LMFDB - Embedded newform 8007.2.a.h.1.8

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			1.8
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)

$f(q)$	$=$	$q-2.14010 q^{2} +1.00000 q^{3} +2.58002 q^{4} -0.881570 q^{5} -2.14010 q^{6} -2.47197 q^{7} -1.24130 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.14010 q^{2} +1.00000 q^{3} +2.58002 q^{4} -0.881570 q^{5} -2.14010 q^{6} -2.47197 q^{7} -1.24130 q^{8} +1.00000 q^{9} +1.88665 q^{10} -4.39701 q^{11} +2.58002 q^{12} +0.817662 q^{13} +5.29026 q^{14} -0.881570 q^{15} -2.50354 q^{16} -1.00000 q^{17} -2.14010 q^{18} -5.73800 q^{19} -2.27447 q^{20} -2.47197 q^{21} +9.41004 q^{22} -3.68733 q^{23} -1.24130 q^{24} -4.22283 q^{25} -1.74988 q^{26} +1.00000 q^{27} -6.37773 q^{28} +6.35222 q^{29} +1.88665 q^{30} +3.63413 q^{31} +7.84041 q^{32} -4.39701 q^{33} +2.14010 q^{34} +2.17921 q^{35} +2.58002 q^{36} +1.04286 q^{37} +12.2799 q^{38} +0.817662 q^{39} +1.09429 q^{40} -9.98744 q^{41} +5.29026 q^{42} -7.19149 q^{43} -11.3444 q^{44} -0.881570 q^{45} +7.89125 q^{46} -6.67559 q^{47} -2.50354 q^{48} -0.889369 q^{49} +9.03728 q^{50} -1.00000 q^{51} +2.10958 q^{52} +6.97068 q^{53} -2.14010 q^{54} +3.87628 q^{55} +3.06845 q^{56} -5.73800 q^{57} -13.5944 q^{58} -0.253239 q^{59} -2.27447 q^{60} -0.406403 q^{61} -7.77740 q^{62} -2.47197 q^{63} -11.7722 q^{64} -0.720826 q^{65} +9.41004 q^{66} -13.9141 q^{67} -2.58002 q^{68} -3.68733 q^{69} -4.66373 q^{70} +1.26017 q^{71} -1.24130 q^{72} +2.46325 q^{73} -2.23183 q^{74} -4.22283 q^{75} -14.8042 q^{76} +10.8693 q^{77} -1.74988 q^{78} -12.2775 q^{79} +2.20704 q^{80} +1.00000 q^{81} +21.3741 q^{82} +12.3191 q^{83} -6.37773 q^{84} +0.881570 q^{85} +15.3905 q^{86} +6.35222 q^{87} +5.45801 q^{88} -0.0913787 q^{89} +1.88665 q^{90} -2.02123 q^{91} -9.51339 q^{92} +3.63413 q^{93} +14.2864 q^{94} +5.05845 q^{95} +7.84041 q^{96} +0.121846 q^{97} +1.90334 q^{98} -4.39701 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.14010	−1.51328	−0.756639	−	0.653833i	$-0.773160\pi$
$2$	−2.14010	−1.51328	−0.756639	+	0.653833i	$0.773160\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.58002	1.29001
$5$	−0.881570	−0.394250	−0.197125	−	0.980378i	$-0.563160\pi$
$5$	−0.881570	−0.394250	−0.197125	+	0.980378i	$0.563160\pi$
$6$	−2.14010	−0.873691
$7$	−2.47197	−0.934316	−0.467158	−	0.884174i	$-0.654722\pi$
$7$	−2.47197	−0.934316	−0.467158	+	0.884174i	$0.654722\pi$
$8$	−1.24130	−0.438866
$9$	1.00000	0.333333
$10$	1.88665	0.596610
$11$	−4.39701	−1.32575	−0.662875	−	0.748730i	$-0.730664\pi$
$11$	−4.39701	−1.32575	−0.662875	+	0.748730i	$0.730664\pi$
$12$	2.58002	0.744788
$13$	0.817662	0.226779	0.113389	−	0.993551i	$-0.463829\pi$
$13$	0.817662	0.226779	0.113389	+	0.993551i	$0.463829\pi$
$14$	5.29026	1.41388
$15$	−0.881570	−0.227620
$16$	−2.50354	−0.625884
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.14010	−0.504426
$19$	−5.73800	−1.31639	−0.658194	−	0.752848i	$-0.728679\pi$
$19$	−5.73800	−1.31639	−0.658194	+	0.752848i	$0.728679\pi$
$20$	−2.27447	−0.508586
$21$	−2.47197	−0.539428
$22$	9.41004	2.00623
$23$	−3.68733	−0.768862	−0.384431	−	0.923154i	$-0.625602\pi$
$23$	−3.68733	−0.768862	−0.384431	+	0.923154i	$0.625602\pi$
$24$	−1.24130	−0.253379
$25$	−4.22283	−0.844567
$26$	−1.74988	−0.343179
$27$	1.00000	0.192450
$28$	−6.37773	−1.20528
$29$	6.35222	1.17958	0.589788	−	0.807558i	$-0.299211\pi$
$29$	6.35222	1.17958	0.589788	+	0.807558i	$0.299211\pi$
$30$	1.88665	0.344453
$31$	3.63413	0.652709	0.326355	−	0.945247i	$-0.394180\pi$
$31$	3.63413	0.652709	0.326355	+	0.945247i	$0.394180\pi$
$32$	7.84041	1.38600
$33$	−4.39701	−0.765422
$34$	2.14010	0.367024
$35$	2.17921	0.368354
$36$	2.58002	0.430003
$37$	1.04286	0.171446	0.0857229	−	0.996319i	$-0.472680\pi$
$37$	1.04286	0.171446	0.0857229	+	0.996319i	$0.472680\pi$
$38$	12.2799	1.99206
$39$	0.817662	0.130931
$40$	1.09429	0.173023
$41$	−9.98744	−1.55978	−0.779888	−	0.625919i	$-0.784724\pi$
$41$	−9.98744	−1.55978	−0.779888	+	0.625919i	$0.784724\pi$
$42$	5.29026	0.816304
$43$	−7.19149	−1.09669	−0.548346	−	0.836251i	$-0.684742\pi$
$43$	−7.19149	−1.09669	−0.548346	+	0.836251i	$0.684742\pi$
$44$	−11.3444	−1.71023
$45$	−0.881570	−0.131417
$46$	7.89125	1.16350
$47$	−6.67559	−0.973735	−0.486867	−	0.873476i	$-0.661861\pi$
$47$	−6.67559	−0.973735	−0.486867	+	0.873476i	$0.661861\pi$
$48$	−2.50354	−0.361354
$49$	−0.889369	−0.127053
$50$	9.03728	1.27806
$51$	−1.00000	−0.140028
$52$	2.10958	0.292547
$53$	6.97068	0.957497	0.478748	−	0.877952i	$-0.341091\pi$
$53$	6.97068	0.957497	0.478748	+	0.877952i	$0.341091\pi$
$54$	−2.14010	−0.291230
$55$	3.87628	0.522677
$56$	3.06845	0.410040
$57$	−5.73800	−0.760017
$58$	−13.5944	−1.78503
$59$	−0.253239	−0.0329690	−0.0164845	−	0.999864i	$-0.505247\pi$
$59$	−0.253239	−0.0329690	−0.0164845	+	0.999864i	$0.505247\pi$
$60$	−2.27447	−0.293633
$61$	−0.406403	−0.0520346	−0.0260173	−	0.999661i	$-0.508282\pi$
$61$	−0.406403	−0.0520346	−0.0260173	+	0.999661i	$0.508282\pi$
$62$	−7.77740	−0.987731
$63$	−2.47197	−0.311439
$64$	−11.7722	−1.47152
$65$	−0.720826	−0.0894075
$66$	9.41004	1.15830
$67$	−13.9141	−1.69987	−0.849936	−	0.526886i	$-0.823360\pi$
$67$	−13.9141	−1.69987	−0.849936	+	0.526886i	$0.823360\pi$
$68$	−2.58002	−0.312873
$69$	−3.68733	−0.443903
$70$	−4.66373	−0.557422
$71$	1.26017	0.149555	0.0747775	−	0.997200i	$-0.476175\pi$
$71$	1.26017	0.149555	0.0747775	+	0.997200i	$0.476175\pi$
$72$	−1.24130	−0.146289
$73$	2.46325	0.288301	0.144151	−	0.989556i	$-0.453955\pi$
$73$	2.46325	0.288301	0.144151	+	0.989556i	$0.453955\pi$
$74$	−2.23183	−0.259445
$75$	−4.22283	−0.487611
$76$	−14.8042	−1.69815
$77$	10.8693	1.23867
$78$	−1.74988	−0.198134
$79$	−12.2775	−1.38133	−0.690664	−	0.723176i	$-0.742682\pi$
$79$	−12.2775	−1.38133	−0.690664	+	0.723176i	$0.742682\pi$
$80$	2.20704	0.246755
$81$	1.00000	0.111111
$82$	21.3741	2.36038
$83$	12.3191	1.35220	0.676098	−	0.736812i	$-0.263670\pi$
$83$	12.3191	1.35220	0.676098	+	0.736812i	$0.263670\pi$
$84$	−6.37773	−0.695867
$85$	0.881570	0.0956197
$86$	15.3905	1.65960
$87$	6.35222	0.681029
$88$	5.45801	0.581826
$89$	−0.0913787	−0.00968613	−0.00484306	−	0.999988i	$-0.501542\pi$
$89$	−0.0913787	−0.00968613	−0.00484306	+	0.999988i	$0.501542\pi$
$90$	1.88665	0.198870
$91$	−2.02123	−0.211883
$92$	−9.51339	−0.991840
$93$	3.63413	0.376842
$94$	14.2864	1.47353
$95$	5.05845	0.518986
$96$	7.84041	0.800209
$97$	0.121846	0.0123716	0.00618579	−	0.999981i	$-0.498031\pi$
$97$	0.121846	0.0123716	0.00618579	+	0.999981i	$0.498031\pi$
$98$	1.90334	0.192266
$99$	−4.39701	−0.441917
$100$	−10.8950	−1.08950
$101$	8.36778	0.832625	0.416313	−	0.909222i	$-0.363322\pi$
$101$	8.36778	0.832625	0.416313	+	0.909222i	$0.363322\pi$
$102$	2.14010	0.211901
$103$	4.62450	0.455665	0.227833	−	0.973700i	$-0.426836\pi$
$103$	4.62450	0.455665	0.227833	+	0.973700i	$0.426836\pi$
$104$	−1.01496	−0.0995253
$105$	2.17921	0.212669
$106$	−14.9179	−1.44896
$107$	−8.59293	−0.830710	−0.415355	−	0.909659i	$-0.636343\pi$
$107$	−8.59293	−0.830710	−0.415355	+	0.909659i	$0.636343\pi$
$108$	2.58002	0.248263
$109$	9.75288	0.934157	0.467078	−	0.884216i	$-0.345307\pi$
$109$	9.75288	0.934157	0.467078	+	0.884216i	$0.345307\pi$
$110$	−8.29561	−0.790955
$111$	1.04286	0.0989843
$112$	6.18867	0.584774
$113$	−12.1553	−1.14347	−0.571737	−	0.820437i	$-0.693730\pi$
$113$	−12.1553	−1.14347	−0.571737	+	0.820437i	$0.693730\pi$
$114$	12.2799	1.15012
$115$	3.25064	0.303124
$116$	16.3888	1.52167
$117$	0.817662	0.0755929
$118$	0.541957	0.0498912
$119$	2.47197	0.226605
$120$	1.09429	0.0998948
$121$	8.33373	0.757612
$122$	0.869743	0.0787428
$123$	−9.98744	−0.900537
$124$	9.37614	0.842002
$125$	8.13057	0.727221
$126$	5.29026	0.471293
$127$	−17.8509	−1.58401	−0.792004	−	0.610516i	$-0.790962\pi$
$127$	−17.8509	−1.58401	−0.792004	+	0.610516i	$0.790962\pi$
$128$	9.51280	0.840820
$129$	−7.19149	−0.633176
$130$	1.54264	0.135298
$131$	0.501756	0.0438386	0.0219193	−	0.999760i	$-0.493022\pi$
$131$	0.501756	0.0438386	0.0219193	+	0.999760i	$0.493022\pi$
$132$	−11.3444	−0.987402
$133$	14.1842	1.22992
$134$	29.7774	2.57238
$135$	−0.881570	−0.0758735
$136$	1.24130	0.106441
$137$	−2.97320	−0.254017	−0.127009	−	0.991902i	$-0.540538\pi$
$137$	−2.97320	−0.254017	−0.127009	+	0.991902i	$0.540538\pi$
$138$	7.89125	0.671748
$139$	1.70852	0.144915	0.0724574	−	0.997372i	$-0.476916\pi$
$139$	1.70852	0.144915	0.0724574	+	0.997372i	$0.476916\pi$
$140$	5.62241	0.475181
$141$	−6.67559	−0.562186
$142$	−2.69689	−0.226318
$143$	−3.59527	−0.300652
$144$	−2.50354	−0.208628
$145$	−5.59992	−0.465048
$146$	−5.27159	−0.436280
$147$	−0.889369	−0.0733539
$148$	2.69061	0.221167
$149$	6.03429	0.494348	0.247174	−	0.968971i	$-0.420498\pi$
$149$	6.03429	0.494348	0.247174	+	0.968971i	$0.420498\pi$
$150$	9.03728	0.737891
$151$	−6.84081	−0.556698	−0.278349	−	0.960480i	$-0.589787\pi$
$151$	−6.84081	−0.556698	−0.278349	+	0.960480i	$0.589787\pi$
$152$	7.12258	0.577718
$153$	−1.00000	−0.0808452
$154$	−23.2613	−1.87445
$155$	−3.20374	−0.257331
$156$	2.10958	0.168902
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	26.2751	2.09033
$159$	6.97068	0.552811
$160$	−6.91187	−0.546431
$161$	9.11497	0.718360
$162$	−2.14010	−0.168142
$163$	4.97205	0.389441	0.194721	−	0.980859i	$-0.437620\pi$
$163$	4.97205	0.389441	0.194721	+	0.980859i	$0.437620\pi$
$164$	−25.7678	−2.01213
$165$	3.87628	0.301768
$166$	−26.3640	−2.04625
$167$	2.72951	0.211216	0.105608	−	0.994408i	$-0.466321\pi$
$167$	2.72951	0.211216	0.105608	+	0.994408i	$0.466321\pi$
$168$	3.06845	0.236736
$169$	−12.3314	−0.948571
$170$	−1.88665	−0.144699
$171$	−5.73800	−0.438796
$172$	−18.5542	−1.41474
$173$	8.88822	0.675759	0.337879	−	0.941189i	$-0.390290\pi$
$173$	8.88822	0.675759	0.337879	+	0.941189i	$0.390290\pi$
$174$	−13.5944	−1.03059
$175$	10.4387	0.789093
$176$	11.0081	0.829766
$177$	−0.253239	−0.0190346
$178$	0.195559	0.0146578
$179$	2.12366	0.158730	0.0793649	−	0.996846i	$-0.474711\pi$
$179$	2.12366	0.158730	0.0793649	+	0.996846i	$0.474711\pi$
$180$	−2.27447	−0.169529
$181$	−0.390811	−0.0290487	−0.0145244	−	0.999895i	$-0.504623\pi$
$181$	−0.390811	−0.0290487	−0.0145244	+	0.999895i	$0.504623\pi$
$182$	4.32564	0.320638
$183$	−0.406403	−0.0300422
$184$	4.57709	0.337427
$185$	−0.919358	−0.0675925
$186$	−7.77740	−0.570267
$187$	4.39701	0.321542
$188$	−17.2232	−1.25613
$189$	−2.47197	−0.179809
$190$	−10.8256	−0.785370
$191$	18.7735	1.35840	0.679200	−	0.733954i	$-0.262327\pi$
$191$	18.7735	1.35840	0.679200	+	0.733954i	$0.262327\pi$
$192$	−11.7722	−0.849584
$193$	15.0657	1.08445	0.542225	−	0.840233i	$-0.317582\pi$
$193$	15.0657	1.08445	0.542225	+	0.840233i	$0.317582\pi$
$194$	−0.260762	−0.0187216
$195$	−0.720826	−0.0516194
$196$	−2.29459	−0.163899
$197$	−24.8741	−1.77221	−0.886105	−	0.463485i	$-0.846599\pi$
$197$	−24.8741	−1.77221	−0.886105	+	0.463485i	$0.846599\pi$
$198$	9.41004	0.668743
$199$	13.4451	0.953098	0.476549	−	0.879148i	$-0.341887\pi$
$199$	13.4451	0.953098	0.476549	+	0.879148i	$0.341887\pi$
$200$	5.24180	0.370652
$201$	−13.9141	−0.981422
$202$	−17.9079	−1.25999
$203$	−15.7025	−1.10210
$204$	−2.58002	−0.180638
$205$	8.80463	0.614942
$206$	−9.89688	−0.689548
$207$	−3.68733	−0.256287
$208$	−2.04705	−0.141937
$209$	25.2301	1.74520
$210$	−4.66373	−0.321828
$211$	−15.3455	−1.05643	−0.528214	−	0.849111i	$-0.677138\pi$
$211$	−15.3455	−1.05643	−0.528214	+	0.849111i	$0.677138\pi$
$212$	17.9845	1.23518
$213$	1.26017	0.0863456
$214$	18.3897	1.25710
$215$	6.33980	0.432371
$216$	−1.24130	−0.0844598
$217$	−8.98346	−0.609837
$218$	−20.8721	−1.41364
$219$	2.46325	0.166451
$220$	10.0009	0.674258
$221$	−0.817662	−0.0550019
$222$	−2.23183	−0.149791
$223$	−3.33836	−0.223553	−0.111777	−	0.993733i	$-0.535654\pi$
$223$	−3.33836	−0.223553	−0.111777	+	0.993733i	$0.535654\pi$
$224$	−19.3813	−1.29496
$225$	−4.22283	−0.281522
$226$	26.0135	1.73039
$227$	1.51252	0.100390	0.0501948	−	0.998739i	$-0.484016\pi$
$227$	1.51252	0.100390	0.0501948	+	0.998739i	$0.484016\pi$
$228$	−14.8042	−0.980429
$229$	3.65826	0.241745	0.120872	−	0.992668i	$-0.461431\pi$
$229$	3.65826	0.241745	0.120872	+	0.992668i	$0.461431\pi$
$230$	−6.95669	−0.458711
$231$	10.8693	0.715146
$232$	−7.88500	−0.517676
$233$	−1.12286	−0.0735610	−0.0367805	−	0.999323i	$-0.511710\pi$
$233$	−1.12286	−0.0735610	−0.0367805	+	0.999323i	$0.511710\pi$
$234$	−1.74988	−0.114393
$235$	5.88500	0.383895
$236$	−0.653363	−0.0425303
$237$	−12.2775	−0.797510
$238$	−5.29026	−0.342916
$239$	2.05527	0.132944	0.0664720	−	0.997788i	$-0.478826\pi$
$239$	2.05527	0.132944	0.0664720	+	0.997788i	$0.478826\pi$
$240$	2.20704	0.142464
$241$	−9.03883	−0.582242	−0.291121	−	0.956686i	$-0.594028\pi$
$241$	−9.03883	−0.582242	−0.291121	+	0.956686i	$0.594028\pi$
$242$	−17.8350	−1.14648
$243$	1.00000	0.0641500
$244$	−1.04853	−0.0671252
$245$	0.784041	0.0500905
$246$	21.3741	1.36276
$247$	−4.69174	−0.298529
$248$	−4.51105	−0.286452
$249$	12.3191	0.780690
$250$	−17.4002	−1.10049
$251$	−4.94002	−0.311811	−0.155906	−	0.987772i	$-0.549830\pi$
$251$	−4.94002	−0.311811	−0.155906	+	0.987772i	$0.549830\pi$
$252$	−6.37773	−0.401759
$253$	16.2133	1.01932
$254$	38.2026	2.39704
$255$	0.881570	0.0552060
$256$	3.18605	0.199128
$257$	24.1712	1.50776	0.753880	−	0.657012i	$-0.228180\pi$
$257$	24.1712	1.50776	0.753880	+	0.657012i	$0.228180\pi$
$258$	15.3905	0.958171
$259$	−2.57793	−0.160185
$260$	−1.85975	−0.115337
$261$	6.35222	0.393192
$262$	−1.07381	−0.0663400
$263$	19.7946	1.22059	0.610293	−	0.792176i	$-0.291052\pi$
$263$	19.7946	1.22059	0.610293	+	0.792176i	$0.291052\pi$
$264$	5.45801	0.335917
$265$	−6.14514	−0.377493
$266$	−30.3555	−1.86121
$267$	−0.0913787	−0.00559229
$268$	−35.8985	−2.19285
$269$	32.5751	1.98614	0.993068	−	0.117542i	$-0.0375013\pi$
$269$	32.5751	1.98614	0.993068	+	0.117542i	$0.0375013\pi$
$270$	1.88665	0.114818
$271$	21.5603	1.30970	0.654848	−	0.755760i	$-0.272733\pi$
$271$	21.5603	1.30970	0.654848	+	0.755760i	$0.272733\pi$
$272$	2.50354	0.151799
$273$	−2.02123	−0.122331
$274$	6.36294	0.384399
$275$	18.5679	1.11968
$276$	−9.51339	−0.572639
$277$	−27.0378	−1.62454	−0.812271	−	0.583280i	$-0.801769\pi$
$277$	−27.0378	−1.62454	−0.812271	+	0.583280i	$0.801769\pi$
$278$	−3.65640	−0.219296
$279$	3.63413	0.217570
$280$	−2.70506	−0.161658
$281$	−26.2192	−1.56410	−0.782052	−	0.623213i	$-0.785827\pi$
$281$	−26.2192	−1.56410	−0.782052	+	0.623213i	$0.785827\pi$
$282$	14.2864	0.850744
$283$	19.1415	1.13784	0.568921	−	0.822392i	$-0.307361\pi$
$283$	19.1415	1.13784	0.568921	+	0.822392i	$0.307361\pi$
$284$	3.25127	0.192927
$285$	5.05845	0.299637
$286$	7.69423	0.454969
$287$	24.6886	1.45732
$288$	7.84041	0.462001
$289$	1.00000	0.0588235
$290$	11.9844	0.703747
$291$	0.121846	0.00714274
$292$	6.35523	0.371912
$293$	27.8120	1.62479	0.812397	−	0.583105i	$-0.198162\pi$
$293$	27.8120	1.62479	0.812397	+	0.583105i	$0.198162\pi$
$294$	1.90334	0.111005
$295$	0.223248	0.0129980
$296$	−1.29451	−0.0752417
$297$	−4.39701	−0.255141
$298$	−12.9140	−0.748086
$299$	−3.01499	−0.174361
$300$	−10.8950	−0.629023
$301$	17.7772	1.02466
$302$	14.6400	0.842438
$303$	8.36778	0.480716
$304$	14.3653	0.823906
$305$	0.358273	0.0205146
$306$	2.14010	0.122341
$307$	−17.0193	−0.971346	−0.485673	−	0.874141i	$-0.661425\pi$
$307$	−17.0193	−0.971346	−0.485673	+	0.874141i	$0.661425\pi$
$308$	28.0430	1.59790
$309$	4.62450	0.263078
$310$	6.85632	0.389413
$311$	7.70438	0.436875	0.218438	−	0.975851i	$-0.429904\pi$
$311$	7.70438	0.436875	0.218438	+	0.975851i	$0.429904\pi$
$312$	−1.01496	−0.0574610
$313$	−12.6441	−0.714689	−0.357344	−	0.933973i	$-0.616318\pi$
$313$	−12.6441	−0.714689	−0.357344	+	0.933973i	$0.616318\pi$
$314$	2.14010	0.120773
$315$	2.17921	0.122785
$316$	−31.6762	−1.78193
$317$	14.5346	0.816343	0.408171	−	0.912905i	$-0.366167\pi$
$317$	14.5346	0.816343	0.408171	+	0.912905i	$0.366167\pi$
$318$	−14.9179	−0.836557
$319$	−27.9308	−1.56382
$320$	10.3780	0.580148
$321$	−8.59293	−0.479611
$322$	−19.5069	−1.08708
$323$	5.73800	0.319271
$324$	2.58002	0.143334
$325$	−3.45285	−0.191530
$326$	−10.6407	−0.589333
$327$	9.75288	0.539336
$328$	12.3974	0.684532
$329$	16.5019	0.909777
$330$	−8.29561	−0.456658
$331$	−11.9795	−0.658455	−0.329227	−	0.944251i	$-0.606788\pi$
$331$	−11.9795	−0.658455	−0.329227	+	0.944251i	$0.606788\pi$
$332$	31.7835	1.74435
$333$	1.04286	0.0571486
$334$	−5.84143	−0.319629
$335$	12.2662	0.670175
$336$	6.18867	0.337619
$337$	−4.54589	−0.247631	−0.123815	−	0.992305i	$-0.539513\pi$
$337$	−4.54589	−0.247631	−0.123815	+	0.992305i	$0.539513\pi$
$338$	26.3905	1.43545
$339$	−12.1553	−0.660185
$340$	2.27447	0.123350
$341$	−15.9793	−0.865329
$342$	12.2799	0.664020
$343$	19.5023	1.05302
$344$	8.92680	0.481301
$345$	3.25064	0.175009
$346$	−19.0217	−1.02261
$347$	12.4071	0.666050	0.333025	−	0.942918i	$-0.391931\pi$
$347$	12.4071	0.666050	0.333025	+	0.942918i	$0.391931\pi$
$348$	16.3888	0.878534
$349$	10.4827	0.561125	0.280563	−	0.959836i	$-0.409479\pi$
$349$	10.4827	0.561125	0.280563	+	0.959836i	$0.409479\pi$
$350$	−22.3399	−1.19412
$351$	0.817662	0.0436436
$352$	−34.4744	−1.83749
$353$	−19.4023	−1.03268	−0.516341	−	0.856383i	$-0.672706\pi$
$353$	−19.4023	−1.03268	−0.516341	+	0.856383i	$0.672706\pi$
$354$	0.541957	0.0288047
$355$	−1.11093	−0.0589620
$356$	−0.235759	−0.0124952
$357$	2.47197	0.130830
$358$	−4.54484	−0.240202
$359$	−1.00055	−0.0528070	−0.0264035	−	0.999651i	$-0.508405\pi$
$359$	−1.00055	−0.0528070	−0.0264035	+	0.999651i	$0.508405\pi$
$360$	1.09429	0.0576743
$361$	13.9247	0.732877
$362$	0.836373	0.0439588
$363$	8.33373	0.437408
$364$	−5.21483	−0.273331
$365$	−2.17152	−0.113663
$366$	0.869743	0.0454622
$367$	−24.5915	−1.28367	−0.641834	−	0.766843i	$-0.721826\pi$
$367$	−24.5915	−1.28367	−0.641834	+	0.766843i	$0.721826\pi$
$368$	9.23137	0.481219
$369$	−9.98744	−0.519925
$370$	1.96752	0.102286
$371$	−17.2313	−0.894605
$372$	9.37614	0.486130
$373$	16.9231	0.876246	0.438123	−	0.898915i	$-0.355643\pi$
$373$	16.9231	0.876246	0.438123	+	0.898915i	$0.355643\pi$
$374$	−9.41004	−0.486582
$375$	8.13057	0.419861
$376$	8.28641	0.427339
$377$	5.19396	0.267503
$378$	5.29026	0.272101
$379$	−37.3918	−1.92069	−0.960343	−	0.278822i	$-0.910056\pi$
$379$	−37.3918	−1.92069	−0.960343	+	0.278822i	$0.910056\pi$
$380$	13.0509	0.669497
$381$	−17.8509	−0.914527
$382$	−40.1770	−2.05564
$383$	−10.5461	−0.538881	−0.269441	−	0.963017i	$-0.586839\pi$
$383$	−10.5461	−0.538881	−0.269441	+	0.963017i	$0.586839\pi$
$384$	9.51280	0.485448
$385$	−9.58203	−0.488346
$386$	−32.2420	−1.64107
$387$	−7.19149	−0.365564
$388$	0.314365	0.0159595
$389$	−5.03436	−0.255252	−0.127626	−	0.991822i	$-0.540736\pi$
$389$	−5.03436	−0.255252	−0.127626	+	0.991822i	$0.540736\pi$
$390$	1.54264	0.0781145
$391$	3.68733	0.186476
$392$	1.10397	0.0557591
$393$	0.501756	0.0253102
$394$	53.2331	2.68185
$395$	10.8235	0.544588
$396$	−11.3444	−0.570077
$397$	30.5986	1.53570	0.767850	−	0.640630i	$-0.221327\pi$
$397$	30.5986	1.53570	0.767850	+	0.640630i	$0.221327\pi$
$398$	−28.7738	−1.44230
$399$	14.1842	0.710096
$400$	10.5720	0.528601
$401$	21.9887	1.09806	0.549031	−	0.835802i	$-0.314997\pi$
$401$	21.9887	1.09806	0.549031	+	0.835802i	$0.314997\pi$
$402$	29.7774	1.48516
$403$	2.97149	0.148021
$404$	21.5890	1.07409
$405$	−0.881570	−0.0438056
$406$	33.6048	1.66778
$407$	−4.58549	−0.227294
$408$	1.24130	0.0614535
$409$	27.9598	1.38253	0.691263	−	0.722603i	$-0.257055\pi$
$409$	27.9598	1.38253	0.691263	+	0.722603i	$0.257055\pi$
$410$	−18.8428	−0.930578
$411$	−2.97320	−0.146657
$412$	11.9313	0.587813
$413$	0.626000	0.0308035
$414$	7.89125	0.387834
$415$	−10.8601	−0.533103
$416$	6.41081	0.314316
$417$	1.70852	0.0836666
$418$	−53.9948	−2.64097
$419$	33.8540	1.65388	0.826938	−	0.562293i	$-0.190081\pi$
$419$	33.8540	1.65388	0.826938	+	0.562293i	$0.190081\pi$
$420$	5.62241	0.274346
$421$	−32.8232	−1.59971	−0.799853	−	0.600196i	$-0.795089\pi$
$421$	−32.8232	−1.59971	−0.799853	+	0.600196i	$0.795089\pi$
$422$	32.8409	1.59867
$423$	−6.67559	−0.324578
$424$	−8.65271	−0.420213
$425$	4.22283	0.204838
$426$	−2.69689	−0.130665
$427$	1.00462	0.0486168
$428$	−22.1699	−1.07162
$429$	−3.59527	−0.173581
$430$	−13.5678	−0.654298
$431$	−38.5361	−1.85622	−0.928109	−	0.372309i	$-0.878566\pi$
$431$	−38.5361	−1.85622	−0.928109	+	0.372309i	$0.878566\pi$
$432$	−2.50354	−0.120451
$433$	12.6145	0.606217	0.303108	−	0.952956i	$-0.401976\pi$
$433$	12.6145	0.606217	0.303108	+	0.952956i	$0.401976\pi$
$434$	19.2255	0.922853
$435$	−5.59992	−0.268496
$436$	25.1626	1.20507
$437$	21.1579	1.01212
$438$	−5.27159	−0.251886
$439$	−7.91175	−0.377607	−0.188804	−	0.982015i	$-0.560461\pi$
$439$	−7.91175	−0.377607	−0.188804	+	0.982015i	$0.560461\pi$
$440$	−4.81162	−0.229385
$441$	−0.889369	−0.0423509
$442$	1.74988	0.0832331
$443$	17.9207	0.851440	0.425720	−	0.904855i	$-0.360021\pi$
$443$	17.9207	0.851440	0.425720	+	0.904855i	$0.360021\pi$
$444$	2.69061	0.127691
$445$	0.0805567	0.00381876
$446$	7.14442	0.338298
$447$	6.03429	0.285412
$448$	29.1005	1.37487
$449$	−12.5869	−0.594015	−0.297007	−	0.954875i	$-0.595989\pi$
$449$	−12.5869	−0.594015	−0.297007	+	0.954875i	$0.595989\pi$
$450$	9.03728	0.426021
$451$	43.9149	2.06787
$452$	−31.3609	−1.47509
$453$	−6.84081	−0.321410
$454$	−3.23694	−0.151917
$455$	1.78186	0.0835349
$456$	7.12258	0.333545
$457$	−24.0733	−1.12610	−0.563050	−	0.826423i	$-0.690372\pi$
$457$	−24.0733	−1.12610	−0.563050	+	0.826423i	$0.690372\pi$
$458$	−7.82904	−0.365827
$459$	−1.00000	−0.0466760
$460$	8.38672	0.391033
$461$	9.04092	0.421077	0.210539	−	0.977586i	$-0.432478\pi$
$461$	9.04092	0.421077	0.210539	+	0.977586i	$0.432478\pi$
$462$	−23.2613	−1.08222
$463$	−25.4948	−1.18484	−0.592421	−	0.805628i	$-0.701828\pi$
$463$	−25.4948	−1.18484	−0.592421	+	0.805628i	$0.701828\pi$
$464$	−15.9030	−0.738278
$465$	−3.20374	−0.148570
$466$	2.40303	0.111318
$467$	16.8833	0.781264	0.390632	−	0.920547i	$-0.372257\pi$
$467$	16.8833	0.781264	0.390632	+	0.920547i	$0.372257\pi$
$468$	2.10958	0.0975155
$469$	34.3951	1.58822
$470$	−12.5945	−0.580940
$471$	−1.00000	−0.0460776
$472$	0.314346	0.0144690
$473$	31.6211	1.45394
$474$	26.2751	1.20685
$475$	24.2306	1.11178
$476$	6.37773	0.292323
$477$	6.97068	0.319166
$478$	−4.39847	−0.201181
$479$	−42.2849	−1.93205	−0.966024	−	0.258452i	$-0.916788\pi$
$479$	−42.2849	−1.93205	−0.966024	+	0.258452i	$0.916788\pi$
$480$	−6.91187	−0.315482
$481$	0.852710	0.0388802
$482$	19.3440	0.881094
$483$	9.11497	0.414746
$484$	21.5012	0.977327
$485$	−0.107416	−0.00487750
$486$	−2.14010	−0.0970768
$487$	9.54387	0.432474	0.216237	−	0.976341i	$-0.430622\pi$
$487$	9.54387	0.432474	0.216237	+	0.976341i	$0.430622\pi$
$488$	0.504468	0.0228362
$489$	4.97205	0.224844
$490$	−1.67792	−0.0758009
$491$	−12.3188	−0.555938	−0.277969	−	0.960590i	$-0.589661\pi$
$491$	−12.3188	−0.555938	−0.277969	+	0.960590i	$0.589661\pi$
$492$	−25.7678	−1.16170
$493$	−6.35222	−0.286089
$494$	10.0408	0.451757
$495$	3.87628	0.174226
$496$	−9.09818	−0.408521
$497$	−3.11511	−0.139732
$498$	−26.3640	−1.18140
$499$	−20.0980	−0.899709	−0.449855	−	0.893102i	$-0.648524\pi$
$499$	−20.0980	−0.899709	−0.449855	+	0.893102i	$0.648524\pi$
$500$	20.9770	0.938122
$501$	2.72951	0.121946
$502$	10.5721	0.471857
$503$	−30.0728	−1.34088	−0.670441	−	0.741963i	$-0.733895\pi$
$503$	−30.0728	−1.34088	−0.670441	+	0.741963i	$0.733895\pi$
$504$	3.06845	0.136680
$505$	−7.37678	−0.328262
$506$	−34.6980	−1.54251
$507$	−12.3314	−0.547658
$508$	−46.0556	−2.04339
$509$	31.1843	1.38222	0.691110	−	0.722750i	$-0.257122\pi$
$509$	31.1843	1.38222	0.691110	+	0.722750i	$0.257122\pi$
$510$	−1.88665	−0.0835421
$511$	−6.08907	−0.269365
$512$	−25.8440	−1.14216
$513$	−5.73800	−0.253339
$514$	−51.7288	−2.28166
$515$	−4.07682	−0.179646
$516$	−18.5542	−0.816803
$517$	29.3527	1.29093
$518$	5.51702	0.242404
$519$	8.88822	0.390150
$520$	0.894761	0.0392379
$521$	−32.7773	−1.43600	−0.718001	−	0.696042i	$-0.754943\pi$
$521$	−32.7773	−1.43600	−0.718001	+	0.696042i	$0.754943\pi$
$522$	−13.5944	−0.595009
$523$	44.5046	1.94605	0.973026	−	0.230697i	$-0.0741006\pi$
$523$	44.5046	1.94605	0.973026	+	0.230697i	$0.0741006\pi$
$524$	1.29454	0.0565523
$525$	10.4387	0.455583
$526$	−42.3623	−1.84708
$527$	−3.63413	−0.158305
$528$	11.0081	0.479065
$529$	−9.40358	−0.408851
$530$	13.1512	0.571252
$531$	−0.253239	−0.0109897
$532$	36.5954	1.58661
$533$	−8.16635	−0.353724
$534$	0.195559	0.00846268
$535$	7.57527	0.327507
$536$	17.2715	0.746016
$537$	2.12366	0.0916427
$538$	−69.7138	−3.00558
$539$	3.91057	0.168440
$540$	−2.27447	−0.0978775
$541$	3.91343	0.168251	0.0841257	−	0.996455i	$-0.473190\pi$
$541$	3.91343	0.168251	0.0841257	+	0.996455i	$0.473190\pi$
$542$	−46.1412	−1.98193
$543$	−0.390811	−0.0167713
$544$	−7.84041	−0.336155
$545$	−8.59785	−0.368291
$546$	4.32564	0.185120
$547$	−41.9736	−1.79466	−0.897330	−	0.441360i	$-0.854496\pi$
$547$	−41.9736	−1.79466	−0.897330	+	0.441360i	$0.854496\pi$
$548$	−7.67091	−0.327685
$549$	−0.406403	−0.0173449
$550$	−39.7371	−1.69439
$551$	−36.4490	−1.55278
$552$	4.57709	0.194814
$553$	30.3496	1.29060
$554$	57.8635	2.45838
$555$	−0.919358	−0.0390246
$556$	4.40802	0.186942
$557$	29.7339	1.25986	0.629932	−	0.776650i	$-0.283083\pi$
$557$	29.7339	1.25986	0.629932	+	0.776650i	$0.283083\pi$
$558$	−7.77740	−0.329244
$559$	−5.88021	−0.248706
$560$	−5.45574	−0.230547
$561$	4.39701	0.185642
$562$	56.1116	2.36692
$563$	35.5038	1.49631	0.748154	−	0.663525i	$-0.230940\pi$
$563$	35.5038	1.49631	0.748154	+	0.663525i	$0.230940\pi$
$564$	−17.2232	−0.725226
$565$	10.7157	0.450815
$566$	−40.9646	−1.72187
$567$	−2.47197	−0.103813
$568$	−1.56425	−0.0656345
$569$	31.0450	1.30147	0.650736	−	0.759304i	$-0.274460\pi$
$569$	31.0450	1.30147	0.650736	+	0.759304i	$0.274460\pi$
$570$	−10.8256	−0.453434
$571$	20.7759	0.869445	0.434723	−	0.900564i	$-0.356846\pi$
$571$	20.7759	0.869445	0.434723	+	0.900564i	$0.356846\pi$
$572$	−9.27587	−0.387844
$573$	18.7735	0.784272
$574$	−52.8361	−2.20534
$575$	15.5710	0.649355
$576$	−11.7722	−0.490508
$577$	−14.5922	−0.607480	−0.303740	−	0.952755i	$-0.598235\pi$
$577$	−14.5922	−0.607480	−0.303740	+	0.952755i	$0.598235\pi$
$578$	−2.14010	−0.0890163
$579$	15.0657	0.626107
$580$	−14.4479	−0.599917
$581$	−30.4524	−1.26338
$582$	−0.260762	−0.0108089
$583$	−30.6502	−1.26940
$584$	−3.05763	−0.126526
$585$	−0.720826	−0.0298025
$586$	−59.5204	−2.45876
$587$	−33.4816	−1.38193	−0.690967	−	0.722886i	$-0.742815\pi$
$587$	−33.4816	−1.38193	−0.690967	+	0.722886i	$0.742815\pi$
$588$	−2.29459	−0.0946273
$589$	−20.8527	−0.859219
$590$	−0.477773	−0.0196696
$591$	−24.8741	−1.02319
$592$	−2.61085	−0.107305
$593$	−18.8359	−0.773496	−0.386748	−	0.922185i	$-0.626402\pi$
$593$	−18.8359	−0.773496	−0.386748	+	0.922185i	$0.626402\pi$
$594$	9.41004	0.386099
$595$	−2.17921	−0.0893390
$596$	15.5686	0.637714
$597$	13.4451	0.550271
$598$	6.45238	0.263857
$599$	−32.0153	−1.30811	−0.654055	−	0.756447i	$-0.726934\pi$
$599$	−32.0153	−1.30811	−0.654055	+	0.756447i	$0.726934\pi$
$600$	5.24180	0.213996
$601$	−2.33741	−0.0953451	−0.0476725	−	0.998863i	$-0.515180\pi$
$601$	−2.33741	−0.0953451	−0.0476725	+	0.998863i	$0.515180\pi$
$602$	−38.0448	−1.55059
$603$	−13.9141	−0.566624
$604$	−17.6494	−0.718145
$605$	−7.34677	−0.298689
$606$	−17.9079	−0.727457
$607$	18.4430	0.748580	0.374290	−	0.927312i	$-0.377886\pi$
$607$	18.4430	0.748580	0.374290	+	0.927312i	$0.377886\pi$
$608$	−44.9883	−1.82452
$609$	−15.7025	−0.636297
$610$	−0.766739	−0.0310444
$611$	−5.45838	−0.220822
$612$	−2.58002	−0.104291
$613$	−6.22344	−0.251362	−0.125681	−	0.992071i	$-0.540112\pi$
$613$	−6.22344	−0.251362	−0.125681	+	0.992071i	$0.540112\pi$
$614$	36.4231	1.46992
$615$	8.80463	0.355037
$616$	−13.4920	−0.543610
$617$	29.8564	1.20197	0.600986	−	0.799260i	$-0.294775\pi$
$617$	29.8564	1.20197	0.600986	+	0.799260i	$0.294775\pi$
$618$	−9.89688	−0.398111
$619$	14.0071	0.562992	0.281496	−	0.959562i	$-0.409169\pi$
$619$	14.0071	0.562992	0.281496	+	0.959562i	$0.409169\pi$
$620$	−8.26572	−0.331959
$621$	−3.68733	−0.147968
$622$	−16.4881	−0.661114
$623$	0.225885	0.00904991
$624$	−2.04705	−0.0819474
$625$	13.9465	0.557860
$626$	27.0597	1.08152
$627$	25.2301	1.00759
$628$	−2.58002	−0.102954
$629$	−1.04286	−0.0415817
$630$	−4.66373	−0.185807
$631$	32.0368	1.27537	0.637683	−	0.770299i	$-0.279893\pi$
$631$	32.0368	1.27537	0.637683	+	0.770299i	$0.279893\pi$
$632$	15.2401	0.606217
$633$	−15.3455	−0.609929
$634$	−31.1054	−1.23535
$635$	15.7368	0.624495
$636$	17.9845	0.713132
$637$	−0.727203	−0.0288128
$638$	59.7746	2.36650
$639$	1.26017	0.0498516
$640$	−8.38619	−0.331493
$641$	4.57156	0.180566	0.0902830	−	0.995916i	$-0.471223\pi$
$641$	4.57156	0.180566	0.0902830	+	0.995916i	$0.471223\pi$
$642$	18.3897	0.725784
$643$	17.4894	0.689715	0.344857	−	0.938655i	$-0.387927\pi$
$643$	17.4894	0.689715	0.344857	+	0.938655i	$0.387927\pi$
$644$	23.5168	0.926692
$645$	6.33980	0.249630
$646$	−12.2799	−0.483146
$647$	20.7390	0.815333	0.407666	−	0.913131i	$-0.366343\pi$
$647$	20.7390	0.815333	0.407666	+	0.913131i	$0.366343\pi$
$648$	−1.24130	−0.0487629
$649$	1.11350	0.0437086
$650$	7.38944	0.289838
$651$	−8.98346	−0.352090
$652$	12.8280	0.502383
$653$	16.1630	0.632505	0.316253	−	0.948675i	$-0.397575\pi$
$653$	16.1630	0.632505	0.316253	+	0.948675i	$0.397575\pi$
$654$	−20.8721	−0.816165
$655$	−0.442333	−0.0172834
$656$	25.0039	0.976239
$657$	2.46325	0.0961004
$658$	−35.3156	−1.37674
$659$	1.39224	0.0542338	0.0271169	−	0.999632i	$-0.491367\pi$
$659$	1.39224	0.0542338	0.0271169	+	0.999632i	$0.491367\pi$
$660$	10.0009	0.389283
$661$	25.6166	0.996370	0.498185	−	0.867071i	$-0.334000\pi$
$661$	25.6166	0.996370	0.498185	+	0.867071i	$0.334000\pi$
$662$	25.6374	0.996425
$663$	−0.817662	−0.0317554
$664$	−15.2917	−0.593432
$665$	−12.5043	−0.484897
$666$	−2.23183	−0.0864817
$667$	−23.4227	−0.906932
$668$	7.04220	0.272471
$669$	−3.33836	−0.129069
$670$	−26.2509	−1.01416
$671$	1.78696	0.0689849
$672$	−19.3813	−0.747648
$673$	46.9033	1.80799	0.903994	−	0.427545i	$-0.140621\pi$
$673$	46.9033	1.80799	0.903994	+	0.427545i	$0.140621\pi$
$674$	9.72866	0.374734
$675$	−4.22283	−0.162537
$676$	−31.8153	−1.22367
$677$	6.16514	0.236946	0.118473	−	0.992957i	$-0.462200\pi$
$677$	6.16514	0.236946	0.118473	+	0.992957i	$0.462200\pi$
$678$	26.0135	0.999044
$679$	−0.301199	−0.0115590
$680$	−1.09429	−0.0419642
$681$	1.51252	0.0579600
$682$	34.1973	1.30948
$683$	26.1733	1.00149	0.500747	−	0.865593i	$-0.333059\pi$
$683$	26.1733	1.00149	0.500747	+	0.865593i	$0.333059\pi$
$684$	−14.8042	−0.566051
$685$	2.62108	0.100146
$686$	−41.7368	−1.59352
$687$	3.65826	0.139571
$688$	18.0042	0.686403
$689$	5.69966	0.217140
$690$	−6.95669	−0.264837
$691$	−18.0459	−0.686497	−0.343248	−	0.939245i	$-0.611527\pi$
$691$	−18.0459	−0.686497	−0.343248	+	0.939245i	$0.611527\pi$
$692$	22.9318	0.871736
$693$	10.8693	0.412890
$694$	−26.5525	−1.00792
$695$	−1.50618	−0.0571327
$696$	−7.88500	−0.298880
$697$	9.98744	0.378301
$698$	−22.4340	−0.849138
$699$	−1.12286	−0.0424704
$700$	26.9321	1.01794
$701$	22.6827	0.856713	0.428357	−	0.903610i	$-0.359093\pi$
$701$	22.6827	0.856713	0.428357	+	0.903610i	$0.359093\pi$
$702$	−1.74988	−0.0660448
$703$	−5.98396	−0.225689
$704$	51.7624	1.95087
$705$	5.88500	0.221642
$706$	41.5229	1.56273
$707$	−20.6849	−0.777935
$708$	−0.653363	−0.0245549
$709$	47.1433	1.77051	0.885253	−	0.465110i	$-0.153985\pi$
$709$	47.1433	1.77051	0.885253	+	0.465110i	$0.153985\pi$
$710$	2.37750	0.0892259
$711$	−12.2775	−0.460443
$712$	0.113428	0.00425091
$713$	−13.4003	−0.501844
$714$	−5.29026	−0.197983
$715$	3.16948	0.118532
$716$	5.47909	0.204763
$717$	2.05527	0.0767553
$718$	2.14128	0.0799117
$719$	3.26137	0.121629	0.0608143	−	0.998149i	$-0.480630\pi$
$719$	3.26137	0.121629	0.0608143	+	0.998149i	$0.480630\pi$
$720$	2.20704	0.0822516
$721$	−11.4316	−0.425736
$722$	−29.8001	−1.10905
$723$	−9.03883	−0.336158
$724$	−1.00830	−0.0374732
$725$	−26.8244	−0.996232
$726$	−17.8350	−0.661919
$727$	6.26372	0.232309	0.116154	−	0.993231i	$-0.462943\pi$
$727$	6.26372	0.232309	0.116154	+	0.993231i	$0.462943\pi$
$728$	2.50896	0.0929882
$729$	1.00000	0.0370370
$730$	4.64728	0.172003
$731$	7.19149	0.265987
$732$	−1.04853	−0.0387547
$733$	−34.9714	−1.29170	−0.645849	−	0.763465i	$-0.723497\pi$
$733$	−34.9714	−1.29170	−0.645849	+	0.763465i	$0.723497\pi$
$734$	52.6283	1.94255
$735$	0.784041	0.0289198
$736$	−28.9102	−1.06564
$737$	61.1803	2.25361
$738$	21.3741	0.786792
$739$	−20.0758	−0.738501	−0.369250	−	0.929330i	$-0.620386\pi$
$739$	−20.0758	−0.738501	−0.369250	+	0.929330i	$0.620386\pi$
$740$	−2.37196	−0.0871950
$741$	−4.69174	−0.172356
$742$	36.8767	1.35379
$743$	−8.89429	−0.326300	−0.163150	−	0.986601i	$-0.552165\pi$
$743$	−8.89429	−0.326300	−0.163150	+	0.986601i	$0.552165\pi$
$744$	−4.51105	−0.165383
$745$	−5.31965	−0.194897
$746$	−36.2171	−1.32600
$747$	12.3191	0.450732
$748$	11.3444	0.414792
$749$	21.2415	0.776146
$750$	−17.4002	−0.635366
$751$	22.2596	0.812264	0.406132	−	0.913814i	$-0.366877\pi$
$751$	22.2596	0.812264	0.406132	+	0.913814i	$0.366877\pi$
$752$	16.7126	0.609445
$753$	−4.94002	−0.180024
$754$	−11.1156	−0.404806
$755$	6.03066	0.219478
$756$	−6.37773	−0.231956
$757$	11.8905	0.432169	0.216084	−	0.976375i	$-0.430671\pi$
$757$	11.8905	0.432169	0.216084	+	0.976375i	$0.430671\pi$
$758$	80.0220	2.90653
$759$	16.2133	0.588504
$760$	−6.27905	−0.227765
$761$	−0.466621	−0.0169150	−0.00845749	−	0.999964i	$-0.502692\pi$
$761$	−0.466621	−0.0169150	−0.00845749	+	0.999964i	$0.502692\pi$
$762$	38.2026	1.38393
$763$	−24.1088	−0.872798
$764$	48.4359	1.75235
$765$	0.881570	0.0318732
$766$	22.5697	0.815477
$767$	−0.207064	−0.00747666
$768$	3.18605	0.114967
$769$	−2.40136	−0.0865952	−0.0432976	−	0.999062i	$-0.513786\pi$
$769$	−2.40136	−0.0865952	−0.0432976	+	0.999062i	$0.513786\pi$
$770$	20.5065	0.739003
$771$	24.1712	0.870506
$772$	38.8697	1.39895
$773$	−8.47913	−0.304973	−0.152487	−	0.988306i	$-0.548728\pi$
$773$	−8.47913	−0.304973	−0.152487	+	0.988306i	$0.548728\pi$
$774$	15.3905	0.553200
$775$	−15.3463	−0.551257
$776$	−0.151247	−0.00542946
$777$	−2.57793	−0.0924827
$778$	10.7740	0.386268
$779$	57.3080	2.05327
$780$	−1.85975	−0.0665896
$781$	−5.54100	−0.198272
$782$	−7.89125	−0.282191
$783$	6.35222	0.227010
$784$	2.22657	0.0795203
$785$	0.881570	0.0314646
$786$	−1.07381	−0.0383014
$787$	−17.7224	−0.631734	−0.315867	−	0.948804i	$-0.602295\pi$
$787$	−17.7224	−0.631734	−0.315867	+	0.948804i	$0.602295\pi$
$788$	−64.1758	−2.28617
$789$	19.7946	0.704705
$790$	−23.1633	−0.824114
$791$	30.0475	1.06837
$792$	5.45801	0.193942
$793$	−0.332300	−0.0118003
$794$	−65.4840	−2.32394
$795$	−6.14514	−0.217946
$796$	34.6886	1.22951
$797$	0.472084	0.0167221	0.00836104	−	0.999965i	$-0.497339\pi$
$797$	0.472084	0.0167221	0.00836104	+	0.999965i	$0.497339\pi$
$798$	−30.3555	−1.07457
$799$	6.67559	0.236165
$800$	−33.1088	−1.17057
$801$	−0.0913787	−0.00322871
$802$	−47.0579	−1.66167
$803$	−10.8309	−0.382215
$804$	−35.8985	−1.26604
$805$	−8.03548	−0.283214
$806$	−6.35928	−0.223996
$807$	32.5751	1.14670
$808$	−10.3869	−0.365411
$809$	−4.08901	−0.143762	−0.0718810	−	0.997413i	$-0.522900\pi$
$809$	−4.08901	−0.143762	−0.0718810	+	0.997413i	$0.522900\pi$
$810$	1.88665	0.0662900
$811$	−38.6292	−1.35645	−0.678227	−	0.734853i	$-0.737251\pi$
$811$	−38.6292	−1.35645	−0.678227	+	0.734853i	$0.737251\pi$
$812$	−40.5127	−1.42172
$813$	21.5603	0.756154
$814$	9.81340	0.343959
$815$	−4.38321	−0.153537
$816$	2.50354	0.0876413
$817$	41.2648	1.44367
$818$	−59.8368	−2.09215
$819$	−2.02123	−0.0706276
$820$	22.7161	0.793281
$821$	−16.4600	−0.574457	−0.287228	−	0.957862i	$-0.592734\pi$
$821$	−16.4600	−0.574457	−0.287228	+	0.957862i	$0.592734\pi$
$822$	6.36294	0.221933
$823$	35.9421	1.25286	0.626431	−	0.779477i	$-0.284515\pi$
$823$	35.9421	1.25286	0.626431	+	0.779477i	$0.284515\pi$
$824$	−5.74039	−0.199976
$825$	18.5679	0.646450
$826$	−1.33970	−0.0466142
$827$	−27.3981	−0.952725	−0.476362	−	0.879249i	$-0.658045\pi$
$827$	−27.3981	−0.952725	−0.476362	+	0.879249i	$0.658045\pi$
$828$	−9.51339	−0.330613
$829$	−1.58689	−0.0551149	−0.0275575	−	0.999620i	$-0.508773\pi$
$829$	−1.58689	−0.0551149	−0.0275575	+	0.999620i	$0.508773\pi$
$830$	23.2417	0.806733
$831$	−27.0378	−0.937930
$832$	−9.62566	−0.333710
$833$	0.889369	0.0308148
$834$	−3.65640	−0.126611
$835$	−2.40626	−0.0832719
$836$	65.0941	2.25133
$837$	3.63413	0.125614
$838$	−72.4509	−2.50277
$839$	45.5689	1.57321	0.786607	−	0.617454i	$-0.211836\pi$
$839$	45.5689	1.57321	0.786607	+	0.617454i	$0.211836\pi$
$840$	−2.70506	−0.0933333
$841$	11.3506	0.391401
$842$	70.2449	2.42080
$843$	−26.2192	−0.903036
$844$	−39.5917	−1.36280
$845$	10.8710	0.373974
$846$	14.2864	0.491177
$847$	−20.6007	−0.707849
$848$	−17.4514	−0.599282
$849$	19.1415	0.656934
$850$	−9.03728	−0.309976
$851$	−3.84539	−0.131818
$852$	3.25127	0.111387
$853$	−15.1494	−0.518705	−0.259353	−	0.965783i	$-0.583509\pi$
$853$	−15.1494	−0.518705	−0.259353	+	0.965783i	$0.583509\pi$
$854$	−2.14998	−0.0735707
$855$	5.05845	0.172995
$856$	10.6664	0.364570
$857$	7.98397	0.272727	0.136364	−	0.990659i	$-0.456458\pi$
$857$	7.98397	0.272727	0.136364	+	0.990659i	$0.456458\pi$
$858$	7.69423	0.262677
$859$	10.7793	0.367783	0.183892	−	0.982947i	$-0.441130\pi$
$859$	10.7793	0.367783	0.183892	+	0.982947i	$0.441130\pi$
$860$	16.3568	0.557763
$861$	24.6886	0.841387
$862$	82.4710	2.80897
$863$	−10.2889	−0.350237	−0.175119	−	0.984547i	$-0.556031\pi$
$863$	−10.2889	−0.350237	−0.175119	+	0.984547i	$0.556031\pi$
$864$	7.84041	0.266736
$865$	−7.83559	−0.266418
$866$	−26.9964	−0.917374
$867$	1.00000	0.0339618
$868$	−23.1775	−0.786696
$869$	53.9844	1.83129
$870$	11.9844	0.406309
$871$	−11.3770	−0.385495
$872$	−12.1063	−0.409969
$873$	0.121846	0.00412386
$874$	−45.2800	−1.53162
$875$	−20.0985	−0.679454
$876$	6.35523	0.214723
$877$	−44.0032	−1.48588	−0.742942	−	0.669356i	$-0.766570\pi$
$877$	−44.0032	−1.48588	−0.742942	+	0.669356i	$0.766570\pi$
$878$	16.9319	0.571425
$879$	27.8120	0.938075
$880$	−9.70440	−0.327135
$881$	4.27019	0.143866	0.0719331	−	0.997409i	$-0.477083\pi$
$881$	4.27019	0.143866	0.0719331	+	0.997409i	$0.477083\pi$
$882$	1.90334	0.0640887
$883$	16.6413	0.560025	0.280013	−	0.959996i	$-0.409661\pi$
$883$	16.6413	0.560025	0.280013	+	0.959996i	$0.409661\pi$
$884$	−2.10958	−0.0709530
$885$	0.223248	0.00750441
$886$	−38.3522	−1.28847
$887$	25.3148	0.849989	0.424994	−	0.905196i	$-0.360276\pi$
$887$	25.3148	0.849989	0.424994	+	0.905196i	$0.360276\pi$
$888$	−1.29451	−0.0434408
$889$	44.1268	1.47996
$890$	−0.172399	−0.00577884
$891$	−4.39701	−0.147306
$892$	−8.61304	−0.288386
$893$	38.3045	1.28181
$894$	−12.9140	−0.431908
$895$	−1.87215	−0.0625792
$896$	−23.5153	−0.785592
$897$	−3.01499	−0.100668
$898$	26.9373	0.898909
$899$	23.0848	0.769921
$900$	−10.8950	−0.363167
$901$	−6.97068	−0.232227
$902$	−93.9823	−3.12927
$903$	17.7772	0.591587
$904$	15.0884	0.501832
$905$	0.344527	0.0114525
$906$	14.6400	0.486382
$907$	41.6481	1.38290	0.691450	−	0.722424i	$-0.256972\pi$
$907$	41.6481	1.38290	0.691450	+	0.722424i	$0.256972\pi$
$908$	3.90234	0.129504
$909$	8.36778	0.277542
$910$	−3.81335	−0.126411
$911$	26.5065	0.878200	0.439100	−	0.898438i	$-0.355297\pi$
$911$	26.5065	0.878200	0.439100	+	0.898438i	$0.355297\pi$
$912$	14.3653	0.475683
$913$	−54.1672	−1.79267
$914$	51.5191	1.70410
$915$	0.358273	0.0118441
$916$	9.43839	0.311853
$917$	−1.24033	−0.0409592
$918$	2.14010	0.0706338
$919$	12.7801	0.421577	0.210789	−	0.977532i	$-0.432397\pi$
$919$	12.7801	0.421577	0.210789	+	0.977532i	$0.432397\pi$
$920$	−4.03502	−0.133031
$921$	−17.0193	−0.560807
$922$	−19.3485	−0.637207
$923$	1.03039	0.0339159
$924$	28.0430	0.922546
$925$	−4.40384	−0.144798
$926$	54.5613	1.79300
$927$	4.62450	0.151888
$928$	49.8040	1.63490
$929$	−14.5892	−0.478657	−0.239328	−	0.970939i	$-0.576927\pi$
$929$	−14.5892	−0.478657	−0.239328	+	0.970939i	$0.576927\pi$
$930$	6.85632	0.224828
$931$	5.10320	0.167251
$932$	−2.89700	−0.0948944
$933$	7.70438	0.252230
$934$	−36.1318	−1.18227
$935$	−3.87628	−0.126768
$936$	−1.01496	−0.0331751
$937$	25.0496	0.818333	0.409167	−	0.912460i	$-0.365819\pi$
$937$	25.0496	0.818333	0.409167	+	0.912460i	$0.365819\pi$
$938$	−73.6089	−2.40342
$939$	−12.6441	−0.412626
$940$	15.1834	0.495228
$941$	56.2836	1.83479	0.917396	−	0.397975i	$-0.130287\pi$
$941$	56.2836	1.83479	0.917396	+	0.397975i	$0.130287\pi$
$942$	2.14010	0.0697282
$943$	36.8270	1.19925
$944$	0.633994	0.0206348
$945$	2.17921	0.0708898
$946$	−67.6723	−2.20021
$947$	−51.8711	−1.68558	−0.842792	−	0.538239i	$-0.819090\pi$
$947$	−51.8711	−1.68558	−0.842792	+	0.538239i	$0.819090\pi$
$948$	−31.6762	−1.02880
$949$	2.01410	0.0653806
$950$	−51.8559	−1.68243
$951$	14.5346	0.471316
$952$	−3.06845	−0.0994492
$953$	0.455325	0.0147494	0.00737472	−	0.999973i	$-0.497653\pi$
$953$	0.455325	0.0147494	0.00737472	+	0.999973i	$0.497653\pi$
$954$	−14.9179	−0.482986
$955$	−16.5501	−0.535549
$956$	5.30263	0.171499
$957$	−27.9308	−0.902874
$958$	90.4939	2.92373
$959$	7.34965	0.237333
$960$	10.3780	0.334949
$961$	−17.7931	−0.573970
$962$	−1.82488	−0.0588366
$963$	−8.59293	−0.276903
$964$	−23.3204	−0.751098
$965$	−13.2814	−0.427544
$966$	−19.5069	−0.627625
$967$	−3.46648	−0.111474	−0.0557372	−	0.998445i	$-0.517751\pi$
$967$	−3.46648	−0.111474	−0.0557372	+	0.998445i	$0.517751\pi$
$968$	−10.3447	−0.332490
$969$	5.73800	0.184331
$970$	0.229880	0.00738101
$971$	7.41569	0.237981	0.118990	−	0.992895i	$-0.462034\pi$
$971$	7.41569	0.237981	0.118990	+	0.992895i	$0.462034\pi$
$972$	2.58002	0.0827542
$973$	−4.22341	−0.135396
$974$	−20.4248	−0.654453
$975$	−3.45285	−0.110580
$976$	1.01745	0.0325676
$977$	32.7096	1.04647	0.523236	−	0.852188i	$-0.324725\pi$
$977$	32.7096	1.04647	0.523236	+	0.852188i	$0.324725\pi$
$978$	−10.6407	−0.340252
$979$	0.401794	0.0128414
$980$	2.02284	0.0646173
$981$	9.75288	0.311386
$982$	26.3634	0.841288
$983$	−0.185502	−0.00591659	−0.00295829	−	0.999996i	$-0.500942\pi$
$983$	−0.185502	−0.00591659	−0.00295829	+	0.999996i	$0.500942\pi$
$984$	12.3974	0.395215
$985$	21.9283	0.698694
$986$	13.5944	0.432933
$987$	16.5019	0.525260
$988$	−12.1048	−0.385105
$989$	26.5174	0.843205
$990$	−8.29561	−0.263652
$991$	30.0728	0.955295	0.477648	−	0.878551i	$-0.341490\pi$
$991$	30.0728	0.955295	0.477648	+	0.878551i	$0.341490\pi$
$992$	28.4931	0.904657
$993$	−11.9795	−0.380159
$994$	6.66663	0.211453
$995$	−11.8528	−0.375759
$996$	31.7835	1.00710
$997$	28.7287	0.909848	0.454924	−	0.890530i	$-0.349666\pi$
$997$	28.7287	0.909848	0.454924	+	0.890530i	$0.349666\pi$
$998$	43.0116	1.36151
$999$	1.04286	0.0329948

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.h.1.8	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.h.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-2.14010 q^{2} +1.00000 q^{3} +2.58002 q^{4} -0.881570 q^{5} -2.14010 q^{6} -2.47197 q^{7} -1.24130 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.14010 q^{2} +1.00000 q^{3} +2.58002 q^{4} -0.881570 q^{5} -2.14010 q^{6} -2.47197 q^{7} -1.24130 q^{8} +1.00000 q^{9} +1.88665 q^{10} -4.39701 q^{11} +2.58002 q^{12} +0.817662 q^{13} +5.29026 q^{14} -0.881570 q^{15} -2.50354 q^{16} -1.00000 q^{17} -2.14010 q^{18} -5.73800 q^{19} -2.27447 q^{20} -2.47197 q^{21} +9.41004 q^{22} -3.68733 q^{23} -1.24130 q^{24} -4.22283 q^{25} -1.74988 q^{26} +1.00000 q^{27} -6.37773 q^{28} +6.35222 q^{29} +1.88665 q^{30} +3.63413 q^{31} +7.84041 q^{32} -4.39701 q^{33} +2.14010 q^{34} +2.17921 q^{35} +2.58002 q^{36} +1.04286 q^{37} +12.2799 q^{38} +0.817662 q^{39} +1.09429 q^{40} -9.98744 q^{41} +5.29026 q^{42} -7.19149 q^{43} -11.3444 q^{44} -0.881570 q^{45} +7.89125 q^{46} -6.67559 q^{47} -2.50354 q^{48} -0.889369 q^{49} +9.03728 q^{50} -1.00000 q^{51} +2.10958 q^{52} +6.97068 q^{53} -2.14010 q^{54} +3.87628 q^{55} +3.06845 q^{56} -5.73800 q^{57} -13.5944 q^{58} -0.253239 q^{59} -2.27447 q^{60} -0.406403 q^{61} -7.77740 q^{62} -2.47197 q^{63} -11.7722 q^{64} -0.720826 q^{65} +9.41004 q^{66} -13.9141 q^{67} -2.58002 q^{68} -3.68733 q^{69} -4.66373 q^{70} +1.26017 q^{71} -1.24130 q^{72} +2.46325 q^{73} -2.23183 q^{74} -4.22283 q^{75} -14.8042 q^{76} +10.8693 q^{77} -1.74988 q^{78} -12.2775 q^{79} +2.20704 q^{80} +1.00000 q^{81} +21.3741 q^{82} +12.3191 q^{83} -6.37773 q^{84} +0.881570 q^{85} +15.3905 q^{86} +6.35222 q^{87} +5.45801 q^{88} -0.0913787 q^{89} +1.88665 q^{90} -2.02123 q^{91} -9.51339 q^{92} +3.63413 q^{93} +14.2864 q^{94} +5.05845 q^{95} +7.84041 q^{96} +0.121846 q^{97} +1.90334 q^{98} -4.39701 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) \) 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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