LMFDB - Embedded newform 8007.2.a.h.1.18

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			1.18
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)

$f(q)$	$=$	$q-1.19021 q^{2} +1.00000 q^{3} -0.583408 q^{4} +2.13314 q^{5} -1.19021 q^{6} -4.67655 q^{7} +3.07479 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.19021 q^{2} +1.00000 q^{3} -0.583408 q^{4} +2.13314 q^{5} -1.19021 q^{6} -4.67655 q^{7} +3.07479 q^{8} +1.00000 q^{9} -2.53888 q^{10} -0.809389 q^{11} -0.583408 q^{12} -4.70444 q^{13} +5.56607 q^{14} +2.13314 q^{15} -2.49282 q^{16} -1.00000 q^{17} -1.19021 q^{18} -7.95258 q^{19} -1.24449 q^{20} -4.67655 q^{21} +0.963340 q^{22} -4.00386 q^{23} +3.07479 q^{24} -0.449707 q^{25} +5.59925 q^{26} +1.00000 q^{27} +2.72834 q^{28} -9.82150 q^{29} -2.53888 q^{30} +3.98647 q^{31} -3.18261 q^{32} -0.809389 q^{33} +1.19021 q^{34} -9.97575 q^{35} -0.583408 q^{36} -0.127133 q^{37} +9.46522 q^{38} -4.70444 q^{39} +6.55896 q^{40} +0.102402 q^{41} +5.56607 q^{42} -9.62523 q^{43} +0.472204 q^{44} +2.13314 q^{45} +4.76543 q^{46} -0.0165903 q^{47} -2.49282 q^{48} +14.8702 q^{49} +0.535244 q^{50} -1.00000 q^{51} +2.74461 q^{52} -2.68178 q^{53} -1.19021 q^{54} -1.72654 q^{55} -14.3794 q^{56} -7.95258 q^{57} +11.6896 q^{58} +5.94969 q^{59} -1.24449 q^{60} +6.72783 q^{61} -4.74472 q^{62} -4.67655 q^{63} +8.77360 q^{64} -10.0352 q^{65} +0.963340 q^{66} +11.4393 q^{67} +0.583408 q^{68} -4.00386 q^{69} +11.8732 q^{70} -5.96276 q^{71} +3.07479 q^{72} +10.2575 q^{73} +0.151314 q^{74} -0.449707 q^{75} +4.63960 q^{76} +3.78515 q^{77} +5.59925 q^{78} -1.52913 q^{79} -5.31754 q^{80} +1.00000 q^{81} -0.121879 q^{82} -7.51023 q^{83} +2.72834 q^{84} -2.13314 q^{85} +11.4560 q^{86} -9.82150 q^{87} -2.48870 q^{88} +8.86483 q^{89} -2.53888 q^{90} +22.0006 q^{91} +2.33589 q^{92} +3.98647 q^{93} +0.0197459 q^{94} -16.9640 q^{95} -3.18261 q^{96} +15.4100 q^{97} -17.6986 q^{98} -0.809389 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) $ 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * 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 $

$2$	−1.19021	−0.841603	−0.420802	−	0.907153i	$-0.638251\pi$
$2$	−1.19021	−0.841603	−0.420802	+	0.907153i	$0.638251\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.583408	−0.291704
$5$	2.13314	0.953970	0.476985	−	0.878911i	$-0.341730\pi$
$5$	2.13314	0.953970	0.476985	+	0.878911i	$0.341730\pi$
$6$	−1.19021	−0.485900
$7$	−4.67655	−1.76757	−0.883786	−	0.467892i	$-0.845014\pi$
$7$	−4.67655	−1.76757	−0.883786	+	0.467892i	$0.845014\pi$
$8$	3.07479	1.08710
$9$	1.00000	0.333333
$10$	−2.53888	−0.802864
$11$	−0.809389	−0.244040	−0.122020	−	0.992528i	$-0.538937\pi$
$11$	−0.809389	−0.244040	−0.122020	+	0.992528i	$0.538937\pi$
$12$	−0.583408	−0.168415
$13$	−4.70444	−1.30478	−0.652388	−	0.757885i	$-0.726233\pi$
$13$	−4.70444	−1.30478	−0.652388	+	0.757885i	$0.726233\pi$
$14$	5.56607	1.48759
$15$	2.13314	0.550775
$16$	−2.49282	−0.623205
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.19021	−0.280534
$19$	−7.95258	−1.82445	−0.912224	−	0.409692i	$-0.865636\pi$
$19$	−7.95258	−1.82445	−0.912224	+	0.409692i	$0.865636\pi$
$20$	−1.24449	−0.278277
$21$	−4.67655	−1.02051
$22$	0.963340	0.205385
$23$	−4.00386	−0.834864	−0.417432	−	0.908708i	$-0.637070\pi$
$23$	−4.00386	−0.834864	−0.417432	+	0.908708i	$0.637070\pi$
$24$	3.07479	0.627639
$25$	−0.449707	−0.0899413
$26$	5.59925	1.09810
$27$	1.00000	0.192450
$28$	2.72834	0.515608
$29$	−9.82150	−1.82381	−0.911903	−	0.410405i	$-0.865387\pi$
$29$	−9.82150	−1.82381	−0.911903	+	0.410405i	$0.865387\pi$
$30$	−2.53888	−0.463534
$31$	3.98647	0.715991	0.357995	−	0.933723i	$-0.383460\pi$
$31$	3.98647	0.715991	0.357995	+	0.933723i	$0.383460\pi$
$32$	−3.18261	−0.562611
$33$	−0.809389	−0.140897
$34$	1.19021	0.204119
$35$	−9.97575	−1.68621
$36$	−0.583408	−0.0972347
$37$	−0.127133	−0.0209005	−0.0104502	−	0.999945i	$-0.503326\pi$
$37$	−0.127133	−0.0209005	−0.0104502	+	0.999945i	$0.503326\pi$
$38$	9.46522	1.53546
$39$	−4.70444	−0.753313
$40$	6.55896	1.03706
$41$	0.102402	0.0159925	0.00799624	−	0.999968i	$-0.497455\pi$
$41$	0.102402	0.0159925	0.00799624	+	0.999968i	$0.497455\pi$
$42$	5.56607	0.858863
$43$	−9.62523	−1.46783	−0.733917	−	0.679240i	$-0.762310\pi$
$43$	−9.62523	−1.46783	−0.733917	+	0.679240i	$0.762310\pi$
$44$	0.472204	0.0711874
$45$	2.13314	0.317990
$46$	4.76543	0.702624
$47$	−0.0165903	−0.00241995	−0.00120998	−	0.999999i	$-0.500385\pi$
$47$	−0.0165903	−0.00241995	−0.00120998	+	0.999999i	$0.500385\pi$
$48$	−2.49282	−0.359807
$49$	14.8702	2.12431
$50$	0.535244	0.0756949
$51$	−1.00000	−0.140028
$52$	2.74461	0.380608
$53$	−2.68178	−0.368371	−0.184185	−	0.982892i	$-0.558965\pi$
$53$	−2.68178	−0.368371	−0.184185	+	0.982892i	$0.558965\pi$
$54$	−1.19021	−0.161967
$55$	−1.72654	−0.232807
$56$	−14.3794	−1.92153
$57$	−7.95258	−1.05335
$58$	11.6896	1.53492
$59$	5.94969	0.774584	0.387292	−	0.921957i	$-0.373411\pi$
$59$	5.94969	0.774584	0.387292	+	0.921957i	$0.373411\pi$
$60$	−1.24449	−0.160663
$61$	6.72783	0.861410	0.430705	−	0.902493i	$-0.358265\pi$
$61$	6.72783	0.861410	0.430705	+	0.902493i	$0.358265\pi$
$62$	−4.74472	−0.602580
$63$	−4.67655	−0.589190
$64$	8.77360	1.09670
$65$	−10.0352	−1.24472
$66$	0.963340	0.118579
$67$	11.4393	1.39753	0.698767	−	0.715350i	$-0.253733\pi$
$67$	11.4393	1.39753	0.698767	+	0.715350i	$0.253733\pi$
$68$	0.583408	0.0707486
$69$	−4.00386	−0.482009
$70$	11.8732	1.41912
$71$	−5.96276	−0.707649	−0.353825	−	0.935312i	$-0.615119\pi$
$71$	−5.96276	−0.707649	−0.353825	+	0.935312i	$0.615119\pi$
$72$	3.07479	0.362367
$73$	10.2575	1.20055	0.600275	−	0.799794i	$-0.295058\pi$
$73$	10.2575	1.20055	0.600275	+	0.799794i	$0.295058\pi$
$74$	0.151314	0.0175899
$75$	−0.449707	−0.0519276
$76$	4.63960	0.532199
$77$	3.78515	0.431358
$78$	5.59925	0.633990
$79$	−1.52913	−0.172040	−0.0860201	−	0.996293i	$-0.527415\pi$
$79$	−1.52913	−0.172040	−0.0860201	+	0.996293i	$0.527415\pi$
$80$	−5.31754	−0.594519
$81$	1.00000	0.111111
$82$	−0.121879	−0.0134593
$83$	−7.51023	−0.824355	−0.412178	−	0.911104i	$-0.635232\pi$
$83$	−7.51023	−0.824355	−0.412178	+	0.911104i	$0.635232\pi$
$84$	2.72834	0.297686
$85$	−2.13314	−0.231372
$86$	11.4560	1.23533
$87$	−9.82150	−1.05298
$88$	−2.48870	−0.265296
$89$	8.86483	0.939671	0.469835	−	0.882754i	$-0.344313\pi$
$89$	8.86483	0.939671	0.469835	+	0.882754i	$0.344313\pi$
$90$	−2.53888	−0.267621
$91$	22.0006	2.30628
$92$	2.33589	0.243533
$93$	3.98647	0.413377
$94$	0.0197459	0.00203664
$95$	−16.9640	−1.74047
$96$	−3.18261	−0.324824
$97$	15.4100	1.56465	0.782325	−	0.622871i	$-0.214034\pi$
$97$	15.4100	1.56465	0.782325	+	0.622871i	$0.214034\pi$
$98$	−17.6986	−1.78782
$99$	−0.809389	−0.0813467
$100$	0.262362	0.0262362
$101$	11.2279	1.11722	0.558608	−	0.829432i	$-0.311336\pi$
$101$	11.2279	1.11722	0.558608	+	0.829432i	$0.311336\pi$
$102$	1.19021	0.117848
$103$	−4.19829	−0.413670	−0.206835	−	0.978376i	$-0.566316\pi$
$103$	−4.19829	−0.413670	−0.206835	+	0.978376i	$0.566316\pi$
$104$	−14.4652	−1.41842
$105$	−9.97575	−0.973534
$106$	3.19187	0.310022
$107$	9.69340	0.937096	0.468548	−	0.883438i	$-0.344777\pi$
$107$	9.69340	0.937096	0.468548	+	0.883438i	$0.344777\pi$
$108$	−0.583408	−0.0561385
$109$	−1.70716	−0.163517	−0.0817583	−	0.996652i	$-0.526054\pi$
$109$	−1.70716	−0.163517	−0.0817583	+	0.996652i	$0.526054\pi$
$110$	2.05494	0.195931
$111$	−0.127133	−0.0120669
$112$	11.6578	1.10156
$113$	7.57675	0.712761	0.356380	−	0.934341i	$-0.384011\pi$
$113$	7.57675	0.712761	0.356380	+	0.934341i	$0.384011\pi$
$114$	9.46522	0.886499
$115$	−8.54081	−0.796435
$116$	5.72994	0.532012
$117$	−4.70444	−0.434925
$118$	−7.08136	−0.651892
$119$	4.67655	0.428699
$120$	6.55896	0.598749
$121$	−10.3449	−0.940445
$122$	−8.00750	−0.724965
$123$	0.102402	0.00923326
$124$	−2.32574	−0.208857
$125$	−11.6250	−1.03977
$126$	5.56607	0.495865
$127$	2.49017	0.220967	0.110484	−	0.993878i	$-0.464760\pi$
$127$	2.49017	0.220967	0.110484	+	0.993878i	$0.464760\pi$
$128$	−4.07718	−0.360375
$129$	−9.62523	−0.847454
$130$	11.9440	1.04756
$131$	−13.3810	−1.16911	−0.584553	−	0.811356i	$-0.698730\pi$
$131$	−13.3810	−1.16911	−0.584553	+	0.811356i	$0.698730\pi$
$132$	0.472204	0.0411001
$133$	37.1907	3.22484
$134$	−13.6151	−1.17617
$135$	2.13314	0.183592
$136$	−3.07479	−0.263661
$137$	11.6618	0.996339	0.498169	−	0.867080i	$-0.334006\pi$
$137$	11.6618	0.996339	0.498169	+	0.867080i	$0.334006\pi$
$138$	4.76543	0.405660
$139$	4.33244	0.367473	0.183736	−	0.982976i	$-0.441181\pi$
$139$	4.33244	0.367473	0.183736	+	0.982976i	$0.441181\pi$
$140$	5.81993	0.491874
$141$	−0.0165903	−0.00139716
$142$	7.09691	0.595560
$143$	3.80772	0.318417
$144$	−2.49282	−0.207735
$145$	−20.9506	−1.73986
$146$	−12.2085	−1.01039
$147$	14.8702	1.22647
$148$	0.0741703	0.00609676
$149$	10.8450	0.888457	0.444229	−	0.895913i	$-0.353478\pi$
$149$	10.8450	0.888457	0.444229	+	0.895913i	$0.353478\pi$
$150$	0.535244	0.0437025
$151$	−3.83702	−0.312252	−0.156126	−	0.987737i	$-0.549901\pi$
$151$	−3.83702	−0.312252	−0.156126	+	0.987737i	$0.549901\pi$
$152$	−24.4525	−1.98336
$153$	−1.00000	−0.0808452
$154$	−4.50511	−0.363032
$155$	8.50370	0.683034
$156$	2.74461	0.219744
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	1.81998	0.144790
$159$	−2.68178	−0.212679
$160$	−6.78896	−0.536714
$161$	18.7243	1.47568
$162$	−1.19021	−0.0935115
$163$	12.9653	1.01552	0.507759	−	0.861499i	$-0.330474\pi$
$163$	12.9653	1.01552	0.507759	+	0.861499i	$0.330474\pi$
$164$	−0.0597420	−0.00466507
$165$	−1.72654	−0.134411
$166$	8.93873	0.693780
$167$	13.1307	1.01608	0.508041	−	0.861333i	$-0.330370\pi$
$167$	13.1307	1.01608	0.508041	+	0.861333i	$0.330370\pi$
$168$	−14.3794	−1.10940
$169$	9.13172	0.702440
$170$	2.53888	0.194723
$171$	−7.95258	−0.608149
$172$	5.61543	0.428173
$173$	−11.8314	−0.899524	−0.449762	−	0.893148i	$-0.648491\pi$
$173$	−11.8314	−0.899524	−0.449762	+	0.893148i	$0.648491\pi$
$174$	11.6896	0.886187
$175$	2.10308	0.158978
$176$	2.01766	0.152087
$177$	5.94969	0.447206
$178$	−10.5510	−0.790830
$179$	2.86286	0.213980	0.106990	−	0.994260i	$-0.465879\pi$
$179$	2.86286	0.213980	0.106990	+	0.994260i	$0.465879\pi$
$180$	−1.24449	−0.0927590
$181$	−0.902276	−0.0670657	−0.0335328	−	0.999438i	$-0.510676\pi$
$181$	−0.902276	−0.0670657	−0.0335328	+	0.999438i	$0.510676\pi$
$182$	−26.1852	−1.94098
$183$	6.72783	0.497335
$184$	−12.3110	−0.907582
$185$	−0.271192	−0.0199384
$186$	−4.74472	−0.347900
$187$	0.809389	0.0591884
$188$	0.00967894	0.000705909 0
$189$	−4.67655	−0.340169
$190$	20.1907	1.46478
$191$	−9.72984	−0.704027	−0.352013	−	0.935995i	$-0.614503\pi$
$191$	−9.72984	−0.704027	−0.352013	+	0.935995i	$0.614503\pi$
$192$	8.77360	0.633180
$193$	14.7474	1.06154	0.530769	−	0.847517i	$-0.321903\pi$
$193$	14.7474	1.06154	0.530769	+	0.847517i	$0.321903\pi$
$194$	−18.3411	−1.31681
$195$	−10.0352	−0.718638
$196$	−8.67537	−0.619669
$197$	−1.20071	−0.0855471	−0.0427735	−	0.999085i	$-0.513619\pi$
$197$	−1.20071	−0.0855471	−0.0427735	+	0.999085i	$0.513619\pi$
$198$	0.963340	0.0684616
$199$	−9.06454	−0.642568	−0.321284	−	0.946983i	$-0.604114\pi$
$199$	−9.06454	−0.642568	−0.321284	+	0.946983i	$0.604114\pi$
$200$	−1.38275	−0.0977754
$201$	11.4393	0.806866
$202$	−13.3635	−0.940253
$203$	45.9308	3.22371
$204$	0.583408	0.0408467
$205$	0.218438	0.0152563
$206$	4.99683	0.348146
$207$	−4.00386	−0.278288
$208$	11.7273	0.813143
$209$	6.43673	0.445238
$210$	11.8732	0.819329
$211$	−20.9605	−1.44298	−0.721489	−	0.692425i	$-0.756542\pi$
$211$	−20.9605	−1.44298	−0.721489	+	0.692425i	$0.756542\pi$
$212$	1.56457	0.107455
$213$	−5.96276	−0.408561
$214$	−11.5371	−0.788663
$215$	−20.5320	−1.40027
$216$	3.07479	0.209213
$217$	−18.6429	−1.26556
$218$	2.03188	0.137616
$219$	10.2575	0.693138
$220$	1.00728	0.0679107
$221$	4.70444	0.316455
$222$	0.151314	0.0101555
$223$	−23.9617	−1.60459	−0.802297	−	0.596925i	$-0.796389\pi$
$223$	−23.9617	−1.60459	−0.802297	+	0.596925i	$0.796389\pi$
$224$	14.8836	0.994455
$225$	−0.449707	−0.0299804
$226$	−9.01790	−0.599862
$227$	−17.5285	−1.16340	−0.581702	−	0.813402i	$-0.697613\pi$
$227$	−17.5285	−1.16340	−0.581702	+	0.813402i	$0.697613\pi$
$228$	4.63960	0.307265
$229$	4.39128	0.290184	0.145092	−	0.989418i	$-0.453652\pi$
$229$	4.39128	0.290184	0.145092	+	0.989418i	$0.453652\pi$
$230$	10.1653	0.670282
$231$	3.78515	0.249045
$232$	−30.1990	−1.98266
$233$	−8.14483	−0.533586	−0.266793	−	0.963754i	$-0.585964\pi$
$233$	−8.14483	−0.533586	−0.266793	+	0.963754i	$0.585964\pi$
$234$	5.59925	0.366035
$235$	−0.0353896	−0.00230856
$236$	−3.47110	−0.225949
$237$	−1.52913	−0.0993274
$238$	−5.56607	−0.360794
$239$	15.0814	0.975536	0.487768	−	0.872973i	$-0.337811\pi$
$239$	15.0814	0.975536	0.487768	+	0.872973i	$0.337811\pi$
$240$	−5.31754	−0.343245
$241$	13.4000	0.863170	0.431585	−	0.902072i	$-0.357955\pi$
$241$	13.4000	0.863170	0.431585	+	0.902072i	$0.357955\pi$
$242$	12.3126	0.791481
$243$	1.00000	0.0641500
$244$	−3.92507	−0.251277
$245$	31.7202	2.02653
$246$	−0.121879	−0.00777074
$247$	37.4124	2.38050
$248$	12.2575	0.778355
$249$	−7.51023	−0.475942
$250$	13.8361	0.875075
$251$	−11.4653	−0.723682	−0.361841	−	0.932240i	$-0.617852\pi$
$251$	−11.4653	−0.723682	−0.361841	+	0.932240i	$0.617852\pi$
$252$	2.72834	0.171869
$253$	3.24068	0.203740
$254$	−2.96382	−0.185967
$255$	−2.13314	−0.133583
$256$	−12.6945	−0.793407
$257$	13.8526	0.864104	0.432052	−	0.901849i	$-0.357790\pi$
$257$	13.8526	0.864104	0.432052	+	0.901849i	$0.357790\pi$
$258$	11.4560	0.713220
$259$	0.594543	0.0369431
$260$	5.85463	0.363089
$261$	−9.82150	−0.607935
$262$	15.9262	0.983923
$263$	2.77629	0.171193	0.0855967	−	0.996330i	$-0.472720\pi$
$263$	2.77629	0.171193	0.0855967	+	0.996330i	$0.472720\pi$
$264$	−2.48870	−0.153169
$265$	−5.72061	−0.351415
$266$	−44.2646	−2.71404
$267$	8.86483	0.542519
$268$	−6.67378	−0.407666
$269$	5.35939	0.326768	0.163384	−	0.986563i	$-0.447759\pi$
$269$	5.35939	0.326768	0.163384	+	0.986563i	$0.447759\pi$
$270$	−2.53888	−0.154511
$271$	−15.0471	−0.914046	−0.457023	−	0.889455i	$-0.651084\pi$
$271$	−15.0471	−0.914046	−0.457023	+	0.889455i	$0.651084\pi$
$272$	2.49282	0.151149
$273$	22.0006	1.33153
$274$	−13.8800	−0.838522
$275$	0.363988	0.0219493
$276$	2.33589	0.140604
$277$	−0.569185	−0.0341990	−0.0170995	−	0.999854i	$-0.505443\pi$
$277$	−0.569185	−0.0341990	−0.0170995	+	0.999854i	$0.505443\pi$
$278$	−5.15650	−0.309266
$279$	3.98647	0.238664
$280$	−30.6733	−1.83308
$281$	−17.1846	−1.02515	−0.512573	−	0.858644i	$-0.671308\pi$
$281$	−17.1846	−1.02515	−0.512573	+	0.858644i	$0.671308\pi$
$282$	0.0197459	0.00117585
$283$	25.3675	1.50794	0.753970	−	0.656909i	$-0.228136\pi$
$283$	25.3675	1.50794	0.753970	+	0.656909i	$0.228136\pi$
$284$	3.47872	0.206424
$285$	−16.9640	−1.00486
$286$	−4.53197	−0.267981
$287$	−0.478888	−0.0282678
$288$	−3.18261	−0.187537
$289$	1.00000	0.0588235
$290$	24.9356	1.46427
$291$	15.4100	0.903351
$292$	−5.98431	−0.350205
$293$	3.63615	0.212426	0.106213	−	0.994343i	$-0.466127\pi$
$293$	3.63615	0.212426	0.106213	+	0.994343i	$0.466127\pi$
$294$	−17.6986	−1.03220
$295$	12.6915	0.738930
$296$	−0.390906	−0.0227210
$297$	−0.809389	−0.0469655
$298$	−12.9078	−0.747729
$299$	18.8359	1.08931
$300$	0.262362	0.0151475
$301$	45.0129	2.59450
$302$	4.56685	0.262792
$303$	11.2279	0.645025
$304$	19.8244	1.13700
$305$	14.3514	0.821759
$306$	1.19021	0.0680396
$307$	23.2288	1.32574	0.662868	−	0.748736i	$-0.269339\pi$
$307$	23.2288	1.32574	0.662868	+	0.748736i	$0.269339\pi$
$308$	−2.20829	−0.125829
$309$	−4.19829	−0.238832
$310$	−10.1212	−0.574843
$311$	11.5818	0.656744	0.328372	−	0.944548i	$-0.393500\pi$
$311$	11.5818	0.656744	0.328372	+	0.944548i	$0.393500\pi$
$312$	−14.4652	−0.818928
$313$	−26.5173	−1.49885	−0.749424	−	0.662090i	$-0.769670\pi$
$313$	−26.5173	−1.49885	−0.749424	+	0.662090i	$0.769670\pi$
$314$	1.19021	0.0671672
$315$	−9.97575	−0.562070
$316$	0.892105	0.0501848
$317$	−25.4271	−1.42813	−0.714065	−	0.700080i	$-0.753148\pi$
$317$	−25.4271	−1.42813	−0.714065	+	0.700080i	$0.753148\pi$
$318$	3.19187	0.178991
$319$	7.94941	0.445082
$320$	18.7153	1.04622
$321$	9.69340	0.541033
$322$	−22.2858	−1.24194
$323$	7.95258	0.442494
$324$	−0.583408	−0.0324116
$325$	2.11562	0.117353
$326$	−15.4314	−0.854663
$327$	−1.70716	−0.0944064
$328$	0.314864	0.0173855
$329$	0.0775856	0.00427744
$330$	2.05494	0.113121
$331$	26.4399	1.45327	0.726634	−	0.687025i	$-0.241084\pi$
$331$	26.4399	1.45327	0.726634	+	0.687025i	$0.241084\pi$
$332$	4.38153	0.240468
$333$	−0.127133	−0.00696683
$334$	−15.6282	−0.855137
$335$	24.4017	1.33320
$336$	11.6578	0.635985
$337$	−4.19685	−0.228617	−0.114308	−	0.993445i	$-0.536465\pi$
$337$	−4.19685	−0.228617	−0.114308	+	0.993445i	$0.536465\pi$
$338$	−10.8686	−0.591176
$339$	7.57675	0.411513
$340$	1.24449	0.0674921
$341$	−3.22660	−0.174730
$342$	9.46522	0.511820
$343$	−36.8052	−1.98729
$344$	−29.5955	−1.59568
$345$	−8.54081	−0.459822
$346$	14.0818	0.757042
$347$	2.68183	0.143968	0.0719840	−	0.997406i	$-0.477067\pi$
$347$	2.68183	0.143968	0.0719840	+	0.997406i	$0.477067\pi$
$348$	5.72994	0.307157
$349$	19.2955	1.03286	0.516432	−	0.856328i	$-0.327260\pi$
$349$	19.2955	1.03286	0.516432	+	0.856328i	$0.327260\pi$
$350$	−2.50310	−0.133796
$351$	−4.70444	−0.251104
$352$	2.57597	0.137300
$353$	4.19349	0.223197	0.111599	−	0.993753i	$-0.464403\pi$
$353$	4.19349	0.223197	0.111599	+	0.993753i	$0.464403\pi$
$354$	−7.08136	−0.376370
$355$	−12.7194	−0.675076
$356$	−5.17182	−0.274106
$357$	4.67655	0.247509
$358$	−3.40739	−0.180086
$359$	−11.0207	−0.581649	−0.290825	−	0.956776i	$-0.593930\pi$
$359$	−11.0207	−0.581649	−0.290825	+	0.956776i	$0.593930\pi$
$360$	6.55896	0.345688
$361$	44.2436	2.32861
$362$	1.07390	0.0564427
$363$	−10.3449	−0.542966
$364$	−12.8353	−0.672753
$365$	21.8807	1.14529
$366$	−8.00750	−0.418559
$367$	−16.6595	−0.869621	−0.434811	−	0.900522i	$-0.643185\pi$
$367$	−16.6595	−0.869621	−0.434811	+	0.900522i	$0.643185\pi$
$368$	9.98091	0.520291
$369$	0.102402	0.00533083
$370$	0.322775	0.0167803
$371$	12.5415	0.651121
$372$	−2.32574	−0.120584
$373$	−15.0562	−0.779579	−0.389789	−	0.920904i	$-0.627452\pi$
$373$	−15.0562	−0.779579	−0.389789	+	0.920904i	$0.627452\pi$
$374$	−0.963340	−0.0498131
$375$	−11.6250	−0.600312
$376$	−0.0510118	−0.00263073
$377$	46.2046	2.37966
$378$	5.56607	0.286288
$379$	−14.3210	−0.735622	−0.367811	−	0.929901i	$-0.619893\pi$
$379$	−14.3210	−0.735622	−0.367811	+	0.929901i	$0.619893\pi$
$380$	9.89693	0.507702
$381$	2.49017	0.127576
$382$	11.5805	0.592511
$383$	2.77782	0.141940	0.0709699	−	0.997478i	$-0.477391\pi$
$383$	2.77782	0.141940	0.0709699	+	0.997478i	$0.477391\pi$
$384$	−4.07718	−0.208063
$385$	8.07426	0.411503
$386$	−17.5524	−0.893394
$387$	−9.62523	−0.489278
$388$	−8.99032	−0.456414
$389$	−10.1381	−0.514020	−0.257010	−	0.966409i	$-0.582737\pi$
$389$	−10.1381	−0.514020	−0.257010	+	0.966409i	$0.582737\pi$
$390$	11.9440	0.604808
$391$	4.00386	0.202484
$392$	45.7226	2.30934
$393$	−13.3810	−0.674984
$394$	1.42909	0.0719967
$395$	−3.26184	−0.164121
$396$	0.472204	0.0237291
$397$	−6.96281	−0.349453	−0.174727	−	0.984617i	$-0.555904\pi$
$397$	−6.96281	−0.349453	−0.174727	+	0.984617i	$0.555904\pi$
$398$	10.7887	0.540788
$399$	37.1907	1.86186
$400$	1.12104	0.0560519
$401$	−8.49338	−0.424139	−0.212070	−	0.977255i	$-0.568020\pi$
$401$	−8.49338	−0.424139	−0.212070	+	0.977255i	$0.568020\pi$
$402$	−13.6151	−0.679061
$403$	−18.7541	−0.934207
$404$	−6.55044	−0.325897
$405$	2.13314	0.105997
$406$	−54.6671	−2.71308
$407$	0.102900	0.00510056
$408$	−3.07479	−0.152225
$409$	−30.5770	−1.51194	−0.755968	−	0.654609i	$-0.772833\pi$
$409$	−30.5770	−1.51194	−0.755968	+	0.654609i	$0.772833\pi$
$410$	−0.259986	−0.0128398
$411$	11.6618	0.575237
$412$	2.44932	0.120669
$413$	−27.8240	−1.36913
$414$	4.76543	0.234208
$415$	−16.0204	−0.786410
$416$	14.9724	0.734082
$417$	4.33244	0.212160
$418$	−7.66104	−0.374714
$419$	−20.6035	−1.00655	−0.503275	−	0.864127i	$-0.667872\pi$
$419$	−20.6035	−1.00655	−0.503275	+	0.864127i	$0.667872\pi$
$420$	5.81993	0.283984
$421$	−16.8585	−0.821631	−0.410816	−	0.911718i	$-0.634756\pi$
$421$	−16.8585	−0.821631	−0.410816	+	0.911718i	$0.634756\pi$
$422$	24.9473	1.21442
$423$	−0.0165903	−0.000806650 0
$424$	−8.24590	−0.400457
$425$	0.449707	0.0218140
$426$	7.09691	0.343847
$427$	−31.4630	−1.52260
$428$	−5.65521	−0.273355
$429$	3.80772	0.183838
$430$	24.4373	1.17847
$431$	2.52837	0.121787	0.0608936	−	0.998144i	$-0.480605\pi$
$431$	2.52837	0.121787	0.0608936	+	0.998144i	$0.480605\pi$
$432$	−2.49282	−0.119936
$433$	13.2264	0.635620	0.317810	−	0.948154i	$-0.397053\pi$
$433$	13.2264	0.635620	0.317810	+	0.948154i	$0.397053\pi$
$434$	22.1889	1.06510
$435$	−20.9506	−1.00451
$436$	0.995973	0.0476985
$437$	31.8411	1.52317
$438$	−12.2085	−0.583347
$439$	20.7044	0.988168	0.494084	−	0.869414i	$-0.335503\pi$
$439$	20.7044	0.988168	0.494084	+	0.869414i	$0.335503\pi$
$440$	−5.30875	−0.253085
$441$	14.8702	0.708103
$442$	−5.59925	−0.266329
$443$	−15.4547	−0.734276	−0.367138	−	0.930167i	$-0.619662\pi$
$443$	−15.4547	−0.734276	−0.367138	+	0.930167i	$0.619662\pi$
$444$	0.0741703	0.00351996
$445$	18.9099	0.896417
$446$	28.5194	1.35043
$447$	10.8450	0.512951
$448$	−41.0302	−1.93850
$449$	−23.0148	−1.08614	−0.543068	−	0.839689i	$-0.682737\pi$
$449$	−23.0148	−1.08614	−0.543068	+	0.839689i	$0.682737\pi$
$450$	0.535244	0.0252316
$451$	−0.0828829	−0.00390280
$452$	−4.42034	−0.207915
$453$	−3.83702	−0.180279
$454$	20.8625	0.979125
$455$	46.9303	2.20013
$456$	−24.4525	−1.14509
$457$	33.3650	1.56075	0.780375	−	0.625312i	$-0.215028\pi$
$457$	33.3650	1.56075	0.780375	+	0.625312i	$0.215028\pi$
$458$	−5.22653	−0.244220
$459$	−1.00000	−0.0466760
$460$	4.98278	0.232323
$461$	−32.6890	−1.52248	−0.761239	−	0.648471i	$-0.775409\pi$
$461$	−32.6890	−1.52248	−0.761239	+	0.648471i	$0.775409\pi$
$462$	−4.50511	−0.209597
$463$	9.42323	0.437935	0.218967	−	0.975732i	$-0.429731\pi$
$463$	9.42323	0.437935	0.218967	+	0.975732i	$0.429731\pi$
$464$	24.4832	1.13660
$465$	8.50370	0.394350
$466$	9.69403	0.449067
$467$	26.7544	1.23804	0.619022	−	0.785374i	$-0.287529\pi$
$467$	26.7544	1.23804	0.619022	+	0.785374i	$0.287529\pi$
$468$	2.74461	0.126869
$469$	−53.4965	−2.47024
$470$	0.0421209	0.00194289
$471$	−1.00000	−0.0460776
$472$	18.2940	0.842052
$473$	7.79055	0.358210
$474$	1.81998	0.0835943
$475$	3.57633	0.164093
$476$	−2.72834	−0.125053
$477$	−2.68178	−0.122790
$478$	−17.9500	−0.821014
$479$	19.9670	0.912315	0.456158	−	0.889899i	$-0.349225\pi$
$479$	19.9670	0.912315	0.456158	+	0.889899i	$0.349225\pi$
$480$	−6.78896	−0.309872
$481$	0.598088	0.0272705
$482$	−15.9488	−0.726446
$483$	18.7243	0.851985
$484$	6.03529	0.274331
$485$	32.8717	1.49263
$486$	−1.19021	−0.0539889
$487$	−31.6470	−1.43406	−0.717031	−	0.697042i	$-0.754499\pi$
$487$	−31.6470	−1.43406	−0.717031	+	0.697042i	$0.754499\pi$
$488$	20.6867	0.936441
$489$	12.9653	0.586310
$490$	−37.7535	−1.70553
$491$	−2.62290	−0.118370	−0.0591850	−	0.998247i	$-0.518850\pi$
$491$	−2.62290	−0.118370	−0.0591850	+	0.998247i	$0.518850\pi$
$492$	−0.0597420	−0.00269338
$493$	9.82150	0.442338
$494$	−44.5285	−2.00343
$495$	−1.72654	−0.0776023
$496$	−9.93754	−0.446209
$497$	27.8852	1.25082
$498$	8.93873	0.400554
$499$	33.3933	1.49489	0.747444	−	0.664325i	$-0.231281\pi$
$499$	33.3933	1.49489	0.747444	+	0.664325i	$0.231281\pi$
$500$	6.78212	0.303305
$501$	13.1307	0.586635
$502$	13.6461	0.609053
$503$	−7.79540	−0.347580	−0.173790	−	0.984783i	$-0.555601\pi$
$503$	−7.79540	−0.347580	−0.173790	+	0.984783i	$0.555601\pi$
$504$	−14.3794	−0.640510
$505$	23.9507	1.06579
$506$	−3.85708	−0.171468
$507$	9.13172	0.405554
$508$	−1.45279	−0.0644570
$509$	−6.17931	−0.273893	−0.136946	−	0.990578i	$-0.543729\pi$
$509$	−6.17931	−0.273893	−0.136946	+	0.990578i	$0.543729\pi$
$510$	2.53888	0.112423
$511$	−47.9698	−2.12206
$512$	23.2635	1.02811
$513$	−7.95258	−0.351115
$514$	−16.4875	−0.727233
$515$	−8.95555	−0.394629
$516$	5.61543	0.247206
$517$	0.0134280	0.000590565 0
$518$	−0.707629	−0.0310914
$519$	−11.8314	−0.519341
$520$	−30.8562	−1.35313
$521$	−0.318751	−0.0139647	−0.00698237	−	0.999976i	$-0.502223\pi$
$521$	−0.318751	−0.0139647	−0.00698237	+	0.999976i	$0.502223\pi$
$522$	11.6896	0.511640
$523$	−21.1204	−0.923531	−0.461765	−	0.887002i	$-0.652784\pi$
$523$	−21.1204	−0.923531	−0.461765	+	0.887002i	$0.652784\pi$
$524$	7.80660	0.341033
$525$	2.10308	0.0917858
$526$	−3.30436	−0.144077
$527$	−3.98647	−0.173653
$528$	2.01766	0.0878074
$529$	−6.96907	−0.303003
$530$	6.80871	0.295752
$531$	5.94969	0.258195
$532$	−21.6974	−0.940699
$533$	−0.481743	−0.0208666
$534$	−10.5510	−0.456586
$535$	20.6774	0.893962
$536$	35.1735	1.51926
$537$	2.86286	0.123541
$538$	−6.37878	−0.275009
$539$	−12.0357	−0.518416
$540$	−1.24449	−0.0535544
$541$	−20.9939	−0.902599	−0.451300	−	0.892373i	$-0.649039\pi$
$541$	−20.9939	−0.902599	−0.451300	+	0.892373i	$0.649039\pi$
$542$	17.9092	0.769264
$543$	−0.902276	−0.0387204
$544$	3.18261	0.136453
$545$	−3.64162	−0.155990
$546$	−26.1852	−1.12062
$547$	−25.3682	−1.08466	−0.542332	−	0.840164i	$-0.682459\pi$
$547$	−25.3682	−1.08466	−0.542332	+	0.840164i	$0.682459\pi$
$548$	−6.80362	−0.290636
$549$	6.72783	0.287137
$550$	−0.433220	−0.0184726
$551$	78.1063	3.32744
$552$	−12.3110	−0.523993
$553$	7.15104	0.304093
$554$	0.677448	0.0287820
$555$	−0.271192	−0.0115115
$556$	−2.52758	−0.107193
$557$	24.6168	1.04305	0.521523	−	0.853237i	$-0.325364\pi$
$557$	24.6168	1.04305	0.521523	+	0.853237i	$0.325364\pi$
$558$	−4.74472	−0.200860
$559$	45.2813	1.91519
$560$	24.8677	1.05085
$561$	0.809389	0.0341724
$562$	20.4532	0.862766
$563$	−33.9123	−1.42924	−0.714618	−	0.699515i	$-0.753399\pi$
$563$	−33.9123	−1.42924	−0.714618	+	0.699515i	$0.753399\pi$
$564$	0.00967894	0.000407557 0
$565$	16.1623	0.679952
$566$	−30.1925	−1.26909
$567$	−4.67655	−0.196397
$568$	−18.3342	−0.769287
$569$	1.21085	0.0507615	0.0253807	−	0.999678i	$-0.491920\pi$
$569$	1.21085	0.0507615	0.0253807	+	0.999678i	$0.491920\pi$
$570$	20.1907	0.845693
$571$	−28.5217	−1.19360	−0.596798	−	0.802392i	$-0.703560\pi$
$571$	−28.5217	−1.19360	−0.596798	+	0.802392i	$0.703560\pi$
$572$	−2.22145	−0.0928837
$573$	−9.72984	−0.406470
$574$	0.569975	0.0237903
$575$	1.80056	0.0750887
$576$	8.77360	0.365567
$577$	29.2087	1.21598	0.607988	−	0.793946i	$-0.291977\pi$
$577$	29.2087	1.21598	0.607988	+	0.793946i	$0.291977\pi$
$578$	−1.19021	−0.0495061
$579$	14.7474	0.612879
$580$	12.2228	0.507523
$581$	35.1220	1.45711
$582$	−18.3411	−0.760263
$583$	2.17060	0.0898971
$584$	31.5397	1.30512
$585$	−10.0352	−0.414906
$586$	−4.32777	−0.178778
$587$	42.5170	1.75486	0.877431	−	0.479703i	$-0.159255\pi$
$587$	42.5170	1.75486	0.877431	+	0.479703i	$0.159255\pi$
$588$	−8.67537	−0.357766
$589$	−31.7027	−1.30629
$590$	−15.1055	−0.621885
$591$	−1.20071	−0.0493906
$592$	0.316919	0.0130253
$593$	−1.46870	−0.0603124	−0.0301562	−	0.999545i	$-0.509600\pi$
$593$	−1.46870	−0.0603124	−0.0301562	+	0.999545i	$0.509600\pi$
$594$	0.963340	0.0395263
$595$	9.97575	0.408966
$596$	−6.32706	−0.259167
$597$	−9.06454	−0.370987
$598$	−22.4186	−0.916767
$599$	45.1844	1.84618	0.923091	−	0.384580i	$-0.125654\pi$
$599$	45.1844	1.84618	0.923091	+	0.384580i	$0.125654\pi$
$600$	−1.38275	−0.0564507
$601$	−5.26942	−0.214944	−0.107472	−	0.994208i	$-0.534276\pi$
$601$	−5.26942	−0.214944	−0.107472	+	0.994208i	$0.534276\pi$
$602$	−53.5746	−2.18354
$603$	11.4393	0.465845
$604$	2.23855	0.0910852
$605$	−22.0671	−0.897156
$606$	−13.3635	−0.542855
$607$	7.24115	0.293909	0.146955	−	0.989143i	$-0.453053\pi$
$607$	7.24115	0.293909	0.146955	+	0.989143i	$0.453053\pi$
$608$	25.3100	1.02645
$609$	45.9308	1.86121
$610$	−17.0811	−0.691595
$611$	0.0780482	0.00315749
$612$	0.583408	0.0235829
$613$	9.20295	0.371704	0.185852	−	0.982578i	$-0.440496\pi$
$613$	9.20295	0.371704	0.185852	+	0.982578i	$0.440496\pi$
$614$	−27.6470	−1.11574
$615$	0.218438	0.00880825
$616$	11.6385	0.468930
$617$	4.26746	0.171802	0.0859008	−	0.996304i	$-0.472623\pi$
$617$	4.26746	0.171802	0.0859008	+	0.996304i	$0.472623\pi$
$618$	4.99683	0.201002
$619$	−0.00223242	−8.97284e−5 0	−4.48642e−5	−	1.00000i	$-0.500014\pi$
$619$	−0.00223242	−8.97284e−5 0	−4.48642e−5		1.00000i	$0.500014\pi$
$620$	−4.96113	−0.199244
$621$	−4.00386	−0.160670
$622$	−13.7847	−0.552718
$623$	−41.4569	−1.66093
$624$	11.7273	0.469468
$625$	−22.5492	−0.901969
$626$	31.5611	1.26144
$627$	6.43673	0.257058
$628$	0.583408	0.0232805
$629$	0.127133	0.00506911
$630$	11.8732	0.473040
$631$	−35.2059	−1.40152	−0.700762	−	0.713395i	$-0.747157\pi$
$631$	−35.2059	−1.40152	−0.700762	+	0.713395i	$0.747157\pi$
$632$	−4.70174	−0.187025
$633$	−20.9605	−0.833104
$634$	30.2635	1.20192
$635$	5.31190	0.210796
$636$	1.56457	0.0620393
$637$	−69.9557	−2.77175
$638$	−9.46144	−0.374582
$639$	−5.96276	−0.235883
$640$	−8.69720	−0.343787
$641$	−4.94147	−0.195176	−0.0975882	−	0.995227i	$-0.531113\pi$
$641$	−4.94147	−0.195176	−0.0975882	+	0.995227i	$0.531113\pi$
$642$	−11.5371	−0.455335
$643$	−5.49445	−0.216680	−0.108340	−	0.994114i	$-0.534554\pi$
$643$	−5.49445	−0.216680	−0.108340	+	0.994114i	$0.534554\pi$
$644$	−10.9239	−0.430462
$645$	−20.5320	−0.808445
$646$	−9.46522	−0.372404
$647$	−18.4469	−0.725223	−0.362611	−	0.931940i	$-0.618115\pi$
$647$	−18.4469	−0.725223	−0.362611	+	0.931940i	$0.618115\pi$
$648$	3.07479	0.120789
$649$	−4.81561	−0.189029
$650$	−2.51802	−0.0987649
$651$	−18.6429	−0.730674
$652$	−7.56404	−0.296231
$653$	−33.6277	−1.31595	−0.657977	−	0.753038i	$-0.728588\pi$
$653$	−33.6277	−1.31595	−0.657977	+	0.753038i	$0.728588\pi$
$654$	2.03188	0.0794527
$655$	−28.5436	−1.11529
$656$	−0.255269	−0.00996659
$657$	10.2575	0.400183
$658$	−0.0923430	−0.00359990
$659$	29.3761	1.14433	0.572165	−	0.820139i	$-0.306104\pi$
$659$	29.3761	1.14433	0.572165	+	0.820139i	$0.306104\pi$
$660$	1.00728	0.0392082
$661$	27.2530	1.06002	0.530010	−	0.847992i	$-0.322188\pi$
$661$	27.2530	1.06002	0.530010	+	0.847992i	$0.322188\pi$
$662$	−31.4689	−1.22308
$663$	4.70444	0.182705
$664$	−23.0924	−0.896158
$665$	79.3330	3.07640
$666$	0.151314	0.00586331
$667$	39.3240	1.52263
$668$	−7.66054	−0.296395
$669$	−23.9617	−0.926413
$670$	−29.0430	−1.12203
$671$	−5.44543	−0.210218
$672$	14.8836	0.574149
$673$	29.0146	1.11843	0.559216	−	0.829022i	$-0.311102\pi$
$673$	29.0146	1.11843	0.559216	+	0.829022i	$0.311102\pi$
$674$	4.99512	0.192405
$675$	−0.449707	−0.0173092
$676$	−5.32752	−0.204905
$677$	20.7791	0.798607	0.399303	−	0.916819i	$-0.369252\pi$
$677$	20.7791	0.798607	0.399303	+	0.916819i	$0.369252\pi$
$678$	−9.01790	−0.346330
$679$	−72.0657	−2.76563
$680$	−6.55896	−0.251525
$681$	−17.5285	−0.671692
$682$	3.84032	0.147054
$683$	−7.05714	−0.270034	−0.135017	−	0.990843i	$-0.543109\pi$
$683$	−7.05714	−0.270034	−0.135017	+	0.990843i	$0.543109\pi$
$684$	4.63960	0.177400
$685$	24.8764	0.950477
$686$	43.8058	1.67251
$687$	4.39128	0.167538
$688$	23.9939	0.914761
$689$	12.6163	0.480641
$690$	10.1653	0.386988
$691$	−19.9888	−0.760412	−0.380206	−	0.924902i	$-0.624147\pi$
$691$	−19.9888	−0.760412	−0.380206	+	0.924902i	$0.624147\pi$
$692$	6.90253	0.262395
$693$	3.78515	0.143786
$694$	−3.19193	−0.121164
$695$	9.24170	0.350558
$696$	−30.1990	−1.14469
$697$	−0.102402	−0.00387875
$698$	−22.9656	−0.869261
$699$	−8.14483	−0.308066
$700$	−1.22695	−0.0463744
$701$	2.52432	0.0953423	0.0476711	−	0.998863i	$-0.484820\pi$
$701$	2.52432	0.0953423	0.0476711	+	0.998863i	$0.484820\pi$
$702$	5.59925	0.211330
$703$	1.01103	0.0381319
$704$	−7.10126	−0.267639
$705$	−0.0353896	−0.00133285
$706$	−4.99112	−0.187843
$707$	−52.5078	−1.97476
$708$	−3.47110	−0.130452
$709$	−13.8953	−0.521851	−0.260925	−	0.965359i	$-0.584028\pi$
$709$	−13.8953	−0.521851	−0.260925	+	0.965359i	$0.584028\pi$
$710$	15.1387	0.568146
$711$	−1.52913	−0.0573467
$712$	27.2575	1.02152
$713$	−15.9613	−0.597755
$714$	−5.56607	−0.208305
$715$	8.12240	0.303761
$716$	−1.67021	−0.0624188
$717$	15.0814	0.563226
$718$	13.1169	0.489518
$719$	14.8706	0.554579	0.277290	−	0.960786i	$-0.410564\pi$
$719$	14.8706	0.554579	0.277290	+	0.960786i	$0.410564\pi$
$720$	−5.31754	−0.198173
$721$	19.6335	0.731191
$722$	−52.6590	−1.95977
$723$	13.4000	0.498351
$724$	0.526395	0.0195633
$725$	4.41679	0.164036
$726$	12.3126	0.456962
$727$	51.7574	1.91957	0.959787	−	0.280728i	$-0.0905760\pi$
$727$	51.7574	1.91957	0.959787	+	0.280728i	$0.0905760\pi$
$728$	67.6471	2.50717
$729$	1.00000	0.0370370
$730$	−26.0426	−0.963878
$731$	9.62523	0.356002
$732$	−3.92507	−0.145075
$733$	26.9866	0.996773	0.498386	−	0.866955i	$-0.333926\pi$
$733$	26.9866	0.996773	0.498386	+	0.866955i	$0.333926\pi$
$734$	19.8283	0.731876
$735$	31.7202	1.17002
$736$	12.7427	0.469704
$737$	−9.25885	−0.341054
$738$	−0.121879	−0.00448644
$739$	−48.2515	−1.77496	−0.887480	−	0.460845i	$-0.847546\pi$
$739$	−48.2515	−1.77496	−0.887480	+	0.460845i	$0.847546\pi$
$740$	0.158216	0.00581612
$741$	37.4124	1.37438
$742$	−14.9270	−0.547986
$743$	−24.0227	−0.881309	−0.440654	−	0.897677i	$-0.645254\pi$
$743$	−24.0227	−0.881309	−0.440654	+	0.897677i	$0.645254\pi$
$744$	12.2575	0.449384
$745$	23.1339	0.847562
$746$	17.9199	0.656096
$747$	−7.51023	−0.274785
$748$	−0.472204	−0.0172655
$749$	−45.3317	−1.65638
$750$	13.8361	0.505225
$751$	52.6557	1.92143	0.960716	−	0.277533i	$-0.0895168\pi$
$751$	52.6557	1.92143	0.960716	+	0.277533i	$0.0895168\pi$
$752$	0.0413567	0.00150812
$753$	−11.4653	−0.417818
$754$	−54.9930	−2.00273
$755$	−8.18490	−0.297879
$756$	2.72834	0.0992287
$757$	−37.2689	−1.35456	−0.677280	−	0.735725i	$-0.736841\pi$
$757$	−37.2689	−1.35456	−0.677280	+	0.735725i	$0.736841\pi$
$758$	17.0450	0.619102
$759$	3.24068	0.117629
$760$	−52.1607	−1.89207
$761$	−47.3740	−1.71731	−0.858653	−	0.512557i	$-0.828698\pi$
$761$	−47.3740	−1.71731	−0.858653	+	0.512557i	$0.828698\pi$
$762$	−2.96382	−0.107368
$763$	7.98364	0.289027
$764$	5.67647	0.205367
$765$	−2.13314	−0.0771239
$766$	−3.30617	−0.119457
$767$	−27.9899	−1.01066
$768$	−12.6945	−0.458074
$769$	−7.09099	−0.255707	−0.127854	−	0.991793i	$-0.540809\pi$
$769$	−7.09099	−0.255707	−0.127854	+	0.991793i	$0.540809\pi$
$770$	−9.61004	−0.346322
$771$	13.8526	0.498891
$772$	−8.60373	−0.309655
$773$	28.2236	1.01513	0.507566	−	0.861613i	$-0.330545\pi$
$773$	28.2236	1.01513	0.507566	+	0.861613i	$0.330545\pi$
$774$	11.4560	0.411778
$775$	−1.79274	−0.0643971
$776$	47.3825	1.70093
$777$	0.594543	0.0213291
$778$	12.0664	0.432601
$779$	−0.814359	−0.0291774
$780$	5.85463	0.209630
$781$	4.82619	0.172695
$782$	−4.76543	−0.170411
$783$	−9.82150	−0.350992
$784$	−37.0686	−1.32388
$785$	−2.13314	−0.0761351
$786$	15.9262	0.568068
$787$	23.8491	0.850128	0.425064	−	0.905163i	$-0.360252\pi$
$787$	23.8491	0.850128	0.425064	+	0.905163i	$0.360252\pi$
$788$	0.700504	0.0249544
$789$	2.77629	0.0988385
$790$	3.88227	0.138125
$791$	−35.4331	−1.25986
$792$	−2.48870	−0.0884321
$793$	−31.6506	−1.12395
$794$	8.28718	0.294101
$795$	−5.72061	−0.202889
$796$	5.28833	0.187440
$797$	−23.0000	−0.814702	−0.407351	−	0.913272i	$-0.633547\pi$
$797$	−23.0000	−0.814702	−0.407351	+	0.913272i	$0.633547\pi$
$798$	−44.2646	−1.56695
$799$	0.0165903	0.000586924 0
$800$	1.43124	0.0506020
$801$	8.86483	0.313224
$802$	10.1089	0.356957
$803$	−8.30231	−0.292982
$804$	−6.67378	−0.235366
$805$	39.9416	1.40776
$806$	22.3212	0.786232
$807$	5.35939	0.188659
$808$	34.5234	1.21453
$809$	−22.7999	−0.801603	−0.400801	−	0.916165i	$-0.631268\pi$
$809$	−22.7999	−0.801603	−0.400801	+	0.916165i	$0.631268\pi$
$810$	−2.53888	−0.0892071
$811$	−25.2555	−0.886840	−0.443420	−	0.896314i	$-0.646235\pi$
$811$	−25.2555	−0.886840	−0.443420	+	0.896314i	$0.646235\pi$
$812$	−26.7964	−0.940369
$813$	−15.0471	−0.527725
$814$	−0.122472	−0.00429264
$815$	27.6568	0.968774
$816$	2.49282	0.0872661
$817$	76.5454	2.67799
$818$	36.3930	1.27245
$819$	22.0006	0.768762
$820$	−0.127438	−0.00445034
$821$	−12.8242	−0.447568	−0.223784	−	0.974639i	$-0.571841\pi$
$821$	−12.8242	−0.447568	−0.223784	+	0.974639i	$0.571841\pi$
$822$	−13.8800	−0.484121
$823$	5.79647	0.202052	0.101026	−	0.994884i	$-0.467787\pi$
$823$	5.79647	0.202052	0.101026	+	0.994884i	$0.467787\pi$
$824$	−12.9089	−0.449701
$825$	0.363988	0.0126724
$826$	33.1164	1.15227
$827$	−21.3477	−0.742332	−0.371166	−	0.928566i	$-0.621042\pi$
$827$	−21.3477	−0.742332	−0.371166	+	0.928566i	$0.621042\pi$
$828$	2.33589	0.0811777
$829$	48.1308	1.67165	0.835827	−	0.548993i	$-0.184989\pi$
$829$	48.1308	1.67165	0.835827	+	0.548993i	$0.184989\pi$
$830$	19.0676	0.661845
$831$	−0.569185	−0.0197448
$832$	−41.2748	−1.43095
$833$	−14.8702	−0.515220
$834$	−5.15650	−0.178555
$835$	28.0096	0.969311
$836$	−3.75524	−0.129878
$837$	3.98647	0.137792
$838$	24.5225	0.847115
$839$	−4.41215	−0.152324	−0.0761621	−	0.997095i	$-0.524267\pi$
$839$	−4.41215	−0.152324	−0.0761621	+	0.997095i	$0.524267\pi$
$840$	−30.6733	−1.05833
$841$	67.4618	2.32627
$842$	20.0651	0.691487
$843$	−17.1846	−0.591868
$844$	12.2285	0.420923
$845$	19.4793	0.670107
$846$	0.0197459	0.000678879 0
$847$	48.3784	1.66230
$848$	6.68519	0.229570
$849$	25.3675	0.870610
$850$	−0.535244	−0.0183587
$851$	0.509022	0.0174491
$852$	3.47872	0.119179
$853$	17.4515	0.597529	0.298765	−	0.954327i	$-0.403425\pi$
$853$	17.4515	0.597529	0.298765	+	0.954327i	$0.403425\pi$
$854$	37.4475	1.28143
$855$	−16.9640	−0.580156
$856$	29.8052	1.01872
$857$	−19.2664	−0.658127	−0.329063	−	0.944308i	$-0.606733\pi$
$857$	−19.2664	−0.658127	−0.329063	+	0.944308i	$0.606733\pi$
$858$	−4.53197	−0.154719
$859$	−3.87735	−0.132294	−0.0661468	−	0.997810i	$-0.521071\pi$
$859$	−3.87735	−0.132294	−0.0661468	+	0.997810i	$0.521071\pi$
$860$	11.9785	0.408464
$861$	−0.478888	−0.0163204
$862$	−3.00928	−0.102496
$863$	49.7422	1.69324	0.846622	−	0.532194i	$-0.178632\pi$
$863$	49.7422	1.69324	0.846622	+	0.532194i	$0.178632\pi$
$864$	−3.18261	−0.108275
$865$	−25.2380	−0.858119
$866$	−15.7421	−0.534940
$867$	1.00000	0.0339618
$868$	10.8764	0.369170
$869$	1.23766	0.0419847
$870$	24.9356	0.845396
$871$	−53.8155	−1.82347
$872$	−5.24917	−0.177759
$873$	15.4100	0.521550
$874$	−37.8975	−1.28190
$875$	54.3649	1.83787
$876$	−5.98431	−0.202191
$877$	41.4394	1.39931	0.699655	−	0.714481i	$-0.253337\pi$
$877$	41.4394	1.39931	0.699655	+	0.714481i	$0.253337\pi$
$878$	−24.6425	−0.831645
$879$	3.63615	0.122644
$880$	4.30395	0.145086
$881$	43.8564	1.47756	0.738779	−	0.673947i	$-0.235403\pi$
$881$	43.8564	1.47756	0.738779	+	0.673947i	$0.235403\pi$
$882$	−17.6986	−0.595942
$883$	−36.0506	−1.21320	−0.606599	−	0.795008i	$-0.707467\pi$
$883$	−36.0506	−1.21320	−0.606599	+	0.795008i	$0.707467\pi$
$884$	−2.74461	−0.0923111
$885$	12.6915	0.426621
$886$	18.3943	0.617969
$887$	30.6445	1.02894	0.514470	−	0.857508i	$-0.327989\pi$
$887$	30.6445	1.02894	0.514470	+	0.857508i	$0.327989\pi$
$888$	−0.390906	−0.0131180
$889$	−11.6454	−0.390575
$890$	−22.5067	−0.754428
$891$	−0.809389	−0.0271156
$892$	13.9794	0.468066
$893$	0.131936	0.00441507
$894$	−12.9078	−0.431701
$895$	6.10688	0.204130
$896$	19.0671	0.636989
$897$	18.8359	0.628913
$898$	27.3924	0.914096
$899$	−39.1531	−1.30583
$900$	0.262362	0.00874542
$901$	2.68178	0.0893430
$902$	0.0986478	0.00328461
$903$	45.0129	1.49794
$904$	23.2969	0.774844
$905$	−1.92468	−0.0639786
$906$	4.56685	0.151723
$907$	35.9464	1.19358	0.596790	−	0.802397i	$-0.296442\pi$
$907$	35.9464	1.19358	0.596790	+	0.802397i	$0.296442\pi$
$908$	10.2262	0.339370
$909$	11.2279	0.372405
$910$	−55.8567	−1.85163
$911$	2.03492	0.0674197	0.0337099	−	0.999432i	$-0.489268\pi$
$911$	2.03492	0.0674197	0.0337099	+	0.999432i	$0.489268\pi$
$912$	19.8244	0.656450
$913$	6.07870	0.201176
$914$	−39.7113	−1.31353
$915$	14.3514	0.474443
$916$	−2.56191	−0.0846478
$917$	62.5771	2.06648
$918$	1.19021	0.0392827
$919$	16.2327	0.535466	0.267733	−	0.963493i	$-0.413726\pi$
$919$	16.2327	0.535466	0.267733	+	0.963493i	$0.413726\pi$
$920$	−26.2612	−0.865806
$921$	23.2288	0.765414
$922$	38.9067	1.28132
$923$	28.0514	0.923323
$924$	−2.20829	−0.0726473
$925$	0.0571724	0.00187982
$926$	−11.2156	−0.368567
$927$	−4.19829	−0.137890
$928$	31.2580	1.02609
$929$	59.3168	1.94612	0.973060	−	0.230551i	$-0.0740528\pi$
$929$	59.3168	1.94612	0.973060	+	0.230551i	$0.0740528\pi$
$930$	−10.1212	−0.331886
$931$	−118.256	−3.87569
$932$	4.75176	0.155649
$933$	11.5818	0.379171
$934$	−31.8432	−1.04194
$935$	1.72654	0.0564639
$936$	−14.4652	−0.472808
$937$	−15.2535	−0.498309	−0.249155	−	0.968464i	$-0.580153\pi$
$937$	−15.2535	−0.498309	−0.249155	+	0.968464i	$0.580153\pi$
$938$	63.6719	2.07896
$939$	−26.5173	−0.865361
$940$	0.0206466	0.000673416 0
$941$	36.5133	1.19030	0.595149	−	0.803615i	$-0.297093\pi$
$941$	36.5133	1.19030	0.595149	+	0.803615i	$0.297093\pi$
$942$	1.19021	0.0387790
$943$	−0.410003	−0.0133515
$944$	−14.8315	−0.482724
$945$	−9.97575	−0.324511
$946$	−9.27237	−0.301471
$947$	21.7705	0.707446	0.353723	−	0.935350i	$-0.384916\pi$
$947$	21.7705	0.707446	0.353723	+	0.935350i	$0.384916\pi$
$948$	0.892105	0.0289742
$949$	−48.2558	−1.56645
$950$	−4.25657	−0.138101
$951$	−25.4271	−0.824531
$952$	14.3794	0.466040
$953$	12.1061	0.392156	0.196078	−	0.980588i	$-0.437179\pi$
$953$	12.1061	0.392156	0.196078	+	0.980588i	$0.437179\pi$
$954$	3.19187	0.103341
$955$	−20.7551	−0.671620
$956$	−8.79862	−0.284568
$957$	7.94941	0.256968
$958$	−23.7649	−0.767807
$959$	−54.5373	−1.76110
$960$	18.7153	0.604035
$961$	−15.1081	−0.487357
$962$	−0.711848	−0.0229509
$963$	9.69340	0.312365
$964$	−7.81767	−0.251790
$965$	31.4582	1.01268
$966$	−22.2858	−0.717033
$967$	16.2061	0.521154	0.260577	−	0.965453i	$-0.416087\pi$
$967$	16.2061	0.521154	0.260577	+	0.965453i	$0.416087\pi$
$968$	−31.8084	−1.02236
$969$	7.95258	0.255474
$970$	−39.1242	−1.25620
$971$	2.48044	0.0796012	0.0398006	−	0.999208i	$-0.487328\pi$
$971$	2.48044	0.0796012	0.0398006	+	0.999208i	$0.487328\pi$
$972$	−0.583408	−0.0187128
$973$	−20.2609	−0.649534
$974$	37.6664	1.20691
$975$	2.11562	0.0677539
$976$	−16.7713	−0.536835
$977$	−16.2029	−0.518378	−0.259189	−	0.965827i	$-0.583455\pi$
$977$	−16.2029	−0.518378	−0.259189	+	0.965827i	$0.583455\pi$
$978$	−15.4314	−0.493440
$979$	−7.17510	−0.229317
$980$	−18.5058	−0.591146
$981$	−1.70716	−0.0545055
$982$	3.12180	0.0996205
$983$	15.6511	0.499194	0.249597	−	0.968350i	$-0.419702\pi$
$983$	15.6511	0.499194	0.249597	+	0.968350i	$0.419702\pi$
$984$	0.314864	0.0100375
$985$	−2.56129	−0.0816094
$986$	−11.6896	−0.372273
$987$	0.0775856	0.00246958
$988$	−21.8267	−0.694400
$989$	38.5381	1.22544
$990$	2.05494	0.0653103
$991$	57.5921	1.82947	0.914737	−	0.404051i	$-0.132398\pi$
$991$	57.5921	1.82947	0.914737	+	0.404051i	$0.132398\pi$
$992$	−12.6874	−0.402824
$993$	26.4399	0.839045
$994$	−33.1891	−1.05269
$995$	−19.3360	−0.612991
$996$	4.38153	0.138834
$997$	26.5685	0.841432	0.420716	−	0.907193i	$-0.361779\pi$
$997$	26.5685	0.841432	0.420716	+	0.907193i	$0.361779\pi$
$998$	−39.7449	−1.25810
$999$	−0.127133	−0.00402230

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.h.1.18	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.h.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-1.19021 q^{2} +1.00000 q^{3} -0.583408 q^{4} +2.13314 q^{5} -1.19021 q^{6} -4.67655 q^{7} +3.07479 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.19021 q^{2} +1.00000 q^{3} -0.583408 q^{4} +2.13314 q^{5} -1.19021 q^{6} -4.67655 q^{7} +3.07479 q^{8} +1.00000 q^{9} -2.53888 q^{10} -0.809389 q^{11} -0.583408 q^{12} -4.70444 q^{13} +5.56607 q^{14} +2.13314 q^{15} -2.49282 q^{16} -1.00000 q^{17} -1.19021 q^{18} -7.95258 q^{19} -1.24449 q^{20} -4.67655 q^{21} +0.963340 q^{22} -4.00386 q^{23} +3.07479 q^{24} -0.449707 q^{25} +5.59925 q^{26} +1.00000 q^{27} +2.72834 q^{28} -9.82150 q^{29} -2.53888 q^{30} +3.98647 q^{31} -3.18261 q^{32} -0.809389 q^{33} +1.19021 q^{34} -9.97575 q^{35} -0.583408 q^{36} -0.127133 q^{37} +9.46522 q^{38} -4.70444 q^{39} +6.55896 q^{40} +0.102402 q^{41} +5.56607 q^{42} -9.62523 q^{43} +0.472204 q^{44} +2.13314 q^{45} +4.76543 q^{46} -0.0165903 q^{47} -2.49282 q^{48} +14.8702 q^{49} +0.535244 q^{50} -1.00000 q^{51} +2.74461 q^{52} -2.68178 q^{53} -1.19021 q^{54} -1.72654 q^{55} -14.3794 q^{56} -7.95258 q^{57} +11.6896 q^{58} +5.94969 q^{59} -1.24449 q^{60} +6.72783 q^{61} -4.74472 q^{62} -4.67655 q^{63} +8.77360 q^{64} -10.0352 q^{65} +0.963340 q^{66} +11.4393 q^{67} +0.583408 q^{68} -4.00386 q^{69} +11.8732 q^{70} -5.96276 q^{71} +3.07479 q^{72} +10.2575 q^{73} +0.151314 q^{74} -0.449707 q^{75} +4.63960 q^{76} +3.78515 q^{77} +5.59925 q^{78} -1.52913 q^{79} -5.31754 q^{80} +1.00000 q^{81} -0.121879 q^{82} -7.51023 q^{83} +2.72834 q^{84} -2.13314 q^{85} +11.4560 q^{86} -9.82150 q^{87} -2.48870 q^{88} +8.86483 q^{89} -2.53888 q^{90} +22.0006 q^{91} +2.33589 q^{92} +3.98647 q^{93} +0.0197459 q^{94} -16.9640 q^{95} -3.18261 q^{96} +15.4100 q^{97} -17.6986 q^{98} -0.809389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * q^99

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