LMFDB - Embedded newform 6035.2.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1897176198$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-2.27701 q^{2} +0.848689 q^{3} +3.18476 q^{4} +1.00000 q^{5} -1.93247 q^{6} +1.85809 q^{7} -2.69770 q^{8} -2.27973 q^{9} +O(q^{10})$	\(q-2.27701 q^{2} +0.848689 q^{3} +3.18476 q^{4} +1.00000 q^{5} -1.93247 q^{6} +1.85809 q^{7} -2.69770 q^{8} -2.27973 q^{9} -2.27701 q^{10} +4.31177 q^{11} +2.70287 q^{12} -4.95696 q^{13} -4.23088 q^{14} +0.848689 q^{15} -0.226840 q^{16} +1.00000 q^{17} +5.19095 q^{18} -0.700242 q^{19} +3.18476 q^{20} +1.57694 q^{21} -9.81792 q^{22} -5.75384 q^{23} -2.28951 q^{24} +1.00000 q^{25} +11.2870 q^{26} -4.48085 q^{27} +5.91757 q^{28} -3.12859 q^{29} -1.93247 q^{30} -1.10131 q^{31} +5.91191 q^{32} +3.65935 q^{33} -2.27701 q^{34} +1.85809 q^{35} -7.26038 q^{36} +11.3629 q^{37} +1.59446 q^{38} -4.20692 q^{39} -2.69770 q^{40} -4.44822 q^{41} -3.59070 q^{42} +6.43005 q^{43} +13.7319 q^{44} -2.27973 q^{45} +13.1015 q^{46} -1.35530 q^{47} -0.192517 q^{48} -3.54750 q^{49} -2.27701 q^{50} +0.848689 q^{51} -15.7867 q^{52} -5.39978 q^{53} +10.2029 q^{54} +4.31177 q^{55} -5.01257 q^{56} -0.594288 q^{57} +7.12381 q^{58} -1.36008 q^{59} +2.70287 q^{60} -3.02094 q^{61} +2.50770 q^{62} -4.23594 q^{63} -13.0078 q^{64} -4.95696 q^{65} -8.33236 q^{66} +10.4731 q^{67} +3.18476 q^{68} -4.88322 q^{69} -4.23088 q^{70} -1.00000 q^{71} +6.15001 q^{72} -11.8306 q^{73} -25.8733 q^{74} +0.848689 q^{75} -2.23010 q^{76} +8.01166 q^{77} +9.57918 q^{78} -2.60660 q^{79} -0.226840 q^{80} +3.03634 q^{81} +10.1286 q^{82} +3.28111 q^{83} +5.02217 q^{84} +1.00000 q^{85} -14.6413 q^{86} -2.65520 q^{87} -11.6318 q^{88} -4.05642 q^{89} +5.19095 q^{90} -9.21048 q^{91} -18.3246 q^{92} -0.934674 q^{93} +3.08602 q^{94} -0.700242 q^{95} +5.01737 q^{96} -17.2876 q^{97} +8.07768 q^{98} -9.82966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.27701	−1.61009	−0.805043	−	0.593216i	$-0.797858\pi$
$2$	−2.27701	−1.61009	−0.805043	+	0.593216i	$0.797858\pi$
$3$	0.848689	0.489991	0.244995	−	0.969524i	$-0.421214\pi$
$3$	0.848689	0.489991	0.244995	+	0.969524i	$0.421214\pi$
$4$	3.18476	1.59238
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.93247	−0.788927
$7$	1.85809	0.702292	0.351146	−	0.936321i	$-0.385792\pi$
$7$	1.85809	0.702292	0.351146	+	0.936321i	$0.385792\pi$
$8$	−2.69770	−0.953780
$9$	−2.27973	−0.759909
$10$	−2.27701	−0.720053
$11$	4.31177	1.30005	0.650024	−	0.759914i	$-0.274759\pi$
$11$	4.31177	1.30005	0.650024	+	0.759914i	$0.274759\pi$
$12$	2.70287	0.780251
$13$	−4.95696	−1.37481	−0.687407	−	0.726273i	$-0.741251\pi$
$13$	−4.95696	−1.37481	−0.687407	+	0.726273i	$0.741251\pi$
$14$	−4.23088	−1.13075
$15$	0.848689	0.219131
$16$	−0.226840	−0.0567101
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	5.19095	1.22352
$19$	−0.700242	−0.160647	−0.0803233	−	0.996769i	$-0.525595\pi$
$19$	−0.700242	−0.160647	−0.0803233	+	0.996769i	$0.525595\pi$
$20$	3.18476	0.712133
$21$	1.57694	0.344117
$22$	−9.81792	−2.09319
$23$	−5.75384	−1.19976	−0.599879	−	0.800091i	$-0.704785\pi$
$23$	−5.75384	−1.19976	−0.599879	+	0.800091i	$0.704785\pi$
$24$	−2.28951	−0.467343
$25$	1.00000	0.200000
$26$	11.2870	2.21357
$27$	−4.48085	−0.862339
$28$	5.91757	1.11831
$29$	−3.12859	−0.580964	−0.290482	−	0.956880i	$-0.593816\pi$
$29$	−3.12859	−0.580964	−0.290482	+	0.956880i	$0.593816\pi$
$30$	−1.93247	−0.352819
$31$	−1.10131	−0.197802	−0.0989010	−	0.995097i	$-0.531533\pi$
$31$	−1.10131	−0.197802	−0.0989010	+	0.995097i	$0.531533\pi$
$32$	5.91191	1.04509
$33$	3.65935	0.637011
$34$	−2.27701	−0.390503
$35$	1.85809	0.314075
$36$	−7.26038	−1.21006
$37$	11.3629	1.86805	0.934023	−	0.357214i	$-0.116273\pi$
$37$	11.3629	1.86805	0.934023	+	0.357214i	$0.116273\pi$
$38$	1.59446	0.258655
$39$	−4.20692	−0.673646
$40$	−2.69770	−0.426543
$41$	−4.44822	−0.694695	−0.347347	−	0.937737i	$-0.612918\pi$
$41$	−4.44822	−0.694695	−0.347347	+	0.937737i	$0.612918\pi$
$42$	−3.59070	−0.554058
$43$	6.43005	0.980574	0.490287	−	0.871561i	$-0.336892\pi$
$43$	6.43005	0.980574	0.490287	+	0.871561i	$0.336892\pi$
$44$	13.7319	2.07017
$45$	−2.27973	−0.339842
$46$	13.1015	1.93171
$47$	−1.35530	−0.197690	−0.0988452	−	0.995103i	$-0.531515\pi$
$47$	−1.35530	−0.197690	−0.0988452	+	0.995103i	$0.531515\pi$
$48$	−0.192517	−0.0277874
$49$	−3.54750	−0.506786
$50$	−2.27701	−0.322017
$51$	0.848689	0.118840
$52$	−15.7867	−2.18922
$53$	−5.39978	−0.741717	−0.370859	−	0.928689i	$-0.620937\pi$
$53$	−5.39978	−0.741717	−0.370859	+	0.928689i	$0.620937\pi$
$54$	10.2029	1.38844
$55$	4.31177	0.581399
$56$	−5.01257	−0.669832
$57$	−0.594288	−0.0787154
$58$	7.12381	0.935402
$59$	−1.36008	−0.177068	−0.0885339	−	0.996073i	$-0.528218\pi$
$59$	−1.36008	−0.177068	−0.0885339	+	0.996073i	$0.528218\pi$
$60$	2.70287	0.348939
$61$	−3.02094	−0.386792	−0.193396	−	0.981121i	$-0.561950\pi$
$61$	−3.02094	−0.386792	−0.193396	+	0.981121i	$0.561950\pi$
$62$	2.50770	0.318478
$63$	−4.23594	−0.533678
$64$	−13.0078	−1.62597
$65$	−4.95696	−0.614835
$66$	−8.33236	−1.02564
$67$	10.4731	1.27949	0.639747	−	0.768585i	$-0.279039\pi$
$67$	10.4731	1.27949	0.639747	+	0.768585i	$0.279039\pi$
$68$	3.18476	0.386208
$69$	−4.88322	−0.587870
$70$	−4.23088	−0.505687
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	6.15001	0.724786
$73$	−11.8306	−1.38467	−0.692333	−	0.721578i	$-0.743417\pi$
$73$	−11.8306	−1.38467	−0.692333	+	0.721578i	$0.743417\pi$
$74$	−25.8733	−3.00771
$75$	0.848689	0.0979982
$76$	−2.23010	−0.255810
$77$	8.01166	0.913013
$78$	9.57918	1.08463
$79$	−2.60660	−0.293265	−0.146633	−	0.989191i	$-0.546843\pi$
$79$	−2.60660	−0.293265	−0.146633	+	0.989191i	$0.546843\pi$
$80$	−0.226840	−0.0253615
$81$	3.03634	0.337371
$82$	10.1286	1.11852
$83$	3.28111	0.360149	0.180074	−	0.983653i	$-0.442366\pi$
$83$	3.28111	0.360149	0.180074	+	0.983653i	$0.442366\pi$
$84$	5.02217	0.547964
$85$	1.00000	0.108465
$86$	−14.6413	−1.57881
$87$	−2.65520	−0.284667
$88$	−11.6318	−1.23996
$89$	−4.05642	−0.429980	−0.214990	−	0.976616i	$-0.568972\pi$
$89$	−4.05642	−0.429980	−0.214990	+	0.976616i	$0.568972\pi$
$90$	5.19095	0.547174
$91$	−9.21048	−0.965521
$92$	−18.3246	−1.91047
$93$	−0.934674	−0.0969212
$94$	3.08602	0.318299
$95$	−0.700242	−0.0718434
$96$	5.01737	0.512084
$97$	−17.2876	−1.75529	−0.877644	−	0.479312i	$-0.840886\pi$
$97$	−17.2876	−1.75529	−0.877644	+	0.479312i	$0.840886\pi$
$98$	8.07768	0.815969
$99$	−9.82966	−0.987918
$100$	3.18476	0.318476
$101$	4.27957	0.425833	0.212917	−	0.977070i	$-0.431704\pi$
$101$	4.27957	0.425833	0.212917	+	0.977070i	$0.431704\pi$
$102$	−1.93247	−0.191343
$103$	3.27159	0.322359	0.161180	−	0.986925i	$-0.448470\pi$
$103$	3.27159	0.322359	0.161180	+	0.986925i	$0.448470\pi$
$104$	13.3724	1.31127
$105$	1.57694	0.153894
$106$	12.2953	1.19423
$107$	−7.64671	−0.739235	−0.369618	−	0.929184i	$-0.620511\pi$
$107$	−7.64671	−0.739235	−0.369618	+	0.929184i	$0.620511\pi$
$108$	−14.2704	−1.37317
$109$	8.89906	0.852376	0.426188	−	0.904635i	$-0.359856\pi$
$109$	8.89906	0.852376	0.426188	+	0.904635i	$0.359856\pi$
$110$	−9.81792	−0.936102
$111$	9.64355	0.915325
$112$	−0.421490	−0.0398271
$113$	9.84989	0.926600	0.463300	−	0.886202i	$-0.346665\pi$
$113$	9.84989	0.926600	0.463300	+	0.886202i	$0.346665\pi$
$114$	1.35320	0.126739
$115$	−5.75384	−0.536548
$116$	−9.96378	−0.925114
$117$	11.3005	1.04473
$118$	3.09692	0.285094
$119$	1.85809	0.170331
$120$	−2.28951	−0.209002
$121$	7.59135	0.690123
$122$	6.87870	0.622768
$123$	−3.77515	−0.340394
$124$	−3.50742	−0.314976
$125$	1.00000	0.0894427
$126$	9.64526	0.859268
$127$	−3.83486	−0.340289	−0.170144	−	0.985419i	$-0.554423\pi$
$127$	−3.83486	−0.340289	−0.170144	+	0.985419i	$0.554423\pi$
$128$	17.7950	1.57287
$129$	5.45711	0.480472
$130$	11.2870	0.989938
$131$	−6.77978	−0.592352	−0.296176	−	0.955133i	$-0.595712\pi$
$131$	−6.77978	−0.592352	−0.296176	+	0.955133i	$0.595712\pi$
$132$	11.6541	1.01436
$133$	−1.30111	−0.112821
$134$	−23.8473	−2.06010
$135$	−4.48085	−0.385650
$136$	−2.69770	−0.231326
$137$	−15.3056	−1.30764	−0.653821	−	0.756649i	$-0.726835\pi$
$137$	−15.3056	−1.30764	−0.653821	+	0.756649i	$0.726835\pi$
$138$	11.1191	0.946522
$139$	−19.0201	−1.61327	−0.806633	−	0.591053i	$-0.798713\pi$
$139$	−19.0201	−1.61327	−0.806633	+	0.591053i	$0.798713\pi$
$140$	5.91757	0.500126
$141$	−1.15023	−0.0968664
$142$	2.27701	0.191082
$143$	−21.3733	−1.78732
$144$	0.517134	0.0430945
$145$	−3.12859	−0.259815
$146$	26.9383	2.22943
$147$	−3.01072	−0.248320
$148$	36.1880	2.97463
$149$	1.05130	0.0861256	0.0430628	−	0.999072i	$-0.486288\pi$
$149$	1.05130	0.0861256	0.0430628	+	0.999072i	$0.486288\pi$
$150$	−1.93247	−0.157785
$151$	−20.0467	−1.63138	−0.815689	−	0.578491i	$-0.803642\pi$
$151$	−20.0467	−1.63138	−0.815689	+	0.578491i	$0.803642\pi$
$152$	1.88904	0.153222
$153$	−2.27973	−0.184305
$154$	−18.2426	−1.47003
$155$	−1.10131	−0.0884597
$156$	−13.3980	−1.07270
$157$	7.80859	0.623194	0.311597	−	0.950214i	$-0.399136\pi$
$157$	7.80859	0.623194	0.311597	+	0.950214i	$0.399136\pi$
$158$	5.93524	0.472182
$159$	−4.58274	−0.363435
$160$	5.91191	0.467378
$161$	−10.6912	−0.842581
$162$	−6.91376	−0.543196
$163$	−17.4897	−1.36990	−0.684950	−	0.728590i	$-0.740176\pi$
$163$	−17.4897	−1.36990	−0.684950	+	0.728590i	$0.740176\pi$
$164$	−14.1665	−1.10622
$165$	3.65935	0.284880
$166$	−7.47111	−0.579871
$167$	−7.38174	−0.571216	−0.285608	−	0.958346i	$-0.592196\pi$
$167$	−7.38174	−0.571216	−0.285608	+	0.958346i	$0.592196\pi$
$168$	−4.25411	−0.328212
$169$	11.5715	0.890113
$170$	−2.27701	−0.174638
$171$	1.59636	0.122077
$172$	20.4782	1.56144
$173$	2.70430	0.205604	0.102802	−	0.994702i	$-0.467219\pi$
$173$	2.70430	0.205604	0.102802	+	0.994702i	$0.467219\pi$
$174$	6.04590	0.458338
$175$	1.85809	0.140458
$176$	−0.978084	−0.0737258
$177$	−1.15429	−0.0867616
$178$	9.23649	0.692304
$179$	7.90075	0.590530	0.295265	−	0.955415i	$-0.404592\pi$
$179$	7.90075	0.590530	0.295265	+	0.955415i	$0.404592\pi$
$180$	−7.26038	−0.541156
$181$	−17.0710	−1.26888	−0.634438	−	0.772974i	$-0.718768\pi$
$181$	−17.0710	−1.26888	−0.634438	+	0.772974i	$0.718768\pi$
$182$	20.9723	1.55457
$183$	−2.56384	−0.189524
$184$	15.5221	1.14431
$185$	11.3629	0.835415
$186$	2.12826	0.156051
$187$	4.31177	0.315308
$188$	−4.31629	−0.314798
$189$	−8.32582	−0.605614
$190$	1.59446	0.115674
$191$	−8.29896	−0.600492	−0.300246	−	0.953862i	$-0.597069\pi$
$191$	−8.29896	−0.600492	−0.300246	+	0.953862i	$0.597069\pi$
$192$	−11.0396	−0.796711
$193$	0.939027	0.0675927	0.0337963	−	0.999429i	$-0.489240\pi$
$193$	0.939027	0.0675927	0.0337963	+	0.999429i	$0.489240\pi$
$194$	39.3639	2.82617
$195$	−4.20692	−0.301264
$196$	−11.2979	−0.806994
$197$	1.64472	0.117181	0.0585906	−	0.998282i	$-0.481339\pi$
$197$	1.64472	0.117181	0.0585906	+	0.998282i	$0.481339\pi$
$198$	22.3822	1.59063
$199$	−17.7420	−1.25770	−0.628848	−	0.777529i	$-0.716473\pi$
$199$	−17.7420	−1.25770	−0.628848	+	0.777529i	$0.716473\pi$
$200$	−2.69770	−0.190756
$201$	8.88841	0.626940
$202$	−9.74461	−0.685628
$203$	−5.81320	−0.408006
$204$	2.70287	0.189239
$205$	−4.44822	−0.310677
$206$	−7.44943	−0.519026
$207$	13.1172	0.911707
$208$	1.12444	0.0779658
$209$	−3.01928	−0.208848
$210$	−3.59070	−0.247782
$211$	13.6066	0.936719	0.468360	−	0.883538i	$-0.344845\pi$
$211$	13.6066	0.936719	0.468360	+	0.883538i	$0.344845\pi$
$212$	−17.1970	−1.18109
$213$	−0.848689	−0.0581512
$214$	17.4116	1.19023
$215$	6.43005	0.438526
$216$	12.0880	0.822482
$217$	−2.04634	−0.138915
$218$	−20.2632	−1.37240
$219$	−10.0405	−0.678474
$220$	13.7319	0.925807
$221$	−4.95696	−0.333441
$222$	−21.9584	−1.47375
$223$	−11.8560	−0.793937	−0.396969	−	0.917832i	$-0.629938\pi$
$223$	−11.8560	−0.793937	−0.396969	+	0.917832i	$0.629938\pi$
$224$	10.9849	0.733957
$225$	−2.27973	−0.151982
$226$	−22.4283	−1.49191
$227$	10.5965	0.703313	0.351656	−	0.936129i	$-0.385619\pi$
$227$	10.5965	0.703313	0.351656	+	0.936129i	$0.385619\pi$
$228$	−1.89266	−0.125345
$229$	4.33935	0.286753	0.143376	−	0.989668i	$-0.454204\pi$
$229$	4.33935	0.286753	0.143376	+	0.989668i	$0.454204\pi$
$230$	13.1015	0.863889
$231$	6.79941	0.447368
$232$	8.43998	0.554112
$233$	16.4994	1.08091	0.540457	−	0.841372i	$-0.318251\pi$
$233$	16.4994	1.08091	0.540457	+	0.841372i	$0.318251\pi$
$234$	−25.7314	−1.68211
$235$	−1.35530	−0.0884098
$236$	−4.33153	−0.281959
$237$	−2.21219	−0.143697
$238$	−4.23088	−0.274247
$239$	18.9187	1.22375	0.611874	−	0.790955i	$-0.290416\pi$
$239$	18.9187	1.22375	0.611874	+	0.790955i	$0.290416\pi$
$240$	−0.192517	−0.0124269
$241$	−27.7964	−1.79052	−0.895261	−	0.445543i	$-0.853011\pi$
$241$	−27.7964	−1.79052	−0.895261	+	0.445543i	$0.853011\pi$
$242$	−17.2856	−1.11116
$243$	16.0194	1.02765
$244$	−9.62096	−0.615919
$245$	−3.54750	−0.226641
$246$	8.59604	0.548064
$247$	3.47107	0.220859
$248$	2.97101	0.188660
$249$	2.78464	0.176470
$250$	−2.27701	−0.144011
$251$	1.28133	0.0808767	0.0404383	−	0.999182i	$-0.487125\pi$
$251$	1.28133	0.0808767	0.0404383	+	0.999182i	$0.487125\pi$
$252$	−13.4904	−0.849818
$253$	−24.8092	−1.55974
$254$	8.73199	0.547894
$255$	0.848689	0.0531470
$256$	−14.5037	−0.906480
$257$	28.6596	1.78774	0.893869	−	0.448328i	$-0.147980\pi$
$257$	28.6596	1.78774	0.893869	+	0.448328i	$0.147980\pi$
$258$	−12.4259	−0.773602
$259$	21.1133	1.31191
$260$	−15.7867	−0.979050
$261$	7.13232	0.441480
$262$	15.4376	0.953738
$263$	−7.26849	−0.448194	−0.224097	−	0.974567i	$-0.571943\pi$
$263$	−7.26849	−0.448194	−0.224097	+	0.974567i	$0.571943\pi$
$264$	−9.87182	−0.607568
$265$	−5.39978	−0.331706
$266$	2.96264	0.181651
$267$	−3.44264	−0.210686
$268$	33.3543	2.03744
$269$	−8.19905	−0.499905	−0.249953	−	0.968258i	$-0.580415\pi$
$269$	−8.19905	−0.499905	−0.249953	+	0.968258i	$0.580415\pi$
$270$	10.2029	0.620929
$271$	−14.5629	−0.884634	−0.442317	−	0.896859i	$-0.645843\pi$
$271$	−14.5629	−0.884634	−0.442317	+	0.896859i	$0.645843\pi$
$272$	−0.226840	−0.0137542
$273$	−7.81684	−0.473096
$274$	34.8508	2.10542
$275$	4.31177	0.260009
$276$	−15.5519	−0.936112
$277$	4.04353	0.242952	0.121476	−	0.992594i	$-0.461237\pi$
$277$	4.04353	0.242952	0.121476	+	0.992594i	$0.461237\pi$
$278$	43.3089	2.59750
$279$	2.51070	0.150312
$280$	−5.01257	−0.299558
$281$	15.1447	0.903455	0.451728	−	0.892156i	$-0.350808\pi$
$281$	15.1447	0.903455	0.451728	+	0.892156i	$0.350808\pi$
$282$	2.61907	0.155963
$283$	−27.4272	−1.63038	−0.815188	−	0.579196i	$-0.803366\pi$
$283$	−27.4272	−1.63038	−0.815188	+	0.579196i	$0.803366\pi$
$284$	−3.18476	−0.188981
$285$	−0.594288	−0.0352026
$286$	48.6671	2.87774
$287$	−8.26519	−0.487879
$288$	−13.4775	−0.794172
$289$	1.00000	0.0588235
$290$	7.12381	0.418325
$291$	−14.6718	−0.860075
$292$	−37.6776	−2.20491
$293$	7.79893	0.455618	0.227809	−	0.973706i	$-0.426844\pi$
$293$	7.79893	0.455618	0.227809	+	0.973706i	$0.426844\pi$
$294$	6.85543	0.399817
$295$	−1.36008	−0.0791871
$296$	−30.6536	−1.78170
$297$	−19.3204	−1.12108
$298$	−2.39381	−0.138670
$299$	28.5216	1.64944
$300$	2.70287	0.156050
$301$	11.9476	0.688649
$302$	45.6465	2.62666
$303$	3.63202	0.208654
$304$	0.158843	0.00911029
$305$	−3.02094	−0.172979
$306$	5.19095	0.296747
$307$	23.5477	1.34394	0.671968	−	0.740580i	$-0.265449\pi$
$307$	23.5477	1.34394	0.671968	+	0.740580i	$0.265449\pi$
$308$	25.5152	1.45386
$309$	2.77656	0.157953
$310$	2.50770	0.142428
$311$	−15.4349	−0.875233	−0.437617	−	0.899162i	$-0.644177\pi$
$311$	−15.4349	−0.875233	−0.437617	+	0.899162i	$0.644177\pi$
$312$	11.3490	0.642510
$313$	−13.6147	−0.769551	−0.384775	−	0.923010i	$-0.625721\pi$
$313$	−13.6147	−0.769551	−0.384775	+	0.923010i	$0.625721\pi$
$314$	−17.7802	−1.00340
$315$	−4.23594	−0.238668
$316$	−8.30138	−0.466989
$317$	−5.39604	−0.303072	−0.151536	−	0.988452i	$-0.548422\pi$
$317$	−5.39604	−0.303072	−0.151536	+	0.988452i	$0.548422\pi$
$318$	10.4349	0.585161
$319$	−13.4897	−0.755281
$320$	−13.0078	−0.727157
$321$	−6.48968	−0.362219
$322$	24.3438	1.35663
$323$	−0.700242	−0.0389625
$324$	9.66999	0.537222
$325$	−4.95696	−0.274963
$326$	39.8242	2.20566
$327$	7.55253	0.417656
$328$	11.9999	0.662586
$329$	−2.51826	−0.138836
$330$	−8.33236	−0.458681
$331$	15.0444	0.826917	0.413458	−	0.910523i	$-0.364321\pi$
$331$	15.0444	0.826917	0.413458	+	0.910523i	$0.364321\pi$
$332$	10.4495	0.573493
$333$	−25.9043	−1.41954
$334$	16.8083	0.919708
$335$	10.4731	0.572207
$336$	−0.357714	−0.0195149
$337$	−8.02836	−0.437332	−0.218666	−	0.975800i	$-0.570171\pi$
$337$	−8.02836	−0.437332	−0.218666	+	0.975800i	$0.570171\pi$
$338$	−26.3483	−1.43316
$339$	8.35949	0.454025
$340$	3.18476	0.172718
$341$	−4.74862	−0.257152
$342$	−3.63492	−0.196554
$343$	−19.5982	−1.05820
$344$	−17.3463	−0.935252
$345$	−4.88322	−0.262904
$346$	−6.15771	−0.331041
$347$	6.95376	0.373297	0.186649	−	0.982427i	$-0.440237\pi$
$347$	6.95376	0.373297	0.186649	+	0.982427i	$0.440237\pi$
$348$	−8.45615	−0.453297
$349$	−14.7046	−0.787118	−0.393559	−	0.919299i	$-0.628756\pi$
$349$	−14.7046	−0.787118	−0.393559	+	0.919299i	$0.628756\pi$
$350$	−4.23088	−0.226150
$351$	22.2114	1.18556
$352$	25.4908	1.35866
$353$	−7.53008	−0.400786	−0.200393	−	0.979716i	$-0.564222\pi$
$353$	−7.53008	−0.400786	−0.200393	+	0.979716i	$0.564222\pi$
$354$	2.62832	0.139694
$355$	−1.00000	−0.0530745
$356$	−12.9187	−0.684690
$357$	1.57694	0.0834606
$358$	−17.9901	−0.950804
$359$	−1.95130	−0.102985	−0.0514927	−	0.998673i	$-0.516398\pi$
$359$	−1.95130	−0.102985	−0.0514927	+	0.998673i	$0.516398\pi$
$360$	6.15001	0.324134
$361$	−18.5097	−0.974193
$362$	38.8707	2.04300
$363$	6.44270	0.338154
$364$	−29.3331	−1.53747
$365$	−11.8306	−0.619242
$366$	5.83788	0.305151
$367$	21.8576	1.14096	0.570479	−	0.821312i	$-0.306758\pi$
$367$	21.8576	1.14096	0.570479	+	0.821312i	$0.306758\pi$
$368$	1.30520	0.0680384
$369$	10.1407	0.527905
$370$	−25.8733	−1.34509
$371$	−10.0333	−0.520902
$372$	−2.97671	−0.154335
$373$	19.2141	0.994870	0.497435	−	0.867501i	$-0.334275\pi$
$373$	19.2141	0.994870	0.497435	+	0.867501i	$0.334275\pi$
$374$	−9.81792	−0.507673
$375$	0.848689	0.0438261
$376$	3.65618	0.188553
$377$	15.5083	0.798717
$378$	18.9579	0.975091
$379$	−33.8623	−1.73939	−0.869695	−	0.493590i	$-0.835684\pi$
$379$	−33.8623	−1.73939	−0.869695	+	0.493590i	$0.835684\pi$
$380$	−2.23010	−0.114402
$381$	−3.25460	−0.166738
$382$	18.8968	0.966844
$383$	13.8025	0.705275	0.352638	−	0.935760i	$-0.385285\pi$
$383$	13.8025	0.705275	0.352638	+	0.935760i	$0.385285\pi$
$384$	15.1024	0.770690
$385$	8.01166	0.408312
$386$	−2.13817	−0.108830
$387$	−14.6588	−0.745147
$388$	−55.0568	−2.79508
$389$	36.2356	1.83722	0.918609	−	0.395168i	$-0.129314\pi$
$389$	36.2356	1.83722	0.918609	+	0.395168i	$0.129314\pi$
$390$	9.57918	0.485061
$391$	−5.75384	−0.290984
$392$	9.57008	0.483362
$393$	−5.75393	−0.290247
$394$	−3.74503	−0.188672
$395$	−2.60660	−0.131152
$396$	−31.3051	−1.57314
$397$	35.1520	1.76423	0.882113	−	0.471038i	$-0.156120\pi$
$397$	35.1520	1.76423	0.882113	+	0.471038i	$0.156120\pi$
$398$	40.3986	2.02500
$399$	−1.10424	−0.0552812
$400$	−0.226840	−0.0113420
$401$	−38.7369	−1.93443	−0.967215	−	0.253958i	$-0.918267\pi$
$401$	−38.7369	−1.93443	−0.967215	+	0.253958i	$0.918267\pi$
$402$	−20.2390	−1.00943
$403$	5.45918	0.271941
$404$	13.6294	0.678087
$405$	3.03634	0.150877
$406$	13.2367	0.656926
$407$	48.9941	2.42855
$408$	−2.28951	−0.113347
$409$	−19.5087	−0.964645	−0.482322	−	0.875994i	$-0.660207\pi$
$409$	−19.5087	−0.964645	−0.482322	+	0.875994i	$0.660207\pi$
$410$	10.1286	0.500217
$411$	−12.9897	−0.640732
$412$	10.4192	0.513318
$413$	−2.52716	−0.124353
$414$	−29.8679	−1.46793
$415$	3.28111	0.161063
$416$	−29.3051	−1.43680
$417$	−16.1422	−0.790485
$418$	6.87493	0.336264
$419$	5.14726	0.251460	0.125730	−	0.992064i	$-0.459873\pi$
$419$	5.14726	0.251460	0.125730	+	0.992064i	$0.459873\pi$
$420$	5.02217	0.245057
$421$	17.6342	0.859438	0.429719	−	0.902963i	$-0.358613\pi$
$421$	17.6342	0.859438	0.429719	+	0.902963i	$0.358613\pi$
$422$	−30.9824	−1.50820
$423$	3.08971	0.150227
$424$	14.5670	0.707435
$425$	1.00000	0.0485071
$426$	1.93247	0.0936285
$427$	−5.61318	−0.271641
$428$	−24.3529	−1.17714
$429$	−18.1393	−0.875772
$430$	−14.6413	−0.706065
$431$	−6.87892	−0.331346	−0.165673	−	0.986181i	$-0.552980\pi$
$431$	−6.87892	−0.331346	−0.165673	+	0.986181i	$0.552980\pi$
$432$	1.01644	0.0489034
$433$	3.05089	0.146616	0.0733082	−	0.997309i	$-0.476644\pi$
$433$	3.05089	0.146616	0.0733082	+	0.997309i	$0.476644\pi$
$434$	4.65954	0.223665
$435$	−2.65520	−0.127307
$436$	28.3413	1.35730
$437$	4.02908	0.192737
$438$	22.8623	1.09240
$439$	−31.9867	−1.52664	−0.763320	−	0.646020i	$-0.776432\pi$
$439$	−31.9867	−1.52664	−0.763320	+	0.646020i	$0.776432\pi$
$440$	−11.6318	−0.554526
$441$	8.08733	0.385111
$442$	11.2870	0.536869
$443$	15.0469	0.714898	0.357449	−	0.933933i	$-0.383647\pi$
$443$	15.0469	0.714898	0.357449	+	0.933933i	$0.383647\pi$
$444$	30.7123	1.45754
$445$	−4.05642	−0.192293
$446$	26.9962	1.27831
$447$	0.892224	0.0422007
$448$	−24.1696	−1.14191
$449$	−3.33734	−0.157499	−0.0787493	−	0.996894i	$-0.525093\pi$
$449$	−3.33734	−0.157499	−0.0787493	+	0.996894i	$0.525093\pi$
$450$	5.19095	0.244704
$451$	−19.1797	−0.903136
$452$	31.3695	1.47550
$453$	−17.0134	−0.799360
$454$	−24.1282	−1.13239
$455$	−9.21048	−0.431794
$456$	1.60321	0.0750771
$457$	36.9162	1.72687	0.863434	−	0.504462i	$-0.168309\pi$
$457$	36.9162	1.72687	0.863434	+	0.504462i	$0.168309\pi$
$458$	−9.88073	−0.461696
$459$	−4.48085	−0.209148
$460$	−18.3246	−0.854388
$461$	17.6072	0.820051	0.410025	−	0.912074i	$-0.365520\pi$
$461$	17.6072	0.820051	0.410025	+	0.912074i	$0.365520\pi$
$462$	−15.4823	−0.720301
$463$	−6.94510	−0.322766	−0.161383	−	0.986892i	$-0.551595\pi$
$463$	−6.94510	−0.322766	−0.161383	+	0.986892i	$0.551595\pi$
$464$	0.709690	0.0329465
$465$	−0.934674	−0.0433445
$466$	−37.5693	−1.74036
$467$	25.9634	1.20144	0.600722	−	0.799458i	$-0.294880\pi$
$467$	25.9634	1.20144	0.600722	+	0.799458i	$0.294880\pi$
$468$	35.9894	1.66361
$469$	19.4600	0.898579
$470$	3.08602	0.142347
$471$	6.62707	0.305359
$472$	3.66909	0.168884
$473$	27.7249	1.27479
$474$	5.03717	0.231365
$475$	−0.700242	−0.0321293
$476$	5.91757	0.271231
$477$	12.3100	0.563638
$478$	−43.0779	−1.97034
$479$	−22.4257	−1.02466	−0.512328	−	0.858790i	$-0.671217\pi$
$479$	−22.4257	−1.02466	−0.512328	+	0.858790i	$0.671217\pi$
$480$	5.01737	0.229011
$481$	−56.3253	−2.56821
$482$	63.2925	2.88289
$483$	−9.07346	−0.412857
$484$	24.1766	1.09894
$485$	−17.2876	−0.784989
$486$	−36.4764	−1.65460
$487$	−14.2627	−0.646306	−0.323153	−	0.946347i	$-0.604743\pi$
$487$	−14.2627	−0.646306	−0.323153	+	0.946347i	$0.604743\pi$
$488$	8.14959	0.368914
$489$	−14.8433	−0.671238
$490$	8.07768	0.364912
$491$	7.53239	0.339932	0.169966	−	0.985450i	$-0.445634\pi$
$491$	7.53239	0.339932	0.169966	+	0.985450i	$0.445634\pi$
$492$	−12.0229	−0.542036
$493$	−3.12859	−0.140904
$494$	−7.90366	−0.355602
$495$	−9.82966	−0.441810
$496$	0.249823	0.0112174
$497$	−1.85809	−0.0833468
$498$	−6.34065	−0.284131
$499$	19.3079	0.864339	0.432170	−	0.901792i	$-0.357748\pi$
$499$	19.3079	0.864339	0.432170	+	0.901792i	$0.357748\pi$
$500$	3.18476	0.142427
$501$	−6.26480	−0.279891
$502$	−2.91759	−0.130218
$503$	−20.2591	−0.903310	−0.451655	−	0.892193i	$-0.649166\pi$
$503$	−20.2591	−0.903310	−0.451655	+	0.892193i	$0.649166\pi$
$504$	11.4273	0.509012
$505$	4.27957	0.190438
$506$	56.4907	2.51132
$507$	9.82058	0.436147
$508$	−12.2131	−0.541868
$509$	16.4087	0.727303	0.363651	−	0.931535i	$-0.381530\pi$
$509$	16.4087	0.727303	0.363651	+	0.931535i	$0.381530\pi$
$510$	−1.93247	−0.0855712
$511$	−21.9823	−0.972440
$512$	−2.56495	−0.113356
$513$	3.13768	0.138532
$514$	−65.2581	−2.87841
$515$	3.27159	0.144163
$516$	17.3796	0.765093
$517$	−5.84373	−0.257007
$518$	−48.0750	−2.11229
$519$	2.29511	0.100744
$520$	13.3724	0.586418
$521$	−18.5740	−0.813744	−0.406872	−	0.913485i	$-0.633380\pi$
$521$	−18.5740	−0.813744	−0.406872	+	0.913485i	$0.633380\pi$
$522$	−16.2403	−0.710820
$523$	−10.5472	−0.461198	−0.230599	−	0.973049i	$-0.574069\pi$
$523$	−10.5472	−0.461198	−0.230599	+	0.973049i	$0.574069\pi$
$524$	−21.5920	−0.943249
$525$	1.57694	0.0688233
$526$	16.5504	0.721631
$527$	−1.10131	−0.0479740
$528$	−0.830089	−0.0361250
$529$	10.1067	0.439420
$530$	12.2953	0.534075
$531$	3.10062	0.134555
$532$	−4.14373	−0.179653
$533$	22.0496	0.955076
$534$	7.83891	0.339223
$535$	−7.64671	−0.330596
$536$	−28.2533	−1.22036
$537$	6.70528	0.289354
$538$	18.6693	0.804891
$539$	−15.2960	−0.658845
$540$	−14.2704	−0.614100
$541$	6.27151	0.269633	0.134817	−	0.990871i	$-0.456955\pi$
$541$	6.27151	0.269633	0.134817	+	0.990871i	$0.456955\pi$
$542$	33.1598	1.42434
$543$	−14.4880	−0.621738
$544$	5.91191	0.253471
$545$	8.89906	0.381194
$546$	17.7990	0.761726
$547$	−3.05895	−0.130791	−0.0653956	−	0.997859i	$-0.520831\pi$
$547$	−3.05895	−0.130791	−0.0653956	+	0.997859i	$0.520831\pi$
$548$	−48.7445	−2.08226
$549$	6.88692	0.293927
$550$	−9.81792	−0.418638
$551$	2.19077	0.0933299
$552$	13.1734	0.560699
$553$	−4.84329	−0.205958
$554$	−9.20714	−0.391174
$555$	9.64355	0.409346
$556$	−60.5745	−2.56893
$557$	−5.06280	−0.214518	−0.107259	−	0.994231i	$-0.534207\pi$
$557$	−5.06280	−0.214518	−0.107259	+	0.994231i	$0.534207\pi$
$558$	−5.71687	−0.242015
$559$	−31.8735	−1.34811
$560$	−0.421490	−0.0178112
$561$	3.65935	0.154498
$562$	−34.4845	−1.45464
$563$	1.89326	0.0797912	0.0398956	−	0.999204i	$-0.487297\pi$
$563$	1.89326	0.0797912	0.0398956	+	0.999204i	$0.487297\pi$
$564$	−3.66319	−0.154248
$565$	9.84989	0.414388
$566$	62.4518	2.62505
$567$	5.64179	0.236933
$568$	2.69770	0.113193
$569$	−27.0456	−1.13381	−0.566905	−	0.823783i	$-0.691859\pi$
$569$	−27.0456	−1.13381	−0.566905	+	0.823783i	$0.691859\pi$
$570$	1.35320	0.0566792
$571$	−7.50403	−0.314034	−0.157017	−	0.987596i	$-0.550188\pi$
$571$	−7.50403	−0.314034	−0.157017	+	0.987596i	$0.550188\pi$
$572$	−68.0687	−2.84609
$573$	−7.04324	−0.294235
$574$	18.8199	0.785527
$575$	−5.75384	−0.239952
$576$	29.6542	1.23559
$577$	−31.6421	−1.31728	−0.658638	−	0.752460i	$-0.728867\pi$
$577$	−31.6421	−1.31728	−0.658638	+	0.752460i	$0.728867\pi$
$578$	−2.27701	−0.0947110
$579$	0.796942	0.0331198
$580$	−9.96378	−0.413724
$581$	6.09660	0.252930
$582$	33.4077	1.38480
$583$	−23.2826	−0.964268
$584$	31.9154	1.32067
$585$	11.3005	0.467219
$586$	−17.7582	−0.733584
$587$	−15.5631	−0.642360	−0.321180	−	0.947018i	$-0.604079\pi$
$587$	−15.5631	−0.642360	−0.321180	+	0.947018i	$0.604079\pi$
$588$	−9.58842	−0.395420
$589$	0.771187	0.0317762
$590$	3.09692	0.127498
$591$	1.39585	0.0574178
$592$	−2.57756	−0.105937
$593$	4.30703	0.176869	0.0884343	−	0.996082i	$-0.471814\pi$
$593$	4.30703	0.176869	0.0884343	+	0.996082i	$0.471814\pi$
$594$	43.9926	1.80504
$595$	1.85809	0.0761743
$596$	3.34812	0.137145
$597$	−15.0574	−0.616259
$598$	−64.9438	−2.65575
$599$	−13.9296	−0.569149	−0.284575	−	0.958654i	$-0.591852\pi$
$599$	−13.9296	−0.569149	−0.284575	+	0.958654i	$0.591852\pi$
$600$	−2.28951	−0.0934687
$601$	10.1956	0.415886	0.207943	−	0.978141i	$-0.433323\pi$
$601$	10.1956	0.415886	0.207943	+	0.978141i	$0.433323\pi$
$602$	−27.2048	−1.10879
$603$	−23.8758	−0.972299
$604$	−63.8439	−2.59777
$605$	7.59135	0.308632
$606$	−8.27014	−0.335951
$607$	11.1442	0.452328	0.226164	−	0.974089i	$-0.427382\pi$
$607$	11.1442	0.452328	0.226164	+	0.974089i	$0.427382\pi$
$608$	−4.13977	−0.167890
$609$	−4.93360	−0.199919
$610$	6.87870	0.278511
$611$	6.71815	0.271787
$612$	−7.26038	−0.293483
$613$	−0.983049	−0.0397050	−0.0198525	−	0.999803i	$-0.506320\pi$
$613$	−0.983049	−0.0397050	−0.0198525	+	0.999803i	$0.506320\pi$
$614$	−53.6181	−2.16385
$615$	−3.77515	−0.152229
$616$	−21.6130	−0.870814
$617$	−25.3623	−1.02105	−0.510524	−	0.859863i	$-0.670549\pi$
$617$	−25.3623	−1.02105	−0.510524	+	0.859863i	$0.670549\pi$
$618$	−6.32224	−0.254318
$619$	−37.9292	−1.52450	−0.762252	−	0.647280i	$-0.775906\pi$
$619$	−37.9292	−1.52450	−0.762252	+	0.647280i	$0.775906\pi$
$620$	−3.50742	−0.140861
$621$	25.7821	1.03460
$622$	35.1454	1.40920
$623$	−7.53720	−0.301971
$624$	0.954299	0.0382025
$625$	1.00000	0.0400000
$626$	31.0009	1.23904
$627$	−2.56243	−0.102334
$628$	24.8685	0.992360
$629$	11.3629	0.453067
$630$	9.64526	0.384276
$631$	−14.9933	−0.596875	−0.298438	−	0.954429i	$-0.596465\pi$
$631$	−14.9933	−0.596875	−0.298438	+	0.954429i	$0.596465\pi$
$632$	7.03181	0.279710
$633$	11.5478	0.458984
$634$	12.2868	0.487971
$635$	−3.83486	−0.152182
$636$	−14.5949	−0.578725
$637$	17.5848	0.696736
$638$	30.7162	1.21607
$639$	2.27973	0.0901846
$640$	17.7950	0.703408
$641$	38.0808	1.50410	0.752051	−	0.659105i	$-0.229065\pi$
$641$	38.0808	1.50410	0.752051	+	0.659105i	$0.229065\pi$
$642$	14.7770	0.583203
$643$	−37.8429	−1.49238	−0.746189	−	0.665735i	$-0.768118\pi$
$643$	−37.8429	−1.49238	−0.746189	+	0.665735i	$0.768118\pi$
$644$	−34.0487	−1.34171
$645$	5.45711	0.214874
$646$	1.59446	0.0627330
$647$	−5.35425	−0.210497	−0.105249	−	0.994446i	$-0.533564\pi$
$647$	−5.35425	−0.210497	−0.105249	+	0.994446i	$0.533564\pi$
$648$	−8.19112	−0.321777
$649$	−5.86437	−0.230196
$650$	11.2870	0.442714
$651$	−1.73671	−0.0680670
$652$	−55.7005	−2.18140
$653$	35.0967	1.37344	0.686721	−	0.726921i	$-0.259050\pi$
$653$	35.0967	1.37344	0.686721	+	0.726921i	$0.259050\pi$
$654$	−17.1972	−0.672462
$655$	−6.77978	−0.264908
$656$	1.00904	0.0393962
$657$	26.9705	1.05222
$658$	5.73410	0.223539
$659$	12.0373	0.468908	0.234454	−	0.972127i	$-0.424670\pi$
$659$	12.0373	0.468908	0.234454	+	0.972127i	$0.424670\pi$
$660$	11.6541	0.453637
$661$	−36.5734	−1.42254	−0.711269	−	0.702920i	$-0.751879\pi$
$661$	−36.5734	−1.42254	−0.711269	+	0.702920i	$0.751879\pi$
$662$	−34.2563	−1.33141
$663$	−4.20692	−0.163383
$664$	−8.85144	−0.343503
$665$	−1.30111	−0.0504550
$666$	58.9841	2.28559
$667$	18.0014	0.697016
$668$	−23.5091	−0.909593
$669$	−10.0621	−0.389022
$670$	−23.8473	−0.921303
$671$	−13.0256	−0.502848
$672$	9.32273	0.359632
$673$	46.9689	1.81052	0.905259	−	0.424860i	$-0.139677\pi$
$673$	46.9689	1.81052	0.905259	+	0.424860i	$0.139677\pi$
$674$	18.2806	0.704143
$675$	−4.48085	−0.172468
$676$	36.8523	1.41740
$677$	−23.5562	−0.905340	−0.452670	−	0.891678i	$-0.649528\pi$
$677$	−23.5562	−0.905340	−0.452670	+	0.891678i	$0.649528\pi$
$678$	−19.0346	−0.731020
$679$	−32.1219	−1.23273
$680$	−2.69770	−0.103452
$681$	8.99311	0.344617
$682$	10.8126	0.414037
$683$	25.1760	0.963332	0.481666	−	0.876355i	$-0.340032\pi$
$683$	25.1760	0.963332	0.481666	+	0.876355i	$0.340032\pi$
$684$	5.08402	0.194392
$685$	−15.3056	−0.584795
$686$	44.6252	1.70380
$687$	3.68276	0.140506
$688$	−1.45860	−0.0556085
$689$	26.7665	1.01972
$690$	11.1191	0.423298
$691$	−36.5838	−1.39171	−0.695856	−	0.718182i	$-0.744975\pi$
$691$	−36.5838	−1.39171	−0.695856	+	0.718182i	$0.744975\pi$
$692$	8.61255	0.327400
$693$	−18.2644	−0.693807
$694$	−15.8337	−0.601041
$695$	−19.0201	−0.721474
$696$	7.16292	0.271510
$697$	−4.44822	−0.168488
$698$	33.4824	1.26733
$699$	14.0029	0.529638
$700$	5.91757	0.223663
$701$	−43.6204	−1.64752	−0.823760	−	0.566939i	$-0.808127\pi$
$701$	−43.6204	−1.64752	−0.823760	+	0.566939i	$0.808127\pi$
$702$	−50.5754	−1.90885
$703$	−7.95677	−0.300095
$704$	−56.0865	−2.11384
$705$	−1.15023	−0.0433200
$706$	17.1460	0.645300
$707$	7.95183	0.299059
$708$	−3.67612	−0.138157
$709$	−36.9406	−1.38733	−0.693667	−	0.720296i	$-0.744006\pi$
$709$	−36.9406	−1.38733	−0.693667	+	0.720296i	$0.744006\pi$
$710$	2.27701	0.0854545
$711$	5.94233	0.222855
$712$	10.9430	0.410106
$713$	6.33679	0.237315
$714$	−3.59070	−0.134379
$715$	−21.3733	−0.799315
$716$	25.1620	0.940346
$717$	16.0561	0.599625
$718$	4.44311	0.165815
$719$	−15.4449	−0.575999	−0.287999	−	0.957631i	$-0.592990\pi$
$719$	−15.4449	−0.575999	−0.287999	+	0.957631i	$0.592990\pi$
$720$	0.517134	0.0192725
$721$	6.07891	0.226390
$722$	42.1466	1.56853
$723$	−23.5905	−0.877339
$724$	−54.3669	−2.02053
$725$	−3.12859	−0.116193
$726$	−14.6701	−0.544457
$727$	12.4365	0.461246	0.230623	−	0.973043i	$-0.425924\pi$
$727$	12.4365	0.461246	0.230623	+	0.973043i	$0.425924\pi$
$728$	24.8471	0.920895
$729$	4.48651	0.166167
$730$	26.9383	0.997032
$731$	6.43005	0.237824
$732$	−8.16520	−0.301795
$733$	−53.2344	−1.96626	−0.983128	−	0.182918i	$-0.941446\pi$
$733$	−53.2344	−1.96626	−0.983128	+	0.182918i	$0.941446\pi$
$734$	−49.7699	−1.83704
$735$	−3.01072	−0.111052
$736$	−34.0162	−1.25385
$737$	45.1576	1.66340
$738$	−23.0905	−0.849972
$739$	−25.3037	−0.930812	−0.465406	−	0.885097i	$-0.654092\pi$
$739$	−25.3037	−0.930812	−0.465406	+	0.885097i	$0.654092\pi$
$740$	36.1880	1.33030
$741$	2.94586	0.108219
$742$	22.8459	0.838698
$743$	−32.8067	−1.20356	−0.601781	−	0.798661i	$-0.705542\pi$
$743$	−32.8067	−1.20356	−0.601781	+	0.798661i	$0.705542\pi$
$744$	2.52147	0.0924415
$745$	1.05130	0.0385165
$746$	−43.7507	−1.60183
$747$	−7.48004	−0.273680
$748$	13.7319	0.502089
$749$	−14.2083	−0.519159
$750$	−1.93247	−0.0705638
$751$	−26.4876	−0.966547	−0.483274	−	0.875469i	$-0.660552\pi$
$751$	−26.4876	−0.966547	−0.483274	+	0.875469i	$0.660552\pi$
$752$	0.307436	0.0112110
$753$	1.08745	0.0396288
$754$	−35.3125	−1.28600
$755$	−20.0467	−0.729574
$756$	−26.5157	−0.964367
$757$	41.9205	1.52363	0.761813	−	0.647797i	$-0.224310\pi$
$757$	41.9205	1.52363	0.761813	+	0.647797i	$0.224310\pi$
$758$	77.1046	2.80057
$759$	−21.0553	−0.764259
$760$	1.88904	0.0685227
$761$	6.55535	0.237631	0.118816	−	0.992916i	$-0.462090\pi$
$761$	6.55535	0.237631	0.118816	+	0.992916i	$0.462090\pi$
$762$	7.41075	0.268463
$763$	16.5353	0.598617
$764$	−26.4302	−0.956210
$765$	−2.27973	−0.0824237
$766$	−31.4284	−1.13555
$767$	6.74188	0.243435
$768$	−12.3091	−0.444167
$769$	32.9757	1.18913	0.594566	−	0.804047i	$-0.297324\pi$
$769$	32.9757	1.18913	0.594566	+	0.804047i	$0.297324\pi$
$770$	−18.2426	−0.657417
$771$	24.3231	0.875975
$772$	2.99057	0.107633
$773$	−21.3368	−0.767433	−0.383716	−	0.923451i	$-0.625356\pi$
$773$	−21.3368	−0.767433	−0.383716	+	0.923451i	$0.625356\pi$
$774$	33.3781	1.19975
$775$	−1.10131	−0.0395604
$776$	46.6367	1.67416
$777$	17.9186	0.642826
$778$	−82.5087	−2.95808
$779$	3.11483	0.111600
$780$	−13.3980	−0.479726
$781$	−4.31177	−0.154287
$782$	13.1015	0.468510
$783$	14.0187	0.500988
$784$	0.804716	0.0287399
$785$	7.80859	0.278701
$786$	13.1017	0.467323
$787$	33.8054	1.20503	0.602516	−	0.798107i	$-0.294165\pi$
$787$	33.8054	1.20503	0.602516	+	0.798107i	$0.294165\pi$
$788$	5.23803	0.186597
$789$	−6.16868	−0.219611
$790$	5.93524	0.211166
$791$	18.3020	0.650744
$792$	26.5174	0.942256
$793$	14.9747	0.531767
$794$	−80.0412	−2.84056
$795$	−4.58274	−0.162533
$796$	−56.5039	−2.00273
$797$	−19.4878	−0.690293	−0.345146	−	0.938549i	$-0.612171\pi$
$797$	−19.4878	−0.690293	−0.345146	+	0.938549i	$0.612171\pi$
$798$	2.51436	0.0890075
$799$	−1.35530	−0.0479470
$800$	5.91191	0.209018
$801$	9.24753	0.326745
$802$	88.2042	3.11460
$803$	−51.0108	−1.80013
$804$	28.3074	0.998326
$805$	−10.6912	−0.376814
$806$	−12.4306	−0.437848
$807$	−6.95845	−0.244949
$808$	−11.5450	−0.406151
$809$	41.1284	1.44600	0.722999	−	0.690849i	$-0.242763\pi$
$809$	41.1284	1.44600	0.722999	+	0.690849i	$0.242763\pi$
$810$	−6.91376	−0.242925
$811$	−24.2150	−0.850303	−0.425151	−	0.905122i	$-0.639779\pi$
$811$	−24.2150	−0.850303	−0.425151	+	0.905122i	$0.639779\pi$
$812$	−18.5136	−0.649701
$813$	−12.3594	−0.433462
$814$	−111.560	−3.91017
$815$	−17.4897	−0.612638
$816$	−0.192517	−0.00673944
$817$	−4.50260	−0.157526
$818$	44.4215	1.55316
$819$	20.9974	0.733708
$820$	−14.1665	−0.494715
$821$	14.7984	0.516467	0.258234	−	0.966083i	$-0.416860\pi$
$821$	14.7984	0.516467	0.258234	+	0.966083i	$0.416860\pi$
$822$	29.5775	1.03163
$823$	8.62312	0.300583	0.150292	−	0.988642i	$-0.451979\pi$
$823$	8.62312	0.300583	0.150292	+	0.988642i	$0.451979\pi$
$824$	−8.82575	−0.307460
$825$	3.65935	0.127402
$826$	5.75435	0.200220
$827$	28.7669	1.00032	0.500161	−	0.865932i	$-0.333274\pi$
$827$	28.7669	1.00032	0.500161	+	0.865932i	$0.333274\pi$
$828$	41.7750	1.45178
$829$	−33.9429	−1.17889	−0.589444	−	0.807810i	$-0.700653\pi$
$829$	−33.9429	−1.17889	−0.589444	+	0.807810i	$0.700653\pi$
$830$	−7.47111	−0.259326
$831$	3.43170	0.119044
$832$	64.4790	2.23541
$833$	−3.54750	−0.122914
$834$	36.7558	1.27275
$835$	−7.38174	−0.255456
$836$	−9.61568	−0.332565
$837$	4.93482	0.170572
$838$	−11.7203	−0.404872
$839$	12.7166	0.439027	0.219514	−	0.975609i	$-0.429553\pi$
$839$	12.7166	0.439027	0.219514	+	0.975609i	$0.429553\pi$
$840$	−4.25411	−0.146781
$841$	−19.2119	−0.662481
$842$	−40.1532	−1.38377
$843$	12.8531	0.442685
$844$	43.3338	1.49161
$845$	11.5715	0.398071
$846$	−7.03528	−0.241878
$847$	14.1054	0.484668
$848$	1.22489	0.0420629
$849$	−23.2771	−0.798869
$850$	−2.27701	−0.0781007
$851$	−65.3801	−2.24120
$852$	−2.70287	−0.0925987
$853$	−22.1437	−0.758186	−0.379093	−	0.925359i	$-0.623764\pi$
$853$	−22.1437	−0.758186	−0.379093	+	0.925359i	$0.623764\pi$
$854$	12.7813	0.437365
$855$	1.59636	0.0545944
$856$	20.6285	0.705068
$857$	50.5189	1.72569	0.862846	−	0.505466i	$-0.168679\pi$
$857$	50.5189	1.72569	0.862846	+	0.505466i	$0.168679\pi$
$858$	41.3032	1.41007
$859$	38.2308	1.30442	0.652208	−	0.758040i	$-0.273843\pi$
$859$	38.2308	1.30442	0.652208	+	0.758040i	$0.273843\pi$
$860$	20.4782	0.698299
$861$	−7.01458	−0.239056
$862$	15.6633	0.533495
$863$	−52.6937	−1.79371	−0.896857	−	0.442320i	$-0.854155\pi$
$863$	−52.6937	−1.79371	−0.896857	+	0.442320i	$0.854155\pi$
$864$	−26.4904	−0.901220
$865$	2.70430	0.0919491
$866$	−6.94689	−0.236065
$867$	0.848689	0.0288230
$868$	−6.51710	−0.221205
$869$	−11.2390	−0.381258
$870$	6.04590	0.204975
$871$	−51.9148	−1.75907
$872$	−24.0070	−0.812979
$873$	39.4110	1.33386
$874$	−9.17424	−0.310323
$875$	1.85809	0.0628149
$876$	−31.9765	−1.08039
$877$	17.3564	0.586085	0.293043	−	0.956099i	$-0.405332\pi$
$877$	17.3564	0.586085	0.293043	+	0.956099i	$0.405332\pi$
$878$	72.8338	2.45802
$879$	6.61886	0.223249
$880$	−0.978084	−0.0329712
$881$	3.43229	0.115637	0.0578183	−	0.998327i	$-0.481586\pi$
$881$	3.43229	0.115637	0.0578183	+	0.998327i	$0.481586\pi$
$882$	−18.4149	−0.620062
$883$	−44.4642	−1.49634	−0.748170	−	0.663508i	$-0.769067\pi$
$883$	−44.4642	−1.49634	−0.748170	+	0.663508i	$0.769067\pi$
$884$	−15.7867	−0.530965
$885$	−1.15429	−0.0388010
$886$	−34.2618	−1.15105
$887$	−38.2377	−1.28390	−0.641948	−	0.766748i	$-0.721874\pi$
$887$	−38.2377	−1.28390	−0.641948	+	0.766748i	$0.721874\pi$
$888$	−26.0154	−0.873018
$889$	−7.12551	−0.238982
$890$	9.23649	0.309608
$891$	13.0920	0.438598
$892$	−37.7585	−1.26425
$893$	0.949036	0.0317583
$894$	−2.03160	−0.0679468
$895$	7.90075	0.264093
$896$	33.0646	1.10461
$897$	24.2059	0.808212
$898$	7.59913	0.253586
$899$	3.44556	0.114916
$900$	−7.26038	−0.242013
$901$	−5.39978	−0.179893
$902$	43.6723	1.45413
$903$	10.1398	0.337432
$904$	−26.5720	−0.883772
$905$	−17.0710	−0.567459
$906$	38.7397	1.28704
$907$	57.9132	1.92298	0.961488	−	0.274846i	$-0.0886268\pi$
$907$	57.9132	1.92298	0.961488	+	0.274846i	$0.0886268\pi$
$908$	33.7472	1.11994
$909$	−9.75625	−0.323594
$910$	20.9723	0.695226
$911$	19.5637	0.648176	0.324088	−	0.946027i	$-0.394943\pi$
$911$	19.5637	0.648176	0.324088	+	0.946027i	$0.394943\pi$
$912$	0.134809	0.00446396
$913$	14.1474	0.468210
$914$	−84.0584	−2.78041
$915$	−2.56384	−0.0847579
$916$	13.8198	0.456618
$917$	−12.5974	−0.416004
$918$	10.2029	0.336746
$919$	−24.7210	−0.815469	−0.407735	−	0.913100i	$-0.633681\pi$
$919$	−24.7210	−0.815469	−0.407735	+	0.913100i	$0.633681\pi$
$920$	15.5221	0.511749
$921$	19.9846	0.658516
$922$	−40.0918	−1.32035
$923$	4.95696	0.163160
$924$	21.6544	0.712379
$925$	11.3629	0.373609
$926$	15.8140	0.519681
$927$	−7.45833	−0.244964
$928$	−18.4959	−0.607158
$929$	14.7518	0.483989	0.241995	−	0.970278i	$-0.422198\pi$
$929$	14.7518	0.483989	0.241995	+	0.970278i	$0.422198\pi$
$930$	2.12826	0.0697883
$931$	2.48411	0.0814134
$932$	52.5467	1.72122
$933$	−13.0994	−0.428856
$934$	−59.1188	−1.93443
$935$	4.31177	0.141010
$936$	−30.4854	−0.996446
$937$	−34.6157	−1.13085	−0.565423	−	0.824801i	$-0.691287\pi$
$937$	−34.6157	−1.13085	−0.565423	+	0.824801i	$0.691287\pi$
$938$	−44.3105	−1.44679
$939$	−11.5547	−0.377073
$940$	−4.31629	−0.140782
$941$	10.5497	0.343909	0.171954	−	0.985105i	$-0.444992\pi$
$941$	10.5497	0.343909	0.171954	+	0.985105i	$0.444992\pi$
$942$	−15.0899	−0.491655
$943$	25.5943	0.833466
$944$	0.308522	0.0100415
$945$	−8.32582	−0.270839
$946$	−63.1298	−2.05253
$947$	36.4039	1.18297	0.591484	−	0.806317i	$-0.298542\pi$
$947$	36.4039	1.18297	0.591484	+	0.806317i	$0.298542\pi$
$948$	−7.04529	−0.228820
$949$	58.6438	1.90366
$950$	1.59446	0.0517310
$951$	−4.57956	−0.148502
$952$	−5.01257	−0.162458
$953$	−15.7625	−0.510599	−0.255299	−	0.966862i	$-0.582174\pi$
$953$	−15.7625	−0.510599	−0.255299	+	0.966862i	$0.582174\pi$
$954$	−28.0300	−0.907505
$955$	−8.29896	−0.268548
$956$	60.2514	1.94867
$957$	−11.4486	−0.370080
$958$	51.0634	1.64978
$959$	−28.4391	−0.918347
$960$	−11.0396	−0.356300
$961$	−29.7871	−0.960874
$962$	128.253	4.13505
$963$	17.4324	0.561752
$964$	−88.5247	−2.85119
$965$	0.939027	0.0302284
$966$	20.6603	0.664735
$967$	56.5339	1.81801	0.909004	−	0.416787i	$-0.136844\pi$
$967$	56.5339	1.81801	0.909004	+	0.416787i	$0.136844\pi$
$968$	−20.4792	−0.658225
$969$	−0.594288	−0.0190913
$970$	39.3639	1.26390
$971$	−2.43033	−0.0779930	−0.0389965	−	0.999239i	$-0.512416\pi$
$971$	−2.43033	−0.0779930	−0.0389965	+	0.999239i	$0.512416\pi$
$972$	51.0180	1.63640
$973$	−35.3411	−1.13298
$974$	32.4763	1.04061
$975$	−4.20692	−0.134729
$976$	0.685272	0.0219350
$977$	−43.0212	−1.37637	−0.688185	−	0.725535i	$-0.741592\pi$
$977$	−43.0212	−1.37637	−0.688185	+	0.725535i	$0.741592\pi$
$978$	33.7983	1.08075
$979$	−17.4903	−0.558994
$980$	−11.2979	−0.360899
$981$	−20.2874	−0.647728
$982$	−17.1513	−0.547320
$983$	−30.6586	−0.977859	−0.488929	−	0.872323i	$-0.662612\pi$
$983$	−30.6586	−0.977859	−0.488929	+	0.872323i	$0.662612\pi$
$984$	10.1842	0.324661
$985$	1.64472	0.0524051
$986$	7.12381	0.226868
$987$	−2.13722	−0.0680286
$988$	11.0545	0.351691
$989$	−36.9975	−1.17645
$990$	22.3822	0.711353
$991$	−53.2859	−1.69268	−0.846341	−	0.532642i	$-0.821199\pi$
$991$	−53.2859	−1.69268	−0.846341	+	0.532642i	$0.821199\pi$
$992$	−6.51088	−0.206721
$993$	12.7680	0.405182
$994$	4.23088	0.134195
$995$	−17.7420	−0.562458
$996$	8.86841	0.281006
$997$	−29.7288	−0.941521	−0.470760	−	0.882261i	$-0.656020\pi$
$997$	−29.7288	−0.941521	−0.470760	+	0.882261i	$0.656020\pi$
$998$	−43.9641	−1.39166
$999$	−50.9153	−1.61089

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.a.1.4	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.a.1.4	✓	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-2.27701 q^{2} +0.848689 q^{3} +3.18476 q^{4} +1.00000 q^{5} -1.93247 q^{6} +1.85809 q^{7} -2.69770 q^{8} -2.27973 q^{9} +O(q^{10})\)	\(q-2.27701 q^{2} +0.848689 q^{3} +3.18476 q^{4} +1.00000 q^{5} -1.93247 q^{6} +1.85809 q^{7} -2.69770 q^{8} -2.27973 q^{9} -2.27701 q^{10} +4.31177 q^{11} +2.70287 q^{12} -4.95696 q^{13} -4.23088 q^{14} +0.848689 q^{15} -0.226840 q^{16} +1.00000 q^{17} +5.19095 q^{18} -0.700242 q^{19} +3.18476 q^{20} +1.57694 q^{21} -9.81792 q^{22} -5.75384 q^{23} -2.28951 q^{24} +1.00000 q^{25} +11.2870 q^{26} -4.48085 q^{27} +5.91757 q^{28} -3.12859 q^{29} -1.93247 q^{30} -1.10131 q^{31} +5.91191 q^{32} +3.65935 q^{33} -2.27701 q^{34} +1.85809 q^{35} -7.26038 q^{36} +11.3629 q^{37} +1.59446 q^{38} -4.20692 q^{39} -2.69770 q^{40} -4.44822 q^{41} -3.59070 q^{42} +6.43005 q^{43} +13.7319 q^{44} -2.27973 q^{45} +13.1015 q^{46} -1.35530 q^{47} -0.192517 q^{48} -3.54750 q^{49} -2.27701 q^{50} +0.848689 q^{51} -15.7867 q^{52} -5.39978 q^{53} +10.2029 q^{54} +4.31177 q^{55} -5.01257 q^{56} -0.594288 q^{57} +7.12381 q^{58} -1.36008 q^{59} +2.70287 q^{60} -3.02094 q^{61} +2.50770 q^{62} -4.23594 q^{63} -13.0078 q^{64} -4.95696 q^{65} -8.33236 q^{66} +10.4731 q^{67} +3.18476 q^{68} -4.88322 q^{69} -4.23088 q^{70} -1.00000 q^{71} +6.15001 q^{72} -11.8306 q^{73} -25.8733 q^{74} +0.848689 q^{75} -2.23010 q^{76} +8.01166 q^{77} +9.57918 q^{78} -2.60660 q^{79} -0.226840 q^{80} +3.03634 q^{81} +10.1286 q^{82} +3.28111 q^{83} +5.02217 q^{84} +1.00000 q^{85} -14.6413 q^{86} -2.65520 q^{87} -11.6318 q^{88} -4.05642 q^{89} +5.19095 q^{90} -9.21048 q^{91} -18.3246 q^{92} -0.934674 q^{93} +3.08602 q^{94} -0.700242 q^{95} +5.01737 q^{96} -17.2876 q^{97} +8.07768 q^{98} -9.82966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

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