LMFDB - Embedded newform 6035.2.a.h.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.75521 q^{2} -3.32287 q^{3} +5.59117 q^{4} +1.00000 q^{5} +9.15519 q^{6} +0.0853844 q^{7} -9.89442 q^{8} +8.04146 q^{9} +O(q^{10})$	\(q-2.75521 q^{2} -3.32287 q^{3} +5.59117 q^{4} +1.00000 q^{5} +9.15519 q^{6} +0.0853844 q^{7} -9.89442 q^{8} +8.04146 q^{9} -2.75521 q^{10} +3.94909 q^{11} -18.5787 q^{12} +2.97854 q^{13} -0.235252 q^{14} -3.32287 q^{15} +16.0788 q^{16} -1.00000 q^{17} -22.1559 q^{18} -3.38818 q^{19} +5.59117 q^{20} -0.283721 q^{21} -10.8806 q^{22} -9.31811 q^{23} +32.8779 q^{24} +1.00000 q^{25} -8.20650 q^{26} -16.7521 q^{27} +0.477399 q^{28} -1.19804 q^{29} +9.15519 q^{30} -3.78504 q^{31} -24.5117 q^{32} -13.1223 q^{33} +2.75521 q^{34} +0.0853844 q^{35} +44.9611 q^{36} +6.69515 q^{37} +9.33513 q^{38} -9.89731 q^{39} -9.89442 q^{40} -10.9963 q^{41} +0.781711 q^{42} +5.90342 q^{43} +22.0800 q^{44} +8.04146 q^{45} +25.6733 q^{46} +5.78097 q^{47} -53.4279 q^{48} -6.99271 q^{49} -2.75521 q^{50} +3.32287 q^{51} +16.6535 q^{52} -5.91100 q^{53} +46.1555 q^{54} +3.94909 q^{55} -0.844830 q^{56} +11.2585 q^{57} +3.30086 q^{58} -10.4892 q^{59} -18.5787 q^{60} -7.71059 q^{61} +10.4286 q^{62} +0.686615 q^{63} +35.3772 q^{64} +2.97854 q^{65} +36.1547 q^{66} -13.4422 q^{67} -5.59117 q^{68} +30.9629 q^{69} -0.235252 q^{70} -1.00000 q^{71} -79.5655 q^{72} +6.17698 q^{73} -18.4465 q^{74} -3.32287 q^{75} -18.9439 q^{76} +0.337191 q^{77} +27.2691 q^{78} +2.51863 q^{79} +16.0788 q^{80} +31.5406 q^{81} +30.2971 q^{82} +5.19752 q^{83} -1.58633 q^{84} -1.00000 q^{85} -16.2652 q^{86} +3.98094 q^{87} -39.0739 q^{88} +15.9243 q^{89} -22.1559 q^{90} +0.254321 q^{91} -52.0991 q^{92} +12.5772 q^{93} -15.9278 q^{94} -3.38818 q^{95} +81.4492 q^{96} +5.85378 q^{97} +19.2664 q^{98} +31.7564 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.75521	−1.94823	−0.974113	−	0.226061i	$-0.927415\pi$
$2$	−2.75521	−1.94823	−0.974113	+	0.226061i	$0.927415\pi$
$3$	−3.32287	−1.91846	−0.959230	−	0.282628i	$-0.908794\pi$
$3$	−3.32287	−1.91846	−0.959230	+	0.282628i	$0.908794\pi$
$4$	5.59117	2.79559
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	9.15519	3.73759
$7$	0.0853844	0.0322723	0.0161361	−	0.999870i	$-0.494863\pi$
$7$	0.0853844	0.0322723	0.0161361	+	0.999870i	$0.494863\pi$
$8$	−9.89442	−3.49821
$9$	8.04146	2.68049
$10$	−2.75521	−0.871273
$11$	3.94909	1.19069	0.595347	−	0.803468i	$-0.297014\pi$
$11$	3.94909	1.19069	0.595347	+	0.803468i	$0.297014\pi$
$12$	−18.5787	−5.36322
$13$	2.97854	0.826099	0.413050	−	0.910709i	$-0.364464\pi$
$13$	2.97854	0.826099	0.413050	+	0.910709i	$0.364464\pi$
$14$	−0.235252	−0.0628737
$15$	−3.32287	−0.857961
$16$	16.0788	4.01971
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−22.1559	−5.22219
$19$	−3.38818	−0.777301	−0.388650	−	0.921385i	$-0.627059\pi$
$19$	−3.38818	−0.777301	−0.388650	+	0.921385i	$0.627059\pi$
$20$	5.59117	1.25022
$21$	−0.283721	−0.0619131
$22$	−10.8806	−2.31974
$23$	−9.31811	−1.94296	−0.971480	−	0.237122i	$-0.923796\pi$
$23$	−9.31811	−1.94296	−0.971480	+	0.237122i	$0.923796\pi$
$24$	32.8779	6.71116
$25$	1.00000	0.200000
$26$	−8.20650	−1.60943
$27$	−16.7521	−3.22394
$28$	0.477399	0.0902199
$29$	−1.19804	−0.222471	−0.111236	−	0.993794i	$-0.535481\pi$
$29$	−1.19804	−0.222471	−0.111236	+	0.993794i	$0.535481\pi$
$30$	9.15519	1.67150
$31$	−3.78504	−0.679814	−0.339907	−	0.940459i	$-0.610396\pi$
$31$	−3.78504	−0.679814	−0.339907	+	0.940459i	$0.610396\pi$
$32$	−24.5117	−4.33310
$33$	−13.1223	−2.28430
$34$	2.75521	0.472514
$35$	0.0853844	0.0144326
$36$	44.9611	7.49352
$37$	6.69515	1.10068	0.550338	−	0.834942i	$-0.314499\pi$
$37$	6.69515	1.10068	0.550338	+	0.834942i	$0.314499\pi$
$38$	9.33513	1.51436
$39$	−9.89731	−1.58484
$40$	−9.89442	−1.56445
$41$	−10.9963	−1.71734	−0.858668	−	0.512533i	$-0.828707\pi$
$41$	−10.9963	−1.71734	−0.858668	+	0.512533i	$0.828707\pi$
$42$	0.781711	0.120621
$43$	5.90342	0.900263	0.450132	−	0.892962i	$-0.351377\pi$
$43$	5.90342	0.900263	0.450132	+	0.892962i	$0.351377\pi$
$44$	22.0800	3.32869
$45$	8.04146	1.19875
$46$	25.6733	3.78533
$47$	5.78097	0.843241	0.421620	−	0.906772i	$-0.361461\pi$
$47$	5.78097	0.843241	0.421620	+	0.906772i	$0.361461\pi$
$48$	−53.4279	−7.71165
$49$	−6.99271	−0.998958
$50$	−2.75521	−0.389645
$51$	3.32287	0.465295
$52$	16.6535	2.30943
$53$	−5.91100	−0.811939	−0.405969	−	0.913887i	$-0.633066\pi$
$53$	−5.91100	−0.811939	−0.405969	+	0.913887i	$0.633066\pi$
$54$	46.1555	6.28097
$55$	3.94909	0.532495
$56$	−0.844830	−0.112895
$57$	11.2585	1.49122
$58$	3.30086	0.433424
$59$	−10.4892	−1.36558	−0.682792	−	0.730613i	$-0.739234\pi$
$59$	−10.4892	−1.36558	−0.682792	+	0.730613i	$0.739234\pi$
$60$	−18.5787	−2.39850
$61$	−7.71059	−0.987240	−0.493620	−	0.869678i	$-0.664327\pi$
$61$	−7.71059	−0.987240	−0.493620	+	0.869678i	$0.664327\pi$
$62$	10.4286	1.32443
$63$	0.686615	0.0865054
$64$	35.3772	4.42215
$65$	2.97854	0.369443
$66$	36.1547	4.45033
$67$	−13.4422	−1.64223	−0.821114	−	0.570764i	$-0.806647\pi$
$67$	−13.4422	−1.64223	−0.821114	+	0.570764i	$0.806647\pi$
$68$	−5.59117	−0.678029
$69$	30.9629	3.72749
$70$	−0.235252	−0.0281180
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−79.5655	−9.37689
$73$	6.17698	0.722961	0.361480	−	0.932380i	$-0.382271\pi$
$73$	6.17698	0.722961	0.361480	+	0.932380i	$0.382271\pi$
$74$	−18.4465	−2.14436
$75$	−3.32287	−0.383692
$76$	−18.9439	−2.17301
$77$	0.337191	0.0384264
$78$	27.2691	3.08762
$79$	2.51863	0.283368	0.141684	−	0.989912i	$-0.454748\pi$
$79$	2.51863	0.283368	0.141684	+	0.989912i	$0.454748\pi$
$80$	16.0788	1.79767
$81$	31.5406	3.50452
$82$	30.2971	3.34576
$83$	5.19752	0.570502	0.285251	−	0.958453i	$-0.407923\pi$
$83$	5.19752	0.570502	0.285251	+	0.958453i	$0.407923\pi$
$84$	−1.58633	−0.173083
$85$	−1.00000	−0.108465
$86$	−16.2652	−1.75392
$87$	3.98094	0.426802
$88$	−39.0739	−4.16530
$89$	15.9243	1.68797	0.843987	−	0.536364i	$-0.180202\pi$
$89$	15.9243	1.68797	0.843987	+	0.536364i	$0.180202\pi$
$90$	−22.1559	−2.33544
$91$	0.254321	0.0266601
$92$	−52.0991	−5.43171
$93$	12.5772	1.30420
$94$	−15.9278	−1.64282
$95$	−3.38818	−0.347620
$96$	81.4492	8.31287
$97$	5.85378	0.594362	0.297181	−	0.954821i	$-0.403954\pi$
$97$	5.85378	0.594362	0.297181	+	0.954821i	$0.403954\pi$
$98$	19.2664	1.94620
$99$	31.7564	3.19164
$100$	5.59117	0.559117
$101$	1.79093	0.178204	0.0891020	−	0.996023i	$-0.471600\pi$
$101$	1.79093	0.178204	0.0891020	+	0.996023i	$0.471600\pi$
$102$	−9.15519	−0.906499
$103$	12.2245	1.20451	0.602257	−	0.798302i	$-0.294268\pi$
$103$	12.2245	1.20451	0.602257	+	0.798302i	$0.294268\pi$
$104$	−29.4710	−2.88986
$105$	−0.283721	−0.0276884
$106$	16.2860	1.58184
$107$	−10.6974	−1.03416	−0.517080	−	0.855937i	$-0.672981\pi$
$107$	−10.6974	−1.03416	−0.517080	+	0.855937i	$0.672981\pi$
$108$	−93.6638	−9.01281
$109$	3.84222	0.368018	0.184009	−	0.982925i	$-0.441093\pi$
$109$	3.84222	0.368018	0.184009	+	0.982925i	$0.441093\pi$
$110$	−10.8806	−1.03742
$111$	−22.2471	−2.11160
$112$	1.37288	0.129725
$113$	12.6667	1.19158	0.595792	−	0.803139i	$-0.296838\pi$
$113$	12.6667	1.19158	0.595792	+	0.803139i	$0.296838\pi$
$114$	−31.0194	−2.90523
$115$	−9.31811	−0.868918
$116$	−6.69846	−0.621937
$117$	23.9518	2.21435
$118$	28.9001	2.66047
$119$	−0.0853844	−0.00782718
$120$	32.8779	3.00132
$121$	4.59530	0.417754
$122$	21.2443	1.92337
$123$	36.5393	3.29464
$124$	−21.1628	−1.90048
$125$	1.00000	0.0894427
$126$	−1.89177	−0.168532
$127$	11.4997	1.02044	0.510218	−	0.860045i	$-0.329565\pi$
$127$	11.4997	1.02044	0.510218	+	0.860045i	$0.329565\pi$
$128$	−48.4481	−4.28224
$129$	−19.6163	−1.72712
$130$	−8.20650	−0.719758
$131$	3.64394	0.318372	0.159186	−	0.987249i	$-0.449113\pi$
$131$	3.64394	0.318372	0.159186	+	0.987249i	$0.449113\pi$
$132$	−73.3690	−6.38595
$133$	−0.289298	−0.0250853
$134$	37.0361	3.19943
$135$	−16.7521	−1.44179
$136$	9.89442	0.848440
$137$	10.5549	0.901763	0.450881	−	0.892584i	$-0.351110\pi$
$137$	10.5549	0.901763	0.450881	+	0.892584i	$0.351110\pi$
$138$	−85.3091	−7.26199
$139$	−2.57107	−0.218075	−0.109038	−	0.994038i	$-0.534777\pi$
$139$	−2.57107	−0.218075	−0.109038	+	0.994038i	$0.534777\pi$
$140$	0.477399	0.0403476
$141$	−19.2094	−1.61772
$142$	2.75521	0.231212
$143$	11.7625	0.983632
$144$	129.297	10.7748
$145$	−1.19804	−0.0994921
$146$	−17.0189	−1.40849
$147$	23.2359	1.91646
$148$	37.4337	3.07703
$149$	−6.22655	−0.510099	−0.255049	−	0.966928i	$-0.582092\pi$
$149$	−6.22655	−0.510099	−0.255049	+	0.966928i	$0.582092\pi$
$150$	9.15519	0.747518
$151$	−9.67017	−0.786947	−0.393473	−	0.919336i	$-0.628727\pi$
$151$	−9.67017	−0.786947	−0.393473	+	0.919336i	$0.628727\pi$
$152$	33.5240	2.71916
$153$	−8.04146	−0.650113
$154$	−0.929030	−0.0748634
$155$	−3.78504	−0.304022
$156$	−55.3375	−4.43055
$157$	18.3630	1.46553	0.732764	−	0.680483i	$-0.238230\pi$
$157$	18.3630	1.46553	0.732764	+	0.680483i	$0.238230\pi$
$158$	−6.93934	−0.552064
$159$	19.6415	1.55767
$160$	−24.5117	−1.93782
$161$	−0.795621	−0.0627038
$162$	−86.9010	−6.82759
$163$	−15.4750	−1.21209	−0.606046	−	0.795430i	$-0.707245\pi$
$163$	−15.4750	−1.21209	−0.606046	+	0.795430i	$0.707245\pi$
$164$	−61.4823	−4.80096
$165$	−13.1223	−1.02157
$166$	−14.3203	−1.11147
$167$	−3.35431	−0.259564	−0.129782	−	0.991543i	$-0.541428\pi$
$167$	−3.35431	−0.259564	−0.129782	+	0.991543i	$0.541428\pi$
$168$	2.80726	0.216585
$169$	−4.12828	−0.317560
$170$	2.75521	0.211315
$171$	−27.2459	−2.08354
$172$	33.0070	2.51676
$173$	4.79067	0.364228	0.182114	−	0.983277i	$-0.441706\pi$
$173$	4.79067	0.364228	0.182114	+	0.983277i	$0.441706\pi$
$174$	−10.9683	−0.831506
$175$	0.0853844	0.00645446
$176$	63.4968	4.78625
$177$	34.8544	2.61982
$178$	−43.8748	−3.28856
$179$	20.0170	1.49614	0.748070	−	0.663620i	$-0.230981\pi$
$179$	20.0170	1.49614	0.748070	+	0.663620i	$0.230981\pi$
$180$	44.9611	3.35121
$181$	8.33915	0.619844	0.309922	−	0.950762i	$-0.399697\pi$
$181$	8.33915	0.619844	0.309922	+	0.950762i	$0.399697\pi$
$182$	−0.700708	−0.0519399
$183$	25.6213	1.89398
$184$	92.1973	6.79687
$185$	6.69515	0.492237
$186$	−34.6528	−2.54087
$187$	−3.94909	−0.288786
$188$	32.3224	2.35735
$189$	−1.43037	−0.104044
$190$	9.33513	0.677242
$191$	7.47330	0.540749	0.270375	−	0.962755i	$-0.412852\pi$
$191$	7.47330	0.540749	0.270375	+	0.962755i	$0.412852\pi$
$192$	−117.554	−8.48371
$193$	−11.0760	−0.797267	−0.398633	−	0.917110i	$-0.630515\pi$
$193$	−11.0760	−0.797267	−0.398633	+	0.917110i	$0.630515\pi$
$194$	−16.1284	−1.15795
$195$	−9.89731	−0.708761
$196$	−39.0974	−2.79267
$197$	10.0958	0.719298	0.359649	−	0.933088i	$-0.382896\pi$
$197$	10.0958	0.719298	0.359649	+	0.933088i	$0.382896\pi$
$198$	−87.4955	−6.21804
$199$	11.4560	0.812091	0.406046	−	0.913853i	$-0.366907\pi$
$199$	11.4560	0.812091	0.406046	+	0.913853i	$0.366907\pi$
$200$	−9.89442	−0.699641
$201$	44.6667	3.15055
$202$	−4.93438	−0.347182
$203$	−0.102294	−0.00717965
$204$	18.5787	1.30077
$205$	−10.9963	−0.768016
$206$	−33.6810	−2.34667
$207$	−74.9312	−5.20808
$208$	47.8915	3.32068
$209$	−13.3802	−0.925528
$210$	0.781711	0.0539432
$211$	−19.4735	−1.34061	−0.670304	−	0.742087i	$-0.733836\pi$
$211$	−19.4735	−1.34061	−0.670304	+	0.742087i	$0.733836\pi$
$212$	−33.0494	−2.26984
$213$	3.32287	0.227679
$214$	29.4736	2.01478
$215$	5.90342	0.402610
$216$	165.752	11.2780
$217$	−0.323184	−0.0219392
$218$	−10.5861	−0.716981
$219$	−20.5253	−1.38697
$220$	22.0800	1.48863
$221$	−2.97854	−0.200358
$222$	61.2954	4.11388
$223$	−19.6009	−1.31257	−0.656285	−	0.754513i	$-0.727873\pi$
$223$	−19.6009	−1.31257	−0.656285	+	0.754513i	$0.727873\pi$
$224$	−2.09292	−0.139839
$225$	8.04146	0.536097
$226$	−34.8994	−2.32148
$227$	−18.9527	−1.25793	−0.628967	−	0.777432i	$-0.716522\pi$
$227$	−18.9527	−1.25793	−0.628967	+	0.777432i	$0.716522\pi$
$228$	62.9480	4.16883
$229$	2.65960	0.175751	0.0878757	−	0.996131i	$-0.471992\pi$
$229$	2.65960	0.175751	0.0878757	+	0.996131i	$0.471992\pi$
$230$	25.6733	1.69285
$231$	−1.12044	−0.0737196
$232$	11.8539	0.778249
$233$	−24.5747	−1.60994	−0.804972	−	0.593313i	$-0.797820\pi$
$233$	−24.5747	−1.60994	−0.804972	+	0.593313i	$0.797820\pi$
$234$	−65.9922	−4.31405
$235$	5.78097	0.377109
$236$	−58.6472	−3.81761
$237$	−8.36907	−0.543629
$238$	0.235252	0.0152491
$239$	−3.60958	−0.233484	−0.116742	−	0.993162i	$-0.537245\pi$
$239$	−3.60958	−0.233484	−0.116742	+	0.993162i	$0.537245\pi$
$240$	−53.4279	−3.44876
$241$	29.6753	1.91156	0.955778	−	0.294089i	$-0.0950162\pi$
$241$	29.6753	1.91156	0.955778	+	0.294089i	$0.0950162\pi$
$242$	−12.6610	−0.813880
$243$	−54.5491	−3.49933
$244$	−43.1112	−2.75991
$245$	−6.99271	−0.446748
$246$	−100.673	−6.41870
$247$	−10.0918	−0.642128
$248$	37.4508	2.37813
$249$	−17.2707	−1.09449
$250$	−2.75521	−0.174255
$251$	1.15782	0.0730809	0.0365404	−	0.999332i	$-0.488366\pi$
$251$	1.15782	0.0730809	0.0365404	+	0.999332i	$0.488366\pi$
$252$	3.83898	0.241833
$253$	−36.7980	−2.31347
$254$	−31.6841	−1.98804
$255$	3.32287	0.208086
$256$	62.7301	3.92063
$257$	4.05842	0.253157	0.126579	−	0.991957i	$-0.459600\pi$
$257$	4.05842	0.253157	0.126579	+	0.991957i	$0.459600\pi$
$258$	54.0470	3.36482
$259$	0.571661	0.0355213
$260$	16.6535	1.03281
$261$	−9.63401	−0.596330
$262$	−10.0398	−0.620261
$263$	0.320763	0.0197791	0.00988955	−	0.999951i	$-0.496852\pi$
$263$	0.320763	0.0197791	0.00988955	+	0.999951i	$0.496852\pi$
$264$	129.838	7.99095
$265$	−5.91100	−0.363110
$266$	0.797075	0.0488718
$267$	−52.9144	−3.23831
$268$	−75.1577	−4.59099
$269$	1.83673	0.111987	0.0559937	−	0.998431i	$-0.482167\pi$
$269$	1.83673	0.111987	0.0559937	+	0.998431i	$0.482167\pi$
$270$	46.1555	2.80893
$271$	29.2285	1.77550	0.887752	−	0.460322i	$-0.152266\pi$
$271$	29.2285	1.77550	0.887752	+	0.460322i	$0.152266\pi$
$272$	−16.0788	−0.974923
$273$	−0.845076	−0.0511463
$274$	−29.0808	−1.75684
$275$	3.94909	0.238139
$276$	173.119	10.4205
$277$	6.30963	0.379109	0.189554	−	0.981870i	$-0.439296\pi$
$277$	6.30963	0.379109	0.189554	+	0.981870i	$0.439296\pi$
$278$	7.08383	0.424860
$279$	−30.4373	−1.82223
$280$	−0.844830	−0.0504882
$281$	−15.2303	−0.908565	−0.454283	−	0.890858i	$-0.650104\pi$
$281$	−15.2303	−0.908565	−0.454283	+	0.890858i	$0.650104\pi$
$282$	52.9259	3.15169
$283$	31.0837	1.84773	0.923867	−	0.382713i	$-0.125010\pi$
$283$	31.0837	1.84773	0.923867	+	0.382713i	$0.125010\pi$
$284$	−5.59117	−0.331775
$285$	11.2585	0.666894
$286$	−32.4082	−1.91634
$287$	−0.938914	−0.0554223
$288$	−197.110	−11.6148
$289$	1.00000	0.0588235
$290$	3.30086	0.193833
$291$	−19.4514	−1.14026
$292$	34.5365	2.02110
$293$	−7.80305	−0.455859	−0.227929	−	0.973678i	$-0.573196\pi$
$293$	−7.80305	−0.455859	−0.227929	+	0.973678i	$0.573196\pi$
$294$	−64.0196	−3.73370
$295$	−10.4892	−0.610708
$296$	−66.2446	−3.85039
$297$	−66.1555	−3.83873
$298$	17.1554	0.993787
$299$	−27.7544	−1.60508
$300$	−18.5787	−1.07264
$301$	0.504060	0.0290536
$302$	26.6433	1.53315
$303$	−5.95102	−0.341877
$304$	−54.4780	−3.12453
$305$	−7.71059	−0.441507
$306$	22.1559	1.26657
$307$	28.2074	1.60988	0.804941	−	0.593355i	$-0.202197\pi$
$307$	28.2074	1.60988	0.804941	+	0.593355i	$0.202197\pi$
$308$	1.88529	0.107424
$309$	−40.6204	−2.31081
$310$	10.4286	0.592304
$311$	−22.4497	−1.27301	−0.636503	−	0.771274i	$-0.719620\pi$
$311$	−22.4497	−1.27301	−0.636503	+	0.771274i	$0.719620\pi$
$312$	97.9281	5.54409
$313$	14.3995	0.813908	0.406954	−	0.913449i	$-0.366591\pi$
$313$	14.3995	0.813908	0.406954	+	0.913449i	$0.366591\pi$
$314$	−50.5939	−2.85518
$315$	0.686615	0.0386864
$316$	14.0821	0.792179
$317$	−10.1232	−0.568577	−0.284289	−	0.958739i	$-0.591757\pi$
$317$	−10.1232	−0.568577	−0.284289	+	0.958739i	$0.591757\pi$
$318$	−54.1164	−3.03470
$319$	−4.73118	−0.264895
$320$	35.3772	1.97764
$321$	35.5461	1.98399
$322$	2.19210	0.122161
$323$	3.38818	0.188523
$324$	176.349	9.79717
$325$	2.97854	0.165220
$326$	42.6367	2.36143
$327$	−12.7672	−0.706027
$328$	108.802	6.00759
$329$	0.493605	0.0272133
$330$	36.1547	1.99025
$331$	30.5191	1.67748	0.838739	−	0.544533i	$-0.183293\pi$
$331$	30.5191	1.67748	0.838739	+	0.544533i	$0.183293\pi$
$332$	29.0602	1.59489
$333$	53.8387	2.95034
$334$	9.24181	0.505689
$335$	−13.4422	−0.734427
$336$	−4.56191	−0.248873
$337$	−8.46649	−0.461199	−0.230600	−	0.973049i	$-0.574069\pi$
$337$	−8.46649	−0.461199	−0.230600	+	0.973049i	$0.574069\pi$
$338$	11.3743	0.618679
$339$	−42.0898	−2.28601
$340$	−5.59117	−0.303224
$341$	−14.9475	−0.809451
$342$	75.0680	4.05921
$343$	−1.19476	−0.0645110
$344$	−58.4109	−3.14931
$345$	30.9629	1.66698
$346$	−13.1993	−0.709598
$347$	2.08787	0.112083	0.0560415	−	0.998428i	$-0.482152\pi$
$347$	2.08787	0.112083	0.0560415	+	0.998428i	$0.482152\pi$
$348$	22.2581	1.19316
$349$	24.7772	1.32629	0.663145	−	0.748491i	$-0.269221\pi$
$349$	24.7772	1.32629	0.663145	+	0.748491i	$0.269221\pi$
$350$	−0.235252	−0.0125747
$351$	−49.8968	−2.66330
$352$	−96.7989	−5.15940
$353$	−5.74074	−0.305549	−0.152774	−	0.988261i	$-0.548821\pi$
$353$	−5.74074	−0.305549	−0.152774	+	0.988261i	$0.548821\pi$
$354$	−96.0311	−5.10400
$355$	−1.00000	−0.0530745
$356$	89.0356	4.71887
$357$	0.283721	0.0150161
$358$	−55.1509	−2.91482
$359$	11.2576	0.594152	0.297076	−	0.954854i	$-0.403989\pi$
$359$	11.2576	0.594152	0.297076	+	0.954854i	$0.403989\pi$
$360$	−79.5655	−4.19347
$361$	−7.52026	−0.395803
$362$	−22.9761	−1.20760
$363$	−15.2696	−0.801445
$364$	1.42195	0.0745306
$365$	6.17698	0.323318
$366$	−70.5920	−3.68990
$367$	30.8864	1.61225	0.806127	−	0.591742i	$-0.201560\pi$
$367$	30.8864	1.61225	0.806127	+	0.591742i	$0.201560\pi$
$368$	−149.824	−7.81014
$369$	−88.4264	−4.60329
$370$	−18.4465	−0.958989
$371$	−0.504708	−0.0262031
$372$	70.3213	3.64599
$373$	−16.7951	−0.869618	−0.434809	−	0.900523i	$-0.643184\pi$
$373$	−16.7951	−0.869618	−0.434809	+	0.900523i	$0.643184\pi$
$374$	10.8806	0.562620
$375$	−3.32287	−0.171592
$376$	−57.1993	−2.94983
$377$	−3.56842	−0.183783
$378$	3.94096	0.202701
$379$	34.7794	1.78650	0.893248	−	0.449564i	$-0.148421\pi$
$379$	34.7794	1.78650	0.893248	+	0.449564i	$0.148421\pi$
$380$	−18.9439	−0.971800
$381$	−38.2121	−1.95766
$382$	−20.5905	−1.05350
$383$	−9.71731	−0.496531	−0.248266	−	0.968692i	$-0.579861\pi$
$383$	−9.71731	−0.496531	−0.248266	+	0.968692i	$0.579861\pi$
$384$	160.987	8.21531
$385$	0.337191	0.0171848
$386$	30.5166	1.55326
$387$	47.4721	2.41314
$388$	32.7295	1.66159
$389$	−13.0108	−0.659676	−0.329838	−	0.944038i	$-0.606994\pi$
$389$	−13.0108	−0.659676	−0.329838	+	0.944038i	$0.606994\pi$
$390$	27.2691	1.38083
$391$	9.31811	0.471237
$392$	69.1888	3.49456
$393$	−12.1083	−0.610784
$394$	−27.8161	−1.40136
$395$	2.51863	0.126726
$396$	177.556	8.92250
$397$	24.2561	1.21738	0.608690	−	0.793408i	$-0.291695\pi$
$397$	24.2561	1.21738	0.608690	+	0.793408i	$0.291695\pi$
$398$	−31.5635	−1.58214
$399$	0.961298	0.0481251
$400$	16.0788	0.803942
$401$	−2.87624	−0.143633	−0.0718164	−	0.997418i	$-0.522880\pi$
$401$	−2.87624	−0.143633	−0.0718164	+	0.997418i	$0.522880\pi$
$402$	−123.066	−6.13798
$403$	−11.2739	−0.561594
$404$	10.0134	0.498184
$405$	31.5406	1.56727
$406$	0.281842	0.0139876
$407$	26.4397	1.31057
$408$	−32.8779	−1.62770
$409$	35.1719	1.73914	0.869568	−	0.493813i	$-0.164397\pi$
$409$	35.1719	1.73914	0.869568	+	0.493813i	$0.164397\pi$
$410$	30.2971	1.49627
$411$	−35.0724	−1.72999
$412$	68.3492	3.36732
$413$	−0.895619	−0.0440705
$414$	206.451	10.1465
$415$	5.19752	0.255136
$416$	−73.0092	−3.57957
$417$	8.54333	0.418369
$418$	36.8653	1.80314
$419$	−15.6115	−0.762672	−0.381336	−	0.924437i	$-0.624536\pi$
$419$	−15.6115	−0.762672	−0.381336	+	0.924437i	$0.624536\pi$
$420$	−1.58633	−0.0774052
$421$	−10.2144	−0.497819	−0.248910	−	0.968527i	$-0.580072\pi$
$421$	−10.2144	−0.497819	−0.248910	+	0.968527i	$0.580072\pi$
$422$	53.6534	2.61181
$423$	46.4874	2.26029
$424$	58.4859	2.84033
$425$	−1.00000	−0.0485071
$426$	−9.15519	−0.443571
$427$	−0.658365	−0.0318605
$428$	−59.8111	−2.89108
$429$	−39.0853	−1.88706
$430$	−16.2652	−0.784375
$431$	−13.2167	−0.636624	−0.318312	−	0.947986i	$-0.603116\pi$
$431$	−13.2167	−0.636624	−0.318312	+	0.947986i	$0.603116\pi$
$432$	−269.354	−12.9593
$433$	13.9293	0.669401	0.334700	−	0.942325i	$-0.391365\pi$
$433$	13.9293	0.669401	0.334700	+	0.942325i	$0.391365\pi$
$434$	0.890439	0.0427424
$435$	3.98094	0.190871
$436$	21.4825	1.02882
$437$	31.5714	1.51026
$438$	56.5514	2.70213
$439$	11.6678	0.556876	0.278438	−	0.960454i	$-0.410183\pi$
$439$	11.6678	0.556876	0.278438	+	0.960454i	$0.410183\pi$
$440$	−39.0739	−1.86278
$441$	−56.2316	−2.67769
$442$	8.20650	0.390344
$443$	18.5942	0.883439	0.441719	−	0.897153i	$-0.354369\pi$
$443$	18.5942	0.883439	0.441719	+	0.897153i	$0.354369\pi$
$444$	−124.387	−5.90316
$445$	15.9243	0.754885
$446$	54.0044	2.55718
$447$	20.6900	0.978603
$448$	3.02066	0.142713
$449$	19.9058	0.939413	0.469706	−	0.882823i	$-0.344360\pi$
$449$	19.9058	0.939413	0.469706	+	0.882823i	$0.344360\pi$
$450$	−22.1559	−1.04444
$451$	−43.4254	−2.04482
$452$	70.8217	3.33117
$453$	32.1327	1.50973
$454$	52.2186	2.45074
$455$	0.254321	0.0119228
$456$	−111.396	−5.21659
$457$	24.2811	1.13582	0.567912	−	0.823089i	$-0.307751\pi$
$457$	24.2811	1.13582	0.567912	+	0.823089i	$0.307751\pi$
$458$	−7.32775	−0.342403
$459$	16.7521	0.781921
$460$	−52.0991	−2.42913
$461$	−5.27515	−0.245688	−0.122844	−	0.992426i	$-0.539201\pi$
$461$	−5.27515	−0.245688	−0.122844	+	0.992426i	$0.539201\pi$
$462$	3.08705	0.143622
$463$	−41.7298	−1.93935	−0.969675	−	0.244397i	$-0.921410\pi$
$463$	−41.7298	−1.93935	−0.969675	+	0.244397i	$0.921410\pi$
$464$	−19.2631	−0.894269
$465$	12.5772	0.583254
$466$	67.7085	3.13654
$467$	−18.7537	−0.867818	−0.433909	−	0.900957i	$-0.642866\pi$
$467$	−18.7537	−0.867818	−0.433909	+	0.900957i	$0.642866\pi$
$468$	133.919	6.19039
$469$	−1.14776	−0.0529985
$470$	−15.9278	−0.734693
$471$	−61.0179	−2.81156
$472$	103.785	4.77709
$473$	23.3131	1.07194
$474$	23.0585	1.05911
$475$	−3.38818	−0.155460
$476$	−0.477399	−0.0218815
$477$	−47.5331	−2.17639
$478$	9.94513	0.454880
$479$	17.0792	0.780367	0.390184	−	0.920737i	$-0.372412\pi$
$479$	17.0792	0.780367	0.390184	+	0.920737i	$0.372412\pi$
$480$	81.4492	3.71763
$481$	19.9418	0.909267
$482$	−81.7617	−3.72414
$483$	2.64375	0.120295
$484$	25.6931	1.16787
$485$	5.85378	0.265807
$486$	150.294	6.81748
$487$	−12.2443	−0.554843	−0.277421	−	0.960748i	$-0.589480\pi$
$487$	−12.2443	−0.554843	−0.277421	+	0.960748i	$0.589480\pi$
$488$	76.2918	3.45357
$489$	51.4212	2.32535
$490$	19.2664	0.870366
$491$	27.8808	1.25824	0.629122	−	0.777307i	$-0.283415\pi$
$491$	27.8808	1.25824	0.629122	+	0.777307i	$0.283415\pi$
$492$	204.297	9.21044
$493$	1.19804	0.0539571
$494$	27.8051	1.25101
$495$	31.7564	1.42734
$496$	−60.8591	−2.73266
$497$	−0.0853844	−0.00383002
$498$	47.5843	2.13230
$499$	−4.33344	−0.193991	−0.0969957	−	0.995285i	$-0.530923\pi$
$499$	−4.33344	−0.193991	−0.0969957	+	0.995285i	$0.530923\pi$
$500$	5.59117	0.250045
$501$	11.1459	0.497963
$502$	−3.19003	−0.142378
$503$	−2.45910	−0.109646	−0.0548229	−	0.998496i	$-0.517459\pi$
$503$	−2.45910	−0.109646	−0.0548229	+	0.998496i	$0.517459\pi$
$504$	−6.79366	−0.302614
$505$	1.79093	0.0796952
$506$	101.386	4.50717
$507$	13.7177	0.609226
$508$	64.2969	2.85271
$509$	33.0106	1.46317	0.731585	−	0.681750i	$-0.238781\pi$
$509$	33.0106	1.46317	0.731585	+	0.681750i	$0.238781\pi$
$510$	−9.15519	−0.405399
$511$	0.527418	0.0233316
$512$	−75.9383	−3.35603
$513$	56.7591	2.50597
$514$	−11.1818	−0.493208
$515$	12.2245	0.538675
$516$	−109.678	−4.82831
$517$	22.8296	1.00404
$518$	−1.57505	−0.0692035
$519$	−15.9188	−0.698756
$520$	−29.4710	−1.29239
$521$	37.9216	1.66138	0.830688	−	0.556738i	$-0.187947\pi$
$521$	37.9216	1.66138	0.830688	+	0.556738i	$0.187947\pi$
$522$	26.5437	1.16179
$523$	−1.85070	−0.0809253	−0.0404626	−	0.999181i	$-0.512883\pi$
$523$	−1.85070	−0.0809253	−0.0404626	+	0.999181i	$0.512883\pi$
$524$	20.3739	0.890037
$525$	−0.283721	−0.0123826
$526$	−0.883769	−0.0385342
$527$	3.78504	0.164879
$528$	−210.991	−9.18222
$529$	63.8271	2.77509
$530$	16.2860	0.707420
$531$	−84.3488	−3.66043
$532$	−1.61751	−0.0701280
$533$	−32.7530	−1.41869
$534$	145.790	6.30896
$535$	−10.6974	−0.462490
$536$	133.003	5.74485
$537$	−66.5138	−2.87028
$538$	−5.06057	−0.218177
$539$	−27.6148	−1.18945
$540$	−93.6638	−4.03065
$541$	−32.7483	−1.40796	−0.703981	−	0.710219i	$-0.748596\pi$
$541$	−32.7483	−1.40796	−0.703981	+	0.710219i	$0.748596\pi$
$542$	−80.5306	−3.45908
$543$	−27.7099	−1.18915
$544$	24.5117	1.05093
$545$	3.84222	0.164582
$546$	2.32836	0.0996446
$547$	−26.0598	−1.11424	−0.557118	−	0.830434i	$-0.688093\pi$
$547$	−26.0598	−1.11424	−0.557118	+	0.830434i	$0.688093\pi$
$548$	59.0140	2.52095
$549$	−62.0044	−2.64628
$550$	−10.8806	−0.463949
$551$	4.05918	0.172927
$552$	−306.359	−13.0395
$553$	0.215052	0.00914492
$554$	−17.3843	−0.738590
$555$	−22.2471	−0.944337
$556$	−14.3753	−0.609648
$557$	36.4395	1.54399	0.771996	−	0.635627i	$-0.219258\pi$
$557$	36.4395	1.54399	0.771996	+	0.635627i	$0.219258\pi$
$558$	83.8610	3.55012
$559$	17.5836	0.743707
$560$	1.37288	0.0580149
$561$	13.1223	0.554024
$562$	41.9627	1.77009
$563$	14.8021	0.623832	0.311916	−	0.950110i	$-0.399029\pi$
$563$	14.8021	0.623832	0.311916	+	0.950110i	$0.399029\pi$
$564$	−107.403	−4.52248
$565$	12.6667	0.532893
$566$	−85.6421	−3.59980
$567$	2.69308	0.113099
$568$	9.89442	0.415161
$569$	−25.3167	−1.06133	−0.530666	−	0.847581i	$-0.678058\pi$
$569$	−25.3167	−1.06133	−0.530666	+	0.847581i	$0.678058\pi$
$570$	−31.0194	−1.29926
$571$	29.5904	1.23832	0.619160	−	0.785265i	$-0.287473\pi$
$571$	29.5904	1.23832	0.619160	+	0.785265i	$0.287473\pi$
$572$	65.7663	2.74983
$573$	−24.8328	−1.03741
$574$	2.58690	0.107975
$575$	−9.31811	−0.388592
$576$	284.484	11.8535
$577$	−30.3767	−1.26460	−0.632299	−	0.774724i	$-0.717889\pi$
$577$	−30.3767	−1.26460	−0.632299	+	0.774724i	$0.717889\pi$
$578$	−2.75521	−0.114602
$579$	36.8040	1.52952
$580$	−6.69846	−0.278139
$581$	0.443788	0.0184114
$582$	53.5925	2.22148
$583$	−23.3431	−0.966771
$584$	−61.1176	−2.52907
$585$	23.9518	0.990286
$586$	21.4990	0.888116
$587$	5.09482	0.210286	0.105143	−	0.994457i	$-0.466470\pi$
$587$	5.09482	0.210286	0.105143	+	0.994457i	$0.466470\pi$
$588$	129.916	5.35763
$589$	12.8244	0.528420
$590$	28.9001	1.18980
$591$	−33.5471	−1.37994
$592$	107.650	4.42440
$593$	29.1118	1.19548	0.597738	−	0.801691i	$-0.296066\pi$
$593$	29.1118	1.19548	0.597738	+	0.801691i	$0.296066\pi$
$594$	182.272	7.47872
$595$	−0.0853844	−0.00350042
$596$	−34.8137	−1.42602
$597$	−38.0666	−1.55796
$598$	76.4691	3.12705
$599$	−35.6551	−1.45683	−0.728413	−	0.685138i	$-0.759742\pi$
$599$	−35.6551	−1.45683	−0.728413	+	0.685138i	$0.759742\pi$
$600$	32.8779	1.34223
$601$	21.5015	0.877067	0.438533	−	0.898715i	$-0.355498\pi$
$601$	21.5015	0.877067	0.438533	+	0.898715i	$0.355498\pi$
$602$	−1.38879	−0.0566029
$603$	−108.095	−4.40197
$604$	−54.0675	−2.19998
$605$	4.59530	0.186825
$606$	16.3963	0.666054
$607$	−26.1776	−1.06252	−0.531258	−	0.847210i	$-0.678280\pi$
$607$	−26.1776	−1.06252	−0.531258	+	0.847210i	$0.678280\pi$
$608$	83.0500	3.36812
$609$	0.339910	0.0137739
$610$	21.2443	0.860156
$611$	17.2189	0.696601
$612$	−44.9611	−1.81745
$613$	−7.66793	−0.309705	−0.154852	−	0.987938i	$-0.549490\pi$
$613$	−7.66793	−0.309705	−0.154852	+	0.987938i	$0.549490\pi$
$614$	−77.7173	−3.13641
$615$	36.5393	1.47341
$616$	−3.33631	−0.134424
$617$	−11.6035	−0.467139	−0.233570	−	0.972340i	$-0.575041\pi$
$617$	−11.6035	−0.467139	−0.233570	+	0.972340i	$0.575041\pi$
$618$	111.918	4.50198
$619$	5.16025	0.207408	0.103704	−	0.994608i	$-0.466931\pi$
$619$	5.16025	0.207408	0.103704	+	0.994608i	$0.466931\pi$
$620$	−21.1628	−0.849920
$621$	156.098	6.26399
$622$	61.8536	2.48010
$623$	1.35969	0.0544748
$624$	−159.137	−6.37059
$625$	1.00000	0.0400000
$626$	−39.6736	−1.58568
$627$	44.4607	1.77559
$628$	102.671	4.09701
$629$	−6.69515	−0.266953
$630$	−1.89177	−0.0753698
$631$	16.1613	0.643373	0.321686	−	0.946846i	$-0.395750\pi$
$631$	16.1613	0.643373	0.321686	+	0.946846i	$0.395750\pi$
$632$	−24.9204	−0.991279
$633$	64.7077	2.57190
$634$	27.8916	1.10772
$635$	11.4997	0.456352
$636$	109.819	4.35460
$637$	−20.8281	−0.825239
$638$	13.0354	0.516076
$639$	−8.04146	−0.318115
$640$	−48.4481	−1.91508
$641$	43.7985	1.72994	0.864968	−	0.501826i	$-0.167338\pi$
$641$	43.7985	1.72994	0.864968	+	0.501826i	$0.167338\pi$
$642$	−97.9370	−3.86526
$643$	13.0890	0.516178	0.258089	−	0.966121i	$-0.416907\pi$
$643$	13.0890	0.516178	0.258089	+	0.966121i	$0.416907\pi$
$644$	−4.44846	−0.175294
$645$	−19.6163	−0.772391
$646$	−9.33513	−0.367286
$647$	−14.8985	−0.585719	−0.292860	−	0.956155i	$-0.594607\pi$
$647$	−14.8985	−0.585719	−0.292860	+	0.956155i	$0.594607\pi$
$648$	−312.076	−12.2595
$649$	−41.4230	−1.62599
$650$	−8.20650	−0.321886
$651$	1.07390	0.0420894
$652$	−86.5231	−3.38851
$653$	32.3179	1.26470	0.632349	−	0.774684i	$-0.282091\pi$
$653$	32.3179	1.26470	0.632349	+	0.774684i	$0.282091\pi$
$654$	35.1762	1.37550
$655$	3.64394	0.142380
$656$	−176.808	−6.90319
$657$	49.6719	1.93789
$658$	−1.35998	−0.0530177
$659$	−6.45366	−0.251399	−0.125699	−	0.992068i	$-0.540117\pi$
$659$	−6.45366	−0.251399	−0.125699	+	0.992068i	$0.540117\pi$
$660$	−73.3690	−2.85589
$661$	−43.0229	−1.67339	−0.836697	−	0.547665i	$-0.815517\pi$
$661$	−43.0229	−1.67339	−0.836697	+	0.547665i	$0.815517\pi$
$662$	−84.0863	−3.26811
$663$	9.89731	0.384380
$664$	−51.4265	−1.99573
$665$	−0.289298	−0.0112185
$666$	−148.337	−5.74794
$667$	11.1635	0.432252
$668$	−18.7545	−0.725633
$669$	65.1311	2.51811
$670$	37.0361	1.43083
$671$	−30.4498	−1.17550
$672$	6.95449	0.268275
$673$	32.9432	1.26987	0.634934	−	0.772566i	$-0.281027\pi$
$673$	32.9432	1.26987	0.634934	+	0.772566i	$0.281027\pi$
$674$	23.3269	0.898520
$675$	−16.7521	−0.644788
$676$	−23.0819	−0.887766
$677$	−32.2168	−1.23819	−0.619097	−	0.785315i	$-0.712501\pi$
$677$	−32.2168	−1.23819	−0.619097	+	0.785315i	$0.712501\pi$
$678$	115.966	4.45365
$679$	0.499822	0.0191814
$680$	9.89442	0.379434
$681$	62.9773	2.41330
$682$	41.1834	1.57699
$683$	−3.18788	−0.121981	−0.0609903	−	0.998138i	$-0.519426\pi$
$683$	−3.18788	−0.121981	−0.0609903	+	0.998138i	$0.519426\pi$
$684$	−152.336	−5.82472
$685$	10.5549	0.403281
$686$	3.29181	0.125682
$687$	−8.83751	−0.337172
$688$	94.9202	3.61880
$689$	−17.6062	−0.670742
$690$	−85.3091	−3.24766
$691$	4.21017	0.160162	0.0800812	−	0.996788i	$-0.474482\pi$
$691$	4.21017	0.160162	0.0800812	+	0.996788i	$0.474482\pi$
$692$	26.7854	1.01823
$693$	2.71150	0.103002
$694$	−5.75253	−0.218363
$695$	−2.57107	−0.0975262
$696$	−39.3891	−1.49304
$697$	10.9963	0.416515
$698$	−68.2662	−2.58391
$699$	81.6586	3.08861
$700$	0.477399	0.0180440
$701$	−2.34706	−0.0886471	−0.0443236	−	0.999017i	$-0.514113\pi$
$701$	−2.34706	−0.0886471	−0.0443236	+	0.999017i	$0.514113\pi$
$702$	137.476	5.18870
$703$	−22.6843	−0.855556
$704$	139.708	5.26543
$705$	−19.2094	−0.723468
$706$	15.8169	0.595278
$707$	0.152917	0.00575105
$708$	194.877	7.32392
$709$	41.3065	1.55130	0.775648	−	0.631165i	$-0.217423\pi$
$709$	41.3065	1.55130	0.775648	+	0.631165i	$0.217423\pi$
$710$	2.75521	0.103401
$711$	20.2534	0.759563
$712$	−157.562	−5.90488
$713$	35.2695	1.32085
$714$	−0.781711	−0.0292548
$715$	11.7625	0.439894
$716$	111.918	4.18258
$717$	11.9941	0.447930
$718$	−31.0170	−1.15754
$719$	38.5648	1.43823	0.719113	−	0.694893i	$-0.244548\pi$
$719$	38.5648	1.43823	0.719113	+	0.694893i	$0.244548\pi$
$720$	129.297	4.81863
$721$	1.04378	0.0388724
$722$	20.7199	0.771114
$723$	−98.6072	−3.66724
$724$	46.6256	1.73283
$725$	−1.19804	−0.0444942
$726$	42.0709	1.56140
$727$	3.80100	0.140971	0.0704856	−	0.997513i	$-0.477545\pi$
$727$	3.80100	0.140971	0.0704856	+	0.997513i	$0.477545\pi$
$728$	−2.51636	−0.0932625
$729$	86.6377	3.20880
$730$	−17.0189	−0.629896
$731$	−5.90342	−0.218346
$732$	143.253	5.29478
$733$	37.6022	1.38887	0.694435	−	0.719555i	$-0.255654\pi$
$733$	37.6022	1.38887	0.694435	+	0.719555i	$0.255654\pi$
$734$	−85.0983	−3.14104
$735$	23.2359	0.857067
$736$	228.403	8.41904
$737$	−53.0845	−1.95539
$738$	243.633	8.96825
$739$	22.7665	0.837479	0.418739	−	0.908107i	$-0.362472\pi$
$739$	22.7665	0.837479	0.418739	+	0.908107i	$0.362472\pi$
$740$	37.4337	1.37609
$741$	33.5338	1.23190
$742$	1.39057	0.0510496
$743$	−9.09312	−0.333594	−0.166797	−	0.985991i	$-0.553342\pi$
$743$	−9.09312	−0.333594	−0.166797	+	0.985991i	$0.553342\pi$
$744$	−124.444	−4.56234
$745$	−6.22655	−0.228123
$746$	46.2740	1.69421
$747$	41.7957	1.52922
$748$	−22.0800	−0.807326
$749$	−0.913394	−0.0333747
$750$	9.15519	0.334300
$751$	−35.2712	−1.28706	−0.643532	−	0.765419i	$-0.722532\pi$
$751$	−35.2712	−1.28706	−0.643532	+	0.765419i	$0.722532\pi$
$752$	92.9513	3.38958
$753$	−3.84728	−0.140203
$754$	9.83175	0.358051
$755$	−9.67017	−0.351933
$756$	−7.99743	−0.290864
$757$	38.6821	1.40592	0.702962	−	0.711227i	$-0.251860\pi$
$757$	38.6821	1.40592	0.702962	+	0.711227i	$0.251860\pi$
$758$	−95.8244	−3.48050
$759$	122.275	4.43830
$760$	33.5240	1.21604
$761$	9.41437	0.341271	0.170635	−	0.985334i	$-0.445418\pi$
$761$	9.41437	0.341271	0.170635	+	0.985334i	$0.445418\pi$
$762$	105.282	3.81397
$763$	0.328065	0.0118768
$764$	41.7845	1.51171
$765$	−8.04146	−0.290739
$766$	26.7732	0.967356
$767$	−31.2427	−1.12811
$768$	−208.444	−7.52157
$769$	6.95937	0.250961	0.125481	−	0.992096i	$-0.459953\pi$
$769$	6.95937	0.250961	0.125481	+	0.992096i	$0.459953\pi$
$770$	−0.929030	−0.0334799
$771$	−13.4856	−0.485672
$772$	−61.9277	−2.22883
$773$	−22.1713	−0.797445	−0.398723	−	0.917072i	$-0.630546\pi$
$773$	−22.1713	−0.797445	−0.398723	+	0.917072i	$0.630546\pi$
$774$	−130.796	−4.70135
$775$	−3.78504	−0.135963
$776$	−57.9198	−2.07920
$777$	−1.89956	−0.0681462
$778$	35.8476	1.28520
$779$	37.2574	1.33489
$780$	−55.3375	−1.98140
$781$	−3.94909	−0.141309
$782$	−25.6733	−0.918076
$783$	20.0697	0.717234
$784$	−112.435	−4.01552
$785$	18.3630	0.655404
$786$	33.3609	1.18995
$787$	1.18573	0.0422668	0.0211334	−	0.999777i	$-0.493273\pi$
$787$	1.18573	0.0422668	0.0211334	+	0.999777i	$0.493273\pi$
$788$	56.4475	2.01086
$789$	−1.06585	−0.0379454
$790$	−6.93934	−0.246891
$791$	1.08154	0.0384551
$792$	−314.211	−11.1650
$793$	−22.9663	−0.815558
$794$	−66.8306	−2.37173
$795$	19.6415	0.696612
$796$	64.0522	2.27027
$797$	35.2048	1.24702	0.623510	−	0.781816i	$-0.285706\pi$
$797$	35.2048	1.24702	0.623510	+	0.781816i	$0.285706\pi$
$798$	−2.64858	−0.0937585
$799$	−5.78097	−0.204516
$800$	−24.5117	−0.866620
$801$	128.055	4.52459
$802$	7.92465	0.279829
$803$	24.3934	0.860826
$804$	249.739	8.80762
$805$	−0.795621	−0.0280420
$806$	31.0620	1.09411
$807$	−6.10321	−0.214843
$808$	−17.7202	−0.623394
$809$	12.7284	0.447505	0.223752	−	0.974646i	$-0.428169\pi$
$809$	12.7284	0.447505	0.223752	+	0.974646i	$0.428169\pi$
$810$	−86.9010	−3.05339
$811$	24.9070	0.874602	0.437301	−	0.899315i	$-0.355934\pi$
$811$	24.9070	0.874602	0.437301	+	0.899315i	$0.355934\pi$
$812$	−0.571944	−0.0200713
$813$	−97.1224	−3.40623
$814$	−72.8469	−2.55328
$815$	−15.4750	−0.542064
$816$	53.4279	1.87035
$817$	−20.0018	−0.699776
$818$	−96.9058	−3.38823
$819$	2.04511	0.0714620
$820$	−61.4823	−2.14705
$821$	−17.3479	−0.605445	−0.302723	−	0.953079i	$-0.597896\pi$
$821$	−17.3479	−0.605445	−0.302723	+	0.953079i	$0.597896\pi$
$822$	96.6318	3.37042
$823$	−45.9201	−1.60067	−0.800337	−	0.599550i	$-0.795346\pi$
$823$	−45.9201	−1.60067	−0.800337	+	0.599550i	$0.795346\pi$
$824$	−120.954	−4.21364
$825$	−13.1223	−0.456860
$826$	2.46762	0.0858593
$827$	3.57807	0.124422	0.0622109	−	0.998063i	$-0.480185\pi$
$827$	3.57807	0.124422	0.0622109	+	0.998063i	$0.480185\pi$
$828$	−418.953	−14.5596
$829$	8.08269	0.280724	0.140362	−	0.990100i	$-0.455173\pi$
$829$	8.08269	0.280724	0.140362	+	0.990100i	$0.455173\pi$
$830$	−14.3203	−0.497063
$831$	−20.9661	−0.727305
$832$	105.372	3.65313
$833$	6.99271	0.242283
$834$	−23.5386	−0.815077
$835$	−3.35431	−0.116081
$836$	−74.8110	−2.58739
$837$	63.4074	2.19168
$838$	43.0129	1.48586
$839$	44.8904	1.54979	0.774895	−	0.632090i	$-0.217803\pi$
$839$	44.8904	1.54979	0.774895	+	0.632090i	$0.217803\pi$
$840$	2.80726	0.0968596
$841$	−27.5647	−0.950507
$842$	28.1428	0.969864
$843$	50.6084	1.74305
$844$	−108.879	−3.74778
$845$	−4.12828	−0.142017
$846$	−128.082	−4.40356
$847$	0.392367	0.0134819
$848$	−95.0421	−3.26376
$849$	−103.287	−3.54480
$850$	2.75521	0.0945028
$851$	−62.3861	−2.13857
$852$	18.5787	0.636497
$853$	16.5069	0.565185	0.282592	−	0.959240i	$-0.408806\pi$
$853$	16.5069	0.565185	0.282592	+	0.959240i	$0.408806\pi$
$854$	1.81393	0.0620715
$855$	−27.2459	−0.931789
$856$	105.845	3.61770
$857$	−51.4377	−1.75708	−0.878540	−	0.477670i	$-0.841482\pi$
$857$	−51.4377	−1.75708	−0.878540	+	0.477670i	$0.841482\pi$
$858$	107.688	3.67642
$859$	−1.93178	−0.0659116	−0.0329558	−	0.999457i	$-0.510492\pi$
$859$	−1.93178	−0.0659116	−0.0329558	+	0.999457i	$0.510492\pi$
$860$	33.0070	1.12553
$861$	3.11989	0.106325
$862$	36.4146	1.24029
$863$	47.3218	1.61085	0.805426	−	0.592696i	$-0.201937\pi$
$863$	47.3218	1.61085	0.805426	+	0.592696i	$0.201937\pi$
$864$	410.623	13.9697
$865$	4.79067	0.162888
$866$	−38.3782	−1.30414
$867$	−3.32287	−0.112851
$868$	−1.80698	−0.0613328
$869$	9.94628	0.337405
$870$	−10.9683	−0.371861
$871$	−40.0382	−1.35664
$872$	−38.0165	−1.28740
$873$	47.0729	1.59318
$874$	−86.9858	−2.94234
$875$	0.0853844	0.00288652
$876$	−114.760	−3.87739
$877$	−9.46866	−0.319734	−0.159867	−	0.987139i	$-0.551107\pi$
$877$	−9.46866	−0.319734	−0.159867	+	0.987139i	$0.551107\pi$
$878$	−32.1473	−1.08492
$879$	25.9285	0.874547
$880$	63.4968	2.14048
$881$	−3.45711	−0.116473	−0.0582365	−	0.998303i	$-0.518548\pi$
$881$	−3.45711	−0.116473	−0.0582365	+	0.998303i	$0.518548\pi$
$882$	154.930	5.21675
$883$	−23.0774	−0.776616	−0.388308	−	0.921530i	$-0.626940\pi$
$883$	−23.0774	−0.776616	−0.388308	+	0.921530i	$0.626940\pi$
$884$	−16.6535	−0.560119
$885$	34.8544	1.17162
$886$	−51.2310	−1.72114
$887$	−2.38203	−0.0799808	−0.0399904	−	0.999200i	$-0.512733\pi$
$887$	−2.38203	−0.0799808	−0.0399904	+	0.999200i	$0.512733\pi$
$888$	220.122	7.38681
$889$	0.981897	0.0329318
$890$	−43.8748	−1.47069
$891$	124.557	4.17281
$892$	−109.592	−3.66940
$893$	−19.5869	−0.655452
$894$	−57.0052	−1.90654
$895$	20.0170	0.669094
$896$	−4.13671	−0.138198
$897$	92.2242	3.07928
$898$	−54.8446	−1.83019
$899$	4.53465	0.151239
$900$	44.9611	1.49870
$901$	5.91100	0.196924
$902$	119.646	3.98378
$903$	−1.67493	−0.0557381
$904$	−125.330	−4.16841
$905$	8.33915	0.277203
$906$	−88.5322	−2.94129
$907$	−24.4192	−0.810827	−0.405413	−	0.914133i	$-0.632872\pi$
$907$	−24.4192	−0.810827	−0.405413	+	0.914133i	$0.632872\pi$
$908$	−105.968	−3.51666
$909$	14.4017	0.477673
$910$	−0.700708	−0.0232282
$911$	−33.3410	−1.10464	−0.552319	−	0.833633i	$-0.686257\pi$
$911$	−33.3410	−1.10464	−0.552319	+	0.833633i	$0.686257\pi$
$912$	181.023	5.99427
$913$	20.5255	0.679294
$914$	−66.8996	−2.21284
$915$	25.6213	0.847014
$916$	14.8703	0.491328
$917$	0.311135	0.0102746
$918$	−46.1555	−1.52336
$919$	−15.0741	−0.497248	−0.248624	−	0.968600i	$-0.579978\pi$
$919$	−15.0741	−0.497248	−0.248624	+	0.968600i	$0.579978\pi$
$920$	92.1973	3.03965
$921$	−93.7295	−3.08849
$922$	14.5341	0.478656
$923$	−2.97854	−0.0980399
$924$	−6.26457	−0.206089
$925$	6.69515	0.220135
$926$	114.974	3.77829
$927$	98.3027	3.22868
$928$	29.3661	0.963989
$929$	−36.1396	−1.18570	−0.592850	−	0.805313i	$-0.701997\pi$
$929$	−36.1396	−1.18570	−0.592850	+	0.805313i	$0.701997\pi$
$930$	−34.6528	−1.13631
$931$	23.6925	0.776491
$932$	−137.402	−4.50074
$933$	74.5975	2.44221
$934$	51.6703	1.69070
$935$	−3.94909	−0.129149
$936$	−236.989	−7.74624
$937$	−54.1919	−1.77037	−0.885186	−	0.465238i	$-0.845969\pi$
$937$	−54.1919	−1.77037	−0.885186	+	0.465238i	$0.845969\pi$
$938$	3.16231	0.103253
$939$	−47.8476	−1.56145
$940$	32.3224	1.05424
$941$	−54.5257	−1.77749	−0.888743	−	0.458405i	$-0.848421\pi$
$941$	−54.5257	−1.77749	−0.888743	+	0.458405i	$0.848421\pi$
$942$	168.117	5.47755
$943$	102.465	3.33671
$944$	−168.655	−5.48925
$945$	−1.43037	−0.0465299
$946$	−64.2325	−2.08838
$947$	−39.7872	−1.29291	−0.646456	−	0.762951i	$-0.723750\pi$
$947$	−39.7872	−1.29291	−0.646456	+	0.762951i	$0.723750\pi$
$948$	−46.7929	−1.51976
$949$	18.3984	0.597237
$950$	9.33513	0.302872
$951$	33.6382	1.09079
$952$	0.844830	0.0273811
$953$	54.7281	1.77282	0.886409	−	0.462903i	$-0.153192\pi$
$953$	54.7281	1.77282	0.886409	+	0.462903i	$0.153192\pi$
$954$	130.963	4.24010
$955$	7.47330	0.241830
$956$	−20.1818	−0.652725
$957$	15.7211	0.508190
$958$	−47.0567	−1.52033
$959$	0.901221	0.0291019
$960$	−117.554	−3.79403
$961$	−16.6734	−0.537853
$962$	−54.9438	−1.77146
$963$	−86.0229	−2.77205
$964$	165.920	5.34392
$965$	−11.0760	−0.356549
$966$	−7.28407	−0.234361
$967$	−27.4190	−0.881735	−0.440868	−	0.897572i	$-0.645329\pi$
$967$	−27.4190	−0.881735	−0.440868	+	0.897572i	$0.645329\pi$
$968$	−45.4678	−1.46139
$969$	−11.2585	−0.361674
$970$	−16.1284	−0.517851
$971$	43.0703	1.38219	0.691096	−	0.722763i	$-0.257128\pi$
$971$	43.0703	1.38219	0.691096	+	0.722763i	$0.257128\pi$
$972$	−304.994	−9.78267
$973$	−0.219529	−0.00703779
$974$	33.7356	1.08096
$975$	−9.89731	−0.316968
$976$	−123.977	−3.96842
$977$	−40.2942	−1.28912	−0.644562	−	0.764552i	$-0.722960\pi$
$977$	−40.2942	−1.28912	−0.644562	+	0.764552i	$0.722960\pi$
$978$	−141.676	−4.53030
$979$	62.8865	2.00986
$980$	−39.0974	−1.24892
$981$	30.8970	0.986466
$982$	−76.8174	−2.45134
$983$	42.7940	1.36492	0.682459	−	0.730924i	$-0.260911\pi$
$983$	42.7940	1.36492	0.682459	+	0.730924i	$0.260911\pi$
$984$	−361.535	−11.5253
$985$	10.0958	0.321680
$986$	−3.30086	−0.105121
$987$	−1.64018	−0.0522076
$988$	−56.4251	−1.79512
$989$	−55.0087	−1.74918
$990$	−87.4955	−2.78079
$991$	−17.3614	−0.551504	−0.275752	−	0.961229i	$-0.588927\pi$
$991$	−17.3614	−0.551504	−0.275752	+	0.961229i	$0.588927\pi$
$992$	92.7779	2.94570
$993$	−101.411	−3.21817
$994$	0.235252	0.00746174
$995$	11.4560	0.363178
$996$	−96.5633	−3.05973
$997$	−29.6623	−0.939414	−0.469707	−	0.882822i	$-0.655640\pi$
$997$	−29.6623	−0.939414	−0.469707	+	0.882822i	$0.655640\pi$
$998$	11.9395	0.377939
$999$	−112.158	−3.54851

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.h.1.2	✓	59

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.h.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-2.75521 q^{2} -3.32287 q^{3} +5.59117 q^{4} +1.00000 q^{5} +9.15519 q^{6} +0.0853844 q^{7} -9.89442 q^{8} +8.04146 q^{9} +O(q^{10})\)	\(q-2.75521 q^{2} -3.32287 q^{3} +5.59117 q^{4} +1.00000 q^{5} +9.15519 q^{6} +0.0853844 q^{7} -9.89442 q^{8} +8.04146 q^{9} -2.75521 q^{10} +3.94909 q^{11} -18.5787 q^{12} +2.97854 q^{13} -0.235252 q^{14} -3.32287 q^{15} +16.0788 q^{16} -1.00000 q^{17} -22.1559 q^{18} -3.38818 q^{19} +5.59117 q^{20} -0.283721 q^{21} -10.8806 q^{22} -9.31811 q^{23} +32.8779 q^{24} +1.00000 q^{25} -8.20650 q^{26} -16.7521 q^{27} +0.477399 q^{28} -1.19804 q^{29} +9.15519 q^{30} -3.78504 q^{31} -24.5117 q^{32} -13.1223 q^{33} +2.75521 q^{34} +0.0853844 q^{35} +44.9611 q^{36} +6.69515 q^{37} +9.33513 q^{38} -9.89731 q^{39} -9.89442 q^{40} -10.9963 q^{41} +0.781711 q^{42} +5.90342 q^{43} +22.0800 q^{44} +8.04146 q^{45} +25.6733 q^{46} +5.78097 q^{47} -53.4279 q^{48} -6.99271 q^{49} -2.75521 q^{50} +3.32287 q^{51} +16.6535 q^{52} -5.91100 q^{53} +46.1555 q^{54} +3.94909 q^{55} -0.844830 q^{56} +11.2585 q^{57} +3.30086 q^{58} -10.4892 q^{59} -18.5787 q^{60} -7.71059 q^{61} +10.4286 q^{62} +0.686615 q^{63} +35.3772 q^{64} +2.97854 q^{65} +36.1547 q^{66} -13.4422 q^{67} -5.59117 q^{68} +30.9629 q^{69} -0.235252 q^{70} -1.00000 q^{71} -79.5655 q^{72} +6.17698 q^{73} -18.4465 q^{74} -3.32287 q^{75} -18.9439 q^{76} +0.337191 q^{77} +27.2691 q^{78} +2.51863 q^{79} +16.0788 q^{80} +31.5406 q^{81} +30.2971 q^{82} +5.19752 q^{83} -1.58633 q^{84} -1.00000 q^{85} -16.2652 q^{86} +3.98094 q^{87} -39.0739 q^{88} +15.9243 q^{89} -22.1559 q^{90} +0.254321 q^{91} -52.0991 q^{92} +12.5772 q^{93} -15.9278 q^{94} -3.38818 q^{95} +81.4492 q^{96} +5.85378 q^{97} +19.2664 q^{98} +31.7564 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) \) 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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