LMFDB - Embedded newform 6010.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + \cdots - 10 $ x^16 - 8x^15 + 9x^14 + 75x^13 - 178x^12 - 232x^11 + 872x^10 + 228x^9 - 1986x^8 + 164x^7 + 2332x^6 - 440x^5 - 1344x^4 + 244x^3 + 295x^2 - 41*x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$1.84416$ of defining polynomial
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.844163 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.844163 q^{6} -0.532701 q^{7} +1.00000 q^{8} -2.28739 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.844163 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.844163 q^{6} -0.532701 q^{7} +1.00000 q^{8} -2.28739 q^{9} +1.00000 q^{10} -0.961430 q^{11} +0.844163 q^{12} -1.20269 q^{13} -0.532701 q^{14} +0.844163 q^{15} +1.00000 q^{16} -5.49260 q^{17} -2.28739 q^{18} -4.34072 q^{19} +1.00000 q^{20} -0.449687 q^{21} -0.961430 q^{22} +6.60521 q^{23} +0.844163 q^{24} +1.00000 q^{25} -1.20269 q^{26} -4.46342 q^{27} -0.532701 q^{28} -7.33783 q^{29} +0.844163 q^{30} +7.02057 q^{31} +1.00000 q^{32} -0.811604 q^{33} -5.49260 q^{34} -0.532701 q^{35} -2.28739 q^{36} -5.84241 q^{37} -4.34072 q^{38} -1.01527 q^{39} +1.00000 q^{40} +9.20135 q^{41} -0.449687 q^{42} -9.44089 q^{43} -0.961430 q^{44} -2.28739 q^{45} +6.60521 q^{46} -7.28325 q^{47} +0.844163 q^{48} -6.71623 q^{49} +1.00000 q^{50} -4.63665 q^{51} -1.20269 q^{52} +6.24445 q^{53} -4.46342 q^{54} -0.961430 q^{55} -0.532701 q^{56} -3.66427 q^{57} -7.33783 q^{58} -9.77782 q^{59} +0.844163 q^{60} -5.61164 q^{61} +7.02057 q^{62} +1.21849 q^{63} +1.00000 q^{64} -1.20269 q^{65} -0.811604 q^{66} +11.5528 q^{67} -5.49260 q^{68} +5.57587 q^{69} -0.532701 q^{70} -3.84683 q^{71} -2.28739 q^{72} +7.54343 q^{73} -5.84241 q^{74} +0.844163 q^{75} -4.34072 q^{76} +0.512155 q^{77} -1.01527 q^{78} -0.0908517 q^{79} +1.00000 q^{80} +3.09431 q^{81} +9.20135 q^{82} -13.2425 q^{83} -0.449687 q^{84} -5.49260 q^{85} -9.44089 q^{86} -6.19432 q^{87} -0.961430 q^{88} -14.0969 q^{89} -2.28739 q^{90} +0.640674 q^{91} +6.60521 q^{92} +5.92651 q^{93} -7.28325 q^{94} -4.34072 q^{95} +0.844163 q^{96} +8.35252 q^{97} -6.71623 q^{98} +2.19917 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.844163	0.487378	0.243689	−	0.969853i	$-0.421642\pi$
$3$	0.844163	0.487378	0.243689	+	0.969853i	$0.421642\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.844163	0.344628
$7$	−0.532701	−0.201342	−0.100671	−	0.994920i	$-0.532099\pi$
$7$	−0.532701	−0.201342	−0.100671	+	0.994920i	$0.532099\pi$
$8$	1.00000	0.353553
$9$	−2.28739	−0.762463
$10$	1.00000	0.316228
$11$	−0.961430	−0.289882	−0.144941	−	0.989440i	$-0.546299\pi$
$11$	−0.961430	−0.289882	−0.144941	+	0.989440i	$0.546299\pi$
$12$	0.844163	0.243689
$13$	−1.20269	−0.333566	−0.166783	−	0.985994i	$-0.553338\pi$
$13$	−1.20269	−0.333566	−0.166783	+	0.985994i	$0.553338\pi$
$14$	−0.532701	−0.142370
$15$	0.844163	0.217962
$16$	1.00000	0.250000
$17$	−5.49260	−1.33215	−0.666076	−	0.745884i	$-0.732027\pi$
$17$	−5.49260	−1.33215	−0.666076	+	0.745884i	$0.732027\pi$
$18$	−2.28739	−0.539143
$19$	−4.34072	−0.995829	−0.497914	−	0.867226i	$-0.665901\pi$
$19$	−4.34072	−0.995829	−0.497914	+	0.867226i	$0.665901\pi$
$20$	1.00000	0.223607
$21$	−0.449687	−0.0981297
$22$	−0.961430	−0.204978
$23$	6.60521	1.37728	0.688641	−	0.725103i	$-0.258208\pi$
$23$	6.60521	1.37728	0.688641	+	0.725103i	$0.258208\pi$
$24$	0.844163	0.172314
$25$	1.00000	0.200000
$26$	−1.20269	−0.235867
$27$	−4.46342	−0.858985
$28$	−0.532701	−0.100671
$29$	−7.33783	−1.36260	−0.681300	−	0.732004i	$-0.738585\pi$
$29$	−7.33783	−1.36260	−0.681300	+	0.732004i	$0.738585\pi$
$30$	0.844163	0.154122
$31$	7.02057	1.26093	0.630466	−	0.776217i	$-0.282864\pi$
$31$	7.02057	1.26093	0.630466	+	0.776217i	$0.282864\pi$
$32$	1.00000	0.176777
$33$	−0.811604	−0.141282
$34$	−5.49260	−0.941974
$35$	−0.532701	−0.0900429
$36$	−2.28739	−0.381231
$37$	−5.84241	−0.960486	−0.480243	−	0.877136i	$-0.659451\pi$
$37$	−5.84241	−0.960486	−0.480243	+	0.877136i	$0.659451\pi$
$38$	−4.34072	−0.704157
$39$	−1.01527	−0.162573
$40$	1.00000	0.158114
$41$	9.20135	1.43701	0.718504	−	0.695522i	$-0.244827\pi$
$41$	9.20135	1.43701	0.718504	+	0.695522i	$0.244827\pi$
$42$	−0.449687	−0.0693881
$43$	−9.44089	−1.43972	−0.719861	−	0.694118i	$-0.755795\pi$
$43$	−9.44089	−1.43972	−0.719861	+	0.694118i	$0.755795\pi$
$44$	−0.961430	−0.144941
$45$	−2.28739	−0.340984
$46$	6.60521	0.973885
$47$	−7.28325	−1.06237	−0.531186	−	0.847255i	$-0.678253\pi$
$47$	−7.28325	−1.06237	−0.531186	+	0.847255i	$0.678253\pi$
$48$	0.844163	0.121844
$49$	−6.71623	−0.959461
$50$	1.00000	0.141421
$51$	−4.63665	−0.649261
$52$	−1.20269	−0.166783
$53$	6.24445	0.857742	0.428871	−	0.903366i	$-0.358912\pi$
$53$	6.24445	0.857742	0.428871	+	0.903366i	$0.358912\pi$
$54$	−4.46342	−0.607394
$55$	−0.961430	−0.129639
$56$	−0.532701	−0.0711852
$57$	−3.66427	−0.485345
$58$	−7.33783	−0.963504
$59$	−9.77782	−1.27296	−0.636482	−	0.771292i	$-0.719611\pi$
$59$	−9.77782	−1.27296	−0.636482	+	0.771292i	$0.719611\pi$
$60$	0.844163	0.108981
$61$	−5.61164	−0.718497	−0.359249	−	0.933242i	$-0.616967\pi$
$61$	−5.61164	−0.718497	−0.359249	+	0.933242i	$0.616967\pi$
$62$	7.02057	0.891614
$63$	1.21849	0.153516
$64$	1.00000	0.125000
$65$	−1.20269	−0.149175
$66$	−0.811604	−0.0999015
$67$	11.5528	1.41140	0.705700	−	0.708511i	$-0.250633\pi$
$67$	11.5528	1.41140	0.705700	+	0.708511i	$0.250633\pi$
$68$	−5.49260	−0.666076
$69$	5.57587	0.671256
$70$	−0.532701	−0.0636700
$71$	−3.84683	−0.456534	−0.228267	−	0.973599i	$-0.573306\pi$
$71$	−3.84683	−0.456534	−0.228267	+	0.973599i	$0.573306\pi$
$72$	−2.28739	−0.269571
$73$	7.54343	0.882891	0.441446	−	0.897288i	$-0.354466\pi$
$73$	7.54343	0.882891	0.441446	+	0.897288i	$0.354466\pi$
$74$	−5.84241	−0.679166
$75$	0.844163	0.0974755
$76$	−4.34072	−0.497914
$77$	0.512155	0.0583655
$78$	−1.01527	−0.114956
$79$	−0.0908517	−0.0102216	−0.00511081	−	0.999987i	$-0.501627\pi$
$79$	−0.0908517	−0.0102216	−0.00511081	+	0.999987i	$0.501627\pi$
$80$	1.00000	0.111803
$81$	3.09431	0.343813
$82$	9.20135	1.01612
$83$	−13.2425	−1.45355	−0.726775	−	0.686876i	$-0.758982\pi$
$83$	−13.2425	−1.45355	−0.726775	+	0.686876i	$0.758982\pi$
$84$	−0.449687	−0.0490648
$85$	−5.49260	−0.595756
$86$	−9.44089	−1.01804
$87$	−6.19432	−0.664101
$88$	−0.961430	−0.102489
$89$	−14.0969	−1.49426	−0.747132	−	0.664675i	$-0.768570\pi$
$89$	−14.0969	−1.49426	−0.747132	+	0.664675i	$0.768570\pi$
$90$	−2.28739	−0.241112
$91$	0.640674	0.0671609
$92$	6.60521	0.688641
$93$	5.92651	0.614550
$94$	−7.28325	−0.751210
$95$	−4.34072	−0.445348
$96$	0.844163	0.0861570
$97$	8.35252	0.848070	0.424035	−	0.905646i	$-0.360613\pi$
$97$	8.35252	0.848070	0.424035	+	0.905646i	$0.360613\pi$
$98$	−6.71623	−0.678442
$99$	2.19917	0.221024
$100$	1.00000	0.100000
$101$	9.85205	0.980315	0.490158	−	0.871634i	$-0.336939\pi$
$101$	9.85205	0.980315	0.490158	+	0.871634i	$0.336939\pi$
$102$	−4.63665	−0.459097
$103$	−15.3763	−1.51507	−0.757534	−	0.652795i	$-0.773596\pi$
$103$	−15.3763	−1.51507	−0.757534	+	0.652795i	$0.773596\pi$
$104$	−1.20269	−0.117933
$105$	−0.449687	−0.0438849
$106$	6.24445	0.606515
$107$	−4.15714	−0.401886	−0.200943	−	0.979603i	$-0.564401\pi$
$107$	−4.15714	−0.401886	−0.200943	+	0.979603i	$0.564401\pi$
$108$	−4.46342	−0.429493
$109$	−0.609510	−0.0583805	−0.0291902	−	0.999574i	$-0.509293\pi$
$109$	−0.609510	−0.0583805	−0.0291902	+	0.999574i	$0.509293\pi$
$110$	−0.961430	−0.0916688
$111$	−4.93194	−0.468119
$112$	−0.532701	−0.0503355
$113$	−5.36554	−0.504748	−0.252374	−	0.967630i	$-0.581211\pi$
$113$	−5.36554	−0.504748	−0.252374	+	0.967630i	$0.581211\pi$
$114$	−3.66427	−0.343191
$115$	6.60521	0.615939
$116$	−7.33783	−0.681300
$117$	2.75102	0.254332
$118$	−9.77782	−0.900121
$119$	2.92592	0.268218
$120$	0.844163	0.0770612
$121$	−10.0757	−0.915968
$122$	−5.61164	−0.508054
$123$	7.76744	0.700366
$124$	7.02057	0.630466
$125$	1.00000	0.0894427
$126$	1.21849	0.108552
$127$	−5.62604	−0.499231	−0.249615	−	0.968345i	$-0.580304\pi$
$127$	−5.62604	−0.499231	−0.249615	+	0.968345i	$0.580304\pi$
$128$	1.00000	0.0883883
$129$	−7.96965	−0.701689
$130$	−1.20269	−0.105483
$131$	0.518832	0.0453306	0.0226653	−	0.999743i	$-0.492785\pi$
$131$	0.518832	0.0453306	0.0226653	+	0.999743i	$0.492785\pi$
$132$	−0.811604	−0.0706411
$133$	2.31231	0.200502
$134$	11.5528	0.998011
$135$	−4.46342	−0.384150
$136$	−5.49260	−0.470987
$137$	−4.41924	−0.377561	−0.188780	−	0.982019i	$-0.560453\pi$
$137$	−4.41924	−0.377561	−0.188780	+	0.982019i	$0.560453\pi$
$138$	5.57587	0.474650
$139$	−22.4968	−1.90815	−0.954076	−	0.299563i	$-0.903159\pi$
$139$	−22.4968	−1.90815	−0.954076	+	0.299563i	$0.903159\pi$
$140$	−0.532701	−0.0450215
$141$	−6.14825	−0.517776
$142$	−3.84683	−0.322819
$143$	1.15630	0.0966948
$144$	−2.28739	−0.190616
$145$	−7.33783	−0.609373
$146$	7.54343	0.624298
$147$	−5.66959	−0.467620
$148$	−5.84241	−0.480243
$149$	19.7775	1.62023	0.810117	−	0.586268i	$-0.199403\pi$
$149$	19.7775	1.62023	0.810117	+	0.586268i	$0.199403\pi$
$150$	0.844163	0.0689256
$151$	−6.89037	−0.560730	−0.280365	−	0.959893i	$-0.590456\pi$
$151$	−6.89037	−0.560730	−0.280365	+	0.959893i	$0.590456\pi$
$152$	−4.34072	−0.352079
$153$	12.5637	1.01572
$154$	0.512155	0.0412706
$155$	7.02057	0.563906
$156$	−1.01527	−0.0812863
$157$	−6.83852	−0.545774	−0.272887	−	0.962046i	$-0.587978\pi$
$157$	−6.83852	−0.545774	−0.272887	+	0.962046i	$0.587978\pi$
$158$	−0.0908517	−0.00722777
$159$	5.27134	0.418044
$160$	1.00000	0.0790569
$161$	−3.51860	−0.277305
$162$	3.09431	0.243112
$163$	−2.76885	−0.216873	−0.108437	−	0.994103i	$-0.534584\pi$
$163$	−2.76885	−0.216873	−0.108437	+	0.994103i	$0.534584\pi$
$164$	9.20135	0.718504
$165$	−0.811604	−0.0631833
$166$	−13.2425	−1.02782
$167$	−4.26084	−0.329714	−0.164857	−	0.986317i	$-0.552716\pi$
$167$	−4.26084	−0.329714	−0.164857	+	0.986317i	$0.552716\pi$
$168$	−0.449687	−0.0346941
$169$	−11.5535	−0.888734
$170$	−5.49260	−0.421263
$171$	9.92891	0.759283
$172$	−9.44089	−0.719861
$173$	8.79251	0.668482	0.334241	−	0.942488i	$-0.391520\pi$
$173$	8.79251	0.668482	0.334241	+	0.942488i	$0.391520\pi$
$174$	−6.19432	−0.469590
$175$	−0.532701	−0.0402684
$176$	−0.961430	−0.0724705
$177$	−8.25407	−0.620414
$178$	−14.0969	−1.05660
$179$	11.7877	0.881051	0.440525	−	0.897740i	$-0.354792\pi$
$179$	11.7877	0.881051	0.440525	+	0.897740i	$0.354792\pi$
$180$	−2.28739	−0.170492
$181$	24.3416	1.80930	0.904648	−	0.426159i	$-0.140133\pi$
$181$	24.3416	1.80930	0.904648	+	0.426159i	$0.140133\pi$
$182$	0.640674	0.0474899
$183$	−4.73714	−0.350180
$184$	6.60521	0.486942
$185$	−5.84241	−0.429542
$186$	5.92651	0.434553
$187$	5.28076	0.386167
$188$	−7.28325	−0.531186
$189$	2.37767	0.172950
$190$	−4.34072	−0.314909
$191$	12.8086	0.926796	0.463398	−	0.886150i	$-0.346630\pi$
$191$	12.8086	0.926796	0.463398	+	0.886150i	$0.346630\pi$
$192$	0.844163	0.0609222
$193$	20.6520	1.48657	0.743283	−	0.668978i	$-0.233268\pi$
$193$	20.6520	1.48657	0.743283	+	0.668978i	$0.233268\pi$
$194$	8.35252	0.599676
$195$	−1.01527	−0.0727047
$196$	−6.71623	−0.479731
$197$	−12.6133	−0.898659	−0.449329	−	0.893366i	$-0.648337\pi$
$197$	−12.6133	−0.898659	−0.449329	+	0.893366i	$0.648337\pi$
$198$	2.19917	0.156288
$199$	22.9659	1.62801	0.814005	−	0.580858i	$-0.197283\pi$
$199$	22.9659	1.62801	0.814005	+	0.580858i	$0.197283\pi$
$200$	1.00000	0.0707107
$201$	9.75245	0.687885
$202$	9.85205	0.693188
$203$	3.90887	0.274349
$204$	−4.63665	−0.324631
$205$	9.20135	0.642650
$206$	−15.3763	−1.07132
$207$	−15.1087	−1.05013
$208$	−1.20269	−0.0833915
$209$	4.17330	0.288673
$210$	−0.449687	−0.0310313
$211$	−20.3893	−1.40366	−0.701830	−	0.712344i	$-0.747633\pi$
$211$	−20.3893	−1.40366	−0.701830	+	0.712344i	$0.747633\pi$
$212$	6.24445	0.428871
$213$	−3.24735	−0.222505
$214$	−4.15714	−0.284176
$215$	−9.44089	−0.643863
$216$	−4.46342	−0.303697
$217$	−3.73987	−0.253879
$218$	−0.609510	−0.0412812
$219$	6.36788	0.430302
$220$	−0.961430	−0.0648196
$221$	6.60589	0.444360
$222$	−4.93194	−0.331010
$223$	−18.2859	−1.22452	−0.612258	−	0.790658i	$-0.709739\pi$
$223$	−18.2859	−1.22452	−0.612258	+	0.790658i	$0.709739\pi$
$224$	−0.532701	−0.0355926
$225$	−2.28739	−0.152493
$226$	−5.36554	−0.356911
$227$	23.9381	1.58883	0.794414	−	0.607376i	$-0.207778\pi$
$227$	23.9381	1.58883	0.794414	+	0.607376i	$0.207778\pi$
$228$	−3.66427	−0.242672
$229$	23.1069	1.52695	0.763473	−	0.645840i	$-0.223493\pi$
$229$	23.1069	1.52695	0.763473	+	0.645840i	$0.223493\pi$
$230$	6.60521	0.435534
$231$	0.432342	0.0284460
$232$	−7.33783	−0.481752
$233$	10.5496	0.691125	0.345562	−	0.938396i	$-0.387688\pi$
$233$	10.5496	0.691125	0.345562	+	0.938396i	$0.387688\pi$
$234$	2.75102	0.179840
$235$	−7.28325	−0.475107
$236$	−9.77782	−0.636482
$237$	−0.0766937	−0.00498179
$238$	2.92592	0.189659
$239$	2.97603	0.192503	0.0962515	−	0.995357i	$-0.469315\pi$
$239$	2.97603	0.192503	0.0962515	+	0.995357i	$0.469315\pi$
$240$	0.844163	0.0544905
$241$	−22.2492	−1.43320	−0.716600	−	0.697484i	$-0.754303\pi$
$241$	−22.2492	−1.43320	−0.716600	+	0.697484i	$0.754303\pi$
$242$	−10.0757	−0.647687
$243$	16.0024	1.02655
$244$	−5.61164	−0.359249
$245$	−6.71623	−0.429084
$246$	7.76744	0.495234
$247$	5.22053	0.332175
$248$	7.02057	0.445807
$249$	−11.1788	−0.708428
$250$	1.00000	0.0632456
$251$	−12.4001	−0.782689	−0.391344	−	0.920244i	$-0.627990\pi$
$251$	−12.4001	−0.782689	−0.391344	+	0.920244i	$0.627990\pi$
$252$	1.21849	0.0767579
$253$	−6.35045	−0.399249
$254$	−5.62604	−0.353009
$255$	−4.63665	−0.290358
$256$	1.00000	0.0625000
$257$	−2.07976	−0.129732	−0.0648659	−	0.997894i	$-0.520662\pi$
$257$	−2.07976	−0.129732	−0.0648659	+	0.997894i	$0.520662\pi$
$258$	−7.96965	−0.496169
$259$	3.11226	0.193386
$260$	−1.20269	−0.0745876
$261$	16.7845	1.03893
$262$	0.518832	0.0320536
$263$	4.98966	0.307675	0.153838	−	0.988096i	$-0.450837\pi$
$263$	4.98966	0.307675	0.153838	+	0.988096i	$0.450837\pi$
$264$	−0.811604	−0.0499508
$265$	6.24445	0.383594
$266$	2.31231	0.141777
$267$	−11.9001	−0.728271
$268$	11.5528	0.705700
$269$	0.908252	0.0553771	0.0276886	−	0.999617i	$-0.491185\pi$
$269$	0.908252	0.0553771	0.0276886	+	0.999617i	$0.491185\pi$
$270$	−4.46342	−0.271635
$271$	16.6795	1.01321	0.506603	−	0.862180i	$-0.330901\pi$
$271$	16.6795	1.01321	0.506603	+	0.862180i	$0.330901\pi$
$272$	−5.49260	−0.333038
$273$	0.540833	0.0327327
$274$	−4.41924	−0.266976
$275$	−0.961430	−0.0579764
$276$	5.57587	0.335628
$277$	27.1449	1.63098	0.815489	−	0.578772i	$-0.196468\pi$
$277$	27.1449	1.63098	0.815489	+	0.578772i	$0.196468\pi$
$278$	−22.4968	−1.34927
$279$	−16.0588	−0.961414
$280$	−0.532701	−0.0318350
$281$	−15.7002	−0.936595	−0.468297	−	0.883571i	$-0.655132\pi$
$281$	−15.7002	−0.936595	−0.468297	+	0.883571i	$0.655132\pi$
$282$	−6.14825	−0.366123
$283$	17.5279	1.04192	0.520962	−	0.853580i	$-0.325573\pi$
$283$	17.5279	1.04192	0.520962	+	0.853580i	$0.325573\pi$
$284$	−3.84683	−0.228267
$285$	−3.66427	−0.217053
$286$	1.15630	0.0683736
$287$	−4.90157	−0.289330
$288$	−2.28739	−0.134786
$289$	13.1687	0.774628
$290$	−7.33783	−0.430892
$291$	7.05089	0.413330
$292$	7.54343	0.441446
$293$	−27.7763	−1.62271	−0.811355	−	0.584553i	$-0.801270\pi$
$293$	−27.7763	−1.62271	−0.811355	+	0.584553i	$0.801270\pi$
$294$	−5.66959	−0.330657
$295$	−9.77782	−0.569287
$296$	−5.84241	−0.339583
$297$	4.29127	0.249005
$298$	19.7775	1.14568
$299$	−7.94401	−0.459414
$300$	0.844163	0.0487378
$301$	5.02917	0.289877
$302$	−6.89037	−0.396496
$303$	8.31673	0.477784
$304$	−4.34072	−0.248957
$305$	−5.61164	−0.321322
$306$	12.5637	0.718220
$307$	30.2322	1.72545	0.862723	−	0.505677i	$-0.168757\pi$
$307$	30.2322	1.72545	0.862723	+	0.505677i	$0.168757\pi$
$308$	0.512155	0.0291827
$309$	−12.9801	−0.738411
$310$	7.02057	0.398742
$311$	12.3450	0.700021	0.350011	−	0.936746i	$-0.386178\pi$
$311$	12.3450	0.700021	0.350011	+	0.936746i	$0.386178\pi$
$312$	−1.01527	−0.0574781
$313$	−31.9710	−1.80711	−0.903554	−	0.428474i	$-0.859051\pi$
$313$	−31.9710	−1.80711	−0.903554	+	0.428474i	$0.859051\pi$
$314$	−6.83852	−0.385920
$315$	1.21849	0.0686544
$316$	−0.0908517	−0.00511081
$317$	−8.44300	−0.474206	−0.237103	−	0.971485i	$-0.576198\pi$
$317$	−8.44300	−0.474206	−0.237103	+	0.971485i	$0.576198\pi$
$318$	5.27134	0.295602
$319$	7.05481	0.394993
$320$	1.00000	0.0559017
$321$	−3.50930	−0.195870
$322$	−3.51860	−0.196084
$323$	23.8418	1.32660
$324$	3.09431	0.171906
$325$	−1.20269	−0.0667132
$326$	−2.76885	−0.153352
$327$	−0.514526	−0.0284533
$328$	9.20135	0.508059
$329$	3.87980	0.213900
$330$	−0.811604	−0.0446773
$331$	16.6072	0.912815	0.456408	−	0.889771i	$-0.349136\pi$
$331$	16.6072	0.912815	0.456408	+	0.889771i	$0.349136\pi$
$332$	−13.2425	−0.726775
$333$	13.3639	0.732335
$334$	−4.26084	−0.233143
$335$	11.5528	0.631197
$336$	−0.449687	−0.0245324
$337$	−14.1086	−0.768543	−0.384272	−	0.923220i	$-0.625547\pi$
$337$	−14.1086	−0.768543	−0.384272	+	0.923220i	$0.625547\pi$
$338$	−11.5535	−0.628430
$339$	−4.52939	−0.246003
$340$	−5.49260	−0.297878
$341$	−6.74979	−0.365522
$342$	9.92891	0.536894
$343$	7.30665	0.394522
$344$	−9.44089	−0.509019
$345$	5.57587	0.300195
$346$	8.79251	0.472688
$347$	−33.9642	−1.82329	−0.911647	−	0.410975i	$-0.865188\pi$
$347$	−33.9642	−1.82329	−0.911647	+	0.410975i	$0.865188\pi$
$348$	−6.19432	−0.332050
$349$	13.0855	0.700453	0.350227	−	0.936665i	$-0.386105\pi$
$349$	13.0855	0.700453	0.350227	+	0.936665i	$0.386105\pi$
$350$	−0.532701	−0.0284741
$351$	5.36810	0.286528
$352$	−0.961430	−0.0512444
$353$	−16.0428	−0.853873	−0.426936	−	0.904282i	$-0.640407\pi$
$353$	−16.0428	−0.853873	−0.426936	+	0.904282i	$0.640407\pi$
$354$	−8.25407	−0.438699
$355$	−3.84683	−0.204168
$356$	−14.0969	−0.747132
$357$	2.46995	0.130724
$358$	11.7877	0.622997
$359$	0.802407	0.0423494	0.0211747	−	0.999776i	$-0.493259\pi$
$359$	0.802407	0.0423494	0.0211747	+	0.999776i	$0.493259\pi$
$360$	−2.28739	−0.120556
$361$	−0.158171	−0.00832478
$362$	24.3416	1.27937
$363$	−8.50549	−0.446423
$364$	0.640674	0.0335804
$365$	7.54343	0.394841
$366$	−4.73714	−0.247614
$367$	7.01696	0.366282	0.183141	−	0.983087i	$-0.441373\pi$
$367$	7.01696	0.366282	0.183141	+	0.983087i	$0.441373\pi$
$368$	6.60521	0.344320
$369$	−21.0471	−1.09567
$370$	−5.84241	−0.303732
$371$	−3.32643	−0.172700
$372$	5.92651	0.307275
$373$	14.4241	0.746854	0.373427	−	0.927660i	$-0.378183\pi$
$373$	14.4241	0.746854	0.373427	+	0.927660i	$0.378183\pi$
$374$	5.28076	0.273061
$375$	0.844163	0.0435924
$376$	−7.28325	−0.375605
$377$	8.82512	0.454517
$378$	2.37767	0.122294
$379$	−0.642511	−0.0330036	−0.0165018	−	0.999864i	$-0.505253\pi$
$379$	−0.642511	−0.0330036	−0.0165018	+	0.999864i	$0.505253\pi$
$380$	−4.34072	−0.222674
$381$	−4.74930	−0.243314
$382$	12.8086	0.655344
$383$	−8.96481	−0.458080	−0.229040	−	0.973417i	$-0.573559\pi$
$383$	−8.96481	−0.458080	−0.229040	+	0.973417i	$0.573559\pi$
$384$	0.844163	0.0430785
$385$	0.512155	0.0261018
$386$	20.6520	1.05116
$387$	21.5950	1.09773
$388$	8.35252	0.424035
$389$	37.1210	1.88211	0.941054	−	0.338257i	$-0.109837\pi$
$389$	37.1210	1.88211	0.941054	+	0.338257i	$0.109837\pi$
$390$	−1.01527	−0.0514100
$391$	−36.2798	−1.83475
$392$	−6.71623	−0.339221
$393$	0.437979	0.0220931
$394$	−12.6133	−0.635448
$395$	−0.0908517	−0.00457125
$396$	2.19917	0.110512
$397$	−19.5965	−0.983522	−0.491761	−	0.870730i	$-0.663647\pi$
$397$	−19.5965	−0.983522	−0.491761	+	0.870730i	$0.663647\pi$
$398$	22.9659	1.15118
$399$	1.95196	0.0977203
$400$	1.00000	0.0500000
$401$	−15.5264	−0.775351	−0.387676	−	0.921796i	$-0.626722\pi$
$401$	−15.5264	−0.775351	−0.387676	+	0.921796i	$0.626722\pi$
$402$	9.75245	0.486408
$403$	−8.44357	−0.420604
$404$	9.85205	0.490158
$405$	3.09431	0.153758
$406$	3.90887	0.193994
$407$	5.61707	0.278428
$408$	−4.63665	−0.229548
$409$	−24.6582	−1.21927	−0.609636	−	0.792682i	$-0.708684\pi$
$409$	−24.6582	−1.21927	−0.609636	+	0.792682i	$0.708684\pi$
$410$	9.20135	0.454422
$411$	−3.73056	−0.184015
$412$	−15.3763	−0.757534
$413$	5.20866	0.256301
$414$	−15.1087	−0.742551
$415$	−13.2425	−0.650047
$416$	−1.20269	−0.0589667
$417$	−18.9910	−0.929991
$418$	4.17330	0.204123
$419$	−17.9818	−0.878470	−0.439235	−	0.898372i	$-0.644750\pi$
$419$	−17.9818	−0.878470	−0.439235	+	0.898372i	$0.644750\pi$
$420$	−0.449687	−0.0219425
$421$	0.752344	0.0366670	0.0183335	−	0.999832i	$-0.494164\pi$
$421$	0.752344	0.0366670	0.0183335	+	0.999832i	$0.494164\pi$
$422$	−20.3893	−0.992538
$423$	16.6596	0.810019
$424$	6.24445	0.303258
$425$	−5.49260	−0.266430
$426$	−3.24735	−0.157335
$427$	2.98933	0.144664
$428$	−4.15714	−0.200943
$429$	0.976107	0.0471269
$430$	−9.44089	−0.455280
$431$	20.3211	0.978832	0.489416	−	0.872050i	$-0.337210\pi$
$431$	20.3211	0.978832	0.489416	+	0.872050i	$0.337210\pi$
$432$	−4.46342	−0.214746
$433$	−33.7894	−1.62381	−0.811907	−	0.583787i	$-0.801570\pi$
$433$	−33.7894	−1.62381	−0.811907	+	0.583787i	$0.801570\pi$
$434$	−3.73987	−0.179519
$435$	−6.19432	−0.296995
$436$	−0.609510	−0.0291902
$437$	−28.6713	−1.37154
$438$	6.36788	0.304269
$439$	−22.3552	−1.06696	−0.533478	−	0.845814i	$-0.679115\pi$
$439$	−22.3552	−1.06696	−0.533478	+	0.845814i	$0.679115\pi$
$440$	−0.961430	−0.0458344
$441$	15.3626	0.731554
$442$	6.60589	0.314210
$443$	21.2089	1.00766	0.503832	−	0.863802i	$-0.331923\pi$
$443$	21.2089	1.00766	0.503832	+	0.863802i	$0.331923\pi$
$444$	−4.93194	−0.234060
$445$	−14.0969	−0.668256
$446$	−18.2859	−0.865863
$447$	16.6954	0.789666
$448$	−0.532701	−0.0251678
$449$	−24.8674	−1.17356	−0.586782	−	0.809745i	$-0.699606\pi$
$449$	−24.8674	−1.17356	−0.586782	+	0.809745i	$0.699606\pi$
$450$	−2.28739	−0.107829
$451$	−8.84645	−0.416563
$452$	−5.36554	−0.252374
$453$	−5.81659	−0.273287
$454$	23.9381	1.12347
$455$	0.640674	0.0300352
$456$	−3.66427	−0.171595
$457$	38.5370	1.80268	0.901342	−	0.433109i	$-0.142583\pi$
$457$	38.5370	1.80268	0.901342	+	0.433109i	$0.142583\pi$
$458$	23.1069	1.07971
$459$	24.5158	1.14430
$460$	6.60521	0.307969
$461$	14.0184	0.652903	0.326451	−	0.945214i	$-0.394147\pi$
$461$	14.0184	0.652903	0.326451	+	0.945214i	$0.394147\pi$
$462$	0.432342	0.0201144
$463$	33.7519	1.56858	0.784291	−	0.620393i	$-0.213027\pi$
$463$	33.7519	1.56858	0.784291	+	0.620393i	$0.213027\pi$
$464$	−7.33783	−0.340650
$465$	5.92651	0.274835
$466$	10.5496	0.488699
$467$	37.4995	1.73527	0.867635	−	0.497201i	$-0.165639\pi$
$467$	37.4995	1.73527	0.867635	+	0.497201i	$0.165639\pi$
$468$	2.75102	0.127166
$469$	−6.15419	−0.284174
$470$	−7.28325	−0.335951
$471$	−5.77283	−0.265998
$472$	−9.77782	−0.450061
$473$	9.07676	0.417350
$474$	−0.0766937	−0.00352266
$475$	−4.34072	−0.199166
$476$	2.92592	0.134109
$477$	−14.2835	−0.653996
$478$	2.97603	0.136120
$479$	−31.2817	−1.42930	−0.714648	−	0.699484i	$-0.753413\pi$
$479$	−31.2817	−1.42930	−0.714648	+	0.699484i	$0.753413\pi$
$480$	0.844163	0.0385306
$481$	7.02660	0.320385
$482$	−22.2492	−1.01343
$483$	−2.97027	−0.135152
$484$	−10.0757	−0.457984
$485$	8.35252	0.379268
$486$	16.0024	0.725882
$487$	9.32490	0.422552	0.211276	−	0.977426i	$-0.432238\pi$
$487$	9.32490	0.422552	0.211276	+	0.977426i	$0.432238\pi$
$488$	−5.61164	−0.254027
$489$	−2.33736	−0.105699
$490$	−6.71623	−0.303408
$491$	34.9844	1.57882	0.789412	−	0.613863i	$-0.210385\pi$
$491$	34.9844	1.57882	0.789412	+	0.613863i	$0.210385\pi$
$492$	7.76744	0.350183
$493$	40.3038	1.81519
$494$	5.22053	0.234883
$495$	2.19917	0.0988451
$496$	7.02057	0.315233
$497$	2.04921	0.0919196
$498$	−11.1788	−0.500934
$499$	−37.5728	−1.68199	−0.840995	−	0.541043i	$-0.818030\pi$
$499$	−37.5728	−1.68199	−0.840995	+	0.541043i	$0.818030\pi$
$500$	1.00000	0.0447214
$501$	−3.59685	−0.160695
$502$	−12.4001	−0.553445
$503$	19.0226	0.848176	0.424088	−	0.905621i	$-0.360595\pi$
$503$	19.0226	0.848176	0.424088	+	0.905621i	$0.360595\pi$
$504$	1.21849	0.0542761
$505$	9.85205	0.438410
$506$	−6.35045	−0.282312
$507$	−9.75307	−0.433149
$508$	−5.62604	−0.249615
$509$	28.1930	1.24963	0.624816	−	0.780772i	$-0.285174\pi$
$509$	28.1930	1.24963	0.624816	+	0.780772i	$0.285174\pi$
$510$	−4.63665	−0.205314
$511$	−4.01839	−0.177763
$512$	1.00000	0.0441942
$513$	19.3744	0.855402
$514$	−2.07976	−0.0917342
$515$	−15.3763	−0.677559
$516$	−7.96965	−0.350844
$517$	7.00234	0.307963
$518$	3.11226	0.136745
$519$	7.42231	0.325803
$520$	−1.20269	−0.0527414
$521$	−13.1659	−0.576808	−0.288404	−	0.957509i	$-0.593125\pi$
$521$	−13.1659	−0.576808	−0.288404	+	0.957509i	$0.593125\pi$
$522$	16.7845	0.734636
$523$	16.5833	0.725136	0.362568	−	0.931957i	$-0.381900\pi$
$523$	16.5833	0.725136	0.362568	+	0.931957i	$0.381900\pi$
$524$	0.518832	0.0226653
$525$	−0.449687	−0.0196259
$526$	4.98966	0.217559
$527$	−38.5612	−1.67975
$528$	−0.811604	−0.0353205
$529$	20.6288	0.896903
$530$	6.24445	0.271242
$531$	22.3657	0.970588
$532$	2.31231	0.100251
$533$	−11.0664	−0.479337
$534$	−11.9001	−0.514966
$535$	−4.15714	−0.179729
$536$	11.5528	0.499005
$537$	9.95070	0.429404
$538$	0.908252	0.0391575
$539$	6.45719	0.278131
$540$	−4.46342	−0.192075
$541$	−5.59725	−0.240644	−0.120322	−	0.992735i	$-0.538393\pi$
$541$	−5.59725	−0.240644	−0.120322	+	0.992735i	$0.538393\pi$
$542$	16.6795	0.716445
$543$	20.5483	0.881811
$544$	−5.49260	−0.235493
$545$	−0.609510	−0.0261085
$546$	0.540833	0.0231455
$547$	30.5086	1.30445	0.652227	−	0.758024i	$-0.273835\pi$
$547$	30.5086	1.30445	0.652227	+	0.758024i	$0.273835\pi$
$548$	−4.41924	−0.188780
$549$	12.8360	0.547827
$550$	−0.961430	−0.0409955
$551$	31.8514	1.35692
$552$	5.57587	0.237325
$553$	0.0483968	0.00205804
$554$	27.1449	1.15328
$555$	−4.93194	−0.209349
$556$	−22.4968	−0.954076
$557$	−15.7133	−0.665793	−0.332896	−	0.942963i	$-0.608026\pi$
$557$	−15.7133	−0.665793	−0.332896	+	0.942963i	$0.608026\pi$
$558$	−16.0588	−0.679822
$559$	11.3545	0.480242
$560$	−0.532701	−0.0225107
$561$	4.45782	0.188209
$562$	−15.7002	−0.662273
$563$	−31.9893	−1.34819	−0.674093	−	0.738646i	$-0.735465\pi$
$563$	−31.9893	−1.34819	−0.674093	+	0.738646i	$0.735465\pi$
$564$	−6.14825	−0.258888
$565$	−5.36554	−0.225730
$566$	17.5279	0.736751
$567$	−1.64834	−0.0692240
$568$	−3.84683	−0.161409
$569$	−18.2157	−0.763643	−0.381821	−	0.924236i	$-0.624703\pi$
$569$	−18.2157	−0.763643	−0.381821	+	0.924236i	$0.624703\pi$
$570$	−3.66427	−0.153480
$571$	28.0809	1.17515	0.587575	−	0.809170i	$-0.300083\pi$
$571$	28.0809	1.17515	0.587575	+	0.809170i	$0.300083\pi$
$572$	1.15630	0.0483474
$573$	10.8125	0.451700
$574$	−4.90157	−0.204587
$575$	6.60521	0.275456
$576$	−2.28739	−0.0953079
$577$	−16.4558	−0.685062	−0.342531	−	0.939506i	$-0.611284\pi$
$577$	−16.4558	−0.685062	−0.342531	+	0.939506i	$0.611284\pi$
$578$	13.1687	0.547745
$579$	17.4337	0.724519
$580$	−7.33783	−0.304687
$581$	7.05428	0.292661
$582$	7.05089	0.292269
$583$	−6.00361	−0.248644
$584$	7.54343	0.312149
$585$	2.75102	0.113741
$586$	−27.7763	−1.14743
$587$	−2.02510	−0.0835848	−0.0417924	−	0.999126i	$-0.513307\pi$
$587$	−2.02510	−0.0835848	−0.0417924	+	0.999126i	$0.513307\pi$
$588$	−5.66959	−0.233810
$589$	−30.4743	−1.25567
$590$	−9.77782	−0.402547
$591$	−10.6477	−0.437986
$592$	−5.84241	−0.240121
$593$	8.40701	0.345234	0.172617	−	0.984989i	$-0.444778\pi$
$593$	8.40701	0.345234	0.172617	+	0.984989i	$0.444778\pi$
$594$	4.29127	0.176073
$595$	2.92592	0.119951
$596$	19.7775	0.810117
$597$	19.3870	0.793456
$598$	−7.94401	−0.324855
$599$	20.3150	0.830049	0.415024	−	0.909810i	$-0.363773\pi$
$599$	20.3150	0.830049	0.415024	+	0.909810i	$0.363773\pi$
$600$	0.844163	0.0344628
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	5.02917	0.204974
$603$	−26.4258	−1.07614
$604$	−6.89037	−0.280365
$605$	−10.0757	−0.409633
$606$	8.31673	0.337844
$607$	−5.70283	−0.231471	−0.115735	−	0.993280i	$-0.536922\pi$
$607$	−5.70283	−0.231471	−0.115735	+	0.993280i	$0.536922\pi$
$608$	−4.34072	−0.176039
$609$	3.29972	0.133711
$610$	−5.61164	−0.227209
$611$	8.75949	0.354371
$612$	12.5637	0.507858
$613$	−32.3291	−1.30576	−0.652880	−	0.757461i	$-0.726440\pi$
$613$	−32.3291	−1.30576	−0.652880	+	0.757461i	$0.726440\pi$
$614$	30.2322	1.22007
$615$	7.76744	0.313213
$616$	0.512155	0.0206353
$617$	−32.7379	−1.31798	−0.658990	−	0.752152i	$-0.729016\pi$
$617$	−32.7379	−1.31798	−0.658990	+	0.752152i	$0.729016\pi$
$618$	−12.9801	−0.522135
$619$	15.0430	0.604629	0.302315	−	0.953208i	$-0.402241\pi$
$619$	15.0430	0.604629	0.302315	+	0.953208i	$0.402241\pi$
$620$	7.02057	0.281953
$621$	−29.4818	−1.18306
$622$	12.3450	0.494990
$623$	7.50942	0.300858
$624$	−1.01527	−0.0406431
$625$	1.00000	0.0400000
$626$	−31.9710	−1.27782
$627$	3.52294	0.140693
$628$	−6.83852	−0.272887
$629$	32.0900	1.27951
$630$	1.21849	0.0485460
$631$	−6.39353	−0.254522	−0.127261	−	0.991869i	$-0.540619\pi$
$631$	−6.39353	−0.254522	−0.127261	+	0.991869i	$0.540619\pi$
$632$	−0.0908517	−0.00361389
$633$	−17.2119	−0.684113
$634$	−8.44300	−0.335314
$635$	−5.62604	−0.223263
$636$	5.27134	0.209022
$637$	8.07753	0.320044
$638$	7.05481	0.279303
$639$	8.79919	0.348091
$640$	1.00000	0.0395285
$641$	−0.779702	−0.0307964	−0.0153982	−	0.999881i	$-0.504902\pi$
$641$	−0.779702	−0.0307964	−0.0153982	+	0.999881i	$0.504902\pi$
$642$	−3.50930	−0.138501
$643$	−4.27884	−0.168741	−0.0843705	−	0.996434i	$-0.526888\pi$
$643$	−4.27884	−0.168741	−0.0843705	+	0.996434i	$0.526888\pi$
$644$	−3.51860	−0.138652
$645$	−7.96965	−0.313805
$646$	23.8418	0.938045
$647$	19.4922	0.766316	0.383158	−	0.923683i	$-0.374836\pi$
$647$	19.4922	0.766316	0.383158	+	0.923683i	$0.374836\pi$
$648$	3.09431	0.121556
$649$	9.40069	0.369010
$650$	−1.20269	−0.0471733
$651$	−3.15706	−0.123735
$652$	−2.76885	−0.108437
$653$	−39.2685	−1.53669	−0.768347	−	0.640034i	$-0.778920\pi$
$653$	−39.2685	−1.53669	−0.768347	+	0.640034i	$0.778920\pi$
$654$	−0.514526	−0.0201196
$655$	0.518832	0.0202725
$656$	9.20135	0.359252
$657$	−17.2548	−0.673172
$658$	3.87980	0.151250
$659$	27.5689	1.07393	0.536966	−	0.843604i	$-0.319570\pi$
$659$	27.5689	1.07393	0.536966	+	0.843604i	$0.319570\pi$
$660$	−0.811604	−0.0315916
$661$	10.0809	0.392101	0.196050	−	0.980594i	$-0.437188\pi$
$661$	10.0809	0.392101	0.196050	+	0.980594i	$0.437188\pi$
$662$	16.6072	0.645458
$663$	5.57645	0.216571
$664$	−13.2425	−0.513908
$665$	2.31231	0.0896673
$666$	13.3639	0.517839
$667$	−48.4679	−1.87668
$668$	−4.26084	−0.164857
$669$	−15.4363	−0.596802
$670$	11.5528	0.446324
$671$	5.39520	0.208280
$672$	−0.449687	−0.0173470
$673$	−20.8497	−0.803698	−0.401849	−	0.915706i	$-0.631632\pi$
$673$	−20.8497	−0.803698	−0.401849	+	0.915706i	$0.631632\pi$
$674$	−14.1086	−0.543442
$675$	−4.46342	−0.171797
$676$	−11.5535	−0.444367
$677$	32.6106	1.25333	0.626664	−	0.779290i	$-0.284420\pi$
$677$	32.6106	1.25333	0.626664	+	0.779290i	$0.284420\pi$
$678$	−4.52939	−0.173950
$679$	−4.44940	−0.170752
$680$	−5.49260	−0.210632
$681$	20.2077	0.774360
$682$	−6.74979	−0.258463
$683$	−37.6401	−1.44026	−0.720129	−	0.693840i	$-0.755917\pi$
$683$	−37.6401	−1.44026	−0.720129	+	0.693840i	$0.755917\pi$
$684$	9.92891	0.379641
$685$	−4.41924	−0.168850
$686$	7.30665	0.278969
$687$	19.5060	0.744200
$688$	−9.44089	−0.359931
$689$	−7.51014	−0.286113
$690$	5.57587	0.212270
$691$	−43.6848	−1.66185	−0.830923	−	0.556387i	$-0.812187\pi$
$691$	−43.6848	−1.66185	−0.830923	+	0.556387i	$0.812187\pi$
$692$	8.79251	0.334241
$693$	−1.17150	−0.0445015
$694$	−33.9642	−1.28926
$695$	−22.4968	−0.853352
$696$	−6.19432	−0.234795
$697$	−50.5393	−1.91431
$698$	13.0855	0.495295
$699$	8.90555	0.336839
$700$	−0.532701	−0.0201342
$701$	−46.4998	−1.75627	−0.878137	−	0.478410i	$-0.841213\pi$
$701$	−46.4998	−1.75627	−0.878137	+	0.478410i	$0.841213\pi$
$702$	5.36810	0.202606
$703$	25.3602	0.956480
$704$	−0.961430	−0.0362353
$705$	−6.14825	−0.231557
$706$	−16.0428	−0.603779
$707$	−5.24820	−0.197379
$708$	−8.25407	−0.310207
$709$	31.5037	1.18315	0.591574	−	0.806251i	$-0.298507\pi$
$709$	31.5037	1.18315	0.591574	+	0.806251i	$0.298507\pi$
$710$	−3.84683	−0.144369
$711$	0.207813	0.00779360
$712$	−14.0969	−0.528302
$713$	46.3723	1.73666
$714$	2.46995	0.0924355
$715$	1.15630	0.0432432
$716$	11.7877	0.440525
$717$	2.51225	0.0938217
$718$	0.802407	0.0299455
$719$	−40.2451	−1.50089	−0.750444	−	0.660934i	$-0.770160\pi$
$719$	−40.2451	−1.50089	−0.750444	+	0.660934i	$0.770160\pi$
$720$	−2.28739	−0.0852459
$721$	8.19096	0.305047
$722$	−0.158171	−0.00588651
$723$	−18.7820	−0.698510
$724$	24.3416	0.904648
$725$	−7.33783	−0.272520
$726$	−8.50549	−0.315668
$727$	29.2020	1.08304	0.541522	−	0.840687i	$-0.317848\pi$
$727$	29.2020	1.08304	0.541522	+	0.840687i	$0.317848\pi$
$728$	0.640674	0.0237449
$729$	4.22566	0.156506
$730$	7.54343	0.279195
$731$	51.8551	1.91793
$732$	−4.73714	−0.175090
$733$	−42.4811	−1.56908	−0.784538	−	0.620080i	$-0.787100\pi$
$733$	−42.4811	−1.56908	−0.784538	+	0.620080i	$0.787100\pi$
$734$	7.01696	0.259001
$735$	−5.66959	−0.209126
$736$	6.60521	0.243471
$737$	−11.1072	−0.409140
$738$	−21.0471	−0.774753
$739$	11.0192	0.405346	0.202673	−	0.979246i	$-0.435037\pi$
$739$	11.0192	0.405346	0.202673	+	0.979246i	$0.435037\pi$
$740$	−5.84241	−0.214771
$741$	4.40698	0.161894
$742$	−3.32643	−0.122117
$743$	35.5120	1.30281	0.651404	−	0.758731i	$-0.274180\pi$
$743$	35.5120	1.30281	0.651404	+	0.758731i	$0.274180\pi$
$744$	5.92651	0.217276
$745$	19.7775	0.724591
$746$	14.4241	0.528106
$747$	30.2907	1.10828
$748$	5.28076	0.193084
$749$	2.21451	0.0809165
$750$	0.844163	0.0308245
$751$	−44.2767	−1.61568	−0.807840	−	0.589402i	$-0.799364\pi$
$751$	−44.2767	−1.61568	−0.807840	+	0.589402i	$0.799364\pi$
$752$	−7.28325	−0.265593
$753$	−10.4677	−0.381465
$754$	8.82512	0.321392
$755$	−6.89037	−0.250766
$756$	2.37767	0.0864749
$757$	17.9051	0.650771	0.325386	−	0.945581i	$-0.394506\pi$
$757$	17.9051	0.650771	0.325386	+	0.945581i	$0.394506\pi$
$758$	−0.642511	−0.0233371
$759$	−5.36081	−0.194585
$760$	−4.34072	−0.157454
$761$	−6.96672	−0.252543	−0.126272	−	0.991996i	$-0.540301\pi$
$761$	−6.96672	−0.252543	−0.126272	+	0.991996i	$0.540301\pi$
$762$	−4.74930	−0.172049
$763$	0.324687	0.0117544
$764$	12.8086	0.463398
$765$	12.5637	0.454242
$766$	−8.96481	−0.323912
$767$	11.7597	0.424617
$768$	0.844163	0.0304611
$769$	−22.6634	−0.817265	−0.408632	−	0.912699i	$-0.633994\pi$
$769$	−22.6634	−0.817265	−0.408632	+	0.912699i	$0.633994\pi$
$770$	0.512155	0.0184568
$771$	−1.75565	−0.0632284
$772$	20.6520	0.743283
$773$	40.9769	1.47384	0.736918	−	0.675982i	$-0.236280\pi$
$773$	40.9769	1.47384	0.736918	+	0.675982i	$0.236280\pi$
$774$	21.5950	0.776216
$775$	7.02057	0.252186
$776$	8.35252	0.299838
$777$	2.62725	0.0942521
$778$	37.1210	1.33085
$779$	−39.9404	−1.43101
$780$	−1.01527	−0.0363523
$781$	3.69846	0.132341
$782$	−36.2798	−1.29736
$783$	32.7518	1.17045
$784$	−6.71623	−0.239865
$785$	−6.83852	−0.244077
$786$	0.437979	0.0156222
$787$	0.254953	0.00908809	0.00454404	−	0.999990i	$-0.498554\pi$
$787$	0.254953	0.00908809	0.00454404	+	0.999990i	$0.498554\pi$
$788$	−12.6133	−0.449329
$789$	4.21208	0.149954
$790$	−0.0908517	−0.00323236
$791$	2.85823	0.101627
$792$	2.19917	0.0781439
$793$	6.74906	0.239666
$794$	−19.5965	−0.695455
$795$	5.27134	0.186955
$796$	22.9659	0.814005
$797$	30.3945	1.07663	0.538313	−	0.842745i	$-0.319062\pi$
$797$	30.3945	1.07663	0.538313	+	0.842745i	$0.319062\pi$
$798$	1.95196	0.0690987
$799$	40.0040	1.41524
$800$	1.00000	0.0353553
$801$	32.2450	1.13932
$802$	−15.5264	−0.548256
$803$	−7.25248	−0.255934
$804$	9.75245	0.343942
$805$	−3.51860	−0.124014
$806$	−8.44357	−0.297412
$807$	0.766713	0.0269896
$808$	9.85205	0.346594
$809$	−54.6837	−1.92258	−0.961289	−	0.275543i	$-0.911142\pi$
$809$	−54.6837	−1.92258	−0.961289	+	0.275543i	$0.911142\pi$
$810$	3.09431	0.108723
$811$	−25.5682	−0.897819	−0.448910	−	0.893577i	$-0.648188\pi$
$811$	−25.5682	−0.897819	−0.448910	+	0.893577i	$0.648188\pi$
$812$	3.90887	0.137174
$813$	14.0802	0.493814
$814$	5.61707	0.196878
$815$	−2.76885	−0.0969886
$816$	−4.63665	−0.162315
$817$	40.9802	1.43372
$818$	−24.6582	−0.862155
$819$	−1.46547	−0.0512077
$820$	9.20135	0.321325
$821$	−19.6687	−0.686441	−0.343221	−	0.939255i	$-0.611518\pi$
$821$	−19.6687	−0.686441	−0.343221	+	0.939255i	$0.611518\pi$
$822$	−3.73056	−0.130118
$823$	−1.93117	−0.0673163	−0.0336582	−	0.999433i	$-0.510716\pi$
$823$	−1.93117	−0.0673163	−0.0336582	+	0.999433i	$0.510716\pi$
$824$	−15.3763	−0.535658
$825$	−0.811604	−0.0282564
$826$	5.20866	0.181232
$827$	−40.2192	−1.39856	−0.699280	−	0.714848i	$-0.746496\pi$
$827$	−40.2192	−1.39856	−0.699280	+	0.714848i	$0.746496\pi$
$828$	−15.1087	−0.525063
$829$	20.8718	0.724907	0.362454	−	0.932002i	$-0.381939\pi$
$829$	20.8718	0.724907	0.362454	+	0.932002i	$0.381939\pi$
$830$	−13.2425	−0.459653
$831$	22.9147	0.794903
$832$	−1.20269	−0.0416957
$833$	36.8896	1.27815
$834$	−18.9910	−0.657603
$835$	−4.26084	−0.147453
$836$	4.17330	0.144337
$837$	−31.3358	−1.08312
$838$	−17.9818	−0.621172
$839$	−13.1018	−0.452325	−0.226162	−	0.974090i	$-0.572618\pi$
$839$	−13.1018	−0.452325	−0.226162	+	0.974090i	$0.572618\pi$
$840$	−0.449687	−0.0155157
$841$	24.8437	0.856679
$842$	0.752344	0.0259275
$843$	−13.2535	−0.456476
$844$	−20.3893	−0.701830
$845$	−11.5535	−0.397454
$846$	16.6596	0.572770
$847$	5.36731	0.184423
$848$	6.24445	0.214435
$849$	14.7964	0.507810
$850$	−5.49260	−0.188395
$851$	−38.5903	−1.32286
$852$	−3.24735	−0.111252
$853$	10.5851	0.362426	0.181213	−	0.983444i	$-0.441998\pi$
$853$	10.5851	0.362426	0.181213	+	0.983444i	$0.441998\pi$
$854$	2.98933	0.102293
$855$	9.92891	0.339562
$856$	−4.15714	−0.142088
$857$	−49.1792	−1.67993	−0.839964	−	0.542642i	$-0.817424\pi$
$857$	−49.1792	−1.67993	−0.839964	+	0.542642i	$0.817424\pi$
$858$	0.976107	0.0333237
$859$	−6.37161	−0.217397	−0.108698	−	0.994075i	$-0.534668\pi$
$859$	−6.37161	−0.217397	−0.108698	+	0.994075i	$0.534668\pi$
$860$	−9.44089	−0.321932
$861$	−4.13772	−0.141013
$862$	20.3211	0.692139
$863$	27.6061	0.939723	0.469861	−	0.882740i	$-0.344304\pi$
$863$	27.6061	0.939723	0.469861	+	0.882740i	$0.344304\pi$
$864$	−4.46342	−0.151849
$865$	8.79251	0.298954
$866$	−33.7894	−1.14821
$867$	11.1165	0.377537
$868$	−3.73987	−0.126939
$869$	0.0873476	0.00296306
$870$	−6.19432	−0.210007
$871$	−13.8944	−0.470795
$872$	−0.609510	−0.0206406
$873$	−19.1055	−0.646622
$874$	−28.6713	−0.969823
$875$	−0.532701	−0.0180086
$876$	6.36788	0.215151
$877$	14.0886	0.475737	0.237869	−	0.971297i	$-0.423551\pi$
$877$	14.0886	0.475737	0.237869	+	0.971297i	$0.423551\pi$
$878$	−22.3552	−0.754451
$879$	−23.4478	−0.790873
$880$	−0.961430	−0.0324098
$881$	24.2259	0.816190	0.408095	−	0.912939i	$-0.366193\pi$
$881$	24.2259	0.816190	0.408095	+	0.912939i	$0.366193\pi$
$882$	15.3626	0.517287
$883$	37.8604	1.27410	0.637052	−	0.770821i	$-0.280154\pi$
$883$	37.8604	1.27410	0.637052	+	0.770821i	$0.280154\pi$
$884$	6.60589	0.222180
$885$	−8.25407	−0.277458
$886$	21.2089	0.712526
$887$	−40.0641	−1.34522	−0.672611	−	0.739996i	$-0.734827\pi$
$887$	−40.0641	−1.34522	−0.672611	+	0.739996i	$0.734827\pi$
$888$	−4.93194	−0.165505
$889$	2.99700	0.100516
$890$	−14.0969	−0.472528
$891$	−2.97497	−0.0996652
$892$	−18.2859	−0.612258
$893$	31.6145	1.05794
$894$	16.6954	0.558378
$895$	11.7877	0.394018
$896$	−0.532701	−0.0177963
$897$	−6.70604	−0.223908
$898$	−24.8674	−0.829835
$899$	−51.5157	−1.71815
$900$	−2.28739	−0.0762463
$901$	−34.2983	−1.14264
$902$	−8.84645	−0.294555
$903$	4.24544	0.141279
$904$	−5.36554	−0.178455
$905$	24.3416	0.809142
$906$	−5.81659	−0.193243
$907$	47.2600	1.56924	0.784621	−	0.619975i	$-0.212857\pi$
$907$	47.2600	1.56924	0.784621	+	0.619975i	$0.212857\pi$
$908$	23.9381	0.794414
$909$	−22.5355	−0.747454
$910$	0.640674	0.0212381
$911$	10.6548	0.353008	0.176504	−	0.984300i	$-0.443521\pi$
$911$	10.6548	0.353008	0.176504	+	0.984300i	$0.443521\pi$
$912$	−3.66427	−0.121336
$913$	12.7317	0.421358
$914$	38.5370	1.27469
$915$	−4.73714	−0.156605
$916$	23.1069	0.763473
$917$	−0.276383	−0.00912696
$918$	24.5158	0.809141
$919$	−4.25145	−0.140242	−0.0701212	−	0.997538i	$-0.522339\pi$
$919$	−4.25145	−0.140242	−0.0701212	+	0.997538i	$0.522339\pi$
$920$	6.60521	0.217767
$921$	25.5209	0.840944
$922$	14.0184	0.461672
$923$	4.62654	0.152284
$924$	0.432342	0.0142230
$925$	−5.84241	−0.192097
$926$	33.7519	1.10915
$927$	35.1715	1.15518
$928$	−7.33783	−0.240876
$929$	44.4081	1.45698	0.728492	−	0.685055i	$-0.240222\pi$
$929$	44.4081	1.45698	0.728492	+	0.685055i	$0.240222\pi$
$930$	5.92651	0.194338
$931$	29.1533	0.955459
$932$	10.5496	0.345562
$933$	10.4212	0.341175
$934$	37.4995	1.22702
$935$	5.28076	0.172699
$936$	2.75102	0.0899198
$937$	5.47272	0.178786	0.0893930	−	0.995996i	$-0.471507\pi$
$937$	5.47272	0.178786	0.0893930	+	0.995996i	$0.471507\pi$
$938$	−6.15419	−0.200942
$939$	−26.9887	−0.880744
$940$	−7.28325	−0.237554
$941$	−50.5208	−1.64693	−0.823466	−	0.567366i	$-0.807963\pi$
$941$	−50.5208	−1.64693	−0.823466	+	0.567366i	$0.807963\pi$
$942$	−5.77283	−0.188089
$943$	60.7768	1.97916
$944$	−9.77782	−0.318241
$945$	2.37767	0.0773455
$946$	9.07676	0.295111
$947$	32.7854	1.06538	0.532691	−	0.846310i	$-0.321181\pi$
$947$	32.7854	1.06538	0.532691	+	0.846310i	$0.321181\pi$
$948$	−0.0766937	−0.00249089
$949$	−9.07240	−0.294502
$950$	−4.34072	−0.140831
$951$	−7.12726	−0.231117
$952$	2.92592	0.0948295
$953$	−13.6612	−0.442528	−0.221264	−	0.975214i	$-0.571018\pi$
$953$	−13.6612	−0.442528	−0.221264	+	0.975214i	$0.571018\pi$
$954$	−14.2835	−0.462445
$955$	12.8086	0.414476
$956$	2.97603	0.0962515
$957$	5.95541	0.192511
$958$	−31.2817	−1.01066
$959$	2.35413	0.0760189
$960$	0.844163	0.0272452
$961$	18.2884	0.589950
$962$	7.02660	0.226547
$963$	9.50899	0.306423
$964$	−22.2492	−0.716600
$965$	20.6520	0.664812
$966$	−2.97027	−0.0955670
$967$	−8.52830	−0.274252	−0.137126	−	0.990554i	$-0.543786\pi$
$967$	−8.52830	−0.274252	−0.137126	+	0.990554i	$0.543786\pi$
$968$	−10.0757	−0.323844
$969$	20.1264	0.646553
$970$	8.35252	0.268183
$971$	−19.4931	−0.625562	−0.312781	−	0.949825i	$-0.601261\pi$
$971$	−19.4931	−0.625562	−0.312781	+	0.949825i	$0.601261\pi$
$972$	16.0024	0.513276
$973$	11.9841	0.384191
$974$	9.32490	0.298789
$975$	−1.01527	−0.0325145
$976$	−5.61164	−0.179624
$977$	−14.6151	−0.467578	−0.233789	−	0.972287i	$-0.575112\pi$
$977$	−14.6151	−0.467578	−0.233789	+	0.972287i	$0.575112\pi$
$978$	−2.33736	−0.0747405
$979$	13.5532	0.433161
$980$	−6.71623	−0.214542
$981$	1.39419	0.0445129
$982$	34.9844	1.11640
$983$	33.2877	1.06171	0.530856	−	0.847462i	$-0.321871\pi$
$983$	33.2877	1.06171	0.530856	+	0.847462i	$0.321871\pi$
$984$	7.76744	0.247617
$985$	−12.6133	−0.401892
$986$	40.3038	1.28353
$987$	3.27518	0.104250
$988$	5.22053	0.166087
$989$	−62.3590	−1.98290
$990$	2.19917	0.0698941
$991$	37.9919	1.20685	0.603426	−	0.797419i	$-0.293802\pi$
$991$	37.9919	1.20685	0.603426	+	0.797419i	$0.293802\pi$
$992$	7.02057	0.222903
$993$	14.0192	0.444886
$994$	2.04921	0.0649970
$995$	22.9659	0.728068
$996$	−11.1788	−0.354214
$997$	−47.0677	−1.49065	−0.745325	−	0.666701i	$-0.767706\pi$
$997$	−47.0677	−1.49065	−0.745325	+	0.666701i	$0.767706\pi$
$998$	−37.5728	−1.18935
$999$	26.0771	0.825043

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.c.1.13	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.c.1.13	✓	16	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.844163 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.844163 q^{6} -0.532701 q^{7} +1.00000 q^{8} -2.28739 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.844163 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.844163 q^{6} -0.532701 q^{7} +1.00000 q^{8} -2.28739 q^{9} +1.00000 q^{10} -0.961430 q^{11} +0.844163 q^{12} -1.20269 q^{13} -0.532701 q^{14} +0.844163 q^{15} +1.00000 q^{16} -5.49260 q^{17} -2.28739 q^{18} -4.34072 q^{19} +1.00000 q^{20} -0.449687 q^{21} -0.961430 q^{22} +6.60521 q^{23} +0.844163 q^{24} +1.00000 q^{25} -1.20269 q^{26} -4.46342 q^{27} -0.532701 q^{28} -7.33783 q^{29} +0.844163 q^{30} +7.02057 q^{31} +1.00000 q^{32} -0.811604 q^{33} -5.49260 q^{34} -0.532701 q^{35} -2.28739 q^{36} -5.84241 q^{37} -4.34072 q^{38} -1.01527 q^{39} +1.00000 q^{40} +9.20135 q^{41} -0.449687 q^{42} -9.44089 q^{43} -0.961430 q^{44} -2.28739 q^{45} +6.60521 q^{46} -7.28325 q^{47} +0.844163 q^{48} -6.71623 q^{49} +1.00000 q^{50} -4.63665 q^{51} -1.20269 q^{52} +6.24445 q^{53} -4.46342 q^{54} -0.961430 q^{55} -0.532701 q^{56} -3.66427 q^{57} -7.33783 q^{58} -9.77782 q^{59} +0.844163 q^{60} -5.61164 q^{61} +7.02057 q^{62} +1.21849 q^{63} +1.00000 q^{64} -1.20269 q^{65} -0.811604 q^{66} +11.5528 q^{67} -5.49260 q^{68} +5.57587 q^{69} -0.532701 q^{70} -3.84683 q^{71} -2.28739 q^{72} +7.54343 q^{73} -5.84241 q^{74} +0.844163 q^{75} -4.34072 q^{76} +0.512155 q^{77} -1.01527 q^{78} -0.0908517 q^{79} +1.00000 q^{80} +3.09431 q^{81} +9.20135 q^{82} -13.2425 q^{83} -0.449687 q^{84} -5.49260 q^{85} -9.44089 q^{86} -6.19432 q^{87} -0.961430 q^{88} -14.0969 q^{89} -2.28739 q^{90} +0.640674 q^{91} +6.60521 q^{92} +5.92651 q^{93} -7.28325 q^{94} -4.34072 q^{95} +0.844163 q^{96} +8.35252 q^{97} -6.71623 q^{98} +2.19917 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * q^99

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