LMFDB - Embedded newform 6013.2.a.c.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$1$
Dimension:	$104$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50501 q^{2} -2.73412 q^{3} +4.27508 q^{4} -0.209181 q^{5} +6.84900 q^{6} -1.00000 q^{7} -5.69911 q^{8} +4.47541 q^{9} +O(q^{10})$	\(q-2.50501 q^{2} -2.73412 q^{3} +4.27508 q^{4} -0.209181 q^{5} +6.84900 q^{6} -1.00000 q^{7} -5.69911 q^{8} +4.47541 q^{9} +0.524002 q^{10} +2.75328 q^{11} -11.6886 q^{12} -1.13411 q^{13} +2.50501 q^{14} +0.571927 q^{15} +5.72618 q^{16} -5.94385 q^{17} -11.2110 q^{18} +1.62878 q^{19} -0.894268 q^{20} +2.73412 q^{21} -6.89699 q^{22} -1.79994 q^{23} +15.5821 q^{24} -4.95624 q^{25} +2.84096 q^{26} -4.03395 q^{27} -4.27508 q^{28} +9.61462 q^{29} -1.43268 q^{30} +9.33189 q^{31} -2.94591 q^{32} -7.52779 q^{33} +14.8894 q^{34} +0.209181 q^{35} +19.1328 q^{36} -2.71377 q^{37} -4.08012 q^{38} +3.10079 q^{39} +1.19215 q^{40} -8.34647 q^{41} -6.84900 q^{42} +1.18372 q^{43} +11.7705 q^{44} -0.936173 q^{45} +4.50888 q^{46} +9.16255 q^{47} -15.6560 q^{48} +1.00000 q^{49} +12.4154 q^{50} +16.2512 q^{51} -4.84842 q^{52} -12.9342 q^{53} +10.1051 q^{54} -0.575934 q^{55} +5.69911 q^{56} -4.45329 q^{57} -24.0847 q^{58} -7.98266 q^{59} +2.44504 q^{60} -0.538901 q^{61} -23.3765 q^{62} -4.47541 q^{63} -4.07281 q^{64} +0.237235 q^{65} +18.8572 q^{66} +5.84932 q^{67} -25.4105 q^{68} +4.92126 q^{69} -0.524002 q^{70} -4.66367 q^{71} -25.5059 q^{72} +5.11185 q^{73} +6.79801 q^{74} +13.5510 q^{75} +6.96319 q^{76} -2.75328 q^{77} -7.76753 q^{78} -8.04099 q^{79} -1.19781 q^{80} -2.39693 q^{81} +20.9080 q^{82} -4.95381 q^{83} +11.6886 q^{84} +1.24334 q^{85} -2.96524 q^{86} -26.2875 q^{87} -15.6912 q^{88} +6.90714 q^{89} +2.34512 q^{90} +1.13411 q^{91} -7.69491 q^{92} -25.5145 q^{93} -22.9523 q^{94} -0.340711 q^{95} +8.05448 q^{96} +11.7487 q^{97} -2.50501 q^{98} +12.3220 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9}+O(q^{10}) $ 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9	\( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9} + 3 q^{10} - 54 q^{11} - 38 q^{12} + 7 q^{13} + 19 q^{14} - 33 q^{15} + 93 q^{16} - 7 q^{17} - 55 q^{18} - 12 q^{19} - 24 q^{20} + 26 q^{21} - 22 q^{22} - 69 q^{23} + 78 q^{25} - 11 q^{26} - 95 q^{27} - 99 q^{28} - 41 q^{29} - 26 q^{30} - 12 q^{31} - 127 q^{32} - 6 q^{33} - 17 q^{34} - 2 q^{35} + 71 q^{36} - 47 q^{37} - 32 q^{38} - 57 q^{39} + 6 q^{40} + 10 q^{41} - 2 q^{42} - 41 q^{43} - 120 q^{44} + 23 q^{45} - 31 q^{46} - 99 q^{47} - 84 q^{48} + 104 q^{49} - 104 q^{50} - 74 q^{51} + 14 q^{52} - 74 q^{53} + 19 q^{54} - 32 q^{55} + 54 q^{56} - 47 q^{57} - 36 q^{58} - 76 q^{59} - 99 q^{60} + 49 q^{61} - 55 q^{62} - 90 q^{63} + 86 q^{64} - 70 q^{65} + 61 q^{66} - 117 q^{67} - 30 q^{68} + 51 q^{69} - 3 q^{70} - 125 q^{71} - 147 q^{72} - 20 q^{73} - 75 q^{74} - 124 q^{75} + 4 q^{76} + 54 q^{77} - 70 q^{78} - 72 q^{79} - 69 q^{80} + 76 q^{81} - 37 q^{82} - 98 q^{83} + 38 q^{84} - 33 q^{85} - 64 q^{86} - 8 q^{87} - 62 q^{88} - 26 q^{89} + 11 q^{90} - 7 q^{91} - 162 q^{92} - 81 q^{93} + 31 q^{94} - 116 q^{95} + 20 q^{96} - 61 q^{97} - 19 q^{98} - 158 q^{99}+O(q^{100}) \) 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9 + 3 * q^10 - 54 * q^11 - 38 * q^12 + 7 * q^13 + 19 * q^14 - 33 * q^15 + 93 * q^16 - 7 * q^17 - 55 * q^18 - 12 * q^19 - 24 * q^20 + 26 * q^21 - 22 * q^22 - 69 * q^23 + 78 * q^25 - 11 * q^26 - 95 * q^27 - 99 * q^28 - 41 * q^29 - 26 * q^30 - 12 * q^31 - 127 * q^32 - 6 * q^33 - 17 * q^34 - 2 * q^35 + 71 * q^36 - 47 * q^37 - 32 * q^38 - 57 * q^39 + 6 * q^40 + 10 * q^41 - 2 * q^42 - 41 * q^43 - 120 * q^44 + 23 * q^45 - 31 * q^46 - 99 * q^47 - 84 * q^48 + 104 * q^49 - 104 * q^50 - 74 * q^51 + 14 * q^52 - 74 * q^53 + 19 * q^54 - 32 * q^55 + 54 * q^56 - 47 * q^57 - 36 * q^58 - 76 * q^59 - 99 * q^60 + 49 * q^61 - 55 * q^62 - 90 * q^63 + 86 * q^64 - 70 * q^65 + 61 * q^66 - 117 * q^67 - 30 * q^68 + 51 * q^69 - 3 * q^70 - 125 * q^71 - 147 * q^72 - 20 * q^73 - 75 * q^74 - 124 * q^75 + 4 * q^76 + 54 * q^77 - 70 * q^78 - 72 * q^79 - 69 * q^80 + 76 * q^81 - 37 * q^82 - 98 * q^83 + 38 * q^84 - 33 * q^85 - 64 * q^86 - 8 * q^87 - 62 * q^88 - 26 * q^89 + 11 * q^90 - 7 * q^91 - 162 * q^92 - 81 * q^93 + 31 * q^94 - 116 * q^95 + 20 * q^96 - 61 * q^97 - 19 * q^98 - 158 * 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 $

$2$	−2.50501	−1.77131	−0.885655	−	0.464343i	$-0.846290\pi$
$2$	−2.50501	−1.77131	−0.885655	+	0.464343i	$0.846290\pi$
$3$	−2.73412	−1.57854	−0.789272	−	0.614043i	$-0.789542\pi$
$3$	−2.73412	−1.57854	−0.789272	+	0.614043i	$0.789542\pi$
$4$	4.27508	2.13754
$5$	−0.209181	−0.0935488	−0.0467744	−	0.998905i	$-0.514894\pi$
$5$	−0.209181	−0.0935488	−0.0467744	+	0.998905i	$0.514894\pi$
$6$	6.84900	2.79609
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−5.69911	−2.01494
$9$	4.47541	1.49180
$10$	0.524002	0.165704
$11$	2.75328	0.830144	0.415072	−	0.909788i	$-0.363756\pi$
$11$	2.75328	0.830144	0.415072	+	0.909788i	$0.363756\pi$
$12$	−11.6886	−3.37421
$13$	−1.13411	−0.314546	−0.157273	−	0.987555i	$-0.550270\pi$
$13$	−1.13411	−0.314546	−0.157273	+	0.987555i	$0.550270\pi$
$14$	2.50501	0.669493
$15$	0.571927	0.147671
$16$	5.72618	1.43154
$17$	−5.94385	−1.44160	−0.720798	−	0.693145i	$-0.756224\pi$
$17$	−5.94385	−1.44160	−0.720798	+	0.693145i	$0.756224\pi$
$18$	−11.2110	−2.64245
$19$	1.62878	0.373669	0.186834	−	0.982391i	$-0.440177\pi$
$19$	1.62878	0.373669	0.186834	+	0.982391i	$0.440177\pi$
$20$	−0.894268	−0.199964
$21$	2.73412	0.596634
$22$	−6.89699	−1.47044
$23$	−1.79994	−0.375314	−0.187657	−	0.982235i	$-0.560089\pi$
$23$	−1.79994	−0.375314	−0.187657	+	0.982235i	$0.560089\pi$
$24$	15.5821	3.18067
$25$	−4.95624	−0.991249
$26$	2.84096	0.557158
$27$	−4.03395	−0.776334
$28$	−4.27508	−0.807915
$29$	9.61462	1.78539	0.892695	−	0.450661i	$-0.148812\pi$
$29$	9.61462	1.78539	0.892695	+	0.450661i	$0.148812\pi$
$30$	−1.43268	−0.261571
$31$	9.33189	1.67606	0.838029	−	0.545626i	$-0.183708\pi$
$31$	9.33189	1.67606	0.838029	+	0.545626i	$0.183708\pi$
$32$	−2.94591	−0.520769
$33$	−7.52779	−1.31042
$34$	14.8894	2.55351
$35$	0.209181	0.0353581
$36$	19.1328	3.18879
$37$	−2.71377	−0.446140	−0.223070	−	0.974802i	$-0.571608\pi$
$37$	−2.71377	−0.446140	−0.223070	+	0.974802i	$0.571608\pi$
$38$	−4.08012	−0.661883
$39$	3.10079	0.496525
$40$	1.19215	0.188495
$41$	−8.34647	−1.30350	−0.651750	−	0.758434i	$-0.725965\pi$
$41$	−8.34647	−1.30350	−0.651750	+	0.758434i	$0.725965\pi$
$42$	−6.84900	−1.05682
$43$	1.18372	0.180516	0.0902579	−	0.995918i	$-0.471231\pi$
$43$	1.18372	0.180516	0.0902579	+	0.995918i	$0.471231\pi$
$44$	11.7705	1.77447
$45$	−0.936173	−0.139556
$46$	4.50888	0.664798
$47$	9.16255	1.33649	0.668247	−	0.743939i	$-0.267045\pi$
$47$	9.16255	1.33649	0.668247	+	0.743939i	$0.267045\pi$
$48$	−15.6560	−2.25976
$49$	1.00000	0.142857
$50$	12.4154	1.75581
$51$	16.2512	2.27562
$52$	−4.84842	−0.672355
$53$	−12.9342	−1.77665	−0.888326	−	0.459213i	$-0.848132\pi$
$53$	−12.9342	−1.77665	−0.888326	+	0.459213i	$0.848132\pi$
$54$	10.1051	1.37513
$55$	−0.575934	−0.0776590
$56$	5.69911	0.761576
$57$	−4.45329	−0.589853
$58$	−24.0847	−3.16248
$59$	−7.98266	−1.03925	−0.519627	−	0.854393i	$-0.673929\pi$
$59$	−7.98266	−1.03925	−0.519627	+	0.854393i	$0.673929\pi$
$60$	2.44504	0.315653
$61$	−0.538901	−0.0689992	−0.0344996	−	0.999405i	$-0.510984\pi$
$61$	−0.538901	−0.0689992	−0.0344996	+	0.999405i	$0.510984\pi$
$62$	−23.3765	−2.96882
$63$	−4.47541	−0.563849
$64$	−4.07281	−0.509101
$65$	0.237235	0.0294254
$66$	18.8572	2.32116
$67$	5.84932	0.714608	0.357304	−	0.933988i	$-0.383696\pi$
$67$	5.84932	0.714608	0.357304	+	0.933988i	$0.383696\pi$
$68$	−25.4105	−3.08147
$69$	4.92126	0.592450
$70$	−0.524002	−0.0626302
$71$	−4.66367	−0.553476	−0.276738	−	0.960945i	$-0.589253\pi$
$71$	−4.66367	−0.553476	−0.276738	+	0.960945i	$0.589253\pi$
$72$	−25.5059	−3.00590
$73$	5.11185	0.598297	0.299148	−	0.954207i	$-0.403297\pi$
$73$	5.11185	0.598297	0.299148	+	0.954207i	$0.403297\pi$
$74$	6.79801	0.790253
$75$	13.5510	1.56473
$76$	6.96319	0.798732
$77$	−2.75328	−0.313765
$78$	−7.76753	−0.879499
$79$	−8.04099	−0.904682	−0.452341	−	0.891845i	$-0.649411\pi$
$79$	−8.04099	−0.904682	−0.452341	+	0.891845i	$0.649411\pi$
$80$	−1.19781	−0.133919
$81$	−2.39693	−0.266326
$82$	20.9080	2.30890
$83$	−4.95381	−0.543751	−0.271876	−	0.962332i	$-0.587644\pi$
$83$	−4.95381	−0.543751	−0.271876	+	0.962332i	$0.587644\pi$
$84$	11.6886	1.27533
$85$	1.24334	0.134860
$86$	−2.96524	−0.319750
$87$	−26.2875	−2.81832
$88$	−15.6912	−1.67269
$89$	6.90714	0.732155	0.366077	−	0.930584i	$-0.380701\pi$
$89$	6.90714	0.732155	0.366077	+	0.930584i	$0.380701\pi$
$90$	2.34512	0.247198
$91$	1.13411	0.118887
$92$	−7.69491	−0.802250
$93$	−25.5145	−2.64573
$94$	−22.9523	−2.36735
$95$	−0.340711	−0.0349562
$96$	8.05448	0.822057
$97$	11.7487	1.19290	0.596450	−	0.802650i	$-0.296577\pi$
$97$	11.7487	1.19290	0.596450	+	0.802650i	$0.296577\pi$
$98$	−2.50501	−0.253044
$99$	12.3220	1.23841
$100$	−21.1884	−2.11884
$101$	6.30607	0.627477	0.313739	−	0.949509i	$-0.398418\pi$
$101$	6.30607	0.627477	0.313739	+	0.949509i	$0.398418\pi$
$102$	−40.7095	−4.03084
$103$	9.19047	0.905564	0.452782	−	0.891621i	$-0.350432\pi$
$103$	9.19047	0.905564	0.452782	+	0.891621i	$0.350432\pi$
$104$	6.46343	0.633791
$105$	−0.571927	−0.0558144
$106$	32.4004	3.14700
$107$	−18.7229	−1.81001	−0.905004	−	0.425403i	$-0.860132\pi$
$107$	−18.7229	−1.81001	−0.905004	+	0.425403i	$0.860132\pi$
$108$	−17.2455	−1.65945
$109$	−5.07555	−0.486150	−0.243075	−	0.970008i	$-0.578156\pi$
$109$	−5.07555	−0.486150	−0.243075	+	0.970008i	$0.578156\pi$
$110$	1.44272	0.137558
$111$	7.41976	0.704252
$112$	−5.72618	−0.541073
$113$	8.97381	0.844185	0.422093	−	0.906553i	$-0.361296\pi$
$113$	8.97381	0.844185	0.422093	+	0.906553i	$0.361296\pi$
$114$	11.1555	1.04481
$115$	0.376515	0.0351102
$116$	41.1033	3.81635
$117$	−5.07561	−0.469240
$118$	19.9966	1.84084
$119$	5.94385	0.544872
$120$	−3.25948	−0.297548
$121$	−3.41947	−0.310860
$122$	1.34995	0.122219
$123$	22.8202	2.05763
$124$	39.8946	3.58264
$125$	2.08266	0.186279
$126$	11.2110	0.998751
$127$	−9.99040	−0.886505	−0.443252	−	0.896397i	$-0.646175\pi$
$127$	−9.99040	−0.886505	−0.443252	+	0.896397i	$0.646175\pi$
$128$	16.0943	1.42254
$129$	−3.23644	−0.284952
$130$	−0.594276	−0.0521215
$131$	20.1501	1.76052	0.880260	−	0.474491i	$-0.157368\pi$
$131$	20.1501	1.76052	0.880260	+	0.474491i	$0.157368\pi$
$132$	−32.1819	−2.80108
$133$	−1.62878	−0.141233
$134$	−14.6526	−1.26579
$135$	0.843827	0.0726251
$136$	33.8747	2.90473
$137$	−19.8653	−1.69721	−0.848605	−	0.529026i	$-0.822557\pi$
$137$	−19.8653	−1.69721	−0.848605	+	0.529026i	$0.822557\pi$
$138$	−12.3278	−1.04941
$139$	7.12987	0.604747	0.302374	−	0.953189i	$-0.402221\pi$
$139$	7.12987	0.604747	0.302374	+	0.953189i	$0.402221\pi$
$140$	0.894268	0.0755794
$141$	−25.0515	−2.10972
$142$	11.6826	0.980378
$143$	−3.12252	−0.261118
$144$	25.6270	2.13558
$145$	−2.01120	−0.167021
$146$	−12.8052	−1.05977
$147$	−2.73412	−0.225506
$148$	−11.6016	−0.953644
$149$	5.70217	0.467140	0.233570	−	0.972340i	$-0.424959\pi$
$149$	5.70217	0.467140	0.233570	+	0.972340i	$0.424959\pi$
$150$	−33.9453	−2.77162
$151$	−19.4537	−1.58312	−0.791562	−	0.611089i	$-0.790732\pi$
$151$	−19.4537	−1.58312	−0.791562	+	0.611089i	$0.790732\pi$
$152$	−9.28262	−0.752920
$153$	−26.6012	−2.15058
$154$	6.89699	0.555775
$155$	−1.95206	−0.156793
$156$	13.2562	1.06134
$157$	16.0174	1.27832	0.639162	−	0.769072i	$-0.279281\pi$
$157$	16.0174	1.27832	0.639162	+	0.769072i	$0.279281\pi$
$158$	20.1428	1.60247
$159$	35.3637	2.80453
$160$	0.616230	0.0487173
$161$	1.79994	0.141855
$162$	6.00434	0.471746
$163$	−5.57128	−0.436376	−0.218188	−	0.975907i	$-0.570015\pi$
$163$	−5.57128	−0.436376	−0.218188	+	0.975907i	$0.570015\pi$
$164$	−35.6818	−2.78628
$165$	1.57467	0.122588
$166$	12.4093	0.963152
$167$	−9.07560	−0.702291	−0.351146	−	0.936321i	$-0.614208\pi$
$167$	−9.07560	−0.702291	−0.351146	+	0.936321i	$0.614208\pi$
$168$	−15.5821	−1.20218
$169$	−11.7138	−0.901061
$170$	−3.11459	−0.238878
$171$	7.28948	0.557440
$172$	5.06051	0.385860
$173$	23.6435	1.79758	0.898790	−	0.438380i	$-0.144448\pi$
$173$	23.6435	1.79758	0.898790	+	0.438380i	$0.144448\pi$
$174$	65.8506	4.99212
$175$	4.95624	0.374657
$176$	15.7657	1.18839
$177$	21.8255	1.64051
$178$	−17.3025	−1.29687
$179$	−11.6640	−0.871809	−0.435905	−	0.899993i	$-0.643571\pi$
$179$	−11.6640	−0.871809	−0.435905	+	0.899993i	$0.643571\pi$
$180$	−4.00222	−0.298308
$181$	−3.96491	−0.294709	−0.147355	−	0.989084i	$-0.547076\pi$
$181$	−3.96491	−0.294709	−0.147355	+	0.989084i	$0.547076\pi$
$182$	−2.84096	−0.210586
$183$	1.47342	0.108918
$184$	10.2581	0.756236
$185$	0.567669	0.0417359
$186$	63.9142	4.68641
$187$	−16.3651	−1.19673
$188$	39.1707	2.85681
$189$	4.03395	0.293427
$190$	0.853486	0.0619184
$191$	−2.13754	−0.154667	−0.0773334	−	0.997005i	$-0.524641\pi$
$191$	−2.13754	−0.154667	−0.0773334	+	0.997005i	$0.524641\pi$
$192$	11.1355	0.803638
$193$	26.6897	1.92117	0.960585	−	0.277988i	$-0.0896675\pi$
$193$	26.6897	1.92117	0.960585	+	0.277988i	$0.0896675\pi$
$194$	−29.4306	−2.11300
$195$	−0.648629	−0.0464493
$196$	4.27508	0.305363
$197$	18.5976	1.32502	0.662512	−	0.749051i	$-0.269490\pi$
$197$	18.5976	1.32502	0.662512	+	0.749051i	$0.269490\pi$
$198$	−30.8669	−2.19361
$199$	−1.85705	−0.131643	−0.0658213	−	0.997831i	$-0.520967\pi$
$199$	−1.85705	−0.131643	−0.0658213	+	0.997831i	$0.520967\pi$
$200$	28.2462	1.99731
$201$	−15.9927	−1.12804
$202$	−15.7968	−1.11146
$203$	−9.61462	−0.674814
$204$	69.4753	4.86424
$205$	1.74593	0.121941
$206$	−23.0222	−1.60403
$207$	−8.05549	−0.559895
$208$	−6.49412	−0.450286
$209$	4.48449	0.310199
$210$	1.43268	0.0988646
$211$	21.8883	1.50685	0.753426	−	0.657533i	$-0.228400\pi$
$211$	21.8883	1.50685	0.753426	+	0.657533i	$0.228400\pi$
$212$	−55.2949	−3.79767
$213$	12.7510	0.873686
$214$	46.9010	3.20609
$215$	−0.247613	−0.0168870
$216$	22.9899	1.56427
$217$	−9.33189	−0.633490
$218$	12.7143	0.861122
$219$	−13.9764	−0.944438
$220$	−2.46217	−0.165999
$221$	6.74099	0.453448
$222$	−18.5866	−1.24745
$223$	16.4246	1.09988	0.549938	−	0.835206i	$-0.314651\pi$
$223$	16.4246	1.09988	0.549938	+	0.835206i	$0.314651\pi$
$224$	2.94591	0.196832
$225$	−22.1812	−1.47875
$226$	−22.4795	−1.49531
$227$	−14.5845	−0.968009	−0.484005	−	0.875065i	$-0.660818\pi$
$227$	−14.5845	−0.968009	−0.484005	+	0.875065i	$0.660818\pi$
$228$	−19.0382	−1.26083
$229$	21.6309	1.42941	0.714705	−	0.699426i	$-0.246561\pi$
$229$	21.6309	1.42941	0.714705	+	0.699426i	$0.246561\pi$
$230$	−0.943174	−0.0621910
$231$	7.52779	0.495292
$232$	−54.7948	−3.59746
$233$	−3.81361	−0.249838	−0.124919	−	0.992167i	$-0.539867\pi$
$233$	−3.81361	−0.249838	−0.124919	+	0.992167i	$0.539867\pi$
$234$	12.7145	0.831171
$235$	−1.91663	−0.125027
$236$	−34.1265	−2.22145
$237$	21.9850	1.42808
$238$	−14.8894	−0.965138
$239$	0.189576	0.0122627	0.00613134	−	0.999981i	$-0.498048\pi$
$239$	0.189576	0.0122627	0.00613134	+	0.999981i	$0.498048\pi$
$240$	3.27495	0.211397
$241$	25.8093	1.66252	0.831261	−	0.555882i	$-0.187619\pi$
$241$	25.8093	1.66252	0.831261	+	0.555882i	$0.187619\pi$
$242$	8.56580	0.550630
$243$	18.6553	1.19674
$244$	−2.30385	−0.147489
$245$	−0.209181	−0.0133641
$246$	−57.1650	−3.64471
$247$	−1.84722	−0.117536
$248$	−53.1835	−3.37716
$249$	13.5443	0.858335
$250$	−5.21709	−0.329958
$251$	11.7399	0.741015	0.370507	−	0.928830i	$-0.379184\pi$
$251$	11.7399	0.741015	0.370507	+	0.928830i	$0.379184\pi$
$252$	−19.1328	−1.20525
$253$	−4.95574	−0.311565
$254$	25.0261	1.57028
$255$	−3.39945	−0.212882
$256$	−32.1707	−2.01067
$257$	6.25673	0.390284	0.195142	−	0.980775i	$-0.437483\pi$
$257$	6.25673	0.390284	0.195142	+	0.980775i	$0.437483\pi$
$258$	8.10731	0.504739
$259$	2.71377	0.168625
$260$	1.01420	0.0628980
$261$	43.0294	2.66345
$262$	−50.4762	−3.11843
$263$	5.86970	0.361941	0.180971	−	0.983489i	$-0.442076\pi$
$263$	5.86970	0.361941	0.180971	+	0.983489i	$0.442076\pi$
$264$	42.9017	2.64042
$265$	2.70560	0.166204
$266$	4.08012	0.250168
$267$	−18.8849	−1.15574
$268$	25.0063	1.52750
$269$	−26.6417	−1.62437	−0.812187	−	0.583398i	$-0.801723\pi$
$269$	−26.6417	−1.62437	−0.812187	+	0.583398i	$0.801723\pi$
$270$	−2.11380	−0.128642
$271$	−27.5199	−1.67171	−0.835857	−	0.548947i	$-0.815029\pi$
$271$	−27.5199	−1.67171	−0.835857	+	0.548947i	$0.815029\pi$
$272$	−34.0355	−2.06371
$273$	−3.10079	−0.187669
$274$	49.7629	3.00629
$275$	−13.6459	−0.822879
$276$	21.0388	1.26639
$277$	31.0706	1.86685	0.933425	−	0.358771i	$-0.116804\pi$
$277$	31.0706	1.86685	0.933425	+	0.358771i	$0.116804\pi$
$278$	−17.8604	−1.07120
$279$	41.7641	2.50035
$280$	−1.19215	−0.0712445
$281$	−15.1363	−0.902957	−0.451479	−	0.892282i	$-0.649103\pi$
$281$	−15.1363	−0.902957	−0.451479	+	0.892282i	$0.649103\pi$
$282$	62.7543	3.73696
$283$	−5.94384	−0.353325	−0.176662	−	0.984271i	$-0.556530\pi$
$283$	−5.94384	−0.353325	−0.176662	+	0.984271i	$0.556530\pi$
$284$	−19.9376	−1.18308
$285$	0.931545	0.0551800
$286$	7.82195	0.462522
$287$	8.34647	0.492676
$288$	−13.1842	−0.776885
$289$	18.3294	1.07820
$290$	5.03808	0.295846
$291$	−32.1224	−1.88305
$292$	21.8536	1.27888
$293$	−9.05814	−0.529182	−0.264591	−	0.964361i	$-0.585237\pi$
$293$	−9.05814	−0.529182	−0.264591	+	0.964361i	$0.585237\pi$
$294$	6.84900	0.399442
$295$	1.66982	0.0972209
$296$	15.4661	0.898946
$297$	−11.1066	−0.644469
$298$	−14.2840	−0.827450
$299$	2.04134	0.118053
$300$	57.9315	3.34468
$301$	−1.18372	−0.0682286
$302$	48.7319	2.80420
$303$	−17.2415	−0.990501
$304$	9.32670	0.534923
$305$	0.112728	0.00645479
$306$	66.6363	3.80934
$307$	19.6836	1.12340	0.561701	−	0.827341i	$-0.310147\pi$
$307$	19.6836	1.12340	0.561701	+	0.827341i	$0.310147\pi$
$308$	−11.7705	−0.670686
$309$	−25.1278	−1.42947
$310$	4.88993	0.277729
$311$	−9.50285	−0.538857	−0.269429	−	0.963020i	$-0.586835\pi$
$311$	−9.50285	−0.538857	−0.269429	+	0.963020i	$0.586835\pi$
$312$	−17.6718	−1.00047
$313$	6.74325	0.381151	0.190575	−	0.981673i	$-0.438965\pi$
$313$	6.74325	0.381151	0.190575	+	0.981673i	$0.438965\pi$
$314$	−40.1237	−2.26431
$315$	0.936173	0.0527473
$316$	−34.3759	−1.93380
$317$	−2.78008	−0.156145	−0.0780725	−	0.996948i	$-0.524877\pi$
$317$	−2.78008	−0.156145	−0.0780725	+	0.996948i	$0.524877\pi$
$318$	−88.5866	−4.96769
$319$	26.4717	1.48213
$320$	0.851955	0.0476257
$321$	51.1906	2.85718
$322$	−4.50888	−0.251270
$323$	−9.68125	−0.538679
$324$	−10.2471	−0.569282
$325$	5.62093	0.311793
$326$	13.9561	0.772958
$327$	13.8772	0.767409
$328$	47.5675	2.62647
$329$	−9.16255	−0.505148
$330$	−3.94458	−0.217142
$331$	5.84736	0.321400	0.160700	−	0.987003i	$-0.448625\pi$
$331$	5.84736	0.321400	0.160700	+	0.987003i	$0.448625\pi$
$332$	−21.1779	−1.16229
$333$	−12.1452	−0.665554
$334$	22.7345	1.24398
$335$	−1.22357	−0.0668507
$336$	15.6560	0.854108
$337$	21.5063	1.17152	0.585760	−	0.810484i	$-0.300796\pi$
$337$	21.5063	1.17152	0.585760	+	0.810484i	$0.300796\pi$
$338$	29.3432	1.59606
$339$	−24.5355	−1.33258
$340$	5.31540	0.288268
$341$	25.6933	1.39137
$342$	−18.2602	−0.987400
$343$	−1.00000	−0.0539949
$344$	−6.74616	−0.363729
$345$	−1.02944	−0.0554230
$346$	−59.2272	−3.18407
$347$	20.1105	1.07959	0.539793	−	0.841798i	$-0.318502\pi$
$347$	20.1105	1.07959	0.539793	+	0.841798i	$0.318502\pi$
$348$	−112.381	−6.02427
$349$	29.5103	1.57965	0.789826	−	0.613330i	$-0.210171\pi$
$349$	29.5103	1.57965	0.789826	+	0.613330i	$0.210171\pi$
$350$	−12.4154	−0.663634
$351$	4.57495	0.244193
$352$	−8.11091	−0.432313
$353$	−19.0779	−1.01541	−0.507707	−	0.861530i	$-0.669507\pi$
$353$	−19.0779	−1.01541	−0.507707	+	0.861530i	$0.669507\pi$
$354$	−54.6732	−2.90585
$355$	0.975553	0.0517770
$356$	29.5286	1.56501
$357$	−16.2512	−0.860105
$358$	29.2185	1.54424
$359$	−12.5996	−0.664983	−0.332491	−	0.943106i	$-0.607889\pi$
$359$	−12.5996	−0.664983	−0.332491	+	0.943106i	$0.607889\pi$
$360$	5.33535	0.281198
$361$	−16.3471	−0.860372
$362$	9.93214	0.522022
$363$	9.34923	0.490707
$364$	4.84842	0.254126
$365$	−1.06930	−0.0559699
$366$	−3.69093	−0.192928
$367$	−13.8728	−0.724152	−0.362076	−	0.932149i	$-0.617932\pi$
$367$	−13.8728	−0.724152	−0.362076	+	0.932149i	$0.617932\pi$
$368$	−10.3068	−0.537279
$369$	−37.3539	−1.94456
$370$	−1.42202	−0.0739272
$371$	12.9342	0.671512
$372$	−109.077	−5.65536
$373$	−17.5881	−0.910677	−0.455339	−	0.890318i	$-0.650482\pi$
$373$	−17.5881	−0.910677	−0.455339	+	0.890318i	$0.650482\pi$
$374$	40.9947	2.11979
$375$	−5.69424	−0.294049
$376$	−52.2184	−2.69296
$377$	−10.9040	−0.561587
$378$	−10.1051	−0.519750
$379$	23.3843	1.20117	0.600584	−	0.799561i	$-0.294935\pi$
$379$	23.3843	1.20117	0.600584	+	0.799561i	$0.294935\pi$
$380$	−1.45657	−0.0747204
$381$	27.3150	1.39939
$382$	5.35456	0.273963
$383$	26.3227	1.34503	0.672513	−	0.740085i	$-0.265215\pi$
$383$	26.3227	1.34503	0.672513	+	0.740085i	$0.265215\pi$
$384$	−44.0036	−2.24555
$385$	0.575934	0.0293523
$386$	−66.8581	−3.40299
$387$	5.29764	0.269294
$388$	50.2267	2.54987
$389$	−35.4121	−1.79546	−0.897732	−	0.440543i	$-0.854786\pi$
$389$	−35.4121	−1.79546	−0.897732	+	0.440543i	$0.854786\pi$
$390$	1.62482	0.0822761
$391$	10.6986	0.541051
$392$	−5.69911	−0.287849
$393$	−55.0927	−2.77906
$394$	−46.5872	−2.34703
$395$	1.68202	0.0846319
$396$	52.6778	2.64716
$397$	19.5752	0.982449	0.491225	−	0.871033i	$-0.336549\pi$
$397$	19.5752	0.982449	0.491225	+	0.871033i	$0.336549\pi$
$398$	4.65193	0.233180
$399$	4.45329	0.222943
$400$	−28.3803	−1.41902
$401$	22.2152	1.10937	0.554687	−	0.832059i	$-0.312838\pi$
$401$	22.2152	1.10937	0.554687	+	0.832059i	$0.312838\pi$
$402$	40.0620	1.99811
$403$	−10.5834	−0.527197
$404$	26.9590	1.34126
$405$	0.501393	0.0249144
$406$	24.0847	1.19531
$407$	−7.47175	−0.370361
$408$	−92.6174	−4.58525
$409$	5.47953	0.270946	0.135473	−	0.990781i	$-0.456745\pi$
$409$	5.47953	0.270946	0.135473	+	0.990781i	$0.456745\pi$
$410$	−4.37356	−0.215995
$411$	54.3142	2.67912
$412$	39.2900	1.93568
$413$	7.98266	0.392801
$414$	20.1791	0.991748
$415$	1.03624	0.0508672
$416$	3.34099	0.163806
$417$	−19.4939	−0.954621
$418$	−11.2337	−0.549459
$419$	−38.9227	−1.90150	−0.950749	−	0.309961i	$-0.899684\pi$
$419$	−38.9227	−1.90150	−0.950749	+	0.309961i	$0.899684\pi$
$420$	−2.44504	−0.119306
$421$	−4.20670	−0.205022	−0.102511	−	0.994732i	$-0.532688\pi$
$421$	−4.20670	−0.205022	−0.102511	+	0.994732i	$0.532688\pi$
$422$	−54.8304	−2.66910
$423$	41.0062	1.99379
$424$	73.7136	3.57985
$425$	29.4592	1.42898
$426$	−31.9415	−1.54757
$427$	0.538901	0.0260792
$428$	−80.0418	−3.86897
$429$	8.53735	0.412187
$430$	0.620272	0.0299122
$431$	−35.0178	−1.68675	−0.843374	−	0.537327i	$-0.819434\pi$
$431$	−35.0178	−1.68675	−0.843374	+	0.537327i	$0.819434\pi$
$432$	−23.0991	−1.11136
$433$	4.81015	0.231161	0.115581	−	0.993298i	$-0.463127\pi$
$433$	4.81015	0.231161	0.115581	+	0.993298i	$0.463127\pi$
$434$	23.3765	1.12211
$435$	5.49886	0.263650
$436$	−21.6984	−1.03917
$437$	−2.93172	−0.140243
$438$	35.0111	1.67289
$439$	14.7277	0.702914	0.351457	−	0.936204i	$-0.385686\pi$
$439$	14.7277	0.702914	0.351457	+	0.936204i	$0.385686\pi$
$440$	3.28231	0.156478
$441$	4.47541	0.213115
$442$	−16.8863	−0.803197
$443$	−6.85486	−0.325684	−0.162842	−	0.986652i	$-0.552066\pi$
$443$	−6.85486	−0.325684	−0.162842	+	0.986652i	$0.552066\pi$
$444$	31.7201	1.50537
$445$	−1.44484	−0.0684922
$446$	−41.1439	−1.94822
$447$	−15.5904	−0.737402
$448$	4.07281	0.192422
$449$	23.2689	1.09813	0.549063	−	0.835781i	$-0.314985\pi$
$449$	23.2689	1.09813	0.549063	+	0.835781i	$0.314985\pi$
$450$	55.5642	2.61932
$451$	−22.9801	−1.08209
$452$	38.3638	1.80448
$453$	53.1889	2.49903
$454$	36.5344	1.71465
$455$	−0.237235	−0.0111217
$456$	25.3798	1.18852
$457$	16.0760	0.752004	0.376002	−	0.926619i	$-0.377299\pi$
$457$	16.0760	0.752004	0.376002	+	0.926619i	$0.377299\pi$
$458$	−54.1857	−2.53193
$459$	23.9772	1.11916
$460$	1.60963	0.0750495
$461$	−9.01182	−0.419723	−0.209861	−	0.977731i	$-0.567301\pi$
$461$	−9.01182	−0.419723	−0.209861	+	0.977731i	$0.567301\pi$
$462$	−18.8572	−0.877316
$463$	23.4172	1.08829	0.544145	−	0.838991i	$-0.316854\pi$
$463$	23.4172	1.08829	0.544145	+	0.838991i	$0.316854\pi$
$464$	55.0550	2.55586
$465$	5.33716	0.247505
$466$	9.55315	0.442541
$467$	−6.10780	−0.282635	−0.141318	−	0.989964i	$-0.545134\pi$
$467$	−6.10780	−0.282635	−0.141318	+	0.989964i	$0.545134\pi$
$468$	−21.6987	−1.00302
$469$	−5.84932	−0.270096
$470$	4.80119	0.221462
$471$	−43.7934	−2.01789
$472$	45.4941	2.09403
$473$	3.25911	0.149854
$474$	−55.0727	−2.52957
$475$	−8.07265	−0.370398
$476$	25.4105	1.16469
$477$	−57.8860	−2.65042
$478$	−0.474891	−0.0217210
$479$	1.57669	0.0720406	0.0360203	−	0.999351i	$-0.488532\pi$
$479$	1.57669	0.0720406	0.0360203	+	0.999351i	$0.488532\pi$
$480$	−1.68485	−0.0769024
$481$	3.07771	0.140332
$482$	−64.6526	−2.94484
$483$	−4.92126	−0.223925
$484$	−14.6185	−0.664477
$485$	−2.45761	−0.111594
$486$	−46.7319	−2.11980
$487$	−39.9325	−1.80952	−0.904758	−	0.425926i	$-0.859948\pi$
$487$	−39.9325	−1.80952	−0.904758	+	0.425926i	$0.859948\pi$
$488$	3.07126	0.139029
$489$	15.2325	0.688840
$490$	0.524002	0.0236720
$491$	−33.5473	−1.51397	−0.756983	−	0.653434i	$-0.773328\pi$
$491$	−33.5473	−1.51397	−0.756983	+	0.653434i	$0.773328\pi$
$492$	97.5584	4.39827
$493$	−57.1479	−2.57381
$494$	4.62731	0.208193
$495$	−2.57754	−0.115852
$496$	53.4361	2.39935
$497$	4.66367	0.209194
$498$	−33.9286	−1.52038
$499$	−21.8562	−0.978418	−0.489209	−	0.872167i	$-0.662714\pi$
$499$	−21.8562	−0.978418	−0.489209	+	0.872167i	$0.662714\pi$
$500$	8.90355	0.398179
$501$	24.8138	1.10860
$502$	−29.4085	−1.31257
$503$	−41.6367	−1.85649	−0.928245	−	0.371970i	$-0.878682\pi$
$503$	−41.6367	−1.85649	−0.928245	+	0.371970i	$0.878682\pi$
$504$	25.5059	1.13612
$505$	−1.31911	−0.0586997
$506$	12.4142	0.551878
$507$	32.0269	1.42237
$508$	−42.7098	−1.89494
$509$	−0.530354	−0.0235075	−0.0117538	−	0.999931i	$-0.503741\pi$
$509$	−0.530354	−0.0235075	−0.0117538	+	0.999931i	$0.503741\pi$
$510$	8.51566	0.377080
$511$	−5.11185	−0.226135
$512$	48.3994	2.13897
$513$	−6.57043	−0.290092
$514$	−15.6732	−0.691314
$515$	−1.92247	−0.0847143
$516$	−13.8360	−0.609098
$517$	25.2270	1.10948
$518$	−6.79801	−0.298688
$519$	−64.6441	−2.83756
$520$	−1.35203	−0.0592904
$521$	−22.3820	−0.980574	−0.490287	−	0.871561i	$-0.663108\pi$
$521$	−22.3820	−0.980574	−0.490287	+	0.871561i	$0.663108\pi$
$522$	−107.789	−4.71780
$523$	−26.4602	−1.15702	−0.578512	−	0.815674i	$-0.696366\pi$
$523$	−26.4602	−1.15702	−0.578512	+	0.815674i	$0.696366\pi$
$524$	86.1433	3.76319
$525$	−13.5510	−0.591412
$526$	−14.7037	−0.641110
$527$	−55.4674	−2.41620
$528$	−43.1054	−1.87592
$529$	−19.7602	−0.859139
$530$	−6.77756	−0.294398
$531$	−35.7257	−1.55036
$532$	−6.96319	−0.301892
$533$	9.46582	0.410010
$534$	47.3070	2.04717
$535$	3.91648	0.169324
$536$	−33.3359	−1.43989
$537$	31.8908	1.37619
$538$	66.7378	2.87727
$539$	2.75328	0.118592
$540$	3.60743	0.155239
$541$	37.5932	1.61626	0.808129	−	0.589006i	$-0.200480\pi$
$541$	37.5932	1.61626	0.808129	+	0.589006i	$0.200480\pi$
$542$	68.9377	2.96113
$543$	10.8405	0.465212
$544$	17.5101	0.750738
$545$	1.06171	0.0454787
$546$	7.76753	0.332419
$547$	−15.5021	−0.662823	−0.331412	−	0.943486i	$-0.607525\pi$
$547$	−15.5021	−0.662823	−0.331412	+	0.943486i	$0.607525\pi$
$548$	−84.9260	−3.62786
$549$	−2.41180	−0.102933
$550$	34.1832	1.45758
$551$	15.6601	0.667144
$552$	−28.0468	−1.19375
$553$	8.04099	0.341938
$554$	−77.8322	−3.30677
$555$	−1.55208	−0.0658819
$556$	30.4808	1.29267
$557$	−12.2121	−0.517445	−0.258722	−	0.965952i	$-0.583301\pi$
$557$	−12.2121	−0.517445	−0.258722	+	0.965952i	$0.583301\pi$
$558$	−104.619	−4.42889
$559$	−1.34247	−0.0567805
$560$	1.19781	0.0506167
$561$	44.7441	1.88910
$562$	37.9167	1.59942
$563$	−33.4587	−1.41012	−0.705058	−	0.709150i	$-0.749079\pi$
$563$	−33.4587	−1.41012	−0.705058	+	0.709150i	$0.749079\pi$
$564$	−107.097	−4.50961
$565$	−1.87715	−0.0789725
$566$	14.8894	0.625848
$567$	2.39693	0.100662
$568$	26.5788	1.11522
$569$	21.4685	0.900007	0.450003	−	0.893027i	$-0.351423\pi$
$569$	21.4685	0.900007	0.450003	+	0.893027i	$0.351423\pi$
$570$	−2.33353	−0.0977409
$571$	−11.1571	−0.466911	−0.233456	−	0.972367i	$-0.575003\pi$
$571$	−11.1571	−0.466911	−0.233456	+	0.972367i	$0.575003\pi$
$572$	−13.3490	−0.558151
$573$	5.84428	0.244149
$574$	−20.9080	−0.872683
$575$	8.92096	0.372030
$576$	−18.2275	−0.759478
$577$	−16.8561	−0.701727	−0.350863	−	0.936427i	$-0.614112\pi$
$577$	−16.8561	−0.701727	−0.350863	+	0.936427i	$0.614112\pi$
$578$	−45.9153	−1.90983
$579$	−72.9729	−3.03265
$580$	−8.59805	−0.357015
$581$	4.95381	0.205519
$582$	80.4669	3.33546
$583$	−35.6115	−1.47488
$584$	−29.1330	−1.20553
$585$	1.06172	0.0438969
$586$	22.6908	0.937347
$587$	21.0060	0.867009	0.433505	−	0.901151i	$-0.357277\pi$
$587$	21.0060	0.867009	0.433505	+	0.901151i	$0.357277\pi$
$588$	−11.6886	−0.482029
$589$	15.1996	0.626290
$590$	−4.18293	−0.172208
$591$	−50.8481	−2.09161
$592$	−15.5395	−0.638669
$593$	4.28589	0.176000	0.0880002	−	0.996120i	$-0.471952\pi$
$593$	4.28589	0.176000	0.0880002	+	0.996120i	$0.471952\pi$
$594$	27.8221	1.14156
$595$	−1.24334	−0.0509721
$596$	24.3773	0.998532
$597$	5.07739	0.207804
$598$	−5.11357	−0.209109
$599$	−25.5025	−1.04200	−0.521002	−	0.853555i	$-0.674442\pi$
$599$	−25.5025	−1.04200	−0.521002	+	0.853555i	$0.674442\pi$
$600$	−77.2285	−3.15284
$601$	−10.3007	−0.420175	−0.210088	−	0.977683i	$-0.567375\pi$
$601$	−10.3007	−0.420175	−0.210088	+	0.977683i	$0.567375\pi$
$602$	2.96524	0.120854
$603$	26.1781	1.06605
$604$	−83.1664	−3.38399
$605$	0.715288	0.0290806
$606$	43.1903	1.75449
$607$	−30.8477	−1.25207	−0.626035	−	0.779795i	$-0.715323\pi$
$607$	−30.8477	−1.25207	−0.626035	+	0.779795i	$0.715323\pi$
$608$	−4.79825	−0.194595
$609$	26.2875	1.06522
$610$	−0.282385	−0.0114334
$611$	−10.3913	−0.420389
$612$	−113.722	−4.59695
$613$	−6.72627	−0.271671	−0.135836	−	0.990731i	$-0.543372\pi$
$613$	−6.72627	−0.271671	−0.135836	+	0.990731i	$0.543372\pi$
$614$	−49.3076	−1.98989
$615$	−4.77357	−0.192489
$616$	15.6912	0.632218
$617$	41.5700	1.67354	0.836772	−	0.547552i	$-0.184440\pi$
$617$	41.5700	1.67354	0.836772	+	0.547552i	$0.184440\pi$
$618$	62.9455	2.53204
$619$	−8.10535	−0.325782	−0.162891	−	0.986644i	$-0.552082\pi$
$619$	−8.10535	−0.325782	−0.162891	+	0.986644i	$0.552082\pi$
$620$	−8.34521	−0.335152
$621$	7.26088	0.291369
$622$	23.8047	0.954483
$623$	−6.90714	−0.276729
$624$	17.7557	0.710797
$625$	24.3456	0.973822
$626$	−16.8919	−0.675136
$627$	−12.2611	−0.489663
$628$	68.4756	2.73247
$629$	16.1302	0.643154
$630$	−2.34512	−0.0934319
$631$	33.9378	1.35104	0.675522	−	0.737340i	$-0.263918\pi$
$631$	33.9378	1.35104	0.675522	+	0.737340i	$0.263918\pi$
$632$	45.8265	1.82288
$633$	−59.8452	−2.37863
$634$	6.96414	0.276581
$635$	2.08981	0.0829314
$636$	151.183	5.99479
$637$	−1.13411	−0.0449351
$638$	−66.3120	−2.62532
$639$	−20.8718	−0.825677
$640$	−3.36662	−0.133077
$641$	−38.1039	−1.50501	−0.752507	−	0.658584i	$-0.771156\pi$
$641$	−38.1039	−1.50501	−0.752507	+	0.658584i	$0.771156\pi$
$642$	−128.233	−5.06095
$643$	35.8433	1.41352	0.706761	−	0.707452i	$-0.250156\pi$
$643$	35.8433	1.41352	0.706761	+	0.707452i	$0.250156\pi$
$644$	7.69491	0.303222
$645$	0.677002	0.0266569
$646$	24.2516	0.954168
$647$	18.9136	0.743571	0.371785	−	0.928319i	$-0.378746\pi$
$647$	18.9136	0.743571	0.371785	+	0.928319i	$0.378746\pi$
$648$	13.6604	0.536630
$649$	−21.9785	−0.862730
$650$	−14.0805	−0.552282
$651$	25.5145	0.999993
$652$	−23.8177	−0.932773
$653$	−12.2471	−0.479265	−0.239633	−	0.970864i	$-0.577027\pi$
$653$	−12.2471	−0.479265	−0.239633	+	0.970864i	$0.577027\pi$
$654$	−34.7625	−1.35932
$655$	−4.21502	−0.164694
$656$	−47.7933	−1.86602
$657$	22.8776	0.892541
$658$	22.9523	0.894773
$659$	−1.59929	−0.0622994	−0.0311497	−	0.999515i	$-0.509917\pi$
$659$	−1.59929	−0.0622994	−0.0311497	+	0.999515i	$0.509917\pi$
$660$	6.73186	0.262037
$661$	14.2805	0.555448	0.277724	−	0.960661i	$-0.410420\pi$
$661$	14.2805	0.555448	0.277724	+	0.960661i	$0.410420\pi$
$662$	−14.6477	−0.569299
$663$	−18.4307	−0.715788
$664$	28.2323	1.09563
$665$	0.340711	0.0132122
$666$	30.4239	1.17890
$667$	−17.3058	−0.670082
$668$	−38.7990	−1.50118
$669$	−44.9069	−1.73620
$670$	3.06505	0.118413
$671$	−1.48374	−0.0572793
$672$	−8.05448	−0.310708
$673$	−12.3021	−0.474210	−0.237105	−	0.971484i	$-0.576198\pi$
$673$	−12.3021	−0.474210	−0.237105	+	0.971484i	$0.576198\pi$
$674$	−53.8734	−2.07513
$675$	19.9932	0.769540
$676$	−50.0774	−1.92606
$677$	−23.9710	−0.921280	−0.460640	−	0.887587i	$-0.652380\pi$
$677$	−23.9710	−0.921280	−0.460640	+	0.887587i	$0.652380\pi$
$678$	61.4616	2.36042
$679$	−11.7487	−0.450874
$680$	−7.08595	−0.271734
$681$	39.8759	1.52805
$682$	−64.3620	−2.46455
$683$	−2.74539	−0.105049	−0.0525246	−	0.998620i	$-0.516727\pi$
$683$	−2.74539	−0.105049	−0.0525246	+	0.998620i	$0.516727\pi$
$684$	31.1631	1.19155
$685$	4.15546	0.158772
$686$	2.50501	0.0956418
$687$	−59.1415	−2.25639
$688$	6.77820	0.258416
$689$	14.6688	0.558839
$690$	2.57875	0.0981713
$691$	−36.4530	−1.38674	−0.693369	−	0.720583i	$-0.743874\pi$
$691$	−36.4530	−1.38674	−0.693369	+	0.720583i	$0.743874\pi$
$692$	101.078	3.84240
$693$	−12.3220	−0.468076
$694$	−50.3769	−1.91228
$695$	−1.49144	−0.0565734
$696$	149.816	5.67874
$697$	49.6102	1.87912
$698$	−73.9238	−2.79806
$699$	10.4269	0.394381
$700$	21.1884	0.800845
$701$	6.81361	0.257346	0.128673	−	0.991687i	$-0.458928\pi$
$701$	6.81361	0.257346	0.128673	+	0.991687i	$0.458928\pi$
$702$	−11.4603	−0.432541
$703$	−4.42014	−0.166709
$704$	−11.2136	−0.422627
$705$	5.24031	0.197361
$706$	47.7904	1.79861
$707$	−6.30607	−0.237164
$708$	93.3060	3.50665
$709$	−29.5890	−1.11124	−0.555620	−	0.831436i	$-0.687519\pi$
$709$	−29.5890	−1.11124	−0.555620	+	0.831436i	$0.687519\pi$
$710$	−2.44377	−0.0917131
$711$	−35.9867	−1.34961
$712$	−39.3645	−1.47525
$713$	−16.7969	−0.629048
$714$	40.7095	1.52351
$715$	0.653173	0.0244273
$716$	−49.8646	−1.86353
$717$	−0.518324	−0.0193572
$718$	31.5622	1.17789
$719$	6.68176	0.249188	0.124594	−	0.992208i	$-0.460237\pi$
$719$	6.68176	0.249188	0.124594	+	0.992208i	$0.460237\pi$
$720$	−5.36069	−0.199781
$721$	−9.19047	−0.342271
$722$	40.9496	1.52399
$723$	−70.5657	−2.62437
$724$	−16.9503	−0.629953
$725$	−47.6524	−1.76977
$726$	−23.4199	−0.869195
$727$	−30.6475	−1.13665	−0.568327	−	0.822803i	$-0.692409\pi$
$727$	−30.6475	−1.13665	−0.568327	+	0.822803i	$0.692409\pi$
$728$	−6.46343	−0.239550
$729$	−43.8152	−1.62278
$730$	2.67862	0.0991401
$731$	−7.03587	−0.260231
$732$	6.29899	0.232817
$733$	−43.2744	−1.59838	−0.799189	−	0.601080i	$-0.794737\pi$
$733$	−43.2744	−1.59838	−0.799189	+	0.601080i	$0.794737\pi$
$734$	34.7514	1.28270
$735$	0.571927	0.0210958
$736$	5.30248	0.195452
$737$	16.1048	0.593228
$738$	93.5719	3.44443
$739$	20.6448	0.759429	0.379715	−	0.925104i	$-0.376022\pi$
$739$	20.6448	0.759429	0.379715	+	0.925104i	$0.376022\pi$
$740$	2.42683	0.0892122
$741$	5.05052	0.185536
$742$	−32.4004	−1.18946
$743$	25.9830	0.953225	0.476612	−	0.879114i	$-0.341865\pi$
$743$	25.9830	0.953225	0.476612	+	0.879114i	$0.341865\pi$
$744$	145.410	5.33099
$745$	−1.19279	−0.0437004
$746$	44.0584	1.61309
$747$	−22.1703	−0.811170
$748$	−69.9621	−2.55807
$749$	18.7229	0.684119
$750$	14.2641	0.520853
$751$	0.873711	0.0318822	0.0159411	−	0.999873i	$-0.494926\pi$
$751$	0.873711	0.0318822	0.0159411	+	0.999873i	$0.494926\pi$
$752$	52.4664	1.91325
$753$	−32.0982	−1.16973
$754$	27.3148	0.994745
$755$	4.06936	0.148099
$756$	17.2455	0.627212
$757$	−37.8746	−1.37657	−0.688287	−	0.725438i	$-0.741637\pi$
$757$	−37.8746	−1.37657	−0.688287	+	0.725438i	$0.741637\pi$
$758$	−58.5779	−2.12764
$759$	13.5496	0.491819
$760$	1.94175	0.0704347
$761$	6.57552	0.238362	0.119181	−	0.992873i	$-0.461973\pi$
$761$	6.57552	0.238362	0.119181	+	0.992873i	$0.461973\pi$
$762$	−68.4243	−2.47875
$763$	5.07555	0.183747
$764$	−9.13815	−0.330607
$765$	5.56447	0.201184
$766$	−65.9386	−2.38246
$767$	9.05322	0.326893
$768$	87.9585	3.17393
$769$	−0.571815	−0.0206202	−0.0103101	−	0.999947i	$-0.503282\pi$
$769$	−0.571815	−0.0206202	−0.0103101	+	0.999947i	$0.503282\pi$
$770$	−1.44272	−0.0519921
$771$	−17.1066	−0.616081
$772$	114.101	4.10658
$773$	28.5266	1.02603	0.513015	−	0.858380i	$-0.328529\pi$
$773$	28.5266	1.02603	0.513015	+	0.858380i	$0.328529\pi$
$774$	−13.2707	−0.477004
$775$	−46.2511	−1.66139
$776$	−66.9572	−2.40362
$777$	−7.41976	−0.266182
$778$	88.7076	3.18032
$779$	−13.5946	−0.487077
$780$	−2.77294	−0.0992872
$781$	−12.8404	−0.459465
$782$	−26.8001	−0.958370
$783$	−38.7849	−1.38606
$784$	5.72618	0.204506
$785$	−3.35053	−0.119586
$786$	138.008	4.92258
$787$	−35.4227	−1.26268	−0.631341	−	0.775506i	$-0.717495\pi$
$787$	−35.4227	−1.26268	−0.631341	+	0.775506i	$0.717495\pi$
$788$	79.5063	2.83229
$789$	−16.0485	−0.571340
$790$	−4.21349	−0.149909
$791$	−8.97381	−0.319072
$792$	−70.2247	−2.49533
$793$	0.611173	0.0217034
$794$	−49.0360	−1.74022
$795$	−7.39743	−0.262360
$796$	−7.93903	−0.281392
$797$	−54.6346	−1.93526	−0.967629	−	0.252378i	$-0.918788\pi$
$797$	−54.6346	−1.93526	−0.967629	+	0.252378i	$0.918788\pi$
$798$	−11.1555	−0.394902
$799$	−54.4608	−1.92669
$800$	14.6007	0.516211
$801$	30.9123	1.09223
$802$	−55.6494	−1.96505
$803$	14.0743	0.496673
$804$	−68.3703	−2.41123
$805$	−0.376515	−0.0132704
$806$	26.5115	0.933829
$807$	72.8416	2.56415
$808$	−35.9390	−1.26433
$809$	11.0765	0.389428	0.194714	−	0.980860i	$-0.437622\pi$
$809$	11.0765	0.389428	0.194714	+	0.980860i	$0.437622\pi$
$810$	−1.25600	−0.0441312
$811$	−3.78283	−0.132833	−0.0664166	−	0.997792i	$-0.521157\pi$
$811$	−3.78283	−0.132833	−0.0664166	+	0.997792i	$0.521157\pi$
$812$	−41.1033	−1.44244
$813$	75.2427	2.63888
$814$	18.7168	0.656024
$815$	1.16541	0.0408225
$816$	93.0573	3.25766
$817$	1.92803	0.0674531
$818$	−13.7263	−0.479929
$819$	5.07561	0.177356
$820$	7.46398	0.260653
$821$	22.3464	0.779893	0.389947	−	0.920837i	$-0.372493\pi$
$821$	22.3464	0.779893	0.389947	+	0.920837i	$0.372493\pi$
$822$	−136.058	−4.74556
$823$	−11.8800	−0.414112	−0.207056	−	0.978329i	$-0.566388\pi$
$823$	−11.8800	−0.414112	−0.207056	+	0.978329i	$0.566388\pi$
$824$	−52.3775	−1.82466
$825$	37.3096	1.29895
$826$	−19.9966	−0.695772
$827$	41.8137	1.45401	0.727003	−	0.686635i	$-0.240913\pi$
$827$	41.8137	1.45401	0.727003	+	0.686635i	$0.240913\pi$
$828$	−34.4379	−1.19680
$829$	−14.1421	−0.491177	−0.245588	−	0.969374i	$-0.578981\pi$
$829$	−14.1421	−0.491177	−0.245588	+	0.969374i	$0.578981\pi$
$830$	−2.59580	−0.0901017
$831$	−84.9507	−2.94691
$832$	4.61901	0.160135
$833$	−5.94385	−0.205942
$834$	48.8325	1.69093
$835$	1.89845	0.0656985
$836$	19.1716	0.663063
$837$	−37.6444	−1.30118
$838$	97.5018	3.36814
$839$	43.6883	1.50829	0.754144	−	0.656709i	$-0.228052\pi$
$839$	43.6883	1.50829	0.754144	+	0.656709i	$0.228052\pi$
$840$	3.25948	0.112463
$841$	63.4409	2.18762
$842$	10.5378	0.363157
$843$	41.3845	1.42536
$844$	93.5743	3.22096
$845$	2.45031	0.0842931
$846$	−102.721	−3.53162
$847$	3.41947	0.117494
$848$	−74.0637	−2.54336
$849$	16.2512	0.557739
$850$	−73.7956	−2.53117
$851$	4.88462	0.167443
$852$	54.5117	1.86754
$853$	−55.1457	−1.88815	−0.944077	−	0.329725i	$-0.893044\pi$
$853$	−55.1457	−1.88815	−0.944077	+	0.329725i	$0.893044\pi$
$854$	−1.34995	−0.0461944
$855$	−1.52482	−0.0521478
$856$	106.704	3.64706
$857$	36.9082	1.26076	0.630381	−	0.776286i	$-0.282899\pi$
$857$	36.9082	1.26076	0.630381	+	0.776286i	$0.282899\pi$
$858$	−21.3862	−0.730111
$859$	−1.00000	−0.0341196
$859$	−1.00000	−0.0341196
$860$	−1.05856	−0.0360967
$861$	−22.8202	−0.777712
$862$	87.7200	2.98776
$863$	−16.3077	−0.555122	−0.277561	−	0.960708i	$-0.589526\pi$
$863$	−16.3077	−0.555122	−0.277561	+	0.960708i	$0.589526\pi$
$864$	11.8837	0.404290
$865$	−4.94577	−0.168161
$866$	−12.0495	−0.409458
$867$	−50.1147	−1.70199
$868$	−39.8946	−1.35411
$869$	−22.1391	−0.751016
$870$	−13.7747	−0.467006
$871$	−6.63378	−0.224777
$872$	28.9261	0.979563
$873$	52.5803	1.77957
$874$	7.34399	0.248414
$875$	−2.08266	−0.0704068
$876$	−59.7503	−2.01878
$877$	−41.5690	−1.40369	−0.701843	−	0.712332i	$-0.747639\pi$
$877$	−41.5690	−1.40369	−0.701843	+	0.712332i	$0.747639\pi$
$878$	−36.8930	−1.24508
$879$	24.7661	0.835338
$880$	−3.29790	−0.111172
$881$	−4.54182	−0.153018	−0.0765089	−	0.997069i	$-0.524377\pi$
$881$	−4.54182	−0.153018	−0.0765089	+	0.997069i	$0.524377\pi$
$882$	−11.2110	−0.377493
$883$	23.9835	0.807109	0.403554	−	0.914956i	$-0.367775\pi$
$883$	23.9835	0.807109	0.403554	+	0.914956i	$0.367775\pi$
$884$	28.8183	0.969264
$885$	−4.56550	−0.153467
$886$	17.1715	0.576888
$887$	−53.2639	−1.78843	−0.894213	−	0.447641i	$-0.852264\pi$
$887$	−53.2639	−1.78843	−0.894213	+	0.447641i	$0.852264\pi$
$888$	−42.2860	−1.41903
$889$	9.99040	0.335067
$890$	3.61935	0.121321
$891$	−6.59942	−0.221089
$892$	70.2167	2.35103
$893$	14.9238	0.499406
$894$	39.0542	1.30617
$895$	2.43989	0.0815566
$896$	−16.0943	−0.537671
$897$	−5.58125	−0.186353
$898$	−58.2888	−1.94512
$899$	89.7226	2.99242
$900$	−94.8266	−3.16089
$901$	76.8791	2.56122
$902$	57.5655	1.91672
$903$	3.23644	0.107702
$904$	−51.1428	−1.70098
$905$	0.829385	0.0275697
$906$	−133.239	−4.42656
$907$	35.4499	1.17709	0.588547	−	0.808463i	$-0.299700\pi$
$907$	35.4499	1.17709	0.588547	+	0.808463i	$0.299700\pi$
$908$	−62.3501	−2.06916
$909$	28.2222	0.936073
$910$	0.594276	0.0197001
$911$	−12.0028	−0.397671	−0.198836	−	0.980033i	$-0.563716\pi$
$911$	−12.0028	−0.397671	−0.198836	+	0.980033i	$0.563716\pi$
$912$	−25.5003	−0.844400
$913$	−13.6392	−0.451392
$914$	−40.2706	−1.33203
$915$	−0.308212	−0.0101892
$916$	92.4739	3.05542
$917$	−20.1501	−0.665414
$918$	−60.0632	−1.98238
$919$	−4.51134	−0.148815	−0.0744076	−	0.997228i	$-0.523707\pi$
$919$	−4.51134	−0.148815	−0.0744076	+	0.997228i	$0.523707\pi$
$920$	−2.14580	−0.0707449
$921$	−53.8173	−1.77334
$922$	22.5747	0.743459
$923$	5.28912	0.174093
$924$	32.1819	1.05871
$925$	13.4501	0.442236
$926$	−58.6603	−1.92770
$927$	41.1311	1.35092
$928$	−28.3238	−0.929775
$929$	−30.8423	−1.01190	−0.505951	−	0.862562i	$-0.668858\pi$
$929$	−30.8423	−1.01190	−0.505951	+	0.862562i	$0.668858\pi$
$930$	−13.3697	−0.438408
$931$	1.62878	0.0533812
$932$	−16.3035	−0.534039
$933$	25.9819	0.850610
$934$	15.3001	0.500635
$935$	3.42327	0.111953
$936$	28.9265	0.945492
$937$	25.9207	0.846791	0.423396	−	0.905945i	$-0.360838\pi$
$937$	25.9207	0.846791	0.423396	+	0.905945i	$0.360838\pi$
$938$	14.6526	0.478425
$939$	−18.4368	−0.601664
$940$	−8.19377	−0.267251
$941$	22.6983	0.739943	0.369971	−	0.929043i	$-0.379368\pi$
$941$	22.6983	0.739943	0.369971	+	0.929043i	$0.379368\pi$
$942$	109.703	3.57431
$943$	15.0232	0.489222
$944$	−45.7101	−1.48774
$945$	−0.843827	−0.0274497
$946$	−8.16412	−0.265438
$947$	49.2576	1.60066	0.800329	−	0.599561i	$-0.204658\pi$
$947$	49.2576	1.60066	0.800329	+	0.599561i	$0.204658\pi$
$948$	93.9878	3.05258
$949$	−5.79740	−0.188192
$950$	20.2221	0.656091
$951$	7.60108	0.246482
$952$	−33.8747	−1.09788
$953$	−41.6771	−1.35005	−0.675026	−	0.737794i	$-0.735868\pi$
$953$	−41.6771	−1.35005	−0.675026	+	0.737794i	$0.735868\pi$
$954$	145.005	4.69471
$955$	0.447133	0.0144689
$956$	0.810455	0.0262120
$957$	−72.3768	−2.33961
$958$	−3.94962	−0.127606
$959$	19.8653	0.641485
$960$	−2.32935	−0.0751794
$961$	56.0842	1.80917
$962$	−7.70970	−0.248571
$963$	−83.7925	−2.70018
$964$	110.337	3.55371
$965$	−5.58300	−0.179723
$966$	12.3278	0.396641
$967$	17.7596	0.571111	0.285556	−	0.958362i	$-0.407822\pi$
$967$	17.7596	0.571111	0.285556	+	0.958362i	$0.407822\pi$
$968$	19.4879	0.626365
$969$	26.4697	0.850329
$970$	6.15634	0.197668
$971$	−4.23870	−0.136026	−0.0680132	−	0.997684i	$-0.521666\pi$
$971$	−4.23870	−0.136026	−0.0680132	+	0.997684i	$0.521666\pi$
$972$	79.7532	2.55808
$973$	−7.12987	−0.228573
$974$	100.031	3.20522
$975$	−15.3683	−0.492179
$976$	−3.08584	−0.0987754
$977$	−41.1990	−1.31807	−0.659037	−	0.752111i	$-0.729036\pi$
$977$	−41.1990	−1.31807	−0.659037	+	0.752111i	$0.729036\pi$
$978$	−38.1577	−1.22015
$979$	19.0173	0.607794
$980$	−0.894268	−0.0285663
$981$	−22.7152	−0.725240
$982$	84.0363	2.68171
$983$	−38.9645	−1.24277	−0.621387	−	0.783504i	$-0.713430\pi$
$983$	−38.9645	−1.24277	−0.621387	+	0.783504i	$0.713430\pi$
$984$	−130.055	−4.14601
$985$	−3.89027	−0.123954
$986$	143.156	4.55902
$987$	25.0515	0.797398
$988$	−7.89703	−0.251238
$989$	−2.13063	−0.0677501
$990$	6.45677	0.205210
$991$	−27.2766	−0.866470	−0.433235	−	0.901281i	$-0.642628\pi$
$991$	−27.2766	−0.866470	−0.433235	+	0.901281i	$0.642628\pi$
$992$	−27.4909	−0.872838
$993$	−15.9874	−0.507344
$994$	−11.6826	−0.370548
$995$	0.388460	0.0123150
$996$	57.9030	1.83473
$997$	1.74286	0.0551968	0.0275984	−	0.999619i	$-0.491214\pi$
$997$	1.74286	0.0551968	0.0275984	+	0.999619i	$0.491214\pi$
$998$	54.7500	1.73308
$999$	10.9472	0.346354

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.c.1.8	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.c.1.8	✓	104	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.50501 q^{2} -2.73412 q^{3} +4.27508 q^{4} -0.209181 q^{5} +6.84900 q^{6} -1.00000 q^{7} -5.69911 q^{8} +4.47541 q^{9} +O(q^{10})\)	\(q-2.50501 q^{2} -2.73412 q^{3} +4.27508 q^{4} -0.209181 q^{5} +6.84900 q^{6} -1.00000 q^{7} -5.69911 q^{8} +4.47541 q^{9} +0.524002 q^{10} +2.75328 q^{11} -11.6886 q^{12} -1.13411 q^{13} +2.50501 q^{14} +0.571927 q^{15} +5.72618 q^{16} -5.94385 q^{17} -11.2110 q^{18} +1.62878 q^{19} -0.894268 q^{20} +2.73412 q^{21} -6.89699 q^{22} -1.79994 q^{23} +15.5821 q^{24} -4.95624 q^{25} +2.84096 q^{26} -4.03395 q^{27} -4.27508 q^{28} +9.61462 q^{29} -1.43268 q^{30} +9.33189 q^{31} -2.94591 q^{32} -7.52779 q^{33} +14.8894 q^{34} +0.209181 q^{35} +19.1328 q^{36} -2.71377 q^{37} -4.08012 q^{38} +3.10079 q^{39} +1.19215 q^{40} -8.34647 q^{41} -6.84900 q^{42} +1.18372 q^{43} +11.7705 q^{44} -0.936173 q^{45} +4.50888 q^{46} +9.16255 q^{47} -15.6560 q^{48} +1.00000 q^{49} +12.4154 q^{50} +16.2512 q^{51} -4.84842 q^{52} -12.9342 q^{53} +10.1051 q^{54} -0.575934 q^{55} +5.69911 q^{56} -4.45329 q^{57} -24.0847 q^{58} -7.98266 q^{59} +2.44504 q^{60} -0.538901 q^{61} -23.3765 q^{62} -4.47541 q^{63} -4.07281 q^{64} +0.237235 q^{65} +18.8572 q^{66} +5.84932 q^{67} -25.4105 q^{68} +4.92126 q^{69} -0.524002 q^{70} -4.66367 q^{71} -25.5059 q^{72} +5.11185 q^{73} +6.79801 q^{74} +13.5510 q^{75} +6.96319 q^{76} -2.75328 q^{77} -7.76753 q^{78} -8.04099 q^{79} -1.19781 q^{80} -2.39693 q^{81} +20.9080 q^{82} -4.95381 q^{83} +11.6886 q^{84} +1.24334 q^{85} -2.96524 q^{86} -26.2875 q^{87} -15.6912 q^{88} +6.90714 q^{89} +2.34512 q^{90} +1.13411 q^{91} -7.69491 q^{92} -25.5145 q^{93} -22.9523 q^{94} -0.340711 q^{95} +8.05448 q^{96} +11.7487 q^{97} -2.50501 q^{98} +12.3220 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9}+O(q^{10}) \) 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9	\( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9} + 3 q^{10} - 54 q^{11} - 38 q^{12} + 7 q^{13} + 19 q^{14} - 33 q^{15} + 93 q^{16} - 7 q^{17} - 55 q^{18} - 12 q^{19} - 24 q^{20} + 26 q^{21} - 22 q^{22} - 69 q^{23} + 78 q^{25} - 11 q^{26} - 95 q^{27} - 99 q^{28} - 41 q^{29} - 26 q^{30} - 12 q^{31} - 127 q^{32} - 6 q^{33} - 17 q^{34} - 2 q^{35} + 71 q^{36} - 47 q^{37} - 32 q^{38} - 57 q^{39} + 6 q^{40} + 10 q^{41} - 2 q^{42} - 41 q^{43} - 120 q^{44} + 23 q^{45} - 31 q^{46} - 99 q^{47} - 84 q^{48} + 104 q^{49} - 104 q^{50} - 74 q^{51} + 14 q^{52} - 74 q^{53} + 19 q^{54} - 32 q^{55} + 54 q^{56} - 47 q^{57} - 36 q^{58} - 76 q^{59} - 99 q^{60} + 49 q^{61} - 55 q^{62} - 90 q^{63} + 86 q^{64} - 70 q^{65} + 61 q^{66} - 117 q^{67} - 30 q^{68} + 51 q^{69} - 3 q^{70} - 125 q^{71} - 147 q^{72} - 20 q^{73} - 75 q^{74} - 124 q^{75} + 4 q^{76} + 54 q^{77} - 70 q^{78} - 72 q^{79} - 69 q^{80} + 76 q^{81} - 37 q^{82} - 98 q^{83} + 38 q^{84} - 33 q^{85} - 64 q^{86} - 8 q^{87} - 62 q^{88} - 26 q^{89} + 11 q^{90} - 7 q^{91} - 162 q^{92} - 81 q^{93} + 31 q^{94} - 116 q^{95} + 20 q^{96} - 61 q^{97} - 19 q^{98} - 158 q^{99}+O(q^{100}) \) 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9 + 3 * q^10 - 54 * q^11 - 38 * q^12 + 7 * q^13 + 19 * q^14 - 33 * q^15 + 93 * q^16 - 7 * q^17 - 55 * q^18 - 12 * q^19 - 24 * q^20 + 26 * q^21 - 22 * q^22 - 69 * q^23 + 78 * q^25 - 11 * q^26 - 95 * q^27 - 99 * q^28 - 41 * q^29 - 26 * q^30 - 12 * q^31 - 127 * q^32 - 6 * q^33 - 17 * q^34 - 2 * q^35 + 71 * q^36 - 47 * q^37 - 32 * q^38 - 57 * q^39 + 6 * q^40 + 10 * q^41 - 2 * q^42 - 41 * q^43 - 120 * q^44 + 23 * q^45 - 31 * q^46 - 99 * q^47 - 84 * q^48 + 104 * q^49 - 104 * q^50 - 74 * q^51 + 14 * q^52 - 74 * q^53 + 19 * q^54 - 32 * q^55 + 54 * q^56 - 47 * q^57 - 36 * q^58 - 76 * q^59 - 99 * q^60 + 49 * q^61 - 55 * q^62 - 90 * q^63 + 86 * q^64 - 70 * q^65 + 61 * q^66 - 117 * q^67 - 30 * q^68 + 51 * q^69 - 3 * q^70 - 125 * q^71 - 147 * q^72 - 20 * q^73 - 75 * q^74 - 124 * q^75 + 4 * q^76 + 54 * q^77 - 70 * q^78 - 72 * q^79 - 69 * q^80 + 76 * q^81 - 37 * q^82 - 98 * q^83 + 38 * q^84 - 33 * q^85 - 64 * q^86 - 8 * q^87 - 62 * q^88 - 26 * q^89 + 11 * q^90 - 7 * q^91 - 162 * q^92 - 81 * q^93 + 31 * q^94 - 116 * q^95 + 20 * q^96 - 61 * q^97 - 19 * q^98 - 158 * q^99

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