LMFDB - Embedded newform 8007.2.a.g.1.15

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:	$0$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-1.59327 q^{2} -1.00000 q^{3} +0.538495 q^{4} +2.65587 q^{5} +1.59327 q^{6} -0.355214 q^{7} +2.32857 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.59327 q^{2} -1.00000 q^{3} +0.538495 q^{4} +2.65587 q^{5} +1.59327 q^{6} -0.355214 q^{7} +2.32857 q^{8} +1.00000 q^{9} -4.23151 q^{10} -0.104408 q^{11} -0.538495 q^{12} -3.69014 q^{13} +0.565950 q^{14} -2.65587 q^{15} -4.78701 q^{16} -1.00000 q^{17} -1.59327 q^{18} +2.03257 q^{19} +1.43018 q^{20} +0.355214 q^{21} +0.166349 q^{22} -2.16340 q^{23} -2.32857 q^{24} +2.05366 q^{25} +5.87937 q^{26} -1.00000 q^{27} -0.191281 q^{28} +9.51910 q^{29} +4.23151 q^{30} -5.97501 q^{31} +2.96985 q^{32} +0.104408 q^{33} +1.59327 q^{34} -0.943404 q^{35} +0.538495 q^{36} -8.13278 q^{37} -3.23843 q^{38} +3.69014 q^{39} +6.18437 q^{40} -9.41516 q^{41} -0.565950 q^{42} +2.65809 q^{43} -0.0562231 q^{44} +2.65587 q^{45} +3.44687 q^{46} -1.66177 q^{47} +4.78701 q^{48} -6.87382 q^{49} -3.27203 q^{50} +1.00000 q^{51} -1.98712 q^{52} +5.87586 q^{53} +1.59327 q^{54} -0.277294 q^{55} -0.827139 q^{56} -2.03257 q^{57} -15.1665 q^{58} +5.92867 q^{59} -1.43018 q^{60} -9.70724 q^{61} +9.51978 q^{62} -0.355214 q^{63} +4.84226 q^{64} -9.80054 q^{65} -0.166349 q^{66} +5.06924 q^{67} -0.538495 q^{68} +2.16340 q^{69} +1.50309 q^{70} +1.19182 q^{71} +2.32857 q^{72} +4.48058 q^{73} +12.9577 q^{74} -2.05366 q^{75} +1.09453 q^{76} +0.0370871 q^{77} -5.87937 q^{78} -12.5188 q^{79} -12.7137 q^{80} +1.00000 q^{81} +15.0008 q^{82} +3.28221 q^{83} +0.191281 q^{84} -2.65587 q^{85} -4.23504 q^{86} -9.51910 q^{87} -0.243120 q^{88} +15.1159 q^{89} -4.23151 q^{90} +1.31079 q^{91} -1.16498 q^{92} +5.97501 q^{93} +2.64764 q^{94} +5.39826 q^{95} -2.96985 q^{96} +11.5399 q^{97} +10.9518 q^{98} -0.104408 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) $ 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * 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 $

$2$	−1.59327	−1.12661	−0.563304	−	0.826249i	$-0.690470\pi$
$2$	−1.59327	−1.12661	−0.563304	+	0.826249i	$0.690470\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.538495	0.269248
$5$	2.65587	1.18774	0.593871	−	0.804560i	$-0.297599\pi$
$5$	2.65587	1.18774	0.593871	+	0.804560i	$0.297599\pi$
$6$	1.59327	0.650448
$7$	−0.355214	−0.134258	−0.0671292	−	0.997744i	$-0.521384\pi$
$7$	−0.355214	−0.134258	−0.0671292	+	0.997744i	$0.521384\pi$
$8$	2.32857	0.823272
$9$	1.00000	0.333333
$10$	−4.23151	−1.33812
$11$	−0.104408	−0.0314801	−0.0157401	−	0.999876i	$-0.505010\pi$
$11$	−0.104408	−0.0314801	−0.0157401	+	0.999876i	$0.505010\pi$
$12$	−0.538495	−0.155450
$13$	−3.69014	−1.02346	−0.511730	−	0.859146i	$-0.670995\pi$
$13$	−3.69014	−1.02346	−0.511730	+	0.859146i	$0.670995\pi$
$14$	0.565950	0.151257
$15$	−2.65587	−0.685743
$16$	−4.78701	−1.19675
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.59327	−0.375536
$19$	2.03257	0.466304	0.233152	−	0.972440i	$-0.425096\pi$
$19$	2.03257	0.466304	0.233152	+	0.972440i	$0.425096\pi$
$20$	1.43018	0.319797
$21$	0.355214	0.0775141
$22$	0.166349	0.0354658
$23$	−2.16340	−0.451101	−0.225550	−	0.974232i	$-0.572418\pi$
$23$	−2.16340	−0.451101	−0.225550	+	0.974232i	$0.572418\pi$
$24$	−2.32857	−0.475316
$25$	2.05366	0.410732
$26$	5.87937	1.15304
$27$	−1.00000	−0.192450
$28$	−0.191281	−0.0361487
$29$	9.51910	1.76765	0.883826	−	0.467815i	$-0.154959\pi$
$29$	9.51910	1.76765	0.883826	+	0.467815i	$0.154959\pi$
$30$	4.23151	0.772565
$31$	−5.97501	−1.07314	−0.536572	−	0.843855i	$-0.680281\pi$
$31$	−5.97501	−1.07314	−0.536572	+	0.843855i	$0.680281\pi$
$32$	2.96985	0.525001
$33$	0.104408	0.0181750
$34$	1.59327	0.273243
$35$	−0.943404	−0.159464
$36$	0.538495	0.0897492
$37$	−8.13278	−1.33702	−0.668511	−	0.743702i	$-0.733068\pi$
$37$	−8.13278	−1.33702	−0.668511	+	0.743702i	$0.733068\pi$
$38$	−3.23843	−0.525343
$39$	3.69014	0.590895
$40$	6.18437	0.977835
$41$	−9.41516	−1.47040	−0.735200	−	0.677850i	$-0.762912\pi$
$41$	−9.41516	−1.47040	−0.735200	+	0.677850i	$0.762912\pi$
$42$	−0.565950	−0.0873281
$43$	2.65809	0.405355	0.202677	−	0.979246i	$-0.435036\pi$
$43$	2.65809	0.405355	0.202677	+	0.979246i	$0.435036\pi$
$44$	−0.0562231	−0.00847595
$45$	2.65587	0.395914
$46$	3.44687	0.508214
$47$	−1.66177	−0.242394	−0.121197	−	0.992628i	$-0.538673\pi$
$47$	−1.66177	−0.242394	−0.121197	+	0.992628i	$0.538673\pi$
$48$	4.78701	0.690946
$49$	−6.87382	−0.981975
$50$	−3.27203	−0.462734
$51$	1.00000	0.140028
$52$	−1.98712	−0.275564
$53$	5.87586	0.807112	0.403556	−	0.914955i	$-0.367774\pi$
$53$	5.87586	0.807112	0.403556	+	0.914955i	$0.367774\pi$
$54$	1.59327	0.216816
$55$	−0.277294	−0.0373903
$56$	−0.827139	−0.110531
$57$	−2.03257	−0.269221
$58$	−15.1665	−1.99145
$59$	5.92867	0.771848	0.385924	−	0.922531i	$-0.373883\pi$
$59$	5.92867	0.771848	0.385924	+	0.922531i	$0.373883\pi$
$60$	−1.43018	−0.184635
$61$	−9.70724	−1.24288	−0.621442	−	0.783460i	$-0.713453\pi$
$61$	−9.70724	−1.24288	−0.621442	+	0.783460i	$0.713453\pi$
$62$	9.51978	1.20901
$63$	−0.355214	−0.0447528
$64$	4.84226	0.605283
$65$	−9.80054	−1.21561
$66$	−0.166349	−0.0204762
$67$	5.06924	0.619306	0.309653	−	0.950850i	$-0.399787\pi$
$67$	5.06924	0.619306	0.309653	+	0.950850i	$0.399787\pi$
$68$	−0.538495	−0.0653022
$69$	2.16340	0.260443
$70$	1.50309	0.179654
$71$	1.19182	0.141443	0.0707213	−	0.997496i	$-0.477470\pi$
$71$	1.19182	0.141443	0.0707213	+	0.997496i	$0.477470\pi$
$72$	2.32857	0.274424
$73$	4.48058	0.524412	0.262206	−	0.965012i	$-0.415550\pi$
$73$	4.48058	0.524412	0.262206	+	0.965012i	$0.415550\pi$
$74$	12.9577	1.50630
$75$	−2.05366	−0.237136
$76$	1.09453	0.125551
$77$	0.0370871	0.00422647
$78$	−5.87937	−0.665708
$79$	−12.5188	−1.40847	−0.704236	−	0.709966i	$-0.748710\pi$
$79$	−12.5188	−1.40847	−0.704236	+	0.709966i	$0.748710\pi$
$80$	−12.7137	−1.42143
$81$	1.00000	0.111111
$82$	15.0008	1.65657
$83$	3.28221	0.360269	0.180135	−	0.983642i	$-0.442347\pi$
$83$	3.28221	0.360269	0.180135	+	0.983642i	$0.442347\pi$
$84$	0.191281	0.0208705
$85$	−2.65587	−0.288070
$86$	−4.23504	−0.456676
$87$	−9.51910	−1.02055
$88$	−0.243120	−0.0259167
$89$	15.1159	1.60228	0.801139	−	0.598479i	$-0.204228\pi$
$89$	15.1159	1.60228	0.801139	+	0.598479i	$0.204228\pi$
$90$	−4.23151	−0.446040
$91$	1.31079	0.137408
$92$	−1.16498	−0.121458
$93$	5.97501	0.619580
$94$	2.64764	0.273083
$95$	5.39826	0.553849
$96$	−2.96985	−0.303109
$97$	11.5399	1.17170	0.585852	−	0.810418i	$-0.300760\pi$
$97$	11.5399	1.17170	0.585852	+	0.810418i	$0.300760\pi$
$98$	10.9518	1.10630
$99$	−0.104408	−0.0104934
$100$	1.10589	0.110589
$101$	−3.50229	−0.348491	−0.174245	−	0.984702i	$-0.555749\pi$
$101$	−3.50229	−0.348491	−0.174245	+	0.984702i	$0.555749\pi$
$102$	−1.59327	−0.157757
$103$	4.55748	0.449062	0.224531	−	0.974467i	$-0.427915\pi$
$103$	4.55748	0.449062	0.224531	+	0.974467i	$0.427915\pi$
$104$	−8.59273	−0.842587
$105$	0.943404	0.0920668
$106$	−9.36181	−0.909299
$107$	12.3236	1.19137	0.595684	−	0.803219i	$-0.296881\pi$
$107$	12.3236	1.19137	0.595684	+	0.803219i	$0.296881\pi$
$108$	−0.538495	−0.0518167
$109$	18.2373	1.74682	0.873410	−	0.486985i	$-0.161903\pi$
$109$	18.2373	1.74682	0.873410	+	0.486985i	$0.161903\pi$
$110$	0.441802	0.0421242
$111$	8.13278	0.771930
$112$	1.70041	0.160674
$113$	4.43096	0.416830	0.208415	−	0.978041i	$-0.433170\pi$
$113$	4.43096	0.416830	0.208415	+	0.978041i	$0.433170\pi$
$114$	3.23843	0.303307
$115$	−5.74572	−0.535791
$116$	5.12599	0.475936
$117$	−3.69014	−0.341154
$118$	−9.44595	−0.869570
$119$	0.355214	0.0325624
$120$	−6.18437	−0.564553
$121$	−10.9891	−0.999009
$122$	15.4662	1.40024
$123$	9.41516	0.848936
$124$	−3.21752	−0.288941
$125$	−7.82510	−0.699899
$126$	0.565950	0.0504189
$127$	−18.2921	−1.62316	−0.811582	−	0.584239i	$-0.801393\pi$
$127$	−18.2921	−1.62316	−0.811582	+	0.584239i	$0.801393\pi$
$128$	−13.6547	−1.20692
$129$	−2.65809	−0.234032
$130$	15.6149	1.36951
$131$	13.8353	1.20879	0.604396	−	0.796684i	$-0.293414\pi$
$131$	13.8353	1.20879	0.604396	+	0.796684i	$0.293414\pi$
$132$	0.0562231	0.00489359
$133$	−0.721999	−0.0626052
$134$	−8.07664	−0.697715
$135$	−2.65587	−0.228581
$136$	−2.32857	−0.199673
$137$	12.5001	1.06796	0.533979	−	0.845498i	$-0.320696\pi$
$137$	12.5001	1.06796	0.533979	+	0.845498i	$0.320696\pi$
$138$	−3.44687	−0.293417
$139$	11.7219	0.994239	0.497119	−	0.867682i	$-0.334391\pi$
$139$	11.7219	0.994239	0.497119	+	0.867682i	$0.334391\pi$
$140$	−0.508019	−0.0429354
$141$	1.66177	0.139946
$142$	−1.89888	−0.159351
$143$	0.385279	0.0322187
$144$	−4.78701	−0.398918
$145$	25.2815	2.09952
$146$	−7.13875	−0.590807
$147$	6.87382	0.566943
$148$	−4.37947	−0.359990
$149$	15.4892	1.26893	0.634464	−	0.772953i	$-0.281221\pi$
$149$	15.4892	1.26893	0.634464	+	0.772953i	$0.281221\pi$
$150$	3.27203	0.267160
$151$	15.8350	1.28863	0.644317	−	0.764758i	$-0.277142\pi$
$151$	15.8350	1.28863	0.644317	+	0.764758i	$0.277142\pi$
$152$	4.73298	0.383895
$153$	−1.00000	−0.0808452
$154$	−0.0590896	−0.00476157
$155$	−15.8689	−1.27462
$156$	1.98712	0.159097
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	19.9457	1.58680
$159$	−5.87586	−0.465986
$160$	7.88755	0.623566
$161$	0.768471	0.0605640
$162$	−1.59327	−0.125179
$163$	12.8303	1.00495	0.502474	−	0.864592i	$-0.332423\pi$
$163$	12.8303	1.00495	0.502474	+	0.864592i	$0.332423\pi$
$164$	−5.07002	−0.395902
$165$	0.277294	0.0215873
$166$	−5.22943	−0.405882
$167$	7.06519	0.546721	0.273360	−	0.961912i	$-0.411865\pi$
$167$	7.06519	0.546721	0.273360	+	0.961912i	$0.411865\pi$
$168$	0.827139	0.0638152
$169$	0.617135	0.0474719
$170$	4.23151	0.324542
$171$	2.03257	0.155435
$172$	1.43137	0.109141
$173$	12.7295	0.967804	0.483902	−	0.875122i	$-0.339219\pi$
$173$	12.7295	0.967804	0.483902	+	0.875122i	$0.339219\pi$
$174$	15.1665	1.14977
$175$	−0.729489	−0.0551442
$176$	0.499801	0.0376739
$177$	−5.92867	−0.445626
$178$	−24.0836	−1.80514
$179$	−10.5497	−0.788524	−0.394262	−	0.918998i	$-0.629000\pi$
$179$	−10.5497	−0.788524	−0.394262	+	0.918998i	$0.629000\pi$
$180$	1.43018	0.106599
$181$	−12.4759	−0.927326	−0.463663	−	0.886012i	$-0.653465\pi$
$181$	−12.4759	−0.927326	−0.463663	+	0.886012i	$0.653465\pi$
$182$	−2.08844	−0.154805
$183$	9.70724	0.717580
$184$	−5.03762	−0.371378
$185$	−21.5996	−1.58804
$186$	−9.51978	−0.698024
$187$	0.104408	0.00763505
$188$	−0.894855	−0.0652640
$189$	0.355214	0.0258380
$190$	−8.60086	−0.623972
$191$	−13.0528	−0.944470	−0.472235	−	0.881473i	$-0.656553\pi$
$191$	−13.0528	−0.944470	−0.472235	+	0.881473i	$0.656553\pi$
$192$	−4.84226	−0.349460
$193$	25.0172	1.80078	0.900388	−	0.435087i	$-0.143283\pi$
$193$	25.0172	1.80078	0.900388	+	0.435087i	$0.143283\pi$
$194$	−18.3862	−1.32005
$195$	9.80054	0.701831
$196$	−3.70152	−0.264394
$197$	−16.6912	−1.18920	−0.594601	−	0.804021i	$-0.702690\pi$
$197$	−16.6912	−1.18920	−0.594601	+	0.804021i	$0.702690\pi$
$198$	0.166349	0.0118219
$199$	1.46184	0.103627	0.0518137	−	0.998657i	$-0.483500\pi$
$199$	1.46184	0.103627	0.0518137	+	0.998657i	$0.483500\pi$
$200$	4.78208	0.338144
$201$	−5.06924	−0.357556
$202$	5.58008	0.392613
$203$	−3.38132	−0.237322
$204$	0.538495	0.0377022
$205$	−25.0055	−1.74646
$206$	−7.26128	−0.505918
$207$	−2.16340	−0.150367
$208$	17.6648	1.22483
$209$	−0.212216	−0.0146793
$210$	−1.50309	−0.103723
$211$	2.09909	0.144508	0.0722538	−	0.997386i	$-0.476981\pi$
$211$	2.09909	0.144508	0.0722538	+	0.997386i	$0.476981\pi$
$212$	3.16412	0.217313
$213$	−1.19182	−0.0816619
$214$	−19.6348	−1.34220
$215$	7.05955	0.481457
$216$	−2.32857	−0.158439
$217$	2.12241	0.144078
$218$	−29.0569	−1.96798
$219$	−4.48058	−0.302770
$220$	−0.149321	−0.0100672
$221$	3.69014	0.248226
$222$	−12.9577	−0.869663
$223$	−11.0798	−0.741958	−0.370979	−	0.928641i	$-0.620978\pi$
$223$	−11.0798	−0.741958	−0.370979	+	0.928641i	$0.620978\pi$
$224$	−1.05493	−0.0704858
$225$	2.05366	0.136911
$226$	−7.05970	−0.469604
$227$	−0.591104	−0.0392329	−0.0196165	−	0.999808i	$-0.506245\pi$
$227$	−0.591104	−0.0392329	−0.0196165	+	0.999808i	$0.506245\pi$
$228$	−1.09453	−0.0724871
$229$	9.79590	0.647331	0.323666	−	0.946172i	$-0.395085\pi$
$229$	9.79590	0.647331	0.323666	+	0.946172i	$0.395085\pi$
$230$	9.15446	0.603627
$231$	−0.0370871	−0.00244015
$232$	22.1658	1.45526
$233$	16.8313	1.10265	0.551326	−	0.834290i	$-0.314122\pi$
$233$	16.8313	1.10265	0.551326	+	0.834290i	$0.314122\pi$
$234$	5.87937	0.384347
$235$	−4.41345	−0.287902
$236$	3.19256	0.207818
$237$	12.5188	0.813182
$238$	−0.565950	−0.0366851
$239$	−27.9430	−1.80748	−0.903740	−	0.428081i	$-0.859190\pi$
$239$	−27.9430	−1.80748	−0.903740	+	0.428081i	$0.859190\pi$
$240$	12.7137	0.820666
$241$	−10.9444	−0.704988	−0.352494	−	0.935814i	$-0.614666\pi$
$241$	−10.9444	−0.704988	−0.352494	+	0.935814i	$0.614666\pi$
$242$	17.5086	1.12549
$243$	−1.00000	−0.0641500
$244$	−5.22730	−0.334644
$245$	−18.2560	−1.16633
$246$	−15.0008	−0.956419
$247$	−7.50048	−0.477244
$248$	−13.9132	−0.883489
$249$	−3.28221	−0.208001
$250$	12.4675	0.788512
$251$	7.54827	0.476442	0.238221	−	0.971211i	$-0.423436\pi$
$251$	7.54827	0.476442	0.238221	+	0.971211i	$0.423436\pi$
$252$	−0.191281	−0.0120496
$253$	0.225876	0.0142007
$254$	29.1442	1.82867
$255$	2.65587	0.166317
$256$	12.0711	0.754442
$257$	7.53436	0.469980	0.234990	−	0.971998i	$-0.424494\pi$
$257$	7.53436	0.469980	0.234990	+	0.971998i	$0.424494\pi$
$258$	4.23504	0.263662
$259$	2.88888	0.179506
$260$	−5.27755	−0.327300
$261$	9.51910	0.589218
$262$	−22.0432	−1.36184
$263$	−20.1581	−1.24300	−0.621501	−	0.783414i	$-0.713477\pi$
$263$	−20.1581	−1.24300	−0.621501	+	0.783414i	$0.713477\pi$
$264$	0.243120	0.0149630
$265$	15.6055	0.958641
$266$	1.15034	0.0705316
$267$	−15.1159	−0.925075
$268$	2.72976	0.166747
$269$	−0.387096	−0.0236017	−0.0118008	−	0.999930i	$-0.503756\pi$
$269$	−0.387096	−0.0236017	−0.0118008	+	0.999930i	$0.503756\pi$
$270$	4.23151	0.257522
$271$	−23.1590	−1.40681	−0.703405	−	0.710790i	$-0.748338\pi$
$271$	−23.1590	−1.40681	−0.703405	+	0.710790i	$0.748338\pi$
$272$	4.78701	0.290255
$273$	−1.31079	−0.0793326
$274$	−19.9160	−1.20317
$275$	−0.214418	−0.0129299
$276$	1.16498	0.0701237
$277$	26.1154	1.56912	0.784562	−	0.620050i	$-0.212888\pi$
$277$	26.1154	1.56912	0.784562	+	0.620050i	$0.212888\pi$
$278$	−18.6761	−1.12012
$279$	−5.97501	−0.357715
$280$	−2.19678	−0.131283
$281$	−19.1380	−1.14168	−0.570840	−	0.821061i	$-0.693382\pi$
$281$	−19.1380	−1.14168	−0.570840	+	0.821061i	$0.693382\pi$
$282$	−2.64764	−0.157665
$283$	−6.91362	−0.410972	−0.205486	−	0.978660i	$-0.565877\pi$
$283$	−6.91362	−0.410972	−0.205486	+	0.978660i	$0.565877\pi$
$284$	0.641788	0.0380831
$285$	−5.39826	−0.319765
$286$	−0.613852	−0.0362978
$287$	3.34440	0.197414
$288$	2.96985	0.175000
$289$	1.00000	0.0588235
$290$	−40.2802	−2.36533
$291$	−11.5399	−0.676484
$292$	2.41277	0.141197
$293$	−12.1362	−0.709004	−0.354502	−	0.935055i	$-0.615350\pi$
$293$	−12.1362	−0.709004	−0.354502	+	0.935055i	$0.615350\pi$
$294$	−10.9518	−0.638723
$295$	15.7458	0.916756
$296$	−18.9377	−1.10073
$297$	0.104408	0.00605835
$298$	−24.6785	−1.42958
$299$	7.98326	0.461684
$300$	−1.10589	−0.0638484
$301$	−0.944191	−0.0544223
$302$	−25.2294	−1.45179
$303$	3.50229	0.201201
$304$	−9.72996	−0.558051
$305$	−25.7812	−1.47623
$306$	1.59327	0.0910809
$307$	23.3307	1.33155	0.665777	−	0.746151i	$-0.268100\pi$
$307$	23.3307	1.33155	0.665777	+	0.746151i	$0.268100\pi$
$308$	0.0199712	0.00113797
$309$	−4.55748	−0.259266
$310$	25.2833	1.43600
$311$	5.25623	0.298054	0.149027	−	0.988833i	$-0.452386\pi$
$311$	5.25623	0.298054	0.149027	+	0.988833i	$0.452386\pi$
$312$	8.59273	0.486468
$313$	−5.36949	−0.303501	−0.151751	−	0.988419i	$-0.548491\pi$
$313$	−5.36949	−0.303501	−0.151751	+	0.988419i	$0.548491\pi$
$314$	−1.59327	−0.0899132
$315$	−0.943404	−0.0531548
$316$	−6.74131	−0.379228
$317$	12.2782	0.689612	0.344806	−	0.938674i	$-0.387945\pi$
$317$	12.2782	0.689612	0.344806	+	0.938674i	$0.387945\pi$
$318$	9.36181	0.524984
$319$	−0.993867	−0.0556459
$320$	12.8604	0.718920
$321$	−12.3236	−0.687836
$322$	−1.22438	−0.0682320
$323$	−2.03257	−0.113095
$324$	0.538495	0.0299164
$325$	−7.57829	−0.420368
$326$	−20.4421	−1.13218
$327$	−18.2373	−1.00853
$328$	−21.9238	−1.21054
$329$	0.590284	0.0325434
$330$	−0.441802	−0.0243204
$331$	1.98195	0.108938	0.0544688	−	0.998515i	$-0.482653\pi$
$331$	1.98195	0.108938	0.0544688	+	0.998515i	$0.482653\pi$
$332$	1.76745	0.0970016
$333$	−8.13278	−0.445674
$334$	−11.2567	−0.615941
$335$	13.4632	0.735576
$336$	−1.70041	−0.0927652
$337$	14.5753	0.793965	0.396983	−	0.917826i	$-0.370057\pi$
$337$	14.5753	0.793965	0.396983	+	0.917826i	$0.370057\pi$
$338$	−0.983260	−0.0534823
$339$	−4.43096	−0.240657
$340$	−1.43018	−0.0775621
$341$	0.623837	0.0337827
$342$	−3.23843	−0.175114
$343$	4.92818	0.266097
$344$	6.18954	0.333717
$345$	5.74572	0.309339
$346$	−20.2814	−1.09034
$347$	−13.0571	−0.700940	−0.350470	−	0.936574i	$-0.613978\pi$
$347$	−13.0571	−0.700940	−0.350470	+	0.936574i	$0.613978\pi$
$348$	−5.12599	−0.274782
$349$	21.9346	1.17413	0.587065	−	0.809540i	$-0.300283\pi$
$349$	21.9346	1.17413	0.587065	+	0.809540i	$0.300283\pi$
$350$	1.16227	0.0621259
$351$	3.69014	0.196965
$352$	−0.310076	−0.0165271
$353$	14.1531	0.753294	0.376647	−	0.926357i	$-0.377077\pi$
$353$	14.1531	0.753294	0.376647	+	0.926357i	$0.377077\pi$
$354$	9.44595	0.502047
$355$	3.16531	0.167997
$356$	8.13982	0.431410
$357$	−0.355214	−0.0187999
$358$	16.8085	0.888359
$359$	−7.07556	−0.373434	−0.186717	−	0.982414i	$-0.559785\pi$
$359$	−7.07556	−0.373434	−0.186717	+	0.982414i	$0.559785\pi$
$360$	6.18437	0.325945
$361$	−14.8686	−0.782560
$362$	19.8774	1.04473
$363$	10.9891	0.576778
$364$	0.705854	0.0369968
$365$	11.8998	0.622867
$366$	−15.4662	−0.808431
$367$	−19.7786	−1.03243	−0.516216	−	0.856458i	$-0.672660\pi$
$367$	−19.7786	−1.03243	−0.516216	+	0.856458i	$0.672660\pi$
$368$	10.3562	0.539856
$369$	−9.41516	−0.490134
$370$	34.4140	1.78910
$371$	−2.08719	−0.108361
$372$	3.21752	0.166820
$373$	−9.49192	−0.491473	−0.245737	−	0.969337i	$-0.579030\pi$
$373$	−9.49192	−0.491473	−0.245737	+	0.969337i	$0.579030\pi$
$374$	−0.166349	−0.00860171
$375$	7.82510	0.404087
$376$	−3.86954	−0.199556
$377$	−35.1268	−1.80912
$378$	−0.565950	−0.0291094
$379$	20.2292	1.03911	0.519553	−	0.854438i	$-0.326099\pi$
$379$	20.2292	1.03911	0.519553	+	0.854438i	$0.326099\pi$
$380$	2.90694	0.149123
$381$	18.2921	0.937134
$382$	20.7966	1.06405
$383$	26.4635	1.35222	0.676112	−	0.736799i	$-0.263664\pi$
$383$	26.4635	1.35222	0.676112	+	0.736799i	$0.263664\pi$
$384$	13.6547	0.696814
$385$	0.0984986	0.00501995
$386$	−39.8590	−2.02877
$387$	2.65809	0.135118
$388$	6.21421	0.315479
$389$	−5.44482	−0.276064	−0.138032	−	0.990428i	$-0.544078\pi$
$389$	−5.44482	−0.276064	−0.138032	+	0.990428i	$0.544078\pi$
$390$	−15.6149	−0.790690
$391$	2.16340	0.109408
$392$	−16.0061	−0.808432
$393$	−13.8353	−0.697897
$394$	26.5936	1.33977
$395$	−33.2483	−1.67290
$396$	−0.0562231	−0.00282532
$397$	20.9914	1.05353	0.526765	−	0.850011i	$-0.323405\pi$
$397$	20.9914	1.05353	0.526765	+	0.850011i	$0.323405\pi$
$398$	−2.32911	−0.116747
$399$	0.721999	0.0361452
$400$	−9.83090	−0.491545
$401$	14.8624	0.742191	0.371096	−	0.928595i	$-0.378982\pi$
$401$	14.8624	0.742191	0.371096	+	0.928595i	$0.378982\pi$
$402$	8.07664	0.402826
$403$	22.0486	1.09832
$404$	−1.88597	−0.0938303
$405$	2.65587	0.131971
$406$	5.38734	0.267369
$407$	0.849125	0.0420896
$408$	2.32857	0.115281
$409$	26.8154	1.32594	0.662968	−	0.748648i	$-0.269297\pi$
$409$	26.8154	1.32594	0.662968	+	0.748648i	$0.269297\pi$
$410$	39.8403	1.96757
$411$	−12.5001	−0.616586
$412$	2.45418	0.120909
$413$	−2.10595	−0.103627
$414$	3.44687	0.169405
$415$	8.71713	0.427907
$416$	−10.9592	−0.537318
$417$	−11.7219	−0.574024
$418$	0.338117	0.0165378
$419$	−25.0876	−1.22561	−0.612804	−	0.790235i	$-0.709958\pi$
$419$	−25.0876	−1.22561	−0.612804	+	0.790235i	$0.709958\pi$
$420$	0.508019	0.0247888
$421$	25.4249	1.23913	0.619567	−	0.784944i	$-0.287308\pi$
$421$	25.4249	1.23913	0.619567	+	0.784944i	$0.287308\pi$
$422$	−3.34441	−0.162804
$423$	−1.66177	−0.0807980
$424$	13.6823	0.664472
$425$	−2.05366	−0.0996172
$426$	1.89888	0.0920011
$427$	3.44815	0.166868
$428$	6.63620	0.320773
$429$	−0.385279	−0.0186014
$430$	−11.2477	−0.542414
$431$	−34.1851	−1.64664	−0.823320	−	0.567578i	$-0.807880\pi$
$431$	−34.1851	−1.64664	−0.823320	+	0.567578i	$0.807880\pi$
$432$	4.78701	0.230315
$433$	30.2170	1.45213	0.726067	−	0.687624i	$-0.241346\pi$
$433$	30.2170	1.45213	0.726067	+	0.687624i	$0.241346\pi$
$434$	−3.38156	−0.162320
$435$	−25.2815	−1.21216
$436$	9.82072	0.470327
$437$	−4.39727	−0.210350
$438$	7.13875	0.341103
$439$	−27.8218	−1.32786	−0.663931	−	0.747794i	$-0.731113\pi$
$439$	−27.8218	−1.32786	−0.663931	+	0.747794i	$0.731113\pi$
$440$	−0.645696	−0.0307824
$441$	−6.87382	−0.327325
$442$	−5.87937	−0.279653
$443$	23.0817	1.09665	0.548323	−	0.836267i	$-0.315267\pi$
$443$	23.0817	1.09665	0.548323	+	0.836267i	$0.315267\pi$
$444$	4.37947	0.207840
$445$	40.1458	1.90309
$446$	17.6531	0.835897
$447$	−15.4892	−0.732615
$448$	−1.72004	−0.0812642
$449$	37.3324	1.76182	0.880912	−	0.473280i	$-0.156930\pi$
$449$	37.3324	1.76182	0.880912	+	0.473280i	$0.156930\pi$
$450$	−3.27203	−0.154245
$451$	0.983015	0.0462884
$452$	2.38605	0.112230
$453$	−15.8350	−0.743993
$454$	0.941785	0.0442002
$455$	3.48129	0.163205
$456$	−4.73298	−0.221642
$457$	20.0380	0.937337	0.468668	−	0.883374i	$-0.344734\pi$
$457$	20.0380	0.937337	0.468668	+	0.883374i	$0.344734\pi$
$458$	−15.6075	−0.729289
$459$	1.00000	0.0466760
$460$	−3.09404	−0.144261
$461$	−9.03337	−0.420726	−0.210363	−	0.977623i	$-0.567465\pi$
$461$	−9.03337	−0.420726	−0.210363	+	0.977623i	$0.567465\pi$
$462$	0.0590896	0.00274910
$463$	−15.5544	−0.722874	−0.361437	−	0.932396i	$-0.617714\pi$
$463$	−15.5544	−0.722874	−0.361437	+	0.932396i	$0.617714\pi$
$464$	−45.5681	−2.11544
$465$	15.8689	0.735901
$466$	−26.8167	−1.24226
$467$	5.20070	0.240660	0.120330	−	0.992734i	$-0.461605\pi$
$467$	5.20070	0.240660	0.120330	+	0.992734i	$0.461605\pi$
$468$	−1.98712	−0.0918548
$469$	−1.80066	−0.0831469
$470$	7.03179	0.324352
$471$	−1.00000	−0.0460776
$472$	13.8053	0.635441
$473$	−0.277525	−0.0127606
$474$	−19.9457	−0.916138
$475$	4.17422	0.191526
$476$	0.191281	0.00876736
$477$	5.87586	0.269037
$478$	44.5206	2.03632
$479$	22.3688	1.02206	0.511028	−	0.859564i	$-0.329265\pi$
$479$	22.3688	1.02206	0.511028	+	0.859564i	$0.329265\pi$
$480$	−7.88755	−0.360016
$481$	30.0111	1.36839
$482$	17.4373	0.794246
$483$	−0.768471	−0.0349666
$484$	−5.91758	−0.268981
$485$	30.6486	1.39168
$486$	1.59327	0.0722720
$487$	−11.2975	−0.511937	−0.255968	−	0.966685i	$-0.582394\pi$
$487$	−11.2975	−0.511937	−0.255968	+	0.966685i	$0.582394\pi$
$488$	−22.6039	−1.02323
$489$	−12.8303	−0.580207
$490$	29.0867	1.31400
$491$	42.5716	1.92123	0.960614	−	0.277885i	$-0.0896334\pi$
$491$	42.5716	1.92123	0.960614	+	0.277885i	$0.0896334\pi$
$492$	5.07002	0.228574
$493$	−9.51910	−0.428719
$494$	11.9503	0.537668
$495$	−0.277294	−0.0124634
$496$	28.6025	1.28429
$497$	−0.423350	−0.0189898
$498$	5.22943	0.234336
$499$	−12.5169	−0.560332	−0.280166	−	0.959952i	$-0.590389\pi$
$499$	−12.5169	−0.560332	−0.280166	+	0.959952i	$0.590389\pi$
$500$	−4.21378	−0.188446
$501$	−7.06519	−0.315649
$502$	−12.0264	−0.536764
$503$	−10.7547	−0.479529	−0.239765	−	0.970831i	$-0.577070\pi$
$503$	−10.7547	−0.479529	−0.239765	+	0.970831i	$0.577070\pi$
$504$	−0.827139	−0.0368437
$505$	−9.30163	−0.413917
$506$	−0.359880	−0.0159986
$507$	−0.617135	−0.0274079
$508$	−9.85023	−0.437033
$509$	−6.83539	−0.302973	−0.151487	−	0.988459i	$-0.548406\pi$
$509$	−6.83539	−0.302973	−0.151487	+	0.988459i	$0.548406\pi$
$510$	−4.23151	−0.187374
$511$	−1.59157	−0.0704067
$512$	8.07701	0.356957
$513$	−2.03257	−0.0897403
$514$	−12.0042	−0.529484
$515$	12.1041	0.533370
$516$	−1.43137	−0.0630125
$517$	0.173501	0.00763059
$518$	−4.60275	−0.202233
$519$	−12.7295	−0.558762
$520$	−22.8212	−1.00078
$521$	−17.4761	−0.765641	−0.382821	−	0.923823i	$-0.625047\pi$
$521$	−17.4761	−0.765641	−0.382821	+	0.923823i	$0.625047\pi$
$522$	−15.1665	−0.663818
$523$	32.5209	1.42204	0.711019	−	0.703173i	$-0.248234\pi$
$523$	32.5209	1.42204	0.711019	+	0.703173i	$0.248234\pi$
$524$	7.45022	0.325465
$525$	0.729489	0.0318375
$526$	32.1172	1.40038
$527$	5.97501	0.260276
$528$	−0.499801	−0.0217510
$529$	−18.3197	−0.796508
$530$	−24.8638	−1.08001
$531$	5.92867	0.257283
$532$	−0.388793	−0.0168563
$533$	34.7433	1.50490
$534$	24.0836	1.04220
$535$	32.7299	1.41504
$536$	11.8040	0.509857
$537$	10.5497	0.455255
$538$	0.616747	0.0265899
$539$	0.717680	0.0309127
$540$	−1.43018	−0.0615449
$541$	46.0758	1.98095	0.990477	−	0.137678i	$-0.0439640\pi$
$541$	46.0758	1.98095	0.990477	+	0.137678i	$0.0439640\pi$
$542$	36.8985	1.58492
$543$	12.4759	0.535392
$544$	−2.96985	−0.127331
$545$	48.4361	2.07477
$546$	2.08844	0.0893768
$547$	−7.95961	−0.340329	−0.170164	−	0.985416i	$-0.554430\pi$
$547$	−7.95961	−0.340329	−0.170164	+	0.985416i	$0.554430\pi$
$548$	6.73126	0.287545
$549$	−9.70724	−0.414295
$550$	0.341625	0.0145669
$551$	19.3483	0.824264
$552$	5.03762	0.214415
$553$	4.44685	0.189099
$554$	−41.6088	−1.76779
$555$	21.5996	0.916854
$556$	6.31219	0.267697
$557$	−7.77856	−0.329588	−0.164794	−	0.986328i	$-0.552696\pi$
$557$	−7.77856	−0.329588	−0.164794	+	0.986328i	$0.552696\pi$
$558$	9.51978	0.403004
$559$	−9.80872	−0.414865
$560$	4.51609	0.190839
$561$	−0.104408	−0.00440810
$562$	30.4920	1.28623
$563$	−30.7573	−1.29627	−0.648133	−	0.761527i	$-0.724450\pi$
$563$	−30.7573	−1.29627	−0.648133	+	0.761527i	$0.724450\pi$
$564$	0.894855	0.0376802
$565$	11.7681	0.495086
$566$	11.0152	0.463005
$567$	−0.355214	−0.0149176
$568$	2.77522	0.116446
$569$	16.3518	0.685501	0.342751	−	0.939426i	$-0.388641\pi$
$569$	16.3518	0.685501	0.342751	+	0.939426i	$0.388641\pi$
$570$	8.60086	0.360250
$571$	12.1566	0.508737	0.254368	−	0.967107i	$-0.418132\pi$
$571$	12.1566	0.508737	0.254368	+	0.967107i	$0.418132\pi$
$572$	0.207471	0.00867480
$573$	13.0528	0.545290
$574$	−5.32851	−0.222408
$575$	−4.44289	−0.185281
$576$	4.84226	0.201761
$577$	−30.0234	−1.24989	−0.624945	−	0.780669i	$-0.714879\pi$
$577$	−30.0234	−1.24989	−0.624945	+	0.780669i	$0.714879\pi$
$578$	−1.59327	−0.0662711
$579$	−25.0172	−1.03968
$580$	13.6140	0.565290
$581$	−1.16589	−0.0483691
$582$	18.3862	0.762133
$583$	−0.613485	−0.0254080
$584$	10.4333	0.431734
$585$	−9.80054	−0.405203
$586$	19.3362	0.798770
$587$	13.5700	0.560093	0.280047	−	0.959986i	$-0.409650\pi$
$587$	13.5700	0.560093	0.280047	+	0.959986i	$0.409650\pi$
$588$	3.70152	0.152648
$589$	−12.1446	−0.500412
$590$	−25.0872	−1.03283
$591$	16.6912	0.686586
$592$	38.9317	1.60008
$593$	21.8489	0.897225	0.448613	−	0.893726i	$-0.351918\pi$
$593$	21.8489	0.897225	0.448613	+	0.893726i	$0.351918\pi$
$594$	−0.166349	−0.00682539
$595$	0.943404	0.0386758
$596$	8.34088	0.341656
$597$	−1.46184	−0.0598293
$598$	−12.7195	−0.520137
$599$	−33.3933	−1.36441	−0.682207	−	0.731159i	$-0.738980\pi$
$599$	−33.3933	−1.36441	−0.682207	+	0.731159i	$0.738980\pi$
$600$	−4.78208	−0.195228
$601$	32.2229	1.31440	0.657199	−	0.753717i	$-0.271741\pi$
$601$	32.2229	1.31440	0.657199	+	0.753717i	$0.271741\pi$
$602$	1.50435	0.0613126
$603$	5.06924	0.206435
$604$	8.52708	0.346962
$605$	−29.1856	−1.18657
$606$	−5.58008	−0.226675
$607$	−22.8666	−0.928127	−0.464064	−	0.885802i	$-0.653609\pi$
$607$	−22.8666	−0.928127	−0.464064	+	0.885802i	$0.653609\pi$
$608$	6.03645	0.244810
$609$	3.38132	0.137018
$610$	41.0763	1.66313
$611$	6.13216	0.248081
$612$	−0.538495	−0.0217674
$613$	19.8073	0.800011	0.400005	−	0.916513i	$-0.369008\pi$
$613$	19.8073	0.800011	0.400005	+	0.916513i	$0.369008\pi$
$614$	−37.1720	−1.50014
$615$	25.0055	1.00832
$616$	0.0863597	0.00347953
$617$	−16.0992	−0.648131	−0.324065	−	0.946035i	$-0.605050\pi$
$617$	−16.0992	−0.648131	−0.324065	+	0.946035i	$0.605050\pi$
$618$	7.26128	0.292092
$619$	15.5901	0.626620	0.313310	−	0.949651i	$-0.398562\pi$
$619$	15.5901	0.626620	0.313310	+	0.949651i	$0.398562\pi$
$620$	−8.54531	−0.343188
$621$	2.16340	0.0868143
$622$	−8.37457	−0.335790
$623$	−5.36937	−0.215119
$624$	−17.6648	−0.707156
$625$	−31.0508	−1.24203
$626$	8.55502	0.341927
$627$	0.212216	0.00847510
$628$	0.538495	0.0214883
$629$	8.13278	0.324275
$630$	1.50309	0.0598846
$631$	−2.59825	−0.103435	−0.0517174	−	0.998662i	$-0.516470\pi$
$631$	−2.59825	−0.103435	−0.0517174	+	0.998662i	$0.516470\pi$
$632$	−29.1508	−1.15956
$633$	−2.09909	−0.0834315
$634$	−19.5624	−0.776923
$635$	−48.5816	−1.92790
$636$	−3.16412	−0.125466
$637$	25.3654	1.00501
$638$	1.58349	0.0626912
$639$	1.19182	0.0471475
$640$	−36.2652	−1.43351
$641$	−4.99500	−0.197291	−0.0986453	−	0.995123i	$-0.531451\pi$
$641$	−4.99500	−0.197291	−0.0986453	+	0.995123i	$0.531451\pi$
$642$	19.6348	0.774922
$643$	20.4733	0.807388	0.403694	−	0.914894i	$-0.367726\pi$
$643$	20.4733	0.807388	0.403694	+	0.914894i	$0.367726\pi$
$644$	0.413818	0.0163067
$645$	−7.05955	−0.277969
$646$	3.23843	0.127414
$647$	45.1754	1.77603	0.888014	−	0.459817i	$-0.152085\pi$
$647$	45.1754	1.77603	0.888014	+	0.459817i	$0.152085\pi$
$648$	2.32857	0.0914747
$649$	−0.618999	−0.0242978
$650$	12.0742	0.473591
$651$	−2.12241	−0.0831837
$652$	6.90906	0.270580
$653$	3.16030	0.123672	0.0618360	−	0.998086i	$-0.480304\pi$
$653$	3.16030	0.123672	0.0618360	+	0.998086i	$0.480304\pi$
$654$	29.0569	1.13622
$655$	36.7447	1.43573
$656$	45.0705	1.75971
$657$	4.48058	0.174804
$658$	−0.940479	−0.0366637
$659$	−3.83712	−0.149473	−0.0747364	−	0.997203i	$-0.523812\pi$
$659$	−3.83712	−0.149473	−0.0747364	+	0.997203i	$0.523812\pi$
$660$	0.149321	0.00581232
$661$	−38.8524	−1.51118	−0.755591	−	0.655044i	$-0.772650\pi$
$661$	−38.8524	−1.51118	−0.755591	+	0.655044i	$0.772650\pi$
$662$	−3.15777	−0.122730
$663$	−3.69014	−0.143313
$664$	7.64283	0.296600
$665$	−1.91754	−0.0743589
$666$	12.9577	0.502100
$667$	−20.5936	−0.797389
$668$	3.80457	0.147203
$669$	11.0798	0.428370
$670$	−21.4505	−0.828706
$671$	1.01351	0.0391261
$672$	1.05493	0.0406950
$673$	7.95383	0.306597	0.153299	−	0.988180i	$-0.451010\pi$
$673$	7.95383	0.306597	0.153299	+	0.988180i	$0.451010\pi$
$674$	−23.2223	−0.894488
$675$	−2.05366	−0.0790454
$676$	0.332324	0.0127817
$677$	3.98435	0.153131	0.0765655	−	0.997065i	$-0.475605\pi$
$677$	3.98435	0.153131	0.0765655	+	0.997065i	$0.475605\pi$
$678$	7.05970	0.271126
$679$	−4.09915	−0.157311
$680$	−6.18437	−0.237160
$681$	0.591104	0.0226511
$682$	−0.993938	−0.0380599
$683$	−37.0763	−1.41868	−0.709342	−	0.704864i	$-0.751008\pi$
$683$	−37.0763	−1.41868	−0.709342	+	0.704864i	$0.751008\pi$
$684$	1.09453	0.0418505
$685$	33.1988	1.26846
$686$	−7.85190	−0.299787
$687$	−9.79590	−0.373737
$688$	−12.7243	−0.485110
$689$	−21.6828	−0.826047
$690$	−9.15446	−0.348504
$691$	−15.6433	−0.595099	−0.297549	−	0.954706i	$-0.596169\pi$
$691$	−15.6433	−0.595099	−0.297549	+	0.954706i	$0.596169\pi$
$692$	6.85477	0.260579
$693$	0.0370871	0.00140882
$694$	20.8034	0.789686
$695$	31.1319	1.18090
$696$	−22.1658	−0.840194
$697$	9.41516	0.356625
$698$	−34.9476	−1.32279
$699$	−16.8313	−0.636617
$700$	−0.392827	−0.0148474
$701$	21.7869	0.822878	0.411439	−	0.911437i	$-0.365026\pi$
$701$	21.7869	0.822878	0.411439	+	0.911437i	$0.365026\pi$
$702$	−5.87937	−0.221903
$703$	−16.5305	−0.623459
$704$	−0.505569	−0.0190544
$705$	4.41345	0.166220
$706$	−22.5496	−0.848667
$707$	1.24406	0.0467878
$708$	−3.19256	−0.119984
$709$	27.6285	1.03761	0.518804	−	0.854893i	$-0.326377\pi$
$709$	27.6285	1.03761	0.518804	+	0.854893i	$0.326377\pi$
$710$	−5.04318	−0.189267
$711$	−12.5188	−0.469491
$712$	35.1983	1.31911
$713$	12.9264	0.484096
$714$	0.565950	0.0211802
$715$	1.02325	0.0382675
$716$	−5.68098	−0.212308
$717$	27.9430	1.04355
$718$	11.2733	0.420714
$719$	−7.27649	−0.271367	−0.135684	−	0.990752i	$-0.543323\pi$
$719$	−7.27649	−0.271367	−0.135684	+	0.990752i	$0.543323\pi$
$720$	−12.7137	−0.473812
$721$	−1.61888	−0.0602904
$722$	23.6897	0.881639
$723$	10.9444	0.407025
$724$	−6.71821	−0.249680
$725$	19.5490	0.726032
$726$	−17.5086	−0.649803
$727$	−2.06235	−0.0764882	−0.0382441	−	0.999268i	$-0.512176\pi$
$727$	−2.06235	−0.0764882	−0.0382441	+	0.999268i	$0.512176\pi$
$728$	3.05226	0.113124
$729$	1.00000	0.0370370
$730$	−18.9596	−0.701727
$731$	−2.65809	−0.0983130
$732$	5.22730	0.193207
$733$	4.03521	0.149044	0.0745218	−	0.997219i	$-0.476257\pi$
$733$	4.03521	0.149044	0.0745218	+	0.997219i	$0.476257\pi$
$734$	31.5125	1.16315
$735$	18.2560	0.673383
$736$	−6.42499	−0.236828
$737$	−0.529267	−0.0194958
$738$	15.0008	0.552189
$739$	45.9886	1.69172	0.845858	−	0.533408i	$-0.179089\pi$
$739$	45.9886	1.69172	0.845858	+	0.533408i	$0.179089\pi$
$740$	−11.6313	−0.427575
$741$	7.50048	0.275537
$742$	3.32545	0.122081
$743$	−5.76065	−0.211338	−0.105669	−	0.994401i	$-0.533698\pi$
$743$	−5.76065	−0.211338	−0.105669	+	0.994401i	$0.533698\pi$
$744$	13.9132	0.510083
$745$	41.1374	1.50716
$746$	15.1232	0.553698
$747$	3.28221	0.120090
$748$	0.0562231	0.00205572
$749$	−4.37752	−0.159951
$750$	−12.4675	−0.455248
$751$	−32.5254	−1.18687	−0.593435	−	0.804882i	$-0.702229\pi$
$751$	−32.5254	−1.18687	−0.593435	+	0.804882i	$0.702229\pi$
$752$	7.95491	0.290086
$753$	−7.54827	−0.275074
$754$	55.9664	2.03817
$755$	42.0557	1.53057
$756$	0.191281	0.00695683
$757$	34.7617	1.26344	0.631718	−	0.775199i	$-0.282350\pi$
$757$	34.7617	1.26344	0.631718	+	0.775199i	$0.282350\pi$
$758$	−32.2305	−1.17067
$759$	−0.225876	−0.00819877
$760$	12.5702	0.455969
$761$	−38.3113	−1.38878	−0.694392	−	0.719597i	$-0.744327\pi$
$761$	−38.3113	−1.38878	−0.694392	+	0.719597i	$0.744327\pi$
$762$	−29.1442	−1.05578
$763$	−6.47816	−0.234525
$764$	−7.02889	−0.254296
$765$	−2.65587	−0.0960233
$766$	−42.1635	−1.52343
$767$	−21.8776	−0.789956
$768$	−12.0711	−0.435577
$769$	15.5751	0.561653	0.280826	−	0.959759i	$-0.409391\pi$
$769$	15.5751	0.561653	0.280826	+	0.959759i	$0.409391\pi$
$770$	−0.156934	−0.00565552
$771$	−7.53436	−0.271343
$772$	13.4716	0.484855
$773$	−38.7783	−1.39476	−0.697379	−	0.716702i	$-0.745651\pi$
$773$	−38.7783	−1.39476	−0.697379	+	0.716702i	$0.745651\pi$
$774$	−4.23504	−0.152225
$775$	−12.2706	−0.440775
$776$	26.8715	0.964631
$777$	−2.88888	−0.103638
$778$	8.67505	0.311016
$779$	−19.1370	−0.685654
$780$	5.27755	0.188967
$781$	−0.124435	−0.00445263
$782$	−3.44687	−0.123260
$783$	−9.51910	−0.340185
$784$	32.9051	1.17518
$785$	2.65587	0.0947922
$786$	22.0432	0.786256
$787$	12.7742	0.455352	0.227676	−	0.973737i	$-0.426887\pi$
$787$	12.7742	0.455352	0.227676	+	0.973737i	$0.426887\pi$
$788$	−8.98816	−0.320190
$789$	20.1581	0.717647
$790$	52.9734	1.88471
$791$	−1.57394	−0.0559629
$792$	−0.243120	−0.00863890
$793$	35.8211	1.27204
$794$	−33.4449	−1.18692
$795$	−15.6055	−0.553471
$796$	0.787196	0.0279014
$797$	53.8997	1.90922	0.954612	−	0.297852i	$-0.0962702\pi$
$797$	53.8997	1.90922	0.954612	+	0.297852i	$0.0962702\pi$
$798$	−1.15034	−0.0407215
$799$	1.66177	0.0587892
$800$	6.09907	0.215635
$801$	15.1159	0.534092
$802$	−23.6797	−0.836159
$803$	−0.467807	−0.0165086
$804$	−2.72976	−0.0962712
$805$	2.04096	0.0719344
$806$	−35.1293	−1.23738
$807$	0.387096	0.0136264
$808$	−8.15531	−0.286903
$809$	9.14749	0.321609	0.160804	−	0.986986i	$-0.448591\pi$
$809$	9.14749	0.321609	0.160804	+	0.986986i	$0.448591\pi$
$810$	−4.23151	−0.148680
$811$	7.50693	0.263604	0.131802	−	0.991276i	$-0.457924\pi$
$811$	7.50693	0.263604	0.131802	+	0.991276i	$0.457924\pi$
$812$	−1.82082	−0.0638984
$813$	23.1590	0.812222
$814$	−1.35288	−0.0474185
$815$	34.0757	1.19362
$816$	−4.78701	−0.167579
$817$	5.40276	0.189019
$818$	−42.7241	−1.49381
$819$	1.31079	0.0458027
$820$	−13.4653	−0.470230
$821$	13.9630	0.487314	0.243657	−	0.969862i	$-0.421653\pi$
$821$	13.9630	0.487314	0.243657	+	0.969862i	$0.421653\pi$
$822$	19.9160	0.694651
$823$	2.05120	0.0715002	0.0357501	−	0.999361i	$-0.488618\pi$
$823$	2.05120	0.0715002	0.0357501	+	0.999361i	$0.488618\pi$
$824$	10.6124	0.369700
$825$	0.214418	0.00746507
$826$	3.35534	0.116747
$827$	7.60483	0.264446	0.132223	−	0.991220i	$-0.457789\pi$
$827$	7.60483	0.264446	0.132223	+	0.991220i	$0.457789\pi$
$828$	−1.16498	−0.0404859
$829$	6.59340	0.228998	0.114499	−	0.993423i	$-0.463474\pi$
$829$	6.59340	0.228998	0.114499	+	0.993423i	$0.463474\pi$
$830$	−13.8887	−0.482084
$831$	−26.1154	−0.905934
$832$	−17.8686	−0.619483
$833$	6.87382	0.238164
$834$	18.6761	0.646701
$835$	18.7642	0.649364
$836$	−0.114278	−0.00395237
$837$	5.97501	0.206527
$838$	39.9711	1.38078
$839$	−19.8431	−0.685061	−0.342531	−	0.939507i	$-0.611284\pi$
$839$	−19.8431	−0.685061	−0.342531	+	0.939507i	$0.611284\pi$
$840$	2.19678	0.0757960
$841$	61.6133	2.12460
$842$	−40.5086	−1.39602
$843$	19.1380	0.659149
$844$	1.13035	0.0389083
$845$	1.63903	0.0563844
$846$	2.64764	0.0910277
$847$	3.90348	0.134125
$848$	−28.1278	−0.965913
$849$	6.91362	0.237275
$850$	3.27203	0.112230
$851$	17.5945	0.603131
$852$	−0.641788	−0.0219873
$853$	51.3594	1.75851	0.879255	−	0.476350i	$-0.158041\pi$
$853$	51.3594	1.75851	0.879255	+	0.476350i	$0.158041\pi$
$854$	−5.49381	−0.187994
$855$	5.39826	0.184616
$856$	28.6963	0.980819
$857$	−43.0240	−1.46967	−0.734835	−	0.678245i	$-0.762741\pi$
$857$	−43.0240	−1.46967	−0.734835	+	0.678245i	$0.762741\pi$
$858$	0.613852	0.0209566
$859$	−31.8754	−1.08757	−0.543787	−	0.839223i	$-0.683010\pi$
$859$	−31.8754	−1.08757	−0.543787	+	0.839223i	$0.683010\pi$
$860$	3.80153	0.129631
$861$	−3.34440	−0.113977
$862$	54.4660	1.85512
$863$	30.2871	1.03099	0.515493	−	0.856894i	$-0.327609\pi$
$863$	30.2871	1.03099	0.515493	+	0.856894i	$0.327609\pi$
$864$	−2.96985	−0.101036
$865$	33.8079	1.14950
$866$	−48.1437	−1.63599
$867$	−1.00000	−0.0339618
$868$	1.14291	0.0387928
$869$	1.30706	0.0443389
$870$	40.2802	1.36563
$871$	−18.7062	−0.633835
$872$	42.4668	1.43811
$873$	11.5399	0.390568
$874$	7.00603	0.236982
$875$	2.77959	0.0939672
$876$	−2.41277	−0.0815200
$877$	38.9184	1.31418	0.657090	−	0.753812i	$-0.271787\pi$
$877$	38.9184	1.31418	0.657090	+	0.753812i	$0.271787\pi$
$878$	44.3275	1.49598
$879$	12.1362	0.409344
$880$	1.32741	0.0447469
$881$	−33.5085	−1.12893	−0.564465	−	0.825457i	$-0.690918\pi$
$881$	−33.5085	−1.12893	−0.564465	+	0.825457i	$0.690918\pi$
$882$	10.9518	0.368767
$883$	50.6620	1.70491	0.852456	−	0.522798i	$-0.175112\pi$
$883$	50.6620	1.70491	0.852456	+	0.522798i	$0.175112\pi$
$884$	1.98712	0.0668342
$885$	−15.7458	−0.529289
$886$	−36.7753	−1.23549
$887$	−29.3265	−0.984688	−0.492344	−	0.870401i	$-0.663860\pi$
$887$	−29.3265	−0.984688	−0.492344	+	0.870401i	$0.663860\pi$
$888$	18.9377	0.635508
$889$	6.49762	0.217923
$890$	−63.9629	−2.14404
$891$	−0.104408	−0.00349779
$892$	−5.96642	−0.199771
$893$	−3.37767	−0.113029
$894$	24.6785	0.825371
$895$	−28.0188	−0.936564
$896$	4.85035	0.162039
$897$	−7.98326	−0.266553
$898$	−59.4804	−1.98489
$899$	−56.8767	−1.89695
$900$	1.10589	0.0368629
$901$	−5.87586	−0.195753
$902$	−1.56620	−0.0521489
$903$	0.944191	0.0314207
$904$	10.3178	0.343164
$905$	−33.1344	−1.10142
$906$	25.2294	0.838189
$907$	46.0355	1.52858	0.764292	−	0.644870i	$-0.223089\pi$
$907$	46.0355	1.52858	0.764292	+	0.644870i	$0.223089\pi$
$908$	−0.318307	−0.0105634
$909$	−3.50229	−0.116164
$910$	−5.54662	−0.183869
$911$	47.0073	1.55742	0.778711	−	0.627382i	$-0.215874\pi$
$911$	47.0073	1.55742	0.778711	+	0.627382i	$0.215874\pi$
$912$	9.72996	0.322191
$913$	−0.342688	−0.0113413
$914$	−31.9258	−1.05601
$915$	25.7812	0.852300
$916$	5.27505	0.174292
$917$	−4.91448	−0.162290
$918$	−1.59327	−0.0525856
$919$	−0.568737	−0.0187609	−0.00938046	−	0.999956i	$-0.502986\pi$
$919$	−0.568737	−0.0187609	−0.00938046	+	0.999956i	$0.502986\pi$
$920$	−13.3793	−0.441102
$921$	−23.3307	−0.768773
$922$	14.3926	0.473994
$923$	−4.39797	−0.144761
$924$	−0.0199712	−0.000657005 0
$925$	−16.7020	−0.549158
$926$	24.7823	0.814397
$927$	4.55748	0.149687
$928$	28.2703	0.928019
$929$	37.8114	1.24055	0.620275	−	0.784384i	$-0.287021\pi$
$929$	37.8114	1.24055	0.620275	+	0.784384i	$0.287021\pi$
$930$	−25.2833	−0.829073
$931$	−13.9716	−0.457899
$932$	9.06356	0.296887
$933$	−5.25623	−0.172081
$934$	−8.28609	−0.271129
$935$	0.277294	0.00906847
$936$	−8.59273	−0.280862
$937$	−34.1051	−1.11416	−0.557082	−	0.830457i	$-0.688079\pi$
$937$	−34.1051	−1.11416	−0.557082	+	0.830457i	$0.688079\pi$
$938$	2.86894	0.0936741
$939$	5.36949	0.175227
$940$	−2.37662	−0.0775168
$941$	−2.14614	−0.0699620	−0.0349810	−	0.999388i	$-0.511137\pi$
$941$	−2.14614	−0.0699620	−0.0349810	+	0.999388i	$0.511137\pi$
$942$	1.59327	0.0519114
$943$	20.3688	0.663299
$944$	−28.3806	−0.923711
$945$	0.943404	0.0306889
$946$	0.442171	0.0143762
$947$	−32.5580	−1.05799	−0.528997	−	0.848624i	$-0.677432\pi$
$947$	−32.5580	−1.05799	−0.528997	+	0.848624i	$0.677432\pi$
$948$	6.74131	0.218947
$949$	−16.5340	−0.536715
$950$	−6.65063	−0.215775
$951$	−12.2782	−0.398147
$952$	0.827139	0.0268077
$953$	31.8899	1.03301	0.516507	−	0.856283i	$-0.327232\pi$
$953$	31.8899	1.03301	0.516507	+	0.856283i	$0.327232\pi$
$954$	−9.36181	−0.303100
$955$	−34.6667	−1.12179
$956$	−15.0472	−0.486660
$957$	0.993867	0.0321272
$958$	−35.6394	−1.15146
$959$	−4.44022	−0.143382
$960$	−12.8604	−0.415069
$961$	4.70076	0.151637
$962$	−47.8157	−1.54164
$963$	12.3236	0.397122
$964$	−5.89348	−0.189816
$965$	66.4425	2.13886
$966$	1.22438	0.0393937
$967$	−22.1755	−0.713117	−0.356558	−	0.934273i	$-0.616050\pi$
$967$	−22.1755	−0.713117	−0.356558	+	0.934273i	$0.616050\pi$
$968$	−25.5888	−0.822456
$969$	2.03257	0.0652957
$970$	−48.8314	−1.56788
$971$	43.2815	1.38897	0.694485	−	0.719507i	$-0.255632\pi$
$971$	43.2815	1.38897	0.694485	+	0.719507i	$0.255632\pi$
$972$	−0.538495	−0.0172722
$973$	−4.16379	−0.133485
$974$	17.9998	0.576752
$975$	7.57829	0.242700
$976$	46.4687	1.48743
$977$	11.1280	0.356015	0.178008	−	0.984029i	$-0.443035\pi$
$977$	11.1280	0.356015	0.178008	+	0.984029i	$0.443035\pi$
$978$	20.4421	0.653666
$979$	−1.57821	−0.0504399
$980$	−9.83077	−0.314032
$981$	18.2373	0.582274
$982$	−67.8278	−2.16447
$983$	44.6307	1.42350	0.711749	−	0.702434i	$-0.247903\pi$
$983$	44.6307	1.42350	0.711749	+	0.702434i	$0.247903\pi$
$984$	21.9238	0.698905
$985$	−44.3298	−1.41247
$986$	15.1665	0.482998
$987$	−0.590284	−0.0187889
$988$	−4.03897	−0.128497
$989$	−5.75052	−0.182856
$990$	0.441802	0.0140414
$991$	−25.1952	−0.800352	−0.400176	−	0.916438i	$-0.631051\pi$
$991$	−25.1952	−0.800352	−0.400176	+	0.916438i	$0.631051\pi$
$992$	−17.7449	−0.563402
$993$	−1.98195	−0.0628952
$994$	0.674509	0.0213941
$995$	3.88247	0.123083
$996$	−1.76745	−0.0560039
$997$	15.0592	0.476928	0.238464	−	0.971151i	$-0.423356\pi$
$997$	15.0592	0.476928	0.238464	+	0.971151i	$0.423356\pi$
$998$	19.9427	0.631275
$999$	8.13278	0.257310

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.g.1.15	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.g.1.15	✓	56	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)

\(f(q)\)	\(=\)	\(q-1.59327 q^{2} -1.00000 q^{3} +0.538495 q^{4} +2.65587 q^{5} +1.59327 q^{6} -0.355214 q^{7} +2.32857 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.59327 q^{2} -1.00000 q^{3} +0.538495 q^{4} +2.65587 q^{5} +1.59327 q^{6} -0.355214 q^{7} +2.32857 q^{8} +1.00000 q^{9} -4.23151 q^{10} -0.104408 q^{11} -0.538495 q^{12} -3.69014 q^{13} +0.565950 q^{14} -2.65587 q^{15} -4.78701 q^{16} -1.00000 q^{17} -1.59327 q^{18} +2.03257 q^{19} +1.43018 q^{20} +0.355214 q^{21} +0.166349 q^{22} -2.16340 q^{23} -2.32857 q^{24} +2.05366 q^{25} +5.87937 q^{26} -1.00000 q^{27} -0.191281 q^{28} +9.51910 q^{29} +4.23151 q^{30} -5.97501 q^{31} +2.96985 q^{32} +0.104408 q^{33} +1.59327 q^{34} -0.943404 q^{35} +0.538495 q^{36} -8.13278 q^{37} -3.23843 q^{38} +3.69014 q^{39} +6.18437 q^{40} -9.41516 q^{41} -0.565950 q^{42} +2.65809 q^{43} -0.0562231 q^{44} +2.65587 q^{45} +3.44687 q^{46} -1.66177 q^{47} +4.78701 q^{48} -6.87382 q^{49} -3.27203 q^{50} +1.00000 q^{51} -1.98712 q^{52} +5.87586 q^{53} +1.59327 q^{54} -0.277294 q^{55} -0.827139 q^{56} -2.03257 q^{57} -15.1665 q^{58} +5.92867 q^{59} -1.43018 q^{60} -9.70724 q^{61} +9.51978 q^{62} -0.355214 q^{63} +4.84226 q^{64} -9.80054 q^{65} -0.166349 q^{66} +5.06924 q^{67} -0.538495 q^{68} +2.16340 q^{69} +1.50309 q^{70} +1.19182 q^{71} +2.32857 q^{72} +4.48058 q^{73} +12.9577 q^{74} -2.05366 q^{75} +1.09453 q^{76} +0.0370871 q^{77} -5.87937 q^{78} -12.5188 q^{79} -12.7137 q^{80} +1.00000 q^{81} +15.0008 q^{82} +3.28221 q^{83} +0.191281 q^{84} -2.65587 q^{85} -4.23504 q^{86} -9.51910 q^{87} -0.243120 q^{88} +15.1159 q^{89} -4.23151 q^{90} +1.31079 q^{91} -1.16498 q^{92} +5.97501 q^{93} +2.64764 q^{94} +5.39826 q^{95} -2.96985 q^{96} +11.5399 q^{97} +10.9518 q^{98} -0.104408 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more