LMFDB - Embedded newform 8007.2.a.e.1.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.498979 q^{2} +1.00000 q^{3} -1.75102 q^{4} +0.0200529 q^{5} -0.498979 q^{6} -2.67003 q^{7} +1.87168 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.498979 q^{2} +1.00000 q^{3} -1.75102 q^{4} +0.0200529 q^{5} -0.498979 q^{6} -2.67003 q^{7} +1.87168 q^{8} +1.00000 q^{9} -0.0100060 q^{10} +0.400083 q^{11} -1.75102 q^{12} +1.83610 q^{13} +1.33229 q^{14} +0.0200529 q^{15} +2.56811 q^{16} -1.00000 q^{17} -0.498979 q^{18} -2.84522 q^{19} -0.0351129 q^{20} -2.67003 q^{21} -0.199633 q^{22} +6.13316 q^{23} +1.87168 q^{24} -4.99960 q^{25} -0.916175 q^{26} +1.00000 q^{27} +4.67528 q^{28} -3.39897 q^{29} -0.0100060 q^{30} -4.05428 q^{31} -5.02480 q^{32} +0.400083 q^{33} +0.498979 q^{34} -0.0535418 q^{35} -1.75102 q^{36} +6.09727 q^{37} +1.41970 q^{38} +1.83610 q^{39} +0.0375325 q^{40} +8.26967 q^{41} +1.33229 q^{42} -0.679491 q^{43} -0.700554 q^{44} +0.0200529 q^{45} -3.06032 q^{46} -5.43829 q^{47} +2.56811 q^{48} +0.129082 q^{49} +2.49470 q^{50} -1.00000 q^{51} -3.21505 q^{52} +9.14306 q^{53} -0.498979 q^{54} +0.00802281 q^{55} -4.99745 q^{56} -2.84522 q^{57} +1.69602 q^{58} -9.11938 q^{59} -0.0351129 q^{60} -5.01919 q^{61} +2.02300 q^{62} -2.67003 q^{63} -2.62895 q^{64} +0.0368190 q^{65} -0.199633 q^{66} +4.00797 q^{67} +1.75102 q^{68} +6.13316 q^{69} +0.0267162 q^{70} +0.282673 q^{71} +1.87168 q^{72} +3.43652 q^{73} -3.04241 q^{74} -4.99960 q^{75} +4.98203 q^{76} -1.06824 q^{77} -0.916175 q^{78} +10.5491 q^{79} +0.0514979 q^{80} +1.00000 q^{81} -4.12640 q^{82} +8.64602 q^{83} +4.67528 q^{84} -0.0200529 q^{85} +0.339052 q^{86} -3.39897 q^{87} +0.748828 q^{88} +4.48328 q^{89} -0.0100060 q^{90} -4.90245 q^{91} -10.7393 q^{92} -4.05428 q^{93} +2.71359 q^{94} -0.0570547 q^{95} -5.02480 q^{96} -10.7121 q^{97} -0.0644093 q^{98} +0.400083 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.498979	−0.352832	−0.176416	−	0.984316i	$-0.556450\pi$
$2$	−0.498979	−0.352832	−0.176416	+	0.984316i	$0.556450\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.75102	−0.875510
$5$	0.0200529	0.00896791	0.00448395	−	0.999990i	$-0.498573\pi$
$5$	0.0200529	0.00896791	0.00448395	+	0.999990i	$0.498573\pi$
$6$	−0.498979	−0.203707
$7$	−2.67003	−1.00918	−0.504589	−	0.863360i	$-0.668356\pi$
$7$	−2.67003	−1.00918	−0.504589	+	0.863360i	$0.668356\pi$
$8$	1.87168	0.661739
$9$	1.00000	0.333333
$10$	−0.0100060	−0.00316416
$11$	0.400083	0.120630	0.0603148	−	0.998179i	$-0.480790\pi$
$11$	0.400083	0.120630	0.0603148	+	0.998179i	$0.480790\pi$
$12$	−1.75102	−0.505476
$13$	1.83610	0.509242	0.254621	−	0.967041i	$-0.418049\pi$
$13$	1.83610	0.509242	0.254621	+	0.967041i	$0.418049\pi$
$14$	1.33229	0.356070
$15$	0.0200529	0.00517762
$16$	2.56811	0.642027
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.498979	−0.117611
$19$	−2.84522	−0.652737	−0.326369	−	0.945243i	$-0.605825\pi$
$19$	−2.84522	−0.652737	−0.326369	+	0.945243i	$0.605825\pi$
$20$	−0.0351129	−0.00785149
$21$	−2.67003	−0.582649
$22$	−0.199633	−0.0425620
$23$	6.13316	1.27885	0.639426	−	0.768852i	$-0.279172\pi$
$23$	6.13316	1.27885	0.639426	+	0.768852i	$0.279172\pi$
$24$	1.87168	0.382055
$25$	−4.99960	−0.999920
$26$	−0.916175	−0.179677
$27$	1.00000	0.192450
$28$	4.67528	0.883545
$29$	−3.39897	−0.631173	−0.315587	−	0.948897i	$-0.602201\pi$
$29$	−3.39897	−0.631173	−0.315587	+	0.948897i	$0.602201\pi$
$30$	−0.0100060	−0.00182683
$31$	−4.05428	−0.728171	−0.364085	−	0.931366i	$-0.618618\pi$
$31$	−4.05428	−0.728171	−0.364085	+	0.931366i	$0.618618\pi$
$32$	−5.02480	−0.888267
$33$	0.400083	0.0696456
$34$	0.498979	0.0855742
$35$	−0.0535418	−0.00905021
$36$	−1.75102	−0.291837
$37$	6.09727	1.00239	0.501193	−	0.865336i	$-0.332895\pi$
$37$	6.09727	1.00239	0.501193	+	0.865336i	$0.332895\pi$
$38$	1.41970	0.230306
$39$	1.83610	0.294011
$40$	0.0375325	0.00593442
$41$	8.26967	1.29151	0.645753	−	0.763546i	$-0.276544\pi$
$41$	8.26967	1.29151	0.645753	+	0.763546i	$0.276544\pi$
$42$	1.33229	0.205577
$43$	−0.679491	−0.103621	−0.0518107	−	0.998657i	$-0.516499\pi$
$43$	−0.679491	−0.103621	−0.0518107	+	0.998657i	$0.516499\pi$
$44$	−0.700554	−0.105612
$45$	0.0200529	0.00298930
$46$	−3.06032	−0.451220
$47$	−5.43829	−0.793256	−0.396628	−	0.917979i	$-0.629820\pi$
$47$	−5.43829	−0.793256	−0.396628	+	0.917979i	$0.629820\pi$
$48$	2.56811	0.370675
$49$	0.129082	0.0184403
$50$	2.49470	0.352803
$51$	−1.00000	−0.140028
$52$	−3.21505	−0.445847
$53$	9.14306	1.25590	0.627948	−	0.778255i	$-0.283895\pi$
$53$	9.14306	1.25590	0.627948	+	0.778255i	$0.283895\pi$
$54$	−0.498979	−0.0679025
$55$	0.00802281	0.00108180
$56$	−4.99745	−0.667813
$57$	−2.84522	−0.376858
$58$	1.69602	0.222698
$59$	−9.11938	−1.18724	−0.593621	−	0.804745i	$-0.702302\pi$
$59$	−9.11938	−1.18724	−0.593621	+	0.804745i	$0.702302\pi$
$60$	−0.0351129	−0.00453306
$61$	−5.01919	−0.642642	−0.321321	−	0.946970i	$-0.604127\pi$
$61$	−5.01919	−0.642642	−0.321321	+	0.946970i	$0.604127\pi$
$62$	2.02300	0.256922
$63$	−2.67003	−0.336393
$64$	−2.62895	−0.328619
$65$	0.0368190	0.00456684
$66$	−0.199633	−0.0245732
$67$	4.00797	0.489652	0.244826	−	0.969567i	$-0.421269\pi$
$67$	4.00797	0.489652	0.244826	+	0.969567i	$0.421269\pi$
$68$	1.75102	0.212342
$69$	6.13316	0.738346
$70$	0.0267162	0.00319320
$71$	0.282673	0.0335471	0.0167736	−	0.999859i	$-0.494661\pi$
$71$	0.282673	0.0335471	0.0167736	+	0.999859i	$0.494661\pi$
$72$	1.87168	0.220580
$73$	3.43652	0.402214	0.201107	−	0.979569i	$-0.435546\pi$
$73$	3.43652	0.402214	0.201107	+	0.979569i	$0.435546\pi$
$74$	−3.04241	−0.353673
$75$	−4.99960	−0.577304
$76$	4.98203	0.571478
$77$	−1.06824	−0.121737
$78$	−0.916175	−0.103736
$79$	10.5491	1.18687	0.593434	−	0.804882i	$-0.297772\pi$
$79$	10.5491	1.18687	0.593434	+	0.804882i	$0.297772\pi$
$80$	0.0514979	0.00575764
$81$	1.00000	0.111111
$82$	−4.12640	−0.455684
$83$	8.64602	0.949024	0.474512	−	0.880249i	$-0.342625\pi$
$83$	8.64602	0.949024	0.474512	+	0.880249i	$0.342625\pi$
$84$	4.67528	0.510115
$85$	−0.0200529	−0.00217504
$86$	0.339052	0.0365609
$87$	−3.39897	−0.364408
$88$	0.748828	0.0798254
$89$	4.48328	0.475227	0.237613	−	0.971360i	$-0.423635\pi$
$89$	4.48328	0.475227	0.237613	+	0.971360i	$0.423635\pi$
$90$	−0.0100060	−0.00105472
$91$	−4.90245	−0.513916
$92$	−10.7393	−1.11965
$93$	−4.05428	−0.420410
$94$	2.71359	0.279886
$95$	−0.0570547	−0.00585369
$96$	−5.02480	−0.512841
$97$	−10.7121	−1.08764	−0.543822	−	0.839201i	$-0.683023\pi$
$97$	−10.7121	−1.08764	−0.543822	+	0.839201i	$0.683023\pi$
$98$	−0.0644093	−0.00650632
$99$	0.400083	0.0402099
$100$	8.75439	0.875439
$101$	−6.23221	−0.620128	−0.310064	−	0.950716i	$-0.600350\pi$
$101$	−6.23221	−0.620128	−0.310064	+	0.950716i	$0.600350\pi$
$102$	0.498979	0.0494063
$103$	−14.3504	−1.41399	−0.706994	−	0.707220i	$-0.749949\pi$
$103$	−14.3504	−1.41399	−0.706994	+	0.707220i	$0.749949\pi$
$104$	3.43659	0.336986
$105$	−0.0535418	−0.00522514
$106$	−4.56220	−0.443120
$107$	15.8232	1.52969	0.764845	−	0.644215i	$-0.222816\pi$
$107$	15.8232	1.52969	0.764845	+	0.644215i	$0.222816\pi$
$108$	−1.75102	−0.168492
$109$	−13.0986	−1.25462	−0.627309	−	0.778771i	$-0.715844\pi$
$109$	−13.0986	−1.25462	−0.627309	+	0.778771i	$0.715844\pi$
$110$	−0.00400322	−0.000381692 0
$111$	6.09727	0.578727
$112$	−6.85694	−0.647920
$113$	−6.35516	−0.597843	−0.298921	−	0.954278i	$-0.596627\pi$
$113$	−6.35516	−0.597843	−0.298921	+	0.954278i	$0.596627\pi$
$114$	1.41970	0.132967
$115$	0.122987	0.0114686
$116$	5.95167	0.552598
$117$	1.83610	0.169747
$118$	4.55038	0.418896
$119$	2.67003	0.244762
$120$	0.0375325	0.00342624
$121$	−10.8399	−0.985448
$122$	2.50447	0.226744
$123$	8.26967	0.745651
$124$	7.09913	0.637521
$125$	−0.200520	−0.0179351
$126$	1.33229	0.118690
$127$	−6.96272	−0.617842	−0.308921	−	0.951088i	$-0.599968\pi$
$127$	−6.96272	−0.617842	−0.308921	+	0.951088i	$0.599968\pi$
$128$	11.3614	1.00421
$129$	−0.679491	−0.0598258
$130$	−0.0183719	−0.00161132
$131$	13.4578	1.17581	0.587907	−	0.808928i	$-0.299952\pi$
$131$	13.4578	1.17581	0.587907	+	0.808928i	$0.299952\pi$
$132$	−0.700554	−0.0609754
$133$	7.59683	0.658728
$134$	−1.99990	−0.172765
$135$	0.0200529	0.00172587
$136$	−1.87168	−0.160495
$137$	17.1696	1.46690	0.733451	−	0.679742i	$-0.237908\pi$
$137$	17.1696	1.46690	0.733451	+	0.679742i	$0.237908\pi$
$138$	−3.06032	−0.260512
$139$	−12.9035	−1.09446	−0.547230	−	0.836982i	$-0.684318\pi$
$139$	−12.9035	−1.09446	−0.547230	+	0.836982i	$0.684318\pi$
$140$	0.0937527	0.00792355
$141$	−5.43829	−0.457986
$142$	−0.141048	−0.0118365
$143$	0.734593	0.0614297
$144$	2.56811	0.214009
$145$	−0.0681591	−0.00566030
$146$	−1.71475	−0.141914
$147$	0.129082	0.0106465
$148$	−10.6764	−0.877598
$149$	5.15235	0.422097	0.211049	−	0.977476i	$-0.432312\pi$
$149$	5.15235	0.422097	0.211049	+	0.977476i	$0.432312\pi$
$150$	2.49470	0.203691
$151$	5.52391	0.449529	0.224765	−	0.974413i	$-0.427839\pi$
$151$	5.52391	0.449529	0.224765	+	0.974413i	$0.427839\pi$
$152$	−5.32534	−0.431942
$153$	−1.00000	−0.0808452
$154$	0.533028	0.0429526
$155$	−0.0812999	−0.00653017
$156$	−3.21505	−0.257410
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−5.26379	−0.418765
$159$	9.14306	0.725092
$160$	−0.100761	−0.00796589
$161$	−16.3758	−1.29059
$162$	−0.498979	−0.0392035
$163$	20.0577	1.57104	0.785520	−	0.618837i	$-0.212396\pi$
$163$	20.0577	1.57104	0.785520	+	0.618837i	$0.212396\pi$
$164$	−14.4804	−1.13073
$165$	0.00802281	0.000624575 0
$166$	−4.31418	−0.334846
$167$	−3.95083	−0.305724	−0.152862	−	0.988248i	$-0.548849\pi$
$167$	−3.95083	−0.305724	−0.152862	+	0.988248i	$0.548849\pi$
$168$	−4.99745	−0.385562
$169$	−9.62874	−0.740672
$170$	0.0100060	0.000767422 0
$171$	−2.84522	−0.217579
$172$	1.18980	0.0907215
$173$	−13.1952	−1.00321	−0.501605	−	0.865097i	$-0.667257\pi$
$173$	−13.1952	−1.00321	−0.501605	+	0.865097i	$0.667257\pi$
$174$	1.69602	0.128575
$175$	13.3491	1.00910
$176$	1.02746	0.0774475
$177$	−9.11938	−0.685454
$178$	−2.23706	−0.167675
$179$	−21.0116	−1.57048	−0.785240	−	0.619191i	$-0.787461\pi$
$179$	−21.0116	−1.57048	−0.785240	+	0.619191i	$0.787461\pi$
$180$	−0.0351129	−0.00261716
$181$	13.9643	1.03796	0.518978	−	0.854788i	$-0.326313\pi$
$181$	13.9643	1.03796	0.518978	+	0.854788i	$0.326313\pi$
$182$	2.44622	0.181326
$183$	−5.01919	−0.371029
$184$	11.4793	0.846267
$185$	0.122268	0.00898930
$186$	2.02300	0.148334
$187$	−0.400083	−0.0292570
$188$	9.52255	0.694503
$189$	−2.67003	−0.194216
$190$	0.0284691	0.00206537
$191$	−10.6350	−0.769524	−0.384762	−	0.923016i	$-0.625716\pi$
$191$	−10.6350	−0.769524	−0.384762	+	0.923016i	$0.625716\pi$
$192$	−2.62895	−0.189728
$193$	−9.56209	−0.688294	−0.344147	−	0.938916i	$-0.611832\pi$
$193$	−9.56209	−0.688294	−0.344147	+	0.938916i	$0.611832\pi$
$194$	5.34509	0.383755
$195$	0.0368190	0.00263666
$196$	−0.226025	−0.0161447
$197$	−23.3666	−1.66480	−0.832401	−	0.554174i	$-0.813034\pi$
$197$	−23.3666	−1.66480	−0.832401	+	0.554174i	$0.813034\pi$
$198$	−0.199633	−0.0141873
$199$	18.9379	1.34247	0.671235	−	0.741245i	$-0.265764\pi$
$199$	18.9379	1.34247	0.671235	+	0.741245i	$0.265764\pi$
$200$	−9.35765	−0.661686
$201$	4.00797	0.282701
$202$	3.10974	0.218801
$203$	9.07537	0.636966
$204$	1.75102	0.122596
$205$	0.165831	0.0115821
$206$	7.16056	0.498900
$207$	6.13316	0.426284
$208$	4.71530	0.326947
$209$	−1.13832	−0.0787395
$210$	0.0267162	0.00184360
$211$	−14.4266	−0.993169	−0.496584	−	0.867988i	$-0.665413\pi$
$211$	−14.4266	−0.993169	−0.496584	+	0.867988i	$0.665413\pi$
$212$	−16.0097	−1.09955
$213$	0.282673	0.0193685
$214$	−7.89546	−0.539723
$215$	−0.0136257	−0.000929267 0
$216$	1.87168	0.127352
$217$	10.8251	0.734854
$218$	6.53593	0.442669
$219$	3.43652	0.232219
$220$	−0.0140481	−0.000947123 0
$221$	−1.83610	−0.123509
$222$	−3.04241	−0.204193
$223$	13.2176	0.885119	0.442559	−	0.896739i	$-0.354071\pi$
$223$	13.2176	0.885119	0.442559	+	0.896739i	$0.354071\pi$
$224$	13.4164	0.896419
$225$	−4.99960	−0.333307
$226$	3.17109	0.210938
$227$	15.6335	1.03763	0.518816	−	0.854886i	$-0.326373\pi$
$227$	15.6335	1.03763	0.518816	+	0.854886i	$0.326373\pi$
$228$	4.98203	0.329943
$229$	−21.5658	−1.42511	−0.712553	−	0.701618i	$-0.752461\pi$
$229$	−21.5658	−1.42511	−0.712553	+	0.701618i	$0.752461\pi$
$230$	−0.0613681	−0.00404650
$231$	−1.06824	−0.0702848
$232$	−6.36179	−0.417672
$233$	12.4843	0.817875	0.408938	−	0.912562i	$-0.365899\pi$
$233$	12.4843	0.817875	0.408938	+	0.912562i	$0.365899\pi$
$234$	−0.916175	−0.0598923
$235$	−0.109053	−0.00711384
$236$	15.9682	1.03944
$237$	10.5491	0.685239
$238$	−1.33229	−0.0863596
$239$	−24.8915	−1.61010	−0.805048	−	0.593210i	$-0.797860\pi$
$239$	−24.8915	−1.61010	−0.805048	+	0.593210i	$0.797860\pi$
$240$	0.0514979	0.00332418
$241$	1.97964	0.127520	0.0637598	−	0.997965i	$-0.479691\pi$
$241$	1.97964	0.127520	0.0637598	+	0.997965i	$0.479691\pi$
$242$	5.40890	0.347697
$243$	1.00000	0.0641500
$244$	8.78870	0.562639
$245$	0.00258846	0.000165371 0
$246$	−4.12640	−0.263089
$247$	−5.22410	−0.332402
$248$	−7.58833	−0.481859
$249$	8.64602	0.547919
$250$	0.100056	0.00632807
$251$	−21.3981	−1.35064	−0.675319	−	0.737526i	$-0.735994\pi$
$251$	−21.3981	−1.35064	−0.675319	+	0.737526i	$0.735994\pi$
$252$	4.67528	0.294515
$253$	2.45378	0.154268
$254$	3.47425	0.217994
$255$	−0.0200529	−0.00125576
$256$	−0.411195	−0.0256997
$257$	−20.1481	−1.25680	−0.628401	−	0.777890i	$-0.716290\pi$
$257$	−20.1481	−1.25680	−0.628401	+	0.777890i	$0.716290\pi$
$258$	0.339052	0.0211084
$259$	−16.2799	−1.01159
$260$	−0.0644708	−0.00399831
$261$	−3.39897	−0.210391
$262$	−6.71517	−0.414865
$263$	24.9365	1.53765	0.768824	−	0.639460i	$-0.220842\pi$
$263$	24.9365	1.53765	0.768824	+	0.639460i	$0.220842\pi$
$264$	0.748828	0.0460872
$265$	0.183344	0.0112628
$266$	−3.79066	−0.232420
$267$	4.48328	0.274372
$268$	−7.01804	−0.428695
$269$	11.9744	0.730091	0.365046	−	0.930990i	$-0.381053\pi$
$269$	11.9744	0.730091	0.365046	+	0.930990i	$0.381053\pi$
$270$	−0.0100060	−0.000608943 0
$271$	−24.1825	−1.46898	−0.734490	−	0.678620i	$-0.762579\pi$
$271$	−24.1825	−1.46898	−0.734490	+	0.678620i	$0.762579\pi$
$272$	−2.56811	−0.155714
$273$	−4.90245	−0.296710
$274$	−8.56730	−0.517569
$275$	−2.00026	−0.120620
$276$	−10.7393	−0.646429
$277$	−20.7634	−1.24755	−0.623776	−	0.781603i	$-0.714402\pi$
$277$	−20.7634	−1.24755	−0.623776	+	0.781603i	$0.714402\pi$
$278$	6.43858	0.386160
$279$	−4.05428	−0.242724
$280$	−0.100213	−0.00598888
$281$	−13.3026	−0.793570	−0.396785	−	0.917912i	$-0.629874\pi$
$281$	−13.3026	−0.793570	−0.396785	+	0.917912i	$0.629874\pi$
$282$	2.71359	0.161592
$283$	−10.4279	−0.619874	−0.309937	−	0.950757i	$-0.600308\pi$
$283$	−10.4279	−0.619874	−0.309937	+	0.950757i	$0.600308\pi$
$284$	−0.494967	−0.0293709
$285$	−0.0570547	−0.00337963
$286$	−0.366547	−0.0216743
$287$	−22.0803	−1.30336
$288$	−5.02480	−0.296089
$289$	1.00000	0.0588235
$290$	0.0340100	0.00199713
$291$	−10.7121	−0.627951
$292$	−6.01742	−0.352143
$293$	−4.17646	−0.243991	−0.121996	−	0.992531i	$-0.538929\pi$
$293$	−4.17646	−0.243991	−0.121996	+	0.992531i	$0.538929\pi$
$294$	−0.0644093	−0.00375642
$295$	−0.182870	−0.0106471
$296$	11.4121	0.663318
$297$	0.400083	0.0232152
$298$	−2.57092	−0.148929
$299$	11.2611	0.651246
$300$	8.75439	0.505435
$301$	1.81426	0.104572
$302$	−2.75632	−0.158608
$303$	−6.23221	−0.358031
$304$	−7.30683	−0.419075
$305$	−0.100649	−0.00576315
$306$	0.498979	0.0285247
$307$	−9.46408	−0.540144	−0.270072	−	0.962840i	$-0.587047\pi$
$307$	−9.46408	−0.540144	−0.270072	+	0.962840i	$0.587047\pi$
$308$	1.87050	0.106582
$309$	−14.3504	−0.816366
$310$	0.0405670	0.00230405
$311$	−2.42780	−0.137668	−0.0688339	−	0.997628i	$-0.521928\pi$
$311$	−2.42780	−0.137668	−0.0688339	+	0.997628i	$0.521928\pi$
$312$	3.43659	0.194559
$313$	−16.6266	−0.939788	−0.469894	−	0.882723i	$-0.655708\pi$
$313$	−16.6266	−0.939788	−0.469894	+	0.882723i	$0.655708\pi$
$314$	−0.498979	−0.0281590
$315$	−0.0535418	−0.00301674
$316$	−18.4717	−1.03912
$317$	−29.1404	−1.63669	−0.818344	−	0.574729i	$-0.805108\pi$
$317$	−29.1404	−1.63669	−0.818344	+	0.574729i	$0.805108\pi$
$318$	−4.56220	−0.255835
$319$	−1.35987	−0.0761382
$320$	−0.0527179	−0.00294702
$321$	15.8232	0.883167
$322$	8.17116	0.455361
$323$	2.84522	0.158312
$324$	−1.75102	−0.0972789
$325$	−9.17976	−0.509201
$326$	−10.0084	−0.554312
$327$	−13.0986	−0.724354
$328$	15.4782	0.854640
$329$	14.5204	0.800536
$330$	−0.00400322	−0.000220370 0
$331$	−15.7212	−0.864113	−0.432056	−	0.901847i	$-0.642212\pi$
$331$	−15.7212	−0.864113	−0.432056	+	0.901847i	$0.642212\pi$
$332$	−15.1393	−0.830880
$333$	6.09727	0.334128
$334$	1.97138	0.107869
$335$	0.0803713	0.00439115
$336$	−6.85694	−0.374077
$337$	−14.1049	−0.768345	−0.384173	−	0.923261i	$-0.625513\pi$
$337$	−14.1049	−0.768345	−0.384173	+	0.923261i	$0.625513\pi$
$338$	4.80454	0.261333
$339$	−6.35516	−0.345165
$340$	0.0351129	0.00190427
$341$	−1.62205	−0.0878390
$342$	1.41970	0.0767688
$343$	18.3456	0.990568
$344$	−1.27179	−0.0685703
$345$	0.122987	0.00662142
$346$	6.58411	0.353964
$347$	−4.73555	−0.254218	−0.127109	−	0.991889i	$-0.540570\pi$
$347$	−4.73555	−0.254218	−0.127109	+	0.991889i	$0.540570\pi$
$348$	5.95167	0.319043
$349$	−24.8812	−1.33186	−0.665930	−	0.746014i	$-0.731965\pi$
$349$	−24.8812	−1.33186	−0.665930	+	0.746014i	$0.731965\pi$
$350$	−6.66092	−0.356041
$351$	1.83610	0.0980037
$352$	−2.01034	−0.107151
$353$	−0.170244	−0.00906120	−0.00453060	−	0.999990i	$-0.501442\pi$
$353$	−0.170244	−0.00906120	−0.00453060	+	0.999990i	$0.501442\pi$
$354$	4.55038	0.241850
$355$	0.00566841	0.000300848 0
$356$	−7.85031	−0.416066
$357$	2.67003	0.141313
$358$	10.4844	0.554115
$359$	4.23018	0.223260	0.111630	−	0.993750i	$-0.464393\pi$
$359$	4.23018	0.223260	0.111630	+	0.993750i	$0.464393\pi$
$360$	0.0375325	0.00197814
$361$	−10.9047	−0.573934
$362$	−6.96788	−0.366224
$363$	−10.8399	−0.568949
$364$	8.58428	0.449939
$365$	0.0689120	0.00360702
$366$	2.50447	0.130911
$367$	18.9966	0.991614	0.495807	−	0.868433i	$-0.334872\pi$
$367$	18.9966	0.991614	0.495807	+	0.868433i	$0.334872\pi$
$368$	15.7506	0.821058
$369$	8.26967	0.430502
$370$	−0.0610090	−0.00317171
$371$	−24.4123	−1.26742
$372$	7.09913	0.368073
$373$	23.9630	1.24076	0.620378	−	0.784303i	$-0.286979\pi$
$373$	23.9630	1.24076	0.620378	+	0.784303i	$0.286979\pi$
$374$	0.199633	0.0103228
$375$	−0.200520	−0.0103548
$376$	−10.1787	−0.524928
$377$	−6.24085	−0.321420
$378$	1.33229	0.0685257
$379$	−3.48659	−0.179094	−0.0895472	−	0.995983i	$-0.528542\pi$
$379$	−3.48659	−0.179094	−0.0895472	+	0.995983i	$0.528542\pi$
$380$	0.0999039	0.00512496
$381$	−6.96272	−0.356711
$382$	5.30666	0.271512
$383$	−0.580625	−0.0296685	−0.0148343	−	0.999890i	$-0.504722\pi$
$383$	−0.580625	−0.0296685	−0.0148343	+	0.999890i	$0.504722\pi$
$384$	11.3614	0.579783
$385$	−0.0214212	−0.00109172
$386$	4.77129	0.242852
$387$	−0.679491	−0.0345404
$388$	18.7570	0.952243
$389$	−4.64656	−0.235590	−0.117795	−	0.993038i	$-0.537583\pi$
$389$	−4.64656	−0.235590	−0.117795	+	0.993038i	$0.537583\pi$
$390$	−0.0183719	−0.000930299 0
$391$	−6.13316	−0.310167
$392$	0.241600	0.0122027
$393$	13.4578	0.678857
$394$	11.6595	0.587395
$395$	0.211540	0.0106437
$396$	−0.700554	−0.0352042
$397$	−5.68293	−0.285218	−0.142609	−	0.989779i	$-0.545549\pi$
$397$	−5.68293	−0.285218	−0.142609	+	0.989779i	$0.545549\pi$
$398$	−9.44960	−0.473666
$399$	7.59683	0.380317
$400$	−12.8395	−0.641976
$401$	−17.4503	−0.871426	−0.435713	−	0.900086i	$-0.643504\pi$
$401$	−17.4503	−0.871426	−0.435713	+	0.900086i	$0.643504\pi$
$402$	−1.99990	−0.0997457
$403$	−7.44407	−0.370815
$404$	10.9127	0.542928
$405$	0.0200529	0.000996434 0
$406$	−4.52842	−0.224742
$407$	2.43942	0.120917
$408$	−1.87168	−0.0926620
$409$	11.0622	0.546991	0.273495	−	0.961873i	$-0.411820\pi$
$409$	11.0622	0.546991	0.273495	+	0.961873i	$0.411820\pi$
$410$	−0.0827460	−0.00408653
$411$	17.1696	0.846916
$412$	25.1278	1.23796
$413$	24.3490	1.19814
$414$	−3.06032	−0.150407
$415$	0.173377	0.00851076
$416$	−9.22602	−0.452343
$417$	−12.9035	−0.631887
$418$	0.568000	0.0277818
$419$	−22.4521	−1.09686	−0.548428	−	0.836198i	$-0.684774\pi$
$419$	−22.4521	−1.09686	−0.548428	+	0.836198i	$0.684774\pi$
$420$	0.0937527	0.00457467
$421$	30.4292	1.48303	0.741515	−	0.670936i	$-0.234108\pi$
$421$	30.4292	1.48303	0.741515	+	0.670936i	$0.234108\pi$
$422$	7.19858	0.350421
$423$	−5.43829	−0.264419
$424$	17.1129	0.831076
$425$	4.99960	0.242516
$426$	−0.141048	−0.00683380
$427$	13.4014	0.648540
$428$	−27.7068	−1.33926
$429$	0.734593	0.0354665
$430$	0.00679895	0.000327875 0
$431$	−22.2573	−1.07209	−0.536047	−	0.844188i	$-0.680083\pi$
$431$	−22.2573	−1.07209	−0.536047	+	0.844188i	$0.680083\pi$
$432$	2.56811	0.123558
$433$	−9.41118	−0.452272	−0.226136	−	0.974096i	$-0.572609\pi$
$433$	−9.41118	−0.452272	−0.226136	+	0.974096i	$0.572609\pi$
$434$	−5.40149	−0.259280
$435$	−0.0681591	−0.00326798
$436$	22.9359	1.09843
$437$	−17.4502	−0.834755
$438$	−1.71475	−0.0819340
$439$	26.0753	1.24451	0.622254	−	0.782815i	$-0.286217\pi$
$439$	26.0753	1.24451	0.622254	+	0.782815i	$0.286217\pi$
$440$	0.0150161	0.000715867 0
$441$	0.129082	0.00614676
$442$	0.916175	0.0435780
$443$	−13.9050	−0.660645	−0.330323	−	0.943868i	$-0.607158\pi$
$443$	−13.9050	−0.660645	−0.330323	+	0.943868i	$0.607158\pi$
$444$	−10.6764	−0.506682
$445$	0.0899026	0.00426179
$446$	−6.59533	−0.312298
$447$	5.15235	0.243698
$448$	7.01939	0.331635
$449$	11.8795	0.560627	0.280313	−	0.959909i	$-0.409562\pi$
$449$	11.8795	0.560627	0.280313	+	0.959909i	$0.409562\pi$
$450$	2.49470	0.117601
$451$	3.30856	0.155794
$452$	11.1280	0.523417
$453$	5.52391	0.259536
$454$	−7.80079	−0.366109
$455$	−0.0983080	−0.00460875
$456$	−5.32534	−0.249382
$457$	−22.0551	−1.03170	−0.515848	−	0.856680i	$-0.672523\pi$
$457$	−22.0551	−1.03170	−0.515848	+	0.856680i	$0.672523\pi$
$458$	10.7609	0.502823
$459$	−1.00000	−0.0466760
$460$	−0.215353	−0.0100409
$461$	−12.1458	−0.565686	−0.282843	−	0.959166i	$-0.591278\pi$
$461$	−12.1458	−0.565686	−0.282843	+	0.959166i	$0.591278\pi$
$462$	0.533028	0.0247987
$463$	−41.9832	−1.95112	−0.975562	−	0.219722i	$-0.929485\pi$
$463$	−41.9832	−1.95112	−0.975562	+	0.219722i	$0.929485\pi$
$464$	−8.72893	−0.405230
$465$	−0.0812999	−0.00377019
$466$	−6.22942	−0.288572
$467$	−6.92597	−0.320496	−0.160248	−	0.987077i	$-0.551229\pi$
$467$	−6.92597	−0.320496	−0.160248	+	0.987077i	$0.551229\pi$
$468$	−3.21505	−0.148616
$469$	−10.7014	−0.494146
$470$	0.0544153	0.00250999
$471$	1.00000	0.0460776
$472$	−17.0686	−0.785644
$473$	−0.271853	−0.0124998
$474$	−5.26379	−0.241774
$475$	14.2249	0.652685
$476$	−4.67528	−0.214291
$477$	9.14306	0.418632
$478$	12.4203	0.568093
$479$	−22.7706	−1.04041	−0.520207	−	0.854040i	$-0.674145\pi$
$479$	−22.7706	−1.04041	−0.520207	+	0.854040i	$0.674145\pi$
$480$	−0.100761	−0.00459911
$481$	11.1952	0.510457
$482$	−0.987798	−0.0449930
$483$	−16.3758	−0.745122
$484$	18.9809	0.862770
$485$	−0.214807	−0.00975389
$486$	−0.498979	−0.0226342
$487$	7.23178	0.327703	0.163852	−	0.986485i	$-0.447608\pi$
$487$	7.23178	0.327703	0.163852	+	0.986485i	$0.447608\pi$
$488$	−9.39433	−0.425261
$489$	20.0577	0.907040
$490$	−0.00129159	−5.83481e−5 0
$491$	−0.0375115	−0.00169287	−0.000846436	−	1.00000i	$-0.500269\pi$
$491$	−0.0375115	−0.00169287	−0.000846436		1.00000i	$0.500269\pi$
$492$	−14.4804	−0.652825
$493$	3.39897	0.153082
$494$	2.60672	0.117282
$495$	0.00802281	0.000360599 0
$496$	−10.4118	−0.467506
$497$	−0.754747	−0.0338550
$498$	−4.31418	−0.193323
$499$	−38.7735	−1.73574	−0.867870	−	0.496792i	$-0.834511\pi$
$499$	−38.7735	−1.73574	−0.867870	+	0.496792i	$0.834511\pi$
$500$	0.351115	0.0157024
$501$	−3.95083	−0.176510
$502$	10.6772	0.476547
$503$	21.7607	0.970261	0.485131	−	0.874442i	$-0.338772\pi$
$503$	21.7607	0.970261	0.485131	+	0.874442i	$0.338772\pi$
$504$	−4.99745	−0.222604
$505$	−0.124973	−0.00556125
$506$	−1.22438	−0.0544305
$507$	−9.62874	−0.427627
$508$	12.1919	0.540927
$509$	0.279327	0.0123810	0.00619048	−	0.999981i	$-0.498029\pi$
$509$	0.279327	0.0123810	0.00619048	+	0.999981i	$0.498029\pi$
$510$	0.0100060	0.000443071 0
$511$	−9.17563	−0.405906
$512$	−22.5176	−0.995146
$513$	−2.84522	−0.125619
$514$	10.0535	0.443439
$515$	−0.287767	−0.0126805
$516$	1.18980	0.0523781
$517$	−2.17577	−0.0956902
$518$	8.12334	0.356919
$519$	−13.1952	−0.579203
$520$	0.0689135	0.00302206
$521$	7.01115	0.307164	0.153582	−	0.988136i	$-0.450919\pi$
$521$	7.01115	0.307164	0.153582	+	0.988136i	$0.450919\pi$
$522$	1.69602	0.0742326
$523$	3.25945	0.142526	0.0712629	−	0.997458i	$-0.477297\pi$
$523$	3.25945	0.142526	0.0712629	+	0.997458i	$0.477297\pi$
$524$	−23.5649	−1.02944
$525$	13.3491	0.582602
$526$	−12.4428	−0.542531
$527$	4.05428	0.176607
$528$	1.02746	0.0447144
$529$	14.6157	0.635464
$530$	−0.0914851	−0.00397386
$531$	−9.11938	−0.395747
$532$	−13.3022	−0.576723
$533$	15.1839	0.657689
$534$	−2.23706	−0.0968072
$535$	0.317301	0.0137181
$536$	7.50165	0.324022
$537$	−21.0116	−0.906718
$538$	−5.97497	−0.257599
$539$	0.0516436	0.00222445
$540$	−0.0351129	−0.00151102
$541$	−25.2857	−1.08712	−0.543559	−	0.839371i	$-0.682924\pi$
$541$	−25.2857	−1.08712	−0.543559	+	0.839371i	$0.682924\pi$
$542$	12.0665	0.518303
$543$	13.9643	0.599264
$544$	5.02480	0.215436
$545$	−0.262664	−0.0112513
$546$	2.44622	0.104689
$547$	−26.5054	−1.13329	−0.566644	−	0.823963i	$-0.691758\pi$
$547$	−26.5054	−1.13329	−0.566644	+	0.823963i	$0.691758\pi$
$548$	−30.0644	−1.28429
$549$	−5.01919	−0.214214
$550$	0.998086	0.0425585
$551$	9.67081	0.411990
$552$	11.4793	0.488592
$553$	−28.1665	−1.19776
$554$	10.3605	0.440176
$555$	0.122268	0.00518997
$556$	22.5943	0.958211
$557$	30.1905	1.27921	0.639607	−	0.768702i	$-0.279097\pi$
$557$	30.1905	1.27921	0.639607	+	0.768702i	$0.279097\pi$
$558$	2.02300	0.0856406
$559$	−1.24761	−0.0527684
$560$	−0.137501	−0.00581049
$561$	−0.400083	−0.0168915
$562$	6.63775	0.279996
$563$	23.0879	0.973037	0.486518	−	0.873670i	$-0.338267\pi$
$563$	23.0879	0.973037	0.486518	+	0.873670i	$0.338267\pi$
$564$	9.52255	0.400972
$565$	−0.127439	−0.00536140
$566$	5.20330	0.218711
$567$	−2.67003	−0.112131
$568$	0.529074	0.0221995
$569$	−26.5541	−1.11320	−0.556602	−	0.830779i	$-0.687895\pi$
$569$	−26.5541	−1.11320	−0.556602	+	0.830779i	$0.687895\pi$
$570$	0.0284691	0.00119244
$571$	23.8209	0.996875	0.498438	−	0.866926i	$-0.333907\pi$
$571$	23.8209	0.996875	0.498438	+	0.866926i	$0.333907\pi$
$572$	−1.28629	−0.0537823
$573$	−10.6350	−0.444285
$574$	11.0176	0.459866
$575$	−30.6633	−1.27875
$576$	−2.62895	−0.109540
$577$	41.8942	1.74408	0.872040	−	0.489435i	$-0.162797\pi$
$577$	41.8942	1.74408	0.872040	+	0.489435i	$0.162797\pi$
$578$	−0.498979	−0.0207548
$579$	−9.56209	−0.397387
$580$	0.119348	0.00495565
$581$	−23.0852	−0.957734
$582$	5.34509	0.221561
$583$	3.65799	0.151498
$584$	6.43207	0.266161
$585$	0.0368190	0.00152228
$586$	2.08397	0.0860879
$587$	−33.2965	−1.37429	−0.687147	−	0.726519i	$-0.741137\pi$
$587$	−33.2965	−1.37429	−0.687147	+	0.726519i	$0.741137\pi$
$588$	−0.226025	−0.00932112
$589$	11.5353	0.475304
$590$	0.0912481	0.00375662
$591$	−23.3666	−0.961174
$592$	15.6585	0.643559
$593$	25.3510	1.04104	0.520521	−	0.853849i	$-0.325738\pi$
$593$	25.3510	1.04104	0.520521	+	0.853849i	$0.325738\pi$
$594$	−0.199633	−0.00819105
$595$	0.0535418	0.00219500
$596$	−9.02187	−0.369550
$597$	18.9379	0.775075
$598$	−5.61905	−0.229780
$599$	0.988603	0.0403932	0.0201966	−	0.999796i	$-0.493571\pi$
$599$	0.988603	0.0403932	0.0201966	+	0.999796i	$0.493571\pi$
$600$	−9.35765	−0.382025
$601$	−34.4351	−1.40464	−0.702319	−	0.711862i	$-0.747852\pi$
$601$	−34.4351	−1.40464	−0.702319	+	0.711862i	$0.747852\pi$
$602$	−0.905280	−0.0368964
$603$	4.00797	0.163217
$604$	−9.67248	−0.393567
$605$	−0.217372	−0.00883741
$606$	3.10974	0.126325
$607$	−7.22058	−0.293074	−0.146537	−	0.989205i	$-0.546813\pi$
$607$	−7.22058	−0.293074	−0.146537	+	0.989205i	$0.546813\pi$
$608$	14.2966	0.579805
$609$	9.07537	0.367753
$610$	0.0502218	0.00203342
$611$	−9.98523	−0.403959
$612$	1.75102	0.0707808
$613$	−15.6935	−0.633856	−0.316928	−	0.948450i	$-0.602651\pi$
$613$	−15.6935	−0.633856	−0.316928	+	0.948450i	$0.602651\pi$
$614$	4.72238	0.190580
$615$	0.165831	0.00668693
$616$	−1.99940	−0.0805580
$617$	−2.70934	−0.109074	−0.0545370	−	0.998512i	$-0.517368\pi$
$617$	−2.70934	−0.109074	−0.0545370	+	0.998512i	$0.517368\pi$
$618$	7.16056	0.288040
$619$	38.1690	1.53414	0.767070	−	0.641564i	$-0.221714\pi$
$619$	38.1690	1.53414	0.767070	+	0.641564i	$0.221714\pi$
$620$	0.142358	0.00571723
$621$	6.13316	0.246115
$622$	1.21142	0.0485736
$623$	−11.9705	−0.479589
$624$	4.71530	0.188763
$625$	24.9940	0.999759
$626$	8.29630	0.331587
$627$	−1.13832	−0.0454603
$628$	−1.75102	−0.0698733
$629$	−6.09727	−0.243114
$630$	0.0267162	0.00106440
$631$	−45.2327	−1.80068	−0.900342	−	0.435182i	$-0.856684\pi$
$631$	−45.2327	−1.80068	−0.900342	+	0.435182i	$0.856684\pi$
$632$	19.7446	0.785397
$633$	−14.4266	−0.573406
$634$	14.5405	0.577475
$635$	−0.139622	−0.00554075
$636$	−16.0097	−0.634825
$637$	0.237007	0.00939058
$638$	0.678548	0.0268640
$639$	0.282673	0.0111824
$640$	0.227828	0.00900570
$641$	−31.2247	−1.23330	−0.616650	−	0.787238i	$-0.711511\pi$
$641$	−31.2247	−1.23330	−0.616650	+	0.787238i	$0.711511\pi$
$642$	−7.89546	−0.311609
$643$	31.1044	1.22664	0.613319	−	0.789835i	$-0.289834\pi$
$643$	31.1044	1.22664	0.613319	+	0.789835i	$0.289834\pi$
$644$	28.6743	1.12992
$645$	−0.0136257	−0.000536512 0
$646$	−1.41970	−0.0558575
$647$	10.7816	0.423867	0.211934	−	0.977284i	$-0.432024\pi$
$647$	10.7816	0.423867	0.211934	+	0.977284i	$0.432024\pi$
$648$	1.87168	0.0735266
$649$	−3.64851	−0.143217
$650$	4.58051	0.179662
$651$	10.8251	0.424268
$652$	−35.1214	−1.37546
$653$	−26.1296	−1.02253	−0.511266	−	0.859423i	$-0.670823\pi$
$653$	−26.1296	−1.02253	−0.511266	+	0.859423i	$0.670823\pi$
$654$	6.53593	0.255575
$655$	0.269868	0.0105446
$656$	21.2374	0.829182
$657$	3.43652	0.134071
$658$	−7.24538	−0.282455
$659$	20.8824	0.813461	0.406730	−	0.913548i	$-0.366669\pi$
$659$	20.8824	0.813461	0.406730	+	0.913548i	$0.366669\pi$
$660$	−0.0140481	−0.000546822 0
$661$	18.2648	0.710420	0.355210	−	0.934787i	$-0.384409\pi$
$661$	18.2648	0.710420	0.355210	+	0.934787i	$0.384409\pi$
$662$	7.84453	0.304886
$663$	−1.83610	−0.0713082
$664$	16.1826	0.628006
$665$	0.152338	0.00590741
$666$	−3.04241	−0.117891
$667$	−20.8464	−0.807177
$668$	6.91798	0.267665
$669$	13.2176	0.511023
$670$	−0.0401036	−0.00154934
$671$	−2.00810	−0.0775217
$672$	13.4164	0.517548
$673$	16.0432	0.618419	0.309209	−	0.950994i	$-0.399936\pi$
$673$	16.0432	0.618419	0.309209	+	0.950994i	$0.399936\pi$
$674$	7.03807	0.271096
$675$	−4.99960	−0.192435
$676$	16.8601	0.648466
$677$	−40.5669	−1.55911	−0.779556	−	0.626332i	$-0.784555\pi$
$677$	−40.5669	−1.55911	−0.779556	+	0.626332i	$0.784555\pi$
$678$	3.17109	0.121785
$679$	28.6015	1.09763
$680$	−0.0375325	−0.00143931
$681$	15.6335	0.599077
$682$	0.809370	0.0309924
$683$	−7.36088	−0.281656	−0.140828	−	0.990034i	$-0.544976\pi$
$683$	−7.36088	−0.281656	−0.140828	+	0.990034i	$0.544976\pi$
$684$	4.98203	0.190493
$685$	0.344300	0.0131550
$686$	−9.15407	−0.349504
$687$	−21.5658	−0.822786
$688$	−1.74501	−0.0665277
$689$	16.7876	0.639555
$690$	−0.0613681	−0.00233625
$691$	25.6155	0.974461	0.487231	−	0.873273i	$-0.338007\pi$
$691$	25.6155	0.974461	0.487231	+	0.873273i	$0.338007\pi$
$692$	23.1050	0.878319
$693$	−1.06824	−0.0405789
$694$	2.36294	0.0896960
$695$	−0.258752	−0.00981502
$696$	−6.36179	−0.241143
$697$	−8.26967	−0.313236
$698$	12.4152	0.469922
$699$	12.4843	0.472200
$700$	−23.3745	−0.883474
$701$	−49.6483	−1.87519	−0.937595	−	0.347729i	$-0.886953\pi$
$701$	−49.6483	−1.87519	−0.937595	+	0.347729i	$0.886953\pi$
$702$	−0.916175	−0.0345788
$703$	−17.3481	−0.654294
$704$	−1.05180	−0.0396412
$705$	−0.109053	−0.00410718
$706$	0.0849484	0.00319708
$707$	16.6402	0.625819
$708$	15.9682	0.600122
$709$	16.1966	0.608274	0.304137	−	0.952628i	$-0.401632\pi$
$709$	16.1966	0.608274	0.304137	+	0.952628i	$0.401632\pi$
$710$	−0.00282842	−0.000106149 0
$711$	10.5491	0.395623
$712$	8.39127	0.314476
$713$	−24.8656	−0.931223
$714$	−1.33229	−0.0498598
$715$	0.0147307	0.000550896 0
$716$	36.7917	1.37497
$717$	−24.8915	−0.929589
$718$	−2.11077	−0.0787733
$719$	−43.9665	−1.63967	−0.819837	−	0.572596i	$-0.805936\pi$
$719$	−43.9665	−1.63967	−0.819837	+	0.572596i	$0.805936\pi$
$720$	0.0514979	0.00191921
$721$	38.3161	1.42697
$722$	5.44124	0.202502
$723$	1.97964	0.0736235
$724$	−24.4517	−0.908741
$725$	16.9935	0.631122
$726$	5.40890	0.200743
$727$	25.2183	0.935295	0.467647	−	0.883915i	$-0.345102\pi$
$727$	25.2183	0.935295	0.467647	+	0.883915i	$0.345102\pi$
$728$	−9.17582	−0.340078
$729$	1.00000	0.0370370
$730$	−0.0343857	−0.00127267
$731$	0.679491	0.0251319
$732$	8.78870	0.324840
$733$	11.9739	0.442268	0.221134	−	0.975243i	$-0.429024\pi$
$733$	11.9739	0.442268	0.221134	+	0.975243i	$0.429024\pi$
$734$	−9.47891	−0.349873
$735$	0.00258846	9.54769e−5 0
$736$	−30.8179	−1.13596
$737$	1.60352	0.0590665
$738$	−4.12640	−0.151895
$739$	13.1334	0.483121	0.241561	−	0.970386i	$-0.422341\pi$
$739$	13.1334	0.483121	0.241561	+	0.970386i	$0.422341\pi$
$740$	−0.214093	−0.00787022
$741$	−5.22410	−0.191912
$742$	12.1812	0.447187
$743$	−33.0900	−1.21395	−0.606977	−	0.794720i	$-0.707618\pi$
$743$	−33.0900	−1.21395	−0.606977	+	0.794720i	$0.707618\pi$
$744$	−7.58833	−0.278202
$745$	0.103319	0.00378533
$746$	−11.9570	−0.437778
$747$	8.64602	0.316341
$748$	0.700554	0.0256148
$749$	−42.2486	−1.54373
$750$	0.100056	0.00365351
$751$	41.2070	1.50366	0.751832	−	0.659355i	$-0.229170\pi$
$751$	41.2070	1.50366	0.751832	+	0.659355i	$0.229170\pi$
$752$	−13.9661	−0.509292
$753$	−21.3981	−0.779791
$754$	3.11405	0.113407
$755$	0.110770	0.00403134
$756$	4.67528	0.170038
$757$	24.6110	0.894504	0.447252	−	0.894408i	$-0.352403\pi$
$757$	24.6110	0.894504	0.447252	+	0.894408i	$0.352403\pi$
$758$	1.73974	0.0631902
$759$	2.45378	0.0890664
$760$	−0.106788	−0.00387362
$761$	22.3140	0.808880	0.404440	−	0.914564i	$-0.367466\pi$
$761$	22.3140	0.808880	0.404440	+	0.914564i	$0.367466\pi$
$762$	3.47425	0.125859
$763$	34.9737	1.26613
$764$	18.6221	0.673725
$765$	−0.0200529	−0.000725012 0
$766$	0.289720	0.0104680
$767$	−16.7441	−0.604594
$768$	−0.411195	−0.0148377
$769$	−18.3132	−0.660392	−0.330196	−	0.943912i	$-0.607115\pi$
$769$	−18.3132	−0.660392	−0.330196	+	0.943912i	$0.607115\pi$
$770$	0.0106887	0.000385195 0
$771$	−20.1481	−0.725614
$772$	16.7434	0.602608
$773$	17.7910	0.639896	0.319948	−	0.947435i	$-0.396335\pi$
$773$	17.7910	0.639896	0.319948	+	0.947435i	$0.396335\pi$
$774$	0.339052	0.0121870
$775$	20.2698	0.728112
$776$	−20.0495	−0.719737
$777$	−16.2799	−0.584039
$778$	2.31854	0.0831236
$779$	−23.5290	−0.843014
$780$	−0.0644708	−0.00230843
$781$	0.113093	0.00404678
$782$	3.06032	0.109437
$783$	−3.39897	−0.121469
$784$	0.331497	0.0118392
$785$	0.0200529	0.000715717 0
$786$	−6.71517	−0.239522
$787$	−5.54796	−0.197764	−0.0988818	−	0.995099i	$-0.531527\pi$
$787$	−5.54796	−0.197764	−0.0988818	+	0.995099i	$0.531527\pi$
$788$	40.9154	1.45755
$789$	24.9365	0.887762
$790$	−0.105554	−0.00375544
$791$	16.9685	0.603330
$792$	0.748828	0.0266085
$793$	−9.21573	−0.327260
$794$	2.83566	0.100634
$795$	0.183344	0.00650256
$796$	−33.1606	−1.17534
$797$	42.9479	1.52129	0.760646	−	0.649166i	$-0.224882\pi$
$797$	42.9479	1.52129	0.760646	+	0.649166i	$0.224882\pi$
$798$	−3.79066	−0.134188
$799$	5.43829	0.192393
$800$	25.1220	0.888195
$801$	4.48328	0.158409
$802$	8.70734	0.307467
$803$	1.37489	0.0485190
$804$	−7.01804	−0.247507
$805$	−0.328380	−0.0115739
$806$	3.71444	0.130835
$807$	11.9744	0.421518
$808$	−11.6647	−0.410363
$809$	−0.516985	−0.0181762	−0.00908811	−	0.999959i	$-0.502893\pi$
$809$	−0.516985	−0.0181762	−0.00908811	+	0.999959i	$0.502893\pi$
$810$	−0.0100060	−0.000351573 0
$811$	−3.54190	−0.124373	−0.0621865	−	0.998065i	$-0.519807\pi$
$811$	−3.54190	−0.124373	−0.0621865	+	0.998065i	$0.519807\pi$
$812$	−15.8912	−0.557670
$813$	−24.1825	−0.848116
$814$	−1.21722	−0.0426635
$815$	0.402214	0.0140889
$816$	−2.56811	−0.0899018
$817$	1.93330	0.0676375
$818$	−5.51981	−0.192996
$819$	−4.90245	−0.171305
$820$	−0.290373	−0.0101402
$821$	16.3811	0.571704	0.285852	−	0.958274i	$-0.407723\pi$
$821$	16.3811	0.571704	0.285852	+	0.958274i	$0.407723\pi$
$822$	−8.56730	−0.298819
$823$	27.4228	0.955900	0.477950	−	0.878387i	$-0.341380\pi$
$823$	27.4228	0.955900	0.477950	+	0.878387i	$0.341380\pi$
$824$	−26.8594	−0.935691
$825$	−2.00026	−0.0696400
$826$	−12.1497	−0.422741
$827$	20.2111	0.702808	0.351404	−	0.936224i	$-0.385704\pi$
$827$	20.2111	0.702808	0.351404	+	0.936224i	$0.385704\pi$
$828$	−10.7393	−0.373216
$829$	−2.22676	−0.0773385	−0.0386692	−	0.999252i	$-0.512312\pi$
$829$	−2.22676	−0.0773385	−0.0386692	+	0.999252i	$0.512312\pi$
$830$	−0.0865117	−0.00300286
$831$	−20.7634	−0.720274
$832$	−4.82701	−0.167347
$833$	−0.129082	−0.00447243
$834$	6.43858	0.222950
$835$	−0.0792254	−0.00274171
$836$	1.99323	0.0689372
$837$	−4.05428	−0.140137
$838$	11.2031	0.387006
$839$	26.4442	0.912956	0.456478	−	0.889735i	$-0.349111\pi$
$839$	26.4442	0.912956	0.456478	+	0.889735i	$0.349111\pi$
$840$	−0.100213	−0.00345768
$841$	−17.4470	−0.601620
$842$	−15.1836	−0.523260
$843$	−13.3026	−0.458168
$844$	25.2613	0.869529
$845$	−0.193084	−0.00664228
$846$	2.71359	0.0932952
$847$	28.9430	0.994493
$848$	23.4804	0.806320
$849$	−10.4279	−0.357884
$850$	−2.49470	−0.0855674
$851$	37.3956	1.28190
$852$	−0.494967	−0.0169573
$853$	−5.79956	−0.198573	−0.0992866	−	0.995059i	$-0.531656\pi$
$853$	−5.79956	−0.198573	−0.0992866	+	0.995059i	$0.531656\pi$
$854$	−6.68703	−0.228825
$855$	−0.0570547	−0.00195123
$856$	29.6160	1.01226
$857$	−34.2365	−1.16950	−0.584748	−	0.811215i	$-0.698807\pi$
$857$	−34.2365	−1.16950	−0.584748	+	0.811215i	$0.698807\pi$
$858$	−0.366547	−0.0125137
$859$	7.56868	0.258240	0.129120	−	0.991629i	$-0.458785\pi$
$859$	7.56868	0.258240	0.129120	+	0.991629i	$0.458785\pi$
$860$	0.0238589	0.000813582 0
$861$	−22.0803	−0.752495
$862$	11.1059	0.378269
$863$	−51.2239	−1.74368	−0.871840	−	0.489790i	$-0.837073\pi$
$863$	−51.2239	−1.74368	−0.871840	+	0.489790i	$0.837073\pi$
$864$	−5.02480	−0.170947
$865$	−0.264600	−0.00899669
$866$	4.69598	0.159576
$867$	1.00000	0.0339618
$868$	−18.9549	−0.643372
$869$	4.22053	0.143172
$870$	0.0340100	0.00115305
$871$	7.35904	0.249351
$872$	−24.5164	−0.830230
$873$	−10.7121	−0.362548
$874$	8.70728	0.294528
$875$	0.535396	0.0180997
$876$	−6.01742	−0.203310
$877$	9.31012	0.314380	0.157190	−	0.987568i	$-0.449756\pi$
$877$	9.31012	0.314380	0.157190	+	0.987568i	$0.449756\pi$
$878$	−13.0111	−0.439102
$879$	−4.17646	−0.140868
$880$	0.0206035	0.000694542 0
$881$	20.8467	0.702345	0.351172	−	0.936311i	$-0.385783\pi$
$881$	20.8467	0.702345	0.351172	+	0.936311i	$0.385783\pi$
$882$	−0.0644093	−0.00216877
$883$	52.7528	1.77527	0.887636	−	0.460546i	$-0.152346\pi$
$883$	52.7528	1.77527	0.887636	+	0.460546i	$0.152346\pi$
$884$	3.21505	0.108134
$885$	−0.182870	−0.00614709
$886$	6.93829	0.233097
$887$	−42.7519	−1.43547	−0.717734	−	0.696317i	$-0.754821\pi$
$887$	−42.7519	−1.43547	−0.717734	+	0.696317i	$0.754821\pi$
$888$	11.4121	0.382967
$889$	18.5907	0.623512
$890$	−0.0448595	−0.00150369
$891$	0.400083	0.0134033
$892$	−23.1443	−0.774930
$893$	15.4731	0.517788
$894$	−2.57092	−0.0859843
$895$	−0.421343	−0.0140839
$896$	−30.3353	−1.01343
$897$	11.2611	0.375997
$898$	−5.92761	−0.197807
$899$	13.7804	0.459602
$900$	8.75439	0.291813
$901$	−9.14306	−0.304600
$902$	−1.65090	−0.0549690
$903$	1.81426	0.0603749
$904$	−11.8948	−0.395616
$905$	0.280023	0.00930829
$906$	−2.75632	−0.0915725
$907$	−1.53635	−0.0510137	−0.0255068	−	0.999675i	$-0.508120\pi$
$907$	−1.53635	−0.0510137	−0.0255068	+	0.999675i	$0.508120\pi$
$908$	−27.3745	−0.908456
$909$	−6.23221	−0.206709
$910$	0.0490537	0.00162611
$911$	46.9295	1.55484	0.777422	−	0.628980i	$-0.216527\pi$
$911$	46.9295	1.55484	0.777422	+	0.628980i	$0.216527\pi$
$912$	−7.30683	−0.241953
$913$	3.45913	0.114480
$914$	11.0051	0.364015
$915$	−0.100649	−0.00332736
$916$	37.7621	1.24769
$917$	−35.9328	−1.18661
$918$	0.498979	0.0164688
$919$	11.4126	0.376467	0.188234	−	0.982124i	$-0.439724\pi$
$919$	11.4126	0.376467	0.188234	+	0.982124i	$0.439724\pi$
$920$	0.230193	0.00758924
$921$	−9.46408	−0.311852
$922$	6.06050	0.199592
$923$	0.519016	0.0170836
$924$	1.87050	0.0615350
$925$	−30.4839	−1.00230
$926$	20.9487	0.688419
$927$	−14.3504	−0.471329
$928$	17.0791	0.560650
$929$	38.5167	1.26369	0.631846	−	0.775094i	$-0.282297\pi$
$929$	38.5167	1.26369	0.631846	+	0.775094i	$0.282297\pi$
$930$	0.0405670	0.00133024
$931$	−0.367266	−0.0120367
$932$	−21.8603	−0.716058
$933$	−2.42780	−0.0794826
$934$	3.45592	0.113081
$935$	−0.00802281	−0.000262374 0
$936$	3.43659	0.112329
$937$	−16.8570	−0.550696	−0.275348	−	0.961345i	$-0.588793\pi$
$937$	−16.8570	−0.550696	−0.275348	+	0.961345i	$0.588793\pi$
$938$	5.33979	0.174350
$939$	−16.6266	−0.542587
$940$	0.190954	0.00622824
$941$	−0.0651012	−0.00212224	−0.00106112	−	0.999999i	$-0.500338\pi$
$941$	−0.0651012	−0.00212224	−0.00106112	+	0.999999i	$0.500338\pi$
$942$	−0.498979	−0.0162576
$943$	50.7192	1.65165
$944$	−23.4196	−0.762242
$945$	−0.0535418	−0.00174171
$946$	0.135649	0.00441033
$947$	−53.5042	−1.73865	−0.869327	−	0.494237i	$-0.835447\pi$
$947$	−53.5042	−1.73865	−0.869327	+	0.494237i	$0.835447\pi$
$948$	−18.4717	−0.599933
$949$	6.30979	0.204825
$950$	−7.09795	−0.230288
$951$	−29.1404	−0.944942
$952$	4.99745	0.161968
$953$	23.4814	0.760639	0.380319	−	0.924855i	$-0.375814\pi$
$953$	23.4814	0.760639	0.380319	+	0.924855i	$0.375814\pi$
$954$	−4.56220	−0.147707
$955$	−0.213263	−0.00690102
$956$	43.5855	1.40965
$957$	−1.35987	−0.0439584
$958$	11.3620	0.367091
$959$	−45.8435	−1.48037
$960$	−0.0527179	−0.00170146
$961$	−14.5628	−0.469767
$962$	−5.58617	−0.180105
$963$	15.8232	0.509896
$964$	−3.46638	−0.111645
$965$	−0.191747	−0.00617256
$966$	8.17116	0.262903
$967$	43.3624	1.39444	0.697220	−	0.716857i	$-0.254420\pi$
$967$	43.3624	1.39444	0.697220	+	0.716857i	$0.254420\pi$
$968$	−20.2889	−0.652110
$969$	2.84522	0.0914015
$970$	0.107184	0.00344148
$971$	−14.9453	−0.479618	−0.239809	−	0.970820i	$-0.577085\pi$
$971$	−14.9453	−0.479618	−0.239809	+	0.970820i	$0.577085\pi$
$972$	−1.75102	−0.0561640
$973$	34.4528	1.10451
$974$	−3.60851	−0.115624
$975$	−9.17976	−0.293988
$976$	−12.8898	−0.412594
$977$	−37.7205	−1.20679	−0.603394	−	0.797444i	$-0.706185\pi$
$977$	−37.7205	−1.20679	−0.603394	+	0.797444i	$0.706185\pi$
$978$	−10.0084	−0.320032
$979$	1.79369	0.0573265
$980$	−0.00453245	−0.000144784 0
$981$	−13.0986	−0.418206
$982$	0.0187175	0.000597299 0
$983$	−37.0759	−1.18254	−0.591269	−	0.806474i	$-0.701373\pi$
$983$	−37.0759	−1.18254	−0.591269	+	0.806474i	$0.701373\pi$
$984$	15.4782	0.493427
$985$	−0.468567	−0.0149298
$986$	−1.69602	−0.0540122
$987$	14.5204	0.462190
$988$	9.14750	0.291021
$989$	−4.16743	−0.132516
$990$	−0.00400322	−0.000127231 0
$991$	−14.4287	−0.458344	−0.229172	−	0.973386i	$-0.573602\pi$
$991$	−14.4287	−0.458344	−0.229172	+	0.973386i	$0.573602\pi$
$992$	20.3719	0.646810
$993$	−15.7212	−0.498896
$994$	0.376603	0.0119451
$995$	0.379758	0.0120391
$996$	−15.1393	−0.479709
$997$	12.2444	0.387784	0.193892	−	0.981023i	$-0.437889\pi$
$997$	12.2444	0.387784	0.193892	+	0.981023i	$0.437889\pi$
$998$	19.3472	0.612424
$999$	6.09727	0.192909

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.22	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.22	✓	46	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-0.498979 q^{2} +1.00000 q^{3} -1.75102 q^{4} +0.0200529 q^{5} -0.498979 q^{6} -2.67003 q^{7} +1.87168 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.498979 q^{2} +1.00000 q^{3} -1.75102 q^{4} +0.0200529 q^{5} -0.498979 q^{6} -2.67003 q^{7} +1.87168 q^{8} +1.00000 q^{9} -0.0100060 q^{10} +0.400083 q^{11} -1.75102 q^{12} +1.83610 q^{13} +1.33229 q^{14} +0.0200529 q^{15} +2.56811 q^{16} -1.00000 q^{17} -0.498979 q^{18} -2.84522 q^{19} -0.0351129 q^{20} -2.67003 q^{21} -0.199633 q^{22} +6.13316 q^{23} +1.87168 q^{24} -4.99960 q^{25} -0.916175 q^{26} +1.00000 q^{27} +4.67528 q^{28} -3.39897 q^{29} -0.0100060 q^{30} -4.05428 q^{31} -5.02480 q^{32} +0.400083 q^{33} +0.498979 q^{34} -0.0535418 q^{35} -1.75102 q^{36} +6.09727 q^{37} +1.41970 q^{38} +1.83610 q^{39} +0.0375325 q^{40} +8.26967 q^{41} +1.33229 q^{42} -0.679491 q^{43} -0.700554 q^{44} +0.0200529 q^{45} -3.06032 q^{46} -5.43829 q^{47} +2.56811 q^{48} +0.129082 q^{49} +2.49470 q^{50} -1.00000 q^{51} -3.21505 q^{52} +9.14306 q^{53} -0.498979 q^{54} +0.00802281 q^{55} -4.99745 q^{56} -2.84522 q^{57} +1.69602 q^{58} -9.11938 q^{59} -0.0351129 q^{60} -5.01919 q^{61} +2.02300 q^{62} -2.67003 q^{63} -2.62895 q^{64} +0.0368190 q^{65} -0.199633 q^{66} +4.00797 q^{67} +1.75102 q^{68} +6.13316 q^{69} +0.0267162 q^{70} +0.282673 q^{71} +1.87168 q^{72} +3.43652 q^{73} -3.04241 q^{74} -4.99960 q^{75} +4.98203 q^{76} -1.06824 q^{77} -0.916175 q^{78} +10.5491 q^{79} +0.0514979 q^{80} +1.00000 q^{81} -4.12640 q^{82} +8.64602 q^{83} +4.67528 q^{84} -0.0200529 q^{85} +0.339052 q^{86} -3.39897 q^{87} +0.748828 q^{88} +4.48328 q^{89} -0.0100060 q^{90} -4.90245 q^{91} -10.7393 q^{92} -4.05428 q^{93} +2.71359 q^{94} -0.0570547 q^{95} -5.02480 q^{96} -10.7121 q^{97} -0.0644093 q^{98} +0.400083 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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