LMFDB - Embedded newform 8002.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, 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("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.03319 q^{3} +1.00000 q^{4} -3.55972 q^{5} -3.03319 q^{6} -4.22109 q^{7} +1.00000 q^{8} +6.20023 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.03319 q^{3} +1.00000 q^{4} -3.55972 q^{5} -3.03319 q^{6} -4.22109 q^{7} +1.00000 q^{8} +6.20023 q^{9} -3.55972 q^{10} +0.539753 q^{11} -3.03319 q^{12} -2.53431 q^{13} -4.22109 q^{14} +10.7973 q^{15} +1.00000 q^{16} -7.56621 q^{17} +6.20023 q^{18} +8.08491 q^{19} -3.55972 q^{20} +12.8033 q^{21} +0.539753 q^{22} -8.07968 q^{23} -3.03319 q^{24} +7.67163 q^{25} -2.53431 q^{26} -9.70689 q^{27} -4.22109 q^{28} +5.32885 q^{29} +10.7973 q^{30} -8.35573 q^{31} +1.00000 q^{32} -1.63717 q^{33} -7.56621 q^{34} +15.0259 q^{35} +6.20023 q^{36} +2.83287 q^{37} +8.08491 q^{38} +7.68703 q^{39} -3.55972 q^{40} +0.736282 q^{41} +12.8033 q^{42} +5.40877 q^{43} +0.539753 q^{44} -22.0711 q^{45} -8.07968 q^{46} +10.8385 q^{47} -3.03319 q^{48} +10.8176 q^{49} +7.67163 q^{50} +22.9497 q^{51} -2.53431 q^{52} +4.18131 q^{53} -9.70689 q^{54} -1.92137 q^{55} -4.22109 q^{56} -24.5231 q^{57} +5.32885 q^{58} -2.94928 q^{59} +10.7973 q^{60} +11.7171 q^{61} -8.35573 q^{62} -26.1717 q^{63} +1.00000 q^{64} +9.02143 q^{65} -1.63717 q^{66} -0.652017 q^{67} -7.56621 q^{68} +24.5072 q^{69} +15.0259 q^{70} +6.46973 q^{71} +6.20023 q^{72} -13.6526 q^{73} +2.83287 q^{74} -23.2695 q^{75} +8.08491 q^{76} -2.27835 q^{77} +7.68703 q^{78} +9.44342 q^{79} -3.55972 q^{80} +10.8421 q^{81} +0.736282 q^{82} -3.28706 q^{83} +12.8033 q^{84} +26.9336 q^{85} +5.40877 q^{86} -16.1634 q^{87} +0.539753 q^{88} -9.91472 q^{89} -22.0711 q^{90} +10.6975 q^{91} -8.07968 q^{92} +25.3445 q^{93} +10.8385 q^{94} -28.7801 q^{95} -3.03319 q^{96} +12.6908 q^{97} +10.8176 q^{98} +3.34659 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * 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
$3$	−3.03319	−1.75121	−0.875606	−	0.483026i	$-0.839538\pi$
$3$	−3.03319	−1.75121	−0.875606	+	0.483026i	$0.839538\pi$
$4$	1.00000	0.500000
$5$	−3.55972	−1.59196	−0.795978	−	0.605325i	$-0.793043\pi$
$5$	−3.55972	−1.59196	−0.795978	+	0.605325i	$0.793043\pi$
$6$	−3.03319	−1.23829
$7$	−4.22109	−1.59542	−0.797710	−	0.603041i	$-0.793956\pi$
$7$	−4.22109	−1.59542	−0.797710	+	0.603041i	$0.793956\pi$
$8$	1.00000	0.353553
$9$	6.20023	2.06674
$10$	−3.55972	−1.12568
$11$	0.539753	0.162742	0.0813709	−	0.996684i	$-0.474070\pi$
$11$	0.539753	0.162742	0.0813709	+	0.996684i	$0.474070\pi$
$12$	−3.03319	−0.875606
$13$	−2.53431	−0.702890	−0.351445	−	0.936209i	$-0.614310\pi$
$13$	−2.53431	−0.702890	−0.351445	+	0.936209i	$0.614310\pi$
$14$	−4.22109	−1.12813
$15$	10.7973	2.78785
$16$	1.00000	0.250000
$17$	−7.56621	−1.83508	−0.917538	−	0.397648i	$-0.869827\pi$
$17$	−7.56621	−1.83508	−0.917538	+	0.397648i	$0.869827\pi$
$18$	6.20023	1.46141
$19$	8.08491	1.85481	0.927403	−	0.374064i	$-0.122036\pi$
$19$	8.08491	1.85481	0.927403	+	0.374064i	$0.122036\pi$
$20$	−3.55972	−0.795978
$21$	12.8033	2.79392
$22$	0.539753	0.115076
$23$	−8.07968	−1.68473	−0.842365	−	0.538908i	$-0.818837\pi$
$23$	−8.07968	−1.68473	−0.842365	+	0.538908i	$0.818837\pi$
$24$	−3.03319	−0.619147
$25$	7.67163	1.53433
$26$	−2.53431	−0.497018
$27$	−9.70689	−1.86809
$28$	−4.22109	−0.797710
$29$	5.32885	0.989542	0.494771	−	0.869023i	$-0.335252\pi$
$29$	5.32885	0.989542	0.494771	+	0.869023i	$0.335252\pi$
$30$	10.7973	1.97131
$31$	−8.35573	−1.50073	−0.750367	−	0.661022i	$-0.770123\pi$
$31$	−8.35573	−1.50073	−0.750367	+	0.661022i	$0.770123\pi$
$32$	1.00000	0.176777
$33$	−1.63717	−0.284995
$34$	−7.56621	−1.29759
$35$	15.0259	2.53984
$36$	6.20023	1.03337
$37$	2.83287	0.465721	0.232861	−	0.972510i	$-0.425191\pi$
$37$	2.83287	0.465721	0.232861	+	0.972510i	$0.425191\pi$
$38$	8.08491	1.31155
$39$	7.68703	1.23091
$40$	−3.55972	−0.562842
$41$	0.736282	0.114988	0.0574940	−	0.998346i	$-0.481689\pi$
$41$	0.736282	0.114988	0.0574940	+	0.998346i	$0.481689\pi$
$42$	12.8033	1.97560
$43$	5.40877	0.824829	0.412414	−	0.910996i	$-0.364686\pi$
$43$	5.40877	0.824829	0.412414	+	0.910996i	$0.364686\pi$
$44$	0.539753	0.0813709
$45$	−22.0711	−3.29016
$46$	−8.07968	−1.19128
$47$	10.8385	1.58096	0.790482	−	0.612486i	$-0.209830\pi$
$47$	10.8385	1.58096	0.790482	+	0.612486i	$0.209830\pi$
$48$	−3.03319	−0.437803
$49$	10.8176	1.54537
$50$	7.67163	1.08493
$51$	22.9497	3.21361
$52$	−2.53431	−0.351445
$53$	4.18131	0.574348	0.287174	−	0.957878i	$-0.407284\pi$
$53$	4.18131	0.574348	0.287174	+	0.957878i	$0.407284\pi$
$54$	−9.70689	−1.32094
$55$	−1.92137	−0.259078
$56$	−4.22109	−0.564066
$57$	−24.5231	−3.24816
$58$	5.32885	0.699712
$59$	−2.94928	−0.383964	−0.191982	−	0.981398i	$-0.561491\pi$
$59$	−2.94928	−0.383964	−0.191982	+	0.981398i	$0.561491\pi$
$60$	10.7973	1.39393
$61$	11.7171	1.50023	0.750113	−	0.661310i	$-0.229999\pi$
$61$	11.7171	1.50023	0.750113	+	0.661310i	$0.229999\pi$
$62$	−8.35573	−1.06118
$63$	−26.1717	−3.29732
$64$	1.00000	0.125000
$65$	9.02143	1.11897
$66$	−1.63717	−0.201522
$67$	−0.652017	−0.0796566	−0.0398283	−	0.999207i	$-0.512681\pi$
$67$	−0.652017	−0.0796566	−0.0398283	+	0.999207i	$0.512681\pi$
$68$	−7.56621	−0.917538
$69$	24.5072	2.95032
$70$	15.0259	1.79594
$71$	6.46973	0.767816	0.383908	−	0.923371i	$-0.374578\pi$
$71$	6.46973	0.767816	0.383908	+	0.923371i	$0.374578\pi$
$72$	6.20023	0.730704
$73$	−13.6526	−1.59791	−0.798957	−	0.601388i	$-0.794614\pi$
$73$	−13.6526	−1.59791	−0.798957	+	0.601388i	$0.794614\pi$
$74$	2.83287	0.329315
$75$	−23.2695	−2.68693
$76$	8.08491	0.927403
$77$	−2.27835	−0.259642
$78$	7.68703	0.870384
$79$	9.44342	1.06247	0.531234	−	0.847225i	$-0.321728\pi$
$79$	9.44342	1.06247	0.531234	+	0.847225i	$0.321728\pi$
$80$	−3.55972	−0.397989
$81$	10.8421	1.20468
$82$	0.736282	0.0813088
$83$	−3.28706	−0.360802	−0.180401	−	0.983593i	$-0.557740\pi$
$83$	−3.28706	−0.360802	−0.180401	+	0.983593i	$0.557740\pi$
$84$	12.8033	1.39696
$85$	26.9336	2.92136
$86$	5.40877	0.583242
$87$	−16.1634	−1.73290
$88$	0.539753	0.0575379
$89$	−9.91472	−1.05096	−0.525479	−	0.850806i	$-0.676114\pi$
$89$	−9.91472	−1.05096	−0.525479	+	0.850806i	$0.676114\pi$
$90$	−22.0711	−2.32650
$91$	10.6975	1.12141
$92$	−8.07968	−0.842365
$93$	25.3445	2.62810
$94$	10.8385	1.11791
$95$	−28.7801	−2.95277
$96$	−3.03319	−0.309573
$97$	12.6908	1.28856	0.644279	−	0.764791i	$-0.277158\pi$
$97$	12.6908	1.28856	0.644279	+	0.764791i	$0.277158\pi$
$98$	10.8176	1.09274
$99$	3.34659	0.336345
$100$	7.67163	0.767163
$101$	−11.7334	−1.16752	−0.583759	−	0.811927i	$-0.698419\pi$
$101$	−11.7334	−1.16752	−0.583759	+	0.811927i	$0.698419\pi$
$102$	22.9497	2.27236
$103$	15.2050	1.49819	0.749095	−	0.662462i	$-0.230488\pi$
$103$	15.2050	1.49819	0.749095	+	0.662462i	$0.230488\pi$
$104$	−2.53431	−0.248509
$105$	−45.5764	−4.44780
$106$	4.18131	0.406125
$107$	−3.30305	−0.319318	−0.159659	−	0.987172i	$-0.551040\pi$
$107$	−3.30305	−0.319318	−0.159659	+	0.987172i	$0.551040\pi$
$108$	−9.70689	−0.934046
$109$	1.08226	0.103662	0.0518308	−	0.998656i	$-0.483494\pi$
$109$	1.08226	0.103662	0.0518308	+	0.998656i	$0.483494\pi$
$110$	−1.92137	−0.183196
$111$	−8.59263	−0.815577
$112$	−4.22109	−0.398855
$113$	11.4581	1.07789	0.538946	−	0.842340i	$-0.318823\pi$
$113$	11.4581	1.07789	0.538946	+	0.842340i	$0.318823\pi$
$114$	−24.5231	−2.29679
$115$	28.7614	2.68202
$116$	5.32885	0.494771
$117$	−15.7133	−1.45269
$118$	−2.94928	−0.271503
$119$	31.9376	2.92772
$120$	10.7973	0.985655
$121$	−10.7087	−0.973515
$122$	11.7171	1.06082
$123$	−2.23328	−0.201368
$124$	−8.35573	−0.750367
$125$	−9.51028	−0.850625
$126$	−26.1717	−2.33156
$127$	12.3867	1.09914	0.549571	−	0.835447i	$-0.314791\pi$
$127$	12.3867	1.09914	0.549571	+	0.835447i	$0.314791\pi$
$128$	1.00000	0.0883883
$129$	−16.4058	−1.44445
$130$	9.02143	0.791232
$131$	11.8748	1.03751	0.518754	−	0.854924i	$-0.326396\pi$
$131$	11.8748	1.03751	0.518754	+	0.854924i	$0.326396\pi$
$132$	−1.63717	−0.142498
$133$	−34.1271	−2.95920
$134$	−0.652017	−0.0563257
$135$	34.5538	2.97392
$136$	−7.56621	−0.648797
$137$	−20.4929	−1.75082	−0.875411	−	0.483379i	$-0.839409\pi$
$137$	−20.4929	−1.75082	−0.875411	+	0.483379i	$0.839409\pi$
$138$	24.5072	2.08619
$139$	−11.0098	−0.933835	−0.466918	−	0.884301i	$-0.654636\pi$
$139$	−11.0098	−0.933835	−0.466918	+	0.884301i	$0.654636\pi$
$140$	15.0259	1.26992
$141$	−32.8753	−2.76860
$142$	6.46973	0.542928
$143$	−1.36790	−0.114390
$144$	6.20023	0.516686
$145$	−18.9692	−1.57531
$146$	−13.6526	−1.12990
$147$	−32.8117	−2.70627
$148$	2.83287	0.232861
$149$	11.0189	0.902703	0.451352	−	0.892346i	$-0.350942\pi$
$149$	11.0189	0.902703	0.451352	+	0.892346i	$0.350942\pi$
$150$	−23.2695	−1.89995
$151$	11.2698	0.917124	0.458562	−	0.888662i	$-0.348365\pi$
$151$	11.2698	0.917124	0.458562	+	0.888662i	$0.348365\pi$
$152$	8.08491	0.655773
$153$	−46.9122	−3.79263
$154$	−2.27835	−0.183594
$155$	29.7441	2.38910
$156$	7.68703	0.615455
$157$	8.35931	0.667145	0.333573	−	0.942724i	$-0.391746\pi$
$157$	8.35931	0.667145	0.333573	+	0.942724i	$0.391746\pi$
$158$	9.44342	0.751279
$159$	−12.6827	−1.00580
$160$	−3.55972	−0.281421
$161$	34.1050	2.68785
$162$	10.8421	0.851839
$163$	8.38009	0.656379	0.328190	−	0.944612i	$-0.393561\pi$
$163$	8.38009	0.656379	0.328190	+	0.944612i	$0.393561\pi$
$164$	0.736282	0.0574940
$165$	5.82788	0.453700
$166$	−3.28706	−0.255126
$167$	−16.8416	−1.30324	−0.651621	−	0.758545i	$-0.725911\pi$
$167$	−16.8416	−1.30324	−0.651621	+	0.758545i	$0.725911\pi$
$168$	12.8033	0.987800
$169$	−6.57729	−0.505945
$170$	26.9336	2.06571
$171$	50.1283	3.83341
$172$	5.40877	0.412414
$173$	17.3463	1.31882	0.659408	−	0.751785i	$-0.270807\pi$
$173$	17.3463	1.31882	0.659408	+	0.751785i	$0.270807\pi$
$174$	−16.1634	−1.22534
$175$	−32.3826	−2.44790
$176$	0.539753	0.0406854
$177$	8.94572	0.672402
$178$	−9.91472	−0.743140
$179$	−3.22549	−0.241085	−0.120542	−	0.992708i	$-0.538463\pi$
$179$	−3.22549	−0.241085	−0.120542	+	0.992708i	$0.538463\pi$
$180$	−22.0711	−1.64508
$181$	−22.3274	−1.65958	−0.829791	−	0.558075i	$-0.811540\pi$
$181$	−22.3274	−1.65958	−0.829791	+	0.558075i	$0.811540\pi$
$182$	10.6975	0.792953
$183$	−35.5403	−2.62721
$184$	−8.07968	−0.595642
$185$	−10.0842	−0.741408
$186$	25.3445	1.85835
$187$	−4.08389	−0.298643
$188$	10.8385	0.790482
$189$	40.9736	2.98039
$190$	−28.7801	−2.08792
$191$	2.14688	0.155343	0.0776713	−	0.996979i	$-0.475252\pi$
$191$	2.14688	0.155343	0.0776713	+	0.996979i	$0.475252\pi$
$192$	−3.03319	−0.218901
$193$	3.12109	0.224661	0.112331	−	0.993671i	$-0.464168\pi$
$193$	3.12109	0.224661	0.112331	+	0.993671i	$0.464168\pi$
$194$	12.6908	0.911148
$195$	−27.3637	−1.95955
$196$	10.8176	0.772684
$197$	−13.9592	−0.994553	−0.497276	−	0.867592i	$-0.665666\pi$
$197$	−13.9592	−0.994553	−0.497276	+	0.867592i	$0.665666\pi$
$198$	3.34659	0.237832
$199$	19.4235	1.37689	0.688447	−	0.725287i	$-0.258293\pi$
$199$	19.4235	1.37689	0.688447	+	0.725287i	$0.258293\pi$
$200$	7.67163	0.542466
$201$	1.97769	0.139495
$202$	−11.7334	−0.825560
$203$	−22.4935	−1.57874
$204$	22.9497	1.60680
$205$	−2.62096	−0.183056
$206$	15.2050	1.05938
$207$	−50.0959	−3.48190
$208$	−2.53431	−0.175723
$209$	4.36386	0.301854
$210$	−45.5764	−3.14507
$211$	−5.94554	−0.409308	−0.204654	−	0.978834i	$-0.565607\pi$
$211$	−5.94554	−0.409308	−0.204654	+	0.978834i	$0.565607\pi$
$212$	4.18131	0.287174
$213$	−19.6239	−1.34461
$214$	−3.30305	−0.225792
$215$	−19.2537	−1.31309
$216$	−9.70689	−0.660470
$217$	35.2703	2.39430
$218$	1.08226	0.0732998
$219$	41.4108	2.79829
$220$	−1.92137	−0.129539
$221$	19.1751	1.28986
$222$	−8.59263	−0.576700
$223$	12.4346	0.832683	0.416342	−	0.909208i	$-0.363312\pi$
$223$	12.4346	0.832683	0.416342	+	0.909208i	$0.363312\pi$
$224$	−4.22109	−0.282033
$225$	47.5659	3.17106
$226$	11.4581	0.762185
$227$	−20.3942	−1.35361	−0.676804	−	0.736164i	$-0.736635\pi$
$227$	−20.3942	−1.35361	−0.676804	+	0.736164i	$0.736635\pi$
$228$	−24.5231	−1.62408
$229$	−9.66862	−0.638921	−0.319460	−	0.947600i	$-0.603502\pi$
$229$	−9.66862	−0.638921	−0.319460	+	0.947600i	$0.603502\pi$
$230$	28.7614	1.89647
$231$	6.91065	0.454687
$232$	5.32885	0.349856
$233$	17.6336	1.15521	0.577607	−	0.816315i	$-0.303987\pi$
$233$	17.6336	1.15521	0.577607	+	0.816315i	$0.303987\pi$
$234$	−15.7133	−1.02721
$235$	−38.5822	−2.51683
$236$	−2.94928	−0.191982
$237$	−28.6437	−1.86061
$238$	31.9376	2.07021
$239$	3.61447	0.233801	0.116900	−	0.993144i	$-0.462704\pi$
$239$	3.61447	0.233801	0.116900	+	0.993144i	$0.462704\pi$
$240$	10.7973	0.696963
$241$	−5.38886	−0.347127	−0.173564	−	0.984823i	$-0.555528\pi$
$241$	−5.38886	−0.347127	−0.173564	+	0.984823i	$0.555528\pi$
$242$	−10.7087	−0.688379
$243$	−3.76556	−0.241561
$244$	11.7171	0.750113
$245$	−38.5076	−2.46016
$246$	−2.23328	−0.142389
$247$	−20.4896	−1.30372
$248$	−8.35573	−0.530589
$249$	9.97028	0.631841
$250$	−9.51028	−0.601483
$251$	−25.1584	−1.58798	−0.793992	−	0.607929i	$-0.792001\pi$
$251$	−25.1584	−1.58798	−0.793992	+	0.607929i	$0.792001\pi$
$252$	−26.1717	−1.64866
$253$	−4.36103	−0.274176
$254$	12.3867	0.777211
$255$	−81.6947	−5.11592
$256$	1.00000	0.0625000
$257$	15.5405	0.969389	0.484695	−	0.874683i	$-0.338931\pi$
$257$	15.5405	0.969389	0.484695	+	0.874683i	$0.338931\pi$
$258$	−16.4058	−1.02138
$259$	−11.9578	−0.743022
$260$	9.02143	0.559485
$261$	33.0401	2.04513
$262$	11.8748	0.733629
$263$	−3.64861	−0.224983	−0.112492	−	0.993653i	$-0.535883\pi$
$263$	−3.64861	−0.224983	−0.112492	+	0.993653i	$0.535883\pi$
$264$	−1.63717	−0.100761
$265$	−14.8843	−0.914337
$266$	−34.1271	−2.09247
$267$	30.0732	1.84045
$268$	−0.652017	−0.0398283
$269$	−26.9893	−1.64556	−0.822782	−	0.568357i	$-0.807579\pi$
$269$	−26.9893	−1.64556	−0.822782	+	0.568357i	$0.807579\pi$
$270$	34.5538	2.10288
$271$	−14.8651	−0.902991	−0.451496	−	0.892273i	$-0.649109\pi$
$271$	−14.8651	−0.902991	−0.451496	+	0.892273i	$0.649109\pi$
$272$	−7.56621	−0.458769
$273$	−32.4476	−1.96382
$274$	−20.4929	−1.23802
$275$	4.14079	0.249699
$276$	24.5072	1.47516
$277$	−15.7356	−0.945458	−0.472729	−	0.881208i	$-0.656731\pi$
$277$	−15.7356	−0.945458	−0.472729	+	0.881208i	$0.656731\pi$
$278$	−11.0098	−0.660321
$279$	−51.8074	−3.10163
$280$	15.0259	0.897969
$281$	−28.3852	−1.69332	−0.846660	−	0.532134i	$-0.821390\pi$
$281$	−28.3852	−1.69332	−0.846660	+	0.532134i	$0.821390\pi$
$282$	−32.8753	−1.95770
$283$	−31.9000	−1.89626	−0.948129	−	0.317886i	$-0.897027\pi$
$283$	−31.9000	−1.89626	−0.948129	+	0.317886i	$0.897027\pi$
$284$	6.46973	0.383908
$285$	87.2953	5.17093
$286$	−1.36790	−0.0808856
$287$	−3.10791	−0.183454
$288$	6.20023	0.365352
$289$	40.2476	2.36750
$290$	−18.9692	−1.11391
$291$	−38.4936	−2.25654
$292$	−13.6526	−0.798957
$293$	30.1448	1.76108	0.880538	−	0.473976i	$-0.157182\pi$
$293$	30.1448	1.76108	0.880538	+	0.473976i	$0.157182\pi$
$294$	−32.8117	−1.91362
$295$	10.4986	0.611254
$296$	2.83287	0.164657
$297$	−5.23933	−0.304016
$298$	11.0189	0.638307
$299$	20.4764	1.18418
$300$	−23.2695	−1.34347
$301$	−22.8309	−1.31595
$302$	11.2698	0.648505
$303$	35.5896	2.04457
$304$	8.08491	0.463701
$305$	−41.7098	−2.38829
$306$	−46.9122	−2.68179
$307$	5.46963	0.312168	0.156084	−	0.987744i	$-0.450113\pi$
$307$	5.46963	0.312168	0.156084	+	0.987744i	$0.450113\pi$
$308$	−2.27835	−0.129821
$309$	−46.1195	−2.62365
$310$	29.7441	1.68935
$311$	22.6979	1.28708	0.643541	−	0.765411i	$-0.277464\pi$
$311$	22.6979	1.28708	0.643541	+	0.765411i	$0.277464\pi$
$312$	7.68703	0.435192
$313$	−14.9946	−0.847542	−0.423771	−	0.905769i	$-0.639294\pi$
$313$	−14.9946	−0.847542	−0.423771	+	0.905769i	$0.639294\pi$
$314$	8.35931	0.471743
$315$	93.1640	5.24920
$316$	9.44342	0.531234
$317$	−15.1517	−0.851004	−0.425502	−	0.904957i	$-0.639903\pi$
$317$	−15.1517	−0.851004	−0.425502	+	0.904957i	$0.639903\pi$
$318$	−12.6827	−0.711211
$319$	2.87626	0.161040
$320$	−3.55972	−0.198995
$321$	10.0188	0.559194
$322$	34.1050	1.90060
$323$	−61.1722	−3.40371
$324$	10.8421	0.602341
$325$	−19.4423	−1.07846
$326$	8.38009	0.464130
$327$	−3.28269	−0.181533
$328$	0.736282	0.0406544
$329$	−45.7504	−2.52230
$330$	5.82788	0.320814
$331$	−21.1767	−1.16398	−0.581988	−	0.813198i	$-0.697725\pi$
$331$	−21.1767	−1.16398	−0.581988	+	0.813198i	$0.697725\pi$
$332$	−3.28706	−0.180401
$333$	17.5645	0.962526
$334$	−16.8416	−0.921531
$335$	2.32100	0.126810
$336$	12.8033	0.698480
$337$	−19.0650	−1.03854	−0.519270	−	0.854610i	$-0.673796\pi$
$337$	−19.0650	−1.03854	−0.519270	+	0.854610i	$0.673796\pi$
$338$	−6.57729	−0.357757
$339$	−34.7547	−1.88762
$340$	26.9336	1.46068
$341$	−4.51003	−0.244232
$342$	50.1283	2.71063
$343$	−16.1143	−0.870090
$344$	5.40877	0.291621
$345$	−87.2388	−4.69678
$346$	17.3463	0.932543
$347$	7.60292	0.408146	0.204073	−	0.978956i	$-0.434582\pi$
$347$	7.60292	0.408146	0.204073	+	0.978956i	$0.434582\pi$
$348$	−16.1634	−0.866449
$349$	20.6054	1.10298	0.551490	−	0.834181i	$-0.314059\pi$
$349$	20.6054	1.10298	0.551490	+	0.834181i	$0.314059\pi$
$350$	−32.3826	−1.73092
$351$	24.6002	1.31306
$352$	0.539753	0.0287689
$353$	2.77705	0.147807	0.0739037	−	0.997265i	$-0.476454\pi$
$353$	2.77705	0.147807	0.0739037	+	0.997265i	$0.476454\pi$
$354$	8.94572	0.475460
$355$	−23.0305	−1.22233
$356$	−9.91472	−0.525479
$357$	−96.8728	−5.12705
$358$	−3.22549	−0.170473
$359$	−21.8966	−1.15566	−0.577828	−	0.816159i	$-0.696100\pi$
$359$	−21.8966	−1.15566	−0.577828	+	0.816159i	$0.696100\pi$
$360$	−22.0711	−1.16325
$361$	46.3658	2.44030
$362$	−22.3274	−1.17350
$363$	32.4814	1.70483
$364$	10.6975	0.560703
$365$	48.5994	2.54381
$366$	−35.5403	−1.85772
$367$	21.9008	1.14321	0.571606	−	0.820529i	$-0.306321\pi$
$367$	21.9008	1.14321	0.571606	+	0.820529i	$0.306321\pi$
$368$	−8.07968	−0.421182
$369$	4.56512	0.237650
$370$	−10.0842	−0.524255
$371$	−17.6497	−0.916326
$372$	25.3445	1.31405
$373$	−12.2184	−0.632645	−0.316323	−	0.948652i	$-0.602448\pi$
$373$	−12.2184	−0.632645	−0.316323	+	0.948652i	$0.602448\pi$
$374$	−4.08389	−0.211173
$375$	28.8465	1.48963
$376$	10.8385	0.558955
$377$	−13.5049	−0.695540
$378$	40.9736	2.10746
$379$	0.908152	0.0466486	0.0233243	−	0.999728i	$-0.492575\pi$
$379$	0.908152	0.0466486	0.0233243	+	0.999728i	$0.492575\pi$
$380$	−28.7801	−1.47639
$381$	−37.5712	−1.92483
$382$	2.14688	0.109844
$383$	−24.3990	−1.24673	−0.623365	−	0.781931i	$-0.714235\pi$
$383$	−24.3990	−1.24673	−0.623365	+	0.781931i	$0.714235\pi$
$384$	−3.03319	−0.154787
$385$	8.11028	0.413338
$386$	3.12109	0.158859
$387$	33.5356	1.70471
$388$	12.6908	0.644279
$389$	23.5296	1.19300	0.596498	−	0.802614i	$-0.296558\pi$
$389$	23.5296	1.19300	0.596498	+	0.802614i	$0.296558\pi$
$390$	−27.3637	−1.38561
$391$	61.1326	3.09161
$392$	10.8176	0.546370
$393$	−36.0186	−1.81690
$394$	−13.9592	−0.703255
$395$	−33.6160	−1.69140
$396$	3.34659	0.168173
$397$	8.10906	0.406982	0.203491	−	0.979077i	$-0.434771\pi$
$397$	8.10906	0.406982	0.203491	+	0.979077i	$0.434771\pi$
$398$	19.4235	0.973611
$399$	103.514	5.18218
$400$	7.67163	0.383582
$401$	−21.3491	−1.06612	−0.533061	−	0.846077i	$-0.678958\pi$
$401$	−21.3491	−1.06612	−0.533061	+	0.846077i	$0.678958\pi$
$402$	1.97769	0.0986382
$403$	21.1760	1.05485
$404$	−11.7334	−0.583759
$405$	−38.5950	−1.91780
$406$	−22.4935	−1.11634
$407$	1.52905	0.0757923
$408$	22.9497	1.13618
$409$	14.4921	0.716586	0.358293	−	0.933609i	$-0.383359\pi$
$409$	14.4921	0.716586	0.358293	+	0.933609i	$0.383359\pi$
$410$	−2.62096	−0.129440
$411$	62.1587	3.06606
$412$	15.2050	0.749095
$413$	12.4492	0.612583
$414$	−50.0959	−2.46208
$415$	11.7010	0.574382
$416$	−2.53431	−0.124255
$417$	33.3946	1.63534
$418$	4.36386	0.213443
$419$	22.3852	1.09359	0.546795	−	0.837266i	$-0.315848\pi$
$419$	22.3852	1.09359	0.546795	+	0.837266i	$0.315848\pi$
$420$	−45.5764	−2.22390
$421$	20.5334	1.00073	0.500367	−	0.865813i	$-0.333198\pi$
$421$	20.5334	1.00073	0.500367	+	0.865813i	$0.333198\pi$
$422$	−5.94554	−0.289424
$423$	67.2014	3.26744
$424$	4.18131	0.203063
$425$	−58.0452	−2.81561
$426$	−19.6239	−0.950781
$427$	−49.4590	−2.39349
$428$	−3.30305	−0.159659
$429$	4.14910	0.200320
$430$	−19.2537	−0.928496
$431$	−20.7962	−1.00172	−0.500860	−	0.865528i	$-0.666983\pi$
$431$	−20.7962	−1.00172	−0.500860	+	0.865528i	$0.666983\pi$
$432$	−9.70689	−0.467023
$433$	−21.9824	−1.05641	−0.528203	−	0.849118i	$-0.677134\pi$
$433$	−21.9824	−1.05641	−0.528203	+	0.849118i	$0.677134\pi$
$434$	35.2703	1.69303
$435$	57.5372	2.75870
$436$	1.08226	0.0518308
$437$	−65.3235	−3.12485
$438$	41.4108	1.97869
$439$	32.2123	1.53741	0.768706	−	0.639603i	$-0.220901\pi$
$439$	32.2123	1.53741	0.768706	+	0.639603i	$0.220901\pi$
$440$	−1.92137	−0.0915979
$441$	67.0714	3.19388
$442$	19.1751	0.912067
$443$	32.4274	1.54067	0.770336	−	0.637639i	$-0.220089\pi$
$443$	32.4274	1.54067	0.770336	+	0.637639i	$0.220089\pi$
$444$	−8.59263	−0.407788
$445$	35.2937	1.67308
$446$	12.4346	0.588796
$447$	−33.4224	−1.58082
$448$	−4.22109	−0.199428
$449$	32.9473	1.55488	0.777440	−	0.628957i	$-0.216518\pi$
$449$	32.9473	1.55488	0.777440	+	0.628957i	$0.216518\pi$
$450$	47.5659	2.24228
$451$	0.397411	0.0187133
$452$	11.4581	0.538946
$453$	−34.1835	−1.60608
$454$	−20.3942	−0.957145
$455$	−38.0802	−1.78523
$456$	−24.5231	−1.14840
$457$	−32.8041	−1.53451	−0.767255	−	0.641343i	$-0.778378\pi$
$457$	−32.8041	−1.53451	−0.767255	+	0.641343i	$0.778378\pi$
$458$	−9.66862	−0.451785
$459$	73.4444	3.42809
$460$	28.7614	1.34101
$461$	−14.4291	−0.672029	−0.336014	−	0.941857i	$-0.609079\pi$
$461$	−14.4291	−0.672029	−0.336014	+	0.941857i	$0.609079\pi$
$462$	6.91065	0.321512
$463$	25.2189	1.17202	0.586011	−	0.810303i	$-0.300697\pi$
$463$	25.2189	1.17202	0.586011	+	0.810303i	$0.300697\pi$
$464$	5.32885	0.247386
$465$	−90.2194	−4.18382
$466$	17.6336	0.816860
$467$	4.84703	0.224294	0.112147	−	0.993692i	$-0.464227\pi$
$467$	4.84703	0.224294	0.112147	+	0.993692i	$0.464227\pi$
$468$	−15.7133	−0.726346
$469$	2.75222	0.127086
$470$	−38.5822	−1.77966
$471$	−25.3554	−1.16831
$472$	−2.94928	−0.135752
$473$	2.91940	0.134234
$474$	−28.6437	−1.31565
$475$	62.0245	2.84588
$476$	31.9376	1.46386
$477$	25.9251	1.18703
$478$	3.61447	0.165322
$479$	−1.02461	−0.0468158	−0.0234079	−	0.999726i	$-0.507452\pi$
$479$	−1.02461	−0.0468158	−0.0234079	+	0.999726i	$0.507452\pi$
$480$	10.7973	0.492828
$481$	−7.17937	−0.327351
$482$	−5.38886	−0.245456
$483$	−103.447	−4.70700
$484$	−10.7087	−0.486758
$485$	−45.1758	−2.05133
$486$	−3.76556	−0.170809
$487$	−2.65034	−0.120098	−0.0600491	−	0.998195i	$-0.519126\pi$
$487$	−2.65034	−0.120098	−0.0600491	+	0.998195i	$0.519126\pi$
$488$	11.7171	0.530410
$489$	−25.4184	−1.14946
$490$	−38.5076	−1.73959
$491$	−30.7111	−1.38597	−0.692987	−	0.720951i	$-0.743705\pi$
$491$	−30.7111	−1.38597	−0.692987	+	0.720951i	$0.743705\pi$
$492$	−2.23328	−0.100684
$493$	−40.3192	−1.81589
$494$	−20.4896	−0.921873
$495$	−11.9129	−0.535447
$496$	−8.35573	−0.375183
$497$	−27.3093	−1.22499
$498$	9.97028	0.446779
$499$	9.11311	0.407959	0.203979	−	0.978975i	$-0.434612\pi$
$499$	9.11311	0.407959	0.203979	+	0.978975i	$0.434612\pi$
$500$	−9.51028	−0.425313
$501$	51.0837	2.28225
$502$	−25.1584	−1.12287
$503$	−6.56059	−0.292522	−0.146261	−	0.989246i	$-0.546724\pi$
$503$	−6.56059	−0.292522	−0.146261	+	0.989246i	$0.546724\pi$
$504$	−26.1717	−1.16578
$505$	41.7677	1.85864
$506$	−4.36103	−0.193872
$507$	19.9502	0.886018
$508$	12.3867	0.549571
$509$	7.46040	0.330676	0.165338	−	0.986237i	$-0.447128\pi$
$509$	7.46040	0.330676	0.165338	+	0.986237i	$0.447128\pi$
$510$	−81.6947	−3.61750
$511$	57.6287	2.54934
$512$	1.00000	0.0441942
$513$	−78.4793	−3.46495
$514$	15.5405	0.685462
$515$	−54.1255	−2.38506
$516$	−16.4058	−0.722225
$517$	5.85014	0.257289
$518$	−11.9578	−0.525396
$519$	−52.6146	−2.30953
$520$	9.02143	0.395616
$521$	3.74531	0.164085	0.0820425	−	0.996629i	$-0.473856\pi$
$521$	3.74531	0.164085	0.0820425	+	0.996629i	$0.473856\pi$
$522$	33.0401	1.44612
$523$	−10.0070	−0.437574	−0.218787	−	0.975773i	$-0.570210\pi$
$523$	−10.0070	−0.437574	−0.218787	+	0.975773i	$0.570210\pi$
$524$	11.8748	0.518754
$525$	98.2226	4.28679
$526$	−3.64861	−0.159087
$527$	63.2212	2.75396
$528$	−1.63717	−0.0712488
$529$	42.2812	1.83831
$530$	−14.8843	−0.646534
$531$	−18.2862	−0.793554
$532$	−34.1271	−1.47960
$533$	−1.86596	−0.0808239
$534$	30.0732	1.30139
$535$	11.7580	0.508341
$536$	−0.652017	−0.0281628
$537$	9.78353	0.422190
$538$	−26.9893	−1.16359
$539$	5.83882	0.251496
$540$	34.5538	1.48696
$541$	−7.73688	−0.332634	−0.166317	−	0.986072i	$-0.553188\pi$
$541$	−7.73688	−0.332634	−0.166317	+	0.986072i	$0.553188\pi$
$542$	−14.8651	−0.638511
$543$	67.7231	2.90628
$544$	−7.56621	−0.324399
$545$	−3.85254	−0.165025
$546$	−32.4476	−1.38863
$547$	9.64163	0.412246	0.206123	−	0.978526i	$-0.433915\pi$
$547$	9.64163	0.412246	0.206123	+	0.978526i	$0.433915\pi$
$548$	−20.4929	−0.875411
$549$	72.6489	3.10058
$550$	4.14079	0.176564
$551$	43.0833	1.83541
$552$	24.5072	1.04310
$553$	−39.8615	−1.69508
$554$	−15.7356	−0.668540
$555$	30.5874	1.29836
$556$	−11.0098	−0.466918
$557$	−13.5265	−0.573135	−0.286568	−	0.958060i	$-0.592514\pi$
$557$	−13.5265	−0.573135	−0.286568	+	0.958060i	$0.592514\pi$
$558$	−51.8074	−2.19318
$559$	−13.7075	−0.579764
$560$	15.0259	0.634960
$561$	12.3872	0.522988
$562$	−28.3852	−1.19736
$563$	43.2512	1.82282	0.911410	−	0.411500i	$-0.134995\pi$
$563$	43.2512	1.82282	0.911410	+	0.411500i	$0.134995\pi$
$564$	−32.8753	−1.38430
$565$	−40.7878	−1.71596
$566$	−31.9000	−1.34086
$567$	−45.7656	−1.92197
$568$	6.46973	0.271464
$569$	13.0064	0.545256	0.272628	−	0.962120i	$-0.412107\pi$
$569$	13.0064	0.545256	0.272628	+	0.962120i	$0.412107\pi$
$570$	87.2953	3.65640
$571$	−13.2514	−0.554552	−0.277276	−	0.960790i	$-0.589432\pi$
$571$	−13.2514	−0.554552	−0.277276	+	0.960790i	$0.589432\pi$
$572$	−1.36790	−0.0571948
$573$	−6.51188	−0.272038
$574$	−3.10791	−0.129722
$575$	−61.9843	−2.58493
$576$	6.20023	0.258343
$577$	−32.4321	−1.35016	−0.675082	−	0.737742i	$-0.735892\pi$
$577$	−32.4321	−1.35016	−0.675082	+	0.737742i	$0.735892\pi$
$578$	40.2476	1.67408
$579$	−9.46686	−0.393429
$580$	−18.9692	−0.787654
$581$	13.8750	0.575631
$582$	−38.4936	−1.59561
$583$	2.25688	0.0934703
$584$	−13.6526	−0.564948
$585$	55.9349	2.31262
$586$	30.1448	1.24527
$587$	4.68966	0.193563	0.0967814	−	0.995306i	$-0.469145\pi$
$587$	4.68966	0.193563	0.0967814	+	0.995306i	$0.469145\pi$
$588$	−32.8117	−1.35313
$589$	−67.5553	−2.78357
$590$	10.4986	0.432221
$591$	42.3409	1.74167
$592$	2.83287	0.116430
$593$	5.61726	0.230673	0.115337	−	0.993326i	$-0.463205\pi$
$593$	5.61726	0.230673	0.115337	+	0.993326i	$0.463205\pi$
$594$	−5.23933	−0.214972
$595$	−113.689	−4.66080
$596$	11.0189	0.451352
$597$	−58.9151	−2.41123
$598$	20.4764	0.837342
$599$	−7.25280	−0.296341	−0.148171	−	0.988962i	$-0.547339\pi$
$599$	−7.25280	−0.296341	−0.148171	+	0.988962i	$0.547339\pi$
$600$	−23.2695	−0.949974
$601$	−2.00906	−0.0819514	−0.0409757	−	0.999160i	$-0.513047\pi$
$601$	−2.00906	−0.0819514	−0.0409757	+	0.999160i	$0.513047\pi$
$602$	−22.8309	−0.930517
$603$	−4.04265	−0.164630
$604$	11.2698	0.458562
$605$	38.1199	1.54979
$606$	35.5896	1.44573
$607$	35.9967	1.46106	0.730531	−	0.682879i	$-0.239272\pi$
$607$	35.9967	1.46106	0.730531	+	0.682879i	$0.239272\pi$
$608$	8.08491	0.327886
$609$	68.2271	2.76470
$610$	−41.7098	−1.68878
$611$	−27.4682	−1.11124
$612$	−46.9122	−1.89631
$613$	7.19977	0.290796	0.145398	−	0.989373i	$-0.453554\pi$
$613$	7.19977	0.290796	0.145398	+	0.989373i	$0.453554\pi$
$614$	5.46963	0.220736
$615$	7.94987	0.320570
$616$	−2.27835	−0.0917971
$617$	5.55936	0.223811	0.111906	−	0.993719i	$-0.464305\pi$
$617$	5.55936	0.223811	0.111906	+	0.993719i	$0.464305\pi$
$618$	−46.1195	−1.85520
$619$	18.6869	0.751088	0.375544	−	0.926804i	$-0.377456\pi$
$619$	18.6869	0.751088	0.375544	+	0.926804i	$0.377456\pi$
$620$	29.7441	1.19455
$621$	78.4286	3.14723
$622$	22.6979	0.910105
$623$	41.8509	1.67672
$624$	7.68703	0.307727
$625$	−4.50420	−0.180168
$626$	−14.9946	−0.599303
$627$	−13.2364	−0.528611
$628$	8.35931	0.333573
$629$	−21.4341	−0.854634
$630$	93.1640	3.71174
$631$	42.8040	1.70400	0.852000	−	0.523541i	$-0.175389\pi$
$631$	42.8040	1.70400	0.852000	+	0.523541i	$0.175389\pi$
$632$	9.44342	0.375639
$633$	18.0339	0.716784
$634$	−15.1517	−0.601751
$635$	−44.0932	−1.74979
$636$	−12.6827	−0.502902
$637$	−27.4150	−1.08622
$638$	2.87626	0.113872
$639$	40.1138	1.58688
$640$	−3.55972	−0.140710
$641$	23.7728	0.938969	0.469484	−	0.882941i	$-0.344440\pi$
$641$	23.7728	0.938969	0.469484	+	0.882941i	$0.344440\pi$
$642$	10.0188	0.395410
$643$	−1.50015	−0.0591601	−0.0295800	−	0.999562i	$-0.509417\pi$
$643$	−1.50015	−0.0591601	−0.0295800	+	0.999562i	$0.509417\pi$
$644$	34.1050	1.34393
$645$	58.4001	2.29950
$646$	−61.1722	−2.40679
$647$	−15.9643	−0.627623	−0.313811	−	0.949485i	$-0.601606\pi$
$647$	−15.9643	−0.627623	−0.313811	+	0.949485i	$0.601606\pi$
$648$	10.8421	0.425919
$649$	−1.59188	−0.0624869
$650$	−19.4423	−0.762589
$651$	−106.981	−4.19293
$652$	8.38009	0.328190
$653$	−5.55533	−0.217397	−0.108698	−	0.994075i	$-0.534668\pi$
$653$	−5.55533	−0.217397	−0.108698	+	0.994075i	$0.534668\pi$
$654$	−3.28269	−0.128363
$655$	−42.2711	−1.65167
$656$	0.736282	0.0287470
$657$	−84.6491	−3.30248
$658$	−45.7504	−1.78354
$659$	−34.2032	−1.33237	−0.666184	−	0.745787i	$-0.732074\pi$
$659$	−34.2032	−1.33237	−0.666184	+	0.745787i	$0.732074\pi$
$660$	5.82788	0.226850
$661$	−40.7184	−1.58376	−0.791880	−	0.610676i	$-0.790898\pi$
$661$	−40.7184	−1.58376	−0.791880	+	0.610676i	$0.790898\pi$
$662$	−21.1767	−0.823055
$663$	−58.1617	−2.25881
$664$	−3.28706	−0.127563
$665$	121.483	4.71091
$666$	17.5645	0.680609
$667$	−43.0554	−1.66711
$668$	−16.8416	−0.651621
$669$	−37.7165	−1.45820
$670$	2.32100	0.0896681
$671$	6.32436	0.244149
$672$	12.8033	0.493900
$673$	−16.4992	−0.635996	−0.317998	−	0.948091i	$-0.603011\pi$
$673$	−16.4992	−0.635996	−0.317998	+	0.948091i	$0.603011\pi$
$674$	−19.0650	−0.734358
$675$	−74.4677	−2.86626
$676$	−6.57729	−0.252973
$677$	−26.5630	−1.02090	−0.510449	−	0.859908i	$-0.670521\pi$
$677$	−26.5630	−1.02090	−0.510449	+	0.859908i	$0.670521\pi$
$678$	−34.7547	−1.33475
$679$	−53.5690	−2.05579
$680$	26.9336	1.03286
$681$	61.8593	2.37045
$682$	−4.51003	−0.172698
$683$	22.5665	0.863484	0.431742	−	0.901997i	$-0.357899\pi$
$683$	22.5665	0.863484	0.431742	+	0.901997i	$0.357899\pi$
$684$	50.1283	1.91670
$685$	72.9489	2.78723
$686$	−16.1143	−0.615247
$687$	29.3267	1.11889
$688$	5.40877	0.206207
$689$	−10.5967	−0.403703
$690$	−87.2388	−3.32112
$691$	14.5618	0.553956	0.276978	−	0.960876i	$-0.410667\pi$
$691$	14.5618	0.553956	0.276978	+	0.960876i	$0.410667\pi$
$692$	17.3463	0.659408
$693$	−14.1263	−0.536612
$694$	7.60292	0.288603
$695$	39.1917	1.48663
$696$	−16.1634	−0.612672
$697$	−5.57087	−0.211012
$698$	20.6054	0.779925
$699$	−53.4860	−2.02302
$700$	−32.3826	−1.22395
$701$	−41.4929	−1.56717	−0.783583	−	0.621287i	$-0.786610\pi$
$701$	−41.4929	−1.56717	−0.783583	+	0.621287i	$0.786610\pi$
$702$	24.6002	0.928476
$703$	22.9035	0.863823
$704$	0.539753	0.0203427
$705$	117.027	4.40749
$706$	2.77705	0.104516
$707$	49.5277	1.86268
$708$	8.94572	0.336201
$709$	42.3149	1.58917	0.794584	−	0.607154i	$-0.207689\pi$
$709$	42.3149	1.58917	0.794584	+	0.607154i	$0.207689\pi$
$710$	−23.0305	−0.864317
$711$	58.5514	2.19585
$712$	−9.91472	−0.371570
$713$	67.5116	2.52833
$714$	−96.8728	−3.62538
$715$	4.86935	0.182103
$716$	−3.22549	−0.120542
$717$	−10.9634	−0.409434
$718$	−21.8966	−0.817172
$719$	2.71602	0.101290	0.0506452	−	0.998717i	$-0.483872\pi$
$719$	2.71602	0.101290	0.0506452	+	0.998717i	$0.483872\pi$
$720$	−22.0711	−0.822541
$721$	−64.1815	−2.39024
$722$	46.3658	1.72556
$723$	16.3454	0.607893
$724$	−22.3274	−0.829791
$725$	40.8810	1.51828
$726$	32.4814	1.20550
$727$	39.8319	1.47728	0.738642	−	0.674097i	$-0.235467\pi$
$727$	39.8319	1.47728	0.738642	+	0.674097i	$0.235467\pi$
$728$	10.6975	0.396477
$729$	−21.1048	−0.781657
$730$	48.5994	1.79875
$731$	−40.9239	−1.51362
$732$	−35.5403	−1.31361
$733$	−21.4927	−0.793850	−0.396925	−	0.917851i	$-0.629923\pi$
$733$	−21.4927	−0.793850	−0.396925	+	0.917851i	$0.629923\pi$
$734$	21.9008	0.808372
$735$	116.801	4.30826
$736$	−8.07968	−0.297821
$737$	−0.351928	−0.0129634
$738$	4.56512	0.168044
$739$	−2.02398	−0.0744533	−0.0372266	−	0.999307i	$-0.511852\pi$
$739$	−2.02398	−0.0744533	−0.0372266	+	0.999307i	$0.511852\pi$
$740$	−10.0842	−0.370704
$741$	62.1489	2.28310
$742$	−17.6497	−0.647940
$743$	−16.5245	−0.606227	−0.303113	−	0.952955i	$-0.598026\pi$
$743$	−16.5245	−0.606227	−0.303113	+	0.952955i	$0.598026\pi$
$744$	25.3445	0.929174
$745$	−39.2242	−1.43706
$746$	−12.2184	−0.447348
$747$	−20.3805	−0.745685
$748$	−4.08389	−0.149322
$749$	13.9425	0.509447
$750$	28.8465	1.05332
$751$	−13.2289	−0.482729	−0.241365	−	0.970435i	$-0.577595\pi$
$751$	−13.2289	−0.482729	−0.241365	+	0.970435i	$0.577595\pi$
$752$	10.8385	0.395241
$753$	76.3101	2.78089
$754$	−13.5049	−0.491821
$755$	−40.1174	−1.46002
$756$	40.9736	1.49020
$757$	−20.0853	−0.730012	−0.365006	−	0.931005i	$-0.618933\pi$
$757$	−20.0853	−0.730012	−0.365006	+	0.931005i	$0.618933\pi$
$758$	0.908152	0.0329856
$759$	13.2278	0.480140
$760$	−28.7801	−1.04396
$761$	−21.7953	−0.790078	−0.395039	−	0.918664i	$-0.629269\pi$
$761$	−21.7953	−0.790078	−0.395039	+	0.918664i	$0.629269\pi$
$762$	−37.5712	−1.36106
$763$	−4.56830	−0.165384
$764$	2.14688	0.0776713
$765$	166.995	6.03770
$766$	−24.3990	−0.881572
$767$	7.47438	0.269884
$768$	−3.03319	−0.109451
$769$	35.0444	1.26373	0.631867	−	0.775077i	$-0.282289\pi$
$769$	35.0444	1.26373	0.631867	+	0.775077i	$0.282289\pi$
$770$	8.11028	0.292274
$771$	−47.1372	−1.69761
$772$	3.12109	0.112331
$773$	21.7085	0.780800	0.390400	−	0.920645i	$-0.372337\pi$
$773$	21.7085	0.780800	0.390400	+	0.920645i	$0.372337\pi$
$774$	33.5356	1.20541
$775$	−64.1021	−2.30262
$776$	12.6908	0.455574
$777$	36.2703	1.30119
$778$	23.5296	0.843576
$779$	5.95278	0.213280
$780$	−27.3637	−0.979777
$781$	3.49206	0.124956
$782$	61.1326	2.18610
$783$	−51.7265	−1.84856
$784$	10.8176	0.386342
$785$	−29.7568	−1.06207
$786$	−36.0186	−1.28474
$787$	3.34765	0.119331	0.0596655	−	0.998218i	$-0.480997\pi$
$787$	3.34765	0.119331	0.0596655	+	0.998218i	$0.480997\pi$
$788$	−13.9592	−0.497276
$789$	11.0669	0.393993
$790$	−33.6160	−1.19600
$791$	−48.3658	−1.71969
$792$	3.34659	0.118916
$793$	−29.6948	−1.05449
$794$	8.10906	0.287780
$795$	45.1469	1.60120
$796$	19.4235	0.688447
$797$	37.3341	1.32244	0.661222	−	0.750191i	$-0.270038\pi$
$797$	37.3341	1.32244	0.661222	+	0.750191i	$0.270038\pi$
$798$	103.514	3.66435
$799$	−82.0067	−2.90119
$800$	7.67163	0.271233
$801$	−61.4735	−2.17206
$802$	−21.3491	−0.753862
$803$	−7.36903	−0.260047
$804$	1.97769	0.0697477
$805$	−121.404	−4.27895
$806$	21.1760	0.745892
$807$	81.8635	2.88173
$808$	−11.7334	−0.412780
$809$	−25.1471	−0.884127	−0.442063	−	0.896984i	$-0.645753\pi$
$809$	−25.1471	−0.884127	−0.442063	+	0.896984i	$0.645753\pi$
$810$	−38.5950	−1.35609
$811$	−33.3245	−1.17018	−0.585091	−	0.810967i	$-0.698941\pi$
$811$	−33.3245	−1.17018	−0.585091	+	0.810967i	$0.698941\pi$
$812$	−22.4935	−0.789368
$813$	45.0887	1.58133
$814$	1.52905	0.0535933
$815$	−29.8308	−1.04493
$816$	22.9497	0.803402
$817$	43.7294	1.52990
$818$	14.4921	0.506703
$819$	66.3271	2.31766
$820$	−2.62096	−0.0915279
$821$	40.8658	1.42623	0.713113	−	0.701050i	$-0.247285\pi$
$821$	40.8658	1.42623	0.713113	+	0.701050i	$0.247285\pi$
$822$	62.1587	2.16803
$823$	12.1096	0.422116	0.211058	−	0.977474i	$-0.432309\pi$
$823$	12.1096	0.422116	0.211058	+	0.977474i	$0.432309\pi$
$824$	15.2050	0.529690
$825$	−12.5598	−0.437276
$826$	12.4492	0.433162
$827$	16.7267	0.581644	0.290822	−	0.956777i	$-0.406071\pi$
$827$	16.7267	0.581644	0.290822	+	0.956777i	$0.406071\pi$
$828$	−50.0959	−1.74095
$829$	−28.6371	−0.994607	−0.497304	−	0.867577i	$-0.665676\pi$
$829$	−28.6371	−0.994607	−0.497304	+	0.867577i	$0.665676\pi$
$830$	11.7010	0.406149
$831$	47.7289	1.65570
$832$	−2.53431	−0.0878613
$833$	−81.8480	−2.83587
$834$	33.3946	1.15636
$835$	59.9514	2.07470
$836$	4.36386	0.150927
$837$	81.1081	2.80351
$838$	22.3852	0.773285
$839$	22.8471	0.788771	0.394386	−	0.918945i	$-0.370957\pi$
$839$	22.8471	0.788771	0.394386	+	0.918945i	$0.370957\pi$
$840$	−45.5764	−1.57253
$841$	−0.603370	−0.0208059
$842$	20.5334	0.707626
$843$	86.0977	2.96536
$844$	−5.94554	−0.204654
$845$	23.4133	0.805443
$846$	67.2014	2.31043
$847$	45.2022	1.55317
$848$	4.18131	0.143587
$849$	96.7587	3.32075
$850$	−58.0452	−1.99093
$851$	−22.8887	−0.784615
$852$	−19.6239	−0.672304
$853$	14.9950	0.513418	0.256709	−	0.966489i	$-0.417362\pi$
$853$	14.9950	0.513418	0.256709	+	0.966489i	$0.417362\pi$
$854$	−49.4590	−1.69245
$855$	−178.443	−6.10262
$856$	−3.30305	−0.112896
$857$	−20.8521	−0.712295	−0.356147	−	0.934430i	$-0.615910\pi$
$857$	−20.8521	−0.712295	−0.356147	+	0.934430i	$0.615910\pi$
$858$	4.14910	0.141648
$859$	38.5565	1.31553	0.657766	−	0.753223i	$-0.271502\pi$
$859$	38.5565	1.31553	0.657766	+	0.753223i	$0.271502\pi$
$860$	−19.2537	−0.656546
$861$	9.42688	0.321267
$862$	−20.7962	−0.708323
$863$	34.8459	1.18617	0.593084	−	0.805141i	$-0.297910\pi$
$863$	34.8459	1.18617	0.593084	+	0.805141i	$0.297910\pi$
$864$	−9.70689	−0.330235
$865$	−61.7481	−2.09950
$866$	−21.9824	−0.746992
$867$	−122.078	−4.14600
$868$	35.2703	1.19715
$869$	5.09712	0.172908
$870$	57.5372	1.95069
$871$	1.65241	0.0559898
$872$	1.08226	0.0366499
$873$	78.6860	2.66312
$874$	−65.3235	−2.20960
$875$	40.1437	1.35711
$876$	41.4108	1.39914
$877$	6.48816	0.219090	0.109545	−	0.993982i	$-0.465061\pi$
$877$	6.48816	0.219090	0.109545	+	0.993982i	$0.465061\pi$
$878$	32.2123	1.08711
$879$	−91.4347	−3.08402
$880$	−1.92137	−0.0647695
$881$	27.8005	0.936624	0.468312	−	0.883563i	$-0.344862\pi$
$881$	27.8005	0.936624	0.468312	+	0.883563i	$0.344862\pi$
$882$	67.0714	2.25841
$883$	12.4166	0.417851	0.208925	−	0.977932i	$-0.433003\pi$
$883$	12.4166	0.417851	0.208925	+	0.977932i	$0.433003\pi$
$884$	19.1751	0.644928
$885$	−31.8443	−1.07043
$886$	32.4274	1.08942
$887$	−24.4194	−0.819923	−0.409962	−	0.912103i	$-0.634458\pi$
$887$	−24.4194	−0.819923	−0.409962	+	0.912103i	$0.634458\pi$
$888$	−8.59263	−0.288350
$889$	−52.2853	−1.75359
$890$	35.2937	1.18305
$891$	5.85208	0.196052
$892$	12.4346	0.416342
$893$	87.6286	2.93238
$894$	−33.4224	−1.11781
$895$	11.4819	0.383797
$896$	−4.22109	−0.141017
$897$	−62.1087	−2.07375
$898$	32.9473	1.09947
$899$	−44.5264	−1.48504
$900$	47.5659	1.58553
$901$	−31.6367	−1.05397
$902$	0.397411	0.0132323
$903$	69.2503	2.30451
$904$	11.4581	0.381092
$905$	79.4793	2.64198
$906$	−34.1835	−1.13567
$907$	16.0534	0.533045	0.266522	−	0.963829i	$-0.414125\pi$
$907$	16.0534	0.533045	0.266522	+	0.963829i	$0.414125\pi$
$908$	−20.3942	−0.676804
$909$	−72.7498	−2.41296
$910$	−38.0802	−1.26235
$911$	47.8056	1.58387	0.791935	−	0.610606i	$-0.209074\pi$
$911$	47.8056	1.58387	0.791935	+	0.610606i	$0.209074\pi$
$912$	−24.5231	−0.812039
$913$	−1.77420	−0.0587176
$914$	−32.8041	−1.08506
$915$	126.514	4.18241
$916$	−9.66862	−0.319460
$917$	−50.1246	−1.65526
$918$	73.4444	2.42403
$919$	13.5636	0.447421	0.223710	−	0.974656i	$-0.428183\pi$
$919$	13.5636	0.447421	0.223710	+	0.974656i	$0.428183\pi$
$920$	28.7614	0.948236
$921$	−16.5904	−0.546672
$922$	−14.4291	−0.475196
$923$	−16.3963	−0.539690
$924$	6.91065	0.227344
$925$	21.7328	0.714569
$926$	25.2189	0.828745
$927$	94.2743	3.09637
$928$	5.32885	0.174928
$929$	−2.98388	−0.0978981	−0.0489490	−	0.998801i	$-0.515587\pi$
$929$	−2.98388	−0.0978981	−0.0489490	+	0.998801i	$0.515587\pi$
$930$	−90.2194	−2.95841
$931$	87.4591	2.86636
$932$	17.6336	0.577607
$933$	−68.8471	−2.25395
$934$	4.84703	0.158600
$935$	14.5375	0.475428
$936$	−15.7133	−0.513604
$937$	17.6311	0.575983	0.287992	−	0.957633i	$-0.407012\pi$
$937$	17.6311	0.575983	0.287992	+	0.957633i	$0.407012\pi$
$938$	2.75222	0.0898632
$939$	45.4813	1.48423
$940$	−38.5822	−1.25841
$941$	37.9482	1.23707	0.618537	−	0.785755i	$-0.287726\pi$
$941$	37.9482	1.23707	0.618537	+	0.785755i	$0.287726\pi$
$942$	−25.3554	−0.826122
$943$	−5.94892	−0.193724
$944$	−2.94928	−0.0959909
$945$	−145.855	−4.74466
$946$	2.91940	0.0949178
$947$	−23.1013	−0.750692	−0.375346	−	0.926885i	$-0.622476\pi$
$947$	−23.1013	−0.750692	−0.375346	+	0.926885i	$0.622476\pi$
$948$	−28.6437	−0.930303
$949$	34.5998	1.12316
$950$	62.0245	2.01234
$951$	45.9580	1.49029
$952$	31.9376	1.03510
$953$	1.09712	0.0355392	0.0177696	−	0.999842i	$-0.494343\pi$
$953$	1.09712	0.0355392	0.0177696	+	0.999842i	$0.494343\pi$
$954$	25.9251	0.839356
$955$	−7.64229	−0.247299
$956$	3.61447	0.116900
$957$	−8.72425	−0.282015
$958$	−1.02461	−0.0331038
$959$	86.5021	2.79330
$960$	10.7973	0.348482
$961$	38.8182	1.25220
$962$	−7.17937	−0.231472
$963$	−20.4797	−0.659949
$964$	−5.38886	−0.173564
$965$	−11.1102	−0.357651
$966$	−103.447	−3.32835
$967$	−48.7805	−1.56868	−0.784338	−	0.620334i	$-0.786997\pi$
$967$	−48.7805	−1.56868	−0.784338	+	0.620334i	$0.786997\pi$
$968$	−10.7087	−0.344190
$969$	185.547	5.96062
$970$	−45.1758	−1.45051
$971$	39.5940	1.27063	0.635316	−	0.772252i	$-0.280870\pi$
$971$	39.5940	1.27063	0.635316	+	0.772252i	$0.280870\pi$
$972$	−3.76556	−0.120780
$973$	46.4731	1.48986
$974$	−2.65034	−0.0849223
$975$	58.9721	1.88862
$976$	11.7171	0.375056
$977$	−19.8300	−0.634419	−0.317209	−	0.948356i	$-0.602746\pi$
$977$	−19.8300	−0.634419	−0.317209	+	0.948356i	$0.602746\pi$
$978$	−25.4184	−0.812790
$979$	−5.35150	−0.171035
$980$	−38.5076	−1.23008
$981$	6.71024	0.214242
$982$	−30.7111	−0.980031
$983$	−39.0525	−1.24558	−0.622791	−	0.782388i	$-0.714001\pi$
$983$	−39.0525	−1.24558	−0.622791	+	0.782388i	$0.714001\pi$
$984$	−2.23328	−0.0711944
$985$	49.6909	1.58328
$986$	−40.3192	−1.28402
$987$	138.770	4.41708
$988$	−20.4896	−0.651862
$989$	−43.7011	−1.38961
$990$	−11.9129	−0.378618
$991$	37.2256	1.18251	0.591255	−	0.806485i	$-0.298633\pi$
$991$	37.2256	1.18251	0.591255	+	0.806485i	$0.298633\pi$
$992$	−8.35573	−0.265295
$993$	64.2328	2.03837
$994$	−27.3093	−0.866198
$995$	−69.1422	−2.19196
$996$	9.97028	0.315921
$997$	1.98664	0.0629175	0.0314588	−	0.999505i	$-0.489985\pi$
$997$	1.98664	0.0629175	0.0314588	+	0.999505i	$0.489985\pi$
$998$	9.11311	0.288470
$999$	−27.4984	−0.870010

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.6	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.6	✓	69	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.03319 q^{3} +1.00000 q^{4} -3.55972 q^{5} -3.03319 q^{6} -4.22109 q^{7} +1.00000 q^{8} +6.20023 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.03319 q^{3} +1.00000 q^{4} -3.55972 q^{5} -3.03319 q^{6} -4.22109 q^{7} +1.00000 q^{8} +6.20023 q^{9} -3.55972 q^{10} +0.539753 q^{11} -3.03319 q^{12} -2.53431 q^{13} -4.22109 q^{14} +10.7973 q^{15} +1.00000 q^{16} -7.56621 q^{17} +6.20023 q^{18} +8.08491 q^{19} -3.55972 q^{20} +12.8033 q^{21} +0.539753 q^{22} -8.07968 q^{23} -3.03319 q^{24} +7.67163 q^{25} -2.53431 q^{26} -9.70689 q^{27} -4.22109 q^{28} +5.32885 q^{29} +10.7973 q^{30} -8.35573 q^{31} +1.00000 q^{32} -1.63717 q^{33} -7.56621 q^{34} +15.0259 q^{35} +6.20023 q^{36} +2.83287 q^{37} +8.08491 q^{38} +7.68703 q^{39} -3.55972 q^{40} +0.736282 q^{41} +12.8033 q^{42} +5.40877 q^{43} +0.539753 q^{44} -22.0711 q^{45} -8.07968 q^{46} +10.8385 q^{47} -3.03319 q^{48} +10.8176 q^{49} +7.67163 q^{50} +22.9497 q^{51} -2.53431 q^{52} +4.18131 q^{53} -9.70689 q^{54} -1.92137 q^{55} -4.22109 q^{56} -24.5231 q^{57} +5.32885 q^{58} -2.94928 q^{59} +10.7973 q^{60} +11.7171 q^{61} -8.35573 q^{62} -26.1717 q^{63} +1.00000 q^{64} +9.02143 q^{65} -1.63717 q^{66} -0.652017 q^{67} -7.56621 q^{68} +24.5072 q^{69} +15.0259 q^{70} +6.46973 q^{71} +6.20023 q^{72} -13.6526 q^{73} +2.83287 q^{74} -23.2695 q^{75} +8.08491 q^{76} -2.27835 q^{77} +7.68703 q^{78} +9.44342 q^{79} -3.55972 q^{80} +10.8421 q^{81} +0.736282 q^{82} -3.28706 q^{83} +12.8033 q^{84} +26.9336 q^{85} +5.40877 q^{86} -16.1634 q^{87} +0.539753 q^{88} -9.91472 q^{89} -22.0711 q^{90} +10.6975 q^{91} -8.07968 q^{92} +25.3445 q^{93} +10.8385 q^{94} -28.7801 q^{95} -3.03319 q^{96} +12.6908 q^{97} +10.8176 q^{98} +3.34659 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

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