pi$
$774$	3.75922	0.135122
$775$	2.43636	0.0875168
$776$	25.0091	0.897775
$777$	3.77194	0.135318
$778$	−17.8197	−0.638869
$779$	−38.2586	−1.37076
$780$	17.6549	0.632148
$781$	−4.46201	−0.159663
$782$	−10.3440	−0.369902
$783$	−0.998454	−0.0356818
$784$	7.08708	0.253110
$785$	−6.80391	−0.242842
$786$	8.50663	0.303421
$787$	−14.2054	−0.506368	−0.253184	−	0.967418i	$-0.581478\pi$
$787$	−14.2054	−0.506368	−0.253184	+	0.967418i	$0.581478\pi$
$788$	36.8642	1.31323
$789$	−25.7004	−0.914957
$790$	18.7601	0.667453
$791$	−5.77733	−0.205418
$792$	−7.52517	−0.267395
$793$	−71.2577	−2.53044
$794$	77.3596	2.74539
$795$	−6.21797	−0.220529
$796$	−64.2971	−2.27895
$797$	−14.5191	−0.514295	−0.257147	−	0.966372i	$-0.582783\pi$
$797$	−14.5191	−0.514295	−0.257147	+	0.966372i	$0.582783\pi$
$798$	−13.2217	−0.468044
$799$	−4.35209	−0.153966
$800$	24.8350	0.878050
$801$	16.8126	0.594045
$802$	73.6638	2.60116
$803$	8.54365	0.301499
$804$	23.3694	0.824174
$805$	1.15413	0.0406779
$806$	−8.18610	−0.288343
$807$	8.97219	0.315836
$808$	−97.9728	−3.44667
$809$	−40.1133	−1.41031	−0.705154	−	0.709054i	$-0.749122\pi$
$809$	−40.1133	−1.41031	−0.705154	+	0.709054i	$0.749122\pi$
$810$	−1.66223	−0.0584047
$811$	−19.9302	−0.699844	−0.349922	−	0.936779i	$-0.613792\pi$
$811$	−19.9302	−0.699844	−0.349922	+	0.936779i	$0.613792\pi$
$812$	−4.46973	−0.156857
$813$	7.59837	0.266486
$814$	−11.4609	−0.401703
$815$	−3.04482	−0.106655
$816$	16.3021	0.570686
$817$	−7.67426	−0.268488
$818$	−19.2922	−0.674536
$819$	6.03807	0.210987
$820$	−21.5320	−0.751929
$821$	−20.8653	−0.728204	−0.364102	−	0.931359i	$-0.618624\pi$
$821$	−20.8653	−0.728204	−0.364102	+	0.931359i	$0.618624\pi$
$822$	−17.6087	−0.614172
$823$	10.8508	0.378235	0.189117	−	0.981954i	$-0.439437\pi$
$823$	10.8508	0.378235	0.189117	+	0.981954i	$0.439437\pi$
$824$	54.7033	1.90568
$825$	5.46029	0.190103
$826$	35.4497	1.23345
$827$	−19.6746	−0.684152	−0.342076	−	0.939672i	$-0.611130\pi$
$827$	−19.6746	−0.684152	−0.342076	+	0.939672i	$0.611130\pi$
$828$	−7.91031	−0.274902
$829$	3.61444	0.125535	0.0627674	−	0.998028i	$-0.480007\pi$
$829$	3.61444	0.125535	0.0627674	+	0.998028i	$0.480007\pi$
$830$	2.32690	0.0807678
$831$	8.65277	0.300161
$832$	2.13979	0.0741839
$833$	−2.30025	−0.0796989
$834$	8.89977	0.308174
$835$	−14.9117	−0.516039
$836$	27.7679	0.960374
$837$	0.532726	0.0184137
$838$	33.0875	1.14299
$839$	−19.9002	−0.687031	−0.343515	−	0.939147i	$-0.611618\pi$
$839$	−19.9002	−0.687031	−0.343515	+	0.939147i	$0.611618\pi$
$840$	−4.11675	−0.142041
$841$	−28.0031	−0.965624
$842$	−64.6518	−2.22805
$843$	−25.8249	−0.889456
$844$	54.9878	1.89276
$845$	15.3219	0.527088
$846$	−4.81502	−0.165544
$847$	9.57454	0.328985
$848$	67.4684	2.31688
$849$	−30.6401	−1.05157
$850$	−26.7725	−0.918288
$851$	−6.66508	−0.228476
$852$	16.7304	0.573174
$853$	−22.9982	−0.787444	−0.393722	−	0.919230i	$-0.628813\pi$
$853$	−22.9982	−0.787444	−0.393722	+	0.919230i	$0.628813\pi$
$854$	30.0337	1.02773
$855$	3.39335	0.116050
$856$	−28.1490	−0.962114
$857$	36.9410	1.26188	0.630940	−	0.775831i	$-0.282669\pi$
$857$	36.9410	1.26188	0.630940	+	0.775831i	$0.282669\pi$
$858$	−18.3464	−0.626335
$859$	−47.0601	−1.60567	−0.802835	−	0.596202i	$-0.796676\pi$
$859$	−47.0601	−1.60567	−0.802835	+	0.596202i	$0.796676\pi$
$860$	−4.31908	−0.147279
$861$	−7.36403	−0.250966
$862$	−30.4860	−1.03836
$863$	3.31507	0.112846	0.0564231	−	0.998407i	$-0.482030\pi$
$863$	3.31507	0.112846	0.0564231	+	0.998407i	$0.482030\pi$
$864$	5.43033	0.184743
$865$	2.06342	0.0701585
$866$	−16.5103	−0.561043
$867$	11.7089	0.397654
$868$	2.38483	0.0809463
$869$	−13.4748	−0.457100
$870$	1.65966	0.0562677
$871$	31.5204	1.06803
$872$	6.81430	0.230761
$873$	−3.96788	−0.134292
$874$	23.3630	0.790266
$875$	6.25290	0.211386
$876$	−32.0346	−1.08235
$877$	13.4082	0.452763	0.226381	−	0.974039i	$-0.427310\pi$
$877$	13.4082	0.452763	0.226381	+	0.974039i	$0.427310\pi$
$878$	7.93566	0.267815
$879$	3.53796	0.119333
$880$	5.52662	0.186302
$881$	−13.4969	−0.454721	−0.227361	−	0.973811i	$-0.573010\pi$
$881$	−13.4969	−0.454721	−0.227361	+	0.973811i	$0.573010\pi$
$882$	−2.54493	−0.0856921
$883$	1.11191	0.0374186	0.0187093	−	0.999825i	$-0.494044\pi$
$883$	1.11191	0.0374186	0.0187093	+	0.999825i	$0.494044\pi$
$884$	62.1764	2.09122
$885$	−9.09815	−0.305831
$886$	−64.4902	−2.16659
$887$	12.5454	0.421234	0.210617	−	0.977569i	$-0.432453\pi$
$887$	12.5454	0.421234	0.210617	+	0.977569i	$0.432453\pi$
$888$	23.7741	0.797807
$889$	−14.5272	−0.487227
$890$	−27.9464	−0.936766
$891$	1.19393	0.0399980
$892$	−127.133	−4.25674
$893$	9.82961	0.328935
$894$	3.91007	0.130772
$895$	−13.4061	−0.448118
$896$	−11.7625	−0.392959
$897$	−10.6694	−0.356240
$898$	3.20173	0.106843
$899$	−0.531903	−0.0177399
$900$	−20.4735	−0.682449
$901$	−21.8982	−0.729534
$902$	22.3753	0.745014
$903$	−1.47714	−0.0491563
$904$	−36.4139	−1.21111
$905$	−2.55839	−0.0850439
$906$	−46.3454	−1.53972
$907$	20.7212	0.688035	0.344018	−	0.938963i	$-0.388212\pi$
$907$	20.7212	0.688035	0.344018	+	0.938963i	$0.388212\pi$
$908$	−53.5610	−1.77749
$909$	15.5441	0.515566
$910$	−10.0366	−0.332712
$911$	−33.7560	−1.11839	−0.559193	−	0.829037i	$-0.688889\pi$
$911$	−33.7560	−1.11839	−0.559193	+	0.829037i	$0.688889\pi$
$912$	−36.8197	−1.21922
$913$	−1.67134	−0.0553131
$914$	20.3139	0.671925
$915$	−7.70813	−0.254823
$916$	−82.4533	−2.72434
$917$	−3.34258	−0.110382
$918$	−5.85396	−0.193210
$919$	−4.88079	−0.161003	−0.0805013	−	0.996755i	$-0.525652\pi$
$919$	−4.88079	−0.161003	−0.0805013	+	0.996755i	$0.525652\pi$
$920$	7.27437	0.239829
$921$	−10.0032	−0.329617
$922$	3.69756	0.121773
$923$	22.5658	0.742763
$924$	5.34478	0.175830
$925$	−17.2506	−0.567195
$926$	6.53906	0.214887
$927$	−8.67908	−0.285058
$928$	−5.42193	−0.177984
$929$	49.6433	1.62875	0.814373	−	0.580342i	$-0.197081\pi$
$929$	49.6433	1.62875	0.814373	+	0.580342i	$0.197081\pi$
$930$	−0.885512	−0.0290371
$931$	5.19533	0.170270
$932$	2.56103	0.0838894
$933$	26.3258	0.861869
$934$	55.4329	1.81382
$935$	−1.79377	−0.0586626
$936$	38.0573	1.24394
$937$	−49.7507	−1.62529	−0.812643	−	0.582762i	$-0.801972\pi$
$937$	−49.7507	−1.62529	−0.812643	+	0.582762i	$0.801972\pi$
$938$	−13.2852	−0.433778
$939$	−3.31813	−0.108283
$940$	5.53212	0.180438
$941$	−46.5993	−1.51909	−0.759547	−	0.650452i	$-0.774579\pi$
$941$	−46.5993	−1.51909	−0.759547	+	0.650452i	$0.774579\pi$
$942$	−26.5105	−0.863759
$943$	13.0124	0.423741
$944$	98.7201	3.21306
$945$	0.653154	0.0212471
$946$	4.48823	0.145925
$947$	40.4419	1.31419	0.657093	−	0.753810i	$-0.271786\pi$
$947$	40.4419	1.31419	0.657093	+	0.753810i	$0.271786\pi$
$948$	50.5239	1.64094
$949$	−43.2080	−1.40259
$950$	60.4682	1.96185
$951$	−9.07897	−0.294406
$952$	−14.4982	−0.469890
$953$	−29.1082	−0.942907	−0.471453	−	0.881891i	$-0.656270\pi$
$953$	−29.1082	−0.942907	−0.471453	+	0.881891i	$0.656270\pi$
$954$	−24.2275	−0.784394
$955$	1.73314	0.0560831
$956$	97.7793	3.16241
$957$	−1.19208	−0.0385345
$958$	38.7329	1.25140
$959$	6.91912	0.223430
$960$	0.231467	0.00747055
$961$	−30.7162	−0.990845
$962$	57.9613	1.86875
$963$	4.46605	0.143917
$964$	−38.7440	−1.24786
$965$	−0.426423	−0.0137270
$966$	4.49693	0.144686
$967$	−43.8908	−1.41143	−0.705716	−	0.708495i	$-0.749374\pi$
$967$	−43.8908	−1.41143	−0.705716	+	0.708495i	$0.749374\pi$
$968$	60.3473	1.93963
$969$	11.9506	0.383907
$970$	6.59552	0.211770
$971$	−56.6431	−1.81776	−0.908882	−	0.417053i	$-0.863063\pi$
$971$	−56.6431	−1.81776	−0.908882	+	0.417053i	$0.863063\pi$
$972$	−4.47665	−0.143589
$973$	−3.49706	−0.112111
$974$	−31.4877	−1.00893
$975$	−27.6144	−0.884370
$976$	83.6376	2.67717
$977$	−41.4031	−1.32460	−0.662301	−	0.749238i	$-0.730420\pi$
$977$	−41.4031	−1.32460	−0.662301	+	0.749238i	$0.730420\pi$
$978$	−11.8637	−0.379360
$979$	20.0730	0.641536
$980$	2.92394	0.0934018
$981$	−1.08114	−0.0345181
$982$	−47.7646	−1.52423
$983$	41.5963	1.32672	0.663359	−	0.748302i	$-0.269130\pi$
$983$	41.5963	1.32672	0.663359	+	0.748302i	$0.269130\pi$
$984$	−46.4147	−1.47965
$985$	5.37857	0.171376
$986$	5.84491	0.186140
$987$	1.89201	0.0602233
$988$	−140.431	−4.46772
$989$	2.61014	0.0829976
$990$	−1.98458	−0.0630739
$991$	−2.25635	−0.0716753	−0.0358377	−	0.999358i	$-0.511410\pi$
$991$	−2.25635	−0.0716753	−0.0358377	+	0.999358i	$0.511410\pi$
$992$	2.89288	0.0918490
$993$	15.8431	0.502766
$994$	−9.51104	−0.301672
$995$	−9.38111	−0.297401
$996$	6.26671	0.198568
$997$	−15.8221	−0.501091	−0.250545	−	0.968105i	$-0.580610\pi$
$997$	−15.8221	−0.501091	−0.250545	+	0.968105i	$0.580610\pi$
$998$	49.4892	1.56655
$999$	−3.77194	−0.119339

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.r.1.3	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.r.1.3	✓	46	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.54493 q^{2} -1.00000 q^{3} +4.47665 q^{4} +0.653154 q^{5} +2.54493 q^{6} -1.00000 q^{7} -6.30289 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.54493 q^{2} -1.00000 q^{3} +4.47665 q^{4} +0.653154 q^{5} +2.54493 q^{6} -1.00000 q^{7} -6.30289 q^{8} +1.00000 q^{9} -1.66223 q^{10} +1.19393 q^{11} -4.47665 q^{12} -6.03807 q^{13} +2.54493 q^{14} -0.653154 q^{15} +7.08708 q^{16} -2.30025 q^{17} -2.54493 q^{18} +5.19533 q^{19} +2.92394 q^{20} +1.00000 q^{21} -3.03845 q^{22} -1.76702 q^{23} +6.30289 q^{24} -4.57339 q^{25} +15.3664 q^{26} -1.00000 q^{27} -4.47665 q^{28} +0.998454 q^{29} +1.66223 q^{30} -0.532726 q^{31} -5.43033 q^{32} -1.19393 q^{33} +5.85396 q^{34} -0.653154 q^{35} +4.47665 q^{36} +3.77194 q^{37} -13.2217 q^{38} +6.03807 q^{39} -4.11675 q^{40} -7.36403 q^{41} -2.54493 q^{42} -1.47714 q^{43} +5.34478 q^{44} +0.653154 q^{45} +4.49693 q^{46} +1.89201 q^{47} -7.08708 q^{48} +1.00000 q^{49} +11.6389 q^{50} +2.30025 q^{51} -27.0303 q^{52} +9.51992 q^{53} +2.54493 q^{54} +0.779817 q^{55} +6.30289 q^{56} -5.19533 q^{57} -2.54099 q^{58} +13.9296 q^{59} -2.92394 q^{60} +11.8014 q^{61} +1.35575 q^{62} -1.00000 q^{63} -0.354383 q^{64} -3.94379 q^{65} +3.03845 q^{66} -5.22028 q^{67} -10.2974 q^{68} +1.76702 q^{69} +1.66223 q^{70} -3.73726 q^{71} -6.30289 q^{72} +7.15594 q^{73} -9.59931 q^{74} +4.57339 q^{75} +23.2577 q^{76} -1.19393 q^{77} -15.3664 q^{78} -11.2861 q^{79} +4.62895 q^{80} +1.00000 q^{81} +18.7409 q^{82} -1.39987 q^{83} +4.47665 q^{84} -1.50242 q^{85} +3.75922 q^{86} -0.998454 q^{87} -7.52517 q^{88} +16.8126 q^{89} -1.66223 q^{90} +6.03807 q^{91} -7.91031 q^{92} +0.532726 q^{93} -4.81502 q^{94} +3.39335 q^{95} +5.43033 q^{96} -3.96788 q^{97} -2.54493 q^{98} +1.19393 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9} - 10 q^{10} + 31 q^{11} - 45 q^{12} - 32 q^{13} - 3 q^{14} + 9 q^{15} + 43 q^{16} - 36 q^{17} + 3 q^{18} - 13 q^{19} - 19 q^{20} + 46 q^{21} - 13 q^{22} + 24 q^{23} - 6 q^{24} + 35 q^{25} - 11 q^{26} - 46 q^{27} - 45 q^{28} + 11 q^{29} + 10 q^{30} - 23 q^{31} + 5 q^{32} - 31 q^{33} - 35 q^{34} + 9 q^{35} + 45 q^{36} - 37 q^{37} - 32 q^{38} + 32 q^{39} - 28 q^{40} - 27 q^{41} + 3 q^{42} - 7 q^{43} + 46 q^{44} - 9 q^{45} + 16 q^{46} - 18 q^{47} - 43 q^{48} + 46 q^{49} + 10 q^{50} + 36 q^{51} - 62 q^{52} - 62 q^{53} - 3 q^{54} - 28 q^{55} - 6 q^{56} + 13 q^{57} - 36 q^{58} - 3 q^{59} + 19 q^{60} - 31 q^{61} - 41 q^{62} - 46 q^{63} + 42 q^{64} + 2 q^{65} + 13 q^{66} - 9 q^{67} - 70 q^{68} - 24 q^{69} + 10 q^{70} + 77 q^{71} + 6 q^{72} - 38 q^{73} + 14 q^{74} - 35 q^{75} - 41 q^{76} - 31 q^{77} + 11 q^{78} + 8 q^{79} - 59 q^{80} + 46 q^{81} - 53 q^{82} - 38 q^{83} + 45 q^{84} - 26 q^{85} + 37 q^{86} - 11 q^{87} - 26 q^{88} - 39 q^{89} - 10 q^{90} + 32 q^{91} + 2 q^{92} + 23 q^{93} - 55 q^{94} + 35 q^{95} - 5 q^{96} - 61 q^{97} + 3 q^{98} + 31 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9 - 10 * q^10 + 31 * q^11 - 45 * q^12 - 32 * q^13 - 3 * q^14 + 9 * q^15 + 43 * q^16 - 36 * q^17 + 3 * q^18 - 13 * q^19 - 19 * q^20 + 46 * q^21 - 13 * q^22 + 24 * q^23 - 6 * q^24 + 35 * q^25 - 11 * q^26 - 46 * q^27 - 45 * q^28 + 11 * q^29 + 10 * q^30 - 23 * q^31 + 5 * q^32 - 31 * q^33 - 35 * q^34 + 9 * q^35 + 45 * q^36 - 37 * q^37 - 32 * q^38 + 32 * q^39 - 28 * q^40 - 27 * q^41 + 3 * q^42 - 7 * q^43 + 46 * q^44 - 9 * q^45 + 16 * q^46 - 18 * q^47 - 43 * q^48 + 46 * q^49 + 10 * q^50 + 36 * q^51 - 62 * q^52 - 62 * q^53 - 3 * q^54 - 28 * q^55 - 6 * q^56 + 13 * q^57 - 36 * q^58 - 3 * q^59 + 19 * q^60 - 31 * q^61 - 41 * q^62 - 46 * q^63 + 42 * q^64 + 2 * q^65 + 13 * q^66 - 9 * q^67 - 70 * q^68 - 24 * q^69 + 10 * q^70 + 77 * q^71 + 6 * q^72 - 38 * q^73 + 14 * q^74 - 35 * q^75 - 41 * q^76 - 31 * q^77 + 11 * q^78 + 8 * q^79 - 59 * q^80 + 46 * q^81 - 53 * q^82 - 38 * q^83 + 45 * q^84 - 26 * q^85 + 37 * q^86 - 11 * q^87 - 26 * q^88 - 39 * q^89 - 10 * q^90 + 32 * q^91 + 2 * q^92 + 23 * q^93 - 55 * q^94 + 35 * q^95 - 5 * q^96 - 61 * q^97 + 3 * q^98 + 31 * q^99

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