LMFDB - Embedded newform 8007.2.a.j.1.47

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:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.47
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)

$f(q)$	$=$	$q+1.68622 q^{2} -1.00000 q^{3} +0.843334 q^{4} -2.71798 q^{5} -1.68622 q^{6} +3.64020 q^{7} -1.95039 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.68622 q^{2} -1.00000 q^{3} +0.843334 q^{4} -2.71798 q^{5} -1.68622 q^{6} +3.64020 q^{7} -1.95039 q^{8} +1.00000 q^{9} -4.58311 q^{10} +2.80504 q^{11} -0.843334 q^{12} -2.41743 q^{13} +6.13818 q^{14} +2.71798 q^{15} -4.97546 q^{16} +1.00000 q^{17} +1.68622 q^{18} -3.85802 q^{19} -2.29216 q^{20} -3.64020 q^{21} +4.72991 q^{22} +5.53727 q^{23} +1.95039 q^{24} +2.38741 q^{25} -4.07632 q^{26} -1.00000 q^{27} +3.06991 q^{28} +1.55802 q^{29} +4.58311 q^{30} -1.77708 q^{31} -4.48892 q^{32} -2.80504 q^{33} +1.68622 q^{34} -9.89400 q^{35} +0.843334 q^{36} +10.3847 q^{37} -6.50546 q^{38} +2.41743 q^{39} +5.30112 q^{40} +1.14782 q^{41} -6.13818 q^{42} -10.9469 q^{43} +2.36558 q^{44} -2.71798 q^{45} +9.33705 q^{46} -12.1594 q^{47} +4.97546 q^{48} +6.25108 q^{49} +4.02570 q^{50} -1.00000 q^{51} -2.03870 q^{52} +2.39403 q^{53} -1.68622 q^{54} -7.62403 q^{55} -7.09982 q^{56} +3.85802 q^{57} +2.62716 q^{58} -0.448557 q^{59} +2.29216 q^{60} +11.5994 q^{61} -2.99655 q^{62} +3.64020 q^{63} +2.38160 q^{64} +6.57053 q^{65} -4.72991 q^{66} -0.902100 q^{67} +0.843334 q^{68} -5.53727 q^{69} -16.6834 q^{70} +14.6733 q^{71} -1.95039 q^{72} +4.66289 q^{73} +17.5108 q^{74} -2.38741 q^{75} -3.25360 q^{76} +10.2109 q^{77} +4.07632 q^{78} +12.4394 q^{79} +13.5232 q^{80} +1.00000 q^{81} +1.93548 q^{82} -10.2940 q^{83} -3.06991 q^{84} -2.71798 q^{85} -18.4589 q^{86} -1.55802 q^{87} -5.47092 q^{88} +0.506212 q^{89} -4.58311 q^{90} -8.79994 q^{91} +4.66977 q^{92} +1.77708 q^{93} -20.5034 q^{94} +10.4860 q^{95} +4.48892 q^{96} +2.42087 q^{97} +10.5407 q^{98} +2.80504 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * 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 $

$2$	1.68622	1.19234	0.596168	−	0.802859i	$-0.296689\pi$
$2$	1.68622	1.19234	0.596168	+	0.802859i	$0.296689\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.843334	0.421667
$5$	−2.71798	−1.21552	−0.607759	−	0.794122i	$-0.707931\pi$
$5$	−2.71798	−1.21552	−0.607759	+	0.794122i	$0.707931\pi$
$6$	−1.68622	−0.688396
$7$	3.64020	1.37587	0.687934	−	0.725773i	$-0.258518\pi$
$7$	3.64020	1.37587	0.687934	+	0.725773i	$0.258518\pi$
$8$	−1.95039	−0.689568
$9$	1.00000	0.333333
$10$	−4.58311	−1.44931
$11$	2.80504	0.845751	0.422875	−	0.906188i	$-0.361021\pi$
$11$	2.80504	0.845751	0.422875	+	0.906188i	$0.361021\pi$
$12$	−0.843334	−0.243450
$13$	−2.41743	−0.670475	−0.335237	−	0.942134i	$-0.608816\pi$
$13$	−2.41743	−0.670475	−0.335237	+	0.942134i	$0.608816\pi$
$14$	6.13818	1.64050
$15$	2.71798	0.701779
$16$	−4.97546	−1.24386
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.68622	0.397446
$19$	−3.85802	−0.885090	−0.442545	−	0.896746i	$-0.645924\pi$
$19$	−3.85802	−0.885090	−0.442545	+	0.896746i	$0.645924\pi$
$20$	−2.29216	−0.512543
$21$	−3.64020	−0.794358
$22$	4.72991	1.00842
$23$	5.53727	1.15460	0.577300	−	0.816532i	$-0.304106\pi$
$23$	5.53727	1.15460	0.577300	+	0.816532i	$0.304106\pi$
$24$	1.95039	0.398122
$25$	2.38741	0.477482
$26$	−4.07632	−0.799431
$27$	−1.00000	−0.192450
$28$	3.06991	0.580158
$29$	1.55802	0.289316	0.144658	−	0.989482i	$-0.453792\pi$
$29$	1.55802	0.289316	0.144658	+	0.989482i	$0.453792\pi$
$30$	4.58311	0.836757
$31$	−1.77708	−0.319173	−0.159587	−	0.987184i	$-0.551016\pi$
$31$	−1.77708	−0.319173	−0.159587	+	0.987184i	$0.551016\pi$
$32$	−4.48892	−0.793537
$33$	−2.80504	−0.488294
$34$	1.68622	0.289184
$35$	−9.89400	−1.67239
$36$	0.843334	0.140556
$37$	10.3847	1.70723	0.853616	−	0.520903i	$-0.174405\pi$
$37$	10.3847	1.70723	0.853616	+	0.520903i	$0.174405\pi$
$38$	−6.50546	−1.05532
$39$	2.41743	0.387099
$40$	5.30112	0.838181
$41$	1.14782	0.179260	0.0896298	−	0.995975i	$-0.471432\pi$
$41$	1.14782	0.179260	0.0896298	+	0.995975i	$0.471432\pi$
$42$	−6.13818	−0.947142
$43$	−10.9469	−1.66939	−0.834693	−	0.550715i	$-0.814355\pi$
$43$	−10.9469	−1.66939	−0.834693	+	0.550715i	$0.814355\pi$
$44$	2.36558	0.356625
$45$	−2.71798	−0.405172
$46$	9.33705	1.37667
$47$	−12.1594	−1.77363	−0.886817	−	0.462121i	$-0.847089\pi$
$47$	−12.1594	−1.77363	−0.886817	+	0.462121i	$0.847089\pi$
$48$	4.97546	0.718145
$49$	6.25108	0.893012
$50$	4.02570	0.569319
$51$	−1.00000	−0.140028
$52$	−2.03870	−0.282717
$53$	2.39403	0.328845	0.164423	−	0.986390i	$-0.447424\pi$
$53$	2.39403	0.328845	0.164423	+	0.986390i	$0.447424\pi$
$54$	−1.68622	−0.229465
$55$	−7.62403	−1.02802
$56$	−7.09982	−0.948754
$57$	3.85802	0.511007
$58$	2.62716	0.344962
$59$	−0.448557	−0.0583971	−0.0291985	−	0.999574i	$-0.509296\pi$
$59$	−0.448557	−0.0583971	−0.0291985	+	0.999574i	$0.509296\pi$
$60$	2.29216	0.295917
$61$	11.5994	1.48516	0.742578	−	0.669760i	$-0.233603\pi$
$61$	11.5994	1.48516	0.742578	+	0.669760i	$0.233603\pi$
$62$	−2.99655	−0.380562
$63$	3.64020	0.458623
$64$	2.38160	0.297701
$65$	6.57053	0.814973
$66$	−4.72991	−0.582211
$67$	−0.902100	−0.110209	−0.0551045	−	0.998481i	$-0.517549\pi$
$67$	−0.902100	−0.110209	−0.0551045	+	0.998481i	$0.517549\pi$
$68$	0.843334	0.102269
$69$	−5.53727	−0.666609
$70$	−16.6834	−1.99405
$71$	14.6733	1.74140	0.870701	−	0.491812i	$-0.163665\pi$
$71$	14.6733	1.74140	0.870701	+	0.491812i	$0.163665\pi$
$72$	−1.95039	−0.229856
$73$	4.66289	0.545750	0.272875	−	0.962049i	$-0.412025\pi$
$73$	4.66289	0.545750	0.272875	+	0.962049i	$0.412025\pi$
$74$	17.5108	2.03559
$75$	−2.38741	−0.275674
$76$	−3.25360	−0.373213
$77$	10.2109	1.16364
$78$	4.07632	0.461552
$79$	12.4394	1.39954	0.699771	−	0.714367i	$-0.253285\pi$
$79$	12.4394	1.39954	0.699771	+	0.714367i	$0.253285\pi$
$80$	13.5232	1.51194
$81$	1.00000	0.111111
$82$	1.93548	0.213738
$83$	−10.2940	−1.12992	−0.564958	−	0.825120i	$-0.691108\pi$
$83$	−10.2940	−1.12992	−0.564958	+	0.825120i	$0.691108\pi$
$84$	−3.06991	−0.334954
$85$	−2.71798	−0.294806
$86$	−18.4589	−1.99047
$87$	−1.55802	−0.167037
$88$	−5.47092	−0.583202
$89$	0.506212	0.0536584	0.0268292	−	0.999640i	$-0.491459\pi$
$89$	0.506212	0.0536584	0.0268292	+	0.999640i	$0.491459\pi$
$90$	−4.58311	−0.483102
$91$	−8.79994	−0.922484
$92$	4.66977	0.486857
$93$	1.77708	0.184275
$94$	−20.5034	−2.11477
$95$	10.4860	1.07584
$96$	4.48892	0.458149
$97$	2.42087	0.245802	0.122901	−	0.992419i	$-0.460780\pi$
$97$	2.42087	0.245802	0.122901	+	0.992419i	$0.460780\pi$
$98$	10.5407	1.06477
$99$	2.80504	0.281917
$100$	2.01338	0.201338
$101$	−4.26142	−0.424027	−0.212014	−	0.977267i	$-0.568002\pi$
$101$	−4.26142	−0.424027	−0.212014	+	0.977267i	$0.568002\pi$
$102$	−1.68622	−0.166961
$103$	7.62497	0.751311	0.375656	−	0.926759i	$-0.377418\pi$
$103$	7.62497	0.751311	0.375656	+	0.926759i	$0.377418\pi$
$104$	4.71494	0.462338
$105$	9.89400	0.965555
$106$	4.03686	0.392094
$107$	−7.95273	−0.768820	−0.384410	−	0.923163i	$-0.625595\pi$
$107$	−7.95273	−0.768820	−0.384410	+	0.923163i	$0.625595\pi$
$108$	−0.843334	−0.0811498
$109$	−4.28218	−0.410158	−0.205079	−	0.978745i	$-0.565745\pi$
$109$	−4.28218	−0.410158	−0.205079	+	0.978745i	$0.565745\pi$
$110$	−12.8558	−1.22575
$111$	−10.3847	−0.985670
$112$	−18.1117	−1.71139
$113$	−17.2560	−1.62331	−0.811655	−	0.584138i	$-0.801433\pi$
$113$	−17.2560	−1.62331	−0.811655	+	0.584138i	$0.801433\pi$
$114$	6.50546	0.609292
$115$	−15.0502	−1.40344
$116$	1.31393	0.121995
$117$	−2.41743	−0.223492
$118$	−0.756365	−0.0696290
$119$	3.64020	0.333697
$120$	−5.30112	−0.483924
$121$	−3.13176	−0.284706
$122$	19.5592	1.77081
$123$	−1.14782	−0.103496
$124$	−1.49867	−0.134585
$125$	7.10096	0.635130
$126$	6.13818	0.546833
$127$	7.61721	0.675918	0.337959	−	0.941161i	$-0.390263\pi$
$127$	7.61721	0.675918	0.337959	+	0.941161i	$0.390263\pi$
$128$	12.9938	1.14850
$129$	10.9469	0.963821
$130$	11.0793	0.971723
$131$	−20.8091	−1.81810	−0.909050	−	0.416688i	$-0.863191\pi$
$131$	−20.8091	−1.81810	−0.909050	+	0.416688i	$0.863191\pi$
$132$	−2.36558	−0.205898
$133$	−14.0440	−1.21777
$134$	−1.52114	−0.131406
$135$	2.71798	0.233926
$136$	−1.95039	−0.167245
$137$	13.6755	1.16838	0.584188	−	0.811619i	$-0.301413\pi$
$137$	13.6755	1.16838	0.584188	+	0.811619i	$0.301413\pi$
$138$	−9.33705	−0.794822
$139$	−18.9758	−1.60950	−0.804752	−	0.593611i	$-0.797702\pi$
$139$	−18.9758	−1.60950	−0.804752	+	0.593611i	$0.797702\pi$
$140$	−8.34394	−0.705192
$141$	12.1594	1.02401
$142$	24.7424	2.07634
$143$	−6.78098	−0.567054
$144$	−4.97546	−0.414621
$145$	−4.23465	−0.351669
$146$	7.86266	0.650718
$147$	−6.25108	−0.515580
$148$	8.75776	0.719883
$149$	22.5544	1.84773	0.923863	−	0.382724i	$-0.125014\pi$
$149$	22.5544	1.84773	0.923863	+	0.382724i	$0.125014\pi$
$150$	−4.02570	−0.328697
$151$	20.4170	1.66151	0.830754	−	0.556639i	$-0.187909\pi$
$151$	20.4170	1.66151	0.830754	+	0.556639i	$0.187909\pi$
$152$	7.52464	0.610329
$153$	1.00000	0.0808452
$154$	17.2178	1.38745
$155$	4.83007	0.387960
$156$	2.03870	0.163227
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	20.9756	1.66873
$159$	−2.39403	−0.189859
$160$	12.2008	0.964558
$161$	20.1568	1.58858
$162$	1.68622	0.132482
$163$	11.3203	0.886674	0.443337	−	0.896355i	$-0.353794\pi$
$163$	11.3203	0.886674	0.443337	+	0.896355i	$0.353794\pi$
$164$	0.967997	0.0755878
$165$	7.62403	0.593530
$166$	−17.3580	−1.34724
$167$	19.4190	1.50269	0.751344	−	0.659911i	$-0.229406\pi$
$167$	19.4190	1.50269	0.751344	+	0.659911i	$0.229406\pi$
$168$	7.09982	0.547763
$169$	−7.15603	−0.550464
$170$	−4.58311	−0.351508
$171$	−3.85802	−0.295030
$172$	−9.23189	−0.703925
$173$	15.9028	1.20906	0.604532	−	0.796581i	$-0.293360\pi$
$173$	15.9028	1.20906	0.604532	+	0.796581i	$0.293360\pi$
$174$	−2.62716	−0.199164
$175$	8.69066	0.656952
$176$	−13.9563	−1.05200
$177$	0.448557	0.0337156
$178$	0.853584	0.0639788
$179$	17.2746	1.29117	0.645583	−	0.763690i	$-0.276614\pi$
$179$	17.2746	1.29117	0.645583	+	0.763690i	$0.276614\pi$
$180$	−2.29216	−0.170848
$181$	−6.42031	−0.477218	−0.238609	−	0.971116i	$-0.576691\pi$
$181$	−6.42031	−0.477218	−0.238609	+	0.971116i	$0.576691\pi$
$182$	−14.8386	−1.09991
$183$	−11.5994	−0.857455
$184$	−10.7998	−0.796175
$185$	−28.2253	−2.07517
$186$	2.99655	0.219717
$187$	2.80504	0.205125
$188$	−10.2545	−0.747883
$189$	−3.64020	−0.264786
$190$	17.6817	1.28277
$191$	−2.06166	−0.149177	−0.0745883	−	0.997214i	$-0.523764\pi$
$191$	−2.06166	−0.149177	−0.0745883	+	0.997214i	$0.523764\pi$
$192$	−2.38160	−0.171878
$193$	25.4040	1.82862	0.914310	−	0.405015i	$-0.132734\pi$
$193$	25.4040	1.82862	0.914310	+	0.405015i	$0.132734\pi$
$194$	4.08212	0.293079
$195$	−6.57053	−0.470525
$196$	5.27175	0.376553
$197$	22.5875	1.60929	0.804645	−	0.593756i	$-0.202356\pi$
$197$	22.5875	1.60929	0.804645	+	0.593756i	$0.202356\pi$
$198$	4.72991	0.336140
$199$	5.61963	0.398365	0.199183	−	0.979962i	$-0.436171\pi$
$199$	5.61963	0.398365	0.199183	+	0.979962i	$0.436171\pi$
$200$	−4.65639	−0.329256
$201$	0.902100	0.0636292
$202$	−7.18569	−0.505583
$203$	5.67150	0.398061
$204$	−0.843334	−0.0590452
$205$	−3.11975	−0.217893
$206$	12.8574	0.895816
$207$	5.53727	0.384867
$208$	12.0278	0.833979
$209$	−10.8219	−0.748565
$210$	16.6834	1.15127
$211$	10.0715	0.693354	0.346677	−	0.937985i	$-0.387310\pi$
$211$	10.0715	0.693354	0.346677	+	0.937985i	$0.387310\pi$
$212$	2.01897	0.138663
$213$	−14.6733	−1.00540
$214$	−13.4100	−0.916692
$215$	29.7534	2.02917
$216$	1.95039	0.132707
$217$	−6.46893	−0.439140
$218$	−7.22069	−0.489047
$219$	−4.66289	−0.315089
$220$	−6.42961	−0.433484
$221$	−2.41743	−0.162614
$222$	−17.5108	−1.17525
$223$	17.0600	1.14242	0.571210	−	0.820804i	$-0.306474\pi$
$223$	17.0600	1.14242	0.571210	+	0.820804i	$0.306474\pi$
$224$	−16.3406	−1.09180
$225$	2.38741	0.159161
$226$	−29.0974	−1.93553
$227$	15.7222	1.04352	0.521758	−	0.853093i	$-0.325276\pi$
$227$	15.7222	1.04352	0.521758	+	0.853093i	$0.325276\pi$
$228$	3.25360	0.215475
$229$	25.6359	1.69407	0.847036	−	0.531536i	$-0.178385\pi$
$229$	25.6359	1.69407	0.847036	+	0.531536i	$0.178385\pi$
$230$	−25.3779	−1.67337
$231$	−10.2109	−0.671828
$232$	−3.03874	−0.199503
$233$	−8.96937	−0.587603	−0.293801	−	0.955866i	$-0.594920\pi$
$233$	−8.96937	−0.587603	−0.293801	+	0.955866i	$0.594920\pi$
$234$	−4.07632	−0.266477
$235$	33.0491	2.15588
$236$	−0.378283	−0.0246241
$237$	−12.4394	−0.808027
$238$	6.13818	0.397879
$239$	−11.2297	−0.726388	−0.363194	−	0.931713i	$-0.618314\pi$
$239$	−11.2297	−0.726388	−0.363194	+	0.931713i	$0.618314\pi$
$240$	−13.5232	−0.872918
$241$	6.73975	0.434146	0.217073	−	0.976155i	$-0.430349\pi$
$241$	6.73975	0.434146	0.217073	+	0.976155i	$0.430349\pi$
$242$	−5.28084	−0.339465
$243$	−1.00000	−0.0641500
$244$	9.78220	0.626241
$245$	−16.9903	−1.08547
$246$	−1.93548	−0.123402
$247$	9.32649	0.593430
$248$	3.46600	0.220091
$249$	10.2940	0.652357
$250$	11.9738	0.757288
$251$	3.31380	0.209165	0.104583	−	0.994516i	$-0.466649\pi$
$251$	3.31380	0.209165	0.104583	+	0.994516i	$0.466649\pi$
$252$	3.06991	0.193386
$253$	15.5323	0.976504
$254$	12.8443	0.805922
$255$	2.71798	0.170206
$256$	17.1471	1.07169
$257$	28.7837	1.79548	0.897740	−	0.440526i	$-0.145208\pi$
$257$	28.7837	1.79548	0.897740	+	0.440526i	$0.145208\pi$
$258$	18.4589	1.14920
$259$	37.8024	2.34892
$260$	5.54115	0.343647
$261$	1.55802	0.0964388
$262$	−35.0887	−2.16779
$263$	−4.43623	−0.273550	−0.136775	−	0.990602i	$-0.543674\pi$
$263$	−4.43623	−0.273550	−0.136775	+	0.990602i	$0.543674\pi$
$264$	5.47092	0.336712
$265$	−6.50692	−0.399717
$266$	−23.6812	−1.45199
$267$	−0.506212	−0.0309797
$268$	−0.760772	−0.0464715
$269$	−13.8240	−0.842865	−0.421432	−	0.906860i	$-0.638473\pi$
$269$	−13.8240	−0.842865	−0.421432	+	0.906860i	$0.638473\pi$
$270$	4.58311	0.278919
$271$	−17.1647	−1.04268	−0.521342	−	0.853348i	$-0.674568\pi$
$271$	−17.1647	−1.04268	−0.521342	+	0.853348i	$0.674568\pi$
$272$	−4.97546	−0.301681
$273$	8.79994	0.532597
$274$	23.0599	1.39310
$275$	6.69678	0.403831
$276$	−4.66977	−0.281087
$277$	6.73769	0.404829	0.202414	−	0.979300i	$-0.435121\pi$
$277$	6.73769	0.404829	0.202414	+	0.979300i	$0.435121\pi$
$278$	−31.9973	−1.91907
$279$	−1.77708	−0.106391
$280$	19.2972	1.15323
$281$	1.66153	0.0991185	0.0495592	−	0.998771i	$-0.484218\pi$
$281$	1.66153	0.0991185	0.0495592	+	0.998771i	$0.484218\pi$
$282$	20.5034	1.22096
$283$	22.1726	1.31802	0.659012	−	0.752133i	$-0.270975\pi$
$283$	22.1726	1.31802	0.659012	+	0.752133i	$0.270975\pi$
$284$	12.3745	0.734292
$285$	−10.4860	−0.621137
$286$	−11.4342	−0.676120
$287$	4.17830	0.246637
$288$	−4.48892	−0.264512
$289$	1.00000	0.0588235
$290$	−7.14055	−0.419308
$291$	−2.42087	−0.141914
$292$	3.93238	0.230125
$293$	−8.42905	−0.492430	−0.246215	−	0.969215i	$-0.579187\pi$
$293$	−8.42905	−0.492430	−0.246215	+	0.969215i	$0.579187\pi$
$294$	−10.5407	−0.614746
$295$	1.21917	0.0709827
$296$	−20.2542	−1.17725
$297$	−2.80504	−0.162765
$298$	38.0316	2.20311
$299$	−13.3860	−0.774130
$300$	−2.01338	−0.116243
$301$	−39.8489	−2.29685
$302$	34.4275	1.98108
$303$	4.26142	0.244812
$304$	19.1954	1.10093
$305$	−31.5270	−1.80523
$306$	1.68622	0.0963947
$307$	8.60152	0.490914	0.245457	−	0.969407i	$-0.421062\pi$
$307$	8.60152	0.490914	0.245457	+	0.969407i	$0.421062\pi$
$308$	8.61121	0.490669
$309$	−7.62497	−0.433770
$310$	8.14455	0.462579
$311$	−1.71041	−0.0969884	−0.0484942	−	0.998823i	$-0.515442\pi$
$311$	−1.71041	−0.0969884	−0.0484942	+	0.998823i	$0.515442\pi$
$312$	−4.71494	−0.266931
$313$	2.07049	0.117031	0.0585156	−	0.998286i	$-0.481363\pi$
$313$	2.07049	0.117031	0.0585156	+	0.998286i	$0.481363\pi$
$314$	−1.68622	−0.0951588
$315$	−9.89400	−0.557464
$316$	10.4906	0.590141
$317$	−1.77085	−0.0994606	−0.0497303	−	0.998763i	$-0.515836\pi$
$317$	−1.77085	−0.0994606	−0.0497303	+	0.998763i	$0.515836\pi$
$318$	−4.03686	−0.226376
$319$	4.37029	0.244689
$320$	−6.47315	−0.361860
$321$	7.95273	0.443878
$322$	33.9888	1.89412
$323$	−3.85802	−0.214666
$324$	0.843334	0.0468519
$325$	−5.77140	−0.320140
$326$	19.0885	1.05721
$327$	4.28218	0.236805
$328$	−2.23870	−0.123612
$329$	−44.2628	−2.44029
$330$	12.8558	0.707688
$331$	−12.7886	−0.702926	−0.351463	−	0.936202i	$-0.614316\pi$
$331$	−12.7886	−0.702926	−0.351463	+	0.936202i	$0.614316\pi$
$332$	−8.68130	−0.476448
$333$	10.3847	0.569077
$334$	32.7447	1.79171
$335$	2.45189	0.133961
$336$	18.1117	0.988073
$337$	0.946426	0.0515551	0.0257776	−	0.999668i	$-0.491794\pi$
$337$	0.946426	0.0515551	0.0257776	+	0.999668i	$0.491794\pi$
$338$	−12.0666	−0.656338
$339$	17.2560	0.937218
$340$	−2.29216	−0.124310
$341$	−4.98478	−0.269941
$342$	−6.50546	−0.351775
$343$	−2.72622	−0.147202
$344$	21.3507	1.15115
$345$	15.0502	0.810275
$346$	26.8155	1.44161
$347$	−32.0192	−1.71888	−0.859441	−	0.511234i	$-0.829188\pi$
$347$	−32.0192	−1.71888	−0.859441	+	0.511234i	$0.829188\pi$
$348$	−1.31393	−0.0704339
$349$	35.7555	1.91395	0.956973	−	0.290176i	$-0.0937139\pi$
$349$	35.7555	1.91395	0.956973	+	0.290176i	$0.0937139\pi$
$350$	14.6544	0.783308
$351$	2.41743	0.129033
$352$	−12.5916	−0.671134
$353$	−32.8991	−1.75104	−0.875520	−	0.483182i	$-0.839481\pi$
$353$	−32.8991	−1.75104	−0.875520	+	0.483182i	$0.839481\pi$
$354$	0.756365	0.0402003
$355$	−39.8818	−2.11670
$356$	0.426906	0.0226260
$357$	−3.64020	−0.192660
$358$	29.1288	1.53951
$359$	30.3882	1.60383	0.801913	−	0.597441i	$-0.203816\pi$
$359$	30.3882	1.60383	0.801913	+	0.597441i	$0.203816\pi$
$360$	5.30112	0.279394
$361$	−4.11571	−0.216616
$362$	−10.8260	−0.569004
$363$	3.13176	0.164375
$364$	−7.42129	−0.388981
$365$	−12.6736	−0.663369
$366$	−19.5592	−1.02238
$367$	38.0309	1.98520	0.992598	−	0.121445i	$-0.0387529\pi$
$367$	38.0309	1.98520	0.992598	+	0.121445i	$0.0387529\pi$
$368$	−27.5504	−1.43617
$369$	1.14782	0.0597532
$370$	−47.5941	−2.47430
$371$	8.71475	0.452447
$372$	1.49867	0.0777025
$373$	22.3479	1.15713	0.578564	−	0.815637i	$-0.303613\pi$
$373$	22.3479	1.15713	0.578564	+	0.815637i	$0.303613\pi$
$374$	4.72991	0.244578
$375$	−7.10096	−0.366692
$376$	23.7156	1.22304
$377$	−3.76640	−0.193979
$378$	−6.13818	−0.315714
$379$	−2.54092	−0.130518	−0.0652592	−	0.997868i	$-0.520787\pi$
$379$	−2.54092	−0.130518	−0.0652592	+	0.997868i	$0.520787\pi$
$380$	8.84321	0.453647
$381$	−7.61721	−0.390242
$382$	−3.47641	−0.177869
$383$	23.5269	1.20217	0.601085	−	0.799185i	$-0.294735\pi$
$383$	23.5269	1.20217	0.601085	+	0.799185i	$0.294735\pi$
$384$	−12.9938	−0.663085
$385$	−27.7530	−1.41443
$386$	42.8367	2.18033
$387$	−10.9469	−0.556462
$388$	2.04160	0.103647
$389$	3.81693	0.193526	0.0967629	−	0.995307i	$-0.469151\pi$
$389$	3.81693	0.193526	0.0967629	+	0.995307i	$0.469151\pi$
$390$	−11.0793	−0.561024
$391$	5.53727	0.280032
$392$	−12.1921	−0.615792
$393$	20.8091	1.04968
$394$	38.0874	1.91882
$395$	−33.8101	−1.70117
$396$	2.36558	0.118875
$397$	1.45010	0.0727785	0.0363892	−	0.999338i	$-0.488414\pi$
$397$	1.45010	0.0727785	0.0363892	+	0.999338i	$0.488414\pi$
$398$	9.47593	0.474985
$399$	14.0440	0.703078
$400$	−11.8785	−0.593923
$401$	29.5262	1.47447	0.737233	−	0.675639i	$-0.236132\pi$
$401$	29.5262	1.47447	0.737233	+	0.675639i	$0.236132\pi$
$402$	1.52114	0.0758675
$403$	4.29597	0.213997
$404$	−3.59380	−0.178798
$405$	−2.71798	−0.135057
$406$	9.56338	0.474623
$407$	29.1294	1.44389
$408$	1.95039	0.0965588
$409$	13.4596	0.665534	0.332767	−	0.943009i	$-0.392018\pi$
$409$	13.4596	0.665534	0.332767	+	0.943009i	$0.392018\pi$
$410$	−5.26059	−0.259802
$411$	−13.6755	−0.674562
$412$	6.43040	0.316803
$413$	−1.63284	−0.0803467
$414$	9.33705	0.458891
$415$	27.9789	1.37343
$416$	10.8517	0.532046
$417$	18.9758	0.929247
$418$	−18.2481	−0.892542
$419$	−35.6750	−1.74284	−0.871419	−	0.490540i	$-0.836800\pi$
$419$	−35.6750	−1.74284	−0.871419	+	0.490540i	$0.836800\pi$
$420$	8.34394	0.407143
$421$	−28.0917	−1.36910	−0.684552	−	0.728964i	$-0.740002\pi$
$421$	−28.0917	−1.36910	−0.684552	+	0.728964i	$0.740002\pi$
$422$	16.9828	0.826712
$423$	−12.1594	−0.591211
$424$	−4.66929	−0.226761
$425$	2.38741	0.115806
$426$	−24.7424	−1.19877
$427$	42.2243	2.04338
$428$	−6.70681	−0.324186
$429$	6.78098	0.327389
$430$	50.1708	2.41945
$431$	−6.01062	−0.289521	−0.144761	−	0.989467i	$-0.546241\pi$
$431$	−6.01062	−0.289521	−0.144761	+	0.989467i	$0.546241\pi$
$432$	4.97546	0.239382
$433$	−12.3410	−0.593068	−0.296534	−	0.955022i	$-0.595831\pi$
$433$	−12.3410	−0.593068	−0.296534	+	0.955022i	$0.595831\pi$
$434$	−10.9080	−0.523603
$435$	4.23465	0.203036
$436$	−3.61131	−0.172950
$437$	−21.3629	−1.02192
$438$	−7.86266	−0.375692
$439$	11.2952	0.539092	0.269546	−	0.962987i	$-0.413126\pi$
$439$	11.2952	0.539092	0.269546	+	0.962987i	$0.413126\pi$
$440$	14.8699	0.708893
$441$	6.25108	0.297671
$442$	−4.07632	−0.193891
$443$	−16.5088	−0.784357	−0.392179	−	0.919889i	$-0.628278\pi$
$443$	−16.5088	−0.784357	−0.392179	+	0.919889i	$0.628278\pi$
$444$	−8.75776	−0.415625
$445$	−1.37587	−0.0652227
$446$	28.7668	1.36215
$447$	−22.5544	−1.06678
$448$	8.66953	0.409597
$449$	−21.3595	−1.00802	−0.504008	−	0.863699i	$-0.668142\pi$
$449$	−21.3595	−1.00802	−0.504008	+	0.863699i	$0.668142\pi$
$450$	4.02570	0.189773
$451$	3.21968	0.151609
$452$	−14.5526	−0.684496
$453$	−20.4170	−0.959272
$454$	26.5110	1.24422
$455$	23.9180	1.12130
$456$	−7.52464	−0.352374
$457$	−0.790303	−0.0369688	−0.0184844	−	0.999829i	$-0.505884\pi$
$457$	−0.790303	−0.0369688	−0.0184844	+	0.999829i	$0.505884\pi$
$458$	43.2278	2.01990
$459$	−1.00000	−0.0466760
$460$	−12.6923	−0.591783
$461$	5.75729	0.268144	0.134072	−	0.990972i	$-0.457195\pi$
$461$	5.75729	0.268144	0.134072	+	0.990972i	$0.457195\pi$
$462$	−17.2178	−0.801046
$463$	−10.7728	−0.500653	−0.250327	−	0.968161i	$-0.580538\pi$
$463$	−10.7728	−0.500653	−0.250327	+	0.968161i	$0.580538\pi$
$464$	−7.75184	−0.359870
$465$	−4.83007	−0.223989
$466$	−15.1243	−0.700620
$467$	−24.5725	−1.13708	−0.568539	−	0.822656i	$-0.692491\pi$
$467$	−24.5725	−1.13708	−0.568539	+	0.822656i	$0.692491\pi$
$468$	−2.03870	−0.0942390
$469$	−3.28383	−0.151633
$470$	55.7279	2.57054
$471$	1.00000	0.0460776
$472$	0.874861	0.0402687
$473$	−30.7065	−1.41188
$474$	−20.9756	−0.963440
$475$	−9.21067	−0.422614
$476$	3.06991	0.140709
$477$	2.39403	0.109615
$478$	−18.9357	−0.866099
$479$	26.0174	1.18876	0.594382	−	0.804183i	$-0.297397\pi$
$479$	26.0174	1.18876	0.594382	+	0.804183i	$0.297397\pi$
$480$	−12.2008	−0.556888
$481$	−25.1042	−1.14466
$482$	11.3647	0.517648
$483$	−20.1568	−0.917166
$484$	−2.64112	−0.120051
$485$	−6.57987	−0.298777
$486$	−1.68622	−0.0764884
$487$	25.7304	1.16596	0.582978	−	0.812488i	$-0.301888\pi$
$487$	25.7304	1.16596	0.582978	+	0.812488i	$0.301888\pi$
$488$	−22.6235	−1.02412
$489$	−11.3203	−0.511922
$490$	−28.6494	−1.29425
$491$	−36.1578	−1.63178	−0.815890	−	0.578208i	$-0.803752\pi$
$491$	−36.1578	−1.63178	−0.815890	+	0.578208i	$0.803752\pi$
$492$	−0.967997	−0.0436407
$493$	1.55802	0.0701695
$494$	15.7265	0.707568
$495$	−7.62403	−0.342675
$496$	8.84179	0.397008
$497$	53.4139	2.39594
$498$	17.3580	0.777830
$499$	−15.2121	−0.680986	−0.340493	−	0.940247i	$-0.610594\pi$
$499$	−15.2121	−0.680986	−0.340493	+	0.940247i	$0.610594\pi$
$500$	5.98848	0.267813
$501$	−19.4190	−0.867577
$502$	5.58779	0.249395
$503$	−4.64739	−0.207217	−0.103609	−	0.994618i	$-0.533039\pi$
$503$	−4.64739	−0.207217	−0.103609	+	0.994618i	$0.533039\pi$
$504$	−7.09982	−0.316251
$505$	11.5825	0.515412
$506$	26.1908	1.16432
$507$	7.15603	0.317810
$508$	6.42385	0.285012
$509$	−7.42284	−0.329012	−0.164506	−	0.986376i	$-0.552603\pi$
$509$	−7.42284	−0.329012	−0.164506	+	0.986376i	$0.552603\pi$
$510$	4.58311	0.202943
$511$	16.9739	0.750880
$512$	2.92626	0.129324
$513$	3.85802	0.170336
$514$	48.5357	2.14082
$515$	−20.7245	−0.913232
$516$	9.23189	0.406411
$517$	−34.1076	−1.50005
$518$	63.7430	2.80071
$519$	−15.9028	−0.698053
$520$	−12.8151	−0.561979
$521$	29.0513	1.27276	0.636381	−	0.771375i	$-0.280431\pi$
$521$	29.0513	1.27276	0.636381	+	0.771375i	$0.280431\pi$
$522$	2.62716	0.114987
$523$	14.7294	0.644073	0.322037	−	0.946727i	$-0.395633\pi$
$523$	14.7294	0.644073	0.322037	+	0.946727i	$0.395633\pi$
$524$	−17.5490	−0.766633
$525$	−8.69066	−0.379291
$526$	−7.48046	−0.326163
$527$	−1.77708	−0.0774108
$528$	13.9563	0.607372
$529$	7.66136	0.333103
$530$	−10.9721	−0.476597
$531$	−0.448557	−0.0194657
$532$	−11.8438	−0.513492
$533$	−2.77478	−0.120189
$534$	−0.853584	−0.0369382
$535$	21.6154	0.934514
$536$	1.75945	0.0759966
$537$	−17.2746	−0.745455
$538$	−23.3103	−1.00498
$539$	17.5345	0.755265
$540$	2.29216	0.0986390
$541$	−10.9380	−0.470260	−0.235130	−	0.971964i	$-0.575552\pi$
$541$	−10.9380	−0.470260	−0.235130	+	0.971964i	$0.575552\pi$
$542$	−28.9435	−1.24323
$543$	6.42031	0.275522
$544$	−4.48892	−0.192461
$545$	11.6389	0.498554
$546$	14.8386	0.635034
$547$	25.4930	1.09000	0.545000	−	0.838436i	$-0.316530\pi$
$547$	25.4930	1.09000	0.545000	+	0.838436i	$0.316530\pi$
$548$	11.5330	0.492665
$549$	11.5994	0.495052
$550$	11.2922	0.481502
$551$	−6.01085	−0.256071
$552$	10.7998	0.459672
$553$	45.2820	1.92559
$554$	11.3612	0.482692
$555$	28.2253	1.19810
$556$	−16.0029	−0.678675
$557$	−26.0536	−1.10393	−0.551963	−	0.833869i	$-0.686121\pi$
$557$	−26.0536	−1.10393	−0.551963	+	0.833869i	$0.686121\pi$
$558$	−2.99655	−0.126854
$559$	26.4634	1.11928
$560$	49.2271	2.08023
$561$	−2.80504	−0.118429
$562$	2.80170	0.118183
$563$	−36.3951	−1.53387	−0.766935	−	0.641725i	$-0.778219\pi$
$563$	−36.3951	−1.53387	−0.766935	+	0.641725i	$0.778219\pi$
$564$	10.2545	0.431790
$565$	46.9015	1.97316
$566$	37.3878	1.57153
$567$	3.64020	0.152874
$568$	−28.6187	−1.20081
$569$	2.18910	0.0917716	0.0458858	−	0.998947i	$-0.485389\pi$
$569$	2.18910	0.0917716	0.0458858	+	0.998947i	$0.485389\pi$
$570$	−17.6817	−0.740605
$571$	1.50687	0.0630607	0.0315304	−	0.999503i	$-0.489962\pi$
$571$	1.50687	0.0630607	0.0315304	+	0.999503i	$0.489962\pi$
$572$	−5.71863	−0.239108
$573$	2.06166	0.0861271
$574$	7.04553	0.294075
$575$	13.2197	0.551301
$576$	2.38160	0.0992335
$577$	−21.6995	−0.903360	−0.451680	−	0.892180i	$-0.649175\pi$
$577$	−21.6995	−0.903360	−0.451680	+	0.892180i	$0.649175\pi$
$578$	1.68622	0.0701375
$579$	−25.4040	−1.05575
$580$	−3.57123	−0.148287
$581$	−37.4723	−1.55461
$582$	−4.08212	−0.169209
$583$	6.71534	0.278121
$584$	−9.09447	−0.376332
$585$	6.57053	0.271658
$586$	−14.2132	−0.587143
$587$	1.61662	0.0667250	0.0333625	−	0.999443i	$-0.489378\pi$
$587$	1.61662	0.0667250	0.0333625	+	0.999443i	$0.489378\pi$
$588$	−5.27175	−0.217403
$589$	6.85601	0.282497
$590$	2.05578	0.0846352
$591$	−22.5875	−0.929124
$592$	−51.6685	−2.12356
$593$	16.6936	0.685524	0.342762	−	0.939422i	$-0.388638\pi$
$593$	16.6936	0.685524	0.342762	+	0.939422i	$0.388638\pi$
$594$	−4.72991	−0.194070
$595$	−9.89400	−0.405614
$596$	19.0209	0.779125
$597$	−5.61963	−0.229996
$598$	−22.5717	−0.923024
$599$	−15.2347	−0.622472	−0.311236	−	0.950333i	$-0.600743\pi$
$599$	−15.2347	−0.622472	−0.311236	+	0.950333i	$0.600743\pi$
$600$	4.65639	0.190096
$601$	−38.9887	−1.59038	−0.795191	−	0.606359i	$-0.792629\pi$
$601$	−38.9887	−1.59038	−0.795191	+	0.606359i	$0.792629\pi$
$602$	−67.1940	−2.73862
$603$	−0.902100	−0.0367364
$604$	17.2183	0.700603
$605$	8.51207	0.346065
$606$	7.18569	0.291899
$607$	13.7120	0.556555	0.278277	−	0.960501i	$-0.410237\pi$
$607$	13.7120	0.556555	0.278277	+	0.960501i	$0.410237\pi$
$608$	17.3183	0.702351
$609$	−5.67150	−0.229821
$610$	−53.1615	−2.15245
$611$	29.3946	1.18918
$612$	0.843334	0.0340898
$613$	−25.2626	−1.02035	−0.510173	−	0.860072i	$-0.670419\pi$
$613$	−25.2626	−1.02035	−0.510173	+	0.860072i	$0.670419\pi$
$614$	14.5040	0.585335
$615$	3.11975	0.125801
$616$	−19.9153	−0.802409
$617$	22.3515	0.899838	0.449919	−	0.893069i	$-0.351453\pi$
$617$	22.3515	0.899838	0.449919	+	0.893069i	$0.351453\pi$
$618$	−12.8574	−0.517200
$619$	17.2427	0.693043	0.346522	−	0.938042i	$-0.387363\pi$
$619$	17.2427	0.693043	0.346522	+	0.938042i	$0.387363\pi$
$620$	4.07336	0.163590
$621$	−5.53727	−0.222203
$622$	−2.88412	−0.115643
$623$	1.84271	0.0738268
$624$	−12.0278	−0.481498
$625$	−31.2373	−1.24949
$626$	3.49131	0.139541
$627$	10.8219	0.432184
$628$	−0.843334	−0.0336527
$629$	10.3847	0.414064
$630$	−16.6834	−0.664684
$631$	25.3457	1.00899	0.504497	−	0.863413i	$-0.331678\pi$
$631$	25.3457	1.00899	0.504497	+	0.863413i	$0.331678\pi$
$632$	−24.2617	−0.965080
$633$	−10.0715	−0.400308
$634$	−2.98603	−0.118591
$635$	−20.7034	−0.821590
$636$	−2.01897	−0.0800572
$637$	−15.1116	−0.598742
$638$	7.36927	0.291752
$639$	14.6733	0.580467
$640$	−35.3167	−1.39602
$641$	−46.8500	−1.85046	−0.925232	−	0.379401i	$-0.876130\pi$
$641$	−46.8500	−1.85046	−0.925232	+	0.379401i	$0.876130\pi$
$642$	13.4100	0.529252
$643$	37.5414	1.48049	0.740244	−	0.672338i	$-0.234710\pi$
$643$	37.5414	1.48049	0.740244	+	0.672338i	$0.234710\pi$
$644$	16.9989	0.669851
$645$	−29.7534	−1.17154
$646$	−6.50546	−0.255954
$647$	−39.9459	−1.57044	−0.785218	−	0.619219i	$-0.787449\pi$
$647$	−39.9459	−1.57044	−0.785218	+	0.619219i	$0.787449\pi$
$648$	−1.95039	−0.0766186
$649$	−1.25822	−0.0493894
$650$	−9.73184	−0.381714
$651$	6.46893	0.253538
$652$	9.54679	0.373881
$653$	−29.7566	−1.16446	−0.582232	−	0.813023i	$-0.697821\pi$
$653$	−29.7566	−1.16446	−0.582232	+	0.813023i	$0.697821\pi$
$654$	7.22069	0.282351
$655$	56.5587	2.20993
$656$	−5.71093	−0.222974
$657$	4.66289	0.181917
$658$	−74.6367	−2.90964
$659$	33.0286	1.28661	0.643307	−	0.765609i	$-0.277562\pi$
$659$	33.0286	1.28661	0.643307	+	0.765609i	$0.277562\pi$
$660$	6.42961	0.250272
$661$	−32.2138	−1.25297	−0.626487	−	0.779432i	$-0.715508\pi$
$661$	−32.2138	−1.25297	−0.626487	+	0.779432i	$0.715508\pi$
$662$	−21.5644	−0.838124
$663$	2.41743	0.0938852
$664$	20.0774	0.779154
$665$	38.1712	1.48022
$666$	17.5108	0.678532
$667$	8.62716	0.334045
$668$	16.3767	0.633634
$669$	−17.0600	−0.659576
$670$	4.13442	0.159727
$671$	32.5369	1.25607
$672$	16.3406	0.630352
$673$	9.56119	0.368557	0.184278	−	0.982874i	$-0.441005\pi$
$673$	9.56119	0.368557	0.184278	+	0.982874i	$0.441005\pi$
$674$	1.59588	0.0614711
$675$	−2.38741	−0.0918915
$676$	−6.03492	−0.232112
$677$	−24.7155	−0.949893	−0.474947	−	0.880015i	$-0.657533\pi$
$677$	−24.7155	−0.949893	−0.474947	+	0.880015i	$0.657533\pi$
$678$	29.0974	1.11748
$679$	8.81246	0.338191
$680$	5.30112	0.203289
$681$	−15.7222	−0.602475
$682$	−8.40543	−0.321860
$683$	−13.9433	−0.533526	−0.266763	−	0.963762i	$-0.585954\pi$
$683$	−13.9433	−0.533526	−0.266763	+	0.963762i	$0.585954\pi$
$684$	−3.25360	−0.124404
$685$	−37.1697	−1.42018
$686$	−4.59700	−0.175514
$687$	−25.6359	−0.978072
$688$	54.4658	2.07649
$689$	−5.78740	−0.220482
$690$	25.3779	0.966120
$691$	−20.9475	−0.796882	−0.398441	−	0.917194i	$-0.630449\pi$
$691$	−20.9475	−0.796882	−0.398441	+	0.917194i	$0.630449\pi$
$692$	13.4113	0.509822
$693$	10.2109	0.387880
$694$	−53.9914	−2.04949
$695$	51.5757	1.95638
$696$	3.03874	0.115183
$697$	1.14782	0.0434768
$698$	60.2915	2.28207
$699$	8.96937	0.339253
$700$	7.32913	0.277015
$701$	18.8092	0.710412	0.355206	−	0.934788i	$-0.384411\pi$
$701$	18.8092	0.710412	0.355206	+	0.934788i	$0.384411\pi$
$702$	4.07632	0.153851
$703$	−40.0643	−1.51105
$704$	6.68049	0.251781
$705$	−33.0491	−1.24470
$706$	−55.4750	−2.08783
$707$	−15.5124	−0.583405
$708$	0.378283	0.0142167
$709$	−12.4572	−0.467839	−0.233920	−	0.972256i	$-0.575155\pi$
$709$	−12.4572	−0.467839	−0.233920	+	0.972256i	$0.575155\pi$
$710$	−67.2494	−2.52382
$711$	12.4394	0.466514
$712$	−0.987312	−0.0370011
$713$	−9.84018	−0.368517
$714$	−6.13818	−0.229716
$715$	18.4306	0.689264
$716$	14.5683	0.544442
$717$	11.2297	0.419380
$718$	51.2411	1.91230
$719$	−45.8444	−1.70971	−0.854855	−	0.518868i	$-0.826354\pi$
$719$	−45.8444	−1.70971	−0.854855	+	0.518868i	$0.826354\pi$
$720$	13.5232	0.503979
$721$	27.7565	1.03370
$722$	−6.93999	−0.258280
$723$	−6.73975	−0.250654
$724$	−5.41446	−0.201227
$725$	3.71962	0.138143
$726$	5.28084	0.195990
$727$	−32.9744	−1.22295	−0.611476	−	0.791263i	$-0.709424\pi$
$727$	−32.9744	−1.22295	−0.611476	+	0.791263i	$0.709424\pi$
$728$	17.1633	0.636115
$729$	1.00000	0.0370370
$730$	−21.3705	−0.790959
$731$	−10.9469	−0.404886
$732$	−9.78220	−0.361561
$733$	34.7910	1.28503	0.642517	−	0.766271i	$-0.277890\pi$
$733$	34.7910	1.28503	0.642517	+	0.766271i	$0.277890\pi$
$734$	64.1284	2.36702
$735$	16.9903	0.626697
$736$	−24.8564	−0.916218
$737$	−2.53042	−0.0932094
$738$	1.93548	0.0712459
$739$	41.4623	1.52522	0.762608	−	0.646860i	$-0.223918\pi$
$739$	41.4623	1.52522	0.762608	+	0.646860i	$0.223918\pi$
$740$	−23.8034	−0.875030
$741$	−9.32649	−0.342617
$742$	14.6950	0.539470
$743$	35.5054	1.30257	0.651284	−	0.758834i	$-0.274231\pi$
$743$	35.5054	1.30257	0.651284	+	0.758834i	$0.274231\pi$
$744$	−3.46600	−0.127070
$745$	−61.3023	−2.24594
$746$	37.6834	1.37969
$747$	−10.2940	−0.376639
$748$	2.36558	0.0864943
$749$	−28.9496	−1.05779
$750$	−11.9738	−0.437221
$751$	25.5039	0.930651	0.465325	−	0.885140i	$-0.345937\pi$
$751$	25.5039	0.930651	0.465325	+	0.885140i	$0.345937\pi$
$752$	60.4987	2.20616
$753$	−3.31380	−0.120762
$754$	−6.35097	−0.231289
$755$	−55.4929	−2.01959
$756$	−3.06991	−0.111651
$757$	−43.5048	−1.58121	−0.790605	−	0.612327i	$-0.790234\pi$
$757$	−43.5048	−1.58121	−0.790605	+	0.612327i	$0.790234\pi$
$758$	−4.28455	−0.155622
$759$	−15.5323	−0.563785
$760$	−20.4518	−0.741866
$761$	40.6089	1.47207	0.736035	−	0.676943i	$-0.236696\pi$
$761$	40.6089	1.47207	0.736035	+	0.676943i	$0.236696\pi$
$762$	−12.8443	−0.465299
$763$	−15.5880	−0.564323
$764$	−1.73867	−0.0629028
$765$	−2.71798	−0.0982687
$766$	39.6715	1.43339
$767$	1.08435	0.0391538
$768$	−17.1471	−0.618743
$769$	−9.26186	−0.333991	−0.166996	−	0.985958i	$-0.553407\pi$
$769$	−9.26186	−0.333991	−0.166996	+	0.985958i	$0.553407\pi$
$770$	−46.7977	−1.68647
$771$	−28.7837	−1.03662
$772$	21.4241	0.771069
$773$	−3.39081	−0.121959	−0.0609795	−	0.998139i	$-0.519422\pi$
$773$	−3.39081	−0.121959	−0.0609795	+	0.998139i	$0.519422\pi$
$774$	−18.4589	−0.663490
$775$	−4.24262	−0.152399
$776$	−4.72164	−0.169497
$777$	−37.8024	−1.35615
$778$	6.43617	0.230748
$779$	−4.42831	−0.158661
$780$	−5.54115	−0.198405
$781$	41.1592	1.47279
$782$	9.33705	0.333892
$783$	−1.55802	−0.0556790
$784$	−31.1020	−1.11078
$785$	2.71798	0.0970088
$786$	35.0887	1.25157
$787$	3.57401	0.127400	0.0636999	−	0.997969i	$-0.479710\pi$
$787$	3.57401	0.127400	0.0636999	+	0.997969i	$0.479710\pi$
$788$	19.0488	0.678584
$789$	4.43623	0.157934
$790$	−57.0112	−2.02837
$791$	−62.8154	−2.23346
$792$	−5.47092	−0.194401
$793$	−28.0408	−0.995759
$794$	2.44519	0.0867765
$795$	6.50692	0.230777
$796$	4.73923	0.167977
$797$	−53.0472	−1.87903	−0.939514	−	0.342509i	$-0.888723\pi$
$797$	−53.0472	−1.87903	−0.939514	+	0.342509i	$0.888723\pi$
$798$	23.6812	0.838305
$799$	−12.1594	−0.430169
$800$	−10.7169	−0.378900
$801$	0.506212	0.0178861
$802$	49.7876	1.75806
$803$	13.0796	0.461569
$804$	0.760772	0.0268303
$805$	−54.7857	−1.93094
$806$	7.24394	0.255157
$807$	13.8240	0.486628
$808$	8.31144	0.292395
$809$	9.92832	0.349061	0.174531	−	0.984652i	$-0.444159\pi$
$809$	9.92832	0.349061	0.174531	+	0.984652i	$0.444159\pi$
$810$	−4.58311	−0.161034
$811$	−7.81028	−0.274256	−0.137128	−	0.990553i	$-0.543787\pi$
$811$	−7.81028	−0.274256	−0.137128	+	0.990553i	$0.543787\pi$
$812$	4.78296	0.167849
$813$	17.1647	0.601993
$814$	49.1186	1.72161
$815$	−30.7683	−1.07777
$816$	4.97546	0.174176
$817$	42.2333	1.47756
$818$	22.6958	0.793541
$819$	−8.79994	−0.307495
$820$	−2.63099	−0.0918783
$821$	17.1918	0.600000	0.300000	−	0.953939i	$-0.403013\pi$
$821$	17.1918	0.600000	0.300000	+	0.953939i	$0.403013\pi$
$822$	−23.0599	−0.804305
$823$	3.09337	0.107828	0.0539141	−	0.998546i	$-0.482830\pi$
$823$	3.09337	0.107828	0.0539141	+	0.998546i	$0.482830\pi$
$824$	−14.8717	−0.518080
$825$	−6.69678	−0.233152
$826$	−2.75332	−0.0958003
$827$	28.5878	0.994095	0.497047	−	0.867723i	$-0.334418\pi$
$827$	28.5878	0.994095	0.497047	+	0.867723i	$0.334418\pi$
$828$	4.66977	0.162286
$829$	40.2307	1.39727	0.698635	−	0.715479i	$-0.253791\pi$
$829$	40.2307	1.39727	0.698635	+	0.715479i	$0.253791\pi$
$830$	47.1786	1.63759
$831$	−6.73769	−0.233728
$832$	−5.75736	−0.199601
$833$	6.25108	0.216587
$834$	31.9973	1.10798
$835$	−52.7805	−1.82654
$836$	−9.12646	−0.315645
$837$	1.77708	0.0614249
$838$	−60.1559	−2.07805
$839$	50.8620	1.75595	0.877976	−	0.478704i	$-0.158893\pi$
$839$	50.8620	1.75595	0.877976	+	0.478704i	$0.158893\pi$
$840$	−19.2972	−0.665816
$841$	−26.5726	−0.916296
$842$	−47.3687	−1.63243
$843$	−1.66153	−0.0572261
$844$	8.49368	0.292365
$845$	19.4499	0.669098
$846$	−20.5034	−0.704923
$847$	−11.4003	−0.391717
$848$	−11.9114	−0.409039
$849$	−22.1726	−0.760961
$850$	4.02570	0.138080
$851$	57.5028	1.97117
$852$	−12.3745	−0.423944
$853$	45.4306	1.55551	0.777757	−	0.628565i	$-0.216357\pi$
$853$	45.4306	1.55551	0.777757	+	0.628565i	$0.216357\pi$
$854$	71.1994	2.43639
$855$	10.4860	0.358614
$856$	15.5109	0.530153
$857$	−26.4008	−0.901834	−0.450917	−	0.892566i	$-0.648903\pi$
$857$	−26.4008	−0.901834	−0.450917	+	0.892566i	$0.648903\pi$
$858$	11.4342	0.390358
$859$	21.9014	0.747267	0.373634	−	0.927576i	$-0.378112\pi$
$859$	21.9014	0.747267	0.373634	+	0.927576i	$0.378112\pi$
$860$	25.0921	0.855633
$861$	−4.17830	−0.142396
$862$	−10.1352	−0.345207
$863$	−12.9142	−0.439604	−0.219802	−	0.975545i	$-0.570541\pi$
$863$	−12.9142	−0.439604	−0.219802	+	0.975545i	$0.570541\pi$
$864$	4.48892	0.152716
$865$	−43.2234	−1.46964
$866$	−20.8095	−0.707137
$867$	−1.00000	−0.0339618
$868$	−5.45547	−0.185171
$869$	34.8930	1.18366
$870$	7.14055	0.242087
$871$	2.18076	0.0738924
$872$	8.35193	0.282832
$873$	2.42087	0.0819340
$874$	−36.0225	−1.21848
$875$	25.8490	0.873854
$876$	−3.93238	−0.132863
$877$	−18.6037	−0.628204	−0.314102	−	0.949389i	$-0.601703\pi$
$877$	−18.6037	−0.628204	−0.314102	+	0.949389i	$0.601703\pi$
$878$	19.0462	0.642780
$879$	8.42905	0.284305
$880$	37.9330	1.27872
$881$	2.44464	0.0823622	0.0411811	−	0.999152i	$-0.486888\pi$
$881$	2.44464	0.0823622	0.0411811	+	0.999152i	$0.486888\pi$
$882$	10.5407	0.354924
$883$	−1.40681	−0.0473429	−0.0236714	−	0.999720i	$-0.507536\pi$
$883$	−1.40681	−0.0473429	−0.0236714	+	0.999720i	$0.507536\pi$
$884$	−2.03870	−0.0685689
$885$	−1.21917	−0.0409819
$886$	−27.8375	−0.935218
$887$	45.5513	1.52946	0.764731	−	0.644349i	$-0.222872\pi$
$887$	45.5513	1.52946	0.764731	+	0.644349i	$0.222872\pi$
$888$	20.2542	0.679687
$889$	27.7282	0.929974
$890$	−2.32002	−0.0777674
$891$	2.80504	0.0939723
$892$	14.3872	0.481721
$893$	46.9112	1.56982
$894$	−38.0316	−1.27197
$895$	−46.9521	−1.56944
$896$	47.2999	1.58018
$897$	13.3860	0.446944
$898$	−36.0168	−1.20190
$899$	−2.76872	−0.0923420
$900$	2.01338	0.0671128
$901$	2.39403	0.0797567
$902$	5.42909	0.180769
$903$	39.8489	1.32609
$904$	33.6560	1.11938
$905$	17.4503	0.580066
$906$	−34.4275	−1.14378
$907$	11.5927	0.384928	0.192464	−	0.981304i	$-0.438352\pi$
$907$	11.5927	0.384928	0.192464	+	0.981304i	$0.438352\pi$
$908$	13.2590	0.440017
$909$	−4.26142	−0.141342
$910$	40.3311	1.33696
$911$	−34.6579	−1.14827	−0.574133	−	0.818762i	$-0.694661\pi$
$911$	−34.6579	−1.14827	−0.574133	+	0.818762i	$0.694661\pi$
$912$	−19.1954	−0.635623
$913$	−28.8751	−0.955627
$914$	−1.33262	−0.0440793
$915$	31.5270	1.04225
$916$	21.6197	0.714334
$917$	−75.7494	−2.50146
$918$	−1.68622	−0.0556535
$919$	−49.7783	−1.64204	−0.821018	−	0.570902i	$-0.806594\pi$
$919$	−49.7783	−1.64204	−0.821018	+	0.570902i	$0.806594\pi$
$920$	29.3538	0.967765
$921$	−8.60152	−0.283430
$922$	9.70805	0.319718
$923$	−35.4717	−1.16757
$924$	−8.61121	−0.283288
$925$	24.7925	0.815172
$926$	−18.1653	−0.596948
$927$	7.62497	0.250437
$928$	−6.99381	−0.229583
$929$	10.5879	0.347379	0.173690	−	0.984800i	$-0.444431\pi$
$929$	10.5879	0.347379	0.173690	+	0.984800i	$0.444431\pi$
$930$	−8.14455	−0.267070
$931$	−24.1168	−0.790395
$932$	−7.56417	−0.247773
$933$	1.71041	0.0559963
$934$	−41.4345	−1.35578
$935$	−7.62403	−0.249333
$936$	4.71494	0.154113
$937$	−12.8454	−0.419642	−0.209821	−	0.977740i	$-0.567288\pi$
$937$	−12.8454	−0.419642	−0.209821	+	0.977740i	$0.567288\pi$
$938$	−5.53725	−0.180798
$939$	−2.07049	−0.0675680
$940$	27.8714	0.909064
$941$	41.4255	1.35043	0.675216	−	0.737620i	$-0.264050\pi$
$941$	41.4255	1.35043	0.675216	+	0.737620i	$0.264050\pi$
$942$	1.68622	0.0549400
$943$	6.35580	0.206973
$944$	2.23177	0.0726380
$945$	9.89400	0.321852
$946$	−51.7778	−1.68344
$947$	52.5648	1.70813	0.854063	−	0.520170i	$-0.174131\pi$
$947$	52.5648	1.70813	0.854063	+	0.520170i	$0.174131\pi$
$948$	−10.4906	−0.340718
$949$	−11.2722	−0.365912
$950$	−15.5312	−0.503899
$951$	1.77085	0.0574236
$952$	−7.09982	−0.230107
$953$	−52.6892	−1.70677	−0.853385	−	0.521281i	$-0.825454\pi$
$953$	−52.6892	−1.70677	−0.853385	+	0.521281i	$0.825454\pi$
$954$	4.03686	0.130698
$955$	5.60355	0.181327
$956$	−9.47038	−0.306294
$957$	−4.37029	−0.141272
$958$	43.8710	1.41741
$959$	49.7815	1.60753
$960$	6.47315	0.208920
$961$	−27.8420	−0.898129
$962$	−42.3313	−1.36481
$963$	−7.95273	−0.256273
$964$	5.68386	0.183065
$965$	−69.0475	−2.22272
$966$	−33.9888	−1.09357
$967$	40.0070	1.28654	0.643270	−	0.765640i	$-0.277577\pi$
$967$	40.0070	1.28654	0.643270	+	0.765640i	$0.277577\pi$
$968$	6.10817	0.196324
$969$	3.85802	0.123937
$970$	−11.0951	−0.356242
$971$	−20.1747	−0.647439	−0.323719	−	0.946153i	$-0.604933\pi$
$971$	−20.1747	−0.647439	−0.323719	+	0.946153i	$0.604933\pi$
$972$	−0.843334	−0.0270499
$973$	−69.0757	−2.21446
$974$	43.3871	1.39021
$975$	5.77140	0.184833
$976$	−57.7125	−1.84733
$977$	−50.6373	−1.62003	−0.810015	−	0.586410i	$-0.800541\pi$
$977$	−50.6373	−1.62003	−0.810015	+	0.586410i	$0.800541\pi$
$978$	−19.0885	−0.610383
$979$	1.41994	0.0453816
$980$	−14.3285	−0.457707
$981$	−4.28218	−0.136719
$982$	−60.9700	−1.94563
$983$	−9.11055	−0.290582	−0.145291	−	0.989389i	$-0.546412\pi$
$983$	−9.11055	−0.290582	−0.145291	+	0.989389i	$0.546412\pi$
$984$	2.23870	0.0713672
$985$	−61.3922	−1.95612
$986$	2.62716	0.0836657
$987$	44.2628	1.40890
$988$	7.86534	0.250230
$989$	−60.6159	−1.92747
$990$	−12.8558	−0.408584
$991$	9.40665	0.298812	0.149406	−	0.988776i	$-0.452264\pi$
$991$	9.40665	0.298812	0.149406	+	0.988776i	$0.452264\pi$
$992$	7.97718	0.253276
$993$	12.7886	0.405834
$994$	90.0675	2.85677
$995$	−15.2740	−0.484220
$996$	8.68130	0.275078
$997$	−18.9865	−0.601308	−0.300654	−	0.953733i	$-0.597205\pi$
$997$	−18.9865	−0.601308	−0.300654	+	0.953733i	$0.597205\pi$
$998$	−25.6509	−0.811964
$999$	−10.3847	−0.328557

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.47	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.47	✓	64	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)

\(f(q)\)	\(=\)	\(q+1.68622 q^{2} -1.00000 q^{3} +0.843334 q^{4} -2.71798 q^{5} -1.68622 q^{6} +3.64020 q^{7} -1.95039 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.68622 q^{2} -1.00000 q^{3} +0.843334 q^{4} -2.71798 q^{5} -1.68622 q^{6} +3.64020 q^{7} -1.95039 q^{8} +1.00000 q^{9} -4.58311 q^{10} +2.80504 q^{11} -0.843334 q^{12} -2.41743 q^{13} +6.13818 q^{14} +2.71798 q^{15} -4.97546 q^{16} +1.00000 q^{17} +1.68622 q^{18} -3.85802 q^{19} -2.29216 q^{20} -3.64020 q^{21} +4.72991 q^{22} +5.53727 q^{23} +1.95039 q^{24} +2.38741 q^{25} -4.07632 q^{26} -1.00000 q^{27} +3.06991 q^{28} +1.55802 q^{29} +4.58311 q^{30} -1.77708 q^{31} -4.48892 q^{32} -2.80504 q^{33} +1.68622 q^{34} -9.89400 q^{35} +0.843334 q^{36} +10.3847 q^{37} -6.50546 q^{38} +2.41743 q^{39} +5.30112 q^{40} +1.14782 q^{41} -6.13818 q^{42} -10.9469 q^{43} +2.36558 q^{44} -2.71798 q^{45} +9.33705 q^{46} -12.1594 q^{47} +4.97546 q^{48} +6.25108 q^{49} +4.02570 q^{50} -1.00000 q^{51} -2.03870 q^{52} +2.39403 q^{53} -1.68622 q^{54} -7.62403 q^{55} -7.09982 q^{56} +3.85802 q^{57} +2.62716 q^{58} -0.448557 q^{59} +2.29216 q^{60} +11.5994 q^{61} -2.99655 q^{62} +3.64020 q^{63} +2.38160 q^{64} +6.57053 q^{65} -4.72991 q^{66} -0.902100 q^{67} +0.843334 q^{68} -5.53727 q^{69} -16.6834 q^{70} +14.6733 q^{71} -1.95039 q^{72} +4.66289 q^{73} +17.5108 q^{74} -2.38741 q^{75} -3.25360 q^{76} +10.2109 q^{77} +4.07632 q^{78} +12.4394 q^{79} +13.5232 q^{80} +1.00000 q^{81} +1.93548 q^{82} -10.2940 q^{83} -3.06991 q^{84} -2.71798 q^{85} -18.4589 q^{86} -1.55802 q^{87} -5.47092 q^{88} +0.506212 q^{89} -4.58311 q^{90} -8.79994 q^{91} +4.66977 q^{92} +1.77708 q^{93} -20.5034 q^{94} +10.4860 q^{95} +4.48892 q^{96} +2.42087 q^{97} +10.5407 q^{98} +2.80504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more