LMFDB - Embedded newform 8006.2.a.c.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8006,2,Mod(1,8006)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8006, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8006 = 2 \cdot 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8006.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:	$63.9282318582$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8006.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.37750 q^{3} +1.00000 q^{4} -3.81814 q^{5} +2.37750 q^{6} -1.26090 q^{7} -1.00000 q^{8} +2.65251 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.37750 q^{3} +1.00000 q^{4} -3.81814 q^{5} +2.37750 q^{6} -1.26090 q^{7} -1.00000 q^{8} +2.65251 q^{9} +3.81814 q^{10} +2.18416 q^{11} -2.37750 q^{12} -3.01629 q^{13} +1.26090 q^{14} +9.07764 q^{15} +1.00000 q^{16} +0.00142453 q^{17} -2.65251 q^{18} -2.62451 q^{19} -3.81814 q^{20} +2.99778 q^{21} -2.18416 q^{22} +4.95049 q^{23} +2.37750 q^{24} +9.57823 q^{25} +3.01629 q^{26} +0.826156 q^{27} -1.26090 q^{28} +7.34737 q^{29} -9.07764 q^{30} -8.40070 q^{31} -1.00000 q^{32} -5.19284 q^{33} -0.00142453 q^{34} +4.81429 q^{35} +2.65251 q^{36} +8.81986 q^{37} +2.62451 q^{38} +7.17123 q^{39} +3.81814 q^{40} +7.26895 q^{41} -2.99778 q^{42} -4.42970 q^{43} +2.18416 q^{44} -10.1277 q^{45} -4.95049 q^{46} -4.08526 q^{47} -2.37750 q^{48} -5.41014 q^{49} -9.57823 q^{50} -0.00338683 q^{51} -3.01629 q^{52} -12.3506 q^{53} -0.826156 q^{54} -8.33943 q^{55} +1.26090 q^{56} +6.23978 q^{57} -7.34737 q^{58} -4.54955 q^{59} +9.07764 q^{60} +1.39860 q^{61} +8.40070 q^{62} -3.34454 q^{63} +1.00000 q^{64} +11.5166 q^{65} +5.19284 q^{66} +13.0305 q^{67} +0.00142453 q^{68} -11.7698 q^{69} -4.81429 q^{70} -5.52241 q^{71} -2.65251 q^{72} -10.0385 q^{73} -8.81986 q^{74} -22.7722 q^{75} -2.62451 q^{76} -2.75400 q^{77} -7.17123 q^{78} +17.5068 q^{79} -3.81814 q^{80} -9.92172 q^{81} -7.26895 q^{82} -8.83997 q^{83} +2.99778 q^{84} -0.00543908 q^{85} +4.42970 q^{86} -17.4684 q^{87} -2.18416 q^{88} -1.72544 q^{89} +10.1277 q^{90} +3.80323 q^{91} +4.95049 q^{92} +19.9727 q^{93} +4.08526 q^{94} +10.0208 q^{95} +2.37750 q^{96} +0.107568 q^{97} +5.41014 q^{98} +5.79350 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9}+O(q^{10}) $ 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9} - 10 q^{10} + 4 q^{11} - 2 q^{12} + 40 q^{13} - 8 q^{14} + 15 q^{15} + 92 q^{16} - 14 q^{17} - 104 q^{18} + 64 q^{19} + 10 q^{20} + 54 q^{21} - 4 q^{22} - 49 q^{23} + 2 q^{24} + 116 q^{25} - 40 q^{26} - 8 q^{27} + 8 q^{28} + 39 q^{29} - 15 q^{30} + 53 q^{31} - 92 q^{32} + q^{33} + 14 q^{34} - 22 q^{35} + 104 q^{36} + 58 q^{37} - 64 q^{38} + 58 q^{39} - 10 q^{40} + 27 q^{41} - 54 q^{42} + 40 q^{43} + 4 q^{44} + 43 q^{45} + 49 q^{46} - 28 q^{47} - 2 q^{48} + 148 q^{49} - 116 q^{50} + 48 q^{51} + 40 q^{52} + 32 q^{53} + 8 q^{54} + 36 q^{55} - 8 q^{56} + 48 q^{57} - 39 q^{58} + 8 q^{59} + 15 q^{60} + 99 q^{61} - 53 q^{62} + 92 q^{64} + 13 q^{65} - q^{66} + 48 q^{67} - 14 q^{68} + 63 q^{69} + 22 q^{70} - 13 q^{71} - 104 q^{72} + 49 q^{73} - 58 q^{74} + 16 q^{75} + 64 q^{76} + 41 q^{77} - 58 q^{78} + 143 q^{79} + 10 q^{80} + 124 q^{81} - 27 q^{82} - 24 q^{83} + 54 q^{84} + 121 q^{85} - 40 q^{86} + 5 q^{87} - 4 q^{88} + 25 q^{89} - 43 q^{90} + 67 q^{91} - 49 q^{92} + 43 q^{93} + 28 q^{94} - 38 q^{95} + 2 q^{96} + 74 q^{97} - 148 q^{98} + 86 q^{99}+O(q^{100}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9 - 10 * q^10 + 4 * q^11 - 2 * q^12 + 40 * q^13 - 8 * q^14 + 15 * q^15 + 92 * q^16 - 14 * q^17 - 104 * q^18 + 64 * q^19 + 10 * q^20 + 54 * q^21 - 4 * q^22 - 49 * q^23 + 2 * q^24 + 116 * q^25 - 40 * q^26 - 8 * q^27 + 8 * q^28 + 39 * q^29 - 15 * q^30 + 53 * q^31 - 92 * q^32 + q^33 + 14 * q^34 - 22 * q^35 + 104 * q^36 + 58 * q^37 - 64 * q^38 + 58 * q^39 - 10 * q^40 + 27 * q^41 - 54 * q^42 + 40 * q^43 + 4 * q^44 + 43 * q^45 + 49 * q^46 - 28 * q^47 - 2 * q^48 + 148 * q^49 - 116 * q^50 + 48 * q^51 + 40 * q^52 + 32 * q^53 + 8 * q^54 + 36 * q^55 - 8 * q^56 + 48 * q^57 - 39 * q^58 + 8 * q^59 + 15 * q^60 + 99 * q^61 - 53 * q^62 + 92 * q^64 + 13 * q^65 - q^66 + 48 * q^67 - 14 * q^68 + 63 * q^69 + 22 * q^70 - 13 * q^71 - 104 * q^72 + 49 * q^73 - 58 * q^74 + 16 * q^75 + 64 * q^76 + 41 * q^77 - 58 * q^78 + 143 * q^79 + 10 * q^80 + 124 * q^81 - 27 * q^82 - 24 * q^83 + 54 * q^84 + 121 * q^85 - 40 * q^86 + 5 * q^87 - 4 * q^88 + 25 * q^89 - 43 * q^90 + 67 * q^91 - 49 * q^92 + 43 * q^93 + 28 * q^94 - 38 * q^95 + 2 * q^96 + 74 * q^97 - 148 * q^98 + 86 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.37750	−1.37265	−0.686325	−	0.727295i	$-0.740777\pi$
$3$	−2.37750	−1.37265	−0.686325	+	0.727295i	$0.740777\pi$
$4$	1.00000	0.500000
$5$	−3.81814	−1.70753	−0.853763	−	0.520662i	$-0.825685\pi$
$5$	−3.81814	−1.70753	−0.853763	+	0.520662i	$0.825685\pi$
$6$	2.37750	0.970611
$7$	−1.26090	−0.476574	−0.238287	−	0.971195i	$-0.576586\pi$
$7$	−1.26090	−0.476574	−0.238287	+	0.971195i	$0.576586\pi$
$8$	−1.00000	−0.353553
$9$	2.65251	0.884170
$10$	3.81814	1.20740
$11$	2.18416	0.658548	0.329274	−	0.944234i	$-0.393196\pi$
$11$	2.18416	0.658548	0.329274	+	0.944234i	$0.393196\pi$
$12$	−2.37750	−0.686325
$13$	−3.01629	−0.836569	−0.418284	−	0.908316i	$-0.637368\pi$
$13$	−3.01629	−0.836569	−0.418284	+	0.908316i	$0.637368\pi$
$14$	1.26090	0.336989
$15$	9.07764	2.34384
$16$	1.00000	0.250000
$17$	0.00142453	0.000345500 0	0.000172750	−	1.00000i	$-0.499945\pi$
$17$	0.00142453	0.000345500 0	0.000172750		1.00000i	$0.499945\pi$
$18$	−2.65251	−0.625203
$19$	−2.62451	−0.602104	−0.301052	−	0.953608i	$-0.597338\pi$
$19$	−2.62451	−0.602104	−0.301052	+	0.953608i	$0.597338\pi$
$20$	−3.81814	−0.853763
$21$	2.99778	0.654170
$22$	−2.18416	−0.465664
$23$	4.95049	1.03225	0.516124	−	0.856514i	$-0.327374\pi$
$23$	4.95049	1.03225	0.516124	+	0.856514i	$0.327374\pi$
$24$	2.37750	0.485305
$25$	9.57823	1.91565
$26$	3.01629	0.591543
$27$	0.826156	0.158994
$28$	−1.26090	−0.238287
$29$	7.34737	1.36437	0.682186	−	0.731179i	$-0.261029\pi$
$29$	7.34737	1.36437	0.682186	+	0.731179i	$0.261029\pi$
$30$	−9.07764	−1.65734
$31$	−8.40070	−1.50881	−0.754406	−	0.656409i	$-0.772075\pi$
$31$	−8.40070	−1.50881	−0.754406	+	0.656409i	$0.772075\pi$
$32$	−1.00000	−0.176777
$33$	−5.19284	−0.903957
$34$	−0.00142453	−0.000244306 0
$35$	4.81429	0.813763
$36$	2.65251	0.442085
$37$	8.81986	1.44998	0.724988	−	0.688761i	$-0.241845\pi$
$37$	8.81986	1.44998	0.724988	+	0.688761i	$0.241845\pi$
$38$	2.62451	0.425752
$39$	7.17123	1.14832
$40$	3.81814	0.603702
$41$	7.26895	1.13522	0.567610	−	0.823298i	$-0.307868\pi$
$41$	7.26895	1.13522	0.567610	+	0.823298i	$0.307868\pi$
$42$	−2.99778	−0.462568
$43$	−4.42970	−0.675524	−0.337762	−	0.941232i	$-0.609670\pi$
$43$	−4.42970	−0.675524	−0.337762	+	0.941232i	$0.609670\pi$
$44$	2.18416	0.329274
$45$	−10.1277	−1.50974
$46$	−4.95049	−0.729910
$47$	−4.08526	−0.595897	−0.297949	−	0.954582i	$-0.596302\pi$
$47$	−4.08526	−0.595897	−0.297949	+	0.954582i	$0.596302\pi$
$48$	−2.37750	−0.343163
$49$	−5.41014	−0.772877
$50$	−9.57823	−1.35457
$51$	−0.00338683	−0.000474251 0
$52$	−3.01629	−0.418284
$53$	−12.3506	−1.69649	−0.848245	−	0.529603i	$-0.822341\pi$
$53$	−12.3506	−1.69649	−0.848245	+	0.529603i	$0.822341\pi$
$54$	−0.826156	−0.112426
$55$	−8.33943	−1.12449
$56$	1.26090	0.168494
$57$	6.23978	0.826479
$58$	−7.34737	−0.964757
$59$	−4.54955	−0.592301	−0.296150	−	0.955141i	$-0.595703\pi$
$59$	−4.54955	−0.592301	−0.296150	+	0.955141i	$0.595703\pi$
$60$	9.07764	1.17192
$61$	1.39860	0.179072	0.0895360	−	0.995984i	$-0.471462\pi$
$61$	1.39860	0.179072	0.0895360	+	0.995984i	$0.471462\pi$
$62$	8.40070	1.06689
$63$	−3.34454	−0.421373
$64$	1.00000	0.125000
$65$	11.5166	1.42846
$66$	5.19284	0.639194
$67$	13.0305	1.59193	0.795966	−	0.605341i	$-0.206963\pi$
$67$	13.0305	1.59193	0.795966	+	0.605341i	$0.206963\pi$
$68$	0.00142453	0.000172750 0
$69$	−11.7698	−1.41692
$70$	−4.81429	−0.575417
$71$	−5.52241	−0.655390	−0.327695	−	0.944784i	$-0.606272\pi$
$71$	−5.52241	−0.655390	−0.327695	+	0.944784i	$0.606272\pi$
$72$	−2.65251	−0.312601
$73$	−10.0385	−1.17492	−0.587459	−	0.809254i	$-0.699872\pi$
$73$	−10.0385	−1.17492	−0.587459	+	0.809254i	$0.699872\pi$
$74$	−8.81986	−1.02529
$75$	−22.7722	−2.62951
$76$	−2.62451	−0.301052
$77$	−2.75400	−0.313847
$78$	−7.17123	−0.811982
$79$	17.5068	1.96967	0.984834	−	0.173502i	$-0.0555082\pi$
$79$	17.5068	1.96967	0.984834	+	0.173502i	$0.0555082\pi$
$80$	−3.81814	−0.426882
$81$	−9.92172	−1.10241
$82$	−7.26895	−0.802721
$83$	−8.83997	−0.970313	−0.485156	−	0.874427i	$-0.661237\pi$
$83$	−8.83997	−0.970313	−0.485156	+	0.874427i	$0.661237\pi$
$84$	2.99778	0.327085
$85$	−0.00543908	−0.000589951 0
$86$	4.42970	0.477667
$87$	−17.4684	−1.87281
$88$	−2.18416	−0.232832
$89$	−1.72544	−0.182896	−0.0914482	−	0.995810i	$-0.529150\pi$
$89$	−1.72544	−0.182896	−0.0914482	+	0.995810i	$0.529150\pi$
$90$	10.1277	1.06755
$91$	3.80323	0.398687
$92$	4.95049	0.516124
$93$	19.9727	2.07107
$94$	4.08526	0.421363
$95$	10.0208	1.02811
$96$	2.37750	0.242653
$97$	0.107568	0.0109218	0.00546092	−	0.999985i	$-0.498262\pi$
$97$	0.107568	0.0109218	0.00546092	+	0.999985i	$0.498262\pi$
$98$	5.41014	0.546507
$99$	5.79350	0.582269
$100$	9.57823	0.957823
$101$	−6.34204	−0.631056	−0.315528	−	0.948916i	$-0.602182\pi$
$101$	−6.34204	−0.631056	−0.315528	+	0.948916i	$0.602182\pi$
$102$	0.00338683	0.000335346 0
$103$	−9.21462	−0.907943	−0.453972	−	0.891016i	$-0.649993\pi$
$103$	−9.21462	−0.907943	−0.453972	+	0.891016i	$0.649993\pi$
$104$	3.01629	0.295772
$105$	−11.4460	−1.11701
$106$	12.3506	1.19960
$107$	−1.73516	−0.167744	−0.0838722	−	0.996477i	$-0.526729\pi$
$107$	−1.73516	−0.167744	−0.0838722	+	0.996477i	$0.526729\pi$
$108$	0.826156	0.0794969
$109$	12.2840	1.17660	0.588299	−	0.808644i	$-0.299798\pi$
$109$	12.2840	1.17660	0.588299	+	0.808644i	$0.299798\pi$
$110$	8.33943	0.795133
$111$	−20.9692	−1.99031
$112$	−1.26090	−0.119144
$113$	−11.5431	−1.08588	−0.542941	−	0.839771i	$-0.682689\pi$
$113$	−11.5431	−1.08588	−0.542941	+	0.839771i	$0.682689\pi$
$114$	−6.23978	−0.584409
$115$	−18.9017	−1.76259
$116$	7.34737	0.682186
$117$	−8.00074	−0.739669
$118$	4.54955	0.418820
$119$	−0.00179619	−0.000164656 0
$120$	−9.07764	−0.828672
$121$	−6.22945	−0.566314
$122$	−1.39860	−0.126623
$123$	−17.2819	−1.55826
$124$	−8.40070	−0.754406
$125$	−17.4803	−1.56349
$126$	3.34454	0.297955
$127$	−11.3103	−1.00363	−0.501813	−	0.864976i	$-0.667333\pi$
$127$	−11.3103	−1.00363	−0.501813	+	0.864976i	$0.667333\pi$
$128$	−1.00000	−0.0883883
$129$	10.5316	0.927258
$130$	−11.5166	−1.01008
$131$	4.65964	0.407115	0.203557	−	0.979063i	$-0.434750\pi$
$131$	4.65964	0.407115	0.203557	+	0.979063i	$0.434750\pi$
$132$	−5.19284	−0.451978
$133$	3.30924	0.286947
$134$	−13.0305	−1.12567
$135$	−3.15438	−0.271486
$136$	−0.00142453	−0.000122153 0
$137$	−1.67235	−0.142879	−0.0714394	−	0.997445i	$-0.522759\pi$
$137$	−1.67235	−0.142879	−0.0714394	+	0.997445i	$0.522759\pi$
$138$	11.7698	1.00191
$139$	19.8411	1.68290	0.841449	−	0.540336i	$-0.181703\pi$
$139$	19.8411	1.68290	0.841449	+	0.540336i	$0.181703\pi$
$140$	4.81429	0.406881
$141$	9.71272	0.817959
$142$	5.52241	0.463431
$143$	−6.58806	−0.550921
$144$	2.65251	0.221043
$145$	−28.0533	−2.32970
$146$	10.0385	0.830793
$147$	12.8626	1.06089
$148$	8.81986	0.724988
$149$	14.9973	1.22862	0.614312	−	0.789063i	$-0.289434\pi$
$149$	14.9973	1.22862	0.614312	+	0.789063i	$0.289434\pi$
$150$	22.7722	1.85935
$151$	4.89617	0.398444	0.199222	−	0.979954i	$-0.436158\pi$
$151$	4.89617	0.398444	0.199222	+	0.979954i	$0.436158\pi$
$152$	2.62451	0.212876
$153$	0.00377859	0.000305481 0
$154$	2.75400	0.221923
$155$	32.0751	2.57633
$156$	7.17123	0.574158
$157$	1.40538	0.112161	0.0560807	−	0.998426i	$-0.482140\pi$
$157$	1.40538	0.112161	0.0560807	+	0.998426i	$0.482140\pi$
$158$	−17.5068	−1.39276
$159$	29.3637	2.32869
$160$	3.81814	0.301851
$161$	−6.24206	−0.491943
$162$	9.92172	0.779524
$163$	−1.53431	−0.120176	−0.0600882	−	0.998193i	$-0.519138\pi$
$163$	−1.53431	−0.120176	−0.0600882	+	0.998193i	$0.519138\pi$
$164$	7.26895	0.567610
$165$	19.8270	1.54353
$166$	8.83997	0.686115
$167$	−11.2632	−0.871570	−0.435785	−	0.900051i	$-0.643529\pi$
$167$	−11.2632	−0.871570	−0.435785	+	0.900051i	$0.643529\pi$
$168$	−2.99778	−0.231284
$169$	−3.90199	−0.300153
$170$	0.00543908	0.000417158 0
$171$	−6.96155	−0.532363
$172$	−4.42970	−0.337762
$173$	−6.17245	−0.469283	−0.234642	−	0.972082i	$-0.575392\pi$
$173$	−6.17245	−0.469283	−0.234642	+	0.972082i	$0.575392\pi$
$174$	17.4684	1.32427
$175$	−12.0772	−0.912947
$176$	2.18416	0.164637
$177$	10.8166	0.813022
$178$	1.72544	0.129327
$179$	−9.19896	−0.687563	−0.343781	−	0.939050i	$-0.611708\pi$
$179$	−9.19896	−0.687563	−0.343781	+	0.939050i	$0.611708\pi$
$180$	−10.1277	−0.754872
$181$	−18.8514	−1.40121	−0.700605	−	0.713549i	$-0.747087\pi$
$181$	−18.8514	−1.40121	−0.700605	+	0.713549i	$0.747087\pi$
$182$	−3.80323	−0.281914
$183$	−3.32517	−0.245803
$184$	−4.95049	−0.364955
$185$	−33.6755	−2.47587
$186$	−19.9727	−1.46447
$187$	0.00311141	0.000227529 0
$188$	−4.08526	−0.297949
$189$	−1.04170	−0.0757723
$190$	−10.0208	−0.726983
$191$	−7.45743	−0.539601	−0.269800	−	0.962916i	$-0.586958\pi$
$191$	−7.45743	−0.539601	−0.269800	+	0.962916i	$0.586958\pi$
$192$	−2.37750	−0.171581
$193$	2.50023	0.179971	0.0899853	−	0.995943i	$-0.471318\pi$
$193$	2.50023	0.179971	0.0899853	+	0.995943i	$0.471318\pi$
$194$	−0.107568	−0.00772291
$195$	−27.3808	−1.96078
$196$	−5.41014	−0.386439
$197$	−10.6323	−0.757523	−0.378762	−	0.925494i	$-0.623650\pi$
$197$	−10.6323	−0.757523	−0.378762	+	0.925494i	$0.623650\pi$
$198$	−5.79350	−0.411726
$199$	−8.04326	−0.570171	−0.285086	−	0.958502i	$-0.592022\pi$
$199$	−8.04326	−0.570171	−0.285086	+	0.958502i	$0.592022\pi$
$200$	−9.57823	−0.677283
$201$	−30.9801	−2.18517
$202$	6.34204	0.446224
$203$	−9.26427	−0.650224
$204$	−0.00338683	−0.000237126 0
$205$	−27.7539	−1.93842
$206$	9.21462	0.642013
$207$	13.1312	0.912683
$208$	−3.01629	−0.209142
$209$	−5.73235	−0.396515
$210$	11.4460	0.789847
$211$	−9.75558	−0.671602	−0.335801	−	0.941933i	$-0.609007\pi$
$211$	−9.75558	−0.671602	−0.335801	+	0.941933i	$0.609007\pi$
$212$	−12.3506	−0.848245
$213$	13.1295	0.899622
$214$	1.73516	0.118613
$215$	16.9132	1.15347
$216$	−0.826156	−0.0562128
$217$	10.5924	0.719060
$218$	−12.2840	−0.831980
$219$	23.8666	1.61275
$220$	−8.33943	−0.562244
$221$	−0.00429681	−0.000289035 0
$222$	20.9692	1.40736
$223$	12.3791	0.828965	0.414483	−	0.910057i	$-0.363963\pi$
$223$	12.3791	0.828965	0.414483	+	0.910057i	$0.363963\pi$
$224$	1.26090	0.0842472
$225$	25.4063	1.69376
$226$	11.5431	0.767835
$227$	−28.7594	−1.90883	−0.954414	−	0.298487i	$-0.903518\pi$
$227$	−28.7594	−1.90883	−0.954414	+	0.298487i	$0.903518\pi$
$228$	6.23978	0.413239
$229$	−11.1296	−0.735465	−0.367733	−	0.929932i	$-0.619866\pi$
$229$	−11.1296	−0.735465	−0.367733	+	0.929932i	$0.619866\pi$
$230$	18.9017	1.24634
$231$	6.54763	0.430802
$232$	−7.34737	−0.482378
$233$	−2.78306	−0.182324	−0.0911620	−	0.995836i	$-0.529058\pi$
$233$	−2.78306	−0.182324	−0.0911620	+	0.995836i	$0.529058\pi$
$234$	8.00074	0.523025
$235$	15.5981	1.01751
$236$	−4.54955	−0.296150
$237$	−41.6224	−2.70367
$238$	0.00179619	0.000116430 0
$239$	−10.7122	−0.692912	−0.346456	−	0.938066i	$-0.612615\pi$
$239$	−10.7122	−0.692912	−0.346456	+	0.938066i	$0.612615\pi$
$240$	9.07764	0.585959
$241$	4.45532	0.286992	0.143496	−	0.989651i	$-0.454166\pi$
$241$	4.45532	0.286992	0.143496	+	0.989651i	$0.454166\pi$
$242$	6.22945	0.400445
$243$	21.1104	1.35423
$244$	1.39860	0.0895360
$245$	20.6567	1.31971
$246$	17.2819	1.10186
$247$	7.91629	0.503701
$248$	8.40070	0.533445
$249$	21.0170	1.33190
$250$	17.4803	1.10555
$251$	−5.47184	−0.345379	−0.172690	−	0.984976i	$-0.555246\pi$
$251$	−5.47184	−0.345379	−0.172690	+	0.984976i	$0.555246\pi$
$252$	−3.34454	−0.210686
$253$	10.8127	0.679786
$254$	11.3103	0.709670
$255$	0.0129314	0.000809796 0
$256$	1.00000	0.0625000
$257$	7.86388	0.490536	0.245268	−	0.969455i	$-0.421124\pi$
$257$	7.86388	0.490536	0.245268	+	0.969455i	$0.421124\pi$
$258$	−10.5316	−0.655670
$259$	−11.1209	−0.691021
$260$	11.5166	0.714231
$261$	19.4890	1.20634
$262$	−4.65964	−0.287873
$263$	−29.8652	−1.84157	−0.920783	−	0.390076i	$-0.872449\pi$
$263$	−29.8652	−1.84157	−0.920783	+	0.390076i	$0.872449\pi$
$264$	5.19284	0.319597
$265$	47.1565	2.89680
$266$	−3.30924	−0.202902
$267$	4.10224	0.251053
$268$	13.0305	0.795966
$269$	21.9157	1.33623	0.668113	−	0.744060i	$-0.267102\pi$
$269$	21.9157	1.33623	0.668113	+	0.744060i	$0.267102\pi$
$270$	3.15438	0.191970
$271$	2.56667	0.155914	0.0779569	−	0.996957i	$-0.475160\pi$
$271$	2.56667	0.155914	0.0779569	+	0.996957i	$0.475160\pi$
$272$	0.00142453	8.63751e−5 0
$273$	−9.04219	−0.547258
$274$	1.67235	0.101031
$275$	20.9204	1.26154
$276$	−11.7698	−0.708458
$277$	−0.547953	−0.0329233	−0.0164617	−	0.999864i	$-0.505240\pi$
$277$	−0.547953	−0.0329233	−0.0164617	+	0.999864i	$0.505240\pi$
$278$	−19.8411	−1.18999
$279$	−22.2830	−1.33405
$280$	−4.81429	−0.287709
$281$	−19.0286	−1.13515	−0.567577	−	0.823320i	$-0.692119\pi$
$281$	−19.0286	−1.13515	−0.567577	+	0.823320i	$0.692119\pi$
$282$	−9.71272	−0.578384
$283$	27.9427	1.66102	0.830511	−	0.557003i	$-0.188049\pi$
$283$	27.9427	1.66102	0.830511	+	0.557003i	$0.188049\pi$
$284$	−5.52241	−0.327695
$285$	−23.8244	−1.41123
$286$	6.58806	0.389560
$287$	−9.16540	−0.541016
$288$	−2.65251	−0.156301
$289$	−17.0000	−1.00000
$290$	28.0533	1.64735
$291$	−0.255742	−0.0149919
$292$	−10.0385	−0.587459
$293$	10.7548	0.628302	0.314151	−	0.949373i	$-0.398280\pi$
$293$	10.7548	0.628302	0.314151	+	0.949373i	$0.398280\pi$
$294$	−12.8626	−0.750163
$295$	17.3708	1.01137
$296$	−8.81986	−0.512644
$297$	1.80445	0.104705
$298$	−14.9973	−0.868768
$299$	−14.9321	−0.863547
$300$	−22.7722	−1.31476
$301$	5.58540	0.321937
$302$	−4.89617	−0.281743
$303$	15.0782	0.866220
$304$	−2.62451	−0.150526
$305$	−5.34005	−0.305770
$306$	−0.00377859	−0.000216008 0
$307$	−10.7355	−0.612706	−0.306353	−	0.951918i	$-0.599109\pi$
$307$	−10.7355	−0.612706	−0.306353	+	0.951918i	$0.599109\pi$
$308$	−2.75400	−0.156924
$309$	21.9078	1.24629
$310$	−32.0751	−1.82174
$311$	33.4549	1.89705	0.948526	−	0.316699i	$-0.102575\pi$
$311$	33.4549	1.89705	0.948526	+	0.316699i	$0.102575\pi$
$312$	−7.17123	−0.405991
$313$	−25.1439	−1.42122	−0.710609	−	0.703587i	$-0.751580\pi$
$313$	−25.1439	−1.42122	−0.710609	+	0.703587i	$0.751580\pi$
$314$	−1.40538	−0.0793101
$315$	12.7699	0.719505
$316$	17.5068	0.984834
$317$	5.69735	0.319995	0.159997	−	0.987117i	$-0.448851\pi$
$317$	5.69735	0.319995	0.159997	+	0.987117i	$0.448851\pi$
$318$	−29.3637	−1.64663
$319$	16.0478	0.898505
$320$	−3.81814	−0.213441
$321$	4.12535	0.230255
$322$	6.24206	0.347856
$323$	−0.00373871	−0.000208027 0
$324$	−9.92172	−0.551207
$325$	−28.8907	−1.60257
$326$	1.53431	0.0849775
$327$	−29.2053	−1.61506
$328$	−7.26895	−0.401361
$329$	5.15110	0.283989
$330$	−19.8270	−1.09144
$331$	−7.99762	−0.439589	−0.219794	−	0.975546i	$-0.570539\pi$
$331$	−7.99762	−0.439589	−0.219794	+	0.975546i	$0.570539\pi$
$332$	−8.83997	−0.485156
$333$	23.3948	1.28203
$334$	11.2632	0.616293
$335$	−49.7525	−2.71827
$336$	2.99778	0.163542
$337$	−11.0795	−0.603541	−0.301771	−	0.953381i	$-0.597578\pi$
$337$	−11.0795	−0.603541	−0.301771	+	0.953381i	$0.597578\pi$
$338$	3.90199	0.212240
$339$	27.4437	1.49054
$340$	−0.00543908	−0.000294975 0
$341$	−18.3485	−0.993625
$342$	6.96155	0.376437
$343$	15.6479	0.844907
$344$	4.42970	0.238834
$345$	44.9388	2.41942
$346$	6.17245	0.331833
$347$	17.5175	0.940390	0.470195	−	0.882562i	$-0.344184\pi$
$347$	17.5175	0.940390	0.470195	+	0.882562i	$0.344184\pi$
$348$	−17.4684	−0.936403
$349$	18.6318	0.997335	0.498668	−	0.866793i	$-0.333823\pi$
$349$	18.6318	0.997335	0.498668	+	0.866793i	$0.333823\pi$
$350$	12.0772	0.645551
$351$	−2.49193	−0.133009
$352$	−2.18416	−0.116416
$353$	−8.48408	−0.451562	−0.225781	−	0.974178i	$-0.572493\pi$
$353$	−8.48408	−0.451562	−0.225781	+	0.974178i	$0.572493\pi$
$354$	−10.8166	−0.574894
$355$	21.0854	1.11910
$356$	−1.72544	−0.0914482
$357$	0.00427044	0.000226016 0
$358$	9.19896	0.486180
$359$	3.70517	0.195551	0.0977756	−	0.995208i	$-0.468827\pi$
$359$	3.70517	0.195551	0.0977756	+	0.995208i	$0.468827\pi$
$360$	10.1277	0.533775
$361$	−12.1119	−0.637470
$362$	18.8514	0.990805
$363$	14.8105	0.777351
$364$	3.80323	0.199343
$365$	38.3285	2.00620
$366$	3.32517	0.173809
$367$	22.5718	1.17824	0.589118	−	0.808047i	$-0.299475\pi$
$367$	22.5718	1.17824	0.589118	+	0.808047i	$0.299475\pi$
$368$	4.95049	0.258062
$369$	19.2810	1.00373
$370$	33.6755	1.75071
$371$	15.5729	0.808504
$372$	19.9727	1.03554
$373$	24.6574	1.27671	0.638356	−	0.769741i	$-0.279615\pi$
$373$	24.6574	1.27671	0.638356	+	0.769741i	$0.279615\pi$
$374$	−0.00311141	−0.000160887 0
$375$	41.5595	2.14612
$376$	4.08526	0.210681
$377$	−22.1618	−1.14139
$378$	1.04170	0.0535791
$379$	13.4534	0.691056	0.345528	−	0.938408i	$-0.387700\pi$
$379$	13.4534	0.691056	0.345528	+	0.938408i	$0.387700\pi$
$380$	10.0208	0.514054
$381$	26.8902	1.37763
$382$	7.45743	0.381556
$383$	−22.5423	−1.15186	−0.575930	−	0.817499i	$-0.695360\pi$
$383$	−22.5423	−1.15186	−0.575930	+	0.817499i	$0.695360\pi$
$384$	2.37750	0.121326
$385$	10.5152	0.535902
$386$	−2.50023	−0.127258
$387$	−11.7498	−0.597278
$388$	0.107568	0.00546092
$389$	8.04535	0.407916	0.203958	−	0.978980i	$-0.434619\pi$
$389$	8.04535	0.407916	0.203958	+	0.978980i	$0.434619\pi$
$390$	27.3808	1.38648
$391$	0.00705214	0.000356642 0
$392$	5.41014	0.273253
$393$	−11.0783	−0.558826
$394$	10.6323	0.535650
$395$	−66.8434	−3.36326
$396$	5.79350	0.291134
$397$	6.43810	0.323119	0.161560	−	0.986863i	$-0.448348\pi$
$397$	6.43810	0.323119	0.161560	+	0.986863i	$0.448348\pi$
$398$	8.04326	0.403172
$399$	−7.86772	−0.393878
$400$	9.57823	0.478911
$401$	30.2639	1.51131	0.755653	−	0.654972i	$-0.227320\pi$
$401$	30.2639	1.51131	0.755653	+	0.654972i	$0.227320\pi$
$402$	30.9801	1.54515
$403$	25.3390	1.26222
$404$	−6.34204	−0.315528
$405$	37.8826	1.88240
$406$	9.26427	0.459778
$407$	19.2640	0.954879
$408$	0.00338683	0.000167673 0
$409$	18.6931	0.924315	0.462157	−	0.886798i	$-0.347076\pi$
$409$	18.6931	0.924315	0.462157	+	0.886798i	$0.347076\pi$
$410$	27.7539	1.37067
$411$	3.97602	0.196123
$412$	−9.21462	−0.453972
$413$	5.73651	0.282275
$414$	−13.1312	−0.645365
$415$	33.7523	1.65683
$416$	3.01629	0.147886
$417$	−47.1722	−2.31003
$418$	5.73235	0.280378
$419$	−2.71641	−0.132705	−0.0663527	−	0.997796i	$-0.521136\pi$
$419$	−2.71641	−0.132705	−0.0663527	+	0.997796i	$0.521136\pi$
$420$	−11.4460	−0.558506
$421$	−1.79074	−0.0872755	−0.0436378	−	0.999047i	$-0.513895\pi$
$421$	−1.79074	−0.0872755	−0.0436378	+	0.999047i	$0.513895\pi$
$422$	9.75558	0.474894
$423$	−10.8362	−0.526874
$424$	12.3506	0.599800
$425$	0.0136445	0.000661856 0
$426$	−13.1295	−0.636129
$427$	−1.76349	−0.0853411
$428$	−1.73516	−0.0838722
$429$	15.6631	0.756222
$430$	−16.9132	−0.815629
$431$	−5.52746	−0.266248	−0.133124	−	0.991099i	$-0.542501\pi$
$431$	−5.52746	−0.266248	−0.133124	+	0.991099i	$0.542501\pi$
$432$	0.826156	0.0397484
$433$	15.2362	0.732203	0.366101	−	0.930575i	$-0.380692\pi$
$433$	15.2362	0.732203	0.366101	+	0.930575i	$0.380692\pi$
$434$	−10.5924	−0.508452
$435$	66.6968	3.19787
$436$	12.2840	0.588299
$437$	−12.9926	−0.621521
$438$	−23.8666	−1.14039
$439$	−22.6246	−1.07981	−0.539907	−	0.841725i	$-0.681540\pi$
$439$	−22.6246	−1.07981	−0.539907	+	0.841725i	$0.681540\pi$
$440$	8.33943	0.397567
$441$	−14.3505	−0.683355
$442$	0.00429681	0.000204378 0
$443$	−18.6103	−0.884201	−0.442101	−	0.896965i	$-0.645767\pi$
$443$	−18.6103	−0.884201	−0.442101	+	0.896965i	$0.645767\pi$
$444$	−20.9692	−0.995155
$445$	6.58798	0.312300
$446$	−12.3791	−0.586167
$447$	−35.6560	−1.68647
$448$	−1.26090	−0.0595718
$449$	−19.9278	−0.940449	−0.470224	−	0.882547i	$-0.655827\pi$
$449$	−19.9278	−0.940449	−0.470224	+	0.882547i	$0.655827\pi$
$450$	−25.4063	−1.19767
$451$	15.8765	0.747597
$452$	−11.5431	−0.542941
$453$	−11.6406	−0.546925
$454$	28.7594	1.34974
$455$	−14.5213	−0.680768
$456$	−6.23978	−0.292204
$457$	27.7247	1.29690	0.648452	−	0.761255i	$-0.275417\pi$
$457$	27.7247	1.29690	0.648452	+	0.761255i	$0.275417\pi$
$458$	11.1296	0.520053
$459$	0.00117689	5.49324e−5 0
$460$	−18.9017	−0.881296
$461$	34.7481	1.61838	0.809190	−	0.587547i	$-0.199906\pi$
$461$	34.7481	1.61838	0.809190	+	0.587547i	$0.199906\pi$
$462$	−6.54763	−0.304623
$463$	20.3787	0.947077	0.473538	−	0.880773i	$-0.342976\pi$
$463$	20.3787	0.947077	0.473538	+	0.880773i	$0.342976\pi$
$464$	7.34737	0.341093
$465$	−76.2586	−3.53641
$466$	2.78306	0.128923
$467$	8.34217	0.386030	0.193015	−	0.981196i	$-0.438173\pi$
$467$	8.34217	0.386030	0.193015	+	0.981196i	$0.438173\pi$
$468$	−8.00074	−0.369835
$469$	−16.4302	−0.758674
$470$	−15.5981	−0.719488
$471$	−3.34129	−0.153958
$472$	4.54955	0.209410
$473$	−9.67517	−0.444865
$474$	41.6224	1.91178
$475$	−25.1382	−1.15342
$476$	−0.00179619	−8.23282e−5 0
$477$	−32.7602	−1.49999
$478$	10.7122	0.489963
$479$	−16.4373	−0.751040	−0.375520	−	0.926814i	$-0.622536\pi$
$479$	−16.4373	−0.751040	−0.375520	+	0.926814i	$0.622536\pi$
$480$	−9.07764	−0.414336
$481$	−26.6033	−1.21300
$482$	−4.45532	−0.202934
$483$	14.8405	0.675266
$484$	−6.22945	−0.283157
$485$	−0.410709	−0.0186493
$486$	−21.1104	−0.957588
$487$	41.0752	1.86130	0.930648	−	0.365915i	$-0.119244\pi$
$487$	41.0752	1.86130	0.930648	+	0.365915i	$0.119244\pi$
$488$	−1.39860	−0.0633115
$489$	3.64782	0.164960
$490$	−20.6567	−0.933174
$491$	−11.2138	−0.506073	−0.253036	−	0.967457i	$-0.581429\pi$
$491$	−11.2138	−0.506073	−0.253036	+	0.967457i	$0.581429\pi$
$492$	−17.2819	−0.779130
$493$	0.0104666	0.000471391 0
$494$	−7.91629	−0.356171
$495$	−22.1204	−0.994239
$496$	−8.40070	−0.377203
$497$	6.96319	0.312342
$498$	−21.0170	−0.941796
$499$	9.03069	0.404269	0.202135	−	0.979358i	$-0.435212\pi$
$499$	9.03069	0.404269	0.202135	+	0.979358i	$0.435212\pi$
$500$	−17.4803	−0.781744
$501$	26.7782	1.19636
$502$	5.47184	0.244220
$503$	−1.26689	−0.0564879	−0.0282440	−	0.999601i	$-0.508992\pi$
$503$	−1.26689	−0.0564879	−0.0282440	+	0.999601i	$0.508992\pi$
$504$	3.34454	0.148978
$505$	24.2148	1.07755
$506$	−10.8127	−0.480681
$507$	9.27698	0.412005
$508$	−11.3103	−0.501813
$509$	19.4522	0.862202	0.431101	−	0.902304i	$-0.358125\pi$
$509$	19.4522	0.862202	0.431101	+	0.902304i	$0.358125\pi$
$510$	−0.0129314	−0.000572612 0
$511$	12.6575	0.559936
$512$	−1.00000	−0.0441942
$513$	−2.16826	−0.0957308
$514$	−7.86388	−0.346861
$515$	35.1827	1.55034
$516$	10.5316	0.463629
$517$	−8.92286	−0.392427
$518$	11.1209	0.488626
$519$	14.6750	0.644162
$520$	−11.5166	−0.505038
$521$	25.9288	1.13596	0.567981	−	0.823042i	$-0.307725\pi$
$521$	25.9288	1.13596	0.567981	+	0.823042i	$0.307725\pi$
$522$	−19.4890	−0.853009
$523$	−7.77959	−0.340178	−0.170089	−	0.985429i	$-0.554405\pi$
$523$	−7.77959	−0.340178	−0.170089	+	0.985429i	$0.554405\pi$
$524$	4.65964	0.203557
$525$	28.7134	1.25316
$526$	29.8652	1.30218
$527$	−0.0119671	−0.000521295 0
$528$	−5.19284	−0.225989
$529$	1.50735	0.0655369
$530$	−47.1565	−2.04835
$531$	−12.0677	−0.523695
$532$	3.30924	0.143474
$533$	−21.9253	−0.949689
$534$	−4.10224	−0.177521
$535$	6.62510	0.286428
$536$	−13.0305	−0.562833
$537$	21.8705	0.943784
$538$	−21.9157	−0.944855
$539$	−11.8166	−0.508977
$540$	−3.15438	−0.135743
$541$	16.1727	0.695317	0.347659	−	0.937621i	$-0.386977\pi$
$541$	16.1727	0.695317	0.347659	+	0.937621i	$0.386977\pi$
$542$	−2.56667	−0.110248
$543$	44.8191	1.92337
$544$	−0.00142453	−6.10764e−5 0
$545$	−46.9022	−2.00907
$546$	9.04219	0.386970
$547$	0.186027	0.00795396	0.00397698	−	0.999992i	$-0.498734\pi$
$547$	0.186027	0.00795396	0.00397698	+	0.999992i	$0.498734\pi$
$548$	−1.67235	−0.0714394
$549$	3.70979	0.158330
$550$	−20.9204	−0.892047
$551$	−19.2833	−0.821494
$552$	11.7698	0.500956
$553$	−22.0742	−0.938692
$554$	0.547953	0.0232803
$555$	80.0635	3.39851
$556$	19.8411	0.841449
$557$	−1.44166	−0.0610849	−0.0305424	−	0.999533i	$-0.509723\pi$
$557$	−1.44166	−0.0610849	−0.0305424	+	0.999533i	$0.509723\pi$
$558$	22.2830	0.943313
$559$	13.3613	0.565122
$560$	4.81429	0.203441
$561$	−0.00739737	−0.000312317 0
$562$	19.0286	0.802675
$563$	−33.8358	−1.42601	−0.713004	−	0.701160i	$-0.752666\pi$
$563$	−33.8358	−1.42601	−0.713004	+	0.701160i	$0.752666\pi$
$564$	9.71272	0.408979
$565$	44.0732	1.85417
$566$	−27.9427	−1.17452
$567$	12.5103	0.525382
$568$	5.52241	0.231715
$569$	−39.6308	−1.66141	−0.830705	−	0.556712i	$-0.812063\pi$
$569$	−39.6308	−1.66141	−0.830705	+	0.556712i	$0.812063\pi$
$570$	23.8244	0.997893
$571$	28.9517	1.21159	0.605796	−	0.795620i	$-0.292855\pi$
$571$	28.9517	1.21159	0.605796	+	0.795620i	$0.292855\pi$
$572$	−6.58806	−0.275460
$573$	17.7301	0.740684
$574$	9.16540	0.382556
$575$	47.4169	1.97742
$576$	2.65251	0.110521
$577$	28.7441	1.19663	0.598317	−	0.801260i	$-0.295836\pi$
$577$	28.7441	1.19663	0.598317	+	0.801260i	$0.295836\pi$
$578$	17.0000	0.707107
$579$	−5.94430	−0.247037
$580$	−28.0533	−1.16485
$581$	11.1463	0.462426
$582$	0.255742	0.0106009
$583$	−26.9757	−1.11722
$584$	10.0385	0.415396
$585$	30.5480	1.26300
$586$	−10.7548	−0.444276
$587$	−34.0478	−1.40530	−0.702652	−	0.711534i	$-0.748001\pi$
$587$	−34.0478	−1.40530	−0.702652	+	0.711534i	$0.748001\pi$
$588$	12.8626	0.530445
$589$	22.0477	0.908462
$590$	−17.3708	−0.715146
$591$	25.2784	1.03981
$592$	8.81986	0.362494
$593$	−12.2844	−0.504458	−0.252229	−	0.967668i	$-0.581164\pi$
$593$	−12.2844	−0.504458	−0.252229	+	0.967668i	$0.581164\pi$
$594$	−1.80445	−0.0740377
$595$	0.00685811	0.000281155 0
$596$	14.9973	0.614312
$597$	19.1229	0.782646
$598$	14.9321	0.610620
$599$	−28.3389	−1.15789	−0.578947	−	0.815365i	$-0.696536\pi$
$599$	−28.3389	−1.15789	−0.578947	+	0.815365i	$0.696536\pi$
$600$	22.7722	0.929673
$601$	−20.6878	−0.843871	−0.421935	−	0.906626i	$-0.638649\pi$
$601$	−20.6878	−0.843871	−0.421935	+	0.906626i	$0.638649\pi$
$602$	−5.58540	−0.227644
$603$	34.5636	1.40754
$604$	4.89617	0.199222
$605$	23.7850	0.966996
$606$	−15.0782	−0.612510
$607$	−36.5985	−1.48549	−0.742744	−	0.669576i	$-0.766476\pi$
$607$	−36.5985	−1.48549	−0.742744	+	0.669576i	$0.766476\pi$
$608$	2.62451	0.106438
$609$	22.0258	0.892531
$610$	5.34005	0.216212
$611$	12.3223	0.498509
$612$	0.00377859	0.000152741 0
$613$	27.4505	1.10871	0.554357	−	0.832279i	$-0.312964\pi$
$613$	27.4505	1.10871	0.554357	+	0.832279i	$0.312964\pi$
$614$	10.7355	0.433249
$615$	65.9849	2.66077
$616$	2.75400	0.110962
$617$	−9.87704	−0.397635	−0.198817	−	0.980037i	$-0.563710\pi$
$617$	−9.87704	−0.397635	−0.198817	+	0.980037i	$0.563710\pi$
$618$	−21.9078	−0.881259
$619$	29.6367	1.19120	0.595600	−	0.803281i	$-0.296915\pi$
$619$	29.6367	1.19120	0.595600	+	0.803281i	$0.296915\pi$
$620$	32.0751	1.28817
$621$	4.08988	0.164121
$622$	−33.4549	−1.34142
$623$	2.17560	0.0871637
$624$	7.17123	0.287079
$625$	18.8513	0.754051
$626$	25.1439	1.00495
$627$	13.6287	0.544276
$628$	1.40538	0.0560807
$629$	0.0125642	0.000500967 0
$630$	−12.7699	−0.508767
$631$	−6.28945	−0.250379	−0.125190	−	0.992133i	$-0.539954\pi$
$631$	−6.28945	−0.250379	−0.125190	+	0.992133i	$0.539954\pi$
$632$	−17.5068	−0.696382
$633$	23.1939	0.921874
$634$	−5.69735	−0.226270
$635$	43.1843	1.71372
$636$	29.3637	1.16434
$637$	16.3186	0.646565
$638$	−16.0478	−0.635339
$639$	−14.6483	−0.579476
$640$	3.81814	0.150925
$641$	27.3703	1.08106	0.540531	−	0.841324i	$-0.318223\pi$
$641$	27.3703	1.08106	0.540531	+	0.841324i	$0.318223\pi$
$642$	−4.12535	−0.162815
$643$	−14.0043	−0.552274	−0.276137	−	0.961118i	$-0.589054\pi$
$643$	−14.0043	−0.552274	−0.276137	+	0.961118i	$0.589054\pi$
$644$	−6.24206	−0.245971
$645$	−40.2113	−1.58332
$646$	0.00373871	0.000147097 0
$647$	−7.96246	−0.313037	−0.156518	−	0.987675i	$-0.550027\pi$
$647$	−7.96246	−0.313037	−0.156518	+	0.987675i	$0.550027\pi$
$648$	9.92172	0.389762
$649$	−9.93693	−0.390059
$650$	28.8907	1.13319
$651$	−25.1835	−0.987019
$652$	−1.53431	−0.0600882
$653$	25.8360	1.01104	0.505520	−	0.862815i	$-0.331301\pi$
$653$	25.8360	1.01104	0.505520	+	0.862815i	$0.331301\pi$
$654$	29.2053	1.14202
$655$	−17.7912	−0.695159
$656$	7.26895	0.283805
$657$	−26.6272	−1.03883
$658$	−5.15110	−0.200811
$659$	−36.7555	−1.43179	−0.715896	−	0.698207i	$-0.753982\pi$
$659$	−36.7555	−1.43179	−0.715896	+	0.698207i	$0.753982\pi$
$660$	19.8270	0.771765
$661$	11.2840	0.438896	0.219448	−	0.975624i	$-0.429574\pi$
$661$	11.2840	0.438896	0.219448	+	0.975624i	$0.429574\pi$
$662$	7.99762	0.310836
$663$	0.0102157	0.000396744 0
$664$	8.83997	0.343057
$665$	−12.6351	−0.489970
$666$	−23.3948	−0.906529
$667$	36.3731	1.40837
$668$	−11.2632	−0.435785
$669$	−29.4313	−1.13788
$670$	49.7525	1.92210
$671$	3.05476	0.117928
$672$	−2.99778	−0.115642
$673$	−34.8200	−1.34221	−0.671107	−	0.741361i	$-0.734181\pi$
$673$	−34.8200	−1.34221	−0.671107	+	0.741361i	$0.734181\pi$
$674$	11.0795	0.426768
$675$	7.91311	0.304576
$676$	−3.90199	−0.150077
$677$	−47.1034	−1.81033	−0.905165	−	0.425061i	$-0.860253\pi$
$677$	−47.1034	−1.81033	−0.905165	+	0.425061i	$0.860253\pi$
$678$	−27.4437	−1.05397
$679$	−0.135632	−0.00520507
$680$	0.00543908	0.000208579 0
$681$	68.3755	2.62015
$682$	18.3485	0.702599
$683$	50.3175	1.92534	0.962672	−	0.270669i	$-0.0872449\pi$
$683$	50.3175	1.92534	0.962672	+	0.270669i	$0.0872449\pi$
$684$	−6.96155	−0.266181
$685$	6.38529	0.243969
$686$	−15.6479	−0.597440
$687$	26.4607	1.00954
$688$	−4.42970	−0.168881
$689$	37.2531	1.41923
$690$	−44.9388	−1.71079
$691$	19.5924	0.745332	0.372666	−	0.927966i	$-0.378444\pi$
$691$	19.5924	0.745332	0.372666	+	0.927966i	$0.378444\pi$
$692$	−6.17245	−0.234642
$693$	−7.30501	−0.277494
$694$	−17.5175	−0.664956
$695$	−75.7561	−2.87359
$696$	17.4684	0.662137
$697$	0.0103549	0.000392219 0
$698$	−18.6318	−0.705223
$699$	6.61672	0.250267
$700$	−12.0772	−0.456473
$701$	−23.3550	−0.882106	−0.441053	−	0.897481i	$-0.645395\pi$
$701$	−23.3550	−0.882106	−0.441053	+	0.897481i	$0.645395\pi$
$702$	2.49193	0.0940517
$703$	−23.1478	−0.873037
$704$	2.18416	0.0823185
$705$	−37.0846	−1.39669
$706$	8.48408	0.319303
$707$	7.99666	0.300745
$708$	10.8166	0.406511
$709$	5.77640	0.216937	0.108469	−	0.994100i	$-0.465405\pi$
$709$	5.77640	0.216937	0.108469	+	0.994100i	$0.465405\pi$
$710$	−21.0854	−0.791320
$711$	46.4369	1.74152
$712$	1.72544	0.0646637
$713$	−41.5876	−1.55747
$714$	−0.00427044	−0.000159817 0
$715$	25.1541	0.940712
$716$	−9.19896	−0.343781
$717$	25.4682	0.951126
$718$	−3.70517	−0.138276
$719$	39.6520	1.47877	0.739384	−	0.673284i	$-0.235117\pi$
$719$	39.6520	1.47877	0.739384	+	0.673284i	$0.235117\pi$
$720$	−10.1277	−0.377436
$721$	11.6187	0.432702
$722$	12.1119	0.450760
$723$	−10.5925	−0.393940
$724$	−18.8514	−0.700605
$725$	70.3748	2.61365
$726$	−14.8105	−0.549670
$727$	−3.83930	−0.142392	−0.0711959	−	0.997462i	$-0.522682\pi$
$727$	−3.83930	−0.142392	−0.0711959	+	0.997462i	$0.522682\pi$
$728$	−3.80323	−0.140957
$729$	−20.4249	−0.756478
$730$	−38.3285	−1.41860
$731$	−0.00631026	−0.000233394 0
$732$	−3.32517	−0.122902
$733$	−12.3312	−0.455465	−0.227732	−	0.973724i	$-0.573131\pi$
$733$	−12.3312	−0.455465	−0.227732	+	0.973724i	$0.573131\pi$
$734$	−22.5718	−0.833139
$735$	−49.1113	−1.81150
$736$	−4.95049	−0.182477
$737$	28.4607	1.04836
$738$	−19.2810	−0.709742
$739$	−12.3217	−0.453261	−0.226631	−	0.973981i	$-0.572771\pi$
$739$	−12.3217	−0.453261	−0.226631	+	0.973981i	$0.572771\pi$
$740$	−33.6755	−1.23794
$741$	−18.8210	−0.691406
$742$	−15.5729	−0.571698
$743$	−49.3405	−1.81013	−0.905064	−	0.425276i	$-0.860177\pi$
$743$	−49.3405	−1.81013	−0.905064	+	0.425276i	$0.860177\pi$
$744$	−19.9727	−0.732234
$745$	−57.2617	−2.09791
$746$	−24.6574	−0.902772
$747$	−23.4481	−0.857922
$748$	0.00311141	0.000113764 0
$749$	2.18786	0.0799427
$750$	−41.5595	−1.51754
$751$	−3.43714	−0.125423	−0.0627115	−	0.998032i	$-0.519975\pi$
$751$	−3.43714	−0.125423	−0.0627115	+	0.998032i	$0.519975\pi$
$752$	−4.08526	−0.148974
$753$	13.0093	0.474085
$754$	22.1618	0.807085
$755$	−18.6943	−0.680354
$756$	−1.04170	−0.0378862
$757$	−11.2418	−0.408590	−0.204295	−	0.978909i	$-0.565490\pi$
$757$	−11.2418	−0.408590	−0.204295	+	0.978909i	$0.565490\pi$
$758$	−13.4534	−0.488651
$759$	−25.7071	−0.933108
$760$	−10.0208	−0.363491
$761$	39.7101	1.43949	0.719746	−	0.694238i	$-0.244258\pi$
$761$	39.7101	1.43949	0.719746	+	0.694238i	$0.244258\pi$
$762$	−26.8902	−0.974129
$763$	−15.4889	−0.560736
$764$	−7.45743	−0.269800
$765$	−0.0144272	−0.000521617 0
$766$	22.5423	0.814488
$767$	13.7228	0.495500
$768$	−2.37750	−0.0857907
$769$	42.0484	1.51630	0.758152	−	0.652078i	$-0.226103\pi$
$769$	42.0484	1.51630	0.758152	+	0.652078i	$0.226103\pi$
$770$	−10.5152	−0.378940
$771$	−18.6964	−0.673334
$772$	2.50023	0.0899853
$773$	3.09019	0.111146	0.0555732	−	0.998455i	$-0.482301\pi$
$773$	3.09019	0.111146	0.0555732	+	0.998455i	$0.482301\pi$
$774$	11.7498	0.422339
$775$	−80.4638	−2.89035
$776$	−0.107568	−0.00386145
$777$	26.4400	0.948531
$778$	−8.04535	−0.288440
$779$	−19.0774	−0.683521
$780$	−27.3808	−0.980390
$781$	−12.0618	−0.431606
$782$	−0.00705214	−0.000252184 0
$783$	6.07007	0.216927
$784$	−5.41014	−0.193219
$785$	−5.36594	−0.191518
$786$	11.0783	0.395150
$787$	−43.5829	−1.55356	−0.776782	−	0.629770i	$-0.783149\pi$
$787$	−43.5829	−1.55356	−0.776782	+	0.629770i	$0.783149\pi$
$788$	−10.6323	−0.378762
$789$	71.0045	2.52783
$790$	66.8434	2.37818
$791$	14.5546	0.517503
$792$	−5.79350	−0.205863
$793$	−4.21858	−0.149806
$794$	−6.43810	−0.228480
$795$	−112.115	−3.97630
$796$	−8.04326	−0.285086
$797$	−36.8969	−1.30695	−0.653477	−	0.756946i	$-0.726690\pi$
$797$	−36.8969	−1.30695	−0.653477	+	0.756946i	$0.726690\pi$
$798$	7.86772	0.278514
$799$	−0.00581960	−0.000205883 0
$800$	−9.57823	−0.338641
$801$	−4.57675	−0.161712
$802$	−30.2639	−1.06865
$803$	−21.9257	−0.773740
$804$	−30.9801	−1.09258
$805$	23.8331	0.840005
$806$	−25.3390	−0.892527
$807$	−52.1047	−1.83417
$808$	6.34204	0.223112
$809$	52.0442	1.82978	0.914888	−	0.403708i	$-0.132279\pi$
$809$	52.0442	1.82978	0.914888	+	0.403708i	$0.132279\pi$
$810$	−37.8826	−1.33106
$811$	16.4060	0.576093	0.288047	−	0.957616i	$-0.406994\pi$
$811$	16.4060	0.576093	0.288047	+	0.957616i	$0.406994\pi$
$812$	−9.26427	−0.325112
$813$	−6.10225	−0.214015
$814$	−19.2640	−0.675202
$815$	5.85821	0.205204
$816$	−0.00338683	−0.000118563 0
$817$	11.6258	0.406736
$818$	−18.6931	−0.653589
$819$	10.0881	0.352507
$820$	−27.7539	−0.969208
$821$	2.95532	0.103141	0.0515707	−	0.998669i	$-0.483577\pi$
$821$	2.95532	0.103141	0.0515707	+	0.998669i	$0.483577\pi$
$822$	−3.97602	−0.138680
$823$	47.8773	1.66890	0.834448	−	0.551086i	$-0.185786\pi$
$823$	47.8773	1.66890	0.834448	+	0.551086i	$0.185786\pi$
$824$	9.21462	0.321006
$825$	−49.7382	−1.73166
$826$	−5.73651	−0.199599
$827$	3.62112	0.125919	0.0629594	−	0.998016i	$-0.479946\pi$
$827$	3.62112	0.125919	0.0629594	+	0.998016i	$0.479946\pi$
$828$	13.1312	0.456342
$829$	55.1641	1.91593	0.957964	−	0.286887i	$-0.0926205\pi$
$829$	55.1641	1.91593	0.957964	+	0.286887i	$0.0926205\pi$
$830$	−33.7523	−1.17156
$831$	1.30276	0.0451922
$832$	−3.01629	−0.104571
$833$	−0.00770693	−0.000267029 0
$834$	47.1722	1.63344
$835$	43.0044	1.48823
$836$	−5.73235	−0.198257
$837$	−6.94029	−0.239892
$838$	2.71641	0.0938369
$839$	36.8190	1.27113	0.635566	−	0.772047i	$-0.280767\pi$
$839$	36.8190	1.27113	0.635566	+	0.772047i	$0.280767\pi$
$840$	11.4460	0.394923
$841$	24.9838	0.861511
$842$	1.79074	0.0617131
$843$	45.2406	1.55817
$844$	−9.75558	−0.335801
$845$	14.8984	0.512519
$846$	10.8362	0.372557
$847$	7.85470	0.269891
$848$	−12.3506	−0.424123
$849$	−66.4338	−2.28000
$850$	−0.0136445	−0.000468003 0
$851$	43.6626	1.49674
$852$	13.1295	0.449811
$853$	10.4156	0.356623	0.178311	−	0.983974i	$-0.442937\pi$
$853$	10.4156	0.356623	0.178311	+	0.983974i	$0.442937\pi$
$854$	1.76349	0.0603453
$855$	26.5802	0.909023
$856$	1.73516	0.0593066
$857$	0.905891	0.0309446	0.0154723	−	0.999880i	$-0.495075\pi$
$857$	0.905891	0.0309446	0.0154723	+	0.999880i	$0.495075\pi$
$858$	−15.6631	−0.534730
$859$	−0.239038	−0.00815587	−0.00407794	−	0.999992i	$-0.501298\pi$
$859$	−0.239038	−0.00815587	−0.00407794	+	0.999992i	$0.501298\pi$
$860$	16.9132	0.576737
$861$	21.7907	0.742626
$862$	5.52746	0.188266
$863$	−0.718040	−0.0244424	−0.0122212	−	0.999925i	$-0.503890\pi$
$863$	−0.718040	−0.0244424	−0.0122212	+	0.999925i	$0.503890\pi$
$864$	−0.826156	−0.0281064
$865$	23.5673	0.801313
$866$	−15.2362	−0.517746
$867$	40.4175	1.37265
$868$	10.5924	0.359530
$869$	38.2376	1.29712
$870$	−66.6968	−2.26123
$871$	−39.3039	−1.33176
$872$	−12.2840	−0.415990
$873$	0.285324	0.00965676
$874$	12.9926	0.439482
$875$	22.0409	0.745118
$876$	23.8666	0.806376
$877$	−20.9613	−0.707813	−0.353906	−	0.935281i	$-0.615147\pi$
$877$	−20.9613	−0.707813	−0.353906	+	0.935281i	$0.615147\pi$
$878$	22.6246	0.763543
$879$	−25.5695	−0.862439
$880$	−8.33943	−0.281122
$881$	45.6740	1.53880	0.769398	−	0.638770i	$-0.220556\pi$
$881$	45.6740	1.53880	0.769398	+	0.638770i	$0.220556\pi$
$882$	14.3505	0.483205
$883$	12.1010	0.407232	0.203616	−	0.979051i	$-0.434731\pi$
$883$	12.1010	0.407232	0.203616	+	0.979051i	$0.434731\pi$
$884$	−0.00429681	−0.000144517 0
$885$	−41.2992	−1.38826
$886$	18.6103	0.625225
$887$	−42.2445	−1.41843	−0.709215	−	0.704992i	$-0.750951\pi$
$887$	−42.2445	−1.41843	−0.709215	+	0.704992i	$0.750951\pi$
$888$	20.9692	0.703681
$889$	14.2611	0.478302
$890$	−6.58798	−0.220830
$891$	−21.6706	−0.725992
$892$	12.3791	0.414483
$893$	10.7218	0.358792
$894$	35.6560	1.19251
$895$	35.1230	1.17403
$896$	1.26090	0.0421236
$897$	35.5011	1.18535
$898$	19.9278	0.664998
$899$	−61.7231	−2.05858
$900$	25.4063	0.846878
$901$	−0.0175939	−0.000586138 0
$902$	−15.8765	−0.528631
$903$	−13.2793	−0.441907
$904$	11.5431	0.383917
$905$	71.9772	2.39260
$906$	11.6406	0.386734
$907$	−20.6020	−0.684078	−0.342039	−	0.939686i	$-0.611118\pi$
$907$	−20.6020	−0.684078	−0.342039	+	0.939686i	$0.611118\pi$
$908$	−28.7594	−0.954414
$909$	−16.8223	−0.557961
$910$	14.5213	0.481376
$911$	−30.7955	−1.02030	−0.510151	−	0.860085i	$-0.670410\pi$
$911$	−30.7955	−1.02030	−0.510151	+	0.860085i	$0.670410\pi$
$912$	6.23978	0.206620
$913$	−19.3079	−0.638998
$914$	−27.7247	−0.917050
$915$	12.6960	0.419716
$916$	−11.1296	−0.367733
$917$	−5.87532	−0.194020
$918$	−0.00117689	−3.88431e−5 0
$919$	−39.0883	−1.28940	−0.644702	−	0.764434i	$-0.723018\pi$
$919$	−39.0883	−1.28940	−0.644702	+	0.764434i	$0.723018\pi$
$920$	18.9017	0.623170
$921$	25.5236	0.841032
$922$	−34.7481	−1.14437
$923$	16.6572	0.548279
$924$	6.54763	0.215401
$925$	84.4786	2.77764
$926$	−20.3787	−0.669685
$927$	−24.4419	−0.802776
$928$	−7.34737	−0.241189
$929$	12.4372	0.408053	0.204026	−	0.978965i	$-0.434597\pi$
$929$	12.4372	0.408053	0.204026	+	0.978965i	$0.434597\pi$
$930$	76.2586	2.50062
$931$	14.1990	0.465353
$932$	−2.78306	−0.0911620
$933$	−79.5390	−2.60399
$934$	−8.34217	−0.272964
$935$	−0.0118798	−0.000388511 0
$936$	8.00074	0.261513
$937$	28.4593	0.929726	0.464863	−	0.885383i	$-0.346104\pi$
$937$	28.4593	0.929726	0.464863	+	0.885383i	$0.346104\pi$
$938$	16.4302	0.536464
$939$	59.7797	1.95084
$940$	15.5981	0.508755
$941$	20.9248	0.682129	0.341064	−	0.940040i	$-0.389213\pi$
$941$	20.9248	0.682129	0.341064	+	0.940040i	$0.389213\pi$
$942$	3.34129	0.108865
$943$	35.9849	1.17183
$944$	−4.54955	−0.148075
$945$	3.97735	0.129383
$946$	9.67517	0.314567
$947$	−60.3908	−1.96244	−0.981219	−	0.192895i	$-0.938212\pi$
$947$	−60.3908	−1.96244	−0.981219	+	0.192895i	$0.938212\pi$
$948$	−41.6224	−1.35183
$949$	30.2791	0.982900
$950$	25.1382	0.815590
$951$	−13.5454	−0.439241
$952$	0.00179619	5.82149e−5 0
$953$	−54.3911	−1.76190	−0.880950	−	0.473210i	$-0.843095\pi$
$953$	−54.3911	−1.76190	−0.880950	+	0.473210i	$0.843095\pi$
$954$	32.7602	1.06065
$955$	28.4736	0.921383
$956$	−10.7122	−0.346456
$957$	−38.1537	−1.23333
$958$	16.4373	0.531066
$959$	2.10866	0.0680923
$960$	9.07764	0.292980
$961$	39.5718	1.27651
$962$	26.6033	0.857724
$963$	−4.60254	−0.148315
$964$	4.45532	0.143496
$965$	−9.54624	−0.307304
$966$	−14.8405	−0.477485
$967$	−47.3142	−1.52152	−0.760761	−	0.649032i	$-0.775174\pi$
$967$	−47.3142	−1.52152	−0.760761	+	0.649032i	$0.775174\pi$
$968$	6.22945	0.200222
$969$	0.00888878	0.000285549 0
$970$	0.410709	0.0131871
$971$	−5.03513	−0.161585	−0.0807925	−	0.996731i	$-0.525745\pi$
$971$	−5.03513	−0.161585	−0.0807925	+	0.996731i	$0.525745\pi$
$972$	21.1104	0.677117
$973$	−25.0176	−0.802026
$974$	−41.0752	−1.31614
$975$	68.6877	2.19977
$976$	1.39860	0.0447680
$977$	33.0989	1.05893	0.529464	−	0.848333i	$-0.322393\pi$
$977$	33.0989	1.05893	0.529464	+	0.848333i	$0.322393\pi$
$978$	−3.64782	−0.116644
$979$	−3.76864	−0.120446
$980$	20.6567	0.659854
$981$	32.5835	1.04031
$982$	11.2138	0.357848
$983$	24.7902	0.790685	0.395342	−	0.918534i	$-0.370626\pi$
$983$	24.7902	0.790685	0.395342	+	0.918534i	$0.370626\pi$
$984$	17.2819	0.550928
$985$	40.5958	1.29349
$986$	−0.0104666	−0.000333324 0
$987$	−12.2467	−0.389818
$988$	7.91629	0.251851
$989$	−21.9292	−0.697308
$990$	22.1204	0.703033
$991$	57.0641	1.81270	0.906350	−	0.422528i	$-0.138857\pi$
$991$	57.0641	1.81270	0.906350	+	0.422528i	$0.138857\pi$
$992$	8.40070	0.266723
$993$	19.0143	0.603402
$994$	−6.96319	−0.220859
$995$	30.7103	0.973582
$996$	21.0170	0.665950
$997$	−15.8868	−0.503141	−0.251571	−	0.967839i	$-0.580947\pi$
$997$	−15.8868	−0.503141	−0.251571	+	0.967839i	$0.580947\pi$
$998$	−9.03069	−0.285862
$999$	7.28658	0.230537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.c.1.16	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.c.1.16	✓	92	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:	\( N \)	\(=\)	\( 8006 = 2 \cdot 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.37750 q^{3} +1.00000 q^{4} -3.81814 q^{5} +2.37750 q^{6} -1.26090 q^{7} -1.00000 q^{8} +2.65251 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.37750 q^{3} +1.00000 q^{4} -3.81814 q^{5} +2.37750 q^{6} -1.26090 q^{7} -1.00000 q^{8} +2.65251 q^{9} +3.81814 q^{10} +2.18416 q^{11} -2.37750 q^{12} -3.01629 q^{13} +1.26090 q^{14} +9.07764 q^{15} +1.00000 q^{16} +0.00142453 q^{17} -2.65251 q^{18} -2.62451 q^{19} -3.81814 q^{20} +2.99778 q^{21} -2.18416 q^{22} +4.95049 q^{23} +2.37750 q^{24} +9.57823 q^{25} +3.01629 q^{26} +0.826156 q^{27} -1.26090 q^{28} +7.34737 q^{29} -9.07764 q^{30} -8.40070 q^{31} -1.00000 q^{32} -5.19284 q^{33} -0.00142453 q^{34} +4.81429 q^{35} +2.65251 q^{36} +8.81986 q^{37} +2.62451 q^{38} +7.17123 q^{39} +3.81814 q^{40} +7.26895 q^{41} -2.99778 q^{42} -4.42970 q^{43} +2.18416 q^{44} -10.1277 q^{45} -4.95049 q^{46} -4.08526 q^{47} -2.37750 q^{48} -5.41014 q^{49} -9.57823 q^{50} -0.00338683 q^{51} -3.01629 q^{52} -12.3506 q^{53} -0.826156 q^{54} -8.33943 q^{55} +1.26090 q^{56} +6.23978 q^{57} -7.34737 q^{58} -4.54955 q^{59} +9.07764 q^{60} +1.39860 q^{61} +8.40070 q^{62} -3.34454 q^{63} +1.00000 q^{64} +11.5166 q^{65} +5.19284 q^{66} +13.0305 q^{67} +0.00142453 q^{68} -11.7698 q^{69} -4.81429 q^{70} -5.52241 q^{71} -2.65251 q^{72} -10.0385 q^{73} -8.81986 q^{74} -22.7722 q^{75} -2.62451 q^{76} -2.75400 q^{77} -7.17123 q^{78} +17.5068 q^{79} -3.81814 q^{80} -9.92172 q^{81} -7.26895 q^{82} -8.83997 q^{83} +2.99778 q^{84} -0.00543908 q^{85} +4.42970 q^{86} -17.4684 q^{87} -2.18416 q^{88} -1.72544 q^{89} +10.1277 q^{90} +3.80323 q^{91} +4.95049 q^{92} +19.9727 q^{93} +4.08526 q^{94} +10.0208 q^{95} +2.37750 q^{96} +0.107568 q^{97} +5.41014 q^{98} +5.79350 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9}+O(q^{10}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9} - 10 q^{10} + 4 q^{11} - 2 q^{12} + 40 q^{13} - 8 q^{14} + 15 q^{15} + 92 q^{16} - 14 q^{17} - 104 q^{18} + 64 q^{19} + 10 q^{20} + 54 q^{21} - 4 q^{22} - 49 q^{23} + 2 q^{24} + 116 q^{25} - 40 q^{26} - 8 q^{27} + 8 q^{28} + 39 q^{29} - 15 q^{30} + 53 q^{31} - 92 q^{32} + q^{33} + 14 q^{34} - 22 q^{35} + 104 q^{36} + 58 q^{37} - 64 q^{38} + 58 q^{39} - 10 q^{40} + 27 q^{41} - 54 q^{42} + 40 q^{43} + 4 q^{44} + 43 q^{45} + 49 q^{46} - 28 q^{47} - 2 q^{48} + 148 q^{49} - 116 q^{50} + 48 q^{51} + 40 q^{52} + 32 q^{53} + 8 q^{54} + 36 q^{55} - 8 q^{56} + 48 q^{57} - 39 q^{58} + 8 q^{59} + 15 q^{60} + 99 q^{61} - 53 q^{62} + 92 q^{64} + 13 q^{65} - q^{66} + 48 q^{67} - 14 q^{68} + 63 q^{69} + 22 q^{70} - 13 q^{71} - 104 q^{72} + 49 q^{73} - 58 q^{74} + 16 q^{75} + 64 q^{76} + 41 q^{77} - 58 q^{78} + 143 q^{79} + 10 q^{80} + 124 q^{81} - 27 q^{82} - 24 q^{83} + 54 q^{84} + 121 q^{85} - 40 q^{86} + 5 q^{87} - 4 q^{88} + 25 q^{89} - 43 q^{90} + 67 q^{91} - 49 q^{92} + 43 q^{93} + 28 q^{94} - 38 q^{95} + 2 q^{96} + 74 q^{97} - 148 q^{98} + 86 q^{99}+O(q^{100}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9 - 10 * q^10 + 4 * q^11 - 2 * q^12 + 40 * q^13 - 8 * q^14 + 15 * q^15 + 92 * q^16 - 14 * q^17 - 104 * q^18 + 64 * q^19 + 10 * q^20 + 54 * q^21 - 4 * q^22 - 49 * q^23 + 2 * q^24 + 116 * q^25 - 40 * q^26 - 8 * q^27 + 8 * q^28 + 39 * q^29 - 15 * q^30 + 53 * q^31 - 92 * q^32 + q^33 + 14 * q^34 - 22 * q^35 + 104 * q^36 + 58 * q^37 - 64 * q^38 + 58 * q^39 - 10 * q^40 + 27 * q^41 - 54 * q^42 + 40 * q^43 + 4 * q^44 + 43 * q^45 + 49 * q^46 - 28 * q^47 - 2 * q^48 + 148 * q^49 - 116 * q^50 + 48 * q^51 + 40 * q^52 + 32 * q^53 + 8 * q^54 + 36 * q^55 - 8 * q^56 + 48 * q^57 - 39 * q^58 + 8 * q^59 + 15 * q^60 + 99 * q^61 - 53 * q^62 + 92 * q^64 + 13 * q^65 - q^66 + 48 * q^67 - 14 * q^68 + 63 * q^69 + 22 * q^70 - 13 * q^71 - 104 * q^72 + 49 * q^73 - 58 * q^74 + 16 * q^75 + 64 * q^76 + 41 * q^77 - 58 * q^78 + 143 * q^79 + 10 * q^80 + 124 * q^81 - 27 * q^82 - 24 * q^83 + 54 * q^84 + 121 * q^85 - 40 * q^86 + 5 * q^87 - 4 * q^88 + 25 * q^89 - 43 * q^90 + 67 * q^91 - 49 * q^92 + 43 * q^93 + 28 * q^94 - 38 * q^95 + 2 * q^96 + 74 * q^97 - 148 * q^98 + 86 * q^99

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