LMFDB - Embedded newform 8007.2.a.h.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.42729 q^{2} +1.00000 q^{3} +3.89172 q^{4} -3.95283 q^{5} -2.42729 q^{6} -4.02222 q^{7} -4.59173 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.42729 q^{2} +1.00000 q^{3} +3.89172 q^{4} -3.95283 q^{5} -2.42729 q^{6} -4.02222 q^{7} -4.59173 q^{8} +1.00000 q^{9} +9.59464 q^{10} +0.425499 q^{11} +3.89172 q^{12} -2.68690 q^{13} +9.76307 q^{14} -3.95283 q^{15} +3.36202 q^{16} -1.00000 q^{17} -2.42729 q^{18} -1.90370 q^{19} -15.3833 q^{20} -4.02222 q^{21} -1.03281 q^{22} +4.66660 q^{23} -4.59173 q^{24} +10.6248 q^{25} +6.52186 q^{26} +1.00000 q^{27} -15.6533 q^{28} -2.85996 q^{29} +9.59464 q^{30} -7.16013 q^{31} +1.02289 q^{32} +0.425499 q^{33} +2.42729 q^{34} +15.8991 q^{35} +3.89172 q^{36} -8.38342 q^{37} +4.62082 q^{38} -2.68690 q^{39} +18.1503 q^{40} +2.91607 q^{41} +9.76307 q^{42} -5.62342 q^{43} +1.65592 q^{44} -3.95283 q^{45} -11.3272 q^{46} -1.96436 q^{47} +3.36202 q^{48} +9.17822 q^{49} -25.7895 q^{50} -1.00000 q^{51} -10.4566 q^{52} -4.44469 q^{53} -2.42729 q^{54} -1.68192 q^{55} +18.4689 q^{56} -1.90370 q^{57} +6.94193 q^{58} -12.6563 q^{59} -15.3833 q^{60} -5.35291 q^{61} +17.3797 q^{62} -4.02222 q^{63} -9.20688 q^{64} +10.6208 q^{65} -1.03281 q^{66} -4.28635 q^{67} -3.89172 q^{68} +4.66660 q^{69} -38.5917 q^{70} +4.91935 q^{71} -4.59173 q^{72} -4.26972 q^{73} +20.3490 q^{74} +10.6248 q^{75} -7.40866 q^{76} -1.71145 q^{77} +6.52186 q^{78} -14.4808 q^{79} -13.2895 q^{80} +1.00000 q^{81} -7.07814 q^{82} -2.68930 q^{83} -15.6533 q^{84} +3.95283 q^{85} +13.6497 q^{86} -2.85996 q^{87} -1.95378 q^{88} -2.16277 q^{89} +9.59464 q^{90} +10.8073 q^{91} +18.1611 q^{92} -7.16013 q^{93} +4.76806 q^{94} +7.52500 q^{95} +1.02289 q^{96} +6.45269 q^{97} -22.2782 q^{98} +0.425499 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.42729	−1.71635	−0.858175	−	0.513357i	$-0.828402\pi$
$2$	−2.42729	−1.71635	−0.858175	+	0.513357i	$0.828402\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.89172	1.94586
$5$	−3.95283	−1.76776	−0.883879	−	0.467715i	$-0.845077\pi$
$5$	−3.95283	−1.76776	−0.883879	+	0.467715i	$0.845077\pi$
$6$	−2.42729	−0.990935
$7$	−4.02222	−1.52025	−0.760127	−	0.649774i	$-0.774863\pi$
$7$	−4.02222	−1.52025	−0.760127	+	0.649774i	$0.774863\pi$
$8$	−4.59173	−1.62342
$9$	1.00000	0.333333
$10$	9.59464	3.03409
$11$	0.425499	0.128293	0.0641464	−	0.997941i	$-0.479568\pi$
$11$	0.425499	0.128293	0.0641464	+	0.997941i	$0.479568\pi$
$12$	3.89172	1.12344
$13$	−2.68690	−0.745211	−0.372605	−	0.927990i	$-0.621535\pi$
$13$	−2.68690	−0.745211	−0.372605	+	0.927990i	$0.621535\pi$
$14$	9.76307	2.60929
$15$	−3.95283	−1.02062
$16$	3.36202	0.840504
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.42729	−0.572117
$19$	−1.90370	−0.436739	−0.218369	−	0.975866i	$-0.570074\pi$
$19$	−1.90370	−0.436739	−0.218369	+	0.975866i	$0.570074\pi$
$20$	−15.3833	−3.43981
$21$	−4.02222	−0.877719
$22$	−1.03281	−0.220195
$23$	4.66660	0.973053	0.486527	−	0.873666i	$-0.338264\pi$
$23$	4.66660	0.973053	0.486527	+	0.873666i	$0.338264\pi$
$24$	−4.59173	−0.937284
$25$	10.6248	2.12497
$26$	6.52186	1.27904
$27$	1.00000	0.192450
$28$	−15.6533	−2.95820
$29$	−2.85996	−0.531080	−0.265540	−	0.964100i	$-0.585550\pi$
$29$	−2.85996	−0.531080	−0.265540	+	0.964100i	$0.585550\pi$
$30$	9.59464	1.75173
$31$	−7.16013	−1.28600	−0.642998	−	0.765868i	$-0.722310\pi$
$31$	−7.16013	−1.28600	−0.642998	+	0.765868i	$0.722310\pi$
$32$	1.02289	0.180823
$33$	0.425499	0.0740699
$34$	2.42729	0.416276
$35$	15.8991	2.68744
$36$	3.89172	0.648619
$37$	−8.38342	−1.37823	−0.689113	−	0.724654i	$-0.742000\pi$
$37$	−8.38342	−1.37823	−0.689113	+	0.724654i	$0.742000\pi$
$38$	4.62082	0.749596
$39$	−2.68690	−0.430248
$40$	18.1503	2.86982
$41$	2.91607	0.455414	0.227707	−	0.973730i	$-0.426877\pi$
$41$	2.91607	0.455414	0.227707	+	0.973730i	$0.426877\pi$
$42$	9.76307	1.50647
$43$	−5.62342	−0.857564	−0.428782	−	0.903408i	$-0.641057\pi$
$43$	−5.62342	−0.857564	−0.428782	+	0.903408i	$0.641057\pi$
$44$	1.65592	0.249639
$45$	−3.95283	−0.589253
$46$	−11.3272	−1.67010
$47$	−1.96436	−0.286531	−0.143266	−	0.989684i	$-0.545760\pi$
$47$	−1.96436	−0.286531	−0.143266	+	0.989684i	$0.545760\pi$
$48$	3.36202	0.485265
$49$	9.17822	1.31117
$50$	−25.7895	−3.64719
$51$	−1.00000	−0.140028
$52$	−10.4566	−1.45007
$53$	−4.44469	−0.610525	−0.305263	−	0.952268i	$-0.598744\pi$
$53$	−4.44469	−0.610525	−0.305263	+	0.952268i	$0.598744\pi$
$54$	−2.42729	−0.330312
$55$	−1.68192	−0.226791
$56$	18.4689	2.46802
$57$	−1.90370	−0.252151
$58$	6.94193	0.911520
$59$	−12.6563	−1.64770	−0.823852	−	0.566805i	$-0.808179\pi$
$59$	−12.6563	−1.64770	−0.823852	+	0.566805i	$0.808179\pi$
$60$	−15.3833	−1.98597
$61$	−5.35291	−0.685370	−0.342685	−	0.939450i	$-0.611336\pi$
$61$	−5.35291	−0.685370	−0.342685	+	0.939450i	$0.611336\pi$
$62$	17.3797	2.20722
$63$	−4.02222	−0.506752
$64$	−9.20688	−1.15086
$65$	10.6208	1.31735
$66$	−1.03281	−0.127130
$67$	−4.28635	−0.523660	−0.261830	−	0.965114i	$-0.584326\pi$
$67$	−4.28635	−0.523660	−0.261830	+	0.965114i	$0.584326\pi$
$68$	−3.89172	−0.471940
$69$	4.66660	0.561793
$70$	−38.5917	−4.61259
$71$	4.91935	0.583819	0.291910	−	0.956446i	$-0.405709\pi$
$71$	4.91935	0.583819	0.291910	+	0.956446i	$0.405709\pi$
$72$	−4.59173	−0.541141
$73$	−4.26972	−0.499733	−0.249866	−	0.968280i	$-0.580387\pi$
$73$	−4.26972	−0.499733	−0.249866	+	0.968280i	$0.580387\pi$
$74$	20.3490	2.36552
$75$	10.6248	1.22685
$76$	−7.40866	−0.849831
$77$	−1.71145	−0.195038
$78$	6.52186	0.738456
$79$	−14.4808	−1.62922	−0.814610	−	0.580009i	$-0.803049\pi$
$79$	−14.4808	−1.62922	−0.814610	+	0.580009i	$0.803049\pi$
$80$	−13.2895	−1.48581
$81$	1.00000	0.111111
$82$	−7.07814	−0.781650
$83$	−2.68930	−0.295189	−0.147595	−	0.989048i	$-0.547153\pi$
$83$	−2.68930	−0.295189	−0.147595	+	0.989048i	$0.547153\pi$
$84$	−15.6533	−1.70792
$85$	3.95283	0.428744
$86$	13.6497	1.47188
$87$	−2.85996	−0.306619
$88$	−1.95378	−0.208273
$89$	−2.16277	−0.229254	−0.114627	−	0.993409i	$-0.536567\pi$
$89$	−2.16277	−0.229254	−0.114627	+	0.993409i	$0.536567\pi$
$90$	9.59464	1.01136
$91$	10.8073	1.13291
$92$	18.1611	1.89342
$93$	−7.16013	−0.742470
$94$	4.76806	0.491788
$95$	7.52500	0.772048
$96$	1.02289	0.104398
$97$	6.45269	0.655172	0.327586	−	0.944821i	$-0.393765\pi$
$97$	6.45269	0.655172	0.327586	+	0.944821i	$0.393765\pi$
$98$	−22.2782	−2.25043
$99$	0.425499	0.0427643
$100$	41.3489	4.13489
$101$	−10.5267	−1.04744	−0.523721	−	0.851890i	$-0.675457\pi$
$101$	−10.5267	−1.04744	−0.523721	+	0.851890i	$0.675457\pi$
$102$	2.42729	0.240337
$103$	5.81712	0.573178	0.286589	−	0.958054i	$-0.407479\pi$
$103$	5.81712	0.573178	0.286589	+	0.958054i	$0.407479\pi$
$104$	12.3375	1.20979
$105$	15.8991	1.55160
$106$	10.7885	1.04787
$107$	−1.37820	−0.133235	−0.0666176	−	0.997779i	$-0.521221\pi$
$107$	−1.37820	−0.133235	−0.0666176	+	0.997779i	$0.521221\pi$
$108$	3.89172	0.374480
$109$	−19.2165	−1.84061	−0.920305	−	0.391202i	$-0.872059\pi$
$109$	−19.2165	−1.84061	−0.920305	+	0.391202i	$0.872059\pi$
$110$	4.08251	0.389252
$111$	−8.38342	−0.795719
$112$	−13.5228	−1.27778
$113$	17.0375	1.60275	0.801377	−	0.598160i	$-0.204101\pi$
$113$	17.0375	1.60275	0.801377	+	0.598160i	$0.204101\pi$
$114$	4.62082	0.432780
$115$	−18.4463	−1.72012
$116$	−11.1301	−1.03341
$117$	−2.68690	−0.248404
$118$	30.7203	2.82804
$119$	4.02222	0.368716
$120$	18.1503	1.65689
$121$	−10.8190	−0.983541
$122$	12.9930	1.17634
$123$	2.91607	0.262933
$124$	−27.8652	−2.50237
$125$	−22.2340	−1.98867
$126$	9.76307	0.869763
$127$	0.786768	0.0698143	0.0349072	−	0.999391i	$-0.488886\pi$
$127$	0.786768	0.0698143	0.0349072	+	0.999391i	$0.488886\pi$
$128$	20.3020	1.79446
$129$	−5.62342	−0.495115
$130$	−25.7798	−2.26104
$131$	−9.14376	−0.798894	−0.399447	−	0.916756i	$-0.630798\pi$
$131$	−9.14376	−0.798894	−0.399447	+	0.916756i	$0.630798\pi$
$132$	1.65592	0.144129
$133$	7.65709	0.663954
$134$	10.4042	0.898785
$135$	−3.95283	−0.340205
$136$	4.59173	0.393738
$137$	−6.59460	−0.563414	−0.281707	−	0.959500i	$-0.590901\pi$
$137$	−6.59460	−0.563414	−0.281707	+	0.959500i	$0.590901\pi$
$138$	−11.3272	−0.964233
$139$	−18.9845	−1.61025	−0.805123	−	0.593108i	$-0.797901\pi$
$139$	−18.9845	−1.61025	−0.805123	+	0.593108i	$0.797901\pi$
$140$	61.8749	5.22938
$141$	−1.96436	−0.165429
$142$	−11.9407	−1.00204
$143$	−1.14327	−0.0956052
$144$	3.36202	0.280168
$145$	11.3049	0.938822
$146$	10.3638	0.857716
$147$	9.17822	0.757007
$148$	−32.6259	−2.68183
$149$	−19.1682	−1.57032	−0.785159	−	0.619294i	$-0.787419\pi$
$149$	−19.1682	−1.57032	−0.785159	+	0.619294i	$0.787419\pi$
$150$	−25.7895	−2.10571
$151$	−12.3592	−1.00578	−0.502889	−	0.864351i	$-0.667730\pi$
$151$	−12.3592	−1.00578	−0.502889	+	0.864351i	$0.667730\pi$
$152$	8.74128	0.709011
$153$	−1.00000	−0.0808452
$154$	4.15417	0.334753
$155$	28.3027	2.27333
$156$	−10.4566	−0.837201
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	35.1491	2.79631
$159$	−4.44469	−0.352487
$160$	−4.04332	−0.319652
$161$	−18.7701	−1.47929
$162$	−2.42729	−0.190706
$163$	−10.9096	−0.854504	−0.427252	−	0.904133i	$-0.640518\pi$
$163$	−10.9096	−0.854504	−0.427252	+	0.904133i	$0.640518\pi$
$164$	11.3485	0.886171
$165$	−1.68192	−0.130938
$166$	6.52770	0.506648
$167$	−2.19027	−0.169488	−0.0847440	−	0.996403i	$-0.527007\pi$
$167$	−2.19027	−0.169488	−0.0847440	+	0.996403i	$0.527007\pi$
$168$	18.4689	1.42491
$169$	−5.78059	−0.444661
$170$	−9.59464	−0.735875
$171$	−1.90370	−0.145580
$172$	−21.8848	−1.66870
$173$	−0.728787	−0.0554087	−0.0277043	−	0.999616i	$-0.508820\pi$
$173$	−0.728787	−0.0554087	−0.0277043	+	0.999616i	$0.508820\pi$
$174$	6.94193	0.526266
$175$	−42.7354	−3.23049
$176$	1.43053	0.107831
$177$	−12.6563	−0.951302
$178$	5.24967	0.393479
$179$	6.12946	0.458138	0.229069	−	0.973410i	$-0.426432\pi$
$179$	6.12946	0.458138	0.229069	+	0.973410i	$0.426432\pi$
$180$	−15.3833	−1.14660
$181$	7.13508	0.530346	0.265173	−	0.964201i	$-0.414571\pi$
$181$	7.13508	0.530346	0.265173	+	0.964201i	$0.414571\pi$
$182$	−26.2323	−1.94447
$183$	−5.35291	−0.395699
$184$	−21.4278	−1.57968
$185$	33.1382	2.43637
$186$	17.3797	1.27434
$187$	−0.425499	−0.0311156
$188$	−7.64472	−0.557549
$189$	−4.02222	−0.292573
$190$	−18.2653	−1.32511
$191$	−19.9757	−1.44539	−0.722696	−	0.691166i	$-0.757097\pi$
$191$	−19.9757	−1.44539	−0.722696	+	0.691166i	$0.757097\pi$
$192$	−9.20688	−0.664450
$193$	7.83115	0.563698	0.281849	−	0.959459i	$-0.409052\pi$
$193$	7.83115	0.563698	0.281849	+	0.959459i	$0.409052\pi$
$194$	−15.6625	−1.12450
$195$	10.6208	0.760574
$196$	35.7190	2.55136
$197$	−11.8751	−0.846068	−0.423034	−	0.906114i	$-0.639035\pi$
$197$	−11.8751	−0.846068	−0.423034	+	0.906114i	$0.639035\pi$
$198$	−1.03281	−0.0733984
$199$	9.34856	0.662702	0.331351	−	0.943508i	$-0.392496\pi$
$199$	9.34856	0.662702	0.331351	+	0.943508i	$0.392496\pi$
$200$	−48.7865	−3.44972
$201$	−4.28635	−0.302336
$202$	25.5512	1.79778
$203$	11.5034	0.807377
$204$	−3.89172	−0.272475
$205$	−11.5267	−0.805062
$206$	−14.1198	−0.983775
$207$	4.66660	0.324351
$208$	−9.03339	−0.626353
$209$	−0.810022	−0.0560304
$210$	−38.5917	−2.66308
$211$	−13.4850	−0.928345	−0.464172	−	0.885745i	$-0.653648\pi$
$211$	−13.4850	−0.928345	−0.464172	+	0.885745i	$0.653648\pi$
$212$	−17.2975	−1.18800
$213$	4.91935	0.337068
$214$	3.34527	0.228678
$215$	22.2284	1.51597
$216$	−4.59173	−0.312428
$217$	28.7996	1.95504
$218$	46.6440	3.15913
$219$	−4.26972	−0.288521
$220$	−6.54557	−0.441302
$221$	2.68690	0.180740
$222$	20.3490	1.36573
$223$	1.88957	0.126535	0.0632674	−	0.997997i	$-0.479848\pi$
$223$	1.88957	0.126535	0.0632674	+	0.997997i	$0.479848\pi$
$224$	−4.11429	−0.274898
$225$	10.6248	0.708323
$226$	−41.3549	−2.75089
$227$	1.62194	0.107652	0.0538261	−	0.998550i	$-0.482858\pi$
$227$	1.62194	0.107652	0.0538261	+	0.998550i	$0.482858\pi$
$228$	−7.40866	−0.490650
$229$	−0.00764999	−0.000505526 0	−0.000252763	−	1.00000i	$-0.500080\pi$
$229$	−0.00764999	−0.000505526 0	−0.000252763		1.00000i	$0.500080\pi$
$230$	44.7744	2.95233
$231$	−1.71145	−0.112605
$232$	13.1322	0.862168
$233$	−1.78235	−0.116766	−0.0583828	−	0.998294i	$-0.518594\pi$
$233$	−1.78235	−0.116766	−0.0583828	+	0.998294i	$0.518594\pi$
$234$	6.52186	0.426348
$235$	7.76477	0.506518
$236$	−49.2545	−3.20620
$237$	−14.4808	−0.940631
$238$	−9.76307	−0.632846
$239$	26.1368	1.69065	0.845325	−	0.534252i	$-0.179407\pi$
$239$	26.1368	1.69065	0.845325	+	0.534252i	$0.179407\pi$
$240$	−13.2895	−0.857832
$241$	29.8342	1.92179	0.960896	−	0.276911i	$-0.0893107\pi$
$241$	29.8342	1.92179	0.960896	+	0.276911i	$0.0893107\pi$
$242$	26.2607	1.68810
$243$	1.00000	0.0641500
$244$	−20.8320	−1.33363
$245$	−36.2799	−2.31784
$246$	−7.07814	−0.451286
$247$	5.11504	0.325462
$248$	32.8774	2.08772
$249$	−2.68930	−0.170428
$250$	53.9684	3.41326
$251$	−7.65313	−0.483061	−0.241531	−	0.970393i	$-0.577649\pi$
$251$	−7.65313	−0.483061	−0.241531	+	0.970393i	$0.577649\pi$
$252$	−15.6533	−0.986066
$253$	1.98563	0.124836
$254$	−1.90971	−0.119826
$255$	3.95283	0.247536
$256$	−30.8649	−1.92905
$257$	15.1715	0.946374	0.473187	−	0.880962i	$-0.343104\pi$
$257$	15.1715	0.946374	0.473187	+	0.880962i	$0.343104\pi$
$258$	13.6497	0.849790
$259$	33.7199	2.09525
$260$	41.3333	2.56338
$261$	−2.85996	−0.177027
$262$	22.1945	1.37118
$263$	−4.38275	−0.270252	−0.135126	−	0.990828i	$-0.543144\pi$
$263$	−4.38275	−0.270252	−0.135126	+	0.990828i	$0.543144\pi$
$264$	−1.95378	−0.120247
$265$	17.5691	1.07926
$266$	−18.5859	−1.13958
$267$	−2.16277	−0.132360
$268$	−16.6812	−1.01897
$269$	−0.638198	−0.0389116	−0.0194558	−	0.999811i	$-0.506193\pi$
$269$	−0.638198	−0.0389116	−0.0194558	+	0.999811i	$0.506193\pi$
$270$	9.59464	0.583911
$271$	−22.9410	−1.39357	−0.696784	−	0.717281i	$-0.745386\pi$
$271$	−22.9410	−1.39357	−0.696784	+	0.717281i	$0.745386\pi$
$272$	−3.36202	−0.203852
$273$	10.8073	0.654086
$274$	16.0070	0.967016
$275$	4.52086	0.272618
$276$	18.1611	1.09317
$277$	−2.67968	−0.161007	−0.0805033	−	0.996754i	$-0.525653\pi$
$277$	−2.67968	−0.161007	−0.0805033	+	0.996754i	$0.525653\pi$
$278$	46.0808	2.76374
$279$	−7.16013	−0.428666
$280$	−73.0045	−4.36286
$281$	10.6523	0.635463	0.317731	−	0.948181i	$-0.397079\pi$
$281$	10.6523	0.635463	0.317731	+	0.948181i	$0.397079\pi$
$282$	4.76806	0.283934
$283$	23.2091	1.37964	0.689818	−	0.723983i	$-0.257691\pi$
$283$	23.2091	1.37964	0.689818	+	0.723983i	$0.257691\pi$
$284$	19.1447	1.13603
$285$	7.52500	0.445742
$286$	2.77505	0.164092
$287$	−11.7291	−0.692345
$288$	1.02289	0.0602745
$289$	1.00000	0.0588235
$290$	−27.4402	−1.61135
$291$	6.45269	0.378264
$292$	−16.6165	−0.972408
$293$	−21.4976	−1.25590	−0.627951	−	0.778253i	$-0.716106\pi$
$293$	−21.4976	−1.25590	−0.627951	+	0.778253i	$0.716106\pi$
$294$	−22.2782	−1.29929
$295$	50.0280	2.91274
$296$	38.4944	2.23744
$297$	0.425499	0.0246900
$298$	46.5266	2.69522
$299$	−12.5387	−0.725130
$300$	41.3489	2.38728
$301$	22.6186	1.30372
$302$	29.9993	1.72627
$303$	−10.5267	−0.604741
$304$	−6.40027	−0.367081
$305$	21.1591	1.21157
$306$	2.42729	0.138759
$307$	−11.9455	−0.681764	−0.340882	−	0.940106i	$-0.610726\pi$
$307$	−11.9455	−0.681764	−0.340882	+	0.940106i	$0.610726\pi$
$308$	−6.66047	−0.379516
$309$	5.81712	0.330925
$310$	−68.6988	−3.90183
$311$	7.47291	0.423750	0.211875	−	0.977297i	$-0.432043\pi$
$311$	7.47291	0.423750	0.211875	+	0.977297i	$0.432043\pi$
$312$	12.3375	0.698474
$313$	−24.3954	−1.37891	−0.689455	−	0.724328i	$-0.742150\pi$
$313$	−24.3954	−1.37891	−0.689455	+	0.724328i	$0.742150\pi$
$314$	2.42729	0.136980
$315$	15.8991	0.895814
$316$	−56.3553	−3.17023
$317$	13.5714	0.762247	0.381124	−	0.924524i	$-0.375537\pi$
$317$	13.5714	0.762247	0.381124	+	0.924524i	$0.375537\pi$
$318$	10.7885	0.604991
$319$	−1.21691	−0.0681338
$320$	36.3932	2.03444
$321$	−1.37820	−0.0769234
$322$	45.5603	2.53898
$323$	1.90370	0.105925
$324$	3.89172	0.216206
$325$	−28.5479	−1.58355
$326$	26.4807	1.46663
$327$	−19.2165	−1.06268
$328$	−13.3898	−0.739330
$329$	7.90107	0.435600
$330$	4.08251	0.224735
$331$	−26.1562	−1.43767	−0.718837	−	0.695179i	$-0.755325\pi$
$331$	−26.1562	−1.43767	−0.718837	+	0.695179i	$0.755325\pi$
$332$	−10.4660	−0.574396
$333$	−8.38342	−0.459409
$334$	5.31640	0.290901
$335$	16.9432	0.925705
$336$	−13.5228	−0.737727
$337$	20.6023	1.12228	0.561138	−	0.827722i	$-0.310364\pi$
$337$	20.6023	1.12228	0.561138	+	0.827722i	$0.310364\pi$
$338$	14.0311	0.763194
$339$	17.0375	0.925350
$340$	15.3833	0.834275
$341$	−3.04663	−0.164984
$342$	4.62082	0.249865
$343$	−8.76126	−0.473064
$344$	25.8213	1.39219
$345$	−18.4463	−0.993114
$346$	1.76898	0.0951007
$347$	8.08706	0.434136	0.217068	−	0.976156i	$-0.430351\pi$
$347$	8.08706	0.434136	0.217068	+	0.976156i	$0.430351\pi$
$348$	−11.1301	−0.596638
$349$	13.8822	0.743099	0.371549	−	0.928413i	$-0.378827\pi$
$349$	13.8822	0.743099	0.371549	+	0.928413i	$0.378827\pi$
$350$	103.731	5.54466
$351$	−2.68690	−0.143416
$352$	0.435240	0.0231983
$353$	−1.03277	−0.0549688	−0.0274844	−	0.999622i	$-0.508750\pi$
$353$	−1.03277	−0.0549688	−0.0274844	+	0.999622i	$0.508750\pi$
$354$	30.7203	1.63277
$355$	−19.4453	−1.03205
$356$	−8.41690	−0.446095
$357$	4.02222	0.212878
$358$	−14.8780	−0.786325
$359$	13.0731	0.689974	0.344987	−	0.938608i	$-0.387883\pi$
$359$	13.0731	0.689974	0.344987	+	0.938608i	$0.387883\pi$
$360$	18.1503	0.956606
$361$	−15.3759	−0.809259
$362$	−17.3189	−0.910260
$363$	−10.8190	−0.567848
$364$	42.0588	2.20448
$365$	16.8775	0.883406
$366$	12.9930	0.679157
$367$	13.9632	0.728873	0.364436	−	0.931228i	$-0.381262\pi$
$367$	13.9632	0.728873	0.364436	+	0.931228i	$0.381262\pi$
$368$	15.6892	0.817855
$369$	2.91607	0.151805
$370$	−80.4359	−4.18167
$371$	17.8775	0.928154
$372$	−27.8652	−1.44474
$373$	29.9006	1.54819	0.774096	−	0.633068i	$-0.218205\pi$
$373$	29.9006	1.54819	0.774096	+	0.633068i	$0.218205\pi$
$374$	1.03281	0.0534052
$375$	−22.2340	−1.14816
$376$	9.01981	0.465161
$377$	7.68440	0.395767
$378$	9.76307	0.502158
$379$	22.3072	1.14584	0.572921	−	0.819611i	$-0.305810\pi$
$379$	22.3072	1.14584	0.572921	+	0.819611i	$0.305810\pi$
$380$	29.2851	1.50230
$381$	0.786768	0.0403073
$382$	48.4867	2.48080
$383$	0.309735	0.0158267	0.00791335	−	0.999969i	$-0.497481\pi$
$383$	0.309735	0.0158267	0.00791335	+	0.999969i	$0.497481\pi$
$384$	20.3020	1.03603
$385$	6.76506	0.344779
$386$	−19.0084	−0.967503
$387$	−5.62342	−0.285855
$388$	25.1120	1.27487
$389$	−4.55469	−0.230932	−0.115466	−	0.993311i	$-0.536836\pi$
$389$	−4.55469	−0.230932	−0.115466	+	0.993311i	$0.536836\pi$
$390$	−25.7798	−1.30541
$391$	−4.66660	−0.236000
$392$	−42.1439	−2.12859
$393$	−9.14376	−0.461242
$394$	28.8243	1.45215
$395$	57.2402	2.88007
$396$	1.65592	0.0832131
$397$	−14.1217	−0.708747	−0.354373	−	0.935104i	$-0.615306\pi$
$397$	−14.1217	−0.708747	−0.354373	+	0.935104i	$0.615306\pi$
$398$	−22.6916	−1.13743
$399$	7.65709	0.383334
$400$	35.7209	1.78605
$401$	12.8338	0.640888	0.320444	−	0.947267i	$-0.396168\pi$
$401$	12.8338	0.640888	0.320444	+	0.947267i	$0.396168\pi$
$402$	10.4042	0.518914
$403$	19.2385	0.958339
$404$	−40.9668	−2.03817
$405$	−3.95283	−0.196418
$406$	−27.9219	−1.38574
$407$	−3.56714	−0.176816
$408$	4.59173	0.227325
$409$	−11.3701	−0.562213	−0.281107	−	0.959677i	$-0.590701\pi$
$409$	−11.3701	−0.562213	−0.281107	+	0.959677i	$0.590701\pi$
$410$	27.9787	1.38177
$411$	−6.59460	−0.325287
$412$	22.6386	1.11532
$413$	50.9062	2.50493
$414$	−11.3272	−0.556700
$415$	10.6303	0.521823
$416$	−2.74840	−0.134752
$417$	−18.9845	−0.929676
$418$	1.96615	0.0961678
$419$	−2.01485	−0.0984319	−0.0492160	−	0.998788i	$-0.515672\pi$
$419$	−2.01485	−0.0984319	−0.0492160	+	0.998788i	$0.515672\pi$
$420$	61.8749	3.01918
$421$	−27.0011	−1.31595	−0.657977	−	0.753038i	$-0.728588\pi$
$421$	−27.0011	−1.31595	−0.657977	+	0.753038i	$0.728588\pi$
$422$	32.7319	1.59336
$423$	−1.96436	−0.0955103
$424$	20.4088	0.991140
$425$	−10.6248	−0.515381
$426$	−11.9407	−0.578527
$427$	21.5306	1.04194
$428$	−5.36354	−0.259257
$429$	−1.14327	−0.0551977
$430$	−53.9547	−2.60193
$431$	32.1940	1.55073	0.775366	−	0.631512i	$-0.217565\pi$
$431$	32.1940	1.55073	0.775366	+	0.631512i	$0.217565\pi$
$432$	3.36202	0.161755
$433$	−1.16561	−0.0560156	−0.0280078	−	0.999608i	$-0.508916\pi$
$433$	−1.16561	−0.0560156	−0.0280078	+	0.999608i	$0.508916\pi$
$434$	−69.9048	−3.35554
$435$	11.3049	0.542029
$436$	−74.7852	−3.58156
$437$	−8.88380	−0.424970
$438$	10.3638	0.495203
$439$	15.5804	0.743610	0.371805	−	0.928311i	$-0.378739\pi$
$439$	15.5804	0.743610	0.371805	+	0.928311i	$0.378739\pi$
$440$	7.72295	0.368177
$441$	9.17822	0.437058
$442$	−6.52186	−0.310213
$443$	−38.8270	−1.84473	−0.922364	−	0.386323i	$-0.873745\pi$
$443$	−38.8270	−1.84473	−0.922364	+	0.386323i	$0.873745\pi$
$444$	−32.6259	−1.54836
$445$	8.54907	0.405265
$446$	−4.58652	−0.217178
$447$	−19.1682	−0.906624
$448$	37.0321	1.74960
$449$	−22.2639	−1.05070	−0.525349	−	0.850887i	$-0.676065\pi$
$449$	−22.2639	−1.05070	−0.525349	+	0.850887i	$0.676065\pi$
$450$	−25.7895	−1.21573
$451$	1.24079	0.0584263
$452$	66.3051	3.11873
$453$	−12.3592	−0.580686
$454$	−3.93692	−0.184769
$455$	−42.7193	−2.00271
$456$	8.74128	0.409348
$457$	18.1488	0.848963	0.424482	−	0.905437i	$-0.360456\pi$
$457$	18.1488	0.848963	0.424482	+	0.905437i	$0.360456\pi$
$458$	0.0185687	0.000867659 0
$459$	−1.00000	−0.0466760
$460$	−71.7876	−3.34711
$461$	−12.9017	−0.600891	−0.300446	−	0.953799i	$-0.597135\pi$
$461$	−12.9017	−0.600891	−0.300446	+	0.953799i	$0.597135\pi$
$462$	4.15417	0.193270
$463$	−19.3447	−0.899026	−0.449513	−	0.893274i	$-0.648402\pi$
$463$	−19.3447	−0.899026	−0.449513	+	0.893274i	$0.648402\pi$
$464$	−9.61522	−0.446375
$465$	28.3027	1.31251
$466$	4.32627	0.200411
$467$	21.2565	0.983632	0.491816	−	0.870699i	$-0.336333\pi$
$467$	21.2565	0.983632	0.491816	+	0.870699i	$0.336333\pi$
$468$	−10.4566	−0.483358
$469$	17.2406	0.796097
$470$	−18.8473	−0.869362
$471$	−1.00000	−0.0460776
$472$	58.1141	2.67492
$473$	−2.39276	−0.110019
$474$	35.1491	1.61445
$475$	−20.2265	−0.928056
$476$	15.6533	0.717469
$477$	−4.44469	−0.203508
$478$	−63.4415	−2.90175
$479$	−28.9484	−1.32269	−0.661343	−	0.750083i	$-0.730013\pi$
$479$	−28.9484	−1.32269	−0.661343	+	0.750083i	$0.730013\pi$
$480$	−4.04332	−0.184551
$481$	22.5254	1.02707
$482$	−72.4162	−3.29847
$483$	−18.7701	−0.854068
$484$	−42.1043	−1.91383
$485$	−25.5064	−1.15819
$486$	−2.42729	−0.110104
$487$	4.09675	0.185641	0.0928207	−	0.995683i	$-0.470412\pi$
$487$	4.09675	0.185641	0.0928207	+	0.995683i	$0.470412\pi$
$488$	24.5791	1.11265
$489$	−10.9096	−0.493348
$490$	88.0617	3.97822
$491$	−29.6873	−1.33977	−0.669884	−	0.742465i	$-0.733656\pi$
$491$	−29.6873	−1.33977	−0.669884	+	0.742465i	$0.733656\pi$
$492$	11.3485	0.511631
$493$	2.85996	0.128806
$494$	−12.4157	−0.558607
$495$	−1.68192	−0.0755969
$496$	−24.0725	−1.08089
$497$	−19.7867	−0.887554
$498$	6.52770	0.292513
$499$	14.3553	0.642630	0.321315	−	0.946972i	$-0.395875\pi$
$499$	14.3553	0.642630	0.321315	+	0.946972i	$0.395875\pi$
$500$	−86.5286	−3.86968
$501$	−2.19027	−0.0978539
$502$	18.5763	0.829103
$503$	9.74151	0.434352	0.217176	−	0.976132i	$-0.430315\pi$
$503$	9.74151	0.434352	0.217176	+	0.976132i	$0.430315\pi$
$504$	18.4689	0.822672
$505$	41.6101	1.85163
$506$	−4.81970	−0.214262
$507$	−5.78059	−0.256725
$508$	3.06188	0.135849
$509$	10.2506	0.454351	0.227175	−	0.973854i	$-0.427051\pi$
$509$	10.2506	0.454351	0.227175	+	0.973854i	$0.427051\pi$
$510$	−9.59464	−0.424858
$511$	17.1737	0.759721
$512$	34.3139	1.51648
$513$	−1.90370	−0.0840504
$514$	−36.8256	−1.62431
$515$	−22.9941	−1.01324
$516$	−21.8848	−0.963423
$517$	−0.835832	−0.0367599
$518$	−81.8479	−3.59619
$519$	−0.728787	−0.0319902
$520$	−48.7680	−2.13862
$521$	−10.6170	−0.465139	−0.232569	−	0.972580i	$-0.574713\pi$
$521$	−10.6170	−0.465139	−0.232569	+	0.972580i	$0.574713\pi$
$522$	6.94193	0.303840
$523$	−0.696347	−0.0304491	−0.0152246	−	0.999884i	$-0.504846\pi$
$523$	−0.696347	−0.0304491	−0.0152246	+	0.999884i	$0.504846\pi$
$524$	−35.5849	−1.55453
$525$	−42.7354	−1.86513
$526$	10.6382	0.463847
$527$	7.16013	0.311900
$528$	1.43053	0.0622560
$529$	−1.22284	−0.0531671
$530$	−42.6452	−1.85239
$531$	−12.6563	−0.549234
$532$	29.7992	1.29196
$533$	−7.83519	−0.339380
$534$	5.24967	0.227175
$535$	5.44777	0.235528
$536$	19.6818	0.850122
$537$	6.12946	0.264506
$538$	1.54909	0.0667860
$539$	3.90532	0.168214
$540$	−15.3833	−0.661991
$541$	−10.9802	−0.472074	−0.236037	−	0.971744i	$-0.575849\pi$
$541$	−10.9802	−0.472074	−0.236037	+	0.971744i	$0.575849\pi$
$542$	55.6844	2.39185
$543$	7.13508	0.306196
$544$	−1.02289	−0.0438561
$545$	75.9596	3.25375
$546$	−26.2323	−1.12264
$547$	−4.37562	−0.187088	−0.0935441	−	0.995615i	$-0.529820\pi$
$547$	−4.37562	−0.187088	−0.0935441	+	0.995615i	$0.529820\pi$
$548$	−25.6643	−1.09632
$549$	−5.35291	−0.228457
$550$	−10.9734	−0.467908
$551$	5.44450	0.231943
$552$	−21.4278	−0.912027
$553$	58.2450	2.47683
$554$	6.50436	0.276344
$555$	33.1382	1.40664
$556$	−73.8823	−3.13331
$557$	−37.1511	−1.57414	−0.787072	−	0.616861i	$-0.788404\pi$
$557$	−37.1511	−1.57414	−0.787072	+	0.616861i	$0.788404\pi$
$558$	17.3797	0.735740
$559$	15.1095	0.639066
$560$	53.4531	2.25881
$561$	−0.425499	−0.0179646
$562$	−25.8562	−1.09068
$563$	30.7195	1.29467	0.647337	−	0.762204i	$-0.275883\pi$
$563$	30.7195	1.29467	0.647337	+	0.762204i	$0.275883\pi$
$564$	−7.64472	−0.321901
$565$	−67.3463	−2.83328
$566$	−56.3350	−2.36794
$567$	−4.02222	−0.168917
$568$	−22.5883	−0.947785
$569$	−14.8349	−0.621910	−0.310955	−	0.950425i	$-0.600649\pi$
$569$	−14.8349	−0.621910	−0.310955	+	0.950425i	$0.600649\pi$
$570$	−18.2653	−0.765050
$571$	43.1200	1.80452	0.902259	−	0.431195i	$-0.141908\pi$
$571$	43.1200	1.80452	0.902259	+	0.431195i	$0.141908\pi$
$572$	−4.44929	−0.186034
$573$	−19.9757	−0.834497
$574$	28.4698	1.18831
$575$	49.5819	2.06771
$576$	−9.20688	−0.383620
$577$	−14.5753	−0.606778	−0.303389	−	0.952867i	$-0.598118\pi$
$577$	−14.5753	−0.606778	−0.303389	+	0.952867i	$0.598118\pi$
$578$	−2.42729	−0.100962
$579$	7.83115	0.325451
$580$	43.9955	1.82681
$581$	10.8170	0.448763
$582$	−15.6625	−0.649233
$583$	−1.89121	−0.0783260
$584$	19.6054	0.811277
$585$	10.6208	0.439118
$586$	52.1807	2.15557
$587$	−7.51332	−0.310108	−0.155054	−	0.987906i	$-0.549555\pi$
$587$	−7.51332	−0.310108	−0.155054	+	0.987906i	$0.549555\pi$
$588$	35.7190	1.47303
$589$	13.6307	0.561644
$590$	−121.432	−4.99928
$591$	−11.8751	−0.488477
$592$	−28.1852	−1.15840
$593$	10.6141	0.435867	0.217934	−	0.975964i	$-0.430068\pi$
$593$	10.6141	0.435867	0.217934	+	0.975964i	$0.430068\pi$
$594$	−1.03281	−0.0423766
$595$	−15.8991	−0.651801
$596$	−74.5971	−3.05562
$597$	9.34856	0.382611
$598$	30.4349	1.24458
$599$	36.1971	1.47897	0.739486	−	0.673172i	$-0.235069\pi$
$599$	36.1971	1.47897	0.739486	+	0.673172i	$0.235069\pi$
$600$	−48.7865	−1.99170
$601$	−8.43585	−0.344105	−0.172053	−	0.985088i	$-0.555040\pi$
$601$	−8.43585	−0.344105	−0.172053	+	0.985088i	$0.555040\pi$
$602$	−54.9018	−2.23763
$603$	−4.28635	−0.174553
$604$	−48.0985	−1.95710
$605$	42.7654	1.73866
$606$	25.5512	1.03795
$607$	−18.6835	−0.758339	−0.379170	−	0.925327i	$-0.623790\pi$
$607$	−18.6835	−0.758339	−0.379170	+	0.925327i	$0.623790\pi$
$608$	−1.94728	−0.0789726
$609$	11.5034	0.466140
$610$	−51.3593	−2.07948
$611$	5.27802	0.213526
$612$	−3.89172	−0.157313
$613$	−35.5911	−1.43751	−0.718756	−	0.695262i	$-0.755288\pi$
$613$	−35.5911	−1.43751	−0.718756	+	0.695262i	$0.755288\pi$
$614$	28.9951	1.17015
$615$	−11.5267	−0.464803
$616$	7.85851	0.316629
$617$	−2.26695	−0.0912638	−0.0456319	−	0.998958i	$-0.514530\pi$
$617$	−2.26695	−0.0912638	−0.0456319	+	0.998958i	$0.514530\pi$
$618$	−14.1198	−0.567983
$619$	6.49106	0.260898	0.130449	−	0.991455i	$-0.458358\pi$
$619$	6.49106	0.260898	0.130449	+	0.991455i	$0.458358\pi$
$620$	110.146	4.42358
$621$	4.66660	0.187264
$622$	−18.1389	−0.727303
$623$	8.69914	0.348524
$624$	−9.03339	−0.361625
$625$	34.7631	1.39053
$626$	59.2147	2.36669
$627$	−0.810022	−0.0323492
$628$	−3.89172	−0.155296
$629$	8.38342	0.334269
$630$	−38.5917	−1.53753
$631$	5.87756	0.233982	0.116991	−	0.993133i	$-0.462675\pi$
$631$	5.87756	0.233982	0.116991	+	0.993133i	$0.462675\pi$
$632$	66.4921	2.64491
$633$	−13.4850	−0.535980
$634$	−32.9417	−1.30828
$635$	−3.10996	−0.123415
$636$	−17.2975	−0.685889
$637$	−24.6609	−0.977101
$638$	2.95378	0.116941
$639$	4.91935	0.194606
$640$	−80.2501	−3.17216
$641$	46.1054	1.82106	0.910528	−	0.413448i	$-0.135676\pi$
$641$	46.1054	1.82106	0.910528	+	0.413448i	$0.135676\pi$
$642$	3.34527	0.132027
$643$	−1.09763	−0.0432863	−0.0216431	−	0.999766i	$-0.506890\pi$
$643$	−1.09763	−0.0432863	−0.0216431	+	0.999766i	$0.506890\pi$
$644$	−73.0478	−2.87849
$645$	22.2284	0.875243
$646$	−4.62082	−0.181804
$647$	15.4945	0.609153	0.304577	−	0.952488i	$-0.401485\pi$
$647$	15.4945	0.609153	0.304577	+	0.952488i	$0.401485\pi$
$648$	−4.59173	−0.180380
$649$	−5.38522	−0.211388
$650$	69.2938	2.71793
$651$	28.7996	1.12874
$652$	−42.4570	−1.66274
$653$	36.9620	1.44643	0.723217	−	0.690621i	$-0.242663\pi$
$653$	36.9620	1.44643	0.723217	+	0.690621i	$0.242663\pi$
$654$	46.6440	1.82392
$655$	36.1437	1.41225
$656$	9.80389	0.382777
$657$	−4.26972	−0.166578
$658$	−19.1782	−0.747642
$659$	−26.6747	−1.03910	−0.519550	−	0.854440i	$-0.673900\pi$
$659$	−26.6747	−1.03910	−0.519550	+	0.854440i	$0.673900\pi$
$660$	−6.54557	−0.254786
$661$	−23.3500	−0.908212	−0.454106	−	0.890948i	$-0.650041\pi$
$661$	−23.3500	−0.908212	−0.454106	+	0.890948i	$0.650041\pi$
$662$	63.4885	2.46755
$663$	2.68690	0.104350
$664$	12.3486	0.479217
$665$	−30.2672	−1.17371
$666$	20.3490	0.788506
$667$	−13.3463	−0.516770
$668$	−8.52390	−0.329799
$669$	1.88957	0.0730549
$670$	−41.1260	−1.58883
$671$	−2.27766	−0.0879280
$672$	−4.11429	−0.158712
$673$	−0.594168	−0.0229035	−0.0114517	−	0.999934i	$-0.503645\pi$
$673$	−0.594168	−0.0229035	−0.0114517	+	0.999934i	$0.503645\pi$
$674$	−50.0076	−1.92622
$675$	10.6248	0.408951
$676$	−22.4964	−0.865247
$677$	−45.0499	−1.73141	−0.865704	−	0.500557i	$-0.833129\pi$
$677$	−45.0499	−1.73141	−0.865704	+	0.500557i	$0.833129\pi$
$678$	−41.3549	−1.58822
$679$	−25.9541	−0.996028
$680$	−18.1503	−0.696033
$681$	1.62194	0.0621530
$682$	7.39503	0.283170
$683$	−11.4815	−0.439327	−0.219663	−	0.975576i	$-0.570496\pi$
$683$	−11.4815	−0.439327	−0.219663	+	0.975576i	$0.570496\pi$
$684$	−7.40866	−0.283277
$685$	26.0673	0.995981
$686$	21.2661	0.811943
$687$	−0.00764999	−0.000291865 0
$688$	−18.9060	−0.720786
$689$	11.9424	0.454970
$690$	44.7744	1.70453
$691$	−41.3688	−1.57374	−0.786872	−	0.617116i	$-0.788301\pi$
$691$	−41.3688	−1.57374	−0.786872	+	0.617116i	$0.788301\pi$
$692$	−2.83623	−0.107817
$693$	−1.71145	−0.0650126
$694$	−19.6296	−0.745129
$695$	75.0425	2.84652
$696$	13.1322	0.497773
$697$	−2.91607	−0.110454
$698$	−33.6961	−1.27542
$699$	−1.78235	−0.0674147
$700$	−166.314	−6.28608
$701$	−28.2311	−1.06627	−0.533136	−	0.846029i	$-0.678987\pi$
$701$	−28.2311	−1.06627	−0.533136	+	0.846029i	$0.678987\pi$
$702$	6.52186	0.246152
$703$	15.9595	0.601925
$704$	−3.91752	−0.147647
$705$	7.76477	0.292438
$706$	2.50683	0.0943457
$707$	42.3405	1.59238
$708$	−49.2545	−1.85110
$709$	39.3096	1.47630	0.738151	−	0.674635i	$-0.235699\pi$
$709$	39.3096	1.47630	0.738151	+	0.674635i	$0.235699\pi$
$710$	47.1994	1.77136
$711$	−14.4808	−0.543074
$712$	9.93088	0.372176
$713$	−33.4134	−1.25134
$714$	−9.76307	−0.365374
$715$	4.51915	0.169007
$716$	23.8541	0.891471
$717$	26.1368	0.976097
$718$	−31.7322	−1.18424
$719$	−36.6981	−1.36861	−0.684305	−	0.729196i	$-0.739894\pi$
$719$	−36.6981	−1.36861	−0.684305	+	0.729196i	$0.739894\pi$
$720$	−13.2895	−0.495269
$721$	−23.3977	−0.871377
$722$	37.3218	1.38897
$723$	29.8342	1.10955
$724$	27.7677	1.03198
$725$	−30.3866	−1.12853
$726$	26.2607	0.974625
$727$	−35.5962	−1.32019	−0.660094	−	0.751183i	$-0.729484\pi$
$727$	−35.5962	−1.32019	−0.660094	+	0.751183i	$0.729484\pi$
$728$	−49.6241	−1.83919
$729$	1.00000	0.0370370
$730$	−40.9664	−1.51623
$731$	5.62342	0.207990
$732$	−20.8320	−0.769973
$733$	23.1560	0.855286	0.427643	−	0.903948i	$-0.359344\pi$
$733$	23.1560	0.855286	0.427643	+	0.903948i	$0.359344\pi$
$734$	−33.8927	−1.25100
$735$	−36.2799	−1.33820
$736$	4.77343	0.175951
$737$	−1.82384	−0.0671819
$738$	−7.07814	−0.260550
$739$	14.4382	0.531118	0.265559	−	0.964095i	$-0.414444\pi$
$739$	14.4382	0.531118	0.265559	+	0.964095i	$0.414444\pi$
$740$	128.965	4.74083
$741$	5.11504	0.187906
$742$	−43.3938	−1.59304
$743$	30.2259	1.10888	0.554441	−	0.832223i	$-0.312932\pi$
$743$	30.2259	1.10888	0.554441	+	0.832223i	$0.312932\pi$
$744$	32.8774	1.20534
$745$	75.7685	2.77594
$746$	−72.5772	−2.65724
$747$	−2.68930	−0.0983964
$748$	−1.65592	−0.0605465
$749$	5.54340	0.202551
$750$	53.9684	1.97065
$751$	−19.5904	−0.714865	−0.357432	−	0.933939i	$-0.616348\pi$
$751$	−19.5904	−0.714865	−0.357432	+	0.933939i	$0.616348\pi$
$752$	−6.60420	−0.240831
$753$	−7.65313	−0.278896
$754$	−18.6522	−0.679274
$755$	48.8538	1.77797
$756$	−15.6533	−0.569306
$757$	21.1631	0.769186	0.384593	−	0.923086i	$-0.374342\pi$
$757$	21.1631	0.769186	0.384593	+	0.923086i	$0.374342\pi$
$758$	−54.1458	−1.96667
$759$	1.98563	0.0720739
$760$	−34.5528	−1.25336
$761$	−46.5139	−1.68613	−0.843064	−	0.537813i	$-0.819251\pi$
$761$	−46.5139	−1.68613	−0.843064	+	0.537813i	$0.819251\pi$
$762$	−1.90971	−0.0691815
$763$	77.2930	2.79819
$764$	−77.7398	−2.81253
$765$	3.95283	0.142915
$766$	−0.751815	−0.0271642
$767$	34.0060	1.22789
$768$	−30.8649	−1.11374
$769$	0.935027	0.0337179	0.0168590	−	0.999858i	$-0.494633\pi$
$769$	0.935027	0.0337179	0.0168590	+	0.999858i	$0.494633\pi$
$770$	−16.4207	−0.591762
$771$	15.1715	0.546389
$772$	30.4766	1.09688
$773$	7.54953	0.271538	0.135769	−	0.990741i	$-0.456650\pi$
$773$	7.54953	0.271538	0.135769	+	0.990741i	$0.456650\pi$
$774$	13.6497	0.490627
$775$	−76.0752	−2.73270
$776$	−29.6290	−1.06362
$777$	33.7199	1.20970
$778$	11.0555	0.396360
$779$	−5.55133	−0.198897
$780$	41.3333	1.47997
$781$	2.09318	0.0748998
$782$	11.3272	0.405059
$783$	−2.85996	−0.102206
$784$	30.8573	1.10205
$785$	3.95283	0.141082
$786$	22.1945	0.791652
$787$	−29.0735	−1.03636	−0.518178	−	0.855273i	$-0.673390\pi$
$787$	−29.0735	−1.03636	−0.518178	+	0.855273i	$0.673390\pi$
$788$	−46.2146	−1.64633
$789$	−4.38275	−0.156030
$790$	−138.938	−4.94321
$791$	−68.5285	−2.43659
$792$	−1.95378	−0.0694245
$793$	14.3827	0.510745
$794$	34.2774	1.21646
$795$	17.5691	0.623112
$796$	36.3820	1.28952
$797$	29.0927	1.03052	0.515259	−	0.857035i	$-0.327696\pi$
$797$	29.0927	1.03052	0.515259	+	0.857035i	$0.327696\pi$
$798$	−18.5859	−0.657935
$799$	1.96436	0.0694940
$800$	10.8681	0.384244
$801$	−2.16277	−0.0764179
$802$	−31.1512	−1.09999
$803$	−1.81676	−0.0641121
$804$	−16.6812	−0.588302
$805$	74.1949	2.61503
$806$	−46.6974	−1.64484
$807$	−0.638198	−0.0224656
$808$	48.3356	1.70044
$809$	27.7379	0.975214	0.487607	−	0.873063i	$-0.337870\pi$
$809$	27.7379	0.975214	0.487607	+	0.873063i	$0.337870\pi$
$810$	9.59464	0.337121
$811$	−17.0700	−0.599409	−0.299704	−	0.954032i	$-0.596888\pi$
$811$	−17.0700	−0.599409	−0.299704	+	0.954032i	$0.596888\pi$
$812$	44.7678	1.57104
$813$	−22.9410	−0.804577
$814$	8.65846	0.303479
$815$	43.1237	1.51056
$816$	−3.36202	−0.117694
$817$	10.7053	0.374531
$818$	27.5984	0.964955
$819$	10.8073	0.377637
$820$	−44.8588	−1.56654
$821$	−5.12512	−0.178868	−0.0894340	−	0.995993i	$-0.528506\pi$
$821$	−5.12512	−0.178868	−0.0894340	+	0.995993i	$0.528506\pi$
$822$	16.0070	0.558307
$823$	−11.5539	−0.402744	−0.201372	−	0.979515i	$-0.564540\pi$
$823$	−11.5539	−0.402744	−0.201372	+	0.979515i	$0.564540\pi$
$824$	−26.7107	−0.930511
$825$	4.52086	0.157396
$826$	−123.564	−4.29933
$827$	−46.6101	−1.62079	−0.810395	−	0.585884i	$-0.800748\pi$
$827$	−46.6101	−1.62079	−0.810395	+	0.585884i	$0.800748\pi$
$828$	18.1611	0.631141
$829$	21.8784	0.759870	0.379935	−	0.925013i	$-0.375946\pi$
$829$	21.8784	0.759870	0.379935	+	0.925013i	$0.375946\pi$
$830$	−25.8029	−0.895631
$831$	−2.67968	−0.0929572
$832$	24.7379	0.857634
$833$	−9.17822	−0.318006
$834$	46.0808	1.59565
$835$	8.65775	0.299614
$836$	−3.15238	−0.109027
$837$	−7.16013	−0.247490
$838$	4.89062	0.168944
$839$	33.8071	1.16715	0.583576	−	0.812059i	$-0.301653\pi$
$839$	33.8071	1.16715	0.583576	+	0.812059i	$0.301653\pi$
$840$	−73.0045	−2.51890
$841$	−20.8207	−0.717954
$842$	65.5395	2.25864
$843$	10.6523	0.366885
$844$	−52.4797	−1.80643
$845$	22.8497	0.786053
$846$	4.76806	0.163929
$847$	43.5162	1.49523
$848$	−14.9431	−0.513149
$849$	23.2091	0.796533
$850$	25.7895	0.884574
$851$	−39.1221	−1.34109
$852$	19.1447	0.655887
$853$	43.2510	1.48089	0.740443	−	0.672119i	$-0.234616\pi$
$853$	43.2510	1.48089	0.740443	+	0.672119i	$0.234616\pi$
$854$	−52.2608	−1.78833
$855$	7.52500	0.257349
$856$	6.32831	0.216297
$857$	44.5925	1.52325	0.761626	−	0.648017i	$-0.224402\pi$
$857$	44.5925	1.52325	0.761626	+	0.648017i	$0.224402\pi$
$858$	2.77505	0.0947385
$859$	57.3810	1.95781	0.978907	−	0.204306i	$-0.0654939\pi$
$859$	57.3810	1.95781	0.978907	+	0.204306i	$0.0654939\pi$
$860$	86.5067	2.94985
$861$	−11.7291	−0.399726
$862$	−78.1441	−2.66160
$863$	9.45152	0.321733	0.160867	−	0.986976i	$-0.448571\pi$
$863$	9.45152	0.321733	0.160867	+	0.986976i	$0.448571\pi$
$864$	1.02289	0.0347995
$865$	2.88077	0.0979492
$866$	2.82927	0.0961424
$867$	1.00000	0.0339618
$868$	112.080	3.80423
$869$	−6.16158	−0.209017
$870$	−27.4402	−0.930312
$871$	11.5170	0.390237
$872$	88.2372	2.98809
$873$	6.45269	0.218391
$874$	21.5635	0.729397
$875$	89.4301	3.02329
$876$	−16.6165	−0.561420
$877$	12.8011	0.432264	0.216132	−	0.976364i	$-0.430656\pi$
$877$	12.8011	0.432264	0.216132	+	0.976364i	$0.430656\pi$
$878$	−37.8180	−1.27630
$879$	−21.4976	−0.725095
$880$	−5.65466	−0.190618
$881$	0.300462	0.0101228	0.00506141	−	0.999987i	$-0.498389\pi$
$881$	0.300462	0.0101228	0.00506141	+	0.999987i	$0.498389\pi$
$882$	−22.2782	−0.750144
$883$	3.17748	0.106931	0.0534653	−	0.998570i	$-0.482973\pi$
$883$	3.17748	0.106931	0.0534653	+	0.998570i	$0.482973\pi$
$884$	10.4566	0.351695
$885$	50.0280	1.68167
$886$	94.2443	3.16620
$887$	−47.9241	−1.60914	−0.804568	−	0.593861i	$-0.797603\pi$
$887$	−47.9241	−1.60914	−0.804568	+	0.593861i	$0.797603\pi$
$888$	38.4944	1.29179
$889$	−3.16455	−0.106136
$890$	−20.7510	−0.695577
$891$	0.425499	0.0142548
$892$	7.35366	0.246219
$893$	3.73955	0.125139
$894$	46.5266	1.55608
$895$	−24.2287	−0.809877
$896$	−81.6588	−2.72803
$897$	−12.5387	−0.418654
$898$	54.0408	1.80336
$899$	20.4776	0.682968
$900$	41.3489	1.37830
$901$	4.44469	0.148074
$902$	−3.01174	−0.100280
$903$	22.6186	0.752700
$904$	−78.2317	−2.60195
$905$	−28.2037	−0.937524
$906$	29.9993	0.996661
$907$	−22.7556	−0.755586	−0.377793	−	0.925890i	$-0.623317\pi$
$907$	−22.7556	−0.755586	−0.377793	+	0.925890i	$0.623317\pi$
$908$	6.31215	0.209476
$909$	−10.5267	−0.349148
$910$	103.692	3.43735
$911$	15.3046	0.507063	0.253532	−	0.967327i	$-0.418408\pi$
$911$	15.3046	0.507063	0.253532	+	0.967327i	$0.418408\pi$
$912$	−6.40027	−0.211934
$913$	−1.14430	−0.0378706
$914$	−44.0522	−1.45712
$915$	21.1591	0.699500
$916$	−0.0297716	−0.000983681 0
$917$	36.7782	1.21452
$918$	2.42729	0.0801124
$919$	−22.2686	−0.734574	−0.367287	−	0.930108i	$-0.619713\pi$
$919$	−22.2686	−0.734574	−0.367287	+	0.930108i	$0.619713\pi$
$920$	84.7003	2.79249
$921$	−11.9455	−0.393616
$922$	31.3161	1.03134
$923$	−13.2178	−0.435068
$924$	−6.66047	−0.219113
$925$	−89.0726	−2.92869
$926$	46.9552	1.54304
$927$	5.81712	0.191059
$928$	−2.92543	−0.0960318
$929$	49.3621	1.61952	0.809759	−	0.586763i	$-0.199598\pi$
$929$	49.3621	1.61952	0.809759	+	0.586763i	$0.199598\pi$
$930$	−68.6988	−2.25272
$931$	−17.4726	−0.572640
$932$	−6.93640	−0.227209
$933$	7.47291	0.244652
$934$	−51.5955	−1.68826
$935$	1.68192	0.0550048
$936$	12.3375	0.403264
$937$	−26.5493	−0.867327	−0.433663	−	0.901075i	$-0.642779\pi$
$937$	−26.5493	−0.867327	−0.433663	+	0.901075i	$0.642779\pi$
$938$	−41.8479	−1.36638
$939$	−24.3954	−0.796115
$940$	30.2183	0.985611
$941$	−10.3644	−0.337868	−0.168934	−	0.985627i	$-0.554033\pi$
$941$	−10.3644	−0.337868	−0.168934	+	0.985627i	$0.554033\pi$
$942$	2.42729	0.0790852
$943$	13.6081	0.443142
$944$	−42.5505	−1.38490
$945$	15.8991	0.517199
$946$	5.80791	0.188832
$947$	38.1287	1.23901	0.619507	−	0.784991i	$-0.287332\pi$
$947$	38.1287	1.23901	0.619507	+	0.784991i	$0.287332\pi$
$948$	−56.3553	−1.83033
$949$	11.4723	0.372406
$950$	49.0955	1.59287
$951$	13.5714	0.440084
$952$	−18.4689	−0.598582
$953$	−34.4068	−1.11454	−0.557272	−	0.830330i	$-0.688152\pi$
$953$	−34.4068	−1.11454	−0.557272	+	0.830330i	$0.688152\pi$
$954$	10.7885	0.349292
$955$	78.9605	2.55510
$956$	101.717	3.28976
$957$	−1.21691	−0.0393371
$958$	70.2661	2.27019
$959$	26.5249	0.856533
$960$	36.3932	1.17459
$961$	20.2674	0.653787
$962$	−54.6755	−1.76281
$963$	−1.37820	−0.0444117
$964$	116.106	3.73953
$965$	−30.9552	−0.996482
$966$	45.5603	1.46588
$967$	41.3894	1.33099	0.665496	−	0.746401i	$-0.268220\pi$
$967$	41.3894	1.33099	0.665496	+	0.746401i	$0.268220\pi$
$968$	49.6777	1.59670
$969$	1.90370	0.0611556
$970$	61.9113	1.98785
$971$	20.1477	0.646571	0.323286	−	0.946301i	$-0.395213\pi$
$971$	20.1477	0.646571	0.323286	+	0.946301i	$0.395213\pi$
$972$	3.89172	0.124827
$973$	76.3598	2.44798
$974$	−9.94398	−0.318626
$975$	−28.5479	−0.914263
$976$	−17.9966	−0.576056
$977$	53.3233	1.70596	0.852982	−	0.521941i	$-0.174792\pi$
$977$	53.3233	1.70596	0.852982	+	0.521941i	$0.174792\pi$
$978$	26.4807	0.846758
$979$	−0.920258	−0.0294116
$980$	−141.191	−4.51018
$981$	−19.2165	−0.613536
$982$	72.0595	2.29951
$983$	−31.5871	−1.00747	−0.503736	−	0.863857i	$-0.668042\pi$
$983$	−31.5871	−1.00747	−0.503736	+	0.863857i	$0.668042\pi$
$984$	−13.3898	−0.426852
$985$	46.9403	1.49564
$986$	−6.94193	−0.221076
$987$	7.90107	0.251494
$988$	19.9063	0.633303
$989$	−26.2423	−0.834455
$990$	4.08251	0.129751
$991$	−12.2880	−0.390340	−0.195170	−	0.980769i	$-0.562526\pi$
$991$	−12.2880	−0.390340	−0.195170	+	0.980769i	$0.562526\pi$
$992$	−7.32404	−0.232538
$993$	−26.1562	−0.830041
$994$	48.0279	1.52335
$995$	−36.9533	−1.17150
$996$	−10.4660	−0.331628
$997$	−25.6707	−0.812998	−0.406499	−	0.913651i	$-0.633251\pi$
$997$	−25.6707	−0.812998	−0.406499	+	0.913651i	$0.633251\pi$
$998$	−34.8443	−1.10298
$999$	−8.38342	−0.265240

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.h.1.6	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.h.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.42729 q^{2} +1.00000 q^{3} +3.89172 q^{4} -3.95283 q^{5} -2.42729 q^{6} -4.02222 q^{7} -4.59173 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.42729 q^{2} +1.00000 q^{3} +3.89172 q^{4} -3.95283 q^{5} -2.42729 q^{6} -4.02222 q^{7} -4.59173 q^{8} +1.00000 q^{9} +9.59464 q^{10} +0.425499 q^{11} +3.89172 q^{12} -2.68690 q^{13} +9.76307 q^{14} -3.95283 q^{15} +3.36202 q^{16} -1.00000 q^{17} -2.42729 q^{18} -1.90370 q^{19} -15.3833 q^{20} -4.02222 q^{21} -1.03281 q^{22} +4.66660 q^{23} -4.59173 q^{24} +10.6248 q^{25} +6.52186 q^{26} +1.00000 q^{27} -15.6533 q^{28} -2.85996 q^{29} +9.59464 q^{30} -7.16013 q^{31} +1.02289 q^{32} +0.425499 q^{33} +2.42729 q^{34} +15.8991 q^{35} +3.89172 q^{36} -8.38342 q^{37} +4.62082 q^{38} -2.68690 q^{39} +18.1503 q^{40} +2.91607 q^{41} +9.76307 q^{42} -5.62342 q^{43} +1.65592 q^{44} -3.95283 q^{45} -11.3272 q^{46} -1.96436 q^{47} +3.36202 q^{48} +9.17822 q^{49} -25.7895 q^{50} -1.00000 q^{51} -10.4566 q^{52} -4.44469 q^{53} -2.42729 q^{54} -1.68192 q^{55} +18.4689 q^{56} -1.90370 q^{57} +6.94193 q^{58} -12.6563 q^{59} -15.3833 q^{60} -5.35291 q^{61} +17.3797 q^{62} -4.02222 q^{63} -9.20688 q^{64} +10.6208 q^{65} -1.03281 q^{66} -4.28635 q^{67} -3.89172 q^{68} +4.66660 q^{69} -38.5917 q^{70} +4.91935 q^{71} -4.59173 q^{72} -4.26972 q^{73} +20.3490 q^{74} +10.6248 q^{75} -7.40866 q^{76} -1.71145 q^{77} +6.52186 q^{78} -14.4808 q^{79} -13.2895 q^{80} +1.00000 q^{81} -7.07814 q^{82} -2.68930 q^{83} -15.6533 q^{84} +3.95283 q^{85} +13.6497 q^{86} -2.85996 q^{87} -1.95378 q^{88} -2.16277 q^{89} +9.59464 q^{90} +10.8073 q^{91} +18.1611 q^{92} -7.16013 q^{93} +4.76806 q^{94} +7.52500 q^{95} +1.02289 q^{96} +6.45269 q^{97} -22.2782 q^{98} +0.425499 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) \) 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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