LMFDB - Embedded newform 6035.2.a.h.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1897176198$
Analytic rank:	$0$
Dimension:	$59$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-2.44774 q^{2} +0.819540 q^{3} +3.99145 q^{4} +1.00000 q^{5} -2.00602 q^{6} +2.11487 q^{7} -4.87457 q^{8} -2.32835 q^{9} +O(q^{10})$	\(q-2.44774 q^{2} +0.819540 q^{3} +3.99145 q^{4} +1.00000 q^{5} -2.00602 q^{6} +2.11487 q^{7} -4.87457 q^{8} -2.32835 q^{9} -2.44774 q^{10} +5.18847 q^{11} +3.27115 q^{12} +3.64508 q^{13} -5.17666 q^{14} +0.819540 q^{15} +3.94879 q^{16} -1.00000 q^{17} +5.69922 q^{18} -2.99970 q^{19} +3.99145 q^{20} +1.73322 q^{21} -12.7000 q^{22} -4.49942 q^{23} -3.99490 q^{24} +1.00000 q^{25} -8.92222 q^{26} -4.36680 q^{27} +8.44141 q^{28} +0.815379 q^{29} -2.00602 q^{30} -4.17338 q^{31} +0.0835062 q^{32} +4.25216 q^{33} +2.44774 q^{34} +2.11487 q^{35} -9.29352 q^{36} -7.95861 q^{37} +7.34251 q^{38} +2.98729 q^{39} -4.87457 q^{40} +12.3801 q^{41} -4.24248 q^{42} +5.72338 q^{43} +20.7095 q^{44} -2.32835 q^{45} +11.0134 q^{46} -12.1863 q^{47} +3.23619 q^{48} -2.52732 q^{49} -2.44774 q^{50} -0.819540 q^{51} +14.5492 q^{52} +13.0466 q^{53} +10.6888 q^{54} +5.18847 q^{55} -10.3091 q^{56} -2.45838 q^{57} -1.99584 q^{58} -3.87844 q^{59} +3.27115 q^{60} +2.07923 q^{61} +10.2154 q^{62} -4.92417 q^{63} -8.10198 q^{64} +3.64508 q^{65} -10.4082 q^{66} +9.67971 q^{67} -3.99145 q^{68} -3.68745 q^{69} -5.17666 q^{70} -1.00000 q^{71} +11.3497 q^{72} +11.8516 q^{73} +19.4806 q^{74} +0.819540 q^{75} -11.9732 q^{76} +10.9729 q^{77} -7.31211 q^{78} +11.9633 q^{79} +3.94879 q^{80} +3.40630 q^{81} -30.3034 q^{82} -1.15382 q^{83} +6.91807 q^{84} -1.00000 q^{85} -14.0094 q^{86} +0.668236 q^{87} -25.2915 q^{88} +1.38177 q^{89} +5.69922 q^{90} +7.70887 q^{91} -17.9592 q^{92} -3.42025 q^{93} +29.8290 q^{94} -2.99970 q^{95} +0.0684366 q^{96} +17.6810 q^{97} +6.18624 q^{98} -12.0806 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) $ 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9} + 2 q^{10} + 6 q^{11} + 16 q^{12} + 25 q^{13} + 8 q^{14} + 6 q^{15} + 114 q^{16} - 59 q^{17} + 3 q^{18} + 35 q^{19} + 76 q^{20} + 41 q^{21} + 13 q^{22} - 2 q^{23} + 35 q^{24} + 59 q^{25} + 10 q^{26} + 27 q^{27} + 28 q^{28} + 10 q^{29} + 14 q^{30} + 15 q^{31} + 19 q^{32} - 3 q^{33} - 2 q^{34} + 9 q^{35} + 160 q^{36} + 56 q^{37} + 17 q^{38} + 25 q^{39} + 6 q^{40} + 47 q^{41} + 46 q^{42} + 27 q^{43} + 39 q^{44} + 97 q^{45} + 4 q^{46} - 8 q^{47} + 58 q^{48} + 174 q^{49} + 2 q^{50} - 6 q^{51} + 13 q^{52} + 17 q^{53} + 48 q^{54} + 6 q^{55} + 33 q^{56} + 6 q^{57} + 32 q^{58} + 30 q^{59} + 16 q^{60} + 85 q^{61} - 3 q^{62} + 14 q^{63} + 168 q^{64} + 25 q^{65} + 87 q^{66} + 21 q^{67} - 76 q^{68} + 111 q^{69} + 8 q^{70} - 59 q^{71} - 52 q^{72} + 41 q^{73} + 11 q^{74} + 6 q^{75} + 118 q^{76} + 55 q^{77} - 54 q^{78} + 43 q^{79} + 114 q^{80} + 207 q^{81} + 45 q^{82} + 10 q^{83} + 62 q^{84} - 59 q^{85} + 19 q^{86} + 8 q^{87} + 35 q^{88} + 86 q^{89} + 3 q^{90} + 47 q^{91} - 98 q^{92} + 41 q^{93} + 30 q^{94} + 35 q^{95} + 69 q^{96} + 72 q^{97} + 14 q^{98} + 25 q^{99}+O(q^{100}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9 + 2 * q^10 + 6 * q^11 + 16 * q^12 + 25 * q^13 + 8 * q^14 + 6 * q^15 + 114 * q^16 - 59 * q^17 + 3 * q^18 + 35 * q^19 + 76 * q^20 + 41 * q^21 + 13 * q^22 - 2 * q^23 + 35 * q^24 + 59 * q^25 + 10 * q^26 + 27 * q^27 + 28 * q^28 + 10 * q^29 + 14 * q^30 + 15 * q^31 + 19 * q^32 - 3 * q^33 - 2 * q^34 + 9 * q^35 + 160 * q^36 + 56 * q^37 + 17 * q^38 + 25 * q^39 + 6 * q^40 + 47 * q^41 + 46 * q^42 + 27 * q^43 + 39 * q^44 + 97 * q^45 + 4 * q^46 - 8 * q^47 + 58 * q^48 + 174 * q^49 + 2 * q^50 - 6 * q^51 + 13 * q^52 + 17 * q^53 + 48 * q^54 + 6 * q^55 + 33 * q^56 + 6 * q^57 + 32 * q^58 + 30 * q^59 + 16 * q^60 + 85 * q^61 - 3 * q^62 + 14 * q^63 + 168 * q^64 + 25 * q^65 + 87 * q^66 + 21 * q^67 - 76 * q^68 + 111 * q^69 + 8 * q^70 - 59 * q^71 - 52 * q^72 + 41 * q^73 + 11 * q^74 + 6 * q^75 + 118 * q^76 + 55 * q^77 - 54 * q^78 + 43 * q^79 + 114 * q^80 + 207 * q^81 + 45 * q^82 + 10 * q^83 + 62 * q^84 - 59 * q^85 + 19 * q^86 + 8 * q^87 + 35 * q^88 + 86 * q^89 + 3 * q^90 + 47 * q^91 - 98 * q^92 + 41 * q^93 + 30 * q^94 + 35 * q^95 + 69 * q^96 + 72 * q^97 + 14 * q^98 + 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.44774	−1.73082	−0.865408	−	0.501067i	$-0.832941\pi$
$2$	−2.44774	−1.73082	−0.865408	+	0.501067i	$0.832941\pi$
$3$	0.819540	0.473162	0.236581	−	0.971612i	$-0.423973\pi$
$3$	0.819540	0.473162	0.236581	+	0.971612i	$0.423973\pi$
$4$	3.99145	1.99573
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.00602	−0.818956
$7$	2.11487	0.799346	0.399673	−	0.916658i	$-0.369124\pi$
$7$	2.11487	0.799346	0.399673	+	0.916658i	$0.369124\pi$
$8$	−4.87457	−1.72342
$9$	−2.32835	−0.776118
$10$	−2.44774	−0.774045
$11$	5.18847	1.56438	0.782191	−	0.623039i	$-0.214102\pi$
$11$	5.18847	1.56438	0.782191	+	0.623039i	$0.214102\pi$
$12$	3.27115	0.944301
$13$	3.64508	1.01096	0.505481	−	0.862838i	$-0.331315\pi$
$13$	3.64508	1.01096	0.505481	+	0.862838i	$0.331315\pi$
$14$	−5.17666	−1.38352
$15$	0.819540	0.211604
$16$	3.94879	0.987198
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	5.69922	1.34332
$19$	−2.99970	−0.688179	−0.344090	−	0.938937i	$-0.611812\pi$
$19$	−2.99970	−0.688179	−0.344090	+	0.938937i	$0.611812\pi$
$20$	3.99145	0.892516
$21$	1.73322	0.378220
$22$	−12.7000	−2.70766
$23$	−4.49942	−0.938193	−0.469096	−	0.883147i	$-0.655420\pi$
$23$	−4.49942	−0.938193	−0.469096	+	0.883147i	$0.655420\pi$
$24$	−3.99490	−0.815456
$25$	1.00000	0.200000
$26$	−8.92222	−1.74979
$27$	−4.36680	−0.840391
$28$	8.44141	1.59528
$29$	0.815379	0.151412	0.0757061	−	0.997130i	$-0.475879\pi$
$29$	0.815379	0.151412	0.0757061	+	0.997130i	$0.475879\pi$
$30$	−2.00602	−0.366248
$31$	−4.17338	−0.749561	−0.374781	−	0.927114i	$-0.622282\pi$
$31$	−4.17338	−0.749561	−0.374781	+	0.927114i	$0.622282\pi$
$32$	0.0835062	0.0147619
$33$	4.25216	0.740205
$34$	2.44774	0.419785
$35$	2.11487	0.357478
$36$	−9.29352	−1.54892
$37$	−7.95861	−1.30839	−0.654194	−	0.756327i	$-0.726992\pi$
$37$	−7.95861	−1.30839	−0.654194	+	0.756327i	$0.726992\pi$
$38$	7.34251	1.19111
$39$	2.98729	0.478348
$40$	−4.87457	−0.770737
$41$	12.3801	1.93345	0.966725	−	0.255818i	$-0.0823448\pi$
$41$	12.3801	1.93345	0.966725	+	0.255818i	$0.0823448\pi$
$42$	−4.24248	−0.654629
$43$	5.72338	0.872807	0.436403	−	0.899751i	$-0.356252\pi$
$43$	5.72338	0.872807	0.436403	+	0.899751i	$0.356252\pi$
$44$	20.7095	3.12208
$45$	−2.32835	−0.347091
$46$	11.0134	1.62384
$47$	−12.1863	−1.77756	−0.888780	−	0.458334i	$-0.848446\pi$
$47$	−12.1863	−1.77756	−0.888780	+	0.458334i	$0.848446\pi$
$48$	3.23619	0.467104
$49$	−2.52732	−0.361046
$50$	−2.44774	−0.346163
$51$	−0.819540	−0.114759
$52$	14.5492	2.01760
$53$	13.0466	1.79209	0.896044	−	0.443965i	$-0.146429\pi$
$53$	13.0466	1.79209	0.896044	+	0.443965i	$0.146429\pi$
$54$	10.6888	1.45456
$55$	5.18847	0.699613
$56$	−10.3091	−1.37761
$57$	−2.45838	−0.325620
$58$	−1.99584	−0.262067
$59$	−3.87844	−0.504931	−0.252465	−	0.967606i	$-0.581241\pi$
$59$	−3.87844	−0.504931	−0.252465	+	0.967606i	$0.581241\pi$
$60$	3.27115	0.422304
$61$	2.07923	0.266218	0.133109	−	0.991101i	$-0.457504\pi$
$61$	2.07923	0.266218	0.133109	+	0.991101i	$0.457504\pi$
$62$	10.2154	1.29735
$63$	−4.92417	−0.620387
$64$	−8.10198	−1.01275
$65$	3.64508	0.452116
$66$	−10.4082	−1.28116
$67$	9.67971	1.18256	0.591282	−	0.806465i	$-0.298622\pi$
$67$	9.67971	1.18256	0.591282	+	0.806465i	$0.298622\pi$
$68$	−3.99145	−0.484035
$69$	−3.68745	−0.443917
$70$	−5.17666	−0.618730
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	11.3497	1.33758
$73$	11.8516	1.38712	0.693562	−	0.720397i	$-0.256040\pi$
$73$	11.8516	1.38712	0.693562	+	0.720397i	$0.256040\pi$
$74$	19.4806	2.26458
$75$	0.819540	0.0946323
$76$	−11.9732	−1.37342
$77$	10.9729	1.25048
$78$	−7.31211	−0.827934
$79$	11.9633	1.34597	0.672987	−	0.739654i	$-0.265011\pi$
$79$	11.9633	1.34597	0.672987	+	0.739654i	$0.265011\pi$
$80$	3.94879	0.441488
$81$	3.40630	0.378477
$82$	−30.3034	−3.34645
$83$	−1.15382	−0.126648	−0.0633242	−	0.997993i	$-0.520170\pi$
$83$	−1.15382	−0.126648	−0.0633242	+	0.997993i	$0.520170\pi$
$84$	6.91807	0.754823
$85$	−1.00000	−0.108465
$86$	−14.0094	−1.51067
$87$	0.668236	0.0716424
$88$	−25.2915	−2.69609
$89$	1.38177	0.146467	0.0732335	−	0.997315i	$-0.476668\pi$
$89$	1.38177	0.146467	0.0732335	+	0.997315i	$0.476668\pi$
$90$	5.69922	0.600750
$91$	7.70887	0.808109
$92$	−17.9592	−1.87238
$93$	−3.42025	−0.354663
$94$	29.8290	3.07663
$95$	−2.99970	−0.307763
$96$	0.0684366	0.00698478
$97$	17.6810	1.79523	0.897616	−	0.440778i	$-0.145297\pi$
$97$	17.6810	1.79523	0.897616	+	0.440778i	$0.145297\pi$
$98$	6.18624	0.624904
$99$	−12.0806	−1.21414
$100$	3.99145	0.399145
$101$	3.93467	0.391515	0.195757	−	0.980652i	$-0.437284\pi$
$101$	3.93467	0.391515	0.195757	+	0.980652i	$0.437284\pi$
$102$	2.00602	0.198626
$103$	−2.89612	−0.285363	−0.142681	−	0.989769i	$-0.545572\pi$
$103$	−2.89612	−0.285363	−0.142681	+	0.989769i	$0.545572\pi$
$104$	−17.7682	−1.74231
$105$	1.73322	0.169145
$106$	−31.9347	−3.10178
$107$	−11.4395	−1.10590	−0.552951	−	0.833214i	$-0.686498\pi$
$107$	−11.4395	−1.10590	−0.552951	+	0.833214i	$0.686498\pi$
$108$	−17.4299	−1.67719
$109$	14.3081	1.37047	0.685235	−	0.728322i	$-0.259699\pi$
$109$	14.3081	1.37047	0.685235	+	0.728322i	$0.259699\pi$
$110$	−12.7000	−1.21090
$111$	−6.52240	−0.619079
$112$	8.35118	0.789112
$113$	−17.4662	−1.64308	−0.821541	−	0.570149i	$-0.806885\pi$
$113$	−17.4662	−1.64308	−0.821541	+	0.570149i	$0.806885\pi$
$114$	6.01748	0.563589
$115$	−4.49942	−0.419573
$116$	3.25455	0.302177
$117$	−8.48703	−0.784626
$118$	9.49344	0.873942
$119$	−2.11487	−0.193870
$120$	−3.99490	−0.364683
$121$	15.9202	1.44729
$122$	−5.08941	−0.460774
$123$	10.1460	0.914834
$124$	−16.6578	−1.49592
$125$	1.00000	0.0894427
$126$	12.0531	1.07378
$127$	6.14794	0.545542	0.272771	−	0.962079i	$-0.412060\pi$
$127$	6.14794	0.545542	0.272771	+	0.962079i	$0.412060\pi$
$128$	19.6646	1.73812
$129$	4.69053	0.412978
$130$	−8.92222	−0.782530
$131$	4.62013	0.403662	0.201831	−	0.979420i	$-0.435311\pi$
$131$	4.62013	0.403662	0.201831	+	0.979420i	$0.435311\pi$
$132$	16.9723	1.47725
$133$	−6.34399	−0.550093
$134$	−23.6934	−2.04680
$135$	−4.36680	−0.375834
$136$	4.87457	0.417991
$137$	−4.03432	−0.344676	−0.172338	−	0.985038i	$-0.555132\pi$
$137$	−4.03432	−0.344676	−0.172338	+	0.985038i	$0.555132\pi$
$138$	9.02594	0.768339
$139$	4.82012	0.408837	0.204419	−	0.978884i	$-0.434470\pi$
$139$	4.82012	0.408837	0.204419	+	0.978884i	$0.434470\pi$
$140$	8.44141	0.713429
$141$	−9.98719	−0.841073
$142$	2.44774	0.205410
$143$	18.9124	1.58153
$144$	−9.19418	−0.766182
$145$	0.815379	0.0677136
$146$	−29.0097	−2.40086
$147$	−2.07124	−0.170833
$148$	−31.7664	−2.61118
$149$	14.4072	1.18029	0.590144	−	0.807298i	$-0.299071\pi$
$149$	14.4072	1.18029	0.590144	+	0.807298i	$0.299071\pi$
$150$	−2.00602	−0.163791
$151$	11.4009	0.927795	0.463897	−	0.885889i	$-0.346451\pi$
$151$	11.4009	0.927795	0.463897	+	0.885889i	$0.346451\pi$
$152$	14.6223	1.18602
$153$	2.32835	0.188236
$154$	−26.8589	−2.16436
$155$	−4.17338	−0.335214
$156$	11.9236	0.954653
$157$	19.2855	1.53915	0.769575	−	0.638557i	$-0.220468\pi$
$157$	19.2855	1.53915	0.769575	+	0.638557i	$0.220468\pi$
$158$	−29.2831	−2.32964
$159$	10.6922	0.847947
$160$	0.0835062	0.00660174
$161$	−9.51568	−0.749941
$162$	−8.33775	−0.655075
$163$	3.94829	0.309254	0.154627	−	0.987973i	$-0.450582\pi$
$163$	3.94829	0.309254	0.154627	+	0.987973i	$0.450582\pi$
$164$	49.4147	3.85864
$165$	4.25216	0.331030
$166$	2.82426	0.219205
$167$	−3.93151	−0.304229	−0.152115	−	0.988363i	$-0.548608\pi$
$167$	−3.93151	−0.304229	−0.152115	+	0.988363i	$0.548608\pi$
$168$	−8.44870	−0.651832
$169$	0.286581	0.0220447
$170$	2.44774	0.187733
$171$	6.98437	0.534108
$172$	22.8446	1.74188
$173$	−3.45287	−0.262517	−0.131259	−	0.991348i	$-0.541902\pi$
$173$	−3.45287	−0.262517	−0.131259	+	0.991348i	$0.541902\pi$
$174$	−1.63567	−0.124000
$175$	2.11487	0.159869
$176$	20.4882	1.54435
$177$	−3.17854	−0.238914
$178$	−3.38221	−0.253508
$179$	−19.8659	−1.48485	−0.742423	−	0.669931i	$-0.766324\pi$
$179$	−19.8659	−1.48485	−0.742423	+	0.669931i	$0.766324\pi$
$180$	−9.29352	−0.692698
$181$	20.4961	1.52346	0.761731	−	0.647893i	$-0.224350\pi$
$181$	20.4961	1.52346	0.761731	+	0.647893i	$0.224350\pi$
$182$	−18.8693	−1.39869
$183$	1.70401	0.125964
$184$	21.9327	1.61690
$185$	−7.95861	−0.585129
$186$	8.37190	0.613857
$187$	−5.18847	−0.379418
$188$	−48.6412	−3.54752
$189$	−9.23522	−0.671763
$190$	7.34251	0.532682
$191$	16.7381	1.21112	0.605562	−	0.795798i	$-0.292948\pi$
$191$	16.7381	1.21112	0.605562	+	0.795798i	$0.292948\pi$
$192$	−6.63990	−0.479193
$193$	19.4519	1.40017	0.700087	−	0.714057i	$-0.253144\pi$
$193$	19.4519	1.40017	0.700087	+	0.714057i	$0.253144\pi$
$194$	−43.2786	−3.10722
$195$	2.98729	0.213924
$196$	−10.0877	−0.720549
$197$	11.9387	0.850600	0.425300	−	0.905052i	$-0.360169\pi$
$197$	11.9387	0.850600	0.425300	+	0.905052i	$0.360169\pi$
$198$	29.5702	2.10146
$199$	8.91274	0.631808	0.315904	−	0.948791i	$-0.397692\pi$
$199$	8.91274	0.631808	0.315904	+	0.948791i	$0.397692\pi$
$200$	−4.87457	−0.344684
$201$	7.93290	0.559544
$202$	−9.63107	−0.677640
$203$	1.72442	0.121031
$204$	−3.27115	−0.229027
$205$	12.3801	0.864665
$206$	7.08895	0.493911
$207$	10.4762	0.728149
$208$	14.3936	0.998019
$209$	−15.5639	−1.07658
$210$	−4.24248	−0.292759
$211$	26.2860	1.80960	0.904800	−	0.425836i	$-0.140020\pi$
$211$	26.2860	1.80960	0.904800	+	0.425836i	$0.140020\pi$
$212$	52.0749	3.57652
$213$	−0.819540	−0.0561539
$214$	28.0011	1.91411
$215$	5.72338	0.390331
$216$	21.2863	1.44835
$217$	−8.82616	−0.599159
$218$	−35.0226	−2.37203
$219$	9.71285	0.656334
$220$	20.7095	1.39624
$221$	−3.64508	−0.245194
$222$	15.9652	1.07151
$223$	−4.81290	−0.322296	−0.161148	−	0.986930i	$-0.551520\pi$
$223$	−4.81290	−0.322296	−0.161148	+	0.986930i	$0.551520\pi$
$224$	0.176605	0.0117999
$225$	−2.32835	−0.155224
$226$	42.7528	2.84387
$227$	−9.01997	−0.598677	−0.299338	−	0.954147i	$-0.596766\pi$
$227$	−9.01997	−0.598677	−0.299338	+	0.954147i	$0.596766\pi$
$228$	−9.81250	−0.649848
$229$	1.24057	0.0819794	0.0409897	−	0.999160i	$-0.486949\pi$
$229$	1.24057	0.0819794	0.0409897	+	0.999160i	$0.486949\pi$
$230$	11.0134	0.726203
$231$	8.99276	0.591680
$232$	−3.97462	−0.260947
$233$	−23.4522	−1.53641	−0.768204	−	0.640206i	$-0.778849\pi$
$233$	−23.4522	−1.53641	−0.768204	+	0.640206i	$0.778849\pi$
$234$	20.7741	1.35804
$235$	−12.1863	−0.794949
$236$	−15.4806	−1.00770
$237$	9.80439	0.636863
$238$	5.17666	0.335553
$239$	8.14994	0.527175	0.263588	−	0.964635i	$-0.415094\pi$
$239$	8.14994	0.527175	0.263588	+	0.964635i	$0.415094\pi$
$240$	3.23619	0.208895
$241$	−9.41956	−0.606767	−0.303384	−	0.952868i	$-0.598116\pi$
$241$	−9.41956	−0.606767	−0.303384	+	0.952868i	$0.598116\pi$
$242$	−38.9685	−2.50499
$243$	15.8920	1.01947
$244$	8.29913	0.531297
$245$	−2.52732	−0.161465
$246$	−24.8348	−1.58341
$247$	−10.9342	−0.695723
$248$	20.3434	1.29181
$249$	−0.945602	−0.0599251
$250$	−2.44774	−0.154809
$251$	18.5053	1.16804	0.584022	−	0.811738i	$-0.301478\pi$
$251$	18.5053	1.16804	0.584022	+	0.811738i	$0.301478\pi$
$252$	−19.6546	−1.23812
$253$	−23.3451	−1.46769
$254$	−15.0486	−0.944233
$255$	−0.819540	−0.0513216
$256$	−31.9299	−1.99562
$257$	7.72118	0.481634	0.240817	−	0.970571i	$-0.422585\pi$
$257$	7.72118	0.481634	0.240817	+	0.970571i	$0.422585\pi$
$258$	−11.4812	−0.714790
$259$	−16.8314	−1.04585
$260$	14.5492	0.902300
$261$	−1.89849	−0.117514
$262$	−11.3089	−0.698665
$263$	−16.6504	−1.02671	−0.513354	−	0.858177i	$-0.671597\pi$
$263$	−16.6504	−1.02671	−0.513354	+	0.858177i	$0.671597\pi$
$264$	−20.7274	−1.27568
$265$	13.0466	0.801446
$266$	15.5285	0.952111
$267$	1.13241	0.0693026
$268$	38.6361	2.36007
$269$	−14.1724	−0.864108	−0.432054	−	0.901848i	$-0.642211\pi$
$269$	−14.1724	−0.864108	−0.432054	+	0.901848i	$0.642211\pi$
$270$	10.6888	0.650500
$271$	−12.8750	−0.782100	−0.391050	−	0.920369i	$-0.627888\pi$
$271$	−12.8750	−0.782100	−0.391050	+	0.920369i	$0.627888\pi$
$272$	−3.94879	−0.239431
$273$	6.31772	0.382366
$274$	9.87499	0.596570
$275$	5.18847	0.312876
$276$	−14.7183	−0.885937
$277$	−11.1994	−0.672904	−0.336452	−	0.941701i	$-0.609227\pi$
$277$	−11.1994	−0.672904	−0.336452	+	0.941701i	$0.609227\pi$
$278$	−11.7984	−0.707622
$279$	9.71711	0.581748
$280$	−10.3091	−0.616085
$281$	31.2158	1.86218	0.931089	−	0.364791i	$-0.118860\pi$
$281$	31.2158	1.86218	0.931089	+	0.364791i	$0.118860\pi$
$282$	24.4461	1.45574
$283$	−2.25362	−0.133964	−0.0669819	−	0.997754i	$-0.521337\pi$
$283$	−2.25362	−0.133964	−0.0669819	+	0.997754i	$0.521337\pi$
$284$	−3.99145	−0.236849
$285$	−2.45838	−0.145622
$286$	−46.2926	−2.73734
$287$	26.1824	1.54550
$288$	−0.194432	−0.0114570
$289$	1.00000	0.0588235
$290$	−1.99584	−0.117200
$291$	14.4903	0.849435
$292$	47.3051	2.76832
$293$	−21.0249	−1.22829	−0.614144	−	0.789194i	$-0.710499\pi$
$293$	−21.0249	−1.22829	−0.614144	+	0.789194i	$0.710499\pi$
$294$	5.06987	0.295681
$295$	−3.87844	−0.225812
$296$	38.7948	2.25490
$297$	−22.6570	−1.31469
$298$	−35.2653	−2.04286
$299$	−16.4007	−0.948478
$300$	3.27115	0.188860
$301$	12.1042	0.697674
$302$	−27.9066	−1.60584
$303$	3.22462	0.185250
$304$	−11.8452	−0.679369
$305$	2.07923	0.119056
$306$	−5.69922	−0.325803
$307$	−8.71836	−0.497583	−0.248791	−	0.968557i	$-0.580033\pi$
$307$	−8.71836	−0.497583	−0.248791	+	0.968557i	$0.580033\pi$
$308$	43.7980	2.49562
$309$	−2.37348	−0.135023
$310$	10.2154	0.580194
$311$	−27.2841	−1.54714	−0.773571	−	0.633710i	$-0.781531\pi$
$311$	−27.2841	−1.54714	−0.773571	+	0.633710i	$0.781531\pi$
$312$	−14.5617	−0.824395
$313$	−15.4149	−0.871304	−0.435652	−	0.900115i	$-0.643482\pi$
$313$	−15.4149	−0.871304	−0.435652	+	0.900115i	$0.643482\pi$
$314$	−47.2059	−2.66398
$315$	−4.92417	−0.277445
$316$	47.7509	2.68620
$317$	−32.0000	−1.79730	−0.898649	−	0.438669i	$-0.855450\pi$
$317$	−32.0000	−1.79730	−0.898649	+	0.438669i	$0.855450\pi$
$318$	−26.1718	−1.46764
$319$	4.23057	0.236866
$320$	−8.10198	−0.452915
$321$	−9.37516	−0.523271
$322$	23.2920	1.29801
$323$	2.99970	0.166908
$324$	13.5961	0.755338
$325$	3.64508	0.202192
$326$	−9.66440	−0.535261
$327$	11.7261	0.648454
$328$	−60.3477	−3.33215
$329$	−25.7725	−1.42089
$330$	−10.4082	−0.572952
$331$	−21.6019	−1.18735	−0.593674	−	0.804706i	$-0.702323\pi$
$331$	−21.6019	−1.18735	−0.593674	+	0.804706i	$0.702323\pi$
$332$	−4.60542	−0.252755
$333$	18.5305	1.01546
$334$	9.62333	0.526565
$335$	9.67971	0.528859
$336$	6.84413	0.373378
$337$	−23.7405	−1.29323	−0.646614	−	0.762817i	$-0.723815\pi$
$337$	−23.7405	−1.29323	−0.646614	+	0.762817i	$0.723815\pi$
$338$	−0.701478	−0.0381554
$339$	−14.3143	−0.777443
$340$	−3.99145	−0.216467
$341$	−21.6534	−1.17260
$342$	−17.0960	−0.924444
$343$	−20.1491	−1.08795
$344$	−27.8990	−1.50421
$345$	−3.68745	−0.198526
$346$	8.45175	0.454369
$347$	2.39346	0.128488	0.0642438	−	0.997934i	$-0.479536\pi$
$347$	2.39346	0.128488	0.0642438	+	0.997934i	$0.479536\pi$
$348$	2.66723	0.142979
$349$	25.5353	1.36687	0.683436	−	0.730010i	$-0.260485\pi$
$349$	25.5353	1.36687	0.683436	+	0.730010i	$0.260485\pi$
$350$	−5.17666	−0.276704
$351$	−15.9173	−0.849603
$352$	0.433269	0.0230933
$353$	18.8439	1.00296	0.501480	−	0.865169i	$-0.332789\pi$
$353$	18.8439	1.00296	0.501480	+	0.865169i	$0.332789\pi$
$354$	7.78025	0.413516
$355$	−1.00000	−0.0530745
$356$	5.51526	0.292308
$357$	−1.73322	−0.0917318
$358$	48.6266	2.57000
$359$	20.1664	1.06434	0.532170	−	0.846637i	$-0.321377\pi$
$359$	20.1664	1.06434	0.532170	+	0.846637i	$0.321377\pi$
$360$	11.3497	0.598183
$361$	−10.0018	−0.526409
$362$	−50.1692	−2.63683
$363$	13.0472	0.684802
$364$	30.7696	1.61276
$365$	11.8516	0.620341
$366$	−4.17098	−0.218020
$367$	−31.1526	−1.62615	−0.813076	−	0.582157i	$-0.802209\pi$
$367$	−31.1526	−1.62615	−0.813076	+	0.582157i	$0.802209\pi$
$368$	−17.7672	−0.926182
$369$	−28.8253	−1.50059
$370$	19.4806	1.01275
$371$	27.5919	1.43250
$372$	−13.6518	−0.707811
$373$	19.1621	0.992177	0.496089	−	0.868272i	$-0.334769\pi$
$373$	19.1621	0.992177	0.496089	+	0.868272i	$0.334769\pi$
$374$	12.7000	0.656703
$375$	0.819540	0.0423209
$376$	59.4031	3.06348
$377$	2.97212	0.153072
$378$	22.6054	1.16270
$379$	9.70622	0.498575	0.249288	−	0.968429i	$-0.419804\pi$
$379$	9.70622	0.498575	0.249288	+	0.968429i	$0.419804\pi$
$380$	−11.9732	−0.614211
$381$	5.03848	0.258129
$382$	−40.9705	−2.09623
$383$	7.39114	0.377669	0.188835	−	0.982009i	$-0.439529\pi$
$383$	7.39114	0.377669	0.188835	+	0.982009i	$0.439529\pi$
$384$	16.1159	0.822411
$385$	10.9729	0.559233
$386$	−47.6132	−2.42345
$387$	−13.3260	−0.677401
$388$	70.5728	3.58279
$389$	18.0073	0.913004	0.456502	−	0.889722i	$-0.349102\pi$
$389$	18.0073	0.913004	0.456502	+	0.889722i	$0.349102\pi$
$390$	−7.31211	−0.370263
$391$	4.49942	0.227545
$392$	12.3196	0.622234
$393$	3.78638	0.190997
$394$	−29.2230	−1.47223
$395$	11.9633	0.601938
$396$	−48.2191	−2.42310
$397$	3.50396	0.175859	0.0879293	−	0.996127i	$-0.471975\pi$
$397$	3.50396	0.175859	0.0879293	+	0.996127i	$0.471975\pi$
$398$	−21.8161	−1.09354
$399$	−5.19915	−0.260283
$400$	3.94879	0.197440
$401$	−3.42619	−0.171096	−0.0855479	−	0.996334i	$-0.527264\pi$
$401$	−3.42619	−0.171096	−0.0855479	+	0.996334i	$0.527264\pi$
$402$	−19.4177	−0.968468
$403$	−15.2123	−0.757778
$404$	15.7051	0.781356
$405$	3.40630	0.169260
$406$	−4.22094	−0.209482
$407$	−41.2930	−2.04682
$408$	3.99490	0.197777
$409$	29.2477	1.44620	0.723102	−	0.690742i	$-0.242716\pi$
$409$	29.2477	1.44620	0.723102	+	0.690742i	$0.242716\pi$
$410$	−30.3034	−1.49658
$411$	−3.30629	−0.163087
$412$	−11.5597	−0.569506
$413$	−8.20241	−0.403614
$414$	−25.6431	−1.26029
$415$	−1.15382	−0.0566388
$416$	0.304386	0.0149238
$417$	3.95028	0.193446
$418$	38.0964	1.86335
$419$	−13.6150	−0.665135	−0.332567	−	0.943080i	$-0.607915\pi$
$419$	−13.6150	−0.665135	−0.332567	+	0.943080i	$0.607915\pi$
$420$	6.91807	0.337567
$421$	−17.5946	−0.857507	−0.428754	−	0.903422i	$-0.641047\pi$
$421$	−17.5946	−0.857507	−0.428754	+	0.903422i	$0.641047\pi$
$422$	−64.3413	−3.13209
$423$	28.3741	1.37960
$424$	−63.5965	−3.08852
$425$	−1.00000	−0.0485071
$426$	2.00602	0.0971922
$427$	4.39729	0.212800
$428$	−45.6604	−2.20708
$429$	15.4994	0.748320
$430$	−14.0094	−0.675591
$431$	11.7472	0.565841	0.282920	−	0.959143i	$-0.408697\pi$
$431$	11.7472	0.565841	0.282920	+	0.959143i	$0.408697\pi$
$432$	−17.2436	−0.829632
$433$	−13.8809	−0.667075	−0.333537	−	0.942737i	$-0.608242\pi$
$433$	−13.8809	−0.667075	−0.333537	+	0.942737i	$0.608242\pi$
$434$	21.6042	1.03703
$435$	0.668236	0.0320395
$436$	57.1102	2.73508
$437$	13.4969	0.645645
$438$	−23.7746	−1.13599
$439$	26.3853	1.25930	0.629651	−	0.776878i	$-0.283198\pi$
$439$	26.3853	1.25930	0.629651	+	0.776878i	$0.283198\pi$
$440$	−25.2915	−1.20573
$441$	5.88450	0.280214
$442$	8.92222	0.424387
$443$	−8.53262	−0.405397	−0.202698	−	0.979241i	$-0.564971\pi$
$443$	−8.53262	−0.405397	−0.202698	+	0.979241i	$0.564971\pi$
$444$	−26.0338	−1.23551
$445$	1.38177	0.0655020
$446$	11.7807	0.557835
$447$	11.8073	0.558467
$448$	−17.1346	−0.809536
$449$	7.02167	0.331373	0.165686	−	0.986178i	$-0.447016\pi$
$449$	7.02167	0.331373	0.165686	+	0.986178i	$0.447016\pi$
$450$	5.69922	0.268664
$451$	64.2338	3.02465
$452$	−69.7155	−3.27914
$453$	9.34352	0.438997
$454$	22.0786	1.03620
$455$	7.70887	0.361397
$456$	11.9835	0.561180
$457$	−13.2924	−0.621794	−0.310897	−	0.950444i	$-0.600629\pi$
$457$	−13.2924	−0.621794	−0.310897	+	0.950444i	$0.600629\pi$
$458$	−3.03661	−0.141891
$459$	4.36680	0.203825
$460$	−17.9592	−0.837352
$461$	−14.1058	−0.656971	−0.328485	−	0.944509i	$-0.606538\pi$
$461$	−14.1058	−0.656971	−0.328485	+	0.944509i	$0.606538\pi$
$462$	−22.0120	−1.02409
$463$	8.71275	0.404916	0.202458	−	0.979291i	$-0.435107\pi$
$463$	8.71275	0.404916	0.202458	+	0.979291i	$0.435107\pi$
$464$	3.21976	0.149474
$465$	−3.42025	−0.158610
$466$	57.4051	2.65924
$467$	−8.73964	−0.404422	−0.202211	−	0.979342i	$-0.564813\pi$
$467$	−8.73964	−0.404422	−0.202211	+	0.979342i	$0.564813\pi$
$468$	−33.8756	−1.56590
$469$	20.4713	0.945278
$470$	29.8290	1.37591
$471$	15.8052	0.728266
$472$	18.9057	0.870207
$473$	29.6955	1.36540
$474$	−23.9986	−1.10229
$475$	−2.99970	−0.137636
$476$	−8.44141	−0.386911
$477$	−30.3771	−1.39087
$478$	−19.9490	−0.912444
$479$	9.97882	0.455944	0.227972	−	0.973668i	$-0.426791\pi$
$479$	9.97882	0.455944	0.227972	+	0.973668i	$0.426791\pi$
$480$	0.0684366	0.00312369
$481$	−29.0097	−1.32273
$482$	23.0567	1.05020
$483$	−7.79848	−0.354843
$484$	63.5447	2.88839
$485$	17.6810	0.802853
$486$	−38.8995	−1.76452
$487$	16.2491	0.736316	0.368158	−	0.929763i	$-0.379989\pi$
$487$	16.2491	0.736316	0.368158	+	0.929763i	$0.379989\pi$
$488$	−10.1353	−0.458805
$489$	3.23578	0.146327
$490$	6.18624	0.279466
$491$	17.9541	0.810257	0.405129	−	0.914260i	$-0.367227\pi$
$491$	17.9541	0.810257	0.405129	+	0.914260i	$0.367227\pi$
$492$	40.4973	1.82576
$493$	−0.815379	−0.0367228
$494$	26.7640	1.20417
$495$	−12.0806	−0.542982
$496$	−16.4798	−0.739965
$497$	−2.11487	−0.0948649
$498$	2.31459	0.103719
$499$	−27.4461	−1.22866	−0.614328	−	0.789051i	$-0.710573\pi$
$499$	−27.4461	−1.22866	−0.614328	+	0.789051i	$0.710573\pi$
$500$	3.99145	0.178503
$501$	−3.22203	−0.143950
$502$	−45.2962	−2.02167
$503$	−20.8281	−0.928679	−0.464339	−	0.885657i	$-0.653708\pi$
$503$	−20.8281	−0.928679	−0.464339	+	0.885657i	$0.653708\pi$
$504$	24.0032	1.06919
$505$	3.93467	0.175091
$506$	57.1428	2.54031
$507$	0.234865	0.0104307
$508$	24.5392	1.08875
$509$	16.3442	0.724443	0.362221	−	0.932092i	$-0.382018\pi$
$509$	16.3442	0.724443	0.362221	+	0.932092i	$0.382018\pi$
$510$	2.00602	0.0888282
$511$	25.0646	1.10879
$512$	38.8270	1.71593
$513$	13.0991	0.578340
$514$	−18.8995	−0.833621
$515$	−2.89612	−0.127618
$516$	18.7220	0.824192
$517$	−63.2284	−2.78078
$518$	41.1990	1.81018
$519$	−2.82977	−0.124213
$520$	−17.7682	−0.779186
$521$	41.2409	1.80680	0.903399	−	0.428800i	$-0.141064\pi$
$521$	41.2409	1.80680	0.903399	+	0.428800i	$0.141064\pi$
$522$	4.64702	0.203395
$523$	−24.7419	−1.08189	−0.540944	−	0.841058i	$-0.681933\pi$
$523$	−24.7419	−1.08189	−0.540944	+	0.841058i	$0.681933\pi$
$524$	18.4410	0.805599
$525$	1.73322	0.0756440
$526$	40.7559	1.77704
$527$	4.17338	0.181795
$528$	16.7909	0.730729
$529$	−2.75526	−0.119794
$530$	−31.9347	−1.38716
$531$	9.03039	0.391886
$532$	−25.3217	−1.09784
$533$	45.1265	1.95464
$534$	−2.77186	−0.119950
$535$	−11.4395	−0.494575
$536$	−47.1844	−2.03805
$537$	−16.2809	−0.702572
$538$	34.6905	1.49561
$539$	−13.1129	−0.564814
$540$	−17.4299	−0.750062
$541$	−8.52292	−0.366429	−0.183215	−	0.983073i	$-0.558650\pi$
$541$	−8.52292	−0.366429	−0.183215	+	0.983073i	$0.558650\pi$
$542$	31.5147	1.35367
$543$	16.7974	0.720844
$544$	−0.0835062	−0.00358030
$545$	14.3081	0.612893
$546$	−15.4642	−0.661805
$547$	−15.8666	−0.678406	−0.339203	−	0.940713i	$-0.610157\pi$
$547$	−15.8666	−0.678406	−0.339203	+	0.940713i	$0.610157\pi$
$548$	−16.1028	−0.687878
$549$	−4.84117	−0.206616
$550$	−12.7000	−0.541532
$551$	−2.44590	−0.104199
$552$	17.9747	0.765055
$553$	25.3008	1.07590
$554$	27.4132	1.16467
$555$	−6.52240	−0.276860
$556$	19.2393	0.815927
$557$	−33.2743	−1.40988	−0.704940	−	0.709267i	$-0.749026\pi$
$557$	−33.2743	−1.40988	−0.704940	+	0.709267i	$0.749026\pi$
$558$	−23.7850	−1.00690
$559$	20.8621	0.882374
$560$	8.35118	0.352902
$561$	−4.25216	−0.179526
$562$	−76.4083	−3.22309
$563$	−0.517863	−0.0218253	−0.0109127	−	0.999940i	$-0.503474\pi$
$563$	−0.517863	−0.0218253	−0.0109127	+	0.999940i	$0.503474\pi$
$564$	−39.8634	−1.67855
$565$	−17.4662	−0.734809
$566$	5.51629	0.231867
$567$	7.20388	0.302534
$568$	4.87457	0.204532
$569$	−30.9949	−1.29937	−0.649686	−	0.760202i	$-0.725100\pi$
$569$	−30.9949	−1.29937	−0.649686	+	0.760202i	$0.725100\pi$
$570$	6.01748	0.252044
$571$	26.9899	1.12949	0.564747	−	0.825264i	$-0.308974\pi$
$571$	26.9899	1.12949	0.564747	+	0.825264i	$0.308974\pi$
$572$	75.4878	3.15630
$573$	13.7175	0.573057
$574$	−64.0877	−2.67497
$575$	−4.49942	−0.187639
$576$	18.8643	0.786012
$577$	−43.0083	−1.79046	−0.895229	−	0.445607i	$-0.852988\pi$
$577$	−43.0083	−1.79046	−0.895229	+	0.445607i	$0.852988\pi$
$578$	−2.44774	−0.101813
$579$	15.9416	0.662509
$580$	3.25455	0.135138
$581$	−2.44018	−0.101236
$582$	−35.4685	−1.47022
$583$	67.6918	2.80351
$584$	−57.7714	−2.39060
$585$	−8.48703	−0.350895
$586$	51.4636	2.12594
$587$	19.6081	0.809312	0.404656	−	0.914469i	$-0.367391\pi$
$587$	19.6081	0.809312	0.404656	+	0.914469i	$0.367391\pi$
$588$	−8.26726	−0.340936
$589$	12.5189	0.515832
$590$	9.49344	0.390839
$591$	9.78427	0.402471
$592$	−31.4269	−1.29164
$593$	35.2207	1.44634	0.723171	−	0.690669i	$-0.242684\pi$
$593$	35.2207	1.44634	0.723171	+	0.690669i	$0.242684\pi$
$594$	55.4585	2.27549
$595$	−2.11487	−0.0867013
$596$	57.5058	2.35553
$597$	7.30435	0.298947
$598$	40.1448	1.64164
$599$	8.62302	0.352327	0.176164	−	0.984361i	$-0.443631\pi$
$599$	8.62302	0.352327	0.176164	+	0.984361i	$0.443631\pi$
$600$	−3.99490	−0.163091
$601$	−10.4218	−0.425113	−0.212556	−	0.977149i	$-0.568179\pi$
$601$	−10.4218	−0.425113	−0.212556	+	0.977149i	$0.568179\pi$
$602$	−29.6280	−1.20755
$603$	−22.5378	−0.917810
$604$	45.5063	1.85162
$605$	15.9202	0.647248
$606$	−7.89305	−0.320633
$607$	28.0258	1.13753	0.568767	−	0.822499i	$-0.307421\pi$
$607$	28.0258	1.13753	0.568767	+	0.822499i	$0.307421\pi$
$608$	−0.250494	−0.0101589
$609$	1.41323	0.0572671
$610$	−5.08941	−0.206064
$611$	−44.4201	−1.79705
$612$	9.29352	0.375668
$613$	31.4194	1.26902	0.634509	−	0.772915i	$-0.281202\pi$
$613$	31.4194	1.26902	0.634509	+	0.772915i	$0.281202\pi$
$614$	21.3403	0.861225
$615$	10.1460	0.409126
$616$	−53.4883	−2.15511
$617$	31.7383	1.27774	0.638868	−	0.769316i	$-0.279403\pi$
$617$	31.7383	1.27774	0.638868	+	0.769316i	$0.279403\pi$
$618$	5.80968	0.233700
$619$	23.8738	0.959569	0.479785	−	0.877386i	$-0.340715\pi$
$619$	23.8738	0.959569	0.479785	+	0.877386i	$0.340715\pi$
$620$	−16.6578	−0.668995
$621$	19.6480	0.788449
$622$	66.7846	2.67782
$623$	2.92226	0.117078
$624$	11.7962	0.472224
$625$	1.00000	0.0400000
$626$	37.7318	1.50807
$627$	−12.7552	−0.509394
$628$	76.9771	3.07172
$629$	7.95861	0.317331
$630$	12.0531	0.480207
$631$	34.0544	1.35569	0.677843	−	0.735207i	$-0.262915\pi$
$631$	34.0544	1.35569	0.677843	+	0.735207i	$0.262915\pi$
$632$	−58.3158	−2.31968
$633$	21.5424	0.856233
$634$	78.3277	3.11079
$635$	6.14794	0.243974
$636$	42.6774	1.69227
$637$	−9.21228	−0.365004
$638$	−10.3553	−0.409972
$639$	2.32835	0.0921083
$640$	19.6646	0.777310
$641$	−11.7766	−0.465147	−0.232573	−	0.972579i	$-0.574715\pi$
$641$	−11.7766	−0.465147	−0.232573	+	0.972579i	$0.574715\pi$
$642$	22.9480	0.905686
$643$	43.9052	1.73145	0.865727	−	0.500517i	$-0.166857\pi$
$643$	43.9052	1.73145	0.865727	+	0.500517i	$0.166857\pi$
$644$	−37.9814	−1.49668
$645$	4.69053	0.184690
$646$	−7.34251	−0.288887
$647$	17.6918	0.695535	0.347768	−	0.937581i	$-0.386940\pi$
$647$	17.6918	0.695535	0.347768	+	0.937581i	$0.386940\pi$
$648$	−16.6042	−0.652276
$649$	−20.1232	−0.789904
$650$	−8.92222	−0.349958
$651$	−7.23339	−0.283499
$652$	15.7594	0.617186
$653$	−14.3024	−0.559695	−0.279848	−	0.960044i	$-0.590284\pi$
$653$	−14.3024	−0.559695	−0.279848	+	0.960044i	$0.590284\pi$
$654$	−28.7025	−1.12235
$655$	4.62013	0.180523
$656$	48.8865	1.90870
$657$	−27.5947	−1.07657
$658$	63.0846	2.45929
$659$	−43.2561	−1.68502	−0.842510	−	0.538681i	$-0.818923\pi$
$659$	−43.2561	−1.68502	−0.842510	+	0.538681i	$0.818923\pi$
$660$	16.9723	0.660645
$661$	−12.1303	−0.471814	−0.235907	−	0.971776i	$-0.575806\pi$
$661$	−12.1303	−0.471814	−0.235907	+	0.971776i	$0.575806\pi$
$662$	52.8759	2.05508
$663$	−2.98729	−0.116017
$664$	5.62438	0.218268
$665$	−6.34399	−0.246009
$666$	−45.3578	−1.75758
$667$	−3.66873	−0.142054
$668$	−15.6924	−0.607158
$669$	−3.94436	−0.152498
$670$	−23.6934	−0.915358
$671$	10.7880	0.416466
$672$	0.144735	0.00558326
$673$	−8.77466	−0.338238	−0.169119	−	0.985596i	$-0.554092\pi$
$673$	−8.77466	−0.338238	−0.169119	+	0.985596i	$0.554092\pi$
$674$	58.1107	2.23834
$675$	−4.36680	−0.168078
$676$	1.14388	0.0439952
$677$	23.3785	0.898508	0.449254	−	0.893404i	$-0.351690\pi$
$677$	23.3785	0.898508	0.449254	+	0.893404i	$0.351690\pi$
$678$	35.0376	1.34561
$679$	37.3930	1.43501
$680$	4.87457	0.186931
$681$	−7.39223	−0.283271
$682$	53.0021	2.02955
$683$	−33.4005	−1.27804	−0.639018	−	0.769192i	$-0.720659\pi$
$683$	−33.4005	−1.27804	−0.639018	+	0.769192i	$0.720659\pi$
$684$	27.8778	1.06593
$685$	−4.03432	−0.154144
$686$	49.3197	1.88304
$687$	1.01670	0.0387895
$688$	22.6004	0.861632
$689$	47.5558	1.81173
$690$	9.02594	0.343612
$691$	−24.3816	−0.927519	−0.463760	−	0.885961i	$-0.653500\pi$
$691$	−24.3816	−0.927519	−0.463760	+	0.885961i	$0.653500\pi$
$692$	−13.7820	−0.523912
$693$	−25.5489	−0.970522
$694$	−5.85858	−0.222389
$695$	4.82012	0.182838
$696$	−3.25736	−0.123470
$697$	−12.3801	−0.468930
$698$	−62.5038	−2.36581
$699$	−19.2200	−0.726969
$700$	8.44141	0.319055
$701$	−2.39908	−0.0906118	−0.0453059	−	0.998973i	$-0.514426\pi$
$701$	−2.39908	−0.0906118	−0.0453059	+	0.998973i	$0.514426\pi$
$702$	38.9615	1.47051
$703$	23.8735	0.900405
$704$	−42.0369	−1.58432
$705$	−9.98719	−0.376139
$706$	−46.1251	−1.73594
$707$	8.32132	0.312956
$708$	−12.6870	−0.476806
$709$	−13.6242	−0.511669	−0.255834	−	0.966721i	$-0.582350\pi$
$709$	−13.6242	−0.511669	−0.255834	+	0.966721i	$0.582350\pi$
$710$	2.44774	0.0918622
$711$	−27.8548	−1.04464
$712$	−6.73552	−0.252424
$713$	18.7778	0.703233
$714$	4.24248	0.158771
$715$	18.9124	0.707282
$716$	−79.2938	−2.96335
$717$	6.67920	0.249439
$718$	−49.3621	−1.84218
$719$	−43.4550	−1.62060	−0.810300	−	0.586016i	$-0.800696\pi$
$719$	−43.4550	−1.62060	−0.810300	+	0.586016i	$0.800696\pi$
$720$	−9.19418	−0.342647
$721$	−6.12491	−0.228104
$722$	24.4818	0.911118
$723$	−7.71971	−0.287099
$724$	81.8092	3.04041
$725$	0.815379	0.0302824
$726$	−31.9363	−1.18527
$727$	−13.7487	−0.509912	−0.254956	−	0.966953i	$-0.582061\pi$
$727$	−13.7487	−0.509912	−0.254956	+	0.966953i	$0.582061\pi$
$728$	−37.5774	−1.39271
$729$	2.80523	0.103897
$730$	−29.0097	−1.07370
$731$	−5.72338	−0.211687
$732$	6.80147	0.251390
$733$	30.0732	1.11078	0.555389	−	0.831591i	$-0.312570\pi$
$733$	30.0732	1.11078	0.555389	+	0.831591i	$0.312570\pi$
$734$	76.2536	2.81457
$735$	−2.07124	−0.0763989
$736$	−0.375729	−0.0138496
$737$	50.2228	1.84998
$738$	70.5570	2.59724
$739$	15.4430	0.568081	0.284041	−	0.958812i	$-0.408325\pi$
$739$	15.4430	0.568081	0.284041	+	0.958812i	$0.408325\pi$
$740$	−31.7664	−1.16776
$741$	−8.96097	−0.329190
$742$	−67.5378	−2.47939
$743$	−7.42586	−0.272428	−0.136214	−	0.990679i	$-0.543494\pi$
$743$	−7.42586	−0.272428	−0.136214	+	0.990679i	$0.543494\pi$
$744$	16.6722	0.611234
$745$	14.4072	0.527841
$746$	−46.9040	−1.71728
$747$	2.68650	0.0982941
$748$	−20.7095	−0.757215
$749$	−24.1932	−0.883999
$750$	−2.00602	−0.0732496
$751$	25.1238	0.916779	0.458390	−	0.888751i	$-0.348426\pi$
$751$	25.1238	0.916779	0.458390	+	0.888751i	$0.348426\pi$
$752$	−48.1213	−1.75480
$753$	15.1658	0.552674
$754$	−7.27499	−0.264939
$755$	11.4009	0.414923
$756$	−36.8619	−1.34066
$757$	−37.5109	−1.36336	−0.681678	−	0.731652i	$-0.738750\pi$
$757$	−37.5109	−1.36336	−0.681678	+	0.731652i	$0.738750\pi$
$758$	−23.7584	−0.862942
$759$	−19.1322	−0.694455
$760$	14.6223	0.530405
$761$	0.0811170	0.00294049	0.00147024	−	0.999999i	$-0.499532\pi$
$761$	0.0811170	0.00294049	0.00147024	+	0.999999i	$0.499532\pi$
$762$	−12.3329	−0.446775
$763$	30.2598	1.09548
$764$	66.8092	2.41707
$765$	2.32835	0.0841818
$766$	−18.0916	−0.653676
$767$	−14.1372	−0.510466
$768$	−26.1678	−0.944249
$769$	27.8680	1.00495	0.502474	−	0.864593i	$-0.332423\pi$
$769$	27.8680	1.00495	0.502474	+	0.864593i	$0.332423\pi$
$770$	−26.8589	−0.967929
$771$	6.32782	0.227891
$772$	77.6411	2.79437
$773$	15.7121	0.565125	0.282562	−	0.959249i	$-0.408816\pi$
$773$	15.7121	0.565125	0.282562	+	0.959249i	$0.408816\pi$
$774$	32.6188	1.17246
$775$	−4.17338	−0.149912
$776$	−86.1872	−3.09394
$777$	−13.7940	−0.494858
$778$	−44.0772	−1.58024
$779$	−37.1367	−1.33056
$780$	11.9236	0.426934
$781$	−5.18847	−0.185658
$782$	−11.0134	−0.393839
$783$	−3.56060	−0.127245
$784$	−9.97986	−0.356424
$785$	19.2855	0.688328
$786$	−9.26808	−0.330582
$787$	−7.79407	−0.277829	−0.138914	−	0.990304i	$-0.544361\pi$
$787$	−7.79407	−0.277829	−0.138914	+	0.990304i	$0.544361\pi$
$788$	47.6529	1.69756
$789$	−13.6457	−0.485799
$790$	−29.2831	−1.04184
$791$	−36.9388	−1.31339
$792$	58.8876	2.09248
$793$	7.57894	0.269136
$794$	−8.57680	−0.304379
$795$	10.6922	0.379213
$796$	35.5748	1.26092
$797$	39.2117	1.38895	0.694475	−	0.719516i	$-0.255637\pi$
$797$	39.2117	1.38895	0.694475	+	0.719516i	$0.255637\pi$
$798$	12.7262	0.450502
$799$	12.1863	0.431122
$800$	0.0835062	0.00295239
$801$	−3.21724	−0.113676
$802$	8.38644	0.296136
$803$	61.4916	2.16999
$804$	31.6638	1.11670
$805$	−9.51568	−0.335384
$806$	37.2358	1.31157
$807$	−11.6149	−0.408862
$808$	−19.1798	−0.674744
$809$	−20.7726	−0.730324	−0.365162	−	0.930944i	$-0.618986\pi$
$809$	−20.7726	−0.730324	−0.365162	+	0.930944i	$0.618986\pi$
$810$	−8.33775	−0.292959
$811$	31.7937	1.11643	0.558214	−	0.829697i	$-0.311487\pi$
$811$	31.7937	1.11643	0.558214	+	0.829697i	$0.311487\pi$
$812$	6.88295	0.241544
$813$	−10.5516	−0.370060
$814$	101.075	3.54267
$815$	3.94829	0.138302
$816$	−3.23619	−0.113289
$817$	−17.1684	−0.600647
$818$	−71.5908	−2.50311
$819$	−17.9490	−0.627188
$820$	49.4147	1.72563
$821$	−49.4095	−1.72440	−0.862201	−	0.506566i	$-0.830914\pi$
$821$	−49.4095	−1.72440	−0.862201	+	0.506566i	$0.830914\pi$
$822$	8.09295	0.282274
$823$	23.2382	0.810032	0.405016	−	0.914310i	$-0.367266\pi$
$823$	23.2382	0.810032	0.405016	+	0.914310i	$0.367266\pi$
$824$	14.1173	0.491800
$825$	4.25216	0.148041
$826$	20.0774	0.698582
$827$	−26.1648	−0.909840	−0.454920	−	0.890532i	$-0.650332\pi$
$827$	−26.1648	−0.909840	−0.454920	+	0.890532i	$0.650332\pi$
$828$	41.8154	1.45319
$829$	−49.3257	−1.71315	−0.856577	−	0.516020i	$-0.827413\pi$
$829$	−49.3257	−1.71315	−0.856577	+	0.516020i	$0.827413\pi$
$830$	2.82426	0.0980315
$831$	−9.17832	−0.318392
$832$	−29.5323	−1.02385
$833$	2.52732	0.0875665
$834$	−9.66928	−0.334820
$835$	−3.93151	−0.136055
$836$	−62.1224	−2.14855
$837$	18.2243	0.629924
$838$	33.3260	1.15123
$839$	27.9872	0.966226	0.483113	−	0.875558i	$-0.339506\pi$
$839$	27.9872	0.966226	0.483113	+	0.875558i	$0.339506\pi$
$840$	−8.44870	−0.291508
$841$	−28.3352	−0.977074
$842$	43.0670	1.48419
$843$	25.5826	0.881111
$844$	104.919	3.61147
$845$	0.286581	0.00985869
$846$	−69.4526	−2.38783
$847$	33.6691	1.15689
$848$	51.5183	1.76914
$849$	−1.84693	−0.0633865
$850$	2.44774	0.0839569
$851$	35.8091	1.22752
$852$	−3.27115	−0.112068
$853$	48.5907	1.66371	0.831857	−	0.554989i	$-0.187278\pi$
$853$	48.5907	1.66371	0.831857	+	0.554989i	$0.187278\pi$
$854$	−10.7635	−0.368318
$855$	6.98437	0.238861
$856$	55.7628	1.90593
$857$	−23.0462	−0.787242	−0.393621	−	0.919273i	$-0.628778\pi$
$857$	−23.0462	−0.787242	−0.393621	+	0.919273i	$0.628778\pi$
$858$	−37.9386	−1.29520
$859$	7.25688	0.247601	0.123801	−	0.992307i	$-0.460492\pi$
$859$	7.25688	0.247601	0.123801	+	0.992307i	$0.460492\pi$
$860$	22.8446	0.778994
$861$	21.4575	0.731269
$862$	−28.7541	−0.979367
$863$	42.3457	1.44146	0.720732	−	0.693214i	$-0.243806\pi$
$863$	42.3457	1.44146	0.720732	+	0.693214i	$0.243806\pi$
$864$	−0.364655	−0.0124058
$865$	−3.45287	−0.117401
$866$	33.9769	1.15458
$867$	0.819540	0.0278330
$868$	−35.2292	−1.19576
$869$	62.0711	2.10562
$870$	−1.63567	−0.0554544
$871$	35.2833	1.19553
$872$	−69.7459	−2.36190
$873$	−41.1676	−1.39331
$874$	−33.0370	−1.11749
$875$	2.11487	0.0714957
$876$	38.7684	1.30986
$877$	−6.88159	−0.232375	−0.116187	−	0.993227i	$-0.537067\pi$
$877$	−6.88159	−0.232375	−0.116187	+	0.993227i	$0.537067\pi$
$878$	−64.5845	−2.17962
$879$	−17.2308	−0.581179
$880$	20.4882	0.690656
$881$	21.0993	0.710852	0.355426	−	0.934704i	$-0.384336\pi$
$881$	21.0993	0.710852	0.355426	+	0.934704i	$0.384336\pi$
$882$	−14.4038	−0.485000
$883$	15.1061	0.508362	0.254181	−	0.967157i	$-0.418194\pi$
$883$	15.1061	0.508362	0.254181	+	0.967157i	$0.418194\pi$
$884$	−14.5492	−0.489341
$885$	−3.17854	−0.106845
$886$	20.8857	0.701668
$887$	−17.0668	−0.573047	−0.286523	−	0.958073i	$-0.592500\pi$
$887$	−17.0668	−0.573047	−0.286523	+	0.958073i	$0.592500\pi$
$888$	31.7939	1.06693
$889$	13.0021	0.436077
$890$	−3.38221	−0.113372
$891$	17.6735	0.592083
$892$	−19.2105	−0.643214
$893$	36.5554	1.22328
$894$	−28.9013	−0.966603
$895$	−19.8659	−0.664044
$896$	41.5880	1.38936
$897$	−13.4410	−0.448783
$898$	−17.1872	−0.573546
$899$	−3.40289	−0.113493
$900$	−9.29352	−0.309784
$901$	−13.0466	−0.434645
$902$	−157.228	−5.23512
$903$	9.91987	0.330113
$904$	85.1402	2.83172
$905$	20.4961	0.681313
$906$	−22.8706	−0.759823
$907$	35.7139	1.18586	0.592930	−	0.805254i	$-0.297971\pi$
$907$	35.7139	1.18586	0.592930	+	0.805254i	$0.297971\pi$
$908$	−36.0028	−1.19479
$909$	−9.16131	−0.303862
$910$	−18.8693	−0.625512
$911$	58.3142	1.93203	0.966017	−	0.258477i	$-0.0832206\pi$
$911$	58.3142	1.93203	0.966017	+	0.258477i	$0.0832206\pi$
$912$	−9.70762	−0.321451
$913$	−5.98656	−0.198126
$914$	32.5365	1.07621
$915$	1.70401	0.0563328
$916$	4.95169	0.163608
$917$	9.77097	0.322666
$918$	−10.6888	−0.352783
$919$	50.0206	1.65003	0.825014	−	0.565112i	$-0.191167\pi$
$919$	50.0206	1.65003	0.825014	+	0.565112i	$0.191167\pi$
$920$	21.9327	0.723100
$921$	−7.14504	−0.235437
$922$	34.5273	1.13710
$923$	−3.64508	−0.119979
$924$	35.8942	1.18083
$925$	−7.95861	−0.261677
$926$	−21.3266	−0.700835
$927$	6.74318	0.221475
$928$	0.0680892	0.00223514
$929$	53.3154	1.74922	0.874610	−	0.484827i	$-0.161117\pi$
$929$	53.3154	1.74922	0.874610	+	0.484827i	$0.161117\pi$
$930$	8.37190	0.274525
$931$	7.58122	0.248464
$932$	−93.6085	−3.06625
$933$	−22.3604	−0.732048
$934$	21.3924	0.699981
$935$	−5.18847	−0.169681
$936$	41.3706	1.35224
$937$	29.4987	0.963682	0.481841	−	0.876259i	$-0.339968\pi$
$937$	29.4987	0.963682	0.481841	+	0.876259i	$0.339968\pi$
$938$	−50.1086	−1.63610
$939$	−12.6332	−0.412268
$940$	−48.6412	−1.58650
$941$	−22.6320	−0.737781	−0.368890	−	0.929473i	$-0.620262\pi$
$941$	−22.6320	−0.737781	−0.368890	+	0.929473i	$0.620262\pi$
$942$	−38.6871	−1.26050
$943$	−55.7033	−1.81395
$944$	−15.3152	−0.498466
$945$	−9.23522	−0.300422
$946$	−72.6871	−2.36326
$947$	41.6269	1.35269	0.676347	−	0.736583i	$-0.263562\pi$
$947$	41.6269	1.35269	0.676347	+	0.736583i	$0.263562\pi$
$948$	39.1338	1.27101
$949$	43.2000	1.40233
$950$	7.34251	0.238222
$951$	−26.2252	−0.850412
$952$	10.3091	0.334119
$953$	−23.2945	−0.754583	−0.377291	−	0.926095i	$-0.623144\pi$
$953$	−23.2945	−0.754583	−0.377291	+	0.926095i	$0.623144\pi$
$954$	74.3554	2.40734
$955$	16.7381	0.541631
$956$	32.5301	1.05210
$957$	3.46712	0.112076
$958$	−24.4256	−0.789155
$959$	−8.53207	−0.275515
$960$	−6.63990	−0.214302
$961$	−13.5829	−0.438158
$962$	71.0084	2.28940
$963$	26.6353	0.858311
$964$	−37.5977	−1.21094
$965$	19.4519	0.626177
$966$	19.0887	0.614168
$967$	−56.0715	−1.80314	−0.901569	−	0.432636i	$-0.857584\pi$
$967$	−56.0715	−1.80314	−0.901569	+	0.432636i	$0.857584\pi$
$968$	−77.6040	−2.49429
$969$	2.45838	0.0789745
$970$	−43.2786	−1.38959
$971$	−32.7476	−1.05092	−0.525460	−	0.850818i	$-0.676107\pi$
$971$	−32.7476	−1.05092	−0.525460	+	0.850818i	$0.676107\pi$
$972$	63.4321	2.03459
$973$	10.1939	0.326802
$974$	−39.7736	−1.27443
$975$	2.98729	0.0956697
$976$	8.21043	0.262809
$977$	−2.24442	−0.0718052	−0.0359026	−	0.999355i	$-0.511431\pi$
$977$	−2.24442	−0.0718052	−0.0359026	+	0.999355i	$0.511431\pi$
$978$	−7.92036	−0.253265
$979$	7.16925	0.229130
$980$	−10.0877	−0.322239
$981$	−33.3144	−1.06365
$982$	−43.9471	−1.40241
$983$	−22.3128	−0.711668	−0.355834	−	0.934549i	$-0.615803\pi$
$983$	−22.3128	−0.711668	−0.355834	+	0.934549i	$0.615803\pi$
$984$	−49.4574	−1.57664
$985$	11.9387	0.380400
$986$	1.99584	0.0635605
$987$	−21.1216	−0.672308
$988$	−43.6431	−1.38847
$989$	−25.7518	−0.818861
$990$	29.5702	0.939802
$991$	4.46451	0.141820	0.0709099	−	0.997483i	$-0.477410\pi$
$991$	4.46451	0.141820	0.0709099	+	0.997483i	$0.477410\pi$
$992$	−0.348503	−0.0110650
$993$	−17.7036	−0.561807
$994$	5.17666	0.164194
$995$	8.91274	0.282553
$996$	−3.77433	−0.119594
$997$	21.9309	0.694560	0.347280	−	0.937762i	$-0.387105\pi$
$997$	21.9309	0.694560	0.347280	+	0.937762i	$0.387105\pi$
$998$	67.1811	2.12658
$999$	34.7536	1.09956

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.h.1.7	✓	59

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.h.1.7	✓	59	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.44774 q^{2} +0.819540 q^{3} +3.99145 q^{4} +1.00000 q^{5} -2.00602 q^{6} +2.11487 q^{7} -4.87457 q^{8} -2.32835 q^{9} +O(q^{10})\)	\(q-2.44774 q^{2} +0.819540 q^{3} +3.99145 q^{4} +1.00000 q^{5} -2.00602 q^{6} +2.11487 q^{7} -4.87457 q^{8} -2.32835 q^{9} -2.44774 q^{10} +5.18847 q^{11} +3.27115 q^{12} +3.64508 q^{13} -5.17666 q^{14} +0.819540 q^{15} +3.94879 q^{16} -1.00000 q^{17} +5.69922 q^{18} -2.99970 q^{19} +3.99145 q^{20} +1.73322 q^{21} -12.7000 q^{22} -4.49942 q^{23} -3.99490 q^{24} +1.00000 q^{25} -8.92222 q^{26} -4.36680 q^{27} +8.44141 q^{28} +0.815379 q^{29} -2.00602 q^{30} -4.17338 q^{31} +0.0835062 q^{32} +4.25216 q^{33} +2.44774 q^{34} +2.11487 q^{35} -9.29352 q^{36} -7.95861 q^{37} +7.34251 q^{38} +2.98729 q^{39} -4.87457 q^{40} +12.3801 q^{41} -4.24248 q^{42} +5.72338 q^{43} +20.7095 q^{44} -2.32835 q^{45} +11.0134 q^{46} -12.1863 q^{47} +3.23619 q^{48} -2.52732 q^{49} -2.44774 q^{50} -0.819540 q^{51} +14.5492 q^{52} +13.0466 q^{53} +10.6888 q^{54} +5.18847 q^{55} -10.3091 q^{56} -2.45838 q^{57} -1.99584 q^{58} -3.87844 q^{59} +3.27115 q^{60} +2.07923 q^{61} +10.2154 q^{62} -4.92417 q^{63} -8.10198 q^{64} +3.64508 q^{65} -10.4082 q^{66} +9.67971 q^{67} -3.99145 q^{68} -3.68745 q^{69} -5.17666 q^{70} -1.00000 q^{71} +11.3497 q^{72} +11.8516 q^{73} +19.4806 q^{74} +0.819540 q^{75} -11.9732 q^{76} +10.9729 q^{77} -7.31211 q^{78} +11.9633 q^{79} +3.94879 q^{80} +3.40630 q^{81} -30.3034 q^{82} -1.15382 q^{83} +6.91807 q^{84} -1.00000 q^{85} -14.0094 q^{86} +0.668236 q^{87} -25.2915 q^{88} +1.38177 q^{89} +5.69922 q^{90} +7.70887 q^{91} -17.9592 q^{92} -3.42025 q^{93} +29.8290 q^{94} -2.99970 q^{95} +0.0684366 q^{96} +17.6810 q^{97} +6.18624 q^{98} -12.0806 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9} + 2 q^{10} + 6 q^{11} + 16 q^{12} + 25 q^{13} + 8 q^{14} + 6 q^{15} + 114 q^{16} - 59 q^{17} + 3 q^{18} + 35 q^{19} + 76 q^{20} + 41 q^{21} + 13 q^{22} - 2 q^{23} + 35 q^{24} + 59 q^{25} + 10 q^{26} + 27 q^{27} + 28 q^{28} + 10 q^{29} + 14 q^{30} + 15 q^{31} + 19 q^{32} - 3 q^{33} - 2 q^{34} + 9 q^{35} + 160 q^{36} + 56 q^{37} + 17 q^{38} + 25 q^{39} + 6 q^{40} + 47 q^{41} + 46 q^{42} + 27 q^{43} + 39 q^{44} + 97 q^{45} + 4 q^{46} - 8 q^{47} + 58 q^{48} + 174 q^{49} + 2 q^{50} - 6 q^{51} + 13 q^{52} + 17 q^{53} + 48 q^{54} + 6 q^{55} + 33 q^{56} + 6 q^{57} + 32 q^{58} + 30 q^{59} + 16 q^{60} + 85 q^{61} - 3 q^{62} + 14 q^{63} + 168 q^{64} + 25 q^{65} + 87 q^{66} + 21 q^{67} - 76 q^{68} + 111 q^{69} + 8 q^{70} - 59 q^{71} - 52 q^{72} + 41 q^{73} + 11 q^{74} + 6 q^{75} + 118 q^{76} + 55 q^{77} - 54 q^{78} + 43 q^{79} + 114 q^{80} + 207 q^{81} + 45 q^{82} + 10 q^{83} + 62 q^{84} - 59 q^{85} + 19 q^{86} + 8 q^{87} + 35 q^{88} + 86 q^{89} + 3 q^{90} + 47 q^{91} - 98 q^{92} + 41 q^{93} + 30 q^{94} + 35 q^{95} + 69 q^{96} + 72 q^{97} + 14 q^{98} + 25 q^{99}+O(q^{100}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9 + 2 * q^10 + 6 * q^11 + 16 * q^12 + 25 * q^13 + 8 * q^14 + 6 * q^15 + 114 * q^16 - 59 * q^17 + 3 * q^18 + 35 * q^19 + 76 * q^20 + 41 * q^21 + 13 * q^22 - 2 * q^23 + 35 * q^24 + 59 * q^25 + 10 * q^26 + 27 * q^27 + 28 * q^28 + 10 * q^29 + 14 * q^30 + 15 * q^31 + 19 * q^32 - 3 * q^33 - 2 * q^34 + 9 * q^35 + 160 * q^36 + 56 * q^37 + 17 * q^38 + 25 * q^39 + 6 * q^40 + 47 * q^41 + 46 * q^42 + 27 * q^43 + 39 * q^44 + 97 * q^45 + 4 * q^46 - 8 * q^47 + 58 * q^48 + 174 * q^49 + 2 * q^50 - 6 * q^51 + 13 * q^52 + 17 * q^53 + 48 * q^54 + 6 * q^55 + 33 * q^56 + 6 * q^57 + 32 * q^58 + 30 * q^59 + 16 * q^60 + 85 * q^61 - 3 * q^62 + 14 * q^63 + 168 * q^64 + 25 * q^65 + 87 * q^66 + 21 * q^67 - 76 * q^68 + 111 * q^69 + 8 * q^70 - 59 * q^71 - 52 * q^72 + 41 * q^73 + 11 * q^74 + 6 * q^75 + 118 * q^76 + 55 * q^77 - 54 * q^78 + 43 * q^79 + 114 * q^80 + 207 * q^81 + 45 * q^82 + 10 * q^83 + 62 * q^84 - 59 * q^85 + 19 * q^86 + 8 * q^87 + 35 * q^88 + 86 * q^89 + 3 * q^90 + 47 * q^91 - 98 * q^92 + 41 * q^93 + 30 * q^94 + 35 * q^95 + 69 * q^96 + 72 * q^97 + 14 * q^98 + 25 * q^99

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