LMFDB - Embedded newform 4970.2.a.z.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4970,2,Mod(1,4970)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4970, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4970.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4970 = 2 \cdot 5 \cdot 7 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4970.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:	$39.6856498046$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 9x^{7} + 47x^{6} + 6x^{5} - 151x^{4} + 80x^{3} + 79x^{2} - 54x + 8 $ x^9 - 4x^8 - 9x^7 + 47x^6 + 6x^5 - 151x^4 + 80x^3 + 79x^2 - 54x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.341239$ of defining polynomial
Character	$\chi$	$=$	4970.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.341239 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.341239 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.88356 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.341239 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.341239 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.88356 q^{9} -1.00000 q^{10} -6.05712 q^{11} +0.341239 q^{12} +0.389409 q^{13} +1.00000 q^{14} -0.341239 q^{15} +1.00000 q^{16} -4.82029 q^{17} -2.88356 q^{18} +5.94443 q^{19} -1.00000 q^{20} +0.341239 q^{21} -6.05712 q^{22} +1.84938 q^{23} +0.341239 q^{24} +1.00000 q^{25} +0.389409 q^{26} -2.00770 q^{27} +1.00000 q^{28} +7.56216 q^{29} -0.341239 q^{30} +5.25675 q^{31} +1.00000 q^{32} -2.06692 q^{33} -4.82029 q^{34} -1.00000 q^{35} -2.88356 q^{36} +9.43253 q^{37} +5.94443 q^{38} +0.132882 q^{39} -1.00000 q^{40} +0.121091 q^{41} +0.341239 q^{42} -4.54945 q^{43} -6.05712 q^{44} +2.88356 q^{45} +1.84938 q^{46} -3.15399 q^{47} +0.341239 q^{48} +1.00000 q^{49} +1.00000 q^{50} -1.64487 q^{51} +0.389409 q^{52} +10.0448 q^{53} -2.00770 q^{54} +6.05712 q^{55} +1.00000 q^{56} +2.02847 q^{57} +7.56216 q^{58} +9.27421 q^{59} -0.341239 q^{60} -3.79382 q^{61} +5.25675 q^{62} -2.88356 q^{63} +1.00000 q^{64} -0.389409 q^{65} -2.06692 q^{66} +10.2060 q^{67} -4.82029 q^{68} +0.631082 q^{69} -1.00000 q^{70} +1.00000 q^{71} -2.88356 q^{72} -2.74242 q^{73} +9.43253 q^{74} +0.341239 q^{75} +5.94443 q^{76} -6.05712 q^{77} +0.132882 q^{78} +3.84938 q^{79} -1.00000 q^{80} +7.96556 q^{81} +0.121091 q^{82} +14.5431 q^{83} +0.341239 q^{84} +4.82029 q^{85} -4.54945 q^{86} +2.58050 q^{87} -6.05712 q^{88} +8.42696 q^{89} +2.88356 q^{90} +0.389409 q^{91} +1.84938 q^{92} +1.79381 q^{93} -3.15399 q^{94} -5.94443 q^{95} +0.341239 q^{96} +16.4915 q^{97} +1.00000 q^{98} +17.4660 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9	\( 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9} - 9 q^{10} - 2 q^{11} + 4 q^{12} + 11 q^{13} + 9 q^{14} - 4 q^{15} + 9 q^{16} + 9 q^{17} + 7 q^{18} + 9 q^{19} - 9 q^{20} + 4 q^{21} - 2 q^{22} + 2 q^{23} + 4 q^{24} + 9 q^{25} + 11 q^{26} + 7 q^{27} + 9 q^{28} + 2 q^{29} - 4 q^{30} + 18 q^{31} + 9 q^{32} + 8 q^{33} + 9 q^{34} - 9 q^{35} + 7 q^{36} + 15 q^{37} + 9 q^{38} - 7 q^{39} - 9 q^{40} + 15 q^{41} + 4 q^{42} + 7 q^{43} - 2 q^{44} - 7 q^{45} + 2 q^{46} + 12 q^{47} + 4 q^{48} + 9 q^{49} + 9 q^{50} + 4 q^{51} + 11 q^{52} + 3 q^{53} + 7 q^{54} + 2 q^{55} + 9 q^{56} + 9 q^{57} + 2 q^{58} + 24 q^{59} - 4 q^{60} + 25 q^{61} + 18 q^{62} + 7 q^{63} + 9 q^{64} - 11 q^{65} + 8 q^{66} - 4 q^{67} + 9 q^{68} + 3 q^{69} - 9 q^{70} + 9 q^{71} + 7 q^{72} + 32 q^{73} + 15 q^{74} + 4 q^{75} + 9 q^{76} - 2 q^{77} - 7 q^{78} + 20 q^{79} - 9 q^{80} - 7 q^{81} + 15 q^{82} + 11 q^{83} + 4 q^{84} - 9 q^{85} + 7 q^{86} + 26 q^{87} - 2 q^{88} + 10 q^{89} - 7 q^{90} + 11 q^{91} + 2 q^{92} + 32 q^{93} + 12 q^{94} - 9 q^{95} + 4 q^{96} + 19 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9 - 9 * q^10 - 2 * q^11 + 4 * q^12 + 11 * q^13 + 9 * q^14 - 4 * q^15 + 9 * q^16 + 9 * q^17 + 7 * q^18 + 9 * q^19 - 9 * q^20 + 4 * q^21 - 2 * q^22 + 2 * q^23 + 4 * q^24 + 9 * q^25 + 11 * q^26 + 7 * q^27 + 9 * q^28 + 2 * q^29 - 4 * q^30 + 18 * q^31 + 9 * q^32 + 8 * q^33 + 9 * q^34 - 9 * q^35 + 7 * q^36 + 15 * q^37 + 9 * q^38 - 7 * q^39 - 9 * q^40 + 15 * q^41 + 4 * q^42 + 7 * q^43 - 2 * q^44 - 7 * q^45 + 2 * q^46 + 12 * q^47 + 4 * q^48 + 9 * q^49 + 9 * q^50 + 4 * q^51 + 11 * q^52 + 3 * q^53 + 7 * q^54 + 2 * q^55 + 9 * q^56 + 9 * q^57 + 2 * q^58 + 24 * q^59 - 4 * q^60 + 25 * q^61 + 18 * q^62 + 7 * q^63 + 9 * q^64 - 11 * q^65 + 8 * q^66 - 4 * q^67 + 9 * q^68 + 3 * q^69 - 9 * q^70 + 9 * q^71 + 7 * q^72 + 32 * q^73 + 15 * q^74 + 4 * q^75 + 9 * q^76 - 2 * q^77 - 7 * q^78 + 20 * q^79 - 9 * q^80 - 7 * q^81 + 15 * q^82 + 11 * q^83 + 4 * q^84 - 9 * q^85 + 7 * q^86 + 26 * q^87 - 2 * q^88 + 10 * q^89 - 7 * q^90 + 11 * q^91 + 2 * q^92 + 32 * q^93 + 12 * q^94 - 9 * q^95 + 4 * q^96 + 19 * q^97 + 9 * q^98 - 7 * 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
$3$	0.341239	0.197014	0.0985072	−	0.995136i	$-0.468593\pi$
$3$	0.341239	0.197014	0.0985072	+	0.995136i	$0.468593\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.341239	0.139310
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−2.88356	−0.961185
$10$	−1.00000	−0.316228
$11$	−6.05712	−1.82629	−0.913145	−	0.407635i	$-0.866354\pi$
$11$	−6.05712	−1.82629	−0.913145	+	0.407635i	$0.866354\pi$
$12$	0.341239	0.0985072
$13$	0.389409	0.108003	0.0540014	−	0.998541i	$-0.482802\pi$
$13$	0.389409	0.108003	0.0540014	+	0.998541i	$0.482802\pi$
$14$	1.00000	0.267261
$15$	−0.341239	−0.0881075
$16$	1.00000	0.250000
$17$	−4.82029	−1.16909	−0.584546	−	0.811361i	$-0.698727\pi$
$17$	−4.82029	−1.16909	−0.584546	+	0.811361i	$0.698727\pi$
$18$	−2.88356	−0.679661
$19$	5.94443	1.36375	0.681873	−	0.731470i	$-0.261166\pi$
$19$	5.94443	1.36375	0.681873	+	0.731470i	$0.261166\pi$
$20$	−1.00000	−0.223607
$21$	0.341239	0.0744644
$22$	−6.05712	−1.29138
$23$	1.84938	0.385623	0.192812	−	0.981236i	$-0.438239\pi$
$23$	1.84938	0.385623	0.192812	+	0.981236i	$0.438239\pi$
$24$	0.341239	0.0696551
$25$	1.00000	0.200000
$26$	0.389409	0.0763695
$27$	−2.00770	−0.386382
$28$	1.00000	0.188982
$29$	7.56216	1.40426	0.702129	−	0.712050i	$-0.252233\pi$
$29$	7.56216	1.40426	0.702129	+	0.712050i	$0.252233\pi$
$30$	−0.341239	−0.0623014
$31$	5.25675	0.944141	0.472071	−	0.881561i	$-0.343507\pi$
$31$	5.25675	0.944141	0.472071	+	0.881561i	$0.343507\pi$
$32$	1.00000	0.176777
$33$	−2.06692	−0.359805
$34$	−4.82029	−0.826673
$35$	−1.00000	−0.169031
$36$	−2.88356	−0.480593
$37$	9.43253	1.55070	0.775349	−	0.631533i	$-0.217574\pi$
$37$	9.43253	1.55070	0.775349	+	0.631533i	$0.217574\pi$
$38$	5.94443	0.964314
$39$	0.132882	0.0212781
$40$	−1.00000	−0.158114
$41$	0.121091	0.0189113	0.00945565	−	0.999955i	$-0.496990\pi$
$41$	0.121091	0.0189113	0.00945565	+	0.999955i	$0.496990\pi$
$42$	0.341239	0.0526543
$43$	−4.54945	−0.693785	−0.346892	−	0.937905i	$-0.612763\pi$
$43$	−4.54945	−0.693785	−0.346892	+	0.937905i	$0.612763\pi$
$44$	−6.05712	−0.913145
$45$	2.88356	0.429855
$46$	1.84938	0.272677
$47$	−3.15399	−0.460057	−0.230029	−	0.973184i	$-0.573882\pi$
$47$	−3.15399	−0.460057	−0.230029	+	0.973184i	$0.573882\pi$
$48$	0.341239	0.0492536
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−1.64487	−0.230328
$52$	0.389409	0.0540014
$53$	10.0448	1.37976	0.689878	−	0.723926i	$-0.257664\pi$
$53$	10.0448	1.37976	0.689878	+	0.723926i	$0.257664\pi$
$54$	−2.00770	−0.273213
$55$	6.05712	0.816742
$56$	1.00000	0.133631
$57$	2.02847	0.268678
$58$	7.56216	0.992960
$59$	9.27421	1.20740	0.603700	−	0.797212i	$-0.293692\pi$
$59$	9.27421	1.20740	0.603700	+	0.797212i	$0.293692\pi$
$60$	−0.341239	−0.0440538
$61$	−3.79382	−0.485748	−0.242874	−	0.970058i	$-0.578090\pi$
$61$	−3.79382	−0.485748	−0.242874	+	0.970058i	$0.578090\pi$
$62$	5.25675	0.667609
$63$	−2.88356	−0.363294
$64$	1.00000	0.125000
$65$	−0.389409	−0.0483003
$66$	−2.06692	−0.254421
$67$	10.2060	1.24686	0.623431	−	0.781878i	$-0.285738\pi$
$67$	10.2060	1.24686	0.623431	+	0.781878i	$0.285738\pi$
$68$	−4.82029	−0.584546
$69$	0.631082	0.0759733
$70$	−1.00000	−0.119523
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−2.88356	−0.339830
$73$	−2.74242	−0.320976	−0.160488	−	0.987038i	$-0.551307\pi$
$73$	−2.74242	−0.320976	−0.160488	+	0.987038i	$0.551307\pi$
$74$	9.43253	1.09651
$75$	0.341239	0.0394029
$76$	5.94443	0.681873
$77$	−6.05712	−0.690273
$78$	0.132882	0.0150459
$79$	3.84938	0.433089	0.216545	−	0.976273i	$-0.430521\pi$
$79$	3.84938	0.433089	0.216545	+	0.976273i	$0.430521\pi$
$80$	−1.00000	−0.111803
$81$	7.96556	0.885063
$82$	0.121091	0.0133723
$83$	14.5431	1.59631	0.798155	−	0.602452i	$-0.205810\pi$
$83$	14.5431	1.59631	0.798155	+	0.602452i	$0.205810\pi$
$84$	0.341239	0.0372322
$85$	4.82029	0.522834
$86$	−4.54945	−0.490580
$87$	2.58050	0.276659
$88$	−6.05712	−0.645691
$89$	8.42696	0.893256	0.446628	−	0.894720i	$-0.352625\pi$
$89$	8.42696	0.893256	0.446628	+	0.894720i	$0.352625\pi$
$90$	2.88356	0.303953
$91$	0.389409	0.0408212
$92$	1.84938	0.192812
$93$	1.79381	0.186009
$94$	−3.15399	−0.325310
$95$	−5.94443	−0.609886
$96$	0.341239	0.0348276
$97$	16.4915	1.67446	0.837230	−	0.546850i	$-0.184173\pi$
$97$	16.4915	1.67446	0.837230	+	0.546850i	$0.184173\pi$
$98$	1.00000	0.101015
$99$	17.4660	1.75540
$100$	1.00000	0.100000
$101$	−12.2528	−1.21920	−0.609601	−	0.792709i	$-0.708670\pi$
$101$	−12.2528	−1.21920	−0.609601	+	0.792709i	$0.708670\pi$
$102$	−1.64487	−0.162866
$103$	−1.45020	−0.142892	−0.0714461	−	0.997444i	$-0.522761\pi$
$103$	−1.45020	−0.142892	−0.0714461	+	0.997444i	$0.522761\pi$
$104$	0.389409	0.0381847
$105$	−0.341239	−0.0333015
$106$	10.0448	0.975634
$107$	0.0223235	0.00215809	0.00107905	−	0.999999i	$-0.499657\pi$
$107$	0.0223235	0.00215809	0.00107905	+	0.999999i	$0.499657\pi$
$108$	−2.00770	−0.193191
$109$	−9.49400	−0.909361	−0.454680	−	0.890655i	$-0.650246\pi$
$109$	−9.49400	−0.909361	−0.454680	+	0.890655i	$0.650246\pi$
$110$	6.05712	0.577524
$111$	3.21875	0.305510
$112$	1.00000	0.0944911
$113$	−1.67130	−0.157223	−0.0786114	−	0.996905i	$-0.525049\pi$
$113$	−1.67130	−0.157223	−0.0786114	+	0.996905i	$0.525049\pi$
$114$	2.02847	0.189984
$115$	−1.84938	−0.172456
$116$	7.56216	0.702129
$117$	−1.12288	−0.103811
$118$	9.27421	0.853761
$119$	−4.82029	−0.441875
$120$	−0.341239	−0.0311507
$121$	25.6887	2.33533
$122$	−3.79382	−0.343476
$123$	0.0413211	0.00372580
$124$	5.25675	0.472071
$125$	−1.00000	−0.0894427
$126$	−2.88356	−0.256888
$127$	−1.33188	−0.118185	−0.0590925	−	0.998253i	$-0.518821\pi$
$127$	−1.33188	−0.118185	−0.0590925	+	0.998253i	$0.518821\pi$
$128$	1.00000	0.0883883
$129$	−1.55245	−0.136686
$130$	−0.389409	−0.0341535
$131$	0.259277	0.0226531	0.0113266	−	0.999936i	$-0.496395\pi$
$131$	0.259277	0.0226531	0.0113266	+	0.999936i	$0.496395\pi$
$132$	−2.06692	−0.179903
$133$	5.94443	0.515448
$134$	10.2060	0.881665
$135$	2.00770	0.172795
$136$	−4.82029	−0.413336
$137$	−14.3749	−1.22813	−0.614064	−	0.789256i	$-0.710466\pi$
$137$	−14.3749	−1.22813	−0.614064	+	0.789256i	$0.710466\pi$
$138$	0.631082	0.0537212
$139$	2.82801	0.239869	0.119934	−	0.992782i	$-0.461732\pi$
$139$	2.82801	0.239869	0.119934	+	0.992782i	$0.461732\pi$
$140$	−1.00000	−0.0845154
$141$	−1.07627	−0.0906379
$142$	1.00000	0.0839181
$143$	−2.35870	−0.197244
$144$	−2.88356	−0.240296
$145$	−7.56216	−0.628003
$146$	−2.74242	−0.226964
$147$	0.341239	0.0281449
$148$	9.43253	0.775349
$149$	5.92749	0.485599	0.242799	−	0.970077i	$-0.421934\pi$
$149$	5.92749	0.485599	0.242799	+	0.970077i	$0.421934\pi$
$150$	0.341239	0.0278620
$151$	−4.51741	−0.367621	−0.183811	−	0.982962i	$-0.558843\pi$
$151$	−4.51741	−0.367621	−0.183811	+	0.982962i	$0.558843\pi$
$152$	5.94443	0.482157
$153$	13.8996	1.12371
$154$	−6.05712	−0.488097
$155$	−5.25675	−0.422233
$156$	0.132882	0.0106390
$157$	−5.38145	−0.429486	−0.214743	−	0.976671i	$-0.568891\pi$
$157$	−5.38145	−0.429486	−0.214743	+	0.976671i	$0.568891\pi$
$158$	3.84938	0.306241
$159$	3.42767	0.271832
$160$	−1.00000	−0.0790569
$161$	1.84938	0.145752
$162$	7.96556	0.625834
$163$	0.201892	0.0158134	0.00790671	−	0.999969i	$-0.497483\pi$
$163$	0.201892	0.0158134	0.00790671	+	0.999969i	$0.497483\pi$
$164$	0.121091	0.00945565
$165$	2.06692	0.160910
$166$	14.5431	1.12876
$167$	0.359218	0.0277971	0.0138985	−	0.999903i	$-0.495576\pi$
$167$	0.359218	0.0277971	0.0138985	+	0.999903i	$0.495576\pi$
$168$	0.341239	0.0263272
$169$	−12.8484	−0.988335
$170$	4.82029	0.369699
$171$	−17.1411	−1.31081
$172$	−4.54945	−0.346892
$173$	−14.9262	−1.13481	−0.567407	−	0.823437i	$-0.692054\pi$
$173$	−14.9262	−1.13481	−0.567407	+	0.823437i	$0.692054\pi$
$174$	2.58050	0.195627
$175$	1.00000	0.0755929
$176$	−6.05712	−0.456572
$177$	3.16472	0.237875
$178$	8.42696	0.631627
$179$	−23.0262	−1.72106	−0.860530	−	0.509400i	$-0.829867\pi$
$179$	−23.0262	−1.72106	−0.860530	+	0.509400i	$0.829867\pi$
$180$	2.88356	0.214928
$181$	9.33842	0.694120	0.347060	−	0.937843i	$-0.387180\pi$
$181$	9.33842	0.694120	0.347060	+	0.937843i	$0.387180\pi$
$182$	0.389409	0.0288649
$183$	−1.29460	−0.0956994
$184$	1.84938	0.136338
$185$	−9.43253	−0.693493
$186$	1.79381	0.131528
$187$	29.1971	2.13510
$188$	−3.15399	−0.230029
$189$	−2.00770	−0.146039
$190$	−5.94443	−0.431254
$191$	−8.87564	−0.642219	−0.321109	−	0.947042i	$-0.604056\pi$
$191$	−8.87564	−0.642219	−0.321109	+	0.947042i	$0.604056\pi$
$192$	0.341239	0.0246268
$193$	4.64996	0.334712	0.167356	−	0.985897i	$-0.446477\pi$
$193$	4.64996	0.334712	0.167356	+	0.985897i	$0.446477\pi$
$194$	16.4915	1.18402
$195$	−0.132882	−0.00951585
$196$	1.00000	0.0714286
$197$	−6.60598	−0.470656	−0.235328	−	0.971916i	$-0.575616\pi$
$197$	−6.60598	−0.470656	−0.235328	+	0.971916i	$0.575616\pi$
$198$	17.4660	1.24126
$199$	−22.5591	−1.59917	−0.799587	−	0.600550i	$-0.794948\pi$
$199$	−22.5591	−1.59917	−0.799587	+	0.600550i	$0.794948\pi$
$200$	1.00000	0.0707107
$201$	3.48269	0.245650
$202$	−12.2528	−0.862105
$203$	7.56216	0.530759
$204$	−1.64487	−0.115164
$205$	−0.121091	−0.00845739
$206$	−1.45020	−0.101040
$207$	−5.33280	−0.370655
$208$	0.389409	0.0270007
$209$	−36.0061	−2.49060
$210$	−0.341239	−0.0235477
$211$	4.35729	0.299968	0.149984	−	0.988688i	$-0.452078\pi$
$211$	4.35729	0.299968	0.149984	+	0.988688i	$0.452078\pi$
$212$	10.0448	0.689878
$213$	0.341239	0.0233813
$214$	0.0223235	0.00152600
$215$	4.54945	0.310270
$216$	−2.00770	−0.136607
$217$	5.25675	0.356852
$218$	−9.49400	−0.643015
$219$	−0.935820	−0.0632368
$220$	6.05712	0.408371
$221$	−1.87707	−0.126265
$222$	3.21875	0.216028
$223$	18.7902	1.25829	0.629143	−	0.777289i	$-0.283406\pi$
$223$	18.7902	1.25829	0.629143	+	0.777289i	$0.283406\pi$
$224$	1.00000	0.0668153
$225$	−2.88356	−0.192237
$226$	−1.67130	−0.111173
$227$	16.0319	1.06407	0.532037	−	0.846721i	$-0.321427\pi$
$227$	16.0319	1.06407	0.532037	+	0.846721i	$0.321427\pi$
$228$	2.02847	0.134339
$229$	−5.31554	−0.351261	−0.175631	−	0.984456i	$-0.556196\pi$
$229$	−5.31554	−0.351261	−0.175631	+	0.984456i	$0.556196\pi$
$230$	−1.84938	−0.121945
$231$	−2.06692	−0.135994
$232$	7.56216	0.496480
$233$	−9.92235	−0.650035	−0.325018	−	0.945708i	$-0.605370\pi$
$233$	−9.92235	−0.650035	−0.325018	+	0.945708i	$0.605370\pi$
$234$	−1.12288	−0.0734052
$235$	3.15399	0.205744
$236$	9.27421	0.603700
$237$	1.31356	0.0853249
$238$	−4.82029	−0.312453
$239$	11.2277	0.726257	0.363129	−	0.931739i	$-0.381709\pi$
$239$	11.2277	0.726257	0.363129	+	0.931739i	$0.381709\pi$
$240$	−0.341239	−0.0220269
$241$	−1.40676	−0.0906175	−0.0453088	−	0.998973i	$-0.514427\pi$
$241$	−1.40676	−0.0906175	−0.0453088	+	0.998973i	$0.514427\pi$
$242$	25.6887	1.65133
$243$	8.74126	0.560752
$244$	−3.79382	−0.242874
$245$	−1.00000	−0.0638877
$246$	0.0413211	0.00263454
$247$	2.31482	0.147288
$248$	5.25675	0.333804
$249$	4.96266	0.314496
$250$	−1.00000	−0.0632456
$251$	−9.35813	−0.590680	−0.295340	−	0.955392i	$-0.595433\pi$
$251$	−9.35813	−0.590680	−0.295340	+	0.955392i	$0.595433\pi$
$252$	−2.88356	−0.181647
$253$	−11.2019	−0.704260
$254$	−1.33188	−0.0835694
$255$	1.64487	0.103006
$256$	1.00000	0.0625000
$257$	−16.6619	−1.03934	−0.519670	−	0.854367i	$-0.673945\pi$
$257$	−16.6619	−1.03934	−0.519670	+	0.854367i	$0.673945\pi$
$258$	−1.55245	−0.0966513
$259$	9.43253	0.586109
$260$	−0.389409	−0.0241501
$261$	−21.8059	−1.34975
$262$	0.259277	0.0160182
$263$	−16.2414	−1.00149	−0.500744	−	0.865595i	$-0.666940\pi$
$263$	−16.2414	−1.00149	−0.500744	+	0.865595i	$0.666940\pi$
$264$	−2.06692	−0.127210
$265$	−10.0448	−0.617045
$266$	5.94443	0.364477
$267$	2.87561	0.175984
$268$	10.2060	0.623431
$269$	13.1702	0.803003	0.401501	−	0.915858i	$-0.368488\pi$
$269$	13.1702	0.803003	0.401501	+	0.915858i	$0.368488\pi$
$270$	2.00770	0.122185
$271$	23.6084	1.43411	0.717053	−	0.697019i	$-0.245491\pi$
$271$	23.6084	1.43411	0.717053	+	0.697019i	$0.245491\pi$
$272$	−4.82029	−0.292273
$273$	0.132882	0.00804236
$274$	−14.3749	−0.868418
$275$	−6.05712	−0.365258
$276$	0.631082	0.0379866
$277$	8.32251	0.500051	0.250025	−	0.968239i	$-0.419561\pi$
$277$	8.32251	0.500051	0.250025	+	0.968239i	$0.419561\pi$
$278$	2.82801	0.169613
$279$	−15.1581	−0.907495
$280$	−1.00000	−0.0597614
$281$	13.4621	0.803080	0.401540	−	0.915841i	$-0.368475\pi$
$281$	13.4621	0.803080	0.401540	+	0.915841i	$0.368475\pi$
$282$	−1.07627	−0.0640907
$283$	12.5067	0.743448	0.371724	−	0.928343i	$-0.378767\pi$
$283$	12.5067	0.743448	0.371724	+	0.928343i	$0.378767\pi$
$284$	1.00000	0.0593391
$285$	−2.02847	−0.120156
$286$	−2.35870	−0.139473
$287$	0.121091	0.00714780
$288$	−2.88356	−0.169915
$289$	6.23519	0.366776
$290$	−7.56216	−0.444065
$291$	5.62755	0.329893
$292$	−2.74242	−0.160488
$293$	11.4204	0.667188	0.333594	−	0.942717i	$-0.391739\pi$
$293$	11.4204	0.667188	0.333594	+	0.942717i	$0.391739\pi$
$294$	0.341239	0.0199015
$295$	−9.27421	−0.539966
$296$	9.43253	0.548255
$297$	12.1609	0.705645
$298$	5.92749	0.343370
$299$	0.720167	0.0416484
$300$	0.341239	0.0197014
$301$	−4.54945	−0.262226
$302$	−4.51741	−0.259948
$303$	−4.18114	−0.240200
$304$	5.94443	0.340937
$305$	3.79382	0.217233
$306$	13.8996	0.794586
$307$	27.2409	1.55472	0.777362	−	0.629054i	$-0.216558\pi$
$307$	27.2409	1.55472	0.777362	+	0.629054i	$0.216558\pi$
$308$	−6.05712	−0.345136
$309$	−0.494864	−0.0281518
$310$	−5.25675	−0.298564
$311$	−13.6565	−0.774388	−0.387194	−	0.921998i	$-0.626556\pi$
$311$	−13.6565	−0.774388	−0.387194	+	0.921998i	$0.626556\pi$
$312$	0.132882	0.00752294
$313$	−7.01758	−0.396657	−0.198328	−	0.980136i	$-0.563551\pi$
$313$	−7.01758	−0.396657	−0.198328	+	0.980136i	$0.563551\pi$
$314$	−5.38145	−0.303693
$315$	2.88356	0.162470
$316$	3.84938	0.216545
$317$	4.38970	0.246550	0.123275	−	0.992373i	$-0.460660\pi$
$317$	4.38970	0.246550	0.123275	+	0.992373i	$0.460660\pi$
$318$	3.42767	0.192214
$319$	−45.8049	−2.56458
$320$	−1.00000	−0.0559017
$321$	0.00761764	0.000425175 0
$322$	1.84938	0.103062
$323$	−28.6539	−1.59434
$324$	7.96556	0.442531
$325$	0.389409	0.0216005
$326$	0.201892	0.0111818
$327$	−3.23972	−0.179157
$328$	0.121091	0.00668616
$329$	−3.15399	−0.173885
$330$	2.06692	0.113780
$331$	33.9097	1.86385	0.931924	−	0.362654i	$-0.118129\pi$
$331$	33.9097	1.86385	0.931924	+	0.362654i	$0.118129\pi$
$332$	14.5431	0.798155
$333$	−27.1992	−1.49051
$334$	0.359218	0.0196555
$335$	−10.2060	−0.557614
$336$	0.341239	0.0186161
$337$	7.73290	0.421238	0.210619	−	0.977568i	$-0.432452\pi$
$337$	7.73290	0.421238	0.210619	+	0.977568i	$0.432452\pi$
$338$	−12.8484	−0.698859
$339$	−0.570313	−0.0309752
$340$	4.82029	0.261417
$341$	−31.8408	−1.72428
$342$	−17.1411	−0.926885
$343$	1.00000	0.0539949
$344$	−4.54945	−0.245290
$345$	−0.631082	−0.0339763
$346$	−14.9262	−0.802435
$347$	7.71891	0.414373	0.207186	−	0.978302i	$-0.433569\pi$
$347$	7.71891	0.414373	0.207186	+	0.978302i	$0.433569\pi$
$348$	2.58050	0.138329
$349$	−25.4149	−1.36043	−0.680215	−	0.733013i	$-0.738113\pi$
$349$	−25.4149	−1.36043	−0.680215	+	0.733013i	$0.738113\pi$
$350$	1.00000	0.0534522
$351$	−0.781817	−0.0417303
$352$	−6.05712	−0.322845
$353$	27.4798	1.46260	0.731301	−	0.682055i	$-0.238913\pi$
$353$	27.4798	1.46260	0.731301	+	0.682055i	$0.238913\pi$
$354$	3.16472	0.168203
$355$	−1.00000	−0.0530745
$356$	8.42696	0.446628
$357$	−1.64487	−0.0870558
$358$	−23.0262	−1.21697
$359$	−20.0101	−1.05609	−0.528047	−	0.849215i	$-0.677076\pi$
$359$	−20.0101	−1.05609	−0.528047	+	0.849215i	$0.677076\pi$
$360$	2.88356	0.151977
$361$	16.3363	0.859804
$362$	9.33842	0.490817
$363$	8.76598	0.460095
$364$	0.389409	0.0204106
$365$	2.74242	0.143545
$366$	−1.29460	−0.0676697
$367$	1.99465	0.104120	0.0520600	−	0.998644i	$-0.483421\pi$
$367$	1.99465	0.104120	0.0520600	+	0.998644i	$0.483421\pi$
$368$	1.84938	0.0964058
$369$	−0.349174	−0.0181773
$370$	−9.43253	−0.490374
$371$	10.0448	0.521498
$372$	1.79381	0.0930047
$373$	5.78346	0.299456	0.149728	−	0.988727i	$-0.452160\pi$
$373$	5.78346	0.299456	0.149728	+	0.988727i	$0.452160\pi$
$374$	29.1971	1.50974
$375$	−0.341239	−0.0176215
$376$	−3.15399	−0.162655
$377$	2.94478	0.151664
$378$	−2.00770	−0.103265
$379$	−22.9688	−1.17983	−0.589915	−	0.807465i	$-0.700839\pi$
$379$	−22.9688	−1.17983	−0.589915	+	0.807465i	$0.700839\pi$
$380$	−5.94443	−0.304943
$381$	−0.454488	−0.0232841
$382$	−8.87564	−0.454117
$383$	5.31881	0.271779	0.135889	−	0.990724i	$-0.456611\pi$
$383$	5.31881	0.271779	0.135889	+	0.990724i	$0.456611\pi$
$384$	0.341239	0.0174138
$385$	6.05712	0.308699
$386$	4.64996	0.236677
$387$	13.1186	0.666856
$388$	16.4915	0.837230
$389$	−29.2890	−1.48501	−0.742507	−	0.669839i	$-0.766363\pi$
$389$	−29.2890	−1.48501	−0.742507	+	0.669839i	$0.766363\pi$
$390$	−0.132882	−0.00672872
$391$	−8.91456	−0.450829
$392$	1.00000	0.0505076
$393$	0.0884755	0.00446300
$394$	−6.60598	−0.332804
$395$	−3.84938	−0.193684
$396$	17.4660	0.877702
$397$	35.7838	1.79594	0.897968	−	0.440061i	$-0.145043\pi$
$397$	35.7838	1.79594	0.897968	+	0.440061i	$0.145043\pi$
$398$	−22.5591	−1.13079
$399$	2.02847	0.101551
$400$	1.00000	0.0500000
$401$	29.3831	1.46732	0.733662	−	0.679515i	$-0.237810\pi$
$401$	29.3831	1.46732	0.733662	+	0.679515i	$0.237810\pi$
$402$	3.48269	0.173701
$403$	2.04703	0.101970
$404$	−12.2528	−0.609601
$405$	−7.96556	−0.395812
$406$	7.56216	0.375304
$407$	−57.1339	−2.83202
$408$	−1.64487	−0.0814332
$409$	30.0395	1.48536	0.742678	−	0.669649i	$-0.233555\pi$
$409$	30.0395	1.48536	0.742678	+	0.669649i	$0.233555\pi$
$410$	−0.121091	−0.00598028
$411$	−4.90527	−0.241959
$412$	−1.45020	−0.0714461
$413$	9.27421	0.456354
$414$	−5.33280	−0.262093
$415$	−14.5431	−0.713891
$416$	0.389409	0.0190924
$417$	0.965027	0.0472576
$418$	−36.0061	−1.76112
$419$	30.2310	1.47688	0.738441	−	0.674318i	$-0.235562\pi$
$419$	30.2310	1.47688	0.738441	+	0.674318i	$0.235562\pi$
$420$	−0.341239	−0.0166508
$421$	23.4715	1.14393	0.571965	−	0.820278i	$-0.306181\pi$
$421$	23.4715	1.14393	0.571965	+	0.820278i	$0.306181\pi$
$422$	4.35729	0.212109
$423$	9.09472	0.442200
$424$	10.0448	0.487817
$425$	−4.82029	−0.233818
$426$	0.341239	0.0165331
$427$	−3.79382	−0.183596
$428$	0.0223235	0.00107905
$429$	−0.804880	−0.0388600
$430$	4.54945	0.219394
$431$	36.9235	1.77854	0.889272	−	0.457379i	$-0.151212\pi$
$431$	36.9235	1.77854	0.889272	+	0.457379i	$0.151212\pi$
$432$	−2.00770	−0.0965954
$433$	34.5057	1.65824	0.829119	−	0.559073i	$-0.188843\pi$
$433$	34.5057	1.65824	0.829119	+	0.559073i	$0.188843\pi$
$434$	5.25675	0.252332
$435$	−2.58050	−0.123726
$436$	−9.49400	−0.454680
$437$	10.9935	0.525892
$438$	−0.935820	−0.0447152
$439$	13.5866	0.648454	0.324227	−	0.945979i	$-0.394896\pi$
$439$	13.5866	0.648454	0.324227	+	0.945979i	$0.394896\pi$
$440$	6.05712	0.288762
$441$	−2.88356	−0.137312
$442$	−1.87707	−0.0892829
$443$	−12.0441	−0.572233	−0.286116	−	0.958195i	$-0.592364\pi$
$443$	−12.0441	−0.572233	−0.286116	+	0.958195i	$0.592364\pi$
$444$	3.21875	0.152755
$445$	−8.42696	−0.399476
$446$	18.7902	0.889743
$447$	2.02269	0.0956700
$448$	1.00000	0.0472456
$449$	−17.1812	−0.810833	−0.405417	−	0.914132i	$-0.632874\pi$
$449$	−17.1812	−0.810833	−0.405417	+	0.914132i	$0.632874\pi$
$450$	−2.88356	−0.135932
$451$	−0.733465	−0.0345375
$452$	−1.67130	−0.0786114
$453$	−1.54152	−0.0724267
$454$	16.0319	0.752414
$455$	−0.389409	−0.0182558
$456$	2.02847	0.0949919
$457$	15.0007	0.701702	0.350851	−	0.936431i	$-0.385892\pi$
$457$	15.0007	0.701702	0.350851	+	0.936431i	$0.385892\pi$
$458$	−5.31554	−0.248379
$459$	9.67769	0.451716
$460$	−1.84938	−0.0862279
$461$	31.1338	1.45004	0.725022	−	0.688725i	$-0.241829\pi$
$461$	31.1338	1.45004	0.725022	+	0.688725i	$0.241829\pi$
$462$	−2.06692	−0.0961620
$463$	−26.5573	−1.23422	−0.617112	−	0.786875i	$-0.711698\pi$
$463$	−26.5573	−1.23422	−0.617112	+	0.786875i	$0.711698\pi$
$464$	7.56216	0.351064
$465$	−1.79381	−0.0831859
$466$	−9.92235	−0.459644
$467$	6.03662	0.279341	0.139671	−	0.990198i	$-0.455396\pi$
$467$	6.03662	0.279341	0.139671	+	0.990198i	$0.455396\pi$
$468$	−1.12288	−0.0519053
$469$	10.2060	0.471270
$470$	3.15399	0.145483
$471$	−1.83636	−0.0846150
$472$	9.27421	0.426880
$473$	27.5566	1.26705
$474$	1.31356	0.0603338
$475$	5.94443	0.272749
$476$	−4.82029	−0.220938
$477$	−28.9647	−1.32620
$478$	11.2277	0.513541
$479$	30.6403	1.39999	0.699996	−	0.714146i	$-0.253185\pi$
$479$	30.6403	1.39999	0.699996	+	0.714146i	$0.253185\pi$
$480$	−0.341239	−0.0155754
$481$	3.67312	0.167480
$482$	−1.40676	−0.0640763
$483$	0.631082	0.0287152
$484$	25.6887	1.16767
$485$	−16.4915	−0.748842
$486$	8.74126	0.396511
$487$	−39.8362	−1.80515	−0.902576	−	0.430531i	$-0.858326\pi$
$487$	−39.8362	−1.80515	−0.902576	+	0.430531i	$0.858326\pi$
$488$	−3.79382	−0.171738
$489$	0.0688935	0.00311547
$490$	−1.00000	−0.0451754
$491$	−16.6319	−0.750585	−0.375293	−	0.926906i	$-0.622458\pi$
$491$	−16.6319	−0.750585	−0.375293	+	0.926906i	$0.622458\pi$
$492$	0.0413211	0.00186290
$493$	−36.4518	−1.64171
$494$	2.31482	0.104149
$495$	−17.4660	−0.785040
$496$	5.25675	0.236035
$497$	1.00000	0.0448561
$498$	4.96266	0.222382
$499$	35.6677	1.59671	0.798353	−	0.602190i	$-0.205705\pi$
$499$	35.6677	1.59671	0.798353	+	0.602190i	$0.205705\pi$
$500$	−1.00000	−0.0447214
$501$	0.122579	0.00547643
$502$	−9.35813	−0.417674
$503$	−12.2550	−0.546421	−0.273211	−	0.961954i	$-0.588086\pi$
$503$	−12.2550	−0.546421	−0.273211	+	0.961954i	$0.588086\pi$
$504$	−2.88356	−0.128444
$505$	12.2528	0.545243
$506$	−11.2019	−0.497987
$507$	−4.38436	−0.194716
$508$	−1.33188	−0.0590925
$509$	−13.3806	−0.593083	−0.296541	−	0.955020i	$-0.595833\pi$
$509$	−13.3806	−0.593083	−0.296541	+	0.955020i	$0.595833\pi$
$510$	1.64487	0.0728361
$511$	−2.74242	−0.121317
$512$	1.00000	0.0441942
$513$	−11.9346	−0.526927
$514$	−16.6619	−0.734924
$515$	1.45020	0.0639034
$516$	−1.55245	−0.0683428
$517$	19.1041	0.840198
$518$	9.43253	0.414442
$519$	−5.09339	−0.223575
$520$	−0.389409	−0.0170767
$521$	−11.1894	−0.490217	−0.245109	−	0.969496i	$-0.578824\pi$
$521$	−11.1894	−0.490217	−0.245109	+	0.969496i	$0.578824\pi$
$522$	−21.8059	−0.954419
$523$	−5.29182	−0.231395	−0.115698	−	0.993284i	$-0.536910\pi$
$523$	−5.29182	−0.231395	−0.115698	+	0.993284i	$0.536910\pi$
$524$	0.259277	0.0113266
$525$	0.341239	0.0148929
$526$	−16.2414	−0.708159
$527$	−25.3391	−1.10379
$528$	−2.06692	−0.0899513
$529$	−19.5798	−0.851295
$530$	−10.0448	−0.436317
$531$	−26.7427	−1.16054
$532$	5.94443	0.257724
$533$	0.0471541	0.00204247
$534$	2.87561	0.124440
$535$	−0.0223235	−0.000965128 0
$536$	10.2060	0.440832
$537$	−7.85744	−0.339074
$538$	13.1702	0.567809
$539$	−6.05712	−0.260899
$540$	2.00770	0.0863976
$541$	26.0430	1.11968	0.559839	−	0.828602i	$-0.310863\pi$
$541$	26.0430	1.11968	0.559839	+	0.828602i	$0.310863\pi$
$542$	23.6084	1.01407
$543$	3.18663	0.136752
$544$	−4.82029	−0.206668
$545$	9.49400	0.406678
$546$	0.132882	0.00568681
$547$	−11.4929	−0.491400	−0.245700	−	0.969346i	$-0.579018\pi$
$547$	−11.4929	−0.491400	−0.245700	+	0.969346i	$0.579018\pi$
$548$	−14.3749	−0.614064
$549$	10.9397	0.466894
$550$	−6.05712	−0.258276
$551$	44.9527	1.91505
$552$	0.631082	0.0268606
$553$	3.84938	0.163692
$554$	8.32251	0.353589
$555$	−3.21875	−0.136628
$556$	2.82801	0.119934
$557$	−36.1832	−1.53313	−0.766565	−	0.642167i	$-0.778036\pi$
$557$	−36.1832	−1.53313	−0.766565	+	0.642167i	$0.778036\pi$
$558$	−15.1581	−0.641696
$559$	−1.77160	−0.0749307
$560$	−1.00000	−0.0422577
$561$	9.96317	0.420646
$562$	13.4621	0.567863
$563$	−0.554149	−0.0233546	−0.0116773	−	0.999932i	$-0.503717\pi$
$563$	−0.554149	−0.0233546	−0.0116773	+	0.999932i	$0.503717\pi$
$564$	−1.07627	−0.0453190
$565$	1.67130	0.0703122
$566$	12.5067	0.525697
$567$	7.96556	0.334522
$568$	1.00000	0.0419591
$569$	21.1674	0.887382	0.443691	−	0.896180i	$-0.353669\pi$
$569$	21.1674	0.887382	0.443691	+	0.896180i	$0.353669\pi$
$570$	−2.02847	−0.0849633
$571$	−29.0844	−1.21714	−0.608571	−	0.793499i	$-0.708257\pi$
$571$	−29.0844	−1.21714	−0.608571	+	0.793499i	$0.708257\pi$
$572$	−2.35870	−0.0986222
$573$	−3.02871	−0.126526
$574$	0.121091	0.00505426
$575$	1.84938	0.0771246
$576$	−2.88356	−0.120148
$577$	−22.8235	−0.950156	−0.475078	−	0.879944i	$-0.657580\pi$
$577$	−22.8235	−0.950156	−0.475078	+	0.879944i	$0.657580\pi$
$578$	6.23519	0.259350
$579$	1.58675	0.0659430
$580$	−7.56216	−0.314002
$581$	14.5431	0.603348
$582$	5.62755	0.233270
$583$	−60.8424	−2.51983
$584$	−2.74242	−0.113482
$585$	1.12288	0.0464255
$586$	11.4204	0.471773
$587$	−27.8036	−1.14758	−0.573789	−	0.819003i	$-0.694527\pi$
$587$	−27.8036	−1.14758	−0.573789	+	0.819003i	$0.694527\pi$
$588$	0.341239	0.0140725
$589$	31.2484	1.28757
$590$	−9.27421	−0.381813
$591$	−2.25422	−0.0927261
$592$	9.43253	0.387675
$593$	−21.5587	−0.885309	−0.442655	−	0.896692i	$-0.645963\pi$
$593$	−21.5587	−0.885309	−0.442655	+	0.896692i	$0.645963\pi$
$594$	12.1609	0.498966
$595$	4.82029	0.197613
$596$	5.92749	0.242799
$597$	−7.69806	−0.315060
$598$	0.720167	0.0294498
$599$	44.0524	1.79993	0.899967	−	0.435958i	$-0.143591\pi$
$599$	44.0524	1.79993	0.899967	+	0.435958i	$0.143591\pi$
$600$	0.341239	0.0139310
$601$	31.6010	1.28903	0.644515	−	0.764591i	$-0.277059\pi$
$601$	31.6010	1.28903	0.644515	+	0.764591i	$0.277059\pi$
$602$	−4.54945	−0.185422
$603$	−29.4296	−1.19847
$604$	−4.51741	−0.183811
$605$	−25.6887	−1.04439
$606$	−4.18114	−0.169847
$607$	31.9382	1.29633	0.648166	−	0.761499i	$-0.275536\pi$
$607$	31.9382	1.29633	0.648166	+	0.761499i	$0.275536\pi$
$608$	5.94443	0.241079
$609$	2.58050	0.104567
$610$	3.79382	0.153607
$611$	−1.22820	−0.0496875
$612$	13.8996	0.561857
$613$	−6.36760	−0.257185	−0.128592	−	0.991698i	$-0.541046\pi$
$613$	−6.36760	−0.257185	−0.128592	+	0.991698i	$0.541046\pi$
$614$	27.2409	1.09936
$615$	−0.0413211	−0.00166623
$616$	−6.05712	−0.244048
$617$	−10.6320	−0.428029	−0.214014	−	0.976831i	$-0.568654\pi$
$617$	−10.6320	−0.428029	−0.214014	+	0.976831i	$0.568654\pi$
$618$	−0.494864	−0.0199063
$619$	18.6417	0.749271	0.374636	−	0.927172i	$-0.377768\pi$
$619$	18.6417	0.749271	0.374636	+	0.927172i	$0.377768\pi$
$620$	−5.25675	−0.211116
$621$	−3.71300	−0.148998
$622$	−13.6565	−0.547575
$623$	8.42696	0.337619
$624$	0.132882	0.00531952
$625$	1.00000	0.0400000
$626$	−7.01758	−0.280479
$627$	−12.2867	−0.490683
$628$	−5.38145	−0.214743
$629$	−45.4675	−1.81291
$630$	2.88356	0.114884
$631$	−18.5452	−0.738272	−0.369136	−	0.929375i	$-0.620346\pi$
$631$	−18.5452	−0.738272	−0.369136	+	0.929375i	$0.620346\pi$
$632$	3.84938	0.153120
$633$	1.48688	0.0590980
$634$	4.38970	0.174337
$635$	1.33188	0.0528539
$636$	3.42767	0.135916
$637$	0.389409	0.0154290
$638$	−45.8049	−1.81343
$639$	−2.88356	−0.114072
$640$	−1.00000	−0.0395285
$641$	21.5229	0.850102	0.425051	−	0.905170i	$-0.360256\pi$
$641$	21.5229	0.850102	0.425051	+	0.905170i	$0.360256\pi$
$642$	0.00761764	0.000300644 0
$643$	−46.3096	−1.82627	−0.913136	−	0.407655i	$-0.866347\pi$
$643$	−46.3096	−1.82627	−0.913136	+	0.407655i	$0.866347\pi$
$644$	1.84938	0.0728759
$645$	1.55245	0.0611277
$646$	−28.6539	−1.12737
$647$	−13.4183	−0.527527	−0.263764	−	0.964587i	$-0.584964\pi$
$647$	−13.4183	−0.527527	−0.263764	+	0.964587i	$0.584964\pi$
$648$	7.96556	0.312917
$649$	−56.1750	−2.20506
$650$	0.389409	0.0152739
$651$	1.79381	0.0703049
$652$	0.201892	0.00790671
$653$	1.86896	0.0731380	0.0365690	−	0.999331i	$-0.488357\pi$
$653$	1.86896	0.0731380	0.0365690	+	0.999331i	$0.488357\pi$
$654$	−3.23972	−0.126683
$655$	−0.259277	−0.0101308
$656$	0.121091	0.00472783
$657$	7.90792	0.308517
$658$	−3.15399	−0.122956
$659$	−28.5222	−1.11107	−0.555534	−	0.831494i	$-0.687486\pi$
$659$	−28.5222	−1.11107	−0.555534	+	0.831494i	$0.687486\pi$
$660$	2.06692	0.0804549
$661$	15.4277	0.600068	0.300034	−	0.953929i	$-0.403002\pi$
$661$	15.4277	0.600068	0.300034	+	0.953929i	$0.403002\pi$
$662$	33.9097	1.31794
$663$	−0.640528	−0.0248760
$664$	14.5431	0.564381
$665$	−5.94443	−0.230515
$666$	−27.1992	−1.05395
$667$	13.9853	0.541514
$668$	0.359218	0.0138985
$669$	6.41196	0.247901
$670$	−10.2060	−0.394292
$671$	22.9796	0.887117
$672$	0.341239	0.0131636
$673$	32.8430	1.26601	0.633003	−	0.774149i	$-0.281822\pi$
$673$	32.8430	1.26601	0.633003	+	0.774149i	$0.281822\pi$
$674$	7.73290	0.297860
$675$	−2.00770	−0.0772763
$676$	−12.8484	−0.494168
$677$	30.4241	1.16929	0.584646	−	0.811289i	$-0.301233\pi$
$677$	30.4241	1.16929	0.584646	+	0.811289i	$0.301233\pi$
$678$	−0.570313	−0.0219027
$679$	16.4915	0.632887
$680$	4.82029	0.184850
$681$	5.47071	0.209638
$682$	−31.8408	−1.21925
$683$	−42.6924	−1.63358	−0.816789	−	0.576936i	$-0.804248\pi$
$683$	−42.6924	−1.63358	−0.816789	+	0.576936i	$0.804248\pi$
$684$	−17.1411	−0.655406
$685$	14.3749	0.549236
$686$	1.00000	0.0381802
$687$	−1.81387	−0.0692035
$688$	−4.54945	−0.173446
$689$	3.91153	0.149017
$690$	−0.631082	−0.0240249
$691$	−12.2370	−0.465519	−0.232760	−	0.972534i	$-0.574776\pi$
$691$	−12.2370	−0.465519	−0.232760	+	0.972534i	$0.574776\pi$
$692$	−14.9262	−0.567407
$693$	17.4660	0.663480
$694$	7.71891	0.293006
$695$	−2.82801	−0.107273
$696$	2.58050	0.0978137
$697$	−0.583696	−0.0221091
$698$	−25.4149	−0.961969
$699$	−3.38589	−0.128066
$700$	1.00000	0.0377964
$701$	−28.5033	−1.07655	−0.538277	−	0.842768i	$-0.680924\pi$
$701$	−28.5033	−1.07655	−0.538277	+	0.842768i	$0.680924\pi$
$702$	−0.781817	−0.0295078
$703$	56.0710	2.11476
$704$	−6.05712	−0.228286
$705$	1.07627	0.0405345
$706$	27.4798	1.03422
$707$	−12.2528	−0.460815
$708$	3.16472	0.118938
$709$	6.62576	0.248836	0.124418	−	0.992230i	$-0.460294\pi$
$709$	6.62576	0.248836	0.124418	+	0.992230i	$0.460294\pi$
$710$	−1.00000	−0.0375293
$711$	−11.0999	−0.416279
$712$	8.42696	0.315814
$713$	9.72176	0.364083
$714$	−1.64487	−0.0615577
$715$	2.35870	0.0882103
$716$	−23.0262	−0.860530
$717$	3.83132	0.143083
$718$	−20.0101	−0.746771
$719$	43.5301	1.62340	0.811700	−	0.584075i	$-0.198543\pi$
$719$	43.5301	1.62340	0.811700	+	0.584075i	$0.198543\pi$
$720$	2.88356	0.107464
$721$	−1.45020	−0.0540082
$722$	16.3363	0.607973
$723$	−0.480042	−0.0178530
$724$	9.33842	0.347060
$725$	7.56216	0.280851
$726$	8.76598	0.325336
$727$	−39.6591	−1.47087	−0.735437	−	0.677594i	$-0.763023\pi$
$727$	−39.6591	−1.47087	−0.735437	+	0.677594i	$0.763023\pi$
$728$	0.389409	0.0144325
$729$	−20.9138	−0.774586
$730$	2.74242	0.101501
$731$	21.9297	0.811098
$732$	−1.29460	−0.0478497
$733$	8.01428	0.296014	0.148007	−	0.988986i	$-0.452714\pi$
$733$	8.01428	0.296014	0.148007	+	0.988986i	$0.452714\pi$
$734$	1.99465	0.0736239
$735$	−0.341239	−0.0125868
$736$	1.84938	0.0681692
$737$	−61.8190	−2.27713
$738$	−0.349174	−0.0128533
$739$	−44.9508	−1.65354	−0.826771	−	0.562538i	$-0.809825\pi$
$739$	−44.9508	−1.65354	−0.826771	+	0.562538i	$0.809825\pi$
$740$	−9.43253	−0.346747
$741$	0.789906	0.0290179
$742$	10.0448	0.368755
$743$	−28.5656	−1.04797	−0.523985	−	0.851727i	$-0.675555\pi$
$743$	−28.5656	−1.04797	−0.523985	+	0.851727i	$0.675555\pi$
$744$	1.79381	0.0657642
$745$	−5.92749	−0.217166
$746$	5.78346	0.211747
$747$	−41.9358	−1.53435
$748$	29.1971	1.06755
$749$	0.0223235	0.000815682 0
$750$	−0.341239	−0.0124603
$751$	−24.8108	−0.905358	−0.452679	−	0.891674i	$-0.649532\pi$
$751$	−24.8108	−0.905358	−0.452679	+	0.891674i	$0.649532\pi$
$752$	−3.15399	−0.115014
$753$	−3.19336	−0.116372
$754$	2.94478	0.107242
$755$	4.51741	0.164405
$756$	−2.00770	−0.0730193
$757$	−39.2199	−1.42547	−0.712736	−	0.701432i	$-0.752544\pi$
$757$	−39.2199	−1.42547	−0.712736	+	0.701432i	$0.752544\pi$
$758$	−22.9688	−0.834266
$759$	−3.82254	−0.138749
$760$	−5.94443	−0.215627
$761$	24.1188	0.874305	0.437153	−	0.899387i	$-0.355987\pi$
$761$	24.1188	0.874305	0.437153	+	0.899387i	$0.355987\pi$
$762$	−0.454488	−0.0164644
$763$	−9.49400	−0.343706
$764$	−8.87564	−0.321109
$765$	−13.8996	−0.502540
$766$	5.31881	0.192177
$767$	3.61147	0.130403
$768$	0.341239	0.0123134
$769$	−28.3804	−1.02342	−0.511712	−	0.859157i	$-0.670989\pi$
$769$	−28.3804	−1.02342	−0.511712	+	0.859157i	$0.670989\pi$
$770$	6.05712	0.218283
$771$	−5.68568	−0.204765
$772$	4.64996	0.167356
$773$	3.92570	0.141198	0.0705989	−	0.997505i	$-0.477509\pi$
$773$	3.92570	0.141198	0.0705989	+	0.997505i	$0.477509\pi$
$774$	13.1186	0.471538
$775$	5.25675	0.188828
$776$	16.4915	0.592011
$777$	3.21875	0.115472
$778$	−29.2890	−1.05006
$779$	0.719820	0.0257902
$780$	−0.132882	−0.00475793
$781$	−6.05712	−0.216741
$782$	−8.91456	−0.318784
$783$	−15.1825	−0.542579
$784$	1.00000	0.0357143
$785$	5.38145	0.192072
$786$	0.0884755	0.00315581
$787$	−0.573355	−0.0204379	−0.0102190	−	0.999948i	$-0.503253\pi$
$787$	−0.573355	−0.0204379	−0.0102190	+	0.999948i	$0.503253\pi$
$788$	−6.60598	−0.235328
$789$	−5.54220	−0.197308
$790$	−3.84938	−0.136955
$791$	−1.67130	−0.0594246
$792$	17.4660	0.620629
$793$	−1.47735	−0.0524621
$794$	35.7838	1.26992
$795$	−3.42767	−0.121567
$796$	−22.5591	−0.799587
$797$	−7.96244	−0.282044	−0.141022	−	0.990006i	$-0.545039\pi$
$797$	−7.96244	−0.282044	−0.141022	+	0.990006i	$0.545039\pi$
$798$	2.02847	0.0718071
$799$	15.2032	0.537849
$800$	1.00000	0.0353553
$801$	−24.2996	−0.858585
$802$	29.3831	1.03755
$803$	16.6111	0.586195
$804$	3.48269	0.122825
$805$	−1.84938	−0.0651822
$806$	2.04703	0.0721036
$807$	4.49419	0.158203
$808$	−12.2528	−0.431053
$809$	−55.5282	−1.95227	−0.976134	−	0.217169i	$-0.930318\pi$
$809$	−55.5282	−1.95227	−0.976134	+	0.217169i	$0.930318\pi$
$810$	−7.96556	−0.279881
$811$	−8.75916	−0.307576	−0.153788	−	0.988104i	$-0.549147\pi$
$811$	−8.75916	−0.307576	−0.153788	+	0.988104i	$0.549147\pi$
$812$	7.56216	0.265380
$813$	8.05609	0.282539
$814$	−57.1339	−2.00254
$815$	−0.201892	−0.00707197
$816$	−1.64487	−0.0575820
$817$	−27.0439	−0.946147
$818$	30.0395	1.05030
$819$	−1.12288	−0.0392367
$820$	−0.121091	−0.00422870
$821$	−37.8847	−1.32219	−0.661093	−	0.750304i	$-0.729907\pi$
$821$	−37.8847	−1.32219	−0.661093	+	0.750304i	$0.729907\pi$
$822$	−4.90527	−0.171091
$823$	−11.8382	−0.412653	−0.206327	−	0.978483i	$-0.566151\pi$
$823$	−11.8382	−0.412653	−0.206327	+	0.978483i	$0.566151\pi$
$824$	−1.45020	−0.0505200
$825$	−2.06692	−0.0719611
$826$	9.27421	0.322691
$827$	13.3232	0.463292	0.231646	−	0.972800i	$-0.425589\pi$
$827$	13.3232	0.463292	0.231646	+	0.972800i	$0.425589\pi$
$828$	−5.33280	−0.185328
$829$	−3.34196	−0.116071	−0.0580355	−	0.998315i	$-0.518484\pi$
$829$	−3.34196	−0.116071	−0.0580355	+	0.998315i	$0.518484\pi$
$830$	−14.5431	−0.504798
$831$	2.83996	0.0985172
$832$	0.389409	0.0135003
$833$	−4.82029	−0.167013
$834$	0.965027	0.0334162
$835$	−0.359218	−0.0124312
$836$	−36.0061	−1.24530
$837$	−10.5540	−0.364799
$838$	30.2310	1.04431
$839$	1.41917	0.0489952	0.0244976	−	0.999700i	$-0.492201\pi$
$839$	1.41917	0.0489952	0.0244976	+	0.999700i	$0.492201\pi$
$840$	−0.341239	−0.0117739
$841$	28.1862	0.971939
$842$	23.4715	0.808880
$843$	4.59378	0.158218
$844$	4.35729	0.149984
$845$	12.8484	0.441997
$846$	9.09472	0.312683
$847$	25.6887	0.882674
$848$	10.0448	0.344939
$849$	4.26779	0.146470
$850$	−4.82029	−0.165335
$851$	17.4444	0.597985
$852$	0.341239	0.0116907
$853$	−30.4161	−1.04143	−0.520714	−	0.853731i	$-0.674334\pi$
$853$	−30.4161	−1.04143	−0.520714	+	0.853731i	$0.674334\pi$
$854$	−3.79382	−0.129822
$855$	17.1411	0.586213
$856$	0.0223235	0.000763001 0
$857$	2.95062	0.100791	0.0503956	−	0.998729i	$-0.483952\pi$
$857$	2.95062	0.100791	0.0503956	+	0.998729i	$0.483952\pi$
$858$	−0.804880	−0.0274781
$859$	−19.8812	−0.678339	−0.339169	−	0.940725i	$-0.610146\pi$
$859$	−19.8812	−0.678339	−0.339169	+	0.940725i	$0.610146\pi$
$860$	4.54945	0.155135
$861$	0.0413211	0.00140822
$862$	36.9235	1.25762
$863$	49.6939	1.69160	0.845800	−	0.533500i	$-0.179123\pi$
$863$	49.6939	1.69160	0.845800	+	0.533500i	$0.179123\pi$
$864$	−2.00770	−0.0683033
$865$	14.9262	0.507505
$866$	34.5057	1.17255
$867$	2.12769	0.0722601
$868$	5.25675	0.178426
$869$	−23.3162	−0.790947
$870$	−2.58050	−0.0874872
$871$	3.97431	0.134665
$872$	−9.49400	−0.321508
$873$	−47.5542	−1.60947
$874$	10.9935	0.371862
$875$	−1.00000	−0.0338062
$876$	−0.935820	−0.0316184
$877$	28.6233	0.966539	0.483269	−	0.875472i	$-0.339449\pi$
$877$	28.6233	0.966539	0.483269	+	0.875472i	$0.339449\pi$
$878$	13.5866	0.458526
$879$	3.89709	0.131446
$880$	6.05712	0.204185
$881$	56.5814	1.90627	0.953137	−	0.302538i	$-0.0978338\pi$
$881$	56.5814	1.90627	0.953137	+	0.302538i	$0.0978338\pi$
$882$	−2.88356	−0.0970944
$883$	5.66972	0.190801	0.0954006	−	0.995439i	$-0.469587\pi$
$883$	5.66972	0.190801	0.0954006	+	0.995439i	$0.469587\pi$
$884$	−1.87707	−0.0631326
$885$	−3.16472	−0.106381
$886$	−12.0441	−0.404630
$887$	5.69231	0.191129	0.0955645	−	0.995423i	$-0.469534\pi$
$887$	5.69231	0.191129	0.0955645	+	0.995423i	$0.469534\pi$
$888$	3.21875	0.108014
$889$	−1.33188	−0.0446697
$890$	−8.42696	−0.282472
$891$	−48.2484	−1.61638
$892$	18.7902	0.629143
$893$	−18.7487	−0.627401
$894$	2.02269	0.0676489
$895$	23.0262	0.769681
$896$	1.00000	0.0334077
$897$	0.245749	0.00820532
$898$	−17.1812	−0.573346
$899$	39.7524	1.32582
$900$	−2.88356	−0.0961185
$901$	−48.4187	−1.61306
$902$	−0.733465	−0.0244217
$903$	−1.55245	−0.0516623
$904$	−1.67130	−0.0555867
$905$	−9.33842	−0.310420
$906$	−1.54152	−0.0512134
$907$	−43.1090	−1.43141	−0.715706	−	0.698402i	$-0.753895\pi$
$907$	−43.1090	−1.43141	−0.715706	+	0.698402i	$0.753895\pi$
$908$	16.0319	0.532037
$909$	35.3317	1.17188
$910$	−0.389409	−0.0129088
$911$	18.5712	0.615293	0.307646	−	0.951501i	$-0.400459\pi$
$911$	18.5712	0.615293	0.307646	+	0.951501i	$0.400459\pi$
$912$	2.02847	0.0671694
$913$	−88.0891	−2.91532
$914$	15.0007	0.496178
$915$	1.29460	0.0427981
$916$	−5.31554	−0.175631
$917$	0.259277	0.00856209
$918$	9.67769	0.319411
$919$	60.0664	1.98141	0.990703	−	0.136041i	$-0.0434378\pi$
$919$	60.0664	1.98141	0.990703	+	0.136041i	$0.0434378\pi$
$920$	−1.84938	−0.0609724
$921$	9.29567	0.306303
$922$	31.1338	1.02534
$923$	0.389409	0.0128176
$924$	−2.06692	−0.0679968
$925$	9.43253	0.310140
$926$	−26.5573	−0.872728
$927$	4.18173	0.137346
$928$	7.56216	0.248240
$929$	31.2621	1.02568	0.512838	−	0.858485i	$-0.328594\pi$
$929$	31.2621	1.02568	0.512838	+	0.858485i	$0.328594\pi$
$930$	−1.79381	−0.0588213
$931$	5.94443	0.194821
$932$	−9.92235	−0.325018
$933$	−4.66013	−0.152566
$934$	6.03662	0.197524
$935$	−29.1971	−0.954846
$936$	−1.12288	−0.0367026
$937$	11.1043	0.362760	0.181380	−	0.983413i	$-0.441944\pi$
$937$	11.1043	0.362760	0.181380	+	0.983413i	$0.441944\pi$
$938$	10.2060	0.333238
$939$	−2.39467	−0.0781471
$940$	3.15399	0.102872
$941$	39.2226	1.27862	0.639311	−	0.768949i	$-0.279220\pi$
$941$	39.2226	1.27862	0.639311	+	0.768949i	$0.279220\pi$
$942$	−1.83636	−0.0598318
$943$	0.223944	0.00729264
$944$	9.27421	0.301850
$945$	2.00770	0.0653104
$946$	27.5566	0.895941
$947$	−21.1101	−0.685986	−0.342993	−	0.939338i	$-0.611441\pi$
$947$	−21.1101	−0.685986	−0.342993	+	0.939338i	$0.611441\pi$
$948$	1.31356	0.0426624
$949$	−1.06792	−0.0346663
$950$	5.94443	0.192863
$951$	1.49794	0.0485739
$952$	−4.82029	−0.156226
$953$	6.78794	0.219883	0.109942	−	0.993938i	$-0.464934\pi$
$953$	6.78794	0.219883	0.109942	+	0.993938i	$0.464934\pi$
$954$	−28.9647	−0.937765
$955$	8.87564	0.287209
$956$	11.2277	0.363129
$957$	−15.6304	−0.505259
$958$	30.6403	0.989944
$959$	−14.3749	−0.464189
$960$	−0.341239	−0.0110134
$961$	−3.36653	−0.108598
$962$	3.67312	0.118426
$963$	−0.0643710	−0.00207433
$964$	−1.40676	−0.0453088
$965$	−4.64996	−0.149688
$966$	0.631082	0.0203047
$967$	17.5881	0.565597	0.282798	−	0.959179i	$-0.408737\pi$
$967$	17.5881	0.565597	0.282798	+	0.959179i	$0.408737\pi$
$968$	25.6887	0.825666
$969$	−9.77782	−0.314109
$970$	−16.4915	−0.529511
$971$	19.1170	0.613493	0.306746	−	0.951791i	$-0.400760\pi$
$971$	19.1170	0.613493	0.306746	+	0.951791i	$0.400760\pi$
$972$	8.74126	0.280376
$973$	2.82801	0.0906618
$974$	−39.8362	−1.27643
$975$	0.132882	0.00425562
$976$	−3.79382	−0.121437
$977$	20.0124	0.640253	0.320126	−	0.947375i	$-0.396275\pi$
$977$	20.0124	0.640253	0.320126	+	0.947375i	$0.396275\pi$
$978$	0.0688935	0.00220297
$979$	−51.0431	−1.63134
$980$	−1.00000	−0.0319438
$981$	27.3765	0.874064
$982$	−16.6319	−0.530744
$983$	−60.0495	−1.91528	−0.957641	−	0.287965i	$-0.907021\pi$
$983$	−60.0495	−1.91528	−0.957641	+	0.287965i	$0.907021\pi$
$984$	0.0413211	0.00131727
$985$	6.60598	0.210484
$986$	−36.4518	−1.16086
$987$	−1.07627	−0.0342579
$988$	2.31482	0.0736442
$989$	−8.41368	−0.267540
$990$	−17.4660	−0.555107
$991$	6.49417	0.206294	0.103147	−	0.994666i	$-0.467109\pi$
$991$	6.49417	0.206294	0.103147	+	0.994666i	$0.467109\pi$
$992$	5.25675	0.166902
$993$	11.5713	0.367205
$994$	1.00000	0.0317181
$995$	22.5591	0.715173
$996$	4.96266	0.157248
$997$	52.4502	1.66111	0.830557	−	0.556934i	$-0.188022\pi$
$997$	52.4502	1.66111	0.830557	+	0.556934i	$0.188022\pi$
$998$	35.6677	1.12904
$999$	−18.9377	−0.599161

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4970.2.a.z.1.5	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4970.2.a.z.1.5	✓	9	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:	\( N \)	\(=\)	\( 4970 = 2 \cdot 5 \cdot 7 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4970.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.341239 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.341239 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.88356 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.341239 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.341239 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.88356 q^{9} -1.00000 q^{10} -6.05712 q^{11} +0.341239 q^{12} +0.389409 q^{13} +1.00000 q^{14} -0.341239 q^{15} +1.00000 q^{16} -4.82029 q^{17} -2.88356 q^{18} +5.94443 q^{19} -1.00000 q^{20} +0.341239 q^{21} -6.05712 q^{22} +1.84938 q^{23} +0.341239 q^{24} +1.00000 q^{25} +0.389409 q^{26} -2.00770 q^{27} +1.00000 q^{28} +7.56216 q^{29} -0.341239 q^{30} +5.25675 q^{31} +1.00000 q^{32} -2.06692 q^{33} -4.82029 q^{34} -1.00000 q^{35} -2.88356 q^{36} +9.43253 q^{37} +5.94443 q^{38} +0.132882 q^{39} -1.00000 q^{40} +0.121091 q^{41} +0.341239 q^{42} -4.54945 q^{43} -6.05712 q^{44} +2.88356 q^{45} +1.84938 q^{46} -3.15399 q^{47} +0.341239 q^{48} +1.00000 q^{49} +1.00000 q^{50} -1.64487 q^{51} +0.389409 q^{52} +10.0448 q^{53} -2.00770 q^{54} +6.05712 q^{55} +1.00000 q^{56} +2.02847 q^{57} +7.56216 q^{58} +9.27421 q^{59} -0.341239 q^{60} -3.79382 q^{61} +5.25675 q^{62} -2.88356 q^{63} +1.00000 q^{64} -0.389409 q^{65} -2.06692 q^{66} +10.2060 q^{67} -4.82029 q^{68} +0.631082 q^{69} -1.00000 q^{70} +1.00000 q^{71} -2.88356 q^{72} -2.74242 q^{73} +9.43253 q^{74} +0.341239 q^{75} +5.94443 q^{76} -6.05712 q^{77} +0.132882 q^{78} +3.84938 q^{79} -1.00000 q^{80} +7.96556 q^{81} +0.121091 q^{82} +14.5431 q^{83} +0.341239 q^{84} +4.82029 q^{85} -4.54945 q^{86} +2.58050 q^{87} -6.05712 q^{88} +8.42696 q^{89} +2.88356 q^{90} +0.389409 q^{91} +1.84938 q^{92} +1.79381 q^{93} -3.15399 q^{94} -5.94443 q^{95} +0.341239 q^{96} +16.4915 q^{97} +1.00000 q^{98} +17.4660 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9	\( 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9} - 9 q^{10} - 2 q^{11} + 4 q^{12} + 11 q^{13} + 9 q^{14} - 4 q^{15} + 9 q^{16} + 9 q^{17} + 7 q^{18} + 9 q^{19} - 9 q^{20} + 4 q^{21} - 2 q^{22} + 2 q^{23} + 4 q^{24} + 9 q^{25} + 11 q^{26} + 7 q^{27} + 9 q^{28} + 2 q^{29} - 4 q^{30} + 18 q^{31} + 9 q^{32} + 8 q^{33} + 9 q^{34} - 9 q^{35} + 7 q^{36} + 15 q^{37} + 9 q^{38} - 7 q^{39} - 9 q^{40} + 15 q^{41} + 4 q^{42} + 7 q^{43} - 2 q^{44} - 7 q^{45} + 2 q^{46} + 12 q^{47} + 4 q^{48} + 9 q^{49} + 9 q^{50} + 4 q^{51} + 11 q^{52} + 3 q^{53} + 7 q^{54} + 2 q^{55} + 9 q^{56} + 9 q^{57} + 2 q^{58} + 24 q^{59} - 4 q^{60} + 25 q^{61} + 18 q^{62} + 7 q^{63} + 9 q^{64} - 11 q^{65} + 8 q^{66} - 4 q^{67} + 9 q^{68} + 3 q^{69} - 9 q^{70} + 9 q^{71} + 7 q^{72} + 32 q^{73} + 15 q^{74} + 4 q^{75} + 9 q^{76} - 2 q^{77} - 7 q^{78} + 20 q^{79} - 9 q^{80} - 7 q^{81} + 15 q^{82} + 11 q^{83} + 4 q^{84} - 9 q^{85} + 7 q^{86} + 26 q^{87} - 2 q^{88} + 10 q^{89} - 7 q^{90} + 11 q^{91} + 2 q^{92} + 32 q^{93} + 12 q^{94} - 9 q^{95} + 4 q^{96} + 19 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9 - 9 * q^10 - 2 * q^11 + 4 * q^12 + 11 * q^13 + 9 * q^14 - 4 * q^15 + 9 * q^16 + 9 * q^17 + 7 * q^18 + 9 * q^19 - 9 * q^20 + 4 * q^21 - 2 * q^22 + 2 * q^23 + 4 * q^24 + 9 * q^25 + 11 * q^26 + 7 * q^27 + 9 * q^28 + 2 * q^29 - 4 * q^30 + 18 * q^31 + 9 * q^32 + 8 * q^33 + 9 * q^34 - 9 * q^35 + 7 * q^36 + 15 * q^37 + 9 * q^38 - 7 * q^39 - 9 * q^40 + 15 * q^41 + 4 * q^42 + 7 * q^43 - 2 * q^44 - 7 * q^45 + 2 * q^46 + 12 * q^47 + 4 * q^48 + 9 * q^49 + 9 * q^50 + 4 * q^51 + 11 * q^52 + 3 * q^53 + 7 * q^54 + 2 * q^55 + 9 * q^56 + 9 * q^57 + 2 * q^58 + 24 * q^59 - 4 * q^60 + 25 * q^61 + 18 * q^62 + 7 * q^63 + 9 * q^64 - 11 * q^65 + 8 * q^66 - 4 * q^67 + 9 * q^68 + 3 * q^69 - 9 * q^70 + 9 * q^71 + 7 * q^72 + 32 * q^73 + 15 * q^74 + 4 * q^75 + 9 * q^76 - 2 * q^77 - 7 * q^78 + 20 * q^79 - 9 * q^80 - 7 * q^81 + 15 * q^82 + 11 * q^83 + 4 * q^84 - 9 * q^85 + 7 * q^86 + 26 * q^87 - 2 * q^88 + 10 * q^89 - 7 * q^90 + 11 * q^91 + 2 * q^92 + 32 * q^93 + 12 * q^94 - 9 * q^95 + 4 * q^96 + 19 * q^97 + 9 * q^98 - 7 * q^99

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