LMFDB - Embedded newform 6035.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1897176198$
Analytic rank:	$0$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-2.76733 q^{2} +1.59965 q^{3} +5.65810 q^{4} -1.00000 q^{5} -4.42674 q^{6} -1.31827 q^{7} -10.1232 q^{8} -0.441134 q^{9} +O(q^{10})$	\(q-2.76733 q^{2} +1.59965 q^{3} +5.65810 q^{4} -1.00000 q^{5} -4.42674 q^{6} -1.31827 q^{7} -10.1232 q^{8} -0.441134 q^{9} +2.76733 q^{10} -3.83158 q^{11} +9.05096 q^{12} +4.38684 q^{13} +3.64809 q^{14} -1.59965 q^{15} +16.6979 q^{16} +1.00000 q^{17} +1.22076 q^{18} -4.93092 q^{19} -5.65810 q^{20} -2.10877 q^{21} +10.6032 q^{22} -5.75887 q^{23} -16.1935 q^{24} +1.00000 q^{25} -12.1398 q^{26} -5.50459 q^{27} -7.45891 q^{28} +1.76425 q^{29} +4.42674 q^{30} -0.136216 q^{31} -25.9623 q^{32} -6.12917 q^{33} -2.76733 q^{34} +1.31827 q^{35} -2.49598 q^{36} +0.346811 q^{37} +13.6455 q^{38} +7.01739 q^{39} +10.1232 q^{40} +4.49656 q^{41} +5.83565 q^{42} +7.94416 q^{43} -21.6795 q^{44} +0.441134 q^{45} +15.9367 q^{46} -6.11099 q^{47} +26.7108 q^{48} -5.26216 q^{49} -2.76733 q^{50} +1.59965 q^{51} +24.8212 q^{52} +1.75966 q^{53} +15.2330 q^{54} +3.83158 q^{55} +13.3451 q^{56} -7.88773 q^{57} -4.88225 q^{58} +3.80727 q^{59} -9.05096 q^{60} +4.29538 q^{61} +0.376954 q^{62} +0.581534 q^{63} +38.4504 q^{64} -4.38684 q^{65} +16.9614 q^{66} +1.42560 q^{67} +5.65810 q^{68} -9.21216 q^{69} -3.64809 q^{70} -1.00000 q^{71} +4.46568 q^{72} +1.77373 q^{73} -0.959739 q^{74} +1.59965 q^{75} -27.8997 q^{76} +5.05106 q^{77} -19.4194 q^{78} -7.57324 q^{79} -16.6979 q^{80} -7.48200 q^{81} -12.4435 q^{82} -17.5713 q^{83} -11.9316 q^{84} -1.00000 q^{85} -21.9841 q^{86} +2.82217 q^{87} +38.7878 q^{88} +1.10444 q^{89} -1.22076 q^{90} -5.78304 q^{91} -32.5843 q^{92} -0.217897 q^{93} +16.9111 q^{94} +4.93092 q^{95} -41.5305 q^{96} +5.83094 q^{97} +14.5621 q^{98} +1.69024 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q + q^{2} + 10 q^{3} + 55 q^{4} - 49 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 43 q^{9}+O(q^{10}) $ 49 * q + q^2 + 10 * q^3 + 55 * q^4 - 49 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 43 * q^9	\( 49 q + q^{2} + 10 q^{3} + 55 q^{4} - 49 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 43 q^{9} - q^{10} - 4 q^{11} + 32 q^{12} + 21 q^{13} + 8 q^{14} - 10 q^{15} + 63 q^{16} + 49 q^{17} + 12 q^{18} + 19 q^{19} - 55 q^{20} + 5 q^{21} + 10 q^{22} + 10 q^{23} + 7 q^{24} + 49 q^{25} - 20 q^{26} + 37 q^{27} + 48 q^{28} + 30 q^{29} - 2 q^{30} + 23 q^{31} + 2 q^{32} - q^{33} + q^{34} - 15 q^{35} + 39 q^{36} + 60 q^{37} + 13 q^{38} + 3 q^{39} - 3 q^{40} - 29 q^{41} + 32 q^{42} + 23 q^{43} + 11 q^{44} - 43 q^{45} + 6 q^{46} - 8 q^{47} + 96 q^{48} + 82 q^{49} + q^{50} + 10 q^{51} + 11 q^{52} + 15 q^{53} - 4 q^{54} + 4 q^{55} - 18 q^{56} + 44 q^{57} + 38 q^{58} - 28 q^{59} - 32 q^{60} + 107 q^{61} + 37 q^{62} + 54 q^{63} + 77 q^{64} - 21 q^{65} + 23 q^{66} + 11 q^{67} + 55 q^{68} + 27 q^{69} - 8 q^{70} - 49 q^{71} - 53 q^{72} + 97 q^{73} + 27 q^{74} + 10 q^{75} + 66 q^{76} + 19 q^{77} + 48 q^{78} + 31 q^{79} - 63 q^{80} - 7 q^{81} + 61 q^{82} + 6 q^{83} + 46 q^{84} - 49 q^{85} - 89 q^{86} + 36 q^{87} + 63 q^{88} - 20 q^{89} - 12 q^{90} + 35 q^{91} - 2 q^{92} + 47 q^{93} - 4 q^{94} - 19 q^{95} + 73 q^{96} + 92 q^{97} + 3 q^{98} + 5 q^{99}+O(q^{100}) \) 49 * q + q^2 + 10 * q^3 + 55 * q^4 - 49 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 43 * q^9 - q^10 - 4 * q^11 + 32 * q^12 + 21 * q^13 + 8 * q^14 - 10 * q^15 + 63 * q^16 + 49 * q^17 + 12 * q^18 + 19 * q^19 - 55 * q^20 + 5 * q^21 + 10 * q^22 + 10 * q^23 + 7 * q^24 + 49 * q^25 - 20 * q^26 + 37 * q^27 + 48 * q^28 + 30 * q^29 - 2 * q^30 + 23 * q^31 + 2 * q^32 - q^33 + q^34 - 15 * q^35 + 39 * q^36 + 60 * q^37 + 13 * q^38 + 3 * q^39 - 3 * q^40 - 29 * q^41 + 32 * q^42 + 23 * q^43 + 11 * q^44 - 43 * q^45 + 6 * q^46 - 8 * q^47 + 96 * q^48 + 82 * q^49 + q^50 + 10 * q^51 + 11 * q^52 + 15 * q^53 - 4 * q^54 + 4 * q^55 - 18 * q^56 + 44 * q^57 + 38 * q^58 - 28 * q^59 - 32 * q^60 + 107 * q^61 + 37 * q^62 + 54 * q^63 + 77 * q^64 - 21 * q^65 + 23 * q^66 + 11 * q^67 + 55 * q^68 + 27 * q^69 - 8 * q^70 - 49 * q^71 - 53 * q^72 + 97 * q^73 + 27 * q^74 + 10 * q^75 + 66 * q^76 + 19 * q^77 + 48 * q^78 + 31 * q^79 - 63 * q^80 - 7 * q^81 + 61 * q^82 + 6 * q^83 + 46 * q^84 - 49 * q^85 - 89 * q^86 + 36 * q^87 + 63 * q^88 - 20 * q^89 - 12 * q^90 + 35 * q^91 - 2 * q^92 + 47 * q^93 - 4 * q^94 - 19 * q^95 + 73 * q^96 + 92 * q^97 + 3 * q^98 + 5 * 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 $

$2$	−2.76733	−1.95680	−0.978398	−	0.206729i	$-0.933718\pi$
$2$	−2.76733	−1.95680	−0.978398	+	0.206729i	$0.933718\pi$
$3$	1.59965	0.923556	0.461778	−	0.886996i	$-0.347212\pi$
$3$	1.59965	0.923556	0.461778	+	0.886996i	$0.347212\pi$
$4$	5.65810	2.82905
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−4.42674	−1.80721
$7$	−1.31827	−0.498260	−0.249130	−	0.968470i	$-0.580145\pi$
$7$	−1.31827	−0.498260	−0.249130	+	0.968470i	$0.580145\pi$
$8$	−10.1232	−3.57908
$9$	−0.441134	−0.147045
$10$	2.76733	0.875106
$11$	−3.83158	−1.15526	−0.577632	−	0.816297i	$-0.696023\pi$
$11$	−3.83158	−1.15526	−0.577632	+	0.816297i	$0.696023\pi$
$12$	9.05096	2.61279
$13$	4.38684	1.21669	0.608345	−	0.793673i	$-0.291834\pi$
$13$	4.38684	1.21669	0.608345	+	0.793673i	$0.291834\pi$
$14$	3.64809	0.974993
$15$	−1.59965	−0.413027
$16$	16.6979	4.17448
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.22076	0.287736
$19$	−4.93092	−1.13123	−0.565616	−	0.824669i	$-0.691361\pi$
$19$	−4.93092	−1.13123	−0.565616	+	0.824669i	$0.691361\pi$
$20$	−5.65810	−1.26519
$21$	−2.10877	−0.460171
$22$	10.6032	2.26062
$23$	−5.75887	−1.20081	−0.600404	−	0.799697i	$-0.704994\pi$
$23$	−5.75887	−1.20081	−0.600404	+	0.799697i	$0.704994\pi$
$24$	−16.1935	−3.30548
$25$	1.00000	0.200000
$26$	−12.1398	−2.38081
$27$	−5.50459	−1.05936
$28$	−7.45891	−1.40960
$29$	1.76425	0.327612	0.163806	−	0.986493i	$-0.447623\pi$
$29$	1.76425	0.327612	0.163806	+	0.986493i	$0.447623\pi$
$30$	4.42674	0.808209
$31$	−0.136216	−0.0244651	−0.0122325	−	0.999925i	$-0.503894\pi$
$31$	−0.136216	−0.0244651	−0.0122325	+	0.999925i	$0.503894\pi$
$32$	−25.9623	−4.58953
$33$	−6.12917	−1.06695
$34$	−2.76733	−0.474593
$35$	1.31827	0.222828
$36$	−2.49598	−0.415997
$37$	0.346811	0.0570153	0.0285077	−	0.999594i	$-0.490925\pi$
$37$	0.346811	0.0570153	0.0285077	+	0.999594i	$0.490925\pi$
$38$	13.6455	2.21359
$39$	7.01739	1.12368
$40$	10.1232	1.60061
$41$	4.49656	0.702245	0.351122	−	0.936330i	$-0.385800\pi$
$41$	4.49656	0.702245	0.351122	+	0.936330i	$0.385800\pi$
$42$	5.83565	0.900460
$43$	7.94416	1.21147	0.605736	−	0.795665i	$-0.292879\pi$
$43$	7.94416	1.21147	0.605736	+	0.795665i	$0.292879\pi$
$44$	−21.6795	−3.26830
$45$	0.441134	0.0657604
$46$	15.9367	2.34974
$47$	−6.11099	−0.891379	−0.445690	−	0.895188i	$-0.647041\pi$
$47$	−6.11099	−0.891379	−0.445690	+	0.895188i	$0.647041\pi$
$48$	26.7108	3.85537
$49$	−5.26216	−0.751737
$50$	−2.76733	−0.391359
$51$	1.59965	0.223995
$52$	24.8212	3.44208
$53$	1.75966	0.241708	0.120854	−	0.992670i	$-0.461437\pi$
$53$	1.75966	0.241708	0.120854	+	0.992670i	$0.461437\pi$
$54$	15.2330	2.07295
$55$	3.83158	0.516650
$56$	13.3451	1.78331
$57$	−7.88773	−1.04476
$58$	−4.88225	−0.641070
$59$	3.80727	0.495665	0.247832	−	0.968803i	$-0.420282\pi$
$59$	3.80727	0.495665	0.247832	+	0.968803i	$0.420282\pi$
$60$	−9.05096	−1.16847
$61$	4.29538	0.549967	0.274983	−	0.961449i	$-0.411328\pi$
$61$	4.29538	0.549967	0.274983	+	0.961449i	$0.411328\pi$
$62$	0.376954	0.0478732
$63$	0.581534	0.0732664
$64$	38.4504	4.80630
$65$	−4.38684	−0.544120
$66$	16.9614	2.08781
$67$	1.42560	0.174165	0.0870825	−	0.996201i	$-0.472246\pi$
$67$	1.42560	0.174165	0.0870825	+	0.996201i	$0.472246\pi$
$68$	5.65810	0.686146
$69$	−9.21216	−1.10901
$70$	−3.64809	−0.436030
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	4.46568	0.526285
$73$	1.77373	0.207599	0.103800	−	0.994598i	$-0.466900\pi$
$73$	1.77373	0.207599	0.103800	+	0.994598i	$0.466900\pi$
$74$	−0.959739	−0.111567
$75$	1.59965	0.184711
$76$	−27.8997	−3.20031
$77$	5.05106	0.575622
$78$	−19.4194	−2.19882
$79$	−7.57324	−0.852057	−0.426028	−	0.904710i	$-0.640088\pi$
$79$	−7.57324	−0.852057	−0.426028	+	0.904710i	$0.640088\pi$
$80$	−16.6979	−1.86689
$81$	−7.48200	−0.831333
$82$	−12.4435	−1.37415
$83$	−17.5713	−1.92870	−0.964348	−	0.264639i	$-0.914747\pi$
$83$	−17.5713	−1.92870	−0.964348	+	0.264639i	$0.914747\pi$
$84$	−11.9316	−1.30185
$85$	−1.00000	−0.108465
$86$	−21.9841	−2.37061
$87$	2.82217	0.302568
$88$	38.7878	4.13479
$89$	1.10444	0.117071	0.0585353	−	0.998285i	$-0.481357\pi$
$89$	1.10444	0.117071	0.0585353	+	0.998285i	$0.481357\pi$
$90$	−1.22076	−0.128680
$91$	−5.78304	−0.606227
$92$	−32.5843	−3.39715
$93$	−0.217897	−0.0225949
$94$	16.9111	1.74425
$95$	4.93092	0.505902
$96$	−41.5305	−4.23869
$97$	5.83094	0.592043	0.296021	−	0.955181i	$-0.404340\pi$
$97$	5.83094	0.592043	0.296021	+	0.955181i	$0.404340\pi$
$98$	14.5621	1.47100
$99$	1.69024	0.169876
$100$	5.65810	0.565810
$101$	−2.85553	−0.284135	−0.142068	−	0.989857i	$-0.545375\pi$
$101$	−2.85553	−0.284135	−0.142068	+	0.989857i	$0.545375\pi$
$102$	−4.42674	−0.438313
$103$	5.02161	0.494794	0.247397	−	0.968914i	$-0.420425\pi$
$103$	5.02161	0.494794	0.247397	+	0.968914i	$0.420425\pi$
$104$	−44.4087	−4.35463
$105$	2.10877	0.205795
$106$	−4.86955	−0.472973
$107$	−0.886394	−0.0856910	−0.0428455	−	0.999082i	$-0.513642\pi$
$107$	−0.886394	−0.0856910	−0.0428455	+	0.999082i	$0.513642\pi$
$108$	−31.1456	−2.99698
$109$	−9.53763	−0.913539	−0.456770	−	0.889585i	$-0.650994\pi$
$109$	−9.53763	−0.913539	−0.456770	+	0.889585i	$0.650994\pi$
$110$	−10.6032	−1.01098
$111$	0.554774	0.0526568
$112$	−22.0124	−2.07998
$113$	20.2004	1.90030	0.950148	−	0.311799i	$-0.100931\pi$
$113$	20.2004	1.90030	0.950148	+	0.311799i	$0.100931\pi$
$114$	21.8279	2.04437
$115$	5.75887	0.537018
$116$	9.98228	0.926832
$117$	−1.93518	−0.178908
$118$	−10.5360	−0.969915
$119$	−1.31827	−0.120846
$120$	16.1935	1.47826
$121$	3.68101	0.334637
$122$	−11.8867	−1.07617
$123$	7.19290	0.648562
$124$	−0.770723	−0.0692130
$125$	−1.00000	−0.0894427
$126$	−1.60930	−0.143367
$127$	13.3919	1.18834	0.594168	−	0.804341i	$-0.297481\pi$
$127$	13.3919	1.18834	0.594168	+	0.804341i	$0.297481\pi$
$128$	−54.4802	−4.81542
$129$	12.7078	1.11886
$130$	12.1398	1.06473
$131$	−15.7911	−1.37968	−0.689838	−	0.723964i	$-0.742318\pi$
$131$	−15.7911	−1.37968	−0.689838	+	0.723964i	$0.742318\pi$
$132$	−34.6795	−3.01846
$133$	6.50029	0.563647
$134$	−3.94511	−0.340805
$135$	5.50459	0.473760
$136$	−10.1232	−0.868055
$137$	1.27034	0.108532	0.0542661	−	0.998527i	$-0.482718\pi$
$137$	1.27034	0.108532	0.0542661	+	0.998527i	$0.482718\pi$
$138$	25.4931	2.17011
$139$	9.03774	0.766571	0.383285	−	0.923630i	$-0.374793\pi$
$139$	9.03774	0.766571	0.383285	+	0.923630i	$0.374793\pi$
$140$	7.45891	0.630393
$141$	−9.77541	−0.823238
$142$	2.76733	0.232229
$143$	−16.8085	−1.40560
$144$	−7.36603	−0.613836
$145$	−1.76425	−0.146513
$146$	−4.90849	−0.406229
$147$	−8.41759	−0.694271
$148$	1.96229	0.161299
$149$	15.2594	1.25009	0.625047	−	0.780587i	$-0.285080\pi$
$149$	15.2594	1.25009	0.625047	+	0.780587i	$0.285080\pi$
$150$	−4.42674	−0.361442
$151$	−22.7065	−1.84783	−0.923914	−	0.382599i	$-0.875029\pi$
$151$	−22.7065	−1.84783	−0.923914	+	0.382599i	$0.875029\pi$
$152$	49.9166	4.04877
$153$	−0.441134	−0.0356636
$154$	−13.9779	−1.12637
$155$	0.136216	0.0109411
$156$	39.7051	3.17895
$157$	−1.52015	−0.121321	−0.0606605	−	0.998158i	$-0.519321\pi$
$157$	−1.52015	−0.121321	−0.0606605	+	0.998158i	$0.519321\pi$
$158$	20.9577	1.66730
$159$	2.81483	0.223231
$160$	25.9623	2.05250
$161$	7.59175	0.598314
$162$	20.7051	1.62675
$163$	18.3027	1.43358	0.716790	−	0.697289i	$-0.245610\pi$
$163$	18.3027	1.43358	0.716790	+	0.697289i	$0.245610\pi$
$164$	25.4420	1.98669
$165$	6.12917	0.477155
$166$	48.6254	3.77406
$167$	19.0964	1.47773	0.738863	−	0.673856i	$-0.235363\pi$
$167$	19.0964	1.47773	0.738863	+	0.673856i	$0.235363\pi$
$168$	21.3474	1.64699
$169$	6.24435	0.480334
$170$	2.76733	0.212244
$171$	2.17520	0.166342
$172$	44.9489	3.42732
$173$	13.3917	1.01815	0.509075	−	0.860722i	$-0.329988\pi$
$173$	13.3917	1.01815	0.509075	+	0.860722i	$0.329988\pi$
$174$	−7.80986	−0.592064
$175$	−1.31827	−0.0996519
$176$	−63.9795	−4.82264
$177$	6.09029	0.457774
$178$	−3.05635	−0.229083
$179$	13.6058	1.01694	0.508472	−	0.861079i	$-0.330211\pi$
$179$	13.6058	1.01694	0.508472	+	0.861079i	$0.330211\pi$
$180$	2.49598	0.186040
$181$	−1.08534	−0.0806724	−0.0403362	−	0.999186i	$-0.512843\pi$
$181$	−1.08534	−0.0806724	−0.0403362	+	0.999186i	$0.512843\pi$
$182$	16.0036	1.18626
$183$	6.87108	0.507925
$184$	58.2981	4.29779
$185$	−0.346811	−0.0254980
$186$	0.602993	0.0442136
$187$	−3.83158	−0.280193
$188$	−34.5766	−2.52176
$189$	7.25655	0.527836
$190$	−13.6455	−0.989947
$191$	−6.21282	−0.449544	−0.224772	−	0.974411i	$-0.572164\pi$
$191$	−6.21282	−0.449544	−0.224772	+	0.974411i	$0.572164\pi$
$192$	61.5070	4.43889
$193$	12.8179	0.922656	0.461328	−	0.887230i	$-0.347373\pi$
$193$	12.8179	0.922656	0.461328	+	0.887230i	$0.347373\pi$
$194$	−16.1361	−1.15851
$195$	−7.01739	−0.502525
$196$	−29.7739	−2.12670
$197$	3.48892	0.248575	0.124288	−	0.992246i	$-0.460335\pi$
$197$	3.48892	0.248575	0.124288	+	0.992246i	$0.460335\pi$
$198$	−4.67745	−0.332412
$199$	11.9665	0.848284	0.424142	−	0.905596i	$-0.360576\pi$
$199$	11.9665	0.848284	0.424142	+	0.905596i	$0.360576\pi$
$200$	−10.1232	−0.715817
$201$	2.28046	0.160851
$202$	7.90218	0.555995
$203$	−2.32575	−0.163236
$204$	9.05096	0.633694
$205$	−4.49656	−0.314053
$206$	−13.8965	−0.968212
$207$	2.54043	0.176572
$208$	73.2512	5.07905
$209$	18.8932	1.30687
$210$	−5.83565	−0.402698
$211$	−17.1035	−1.17745	−0.588726	−	0.808333i	$-0.700370\pi$
$211$	−17.1035	−1.17745	−0.588726	+	0.808333i	$0.700370\pi$
$212$	9.95633	0.683804
$213$	−1.59965	−0.109606
$214$	2.45294	0.167680
$215$	−7.94416	−0.541787
$216$	55.7240	3.79154
$217$	0.179569	0.0121900
$218$	26.3937	1.78761
$219$	2.83734	0.191729
$220$	21.6795	1.46163
$221$	4.38684	0.295091
$222$	−1.53524	−0.103039
$223$	12.9420	0.866658	0.433329	−	0.901236i	$-0.357339\pi$
$223$	12.9420	0.866658	0.433329	+	0.901236i	$0.357339\pi$
$224$	34.2254	2.28678
$225$	−0.441134	−0.0294089
$226$	−55.9012	−3.71849
$227$	3.72341	0.247132	0.123566	−	0.992336i	$-0.460567\pi$
$227$	3.72341	0.247132	0.123566	+	0.992336i	$0.460567\pi$
$228$	−44.6296	−2.95567
$229$	29.6800	1.96131	0.980654	−	0.195749i	$-0.0627139\pi$
$229$	29.6800	1.96131	0.980654	+	0.195749i	$0.0627139\pi$
$230$	−15.9367	−1.05083
$231$	8.07991	0.531619
$232$	−17.8598	−1.17255
$233$	−18.5709	−1.21662	−0.608310	−	0.793699i	$-0.708152\pi$
$233$	−18.5709	−1.21662	−0.608310	+	0.793699i	$0.708152\pi$
$234$	5.35529	0.350086
$235$	6.11099	0.398637
$236$	21.5420	1.40226
$237$	−12.1145	−0.786922
$238$	3.64809	0.236470
$239$	−14.6487	−0.947542	−0.473771	−	0.880648i	$-0.657108\pi$
$239$	−14.6487	−0.947542	−0.473771	+	0.880648i	$0.657108\pi$
$240$	−26.7108	−1.72417
$241$	−27.7458	−1.78726	−0.893632	−	0.448801i	$-0.851851\pi$
$241$	−27.7458	−1.78726	−0.893632	+	0.448801i	$0.851851\pi$
$242$	−10.1866	−0.654816
$243$	4.54524	0.291577
$244$	24.3037	1.55588
$245$	5.26216	0.336187
$246$	−19.9051	−1.26910
$247$	−21.6312	−1.37636
$248$	1.37894	0.0875626
$249$	−28.1078	−1.78126
$250$	2.76733	0.175021
$251$	−3.36442	−0.212360	−0.106180	−	0.994347i	$-0.533862\pi$
$251$	−3.36442	−0.212360	−0.106180	+	0.994347i	$0.533862\pi$
$252$	3.29038	0.207275
$253$	22.0656	1.38725
$254$	−37.0597	−2.32533
$255$	−1.59965	−0.100174
$256$	73.8638	4.61649
$257$	15.0463	0.938560	0.469280	−	0.883049i	$-0.344513\pi$
$257$	15.0463	0.938560	0.469280	+	0.883049i	$0.344513\pi$
$258$	−35.1668	−2.18939
$259$	−0.457190	−0.0284084
$260$	−24.8212	−1.53934
$261$	−0.778269	−0.0481736
$262$	43.6992	2.69974
$263$	21.4590	1.32322	0.661610	−	0.749848i	$-0.269874\pi$
$263$	21.4590	1.32322	0.661610	+	0.749848i	$0.269874\pi$
$264$	62.0467	3.81871
$265$	−1.75966	−0.108095
$266$	−17.9884	−1.10294
$267$	1.76672	0.108121
$268$	8.06620	0.492722
$269$	−0.878202	−0.0535449	−0.0267724	−	0.999642i	$-0.508523\pi$
$269$	−0.878202	−0.0535449	−0.0267724	+	0.999642i	$0.508523\pi$
$270$	−15.2330	−0.927052
$271$	−11.8394	−0.719190	−0.359595	−	0.933109i	$-0.617085\pi$
$271$	−11.8394	−0.719190	−0.359595	+	0.933109i	$0.617085\pi$
$272$	16.6979	1.01246
$273$	−9.25082	−0.559885
$274$	−3.51544	−0.212375
$275$	−3.83158	−0.231053
$276$	−52.1233	−3.13746
$277$	−6.56276	−0.394318	−0.197159	−	0.980372i	$-0.563172\pi$
$277$	−6.56276	−0.394318	−0.197159	+	0.980372i	$0.563172\pi$
$278$	−25.0104	−1.50002
$279$	0.0600894	0.00359746
$280$	−13.3451	−0.797522
$281$	17.2917	1.03154	0.515768	−	0.856729i	$-0.327507\pi$
$281$	17.2917	1.03154	0.515768	+	0.856729i	$0.327507\pi$
$282$	27.0518	1.61091
$283$	14.0270	0.833819	0.416909	−	0.908948i	$-0.363113\pi$
$283$	14.0270	0.833819	0.416909	+	0.908948i	$0.363113\pi$
$284$	−5.65810	−0.335747
$285$	7.88773	0.467229
$286$	46.5147	2.75047
$287$	−5.92769	−0.349900
$288$	11.4529	0.674867
$289$	1.00000	0.0588235
$290$	4.88225	0.286695
$291$	9.32744	0.546784
$292$	10.0359	0.587309
$293$	−2.36500	−0.138165	−0.0690823	−	0.997611i	$-0.522007\pi$
$293$	−2.36500	−0.138165	−0.0690823	+	0.997611i	$0.522007\pi$
$294$	23.2942	1.35855
$295$	−3.80727	−0.221668
$296$	−3.51083	−0.204063
$297$	21.0913	1.22384
$298$	−42.2276	−2.44618
$299$	−25.2632	−1.46101
$300$	9.05096	0.522558
$301$	−10.4726	−0.603628
$302$	62.8363	3.61583
$303$	−4.56783	−0.262415
$304$	−82.3362	−4.72231
$305$	−4.29538	−0.245953
$306$	1.22076	0.0697864
$307$	13.0953	0.747390	0.373695	−	0.927552i	$-0.378091\pi$
$307$	13.0953	0.747390	0.373695	+	0.927552i	$0.378091\pi$
$308$	28.5794	1.62846
$309$	8.03280	0.456970
$310$	−0.376954	−0.0214095
$311$	−6.23692	−0.353663	−0.176832	−	0.984241i	$-0.556585\pi$
$311$	−6.23692	−0.353663	−0.176832	+	0.984241i	$0.556585\pi$
$312$	−71.0382	−4.02175
$313$	33.5505	1.89639	0.948193	−	0.317696i	$-0.102909\pi$
$313$	33.5505	1.89639	0.948193	+	0.317696i	$0.102909\pi$
$314$	4.20675	0.237401
$315$	−0.581534	−0.0327657
$316$	−42.8502	−2.41051
$317$	14.4127	0.809496	0.404748	−	0.914428i	$-0.367359\pi$
$317$	14.4127	0.809496	0.404748	+	0.914428i	$0.367359\pi$
$318$	−7.78956	−0.436817
$319$	−6.75985	−0.378479
$320$	−38.4504	−2.14944
$321$	−1.41792	−0.0791404
$322$	−21.0089	−1.17078
$323$	−4.93092	−0.274364
$324$	−42.3339	−2.35189
$325$	4.38684	0.243338
$326$	−50.6497	−2.80523
$327$	−15.2568	−0.843704
$328$	−45.5195	−2.51339
$329$	8.05594	0.444138
$330$	−16.9614	−0.933696
$331$	−6.11172	−0.335931	−0.167965	−	0.985793i	$-0.553720\pi$
$331$	−6.11172	−0.335931	−0.167965	+	0.985793i	$0.553720\pi$
$332$	−99.4200	−5.45638
$333$	−0.152990	−0.00838380
$334$	−52.8461	−2.89161
$335$	−1.42560	−0.0778890
$336$	−35.2121	−1.92097
$337$	33.2447	1.81095	0.905477	−	0.424396i	$-0.139514\pi$
$337$	33.2447	1.81095	0.905477	+	0.424396i	$0.139514\pi$
$338$	−17.2802	−0.939917
$339$	32.3135	1.75503
$340$	−5.65810	−0.306854
$341$	0.521922	0.0282637
$342$	−6.01949	−0.325496
$343$	16.1649	0.872820
$344$	−80.4201	−4.33596
$345$	9.21216	0.495966
$346$	−37.0591	−1.99231
$347$	19.7806	1.06188	0.530940	−	0.847409i	$-0.321839\pi$
$347$	19.7806	1.06188	0.530940	+	0.847409i	$0.321839\pi$
$348$	15.9681	0.855981
$349$	11.6503	0.623626	0.311813	−	0.950144i	$-0.399064\pi$
$349$	11.6503	0.623626	0.311813	+	0.950144i	$0.399064\pi$
$350$	3.64809	0.194999
$351$	−24.1478	−1.28891
$352$	99.4767	5.30213
$353$	15.4010	0.819712	0.409856	−	0.912150i	$-0.365579\pi$
$353$	15.4010	0.819712	0.409856	+	0.912150i	$0.365579\pi$
$354$	−16.8538	−0.895771
$355$	1.00000	0.0530745
$356$	6.24905	0.331199
$357$	−2.10877	−0.111608
$358$	−37.6516	−1.98995
$359$	−22.5125	−1.18816	−0.594082	−	0.804404i	$-0.702485\pi$
$359$	−22.5125	−1.18816	−0.594082	+	0.804404i	$0.702485\pi$
$360$	−4.46568	−0.235362
$361$	5.31399	0.279684
$362$	3.00348	0.157859
$363$	5.88830	0.309056
$364$	−32.7211	−1.71505
$365$	−1.77373	−0.0928411
$366$	−19.0145	−0.993905
$367$	4.43588	0.231551	0.115776	−	0.993275i	$-0.463065\pi$
$367$	4.43588	0.231551	0.115776	+	0.993275i	$0.463065\pi$
$368$	−96.1613	−5.01275
$369$	−1.98359	−0.103261
$370$	0.959739	0.0498944
$371$	−2.31971	−0.120433
$372$	−1.23288	−0.0639221
$373$	25.1568	1.30257	0.651286	−	0.758832i	$-0.274230\pi$
$373$	25.1568	1.30257	0.651286	+	0.758832i	$0.274230\pi$
$374$	10.6032	0.548280
$375$	−1.59965	−0.0826053
$376$	61.8626	3.19032
$377$	7.73946	0.398602
$378$	−20.0812	−1.03287
$379$	−15.8566	−0.814500	−0.407250	−	0.913317i	$-0.633512\pi$
$379$	−15.8566	−0.814500	−0.407250	+	0.913317i	$0.633512\pi$
$380$	27.8997	1.43122
$381$	21.4223	1.09750
$382$	17.1929	0.879666
$383$	−34.2218	−1.74865	−0.874325	−	0.485340i	$-0.838696\pi$
$383$	−34.2218	−1.74865	−0.874325	+	0.485340i	$0.838696\pi$
$384$	−87.1490	−4.44730
$385$	−5.05106	−0.257426
$386$	−35.4714	−1.80545
$387$	−3.50444	−0.178141
$388$	32.9921	1.67492
$389$	−6.68802	−0.339096	−0.169548	−	0.985522i	$-0.554231\pi$
$389$	−6.68802	−0.339096	−0.169548	+	0.985522i	$0.554231\pi$
$390$	19.4194	0.983340
$391$	−5.75887	−0.291239
$392$	53.2698	2.69053
$393$	−25.2602	−1.27421
$394$	−9.65498	−0.486411
$395$	7.57324	0.381051
$396$	9.56356	0.480587
$397$	−28.1220	−1.41140	−0.705701	−	0.708509i	$-0.749368\pi$
$397$	−28.1220	−1.41140	−0.705701	+	0.708509i	$0.749368\pi$
$398$	−33.1153	−1.65992
$399$	10.3982	0.520559
$400$	16.6979	0.834897
$401$	29.0332	1.44985	0.724925	−	0.688828i	$-0.241875\pi$
$401$	29.0332	1.44985	0.724925	+	0.688828i	$0.241875\pi$
$402$	−6.31077	−0.314753
$403$	−0.597557	−0.0297664
$404$	−16.1569	−0.803834
$405$	7.48200	0.371784
$406$	6.43612	0.319419
$407$	−1.32883	−0.0658678
$408$	−16.1935	−0.801697
$409$	18.3675	0.908215	0.454108	−	0.890947i	$-0.349958\pi$
$409$	18.3675	0.908215	0.454108	+	0.890947i	$0.349958\pi$
$410$	12.4435	0.614539
$411$	2.03209	0.100235
$412$	28.4128	1.39980
$413$	−5.01902	−0.246970
$414$	−7.03022	−0.345516
$415$	17.5713	0.862539
$416$	−113.893	−5.58404
$417$	14.4572	0.707971
$418$	−52.2837	−2.55728
$419$	−1.24626	−0.0608837	−0.0304418	−	0.999537i	$-0.509691\pi$
$419$	−1.24626	−0.0608837	−0.0304418	+	0.999537i	$0.509691\pi$
$420$	11.9316	0.582203
$421$	15.8117	0.770617	0.385308	−	0.922788i	$-0.374095\pi$
$421$	15.8117	0.770617	0.385308	+	0.922788i	$0.374095\pi$
$422$	47.3310	2.30403
$423$	2.69576	0.131073
$424$	−17.8133	−0.865092
$425$	1.00000	0.0485071
$426$	4.42674	0.214476
$427$	−5.66247	−0.274026
$428$	−5.01531	−0.242424
$429$	−26.8877	−1.29815
$430$	21.9841	1.06017
$431$	18.4450	0.888465	0.444232	−	0.895912i	$-0.353476\pi$
$431$	18.4450	0.888465	0.444232	+	0.895912i	$0.353476\pi$
$432$	−91.9154	−4.42228
$433$	5.66394	0.272192	0.136096	−	0.990696i	$-0.456545\pi$
$433$	5.66394	0.272192	0.136096	+	0.990696i	$0.456545\pi$
$434$	−0.496927	−0.0238533
$435$	−2.82217	−0.135313
$436$	−53.9649	−2.58445
$437$	28.3966	1.35839
$438$	−7.85184	−0.375175
$439$	4.22466	0.201632	0.100816	−	0.994905i	$-0.467855\pi$
$439$	4.22466	0.201632	0.100816	+	0.994905i	$0.467855\pi$
$440$	−38.7878	−1.84913
$441$	2.32132	0.110539
$442$	−12.1398	−0.577432
$443$	−23.9614	−1.13844	−0.569221	−	0.822185i	$-0.692755\pi$
$443$	−23.9614	−1.13844	−0.569221	+	0.822185i	$0.692755\pi$
$444$	3.13897	0.148969
$445$	−1.10444	−0.0523556
$446$	−35.8147	−1.69587
$447$	24.4096	1.15453
$448$	−50.6880	−2.39478
$449$	−9.74002	−0.459660	−0.229830	−	0.973231i	$-0.573817\pi$
$449$	−9.74002	−0.459660	−0.229830	+	0.973231i	$0.573817\pi$
$450$	1.22076	0.0575473
$451$	−17.2289	−0.811279
$452$	114.296	5.37604
$453$	−36.3224	−1.70657
$454$	−10.3039	−0.483586
$455$	5.78304	0.271113
$456$	79.8489	3.73927
$457$	−17.3167	−0.810040	−0.405020	−	0.914308i	$-0.632735\pi$
$457$	−17.3167	−0.810040	−0.405020	+	0.914308i	$0.632735\pi$
$458$	−82.1342	−3.83788
$459$	−5.50459	−0.256932
$460$	32.5843	1.51925
$461$	10.5995	0.493666	0.246833	−	0.969058i	$-0.420610\pi$
$461$	10.5995	0.493666	0.246833	+	0.969058i	$0.420610\pi$
$462$	−22.3598	−1.04027
$463$	−18.1943	−0.845563	−0.422782	−	0.906232i	$-0.638946\pi$
$463$	−18.1943	−0.845563	−0.422782	+	0.906232i	$0.638946\pi$
$464$	29.4593	1.36761
$465$	0.217897	0.0101047
$466$	51.3918	2.38068
$467$	9.67503	0.447707	0.223854	−	0.974623i	$-0.428136\pi$
$467$	9.67503	0.447707	0.223854	+	0.974623i	$0.428136\pi$
$468$	−10.9495	−0.506139
$469$	−1.87933	−0.0867794
$470$	−16.9111	−0.780051
$471$	−2.43170	−0.112047
$472$	−38.5417	−1.77403
$473$	−30.4387	−1.39957
$474$	33.5248	1.53985
$475$	−4.93092	−0.226246
$476$	−7.45891	−0.341879
$477$	−0.776245	−0.0355418
$478$	40.5376	1.85415
$479$	25.2354	1.15303	0.576517	−	0.817085i	$-0.304412\pi$
$479$	25.2354	1.15303	0.576517	+	0.817085i	$0.304412\pi$
$480$	41.5305	1.89560
$481$	1.52140	0.0693700
$482$	76.7817	3.49731
$483$	12.1441	0.552576
$484$	20.8275	0.946705
$485$	−5.83094	−0.264769
$486$	−12.5782	−0.570557
$487$	−26.7226	−1.21092	−0.605459	−	0.795876i	$-0.707010\pi$
$487$	−26.7226	−1.21092	−0.605459	+	0.795876i	$0.707010\pi$
$488$	−43.4828	−1.96838
$489$	29.2779	1.32399
$490$	−14.5621	−0.657850
$491$	9.86526	0.445213	0.222606	−	0.974908i	$-0.428543\pi$
$491$	9.86526	0.445213	0.222606	+	0.974908i	$0.428543\pi$
$492$	40.6982	1.83482
$493$	1.76425	0.0794576
$494$	59.8605	2.69325
$495$	−1.69024	−0.0759707
$496$	−2.27452	−0.102129
$497$	1.31827	0.0591325
$498$	77.7834	3.48556
$499$	17.1184	0.766327	0.383163	−	0.923681i	$-0.374835\pi$
$499$	17.1184	0.766327	0.383163	+	0.923681i	$0.374835\pi$
$500$	−5.65810	−0.253038
$501$	30.5475	1.36476
$502$	9.31045	0.415546
$503$	−16.4355	−0.732822	−0.366411	−	0.930453i	$-0.619414\pi$
$503$	−16.4355	−0.732822	−0.366411	+	0.930453i	$0.619414\pi$
$504$	−5.88697	−0.262227
$505$	2.85553	0.127069
$506$	−61.0627	−2.71457
$507$	9.98874	0.443616
$508$	75.7726	3.36187
$509$	25.5309	1.13164	0.565818	−	0.824530i	$-0.308560\pi$
$509$	25.5309	1.13164	0.565818	+	0.824530i	$0.308560\pi$
$510$	4.42674	0.196020
$511$	−2.33825	−0.103438
$512$	−95.4450	−4.21811
$513$	27.1427	1.19838
$514$	−41.6380	−1.83657
$515$	−5.02161	−0.221279
$516$	71.9023	3.16532
$517$	23.4147	1.02978
$518$	1.26520	0.0555895
$519$	21.4219	0.940318
$520$	44.4087	1.94745
$521$	25.7897	1.12987	0.564933	−	0.825137i	$-0.308902\pi$
$521$	25.7897	1.12987	0.564933	+	0.825137i	$0.308902\pi$
$522$	2.15372	0.0942660
$523$	−28.6318	−1.25198	−0.625990	−	0.779831i	$-0.715305\pi$
$523$	−28.6318	−1.25198	−0.625990	+	0.779831i	$0.715305\pi$
$524$	−89.3477	−3.90317
$525$	−2.10877	−0.0920341
$526$	−59.3841	−2.58927
$527$	−0.136216	−0.00593365
$528$	−102.345	−4.45397
$529$	10.1646	0.441940
$530$	4.86955	0.211520
$531$	−1.67952	−0.0728849
$532$	36.7793	1.59459
$533$	19.7257	0.854414
$534$	−4.88908	−0.211571
$535$	0.886394	0.0383222
$536$	−14.4316	−0.623351
$537$	21.7644	0.939204
$538$	2.43027	0.104776
$539$	20.1624	0.868456
$540$	31.1456	1.34029
$541$	−38.3135	−1.64723	−0.823613	−	0.567152i	$-0.808045\pi$
$541$	−38.3135	−1.64723	−0.823613	+	0.567152i	$0.808045\pi$
$542$	32.7634	1.40731
$543$	−1.73615	−0.0745055
$544$	−25.9623	−1.11313
$545$	9.53763	0.408547
$546$	25.6000	1.09558
$547$	9.53880	0.407850	0.203925	−	0.978987i	$-0.434630\pi$
$547$	9.53880	0.407850	0.203925	+	0.978987i	$0.434630\pi$
$548$	7.18769	0.307043
$549$	−1.89484	−0.0808696
$550$	10.6032	0.452124
$551$	−8.69936	−0.370605
$552$	93.2563	3.96925
$553$	9.98359	0.424545
$554$	18.1613	0.771600
$555$	−0.554774	−0.0235489
$556$	51.1365	2.16867
$557$	−10.9329	−0.463242	−0.231621	−	0.972806i	$-0.574403\pi$
$557$	−10.9329	−0.463242	−0.231621	+	0.972806i	$0.574403\pi$
$558$	−0.166287	−0.00703950
$559$	34.8497	1.47399
$560$	22.0124	0.930194
$561$	−6.12917	−0.258774
$562$	−47.8517	−2.01850
$563$	−2.32191	−0.0978570	−0.0489285	−	0.998802i	$-0.515581\pi$
$563$	−2.32191	−0.0978570	−0.0489285	+	0.998802i	$0.515581\pi$
$564$	−55.3103	−2.32898
$565$	−20.2004	−0.849838
$566$	−38.8173	−1.63161
$567$	9.86330	0.414220
$568$	10.1232	0.424759
$569$	18.3970	0.771243	0.385621	−	0.922657i	$-0.373987\pi$
$569$	18.3970	0.771243	0.385621	+	0.922657i	$0.373987\pi$
$570$	−21.8279	−0.914271
$571$	−23.9193	−1.00099	−0.500496	−	0.865739i	$-0.666849\pi$
$571$	−23.9193	−1.00099	−0.500496	+	0.865739i	$0.666849\pi$
$572$	−95.1044	−3.97651
$573$	−9.93831	−0.415179
$574$	16.4039	0.684683
$575$	−5.75887	−0.240162
$576$	−16.9618	−0.706741
$577$	−39.1686	−1.63061	−0.815305	−	0.579032i	$-0.803431\pi$
$577$	−39.1686	−1.63061	−0.815305	+	0.579032i	$0.803431\pi$
$578$	−2.76733	−0.115106
$579$	20.5042	0.852124
$580$	−9.98228	−0.414492
$581$	23.1637	0.960991
$582$	−25.8121	−1.06995
$583$	−6.74227	−0.279236
$584$	−17.9558	−0.743014
$585$	1.93518	0.0800100
$586$	6.54473	0.270360
$587$	−27.3374	−1.12833	−0.564167	−	0.825661i	$-0.690803\pi$
$587$	−27.3374	−1.12833	−0.564167	+	0.825661i	$0.690803\pi$
$588$	−47.6276	−1.96413
$589$	0.671670	0.0276757
$590$	10.5360	0.433759
$591$	5.58103	0.229573
$592$	5.79102	0.238010
$593$	−38.9305	−1.59869	−0.799343	−	0.600875i	$-0.794819\pi$
$593$	−38.9305	−1.59869	−0.799343	+	0.600875i	$0.794819\pi$
$594$	−58.3665	−2.39481
$595$	1.31827	0.0540438
$596$	86.3390	3.53658
$597$	19.1422	0.783438
$598$	69.9117	2.85890
$599$	28.7000	1.17265	0.586326	−	0.810075i	$-0.300574\pi$
$599$	28.7000	1.17265	0.586326	+	0.810075i	$0.300574\pi$
$600$	−16.1935	−0.661097
$601$	−2.72144	−0.111010	−0.0555048	−	0.998458i	$-0.517677\pi$
$601$	−2.72144	−0.111010	−0.0555048	+	0.998458i	$0.517677\pi$
$602$	28.9810	1.18118
$603$	−0.628881	−0.0256100
$604$	−128.476	−5.22760
$605$	−3.68101	−0.149654
$606$	12.6407	0.513493
$607$	44.1385	1.79153	0.895763	−	0.444532i	$-0.146630\pi$
$607$	44.1385	1.79153	0.895763	+	0.444532i	$0.146630\pi$
$608$	128.018	5.19182
$609$	−3.72038	−0.150757
$610$	11.8867	0.481279
$611$	−26.8079	−1.08453
$612$	−2.49598	−0.100894
$613$	12.4413	0.502497	0.251249	−	0.967923i	$-0.419159\pi$
$613$	12.4413	0.502497	0.251249	+	0.967923i	$0.419159\pi$
$614$	−36.2391	−1.46249
$615$	−7.19290	−0.290046
$616$	−51.1328	−2.06020
$617$	4.01754	0.161740	0.0808701	−	0.996725i	$-0.474230\pi$
$617$	4.01754	0.161740	0.0808701	+	0.996725i	$0.474230\pi$
$618$	−22.2294	−0.894198
$619$	−16.3236	−0.656102	−0.328051	−	0.944660i	$-0.606392\pi$
$619$	−16.3236	−0.656102	−0.328051	+	0.944660i	$0.606392\pi$
$620$	0.770723	0.0309530
$621$	31.7003	1.27209
$622$	17.2596	0.692047
$623$	−1.45595	−0.0583315
$624$	117.176	4.69079
$625$	1.00000	0.0400000
$626$	−92.8452	−3.71084
$627$	30.2225	1.20697
$628$	−8.60116	−0.343224
$629$	0.346811	0.0138282
$630$	1.60930	0.0641159
$631$	25.7614	1.02555	0.512773	−	0.858524i	$-0.328618\pi$
$631$	25.7614	1.02555	0.512773	+	0.858524i	$0.328618\pi$
$632$	76.6653	3.04958
$633$	−27.3595	−1.08744
$634$	−39.8846	−1.58402
$635$	−13.3919	−0.531440
$636$	15.9266	0.631531
$637$	−23.0843	−0.914631
$638$	18.7067	0.740606
$639$	0.441134	0.0174510
$640$	54.4802	2.15352
$641$	26.5839	1.05000	0.525001	−	0.851102i	$-0.324065\pi$
$641$	26.5839	1.05000	0.525001	+	0.851102i	$0.324065\pi$
$642$	3.92384	0.154862
$643$	−19.0764	−0.752301	−0.376151	−	0.926559i	$-0.622752\pi$
$643$	−19.0764	−0.752301	−0.376151	+	0.926559i	$0.622752\pi$
$644$	42.9549	1.69266
$645$	−12.7078	−0.500371
$646$	13.6455	0.536874
$647$	26.0471	1.02402	0.512008	−	0.858981i	$-0.328902\pi$
$647$	26.0471	1.02402	0.512008	+	0.858981i	$0.328902\pi$
$648$	75.7416	2.97541
$649$	−14.5879	−0.572624
$650$	−12.1398	−0.476163
$651$	0.287247	0.0112581
$652$	103.559	4.05567
$653$	19.7911	0.774486	0.387243	−	0.921978i	$-0.373427\pi$
$653$	19.7911	0.774486	0.387243	+	0.921978i	$0.373427\pi$
$654$	42.2206	1.65096
$655$	15.7911	0.617010
$656$	75.0833	2.93151
$657$	−0.782451	−0.0305263
$658$	−22.2934	−0.869088
$659$	19.3589	0.754115	0.377057	−	0.926190i	$-0.376936\pi$
$659$	19.3589	0.754115	0.377057	+	0.926190i	$0.376936\pi$
$660$	34.6795	1.34990
$661$	−8.76614	−0.340963	−0.170482	−	0.985361i	$-0.554532\pi$
$661$	−8.76614	−0.340963	−0.170482	+	0.985361i	$0.554532\pi$
$662$	16.9131	0.657348
$663$	7.01739	0.272533
$664$	177.877	6.90296
$665$	−6.50029	−0.252070
$666$	0.423373	0.0164054
$667$	−10.1601	−0.393399
$668$	108.050	4.18057
$669$	20.7026	0.800407
$670$	3.94511	0.152413
$671$	−16.4581	−0.635357
$672$	54.7485	2.11197
$673$	15.4615	0.595999	0.297999	−	0.954566i	$-0.403681\pi$
$673$	15.4615	0.595999	0.297999	+	0.954566i	$0.403681\pi$
$674$	−91.9989	−3.54367
$675$	−5.50459	−0.211872
$676$	35.3312	1.35889
$677$	−33.5727	−1.29030	−0.645151	−	0.764055i	$-0.723206\pi$
$677$	−33.5727	−1.29030	−0.645151	+	0.764055i	$0.723206\pi$
$678$	−89.4221	−3.43424
$679$	−7.68676	−0.294991
$680$	10.1232	0.388206
$681$	5.95614	0.228240
$682$	−1.44433	−0.0553062
$683$	30.5459	1.16881	0.584403	−	0.811464i	$-0.301329\pi$
$683$	30.5459	1.16881	0.584403	+	0.811464i	$0.301329\pi$
$684$	12.3075	0.470589
$685$	−1.27034	−0.0485370
$686$	−44.7334	−1.70793
$687$	47.4774	1.81138
$688$	132.651	5.05728
$689$	7.71934	0.294083
$690$	−25.4931	−0.970504
$691$	37.5619	1.42892	0.714461	−	0.699675i	$-0.246672\pi$
$691$	37.5619	1.42892	0.714461	+	0.699675i	$0.246672\pi$
$692$	75.7714	2.88040
$693$	−2.22819	−0.0846421
$694$	−54.7395	−2.07788
$695$	−9.03774	−0.342821
$696$	−28.5693	−1.08292
$697$	4.49656	0.170319
$698$	−32.2402	−1.22031
$699$	−29.7069	−1.12362
$700$	−7.45891	−0.281920
$701$	−35.3185	−1.33396	−0.666980	−	0.745076i	$-0.732413\pi$
$701$	−35.3185	−1.33396	−0.666980	+	0.745076i	$0.732413\pi$
$702$	66.8248	2.52214
$703$	−1.71010	−0.0644975
$704$	−147.326	−5.55255
$705$	9.77541	0.368163
$706$	−42.6196	−1.60401
$707$	3.76436	0.141573
$708$	34.4595	1.29507
$709$	4.62246	0.173600	0.0868000	−	0.996226i	$-0.472336\pi$
$709$	4.62246	0.173600	0.0868000	+	0.996226i	$0.472336\pi$
$710$	−2.76733	−0.103856
$711$	3.34082	0.125290
$712$	−11.1805	−0.419005
$713$	0.784450	0.0293779
$714$	5.83565	0.218394
$715$	16.8085	0.628603
$716$	76.9829	2.87699
$717$	−23.4326	−0.875108
$718$	62.2995	2.32500
$719$	10.3574	0.386267	0.193134	−	0.981172i	$-0.438135\pi$
$719$	10.3574	0.386267	0.193134	+	0.981172i	$0.438135\pi$
$720$	7.36603	0.274516
$721$	−6.61985	−0.246536
$722$	−14.7056	−0.547284
$723$	−44.3834	−1.65064
$724$	−6.14095	−0.228226
$725$	1.76425	0.0655224
$726$	−16.2949	−0.604759
$727$	45.2325	1.67758	0.838791	−	0.544454i	$-0.183263\pi$
$727$	45.2325	1.67758	0.838791	+	0.544454i	$0.183263\pi$
$728$	58.5427	2.16974
$729$	29.7168	1.10062
$730$	4.90849	0.181671
$731$	7.94416	0.293825
$732$	38.8773	1.43695
$733$	−51.9425	−1.91854	−0.959269	−	0.282493i	$-0.908838\pi$
$733$	−51.9425	−1.91854	−0.959269	+	0.282493i	$0.908838\pi$
$734$	−12.2755	−0.453099
$735$	8.41759	0.310488
$736$	149.514	5.51115
$737$	−5.46231	−0.201207
$738$	5.48923	0.202061
$739$	−1.15946	−0.0426515	−0.0213258	−	0.999773i	$-0.506789\pi$
$739$	−1.15946	−0.0426515	−0.0213258	+	0.999773i	$0.506789\pi$
$740$	−1.96229	−0.0721353
$741$	−34.6022	−1.27114
$742$	6.41939	0.235663
$743$	−22.3224	−0.818929	−0.409464	−	0.912326i	$-0.634284\pi$
$743$	−22.3224	−0.818929	−0.409464	+	0.912326i	$0.634284\pi$
$744$	2.20581	0.0808689
$745$	−15.2594	−0.559059
$746$	−69.6173	−2.54887
$747$	7.75128	0.283604
$748$	−21.6795	−0.792680
$749$	1.16851	0.0426963
$750$	4.42674	0.161642
$751$	−6.39691	−0.233427	−0.116713	−	0.993166i	$-0.537236\pi$
$751$	−6.39691	−0.233427	−0.116713	+	0.993166i	$0.537236\pi$
$752$	−102.041	−3.72105
$753$	−5.38188	−0.196126
$754$	−21.4176	−0.779984
$755$	22.7065	0.826374
$756$	41.0583	1.49328
$757$	5.18467	0.188440	0.0942200	−	0.995551i	$-0.469964\pi$
$757$	5.18467	0.188440	0.0942200	+	0.995551i	$0.469964\pi$
$758$	43.8805	1.59381
$759$	35.2971	1.28120
$760$	−49.9166	−1.81067
$761$	10.0731	0.365150	0.182575	−	0.983192i	$-0.441557\pi$
$761$	10.0731	0.365150	0.182575	+	0.983192i	$0.441557\pi$
$762$	−59.2824	−2.14758
$763$	12.5732	0.455180
$764$	−35.1528	−1.27178
$765$	0.441134	0.0159492
$766$	94.7029	3.42175
$767$	16.7019	0.603071
$768$	118.156	4.26358
$769$	47.9006	1.72734	0.863671	−	0.504057i	$-0.168160\pi$
$769$	47.9006	1.72734	0.863671	+	0.504057i	$0.168160\pi$
$770$	13.9779	0.503730
$771$	24.0687	0.866813
$772$	72.5252	2.61024
$773$	41.9076	1.50731	0.753655	−	0.657270i	$-0.228289\pi$
$773$	41.9076	1.50731	0.753655	+	0.657270i	$0.228289\pi$
$774$	9.69793	0.348585
$775$	−0.136216	−0.00489302
$776$	−59.0277	−2.11897
$777$	−0.731343	−0.0262368
$778$	18.5079	0.663542
$779$	−22.1722	−0.794401
$780$	−39.7051	−1.42167
$781$	3.83158	0.137105
$782$	15.9367	0.569895
$783$	−9.71145	−0.347059
$784$	−87.8673	−3.13812
$785$	1.52015	0.0542564
$786$	69.9032	2.49336
$787$	−24.9984	−0.891097	−0.445549	−	0.895258i	$-0.646991\pi$
$787$	−24.9984	−0.891097	−0.445549	+	0.895258i	$0.646991\pi$
$788$	19.7407	0.703232
$789$	34.3268	1.22207
$790$	−20.9577	−0.745640
$791$	−26.6296	−0.946841
$792$	−17.1106	−0.607999
$793$	18.8431	0.669139
$794$	77.8228	2.76183
$795$	−2.81483	−0.0998317
$796$	67.7078	2.39984
$797$	−30.1142	−1.06670	−0.533350	−	0.845894i	$-0.679067\pi$
$797$	−30.1142	−1.06670	−0.533350	+	0.845894i	$0.679067\pi$
$798$	−28.7751	−1.01863
$799$	−6.11099	−0.216191
$800$	−25.9623	−0.917907
$801$	−0.487207	−0.0172146
$802$	−80.3444	−2.83706
$803$	−6.79618	−0.239832
$804$	12.9031	0.455056
$805$	−7.59175	−0.267574
$806$	1.65364	0.0582468
$807$	−1.40481	−0.0494517
$808$	28.9070	1.01694
$809$	32.8517	1.15500	0.577502	−	0.816389i	$-0.304027\pi$
$809$	32.8517	1.15500	0.577502	+	0.816389i	$0.304027\pi$
$810$	−20.7051	−0.727505
$811$	35.2505	1.23781	0.618906	−	0.785465i	$-0.287576\pi$
$811$	35.2505	1.23781	0.618906	+	0.785465i	$0.287576\pi$
$812$	−13.1594	−0.461803
$813$	−18.9388	−0.664212
$814$	3.67732	0.128890
$815$	−18.3027	−0.641117
$816$	26.7108	0.935065
$817$	−39.1720	−1.37046
$818$	−50.8289	−1.77719
$819$	2.55110	0.0891425
$820$	−25.4420	−0.888474
$821$	−23.1845	−0.809145	−0.404572	−	0.914506i	$-0.632580\pi$
$821$	−23.1845	−0.809145	−0.404572	+	0.914506i	$0.632580\pi$
$822$	−5.62345	−0.196140
$823$	0.692263	0.0241308	0.0120654	−	0.999927i	$-0.496159\pi$
$823$	0.692263	0.0241308	0.0120654	+	0.999927i	$0.496159\pi$
$824$	−50.8347	−1.77091
$825$	−6.12917	−0.213390
$826$	13.8893	0.483270
$827$	−47.4535	−1.65012	−0.825060	−	0.565046i	$-0.808859\pi$
$827$	−47.4535	−1.65012	−0.825060	+	0.565046i	$0.808859\pi$
$828$	14.3740	0.499533
$829$	1.57049	0.0545455	0.0272727	−	0.999628i	$-0.491318\pi$
$829$	1.57049	0.0545455	0.0272727	+	0.999628i	$0.491318\pi$
$830$	−48.6254	−1.68781
$831$	−10.4981	−0.364175
$832$	168.676	5.84778
$833$	−5.26216	−0.182323
$834$	−40.0078	−1.38536
$835$	−19.0964	−0.660859
$836$	106.900	3.69721
$837$	0.749813	0.0259173
$838$	3.44880	0.119137
$839$	13.3656	0.461433	0.230716	−	0.973021i	$-0.425893\pi$
$839$	13.3656	0.461433	0.230716	+	0.973021i	$0.425893\pi$
$840$	−21.3474	−0.736556
$841$	−25.8874	−0.892670
$842$	−43.7563	−1.50794
$843$	27.6606	0.952680
$844$	−96.7733	−3.33107
$845$	−6.24435	−0.214812
$846$	−7.46006	−0.256482
$847$	−4.85256	−0.166736
$848$	29.3827	1.00901
$849$	22.4382	0.770078
$850$	−2.76733	−0.0949186
$851$	−1.99724	−0.0684644
$852$	−9.05096	−0.310081
$853$	−25.1830	−0.862248	−0.431124	−	0.902293i	$-0.641883\pi$
$853$	−25.1830	−0.862248	−0.431124	+	0.902293i	$0.641883\pi$
$854$	15.6699	0.536213
$855$	−2.17520	−0.0743902
$856$	8.97312	0.306695
$857$	51.7376	1.76732	0.883662	−	0.468126i	$-0.155071\pi$
$857$	51.7376	1.76732	0.883662	+	0.468126i	$0.155071\pi$
$858$	74.4070	2.54021
$859$	−26.0192	−0.887764	−0.443882	−	0.896085i	$-0.646399\pi$
$859$	−26.0192	−0.887764	−0.443882	+	0.896085i	$0.646399\pi$
$860$	−44.9489	−1.53274
$861$	−9.48220	−0.323152
$862$	−51.0434	−1.73854
$863$	−25.7491	−0.876508	−0.438254	−	0.898851i	$-0.644403\pi$
$863$	−25.7491	−0.876508	−0.438254	+	0.898851i	$0.644403\pi$
$864$	142.912	4.86197
$865$	−13.3917	−0.455330
$866$	−15.6740	−0.532623
$867$	1.59965	0.0543268
$868$	1.01602	0.0344860
$869$	29.0175	0.984351
$870$	7.80986	0.264779
$871$	6.25388	0.211905
$872$	96.5511	3.26963
$873$	−2.57223	−0.0870567
$874$	−78.5826	−2.65810
$875$	1.31827	0.0445657
$876$	16.0539	0.542412
$877$	33.2874	1.12404	0.562018	−	0.827125i	$-0.310025\pi$
$877$	33.2874	1.12404	0.562018	+	0.827125i	$0.310025\pi$
$878$	−11.6910	−0.394553
$879$	−3.78316	−0.127603
$880$	63.9795	2.15675
$881$	−53.0141	−1.78609	−0.893045	−	0.449968i	$-0.851435\pi$
$881$	−53.0141	−1.78609	−0.893045	+	0.449968i	$0.851435\pi$
$882$	−6.42385	−0.216302
$883$	37.3341	1.25639	0.628197	−	0.778054i	$-0.283793\pi$
$883$	37.3341	1.25639	0.628197	+	0.778054i	$0.283793\pi$
$884$	24.8212	0.834827
$885$	−6.09029	−0.204723
$886$	66.3091	2.22770
$887$	−44.4856	−1.49368	−0.746840	−	0.665004i	$-0.768430\pi$
$887$	−44.4856	−1.49368	−0.746840	+	0.665004i	$0.768430\pi$
$888$	−5.61608	−0.188463
$889$	−17.6541	−0.592100
$890$	3.05635	0.102449
$891$	28.6679	0.960410
$892$	73.2270	2.45182
$893$	30.1328	1.00836
$894$	−67.5492	−2.25918
$895$	−13.6058	−0.454791
$896$	71.8197	2.39933
$897$	−40.4122	−1.34933
$898$	26.9538	0.899461
$899$	−0.240318	−0.00801506
$900$	−2.49598	−0.0831994
$901$	1.75966	0.0586227
$902$	47.6781	1.58751
$903$	−16.7524	−0.557484
$904$	−204.492	−6.80132
$905$	1.08534	0.0360778
$906$	100.516	3.33942
$907$	36.2357	1.20319	0.601593	−	0.798803i	$-0.294533\pi$
$907$	36.2357	1.20319	0.601593	+	0.798803i	$0.294533\pi$
$908$	21.0675	0.699148
$909$	1.25967	0.0417806
$910$	−16.0036	−0.530513
$911$	51.2016	1.69639	0.848193	−	0.529688i	$-0.177691\pi$
$911$	51.2016	1.69639	0.848193	+	0.529688i	$0.177691\pi$
$912$	−131.709	−4.36131
$913$	67.3257	2.22815
$914$	47.9209	1.58508
$915$	−6.87108	−0.227151
$916$	167.932	5.54864
$917$	20.8170	0.687436
$918$	15.2330	0.502765
$919$	−48.9079	−1.61332	−0.806661	−	0.591015i	$-0.798728\pi$
$919$	−48.9079	−1.61332	−0.806661	+	0.591015i	$0.798728\pi$
$920$	−58.2981	−1.92203
$921$	20.9479	0.690256
$922$	−29.3322	−0.966003
$923$	−4.38684	−0.144395
$924$	45.7170	1.50398
$925$	0.346811	0.0114031
$926$	50.3497	1.65459
$927$	−2.21520	−0.0727569
$928$	−45.8039	−1.50359
$929$	22.6880	0.744370	0.372185	−	0.928159i	$-0.378609\pi$
$929$	22.6880	0.744370	0.372185	+	0.928159i	$0.378609\pi$
$930$	−0.602993	−0.0197729
$931$	25.9473	0.850389
$932$	−105.076	−3.44188
$933$	−9.97686	−0.326628
$934$	−26.7740	−0.876072
$935$	3.83158	0.125306
$936$	19.5902	0.640326
$937$	47.0499	1.53705	0.768526	−	0.639819i	$-0.220991\pi$
$937$	47.0499	1.53705	0.768526	+	0.639819i	$0.220991\pi$
$938$	5.20072	0.169810
$939$	53.6689	1.75142
$940$	34.5766	1.12776
$941$	2.91523	0.0950339	0.0475169	−	0.998870i	$-0.484869\pi$
$941$	2.91523	0.0950339	0.0475169	+	0.998870i	$0.484869\pi$
$942$	6.72931	0.219253
$943$	−25.8951	−0.843261
$944$	63.5736	2.06915
$945$	−7.25655	−0.236056
$946$	84.2338	2.73868
$947$	35.8042	1.16348	0.581740	−	0.813375i	$-0.302372\pi$
$947$	35.8042	1.16348	0.581740	+	0.813375i	$0.302372\pi$
$948$	−68.5451	−2.22624
$949$	7.78105	0.252584
$950$	13.6455	0.442718
$951$	23.0552	0.747615
$952$	13.3451	0.432517
$953$	−5.50401	−0.178292	−0.0891461	−	0.996019i	$-0.528414\pi$
$953$	−5.50401	−0.178292	−0.0891461	+	0.996019i	$0.528414\pi$
$954$	2.14813	0.0695481
$955$	6.21282	0.201042
$956$	−82.8836	−2.68065
$957$	−10.8134	−0.349546
$958$	−69.8345	−2.25625
$959$	−1.67465	−0.0540772
$960$	−61.5070	−1.98513
$961$	−30.9814	−0.999401
$962$	−4.21022	−0.135743
$963$	0.391019	0.0126004
$964$	−156.989	−5.05626
$965$	−12.8179	−0.412624
$966$	−33.6068	−1.08128
$967$	16.2904	0.523863	0.261931	−	0.965087i	$-0.415641\pi$
$967$	16.2904	0.523863	0.261931	+	0.965087i	$0.415641\pi$
$968$	−37.2635	−1.19769
$969$	−7.88773	−0.253390
$970$	16.1361	0.518100
$971$	42.5964	1.36698	0.683492	−	0.729958i	$-0.260461\pi$
$971$	42.5964	1.36698	0.683492	+	0.729958i	$0.260461\pi$
$972$	25.7174	0.824887
$973$	−11.9142	−0.381951
$974$	73.9503	2.36952
$975$	7.01739	0.224736
$976$	71.7239	2.29583
$977$	−8.30982	−0.265855	−0.132927	−	0.991126i	$-0.542438\pi$
$977$	−8.30982	−0.265855	−0.132927	+	0.991126i	$0.542438\pi$
$978$	−81.0215	−2.59078
$979$	−4.23176	−0.135248
$980$	29.7739	0.951091
$981$	4.20737	0.134331
$982$	−27.3004	−0.871191
$983$	33.3819	1.06472	0.532358	−	0.846519i	$-0.321306\pi$
$983$	33.3819	1.06472	0.532358	+	0.846519i	$0.321306\pi$
$984$	−72.8150	−2.32126
$985$	−3.48892	−0.111166
$986$	−4.88225	−0.155482
$987$	12.8866	0.410186
$988$	−122.391	−3.89379
$989$	−45.7494	−1.45475
$990$	4.67745	0.148659
$991$	41.3204	1.31258	0.656292	−	0.754507i	$-0.272124\pi$
$991$	41.3204	1.31258	0.656292	+	0.754507i	$0.272124\pi$
$992$	3.53648	0.112283
$993$	−9.77659	−0.310251
$994$	−3.64809	−0.115710
$995$	−11.9665	−0.379364
$996$	−159.037	−5.03927
$997$	3.24343	0.102720	0.0513602	−	0.998680i	$-0.483644\pi$
$997$	3.24343	0.102720	0.0513602	+	0.998680i	$0.483644\pi$
$998$	−47.3724	−1.49955
$999$	−1.90905	−0.0603997

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.e.1.1	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.e.1.1	✓	49	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)

\(f(q)\)	\(=\)	\(q-2.76733 q^{2} +1.59965 q^{3} +5.65810 q^{4} -1.00000 q^{5} -4.42674 q^{6} -1.31827 q^{7} -10.1232 q^{8} -0.441134 q^{9} +O(q^{10})\)	\(q-2.76733 q^{2} +1.59965 q^{3} +5.65810 q^{4} -1.00000 q^{5} -4.42674 q^{6} -1.31827 q^{7} -10.1232 q^{8} -0.441134 q^{9} +2.76733 q^{10} -3.83158 q^{11} +9.05096 q^{12} +4.38684 q^{13} +3.64809 q^{14} -1.59965 q^{15} +16.6979 q^{16} +1.00000 q^{17} +1.22076 q^{18} -4.93092 q^{19} -5.65810 q^{20} -2.10877 q^{21} +10.6032 q^{22} -5.75887 q^{23} -16.1935 q^{24} +1.00000 q^{25} -12.1398 q^{26} -5.50459 q^{27} -7.45891 q^{28} +1.76425 q^{29} +4.42674 q^{30} -0.136216 q^{31} -25.9623 q^{32} -6.12917 q^{33} -2.76733 q^{34} +1.31827 q^{35} -2.49598 q^{36} +0.346811 q^{37} +13.6455 q^{38} +7.01739 q^{39} +10.1232 q^{40} +4.49656 q^{41} +5.83565 q^{42} +7.94416 q^{43} -21.6795 q^{44} +0.441134 q^{45} +15.9367 q^{46} -6.11099 q^{47} +26.7108 q^{48} -5.26216 q^{49} -2.76733 q^{50} +1.59965 q^{51} +24.8212 q^{52} +1.75966 q^{53} +15.2330 q^{54} +3.83158 q^{55} +13.3451 q^{56} -7.88773 q^{57} -4.88225 q^{58} +3.80727 q^{59} -9.05096 q^{60} +4.29538 q^{61} +0.376954 q^{62} +0.581534 q^{63} +38.4504 q^{64} -4.38684 q^{65} +16.9614 q^{66} +1.42560 q^{67} +5.65810 q^{68} -9.21216 q^{69} -3.64809 q^{70} -1.00000 q^{71} +4.46568 q^{72} +1.77373 q^{73} -0.959739 q^{74} +1.59965 q^{75} -27.8997 q^{76} +5.05106 q^{77} -19.4194 q^{78} -7.57324 q^{79} -16.6979 q^{80} -7.48200 q^{81} -12.4435 q^{82} -17.5713 q^{83} -11.9316 q^{84} -1.00000 q^{85} -21.9841 q^{86} +2.82217 q^{87} +38.7878 q^{88} +1.10444 q^{89} -1.22076 q^{90} -5.78304 q^{91} -32.5843 q^{92} -0.217897 q^{93} +16.9111 q^{94} +4.93092 q^{95} -41.5305 q^{96} +5.83094 q^{97} +14.5621 q^{98} +1.69024 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q + q^{2} + 10 q^{3} + 55 q^{4} - 49 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 43 q^{9}+O(q^{10}) \) 49 * q + q^2 + 10 * q^3 + 55 * q^4 - 49 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 43 * q^9	\( 49 q + q^{2} + 10 q^{3} + 55 q^{4} - 49 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 43 q^{9} - q^{10} - 4 q^{11} + 32 q^{12} + 21 q^{13} + 8 q^{14} - 10 q^{15} + 63 q^{16} + 49 q^{17} + 12 q^{18} + 19 q^{19} - 55 q^{20} + 5 q^{21} + 10 q^{22} + 10 q^{23} + 7 q^{24} + 49 q^{25} - 20 q^{26} + 37 q^{27} + 48 q^{28} + 30 q^{29} - 2 q^{30} + 23 q^{31} + 2 q^{32} - q^{33} + q^{34} - 15 q^{35} + 39 q^{36} + 60 q^{37} + 13 q^{38} + 3 q^{39} - 3 q^{40} - 29 q^{41} + 32 q^{42} + 23 q^{43} + 11 q^{44} - 43 q^{45} + 6 q^{46} - 8 q^{47} + 96 q^{48} + 82 q^{49} + q^{50} + 10 q^{51} + 11 q^{52} + 15 q^{53} - 4 q^{54} + 4 q^{55} - 18 q^{56} + 44 q^{57} + 38 q^{58} - 28 q^{59} - 32 q^{60} + 107 q^{61} + 37 q^{62} + 54 q^{63} + 77 q^{64} - 21 q^{65} + 23 q^{66} + 11 q^{67} + 55 q^{68} + 27 q^{69} - 8 q^{70} - 49 q^{71} - 53 q^{72} + 97 q^{73} + 27 q^{74} + 10 q^{75} + 66 q^{76} + 19 q^{77} + 48 q^{78} + 31 q^{79} - 63 q^{80} - 7 q^{81} + 61 q^{82} + 6 q^{83} + 46 q^{84} - 49 q^{85} - 89 q^{86} + 36 q^{87} + 63 q^{88} - 20 q^{89} - 12 q^{90} + 35 q^{91} - 2 q^{92} + 47 q^{93} - 4 q^{94} - 19 q^{95} + 73 q^{96} + 92 q^{97} + 3 q^{98} + 5 q^{99}+O(q^{100}) \) 49 * q + q^2 + 10 * q^3 + 55 * q^4 - 49 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 43 * q^9 - q^10 - 4 * q^11 + 32 * q^12 + 21 * q^13 + 8 * q^14 - 10 * q^15 + 63 * q^16 + 49 * q^17 + 12 * q^18 + 19 * q^19 - 55 * q^20 + 5 * q^21 + 10 * q^22 + 10 * q^23 + 7 * q^24 + 49 * q^25 - 20 * q^26 + 37 * q^27 + 48 * q^28 + 30 * q^29 - 2 * q^30 + 23 * q^31 + 2 * q^32 - q^33 + q^34 - 15 * q^35 + 39 * q^36 + 60 * q^37 + 13 * q^38 + 3 * q^39 - 3 * q^40 - 29 * q^41 + 32 * q^42 + 23 * q^43 + 11 * q^44 - 43 * q^45 + 6 * q^46 - 8 * q^47 + 96 * q^48 + 82 * q^49 + q^50 + 10 * q^51 + 11 * q^52 + 15 * q^53 - 4 * q^54 + 4 * q^55 - 18 * q^56 + 44 * q^57 + 38 * q^58 - 28 * q^59 - 32 * q^60 + 107 * q^61 + 37 * q^62 + 54 * q^63 + 77 * q^64 - 21 * q^65 + 23 * q^66 + 11 * q^67 + 55 * q^68 + 27 * q^69 - 8 * q^70 - 49 * q^71 - 53 * q^72 + 97 * q^73 + 27 * q^74 + 10 * q^75 + 66 * q^76 + 19 * q^77 + 48 * q^78 + 31 * q^79 - 63 * q^80 - 7 * q^81 + 61 * q^82 + 6 * q^83 + 46 * q^84 - 49 * q^85 - 89 * q^86 + 36 * q^87 + 63 * q^88 - 20 * q^89 - 12 * q^90 + 35 * q^91 - 2 * q^92 + 47 * q^93 - 4 * q^94 - 19 * q^95 + 73 * q^96 + 92 * q^97 + 3 * q^98 + 5 * q^99

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