LMFDB - Embedded newform 8042.2.a.a.1.66

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8042,2,Mod(1,8042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8042, 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("8042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8042 = 2 \cdot 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8042.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:	$64.2156933055$
Analytic rank:	$1$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.66
Character	$\chi$	$=$	8042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.99809 q^{3} +1.00000 q^{4} -2.44064 q^{5} +2.99809 q^{6} +0.433551 q^{7} +1.00000 q^{8} +5.98855 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.99809 q^{3} +1.00000 q^{4} -2.44064 q^{5} +2.99809 q^{6} +0.433551 q^{7} +1.00000 q^{8} +5.98855 q^{9} -2.44064 q^{10} -2.66317 q^{11} +2.99809 q^{12} -1.80345 q^{13} +0.433551 q^{14} -7.31725 q^{15} +1.00000 q^{16} -3.31595 q^{17} +5.98855 q^{18} -2.80855 q^{19} -2.44064 q^{20} +1.29982 q^{21} -2.66317 q^{22} -3.30111 q^{23} +2.99809 q^{24} +0.956705 q^{25} -1.80345 q^{26} +8.95993 q^{27} +0.433551 q^{28} -7.23750 q^{29} -7.31725 q^{30} -6.92416 q^{31} +1.00000 q^{32} -7.98442 q^{33} -3.31595 q^{34} -1.05814 q^{35} +5.98855 q^{36} -7.15663 q^{37} -2.80855 q^{38} -5.40690 q^{39} -2.44064 q^{40} +0.953394 q^{41} +1.29982 q^{42} +8.60247 q^{43} -2.66317 q^{44} -14.6159 q^{45} -3.30111 q^{46} -5.12634 q^{47} +2.99809 q^{48} -6.81203 q^{49} +0.956705 q^{50} -9.94152 q^{51} -1.80345 q^{52} +10.1070 q^{53} +8.95993 q^{54} +6.49982 q^{55} +0.433551 q^{56} -8.42028 q^{57} -7.23750 q^{58} -1.99384 q^{59} -7.31725 q^{60} -7.73628 q^{61} -6.92416 q^{62} +2.59634 q^{63} +1.00000 q^{64} +4.40156 q^{65} -7.98442 q^{66} -5.20003 q^{67} -3.31595 q^{68} -9.89702 q^{69} -1.05814 q^{70} -1.76385 q^{71} +5.98855 q^{72} +12.1968 q^{73} -7.15663 q^{74} +2.86829 q^{75} -2.80855 q^{76} -1.15462 q^{77} -5.40690 q^{78} +8.31990 q^{79} -2.44064 q^{80} +8.89704 q^{81} +0.953394 q^{82} -3.61740 q^{83} +1.29982 q^{84} +8.09303 q^{85} +8.60247 q^{86} -21.6987 q^{87} -2.66317 q^{88} +5.01505 q^{89} -14.6159 q^{90} -0.781887 q^{91} -3.30111 q^{92} -20.7593 q^{93} -5.12634 q^{94} +6.85464 q^{95} +2.99809 q^{96} -2.79783 q^{97} -6.81203 q^{98} -15.9485 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9}+O(q^{10}) $ 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9	\( 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9} - 20 q^{10} - 13 q^{11} - 11 q^{12} - 51 q^{13} - 40 q^{14} - 31 q^{15} + 67 q^{16} - 34 q^{17} + 24 q^{18} - 33 q^{19} - 20 q^{20} - 39 q^{21} - 13 q^{22} - 43 q^{23} - 11 q^{24} - 9 q^{25} - 51 q^{26} - 29 q^{27} - 40 q^{28} - 63 q^{29} - 31 q^{30} - 43 q^{31} + 67 q^{32} - 49 q^{33} - 34 q^{34} - 20 q^{35} + 24 q^{36} - 77 q^{37} - 33 q^{38} - 40 q^{39} - 20 q^{40} - 50 q^{41} - 39 q^{42} - 56 q^{43} - 13 q^{44} - 48 q^{45} - 43 q^{46} - 48 q^{47} - 11 q^{48} + q^{49} - 9 q^{50} - 18 q^{51} - 51 q^{52} - 91 q^{53} - 29 q^{54} - 58 q^{55} - 40 q^{56} - 65 q^{57} - 63 q^{58} - 17 q^{59} - 31 q^{60} - 45 q^{61} - 43 q^{62} - 67 q^{63} + 67 q^{64} - 65 q^{65} - 49 q^{66} - 112 q^{67} - 34 q^{68} - 57 q^{69} - 20 q^{70} - 75 q^{71} + 24 q^{72} - 79 q^{73} - 77 q^{74} - 5 q^{75} - 33 q^{76} - 85 q^{77} - 40 q^{78} - 80 q^{79} - 20 q^{80} - 77 q^{81} - 50 q^{82} - 22 q^{83} - 39 q^{84} - 134 q^{85} - 56 q^{86} - 49 q^{87} - 13 q^{88} - 77 q^{89} - 48 q^{90} - 17 q^{91} - 43 q^{92} - 97 q^{93} - 48 q^{94} - 73 q^{95} - 11 q^{96} - 87 q^{97} + q^{98} - 44 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9 - 20 * q^10 - 13 * q^11 - 11 * q^12 - 51 * q^13 - 40 * q^14 - 31 * q^15 + 67 * q^16 - 34 * q^17 + 24 * q^18 - 33 * q^19 - 20 * q^20 - 39 * q^21 - 13 * q^22 - 43 * q^23 - 11 * q^24 - 9 * q^25 - 51 * q^26 - 29 * q^27 - 40 * q^28 - 63 * q^29 - 31 * q^30 - 43 * q^31 + 67 * q^32 - 49 * q^33 - 34 * q^34 - 20 * q^35 + 24 * q^36 - 77 * q^37 - 33 * q^38 - 40 * q^39 - 20 * q^40 - 50 * q^41 - 39 * q^42 - 56 * q^43 - 13 * q^44 - 48 * q^45 - 43 * q^46 - 48 * q^47 - 11 * q^48 + q^49 - 9 * q^50 - 18 * q^51 - 51 * q^52 - 91 * q^53 - 29 * q^54 - 58 * q^55 - 40 * q^56 - 65 * q^57 - 63 * q^58 - 17 * q^59 - 31 * q^60 - 45 * q^61 - 43 * q^62 - 67 * q^63 + 67 * q^64 - 65 * q^65 - 49 * q^66 - 112 * q^67 - 34 * q^68 - 57 * q^69 - 20 * q^70 - 75 * q^71 + 24 * q^72 - 79 * q^73 - 77 * q^74 - 5 * q^75 - 33 * q^76 - 85 * q^77 - 40 * q^78 - 80 * q^79 - 20 * q^80 - 77 * q^81 - 50 * q^82 - 22 * q^83 - 39 * q^84 - 134 * q^85 - 56 * q^86 - 49 * q^87 - 13 * q^88 - 77 * q^89 - 48 * q^90 - 17 * q^91 - 43 * q^92 - 97 * q^93 - 48 * q^94 - 73 * q^95 - 11 * q^96 - 87 * q^97 + q^98 - 44 * 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
$3$	2.99809	1.73095	0.865474	−	0.500954i	$-0.167017\pi$
$3$	2.99809	1.73095	0.865474	+	0.500954i	$0.167017\pi$
$4$	1.00000	0.500000
$5$	−2.44064	−1.09149	−0.545743	−	0.837953i	$-0.683752\pi$
$5$	−2.44064	−1.09149	−0.545743	+	0.837953i	$0.683752\pi$
$6$	2.99809	1.22397
$7$	0.433551	0.163867	0.0819334	−	0.996638i	$-0.473891\pi$
$7$	0.433551	0.163867	0.0819334	+	0.996638i	$0.473891\pi$
$8$	1.00000	0.353553
$9$	5.98855	1.99618
$10$	−2.44064	−0.771797
$11$	−2.66317	−0.802975	−0.401488	−	0.915864i	$-0.631507\pi$
$11$	−2.66317	−0.802975	−0.401488	+	0.915864i	$0.631507\pi$
$12$	2.99809	0.865474
$13$	−1.80345	−0.500187	−0.250093	−	0.968222i	$-0.580461\pi$
$13$	−1.80345	−0.500187	−0.250093	+	0.968222i	$0.580461\pi$
$14$	0.433551	0.115871
$15$	−7.31725	−1.88931
$16$	1.00000	0.250000
$17$	−3.31595	−0.804236	−0.402118	−	0.915588i	$-0.631726\pi$
$17$	−3.31595	−0.804236	−0.402118	+	0.915588i	$0.631726\pi$
$18$	5.98855	1.41151
$19$	−2.80855	−0.644325	−0.322163	−	0.946684i	$-0.604410\pi$
$19$	−2.80855	−0.644325	−0.322163	+	0.946684i	$0.604410\pi$
$20$	−2.44064	−0.545743
$21$	1.29982	0.283645
$22$	−2.66317	−0.567789
$23$	−3.30111	−0.688329	−0.344164	−	0.938909i	$-0.611838\pi$
$23$	−3.30111	−0.688329	−0.344164	+	0.938909i	$0.611838\pi$
$24$	2.99809	0.611983
$25$	0.956705	0.191341
$26$	−1.80345	−0.353685
$27$	8.95993	1.72434
$28$	0.433551	0.0819334
$29$	−7.23750	−1.34397	−0.671985	−	0.740565i	$-0.734558\pi$
$29$	−7.23750	−1.34397	−0.671985	+	0.740565i	$0.734558\pi$
$30$	−7.31725	−1.33594
$31$	−6.92416	−1.24362	−0.621808	−	0.783170i	$-0.713601\pi$
$31$	−6.92416	−1.24362	−0.621808	+	0.783170i	$0.713601\pi$
$32$	1.00000	0.176777
$33$	−7.98442	−1.38991
$34$	−3.31595	−0.568681
$35$	−1.05814	−0.178858
$36$	5.98855	0.998091
$37$	−7.15663	−1.17654	−0.588272	−	0.808663i	$-0.700191\pi$
$37$	−7.15663	−1.17654	−0.588272	+	0.808663i	$0.700191\pi$
$38$	−2.80855	−0.455607
$39$	−5.40690	−0.865797
$40$	−2.44064	−0.385898
$41$	0.953394	0.148895	0.0744476	−	0.997225i	$-0.476281\pi$
$41$	0.953394	0.148895	0.0744476	+	0.997225i	$0.476281\pi$
$42$	1.29982	0.200567
$43$	8.60247	1.31187	0.655933	−	0.754820i	$-0.272276\pi$
$43$	8.60247	1.31187	0.655933	+	0.754820i	$0.272276\pi$
$44$	−2.66317	−0.401488
$45$	−14.6159	−2.17880
$46$	−3.30111	−0.486722
$47$	−5.12634	−0.747754	−0.373877	−	0.927478i	$-0.621972\pi$
$47$	−5.12634	−0.747754	−0.373877	+	0.927478i	$0.621972\pi$
$48$	2.99809	0.432737
$49$	−6.81203	−0.973148
$50$	0.956705	0.135298
$51$	−9.94152	−1.39209
$52$	−1.80345	−0.250093
$53$	10.1070	1.38830	0.694152	−	0.719828i	$-0.255779\pi$
$53$	10.1070	1.38830	0.694152	+	0.719828i	$0.255779\pi$
$54$	8.95993	1.21929
$55$	6.49982	0.876436
$56$	0.433551	0.0579357
$57$	−8.42028	−1.11529
$58$	−7.23750	−0.950330
$59$	−1.99384	−0.259576	−0.129788	−	0.991542i	$-0.541430\pi$
$59$	−1.99384	−0.259576	−0.129788	+	0.991542i	$0.541430\pi$
$60$	−7.31725	−0.944653
$61$	−7.73628	−0.990530	−0.495265	−	0.868742i	$-0.664929\pi$
$61$	−7.73628	−0.990530	−0.495265	+	0.868742i	$0.664929\pi$
$62$	−6.92416	−0.879369
$63$	2.59634	0.327108
$64$	1.00000	0.125000
$65$	4.40156	0.545946
$66$	−7.98442	−0.982814
$67$	−5.20003	−0.635285	−0.317642	−	0.948211i	$-0.602891\pi$
$67$	−5.20003	−0.635285	−0.317642	+	0.948211i	$0.602891\pi$
$68$	−3.31595	−0.402118
$69$	−9.89702	−1.19146
$70$	−1.05814	−0.126472
$71$	−1.76385	−0.209331	−0.104665	−	0.994507i	$-0.533377\pi$
$71$	−1.76385	−0.209331	−0.104665	+	0.994507i	$0.533377\pi$
$72$	5.98855	0.705757
$73$	12.1968	1.42752	0.713762	−	0.700388i	$-0.246990\pi$
$73$	12.1968	1.42752	0.713762	+	0.700388i	$0.246990\pi$
$74$	−7.15663	−0.831942
$75$	2.86829	0.331201
$76$	−2.80855	−0.322163
$77$	−1.15462	−0.131581
$78$	−5.40690	−0.612211
$79$	8.31990	0.936062	0.468031	−	0.883712i	$-0.344964\pi$
$79$	8.31990	0.936062	0.468031	+	0.883712i	$0.344964\pi$
$80$	−2.44064	−0.272871
$81$	8.89704	0.988560
$82$	0.953394	0.105285
$83$	−3.61740	−0.397061	−0.198531	−	0.980095i	$-0.563617\pi$
$83$	−3.61740	−0.397061	−0.198531	+	0.980095i	$0.563617\pi$
$84$	1.29982	0.141823
$85$	8.09303	0.877812
$86$	8.60247	0.927629
$87$	−21.6987	−2.32634
$88$	−2.66317	−0.283895
$89$	5.01505	0.531594	0.265797	−	0.964029i	$-0.414365\pi$
$89$	5.01505	0.531594	0.265797	+	0.964029i	$0.414365\pi$
$90$	−14.6159	−1.54065
$91$	−0.781887	−0.0819640
$92$	−3.30111	−0.344164
$93$	−20.7593	−2.15263
$94$	−5.12634	−0.528742
$95$	6.85464	0.703272
$96$	2.99809	0.305991
$97$	−2.79783	−0.284077	−0.142038	−	0.989861i	$-0.545366\pi$
$97$	−2.79783	−0.284077	−0.142038	+	0.989861i	$0.545366\pi$
$98$	−6.81203	−0.688119
$99$	−15.9485	−1.60288
$100$	0.956705	0.0956705
$101$	19.3419	1.92459	0.962293	−	0.272014i	$-0.0876898\pi$
$101$	19.3419	1.92459	0.962293	+	0.272014i	$0.0876898\pi$
$102$	−9.94152	−0.984357
$103$	−8.59575	−0.846965	−0.423482	−	0.905904i	$-0.639192\pi$
$103$	−8.59575	−0.846965	−0.423482	+	0.905904i	$0.639192\pi$
$104$	−1.80345	−0.176843
$105$	−3.17240	−0.309595
$106$	10.1070	0.981680
$107$	1.46386	0.141516	0.0707582	−	0.997493i	$-0.477458\pi$
$107$	1.46386	0.141516	0.0707582	+	0.997493i	$0.477458\pi$
$108$	8.95993	0.862170
$109$	−2.58152	−0.247264	−0.123632	−	0.992328i	$-0.539454\pi$
$109$	−2.58152	−0.247264	−0.123632	+	0.992328i	$0.539454\pi$
$110$	6.49982	0.619734
$111$	−21.4562	−2.03654
$112$	0.433551	0.0409667
$113$	14.0181	1.31871	0.659354	−	0.751833i	$-0.270830\pi$
$113$	14.0181	1.31871	0.659354	+	0.751833i	$0.270830\pi$
$114$	−8.42028	−0.788632
$115$	8.05681	0.751301
$116$	−7.23750	−0.671985
$117$	−10.8000	−0.998463
$118$	−1.99384	−0.183548
$119$	−1.43763	−0.131788
$120$	−7.31725	−0.667970
$121$	−3.90754	−0.355231
$122$	−7.73628	−0.700410
$123$	2.85836	0.257730
$124$	−6.92416	−0.621808
$125$	9.86821	0.882640
$126$	2.59634	0.231300
$127$	16.2451	1.44152	0.720758	−	0.693186i	$-0.243794\pi$
$127$	16.2451	1.44152	0.720758	+	0.693186i	$0.243794\pi$
$128$	1.00000	0.0883883
$129$	25.7910	2.27077
$130$	4.40156	0.386042
$131$	11.4376	0.999305	0.499652	−	0.866226i	$-0.333461\pi$
$131$	11.4376	0.999305	0.499652	+	0.866226i	$0.333461\pi$
$132$	−7.98442	−0.694954
$133$	−1.21765	−0.105584
$134$	−5.20003	−0.449214
$135$	−21.8679	−1.88209
$136$	−3.31595	−0.284340
$137$	5.48573	0.468677	0.234339	−	0.972155i	$-0.424708\pi$
$137$	5.48573	0.468677	0.234339	+	0.972155i	$0.424708\pi$
$138$	−9.89702	−0.842490
$139$	16.6141	1.40919	0.704596	−	0.709609i	$-0.251128\pi$
$139$	16.6141	1.40919	0.704596	+	0.709609i	$0.251128\pi$
$140$	−1.05814	−0.0894292
$141$	−15.3692	−1.29432
$142$	−1.76385	−0.148019
$143$	4.80288	0.401637
$144$	5.98855	0.499045
$145$	17.6641	1.46692
$146$	12.1968	1.00941
$147$	−20.4231	−1.68447
$148$	−7.15663	−0.588272
$149$	−12.2942	−1.00718	−0.503588	−	0.863944i	$-0.667987\pi$
$149$	−12.2942	−1.00718	−0.503588	+	0.863944i	$0.667987\pi$
$150$	2.86829	0.234195
$151$	−19.9604	−1.62435	−0.812176	−	0.583413i	$-0.801717\pi$
$151$	−19.9604	−1.62435	−0.812176	+	0.583413i	$0.801717\pi$
$152$	−2.80855	−0.227803
$153$	−19.8577	−1.60540
$154$	−1.15462	−0.0930418
$155$	16.8994	1.35739
$156$	−5.40690	−0.432898
$157$	−9.64852	−0.770035	−0.385018	−	0.922909i	$-0.625805\pi$
$157$	−9.64852	−0.770035	−0.385018	+	0.922909i	$0.625805\pi$
$158$	8.31990	0.661896
$159$	30.3017	2.40308
$160$	−2.44064	−0.192949
$161$	−1.43120	−0.112794
$162$	8.89704	0.699018
$163$	−15.5150	−1.21523	−0.607613	−	0.794234i	$-0.707873\pi$
$163$	−15.5150	−1.21523	−0.607613	+	0.794234i	$0.707873\pi$
$164$	0.953394	0.0744476
$165$	19.4871	1.51707
$166$	−3.61740	−0.280765
$167$	−18.0735	−1.39857	−0.699283	−	0.714845i	$-0.746497\pi$
$167$	−18.0735	−1.39857	−0.699283	+	0.714845i	$0.746497\pi$
$168$	1.29982	0.100284
$169$	−9.74757	−0.749813
$170$	8.09303	0.620707
$171$	−16.8191	−1.28619
$172$	8.60247	0.655933
$173$	−15.0356	−1.14313	−0.571567	−	0.820556i	$-0.693664\pi$
$173$	−15.0356	−1.14313	−0.571567	+	0.820556i	$0.693664\pi$
$174$	−21.6987	−1.64497
$175$	0.414780	0.0313544
$176$	−2.66317	−0.200744
$177$	−5.97772	−0.449313
$178$	5.01505	0.375894
$179$	2.39661	0.179131	0.0895657	−	0.995981i	$-0.471452\pi$
$179$	2.39661	0.179131	0.0895657	+	0.995981i	$0.471452\pi$
$180$	−14.6159	−1.08940
$181$	−0.779695	−0.0579542	−0.0289771	−	0.999580i	$-0.509225\pi$
$181$	−0.779695	−0.0579542	−0.0289771	+	0.999580i	$0.509225\pi$
$182$	−0.781887	−0.0579573
$183$	−23.1941	−1.71456
$184$	−3.30111	−0.243361
$185$	17.4667	1.28418
$186$	−20.7593	−1.52214
$187$	8.83093	0.645782
$188$	−5.12634	−0.373877
$189$	3.88459	0.282562
$190$	6.85464	0.497288
$191$	−9.18007	−0.664246	−0.332123	−	0.943236i	$-0.607765\pi$
$191$	−9.18007	−0.664246	−0.332123	+	0.943236i	$0.607765\pi$
$192$	2.99809	0.216369
$193$	−0.632185	−0.0455057	−0.0227528	−	0.999741i	$-0.507243\pi$
$193$	−0.632185	−0.0455057	−0.0227528	+	0.999741i	$0.507243\pi$
$194$	−2.79783	−0.200873
$195$	13.1963	0.945005
$196$	−6.81203	−0.486574
$197$	15.4307	1.09939	0.549694	−	0.835366i	$-0.314744\pi$
$197$	15.4307	1.09939	0.549694	+	0.835366i	$0.314744\pi$
$198$	−15.9485	−1.13341
$199$	14.4421	1.02378	0.511888	−	0.859052i	$-0.328946\pi$
$199$	14.4421	1.02378	0.511888	+	0.859052i	$0.328946\pi$
$200$	0.956705	0.0676492
$201$	−15.5902	−1.09964
$202$	19.3419	1.36089
$203$	−3.13782	−0.220232
$204$	−9.94152	−0.696046
$205$	−2.32689	−0.162517
$206$	−8.59575	−0.598894
$207$	−19.7688	−1.37403
$208$	−1.80345	−0.125047
$209$	7.47963	0.517377
$210$	−3.17240	−0.218916
$211$	5.84408	0.402323	0.201162	−	0.979558i	$-0.435528\pi$
$211$	5.84408	0.402323	0.201162	+	0.979558i	$0.435528\pi$
$212$	10.1070	0.694152
$213$	−5.28819	−0.362341
$214$	1.46386	0.100067
$215$	−20.9955	−1.43188
$216$	8.95993	0.609646
$217$	−3.00198	−0.203787
$218$	−2.58152	−0.174842
$219$	36.5670	2.47097
$220$	6.49982	0.438218
$221$	5.98014	0.402268
$222$	−21.4562	−1.44005
$223$	22.0493	1.47653	0.738266	−	0.674510i	$-0.235645\pi$
$223$	22.0493	1.47653	0.738266	+	0.674510i	$0.235645\pi$
$224$	0.433551	0.0289678
$225$	5.72927	0.381951
$226$	14.0181	0.932467
$227$	18.4636	1.22547	0.612735	−	0.790288i	$-0.290069\pi$
$227$	18.4636	1.22547	0.612735	+	0.790288i	$0.290069\pi$
$228$	−8.42028	−0.557647
$229$	−20.2709	−1.33954	−0.669768	−	0.742571i	$-0.733606\pi$
$229$	−20.2709	−1.33954	−0.669768	+	0.742571i	$0.733606\pi$
$230$	8.05681	0.531250
$231$	−3.46165	−0.227760
$232$	−7.23750	−0.475165
$233$	0.418650	0.0274267	0.0137133	−	0.999906i	$-0.495635\pi$
$233$	0.418650	0.0274267	0.0137133	+	0.999906i	$0.495635\pi$
$234$	−10.8000	−0.706020
$235$	12.5115	0.816163
$236$	−1.99384	−0.129788
$237$	24.9438	1.62027
$238$	−1.43763	−0.0931879
$239$	−2.96877	−0.192034	−0.0960169	−	0.995380i	$-0.530610\pi$
$239$	−2.96877	−0.192034	−0.0960169	+	0.995380i	$0.530610\pi$
$240$	−7.31725	−0.472326
$241$	−26.7643	−1.72404	−0.862020	−	0.506875i	$-0.830801\pi$
$241$	−26.7643	−1.72404	−0.862020	+	0.506875i	$0.830801\pi$
$242$	−3.90754	−0.251186
$243$	−0.205651	−0.0131925
$244$	−7.73628	−0.495265
$245$	16.6257	1.06218
$246$	2.85836	0.182242
$247$	5.06507	0.322283
$248$	−6.92416	−0.439685
$249$	−10.8453	−0.687293
$250$	9.86821	0.624121
$251$	26.4182	1.66750	0.833750	−	0.552143i	$-0.186190\pi$
$251$	26.4182	1.66750	0.833750	+	0.552143i	$0.186190\pi$
$252$	2.59634	0.163554
$253$	8.79140	0.552711
$254$	16.2451	1.01931
$255$	24.2636	1.51945
$256$	1.00000	0.0625000
$257$	−30.2319	−1.88581	−0.942906	−	0.333059i	$-0.891919\pi$
$257$	−30.2319	−1.88581	−0.942906	+	0.333059i	$0.891919\pi$
$258$	25.7910	1.60568
$259$	−3.10277	−0.192796
$260$	4.40156	0.272973
$261$	−43.3421	−2.68281
$262$	11.4376	0.706615
$263$	11.7337	0.723529	0.361764	−	0.932270i	$-0.382174\pi$
$263$	11.7337	0.723529	0.361764	+	0.932270i	$0.382174\pi$
$264$	−7.98442	−0.491407
$265$	−24.6675	−1.51531
$266$	−1.21765	−0.0746588
$267$	15.0356	0.920162
$268$	−5.20003	−0.317642
$269$	−8.46593	−0.516177	−0.258088	−	0.966121i	$-0.583093\pi$
$269$	−8.46593	−0.516177	−0.258088	+	0.966121i	$0.583093\pi$
$270$	−21.8679	−1.33084
$271$	−18.3287	−1.11339	−0.556695	−	0.830717i	$-0.687931\pi$
$271$	−18.3287	−1.11339	−0.556695	+	0.830717i	$0.687931\pi$
$272$	−3.31595	−0.201059
$273$	−2.34417	−0.141875
$274$	5.48573	0.331405
$275$	−2.54786	−0.153642
$276$	−9.89702	−0.595731
$277$	−14.2392	−0.855549	−0.427774	−	0.903886i	$-0.640702\pi$
$277$	−14.2392	−0.855549	−0.427774	+	0.903886i	$0.640702\pi$
$278$	16.6141	0.996449
$279$	−41.4656	−2.48248
$280$	−1.05814	−0.0632360
$281$	20.4002	1.21697	0.608487	−	0.793564i	$-0.291777\pi$
$281$	20.4002	1.21697	0.608487	+	0.793564i	$0.291777\pi$
$282$	−15.3692	−0.915225
$283$	17.0246	1.01201	0.506003	−	0.862532i	$-0.331123\pi$
$283$	17.0246	1.01201	0.506003	+	0.862532i	$0.331123\pi$
$284$	−1.76385	−0.104665
$285$	20.5508	1.21733
$286$	4.80288	0.284000
$287$	0.413345	0.0243990
$288$	5.98855	0.352878
$289$	−6.00447	−0.353204
$290$	17.6641	1.03727
$291$	−8.38815	−0.491722
$292$	12.1968	0.713762
$293$	−7.07380	−0.413256	−0.206628	−	0.978420i	$-0.566249\pi$
$293$	−7.07380	−0.413256	−0.206628	+	0.978420i	$0.566249\pi$
$294$	−20.4231	−1.19110
$295$	4.86625	0.283324
$296$	−7.15663	−0.415971
$297$	−23.8618	−1.38460
$298$	−12.2942	−0.712181
$299$	5.95338	0.344293
$300$	2.86829	0.165601
$301$	3.72961	0.214971
$302$	−19.9604	−1.14859
$303$	57.9886	3.33136
$304$	−2.80855	−0.161081
$305$	18.8815	1.08115
$306$	−19.8577	−1.13519
$307$	−8.35404	−0.476790	−0.238395	−	0.971168i	$-0.576621\pi$
$307$	−8.35404	−0.476790	−0.238395	+	0.971168i	$0.576621\pi$
$308$	−1.15462	−0.0657905
$309$	−25.7708	−1.46605
$310$	16.8994	0.959819
$311$	9.17224	0.520110	0.260055	−	0.965594i	$-0.416259\pi$
$311$	9.17224	0.520110	0.260055	+	0.965594i	$0.416259\pi$
$312$	−5.40690	−0.306105
$313$	26.2952	1.48629	0.743145	−	0.669130i	$-0.233333\pi$
$313$	26.2952	1.48629	0.743145	+	0.669130i	$0.233333\pi$
$314$	−9.64852	−0.544497
$315$	−6.33672	−0.357034
$316$	8.31990	0.468031
$317$	30.2750	1.70041	0.850207	−	0.526449i	$-0.176477\pi$
$317$	30.2750	1.70041	0.850207	+	0.526449i	$0.176477\pi$
$318$	30.3017	1.69924
$319$	19.2747	1.07917
$320$	−2.44064	−0.136436
$321$	4.38878	0.244958
$322$	−1.43120	−0.0797576
$323$	9.31301	0.518189
$324$	8.89704	0.494280
$325$	−1.72537	−0.0957062
$326$	−15.5150	−0.859294
$327$	−7.73962	−0.428002
$328$	0.953394	0.0526424
$329$	−2.22253	−0.122532
$330$	19.4871	1.07273
$331$	−27.4671	−1.50973	−0.754865	−	0.655880i	$-0.772298\pi$
$331$	−27.4671	−1.50973	−0.754865	+	0.655880i	$0.772298\pi$
$332$	−3.61740	−0.198531
$333$	−42.8578	−2.34859
$334$	−18.0735	−0.988936
$335$	12.6914	0.693404
$336$	1.29982	0.0709113
$337$	20.1346	1.09680	0.548400	−	0.836216i	$-0.315237\pi$
$337$	20.1346	1.09680	0.548400	+	0.836216i	$0.315237\pi$
$338$	−9.74757	−0.530198
$339$	42.0274	2.28262
$340$	8.09303	0.438906
$341$	18.4402	0.998592
$342$	−16.8191	−0.909474
$343$	−5.98822	−0.323333
$344$	8.60247	0.463814
$345$	24.1550	1.30046
$346$	−15.0356	−0.808318
$347$	−35.8913	−1.92675	−0.963373	−	0.268164i	$-0.913583\pi$
$347$	−35.8913	−1.92675	−0.963373	+	0.268164i	$0.913583\pi$
$348$	−21.6987	−1.16317
$349$	13.7112	0.733946	0.366973	−	0.930232i	$-0.380394\pi$
$349$	13.7112	0.733946	0.366973	+	0.930232i	$0.380394\pi$
$350$	0.414780	0.0221709
$351$	−16.1588	−0.862491
$352$	−2.66317	−0.141947
$353$	10.6177	0.565125	0.282562	−	0.959249i	$-0.408816\pi$
$353$	10.6177	0.565125	0.282562	+	0.959249i	$0.408816\pi$
$354$	−5.97772	−0.317712
$355$	4.30493	0.228482
$356$	5.01505	0.265797
$357$	−4.31015	−0.228118
$358$	2.39661	0.126665
$359$	−15.4571	−0.815797	−0.407898	−	0.913027i	$-0.633738\pi$
$359$	−15.4571	−0.815797	−0.407898	+	0.913027i	$0.633738\pi$
$360$	−14.6159	−0.770324
$361$	−11.1121	−0.584845
$362$	−0.779695	−0.0409798
$363$	−11.7152	−0.614886
$364$	−0.781887	−0.0409820
$365$	−29.7679	−1.55812
$366$	−23.1941	−1.21237
$367$	9.21218	0.480872	0.240436	−	0.970665i	$-0.422710\pi$
$367$	9.21218	0.480872	0.240436	+	0.970665i	$0.422710\pi$
$368$	−3.30111	−0.172082
$369$	5.70944	0.297222
$370$	17.4667	0.908052
$371$	4.38190	0.227497
$372$	−20.7593	−1.07632
$373$	16.6788	0.863597	0.431798	−	0.901970i	$-0.357879\pi$
$373$	16.6788	0.863597	0.431798	+	0.901970i	$0.357879\pi$
$374$	8.83093	0.456637
$375$	29.5858	1.52780
$376$	−5.12634	−0.264371
$377$	13.0525	0.672235
$378$	3.88459	0.199802
$379$	−29.9458	−1.53821	−0.769107	−	0.639120i	$-0.779299\pi$
$379$	−29.9458	−1.53821	−0.769107	+	0.639120i	$0.779299\pi$
$380$	6.85464	0.351636
$381$	48.7042	2.49519
$382$	−9.18007	−0.469693
$383$	24.9057	1.27262	0.636310	−	0.771433i	$-0.280460\pi$
$383$	24.9057	1.27262	0.636310	+	0.771433i	$0.280460\pi$
$384$	2.99809	0.152996
$385$	2.81800	0.143619
$386$	−0.632185	−0.0321774
$387$	51.5163	2.61872
$388$	−2.79783	−0.142038
$389$	−33.5062	−1.69883	−0.849415	−	0.527726i	$-0.823045\pi$
$389$	−33.5062	−1.69883	−0.849415	+	0.527726i	$0.823045\pi$
$390$	13.1963	0.668219
$391$	10.9463	0.553579
$392$	−6.81203	−0.344060
$393$	34.2909	1.72974
$394$	15.4307	0.777385
$395$	−20.3058	−1.02170
$396$	−15.9485	−0.801442
$397$	−18.2826	−0.917576	−0.458788	−	0.888546i	$-0.651716\pi$
$397$	−18.2826	−0.917576	−0.458788	+	0.888546i	$0.651716\pi$
$398$	14.4421	0.723918
$399$	−3.65062	−0.182760
$400$	0.956705	0.0478352
$401$	−9.70488	−0.484639	−0.242319	−	0.970197i	$-0.577908\pi$
$401$	−9.70488	−0.484639	−0.242319	+	0.970197i	$0.577908\pi$
$402$	−15.5902	−0.777566
$403$	12.4874	0.622040
$404$	19.3419	0.962293
$405$	−21.7144	−1.07900
$406$	−3.13782	−0.155728
$407$	19.0593	0.944735
$408$	−9.94152	−0.492179
$409$	11.6359	0.575358	0.287679	−	0.957727i	$-0.407116\pi$
$409$	11.6359	0.575358	0.287679	+	0.957727i	$0.407116\pi$
$410$	−2.32689	−0.114917
$411$	16.4467	0.811256
$412$	−8.59575	−0.423482
$413$	−0.864433	−0.0425360
$414$	−19.7688	−0.971585
$415$	8.82876	0.433387
$416$	−1.80345	−0.0884213
$417$	49.8106	2.43924
$418$	7.47963	0.365841
$419$	−20.7964	−1.01597	−0.507986	−	0.861365i	$-0.669610\pi$
$419$	−20.7964	−1.01597	−0.507986	+	0.861365i	$0.669610\pi$
$420$	−3.17240	−0.154797
$421$	−23.6360	−1.15195	−0.575975	−	0.817468i	$-0.695377\pi$
$421$	−23.6360	−1.15195	−0.575975	+	0.817468i	$0.695377\pi$
$422$	5.84408	0.284485
$423$	−30.6993	−1.49265
$424$	10.1070	0.490840
$425$	−3.17239	−0.153883
$426$	−5.28819	−0.256214
$427$	−3.35407	−0.162315
$428$	1.46386	0.0707582
$429$	14.3995	0.695213
$430$	−20.9955	−1.01249
$431$	18.4959	0.890915	0.445458	−	0.895303i	$-0.353041\pi$
$431$	18.4959	0.890915	0.445458	+	0.895303i	$0.353041\pi$
$432$	8.95993	0.431085
$433$	−14.8900	−0.715568	−0.357784	−	0.933804i	$-0.616468\pi$
$433$	−14.8900	−0.715568	−0.357784	+	0.933804i	$0.616468\pi$
$434$	−3.00198	−0.144099
$435$	52.9586	2.53917
$436$	−2.58152	−0.123632
$437$	9.27132	0.443507
$438$	36.5670	1.74724
$439$	−17.9956	−0.858882	−0.429441	−	0.903095i	$-0.641289\pi$
$439$	−17.9956	−0.858882	−0.429441	+	0.903095i	$0.641289\pi$
$440$	6.49982	0.309867
$441$	−40.7942	−1.94258
$442$	5.98014	0.284446
$443$	6.29526	0.299097	0.149548	−	0.988754i	$-0.452218\pi$
$443$	6.29526	0.299097	0.149548	+	0.988754i	$0.452218\pi$
$444$	−21.4562	−1.01827
$445$	−12.2399	−0.580227
$446$	22.0493	1.04407
$447$	−36.8590	−1.74337
$448$	0.433551	0.0204834
$449$	−36.8567	−1.73938	−0.869688	−	0.493602i	$-0.835680\pi$
$449$	−36.8567	−1.73938	−0.869688	+	0.493602i	$0.835680\pi$
$450$	5.72927	0.270080
$451$	−2.53905	−0.119559
$452$	14.0181	0.659354
$453$	−59.8430	−2.81167
$454$	18.4636	0.866538
$455$	1.90830	0.0894625
$456$	−8.42028	−0.394316
$457$	−29.9173	−1.39947	−0.699735	−	0.714402i	$-0.746699\pi$
$457$	−29.9173	−1.39947	−0.699735	+	0.714402i	$0.746699\pi$
$458$	−20.2709	−0.947195
$459$	−29.7107	−1.38678
$460$	8.05681	0.375650
$461$	19.1764	0.893132	0.446566	−	0.894751i	$-0.352647\pi$
$461$	19.1764	0.893132	0.446566	+	0.894751i	$0.352647\pi$
$462$	−3.46165	−0.161051
$463$	−37.5403	−1.74465	−0.872323	−	0.488931i	$-0.837387\pi$
$463$	−37.5403	−1.74465	−0.872323	+	0.488931i	$0.837387\pi$
$464$	−7.23750	−0.335992
$465$	50.6658	2.34957
$466$	0.418650	0.0193936
$467$	−21.9479	−1.01563	−0.507815	−	0.861466i	$-0.669547\pi$
$467$	−21.9479	−1.01563	−0.507815	+	0.861466i	$0.669547\pi$
$468$	−10.8000	−0.499232
$469$	−2.25448	−0.104102
$470$	12.5115	0.577114
$471$	−28.9271	−1.33289
$472$	−1.99384	−0.0917741
$473$	−22.9098	−1.05340
$474$	24.9438	1.14571
$475$	−2.68695	−0.123286
$476$	−1.43763	−0.0658938
$477$	60.5263	2.77131
$478$	−2.96877	−0.135788
$479$	−0.990759	−0.0452689	−0.0226345	−	0.999744i	$-0.507205\pi$
$479$	−0.990759	−0.0452689	−0.0226345	+	0.999744i	$0.507205\pi$
$480$	−7.31725	−0.333985
$481$	12.9066	0.588491
$482$	−26.7643	−1.21908
$483$	−4.29086	−0.195241
$484$	−3.90754	−0.177615
$485$	6.82849	0.310066
$486$	−0.205651	−0.00932853
$487$	−33.8957	−1.53596	−0.767979	−	0.640475i	$-0.778738\pi$
$487$	−33.8957	−1.53596	−0.767979	+	0.640475i	$0.778738\pi$
$488$	−7.73628	−0.350205
$489$	−46.5152	−2.10349
$490$	16.6257	0.751072
$491$	−31.3511	−1.41486	−0.707428	−	0.706786i	$-0.750145\pi$
$491$	−31.3511	−1.41486	−0.707428	+	0.706786i	$0.750145\pi$
$492$	2.85836	0.128865
$493$	23.9992	1.08087
$494$	5.06507	0.227888
$495$	38.9245	1.74953
$496$	−6.92416	−0.310904
$497$	−0.764720	−0.0343024
$498$	−10.8453	−0.485989
$499$	33.3380	1.49242	0.746208	−	0.665713i	$-0.231872\pi$
$499$	33.3380	1.49242	0.746208	+	0.665713i	$0.231872\pi$
$500$	9.86821	0.441320
$501$	−54.1859	−2.42085
$502$	26.4182	1.17910
$503$	−6.82306	−0.304225	−0.152112	−	0.988363i	$-0.548608\pi$
$503$	−6.82306	−0.304225	−0.152112	+	0.988363i	$0.548608\pi$
$504$	2.59634	0.115650
$505$	−47.2064	−2.10066
$506$	8.79140	0.390826
$507$	−29.2241	−1.29789
$508$	16.2451	0.720758
$509$	37.9790	1.68339	0.841694	−	0.539955i	$-0.181559\pi$
$509$	37.9790	1.68339	0.841694	+	0.539955i	$0.181559\pi$
$510$	24.2636	1.07441
$511$	5.28792	0.233924
$512$	1.00000	0.0441942
$513$	−25.1644	−1.11104
$514$	−30.2319	−1.33347
$515$	20.9791	0.924450
$516$	25.7910	1.13539
$517$	13.6523	0.600428
$518$	−3.10277	−0.136328
$519$	−45.0780	−1.97871
$520$	4.40156	0.193021
$521$	16.4735	0.721716	0.360858	−	0.932621i	$-0.382484\pi$
$521$	16.4735	0.721716	0.360858	+	0.932621i	$0.382484\pi$
$522$	−43.3421	−1.89703
$523$	−1.83739	−0.0803434	−0.0401717	−	0.999193i	$-0.512790\pi$
$523$	−1.83739	−0.0803434	−0.0401717	+	0.999193i	$0.512790\pi$
$524$	11.4376	0.499652
$525$	1.24355	0.0542729
$526$	11.7337	0.511612
$527$	22.9602	1.00016
$528$	−7.98442	−0.347477
$529$	−12.1027	−0.526204
$530$	−24.6675	−1.07149
$531$	−11.9402	−0.518162
$532$	−1.21765	−0.0527918
$533$	−1.71940	−0.0744753
$534$	15.0356	0.650653
$535$	−3.57274	−0.154463
$536$	−5.20003	−0.224607
$537$	7.18527	0.310067
$538$	−8.46593	−0.364992
$539$	18.1416	0.781413
$540$	−21.8679	−0.941046
$541$	−18.7454	−0.805927	−0.402964	−	0.915216i	$-0.632020\pi$
$541$	−18.7454	−0.805927	−0.402964	+	0.915216i	$0.632020\pi$
$542$	−18.3287	−0.787286
$543$	−2.33759	−0.100316
$544$	−3.31595	−0.142170
$545$	6.30054	0.269886
$546$	−2.34417	−0.100321
$547$	5.04330	0.215636	0.107818	−	0.994171i	$-0.465614\pi$
$547$	5.04330	0.215636	0.107818	+	0.994171i	$0.465614\pi$
$548$	5.48573	0.234339
$549$	−46.3291	−1.97728
$550$	−2.54786	−0.108641
$551$	20.3269	0.865953
$552$	−9.89702	−0.421245
$553$	3.60710	0.153389
$554$	−14.2392	−0.604964
$555$	52.3669	2.22285
$556$	16.6141	0.704596
$557$	7.22155	0.305987	0.152993	−	0.988227i	$-0.451109\pi$
$557$	7.22155	0.305987	0.152993	+	0.988227i	$0.451109\pi$
$558$	−41.4656	−1.75538
$559$	−15.5141	−0.656177
$560$	−1.05814	−0.0447146
$561$	26.4759	1.11781
$562$	20.4002	0.860531
$563$	9.41307	0.396713	0.198357	−	0.980130i	$-0.436440\pi$
$563$	9.41307	0.396713	0.198357	+	0.980130i	$0.436440\pi$
$564$	−15.3692	−0.647162
$565$	−34.2130	−1.43935
$566$	17.0246	0.715596
$567$	3.85732	0.161992
$568$	−1.76385	−0.0740097
$569$	−29.7576	−1.24750	−0.623751	−	0.781623i	$-0.714392\pi$
$569$	−29.7576	−1.24750	−0.623751	+	0.781623i	$0.714392\pi$
$570$	20.5508	0.860780
$571$	−36.6020	−1.53175	−0.765874	−	0.642991i	$-0.777693\pi$
$571$	−36.6020	−1.53175	−0.765874	+	0.642991i	$0.777693\pi$
$572$	4.80288	0.200819
$573$	−27.5227	−1.14978
$574$	0.413345	0.0172527
$575$	−3.15819	−0.131705
$576$	5.98855	0.249523
$577$	27.7533	1.15538	0.577692	−	0.816255i	$-0.303954\pi$
$577$	27.7533	1.15538	0.577692	+	0.816255i	$0.303954\pi$
$578$	−6.00447	−0.249753
$579$	−1.89535	−0.0787679
$580$	17.6641	0.733462
$581$	−1.56833	−0.0650652
$582$	−8.38815	−0.347700
$583$	−26.9167	−1.11477
$584$	12.1968	0.504706
$585$	26.3589	1.08981
$586$	−7.07380	−0.292216
$587$	−3.52040	−0.145302	−0.0726512	−	0.997357i	$-0.523146\pi$
$587$	−3.52040	−0.145302	−0.0726512	+	0.997357i	$0.523146\pi$
$588$	−20.4231	−0.842234
$589$	19.4468	0.801293
$590$	4.86625	0.200340
$591$	46.2625	1.90299
$592$	−7.15663	−0.294136
$593$	20.0822	0.824678	0.412339	−	0.911030i	$-0.364712\pi$
$593$	20.0822	0.824678	0.412339	+	0.911030i	$0.364712\pi$
$594$	−23.8618	−0.979061
$595$	3.50874	0.143844
$596$	−12.2942	−0.503588
$597$	43.2988	1.77210
$598$	5.95338	0.243452
$599$	4.27644	0.174731	0.0873654	−	0.996176i	$-0.472155\pi$
$599$	4.27644	0.174731	0.0873654	+	0.996176i	$0.472155\pi$
$600$	2.86829	0.117097
$601$	44.6068	1.81955	0.909774	−	0.415104i	$-0.136255\pi$
$601$	44.6068	1.81955	0.909774	+	0.415104i	$0.136255\pi$
$602$	3.72961	0.152008
$603$	−31.1406	−1.26814
$604$	−19.9604	−0.812176
$605$	9.53688	0.387729
$606$	57.9886	2.35563
$607$	−6.73127	−0.273214	−0.136607	−	0.990625i	$-0.543620\pi$
$607$	−6.73127	−0.273214	−0.136607	+	0.990625i	$0.543620\pi$
$608$	−2.80855	−0.113902
$609$	−9.40748	−0.381210
$610$	18.8815	0.764488
$611$	9.24510	0.374017
$612$	−19.8577	−0.802701
$613$	20.2719	0.818776	0.409388	−	0.912360i	$-0.365742\pi$
$613$	20.2719	0.818776	0.409388	+	0.912360i	$0.365742\pi$
$614$	−8.35404	−0.337142
$615$	−6.97622	−0.281308
$616$	−1.15462	−0.0465209
$617$	35.7966	1.44112	0.720558	−	0.693394i	$-0.243886\pi$
$617$	35.7966	1.44112	0.720558	+	0.693394i	$0.243886\pi$
$618$	−25.7708	−1.03666
$619$	−30.0946	−1.20960	−0.604801	−	0.796377i	$-0.706747\pi$
$619$	−30.0946	−1.20960	−0.604801	+	0.796377i	$0.706747\pi$
$620$	16.8994	0.678694
$621$	−29.5777	−1.18691
$622$	9.17224	0.367773
$623$	2.17428	0.0871106
$624$	−5.40690	−0.216449
$625$	−28.8682	−1.15473
$626$	26.2952	1.05097
$627$	22.4246	0.895553
$628$	−9.64852	−0.385018
$629$	23.7310	0.946219
$630$	−6.33672	−0.252461
$631$	26.4042	1.05113	0.525567	−	0.850752i	$-0.323853\pi$
$631$	26.4042	1.05113	0.525567	+	0.850752i	$0.323853\pi$
$632$	8.31990	0.330948
$633$	17.5211	0.696400
$634$	30.2750	1.20237
$635$	−39.6483	−1.57339
$636$	30.3017	1.20154
$637$	12.2851	0.486755
$638$	19.2747	0.763091
$639$	−10.5629	−0.417863
$640$	−2.44064	−0.0964746
$641$	31.7736	1.25498	0.627490	−	0.778625i	$-0.284082\pi$
$641$	31.7736	1.25498	0.627490	+	0.778625i	$0.284082\pi$
$642$	4.38878	0.173211
$643$	0.763822	0.0301222	0.0150611	−	0.999887i	$-0.495206\pi$
$643$	0.763822	0.0301222	0.0150611	+	0.999887i	$0.495206\pi$
$644$	−1.43120	−0.0563971
$645$	−62.9464	−2.47851
$646$	9.31301	0.366415
$647$	−3.98169	−0.156536	−0.0782681	−	0.996932i	$-0.524939\pi$
$647$	−3.98169	−0.156536	−0.0782681	+	0.996932i	$0.524939\pi$
$648$	8.89704	0.349509
$649$	5.30994	0.208433
$650$	−1.72537	−0.0676745
$651$	−9.00019	−0.352745
$652$	−15.5150	−0.607613
$653$	−22.2231	−0.869659	−0.434829	−	0.900513i	$-0.643191\pi$
$653$	−22.2231	−0.869659	−0.434829	+	0.900513i	$0.643191\pi$
$654$	−7.73962	−0.302643
$655$	−27.9149	−1.09073
$656$	0.953394	0.0372238
$657$	73.0410	2.84960
$658$	−2.22253	−0.0866433
$659$	1.59830	0.0622608	0.0311304	−	0.999515i	$-0.490089\pi$
$659$	1.59830	0.0622608	0.0311304	+	0.999515i	$0.490089\pi$
$660$	19.4871	0.758533
$661$	−9.66591	−0.375960	−0.187980	−	0.982173i	$-0.560194\pi$
$661$	−9.66591	−0.375960	−0.187980	+	0.982173i	$0.560194\pi$
$662$	−27.4671	−1.06754
$663$	17.9290	0.696305
$664$	−3.61740	−0.140382
$665$	2.97184	0.115243
$666$	−42.8578	−1.66071
$667$	23.8918	0.925093
$668$	−18.0735	−0.699283
$669$	66.1059	2.55580
$670$	12.6914	0.490311
$671$	20.6030	0.795371
$672$	1.29982	0.0501418
$673$	35.3019	1.36079	0.680394	−	0.732847i	$-0.261809\pi$
$673$	35.3019	1.36079	0.680394	+	0.732847i	$0.261809\pi$
$674$	20.1346	0.775554
$675$	8.57201	0.329937
$676$	−9.74757	−0.374907
$677$	−25.3867	−0.975691	−0.487845	−	0.872930i	$-0.662217\pi$
$677$	−25.3867	−0.975691	−0.487845	+	0.872930i	$0.662217\pi$
$678$	42.0274	1.61405
$679$	−1.21300	−0.0465508
$680$	8.09303	0.310353
$681$	55.3554	2.12122
$682$	18.4402	0.706111
$683$	38.5867	1.47648	0.738240	−	0.674538i	$-0.235657\pi$
$683$	38.5867	1.47648	0.738240	+	0.674538i	$0.235657\pi$
$684$	−16.8191	−0.643095
$685$	−13.3887	−0.511555
$686$	−5.98822	−0.228631
$687$	−60.7738	−2.31867
$688$	8.60247	0.327966
$689$	−18.2275	−0.694411
$690$	24.1550	0.919566
$691$	8.27278	0.314711	0.157356	−	0.987542i	$-0.449703\pi$
$691$	8.27278	0.314711	0.157356	+	0.987542i	$0.449703\pi$
$692$	−15.0356	−0.571567
$693$	−6.91449	−0.262660
$694$	−35.8913	−1.36242
$695$	−40.5490	−1.53811
$696$	−21.6987	−0.822486
$697$	−3.16141	−0.119747
$698$	13.7112	0.518978
$699$	1.25515	0.0474742
$700$	0.414780	0.0156772
$701$	−12.7520	−0.481636	−0.240818	−	0.970570i	$-0.577416\pi$
$701$	−12.7520	−0.481636	−0.240818	+	0.970570i	$0.577416\pi$
$702$	−16.1588	−0.609873
$703$	20.0997	0.758076
$704$	−2.66317	−0.100372
$705$	37.5107	1.41274
$706$	10.6177	0.399604
$707$	8.38568	0.315376
$708$	−5.97772	−0.224657
$709$	10.0529	0.377543	0.188772	−	0.982021i	$-0.439549\pi$
$709$	10.0529	0.377543	0.188772	+	0.982021i	$0.439549\pi$
$710$	4.30493	0.161561
$711$	49.8241	1.86855
$712$	5.01505	0.187947
$713$	22.8574	0.856016
$714$	−4.31015	−0.161303
$715$	−11.7221	−0.438381
$716$	2.39661	0.0895657
$717$	−8.90064	−0.332401
$718$	−15.4571	−0.576855
$719$	−7.15080	−0.266680	−0.133340	−	0.991070i	$-0.542570\pi$
$719$	−7.15080	−0.266680	−0.133340	+	0.991070i	$0.542570\pi$
$720$	−14.6159	−0.544701
$721$	−3.72670	−0.138789
$722$	−11.1121	−0.413548
$723$	−80.2418	−2.98422
$724$	−0.779695	−0.0289771
$725$	−6.92415	−0.257156
$726$	−11.7152	−0.434790
$727$	−26.2428	−0.973293	−0.486647	−	0.873599i	$-0.661780\pi$
$727$	−26.2428	−0.973293	−0.486647	+	0.873599i	$0.661780\pi$
$728$	−0.781887	−0.0289786
$729$	−27.3077	−1.01140
$730$	−29.7679	−1.10176
$731$	−28.5254	−1.05505
$732$	−23.1941	−0.857278
$733$	−40.4270	−1.49321	−0.746603	−	0.665270i	$-0.768316\pi$
$733$	−40.4270	−1.49321	−0.746603	+	0.665270i	$0.768316\pi$
$734$	9.21218	0.340028
$735$	49.8453	1.83857
$736$	−3.30111	−0.121680
$737$	13.8485	0.510118
$738$	5.70944	0.210168
$739$	23.7820	0.874834	0.437417	−	0.899259i	$-0.355893\pi$
$739$	23.7820	0.874834	0.437417	+	0.899259i	$0.355893\pi$
$740$	17.4667	0.642090
$741$	15.1855	0.557855
$742$	4.38190	0.160865
$743$	−28.9743	−1.06296	−0.531481	−	0.847070i	$-0.678364\pi$
$743$	−28.9743	−1.06296	−0.531481	+	0.847070i	$0.678364\pi$
$744$	−20.7593	−0.761071
$745$	30.0056	1.09932
$746$	16.6788	0.610655
$747$	−21.6630	−0.792607
$748$	8.83093	0.322891
$749$	0.634657	0.0231898
$750$	29.5858	1.08032
$751$	52.4555	1.91413	0.957064	−	0.289876i	$-0.0936142\pi$
$751$	52.4555	1.91413	0.957064	+	0.289876i	$0.0936142\pi$
$752$	−5.12634	−0.186939
$753$	79.2040	2.88636
$754$	13.0525	0.475342
$755$	48.7160	1.77296
$756$	3.88459	0.141281
$757$	32.5623	1.18350	0.591749	−	0.806122i	$-0.298438\pi$
$757$	32.5623	1.18350	0.591749	+	0.806122i	$0.298438\pi$
$758$	−29.9458	−1.08768
$759$	26.3574	0.956714
$760$	6.85464	0.248644
$761$	−12.5623	−0.455382	−0.227691	−	0.973733i	$-0.573118\pi$
$761$	−12.5623	−0.455382	−0.227691	+	0.973733i	$0.573118\pi$
$762$	48.7042	1.76437
$763$	−1.11922	−0.0405184
$764$	−9.18007	−0.332123
$765$	48.4655	1.75227
$766$	24.9057	0.899879
$767$	3.59579	0.129837
$768$	2.99809	0.108184
$769$	50.5382	1.82245	0.911227	−	0.411906i	$-0.135137\pi$
$769$	50.5382	1.82245	0.911227	+	0.411906i	$0.135137\pi$
$770$	2.81800	0.101554
$771$	−90.6379	−3.26424
$772$	−0.632185	−0.0227528
$773$	13.2828	0.477748	0.238874	−	0.971051i	$-0.423222\pi$
$773$	13.2828	0.477748	0.238874	+	0.971051i	$0.423222\pi$
$774$	51.5163	1.85172
$775$	−6.62438	−0.237955
$776$	−2.79783	−0.100436
$777$	−9.30237	−0.333721
$778$	−33.5062	−1.20125
$779$	−2.67765	−0.0959369
$780$	13.1963	0.472503
$781$	4.69744	0.168088
$782$	10.9463	0.391439
$783$	−64.8475	−2.31746
$784$	−6.81203	−0.243287
$785$	23.5485	0.840483
$786$	34.2909	1.22311
$787$	−43.3076	−1.54375	−0.771874	−	0.635775i	$-0.780681\pi$
$787$	−43.3076	−1.54375	−0.771874	+	0.635775i	$0.780681\pi$
$788$	15.4307	0.549694
$789$	35.1786	1.25239
$790$	−20.3058	−0.722449
$791$	6.07754	0.216093
$792$	−15.9485	−0.566705
$793$	13.9520	0.495450
$794$	−18.2826	−0.648824
$795$	−73.9555	−2.62293
$796$	14.4421	0.511888
$797$	0.0860722	0.00304883	0.00152442	−	0.999999i	$-0.499515\pi$
$797$	0.0860722	0.00304883	0.00152442	+	0.999999i	$0.499515\pi$
$798$	−3.65062	−0.129231
$799$	16.9987	0.601371
$800$	0.956705	0.0338246
$801$	30.0328	1.06116
$802$	−9.70488	−0.342691
$803$	−32.4821	−1.14627
$804$	−15.5902	−0.549822
$805$	3.49304	0.123113
$806$	12.4874	0.439849
$807$	−25.3816	−0.893476
$808$	19.3419	0.680444
$809$	−54.2684	−1.90797	−0.953987	−	0.299848i	$-0.903064\pi$
$809$	−54.2684	−1.90797	−0.953987	+	0.299848i	$0.903064\pi$
$810$	−21.7144	−0.762968
$811$	15.3113	0.537652	0.268826	−	0.963189i	$-0.413364\pi$
$811$	15.3113	0.537652	0.268826	+	0.963189i	$0.413364\pi$
$812$	−3.13782	−0.110116
$813$	−54.9512	−1.92722
$814$	19.0593	0.668029
$815$	37.8664	1.32640
$816$	−9.94152	−0.348023
$817$	−24.1605	−0.845268
$818$	11.6359	0.406840
$819$	−4.68236	−0.163615
$820$	−2.32689	−0.0812585
$821$	23.1824	0.809073	0.404536	−	0.914522i	$-0.367433\pi$
$821$	23.1824	0.809073	0.404536	+	0.914522i	$0.367433\pi$
$822$	16.4467	0.573645
$823$	36.2684	1.26424	0.632119	−	0.774872i	$-0.282186\pi$
$823$	36.2684	1.26424	0.632119	+	0.774872i	$0.282186\pi$
$824$	−8.59575	−0.299447
$825$	−7.63873	−0.265946
$826$	−0.864433	−0.0300775
$827$	43.3818	1.50853	0.754267	−	0.656568i	$-0.227992\pi$
$827$	43.3818	1.50853	0.754267	+	0.656568i	$0.227992\pi$
$828$	−19.7688	−0.687015
$829$	−3.09870	−0.107622	−0.0538112	−	0.998551i	$-0.517137\pi$
$829$	−3.09870	−0.107622	−0.0538112	+	0.998551i	$0.517137\pi$
$830$	8.82876	0.306451
$831$	−42.6903	−1.48091
$832$	−1.80345	−0.0625233
$833$	22.5884	0.782640
$834$	49.8106	1.72480
$835$	44.1107	1.52652
$836$	7.47963	0.258689
$837$	−62.0400	−2.14442
$838$	−20.7964	−0.718400
$839$	−24.0657	−0.830840	−0.415420	−	0.909630i	$-0.636365\pi$
$839$	−24.0657	−0.830840	−0.415420	+	0.909630i	$0.636365\pi$
$840$	−3.17240	−0.109458
$841$	23.3814	0.806254
$842$	−23.6360	−0.814551
$843$	61.1617	2.10652
$844$	5.84408	0.201162
$845$	23.7903	0.818411
$846$	−30.6993	−1.05547
$847$	−1.69412	−0.0582106
$848$	10.1070	0.347076
$849$	51.0412	1.75173
$850$	−3.17239	−0.108812
$851$	23.6248	0.809849
$852$	−5.28819	−0.181171
$853$	42.7121	1.46243	0.731217	−	0.682145i	$-0.238953\pi$
$853$	42.7121	1.46243	0.731217	+	0.682145i	$0.238953\pi$
$854$	−3.35407	−0.114774
$855$	41.0493	1.40386
$856$	1.46386	0.0500336
$857$	1.00755	0.0344171	0.0172086	−	0.999852i	$-0.494522\pi$
$857$	1.00755	0.0344171	0.0172086	+	0.999852i	$0.494522\pi$
$858$	14.3995	0.491590
$859$	−46.9157	−1.60074	−0.800372	−	0.599504i	$-0.795365\pi$
$859$	−46.9157	−1.60074	−0.800372	+	0.599504i	$0.795365\pi$
$860$	−20.9955	−0.715941
$861$	1.23925	0.0422334
$862$	18.4959	0.629972
$863$	15.4026	0.524310	0.262155	−	0.965026i	$-0.415567\pi$
$863$	15.4026	0.524310	0.262155	+	0.965026i	$0.415567\pi$
$864$	8.95993	0.304823
$865$	36.6964	1.24771
$866$	−14.8900	−0.505983
$867$	−18.0020	−0.611378
$868$	−3.00198	−0.101894
$869$	−22.1573	−0.751634
$870$	52.9586	1.79546
$871$	9.37798	0.317761
$872$	−2.58152	−0.0874212
$873$	−16.7549	−0.567069
$874$	9.27132	0.313607
$875$	4.27837	0.144635
$876$	36.5670	1.23549
$877$	−30.5459	−1.03146	−0.515732	−	0.856750i	$-0.672480\pi$
$877$	−30.5459	−1.03146	−0.515732	+	0.856750i	$0.672480\pi$
$878$	−17.9956	−0.607321
$879$	−21.2079	−0.715325
$880$	6.49982	0.219109
$881$	13.2878	0.447678	0.223839	−	0.974626i	$-0.428141\pi$
$881$	13.2878	0.447678	0.223839	+	0.974626i	$0.428141\pi$
$882$	−40.7942	−1.37361
$883$	52.2711	1.75906	0.879532	−	0.475840i	$-0.157856\pi$
$883$	52.2711	1.75906	0.879532	+	0.475840i	$0.157856\pi$
$884$	5.98014	0.201134
$885$	14.5895	0.490419
$886$	6.29526	0.211493
$887$	−28.0977	−0.943430	−0.471715	−	0.881751i	$-0.656365\pi$
$887$	−28.0977	−0.943430	−0.471715	+	0.881751i	$0.656365\pi$
$888$	−21.4562	−0.720024
$889$	7.04306	0.236217
$890$	−12.2399	−0.410283
$891$	−23.6943	−0.793789
$892$	22.0493	0.738266
$893$	14.3976	0.481797
$894$	−36.8590	−1.23275
$895$	−5.84926	−0.195519
$896$	0.433551	0.0144839
$897$	17.8488	0.595953
$898$	−36.8567	−1.22992
$899$	50.1136	1.67138
$900$	5.72927	0.190976
$901$	−33.5143	−1.11652
$902$	−2.53905	−0.0845411
$903$	11.1817	0.372104
$904$	14.0181	0.466234
$905$	1.90295	0.0632562
$906$	−59.8430	−1.98815
$907$	−3.48173	−0.115609	−0.0578045	−	0.998328i	$-0.518410\pi$
$907$	−3.48173	−0.115609	−0.0578045	+	0.998328i	$0.518410\pi$
$908$	18.4636	0.612735
$909$	115.830	3.84182
$910$	1.90830	0.0632596
$911$	−24.0793	−0.797781	−0.398891	−	0.916999i	$-0.630605\pi$
$911$	−24.0793	−0.797781	−0.398891	+	0.916999i	$0.630605\pi$
$912$	−8.42028	−0.278823
$913$	9.63374	0.318830
$914$	−29.9173	−0.989575
$915$	56.6083	1.87141
$916$	−20.2709	−0.669768
$917$	4.95877	0.163753
$918$	−29.7107	−0.980599
$919$	7.44078	0.245449	0.122724	−	0.992441i	$-0.460837\pi$
$919$	7.44078	0.245449	0.122724	+	0.992441i	$0.460837\pi$
$920$	8.05681	0.265625
$921$	−25.0462	−0.825299
$922$	19.1764	0.631540
$923$	3.18102	0.104705
$924$	−3.46165	−0.113880
$925$	−6.84679	−0.225121
$926$	−37.5403	−1.23365
$927$	−51.4761	−1.69070
$928$	−7.23750	−0.237582
$929$	24.9693	0.819217	0.409608	−	0.912261i	$-0.365665\pi$
$929$	24.9693	0.819217	0.409608	+	0.912261i	$0.365665\pi$
$930$	50.6658	1.66140
$931$	19.1319	0.627023
$932$	0.418650	0.0137133
$933$	27.4992	0.900284
$934$	−21.9479	−0.718158
$935$	−21.5531	−0.704861
$936$	−10.8000	−0.353010
$937$	45.2086	1.47690	0.738451	−	0.674307i	$-0.235558\pi$
$937$	45.2086	1.47690	0.738451	+	0.674307i	$0.235558\pi$
$938$	−2.25448	−0.0736113
$939$	78.8352	2.57269
$940$	12.5115	0.408081
$941$	0.453202	0.0147740	0.00738698	−	0.999973i	$-0.497649\pi$
$941$	0.453202	0.0147740	0.00738698	+	0.999973i	$0.497649\pi$
$942$	−28.9271	−0.942497
$943$	−3.14726	−0.102489
$944$	−1.99384	−0.0648941
$945$	−9.48086	−0.308412
$946$	−22.9098	−0.744863
$947$	47.0861	1.53009	0.765047	−	0.643975i	$-0.222716\pi$
$947$	47.0861	1.53009	0.765047	+	0.643975i	$0.222716\pi$
$948$	24.9438	0.810137
$949$	−21.9963	−0.714029
$950$	−2.68695	−0.0871762
$951$	90.7672	2.94333
$952$	−1.43763	−0.0465940
$953$	−27.7443	−0.898727	−0.449364	−	0.893349i	$-0.648349\pi$
$953$	−27.7443	−0.898727	−0.449364	+	0.893349i	$0.648349\pi$
$954$	60.5263	1.95961
$955$	22.4052	0.725015
$956$	−2.96877	−0.0960169
$957$	57.7872	1.86799
$958$	−0.990759	−0.0320100
$959$	2.37834	0.0768007
$960$	−7.31725	−0.236163
$961$	16.9440	0.546580
$962$	12.9066	0.416126
$963$	8.76637	0.282492
$964$	−26.7643	−0.862020
$965$	1.54293	0.0496688
$966$	−4.29086	−0.138056
$967$	−39.6524	−1.27513	−0.637567	−	0.770395i	$-0.720059\pi$
$967$	−39.6524	−1.27513	−0.637567	+	0.770395i	$0.720059\pi$
$968$	−3.90754	−0.125593
$969$	27.9212	0.896959
$970$	6.82849	0.219250
$971$	42.6714	1.36939	0.684695	−	0.728829i	$-0.259935\pi$
$971$	42.6714	1.36939	0.684695	+	0.728829i	$0.259935\pi$
$972$	−0.205651	−0.00659627
$973$	7.20307	0.230920
$974$	−33.8957	−1.08609
$975$	−5.17281	−0.165662
$976$	−7.73628	−0.247632
$977$	0.460044	0.0147181	0.00735905	−	0.999973i	$-0.497658\pi$
$977$	0.460044	0.0147181	0.00735905	+	0.999973i	$0.497658\pi$
$978$	−46.5152	−1.48739
$979$	−13.3559	−0.426857
$980$	16.6257	0.531088
$981$	−15.4595	−0.493585
$982$	−31.3511	−1.00045
$983$	−24.6004	−0.784630	−0.392315	−	0.919831i	$-0.628326\pi$
$983$	−24.6004	−0.784630	−0.392315	+	0.919831i	$0.628326\pi$
$984$	2.85836	0.0911212
$985$	−37.6606	−1.19997
$986$	23.9992	0.764290
$987$	−6.66335	−0.212097
$988$	5.06507	0.161141
$989$	−28.3977	−0.902994
$990$	38.9245	1.23710
$991$	−55.4645	−1.76189	−0.880944	−	0.473221i	$-0.843091\pi$
$991$	−55.4645	−1.76189	−0.880944	+	0.473221i	$0.843091\pi$
$992$	−6.92416	−0.219842
$993$	−82.3489	−2.61326
$994$	−0.764720	−0.0242555
$995$	−35.2480	−1.11744
$996$	−10.8453	−0.343646
$997$	15.4399	0.488986	0.244493	−	0.969651i	$-0.421379\pi$
$997$	15.4399	0.488986	0.244493	+	0.969651i	$0.421379\pi$
$998$	33.3380	1.05530
$999$	−64.1229	−2.02876

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8042.2.a.a.1.66	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8042.2.a.a.1.66	✓	67	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:	\( N \)	\(=\)	\( 8042 = 2 \cdot 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.99809 q^{3} +1.00000 q^{4} -2.44064 q^{5} +2.99809 q^{6} +0.433551 q^{7} +1.00000 q^{8} +5.98855 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.99809 q^{3} +1.00000 q^{4} -2.44064 q^{5} +2.99809 q^{6} +0.433551 q^{7} +1.00000 q^{8} +5.98855 q^{9} -2.44064 q^{10} -2.66317 q^{11} +2.99809 q^{12} -1.80345 q^{13} +0.433551 q^{14} -7.31725 q^{15} +1.00000 q^{16} -3.31595 q^{17} +5.98855 q^{18} -2.80855 q^{19} -2.44064 q^{20} +1.29982 q^{21} -2.66317 q^{22} -3.30111 q^{23} +2.99809 q^{24} +0.956705 q^{25} -1.80345 q^{26} +8.95993 q^{27} +0.433551 q^{28} -7.23750 q^{29} -7.31725 q^{30} -6.92416 q^{31} +1.00000 q^{32} -7.98442 q^{33} -3.31595 q^{34} -1.05814 q^{35} +5.98855 q^{36} -7.15663 q^{37} -2.80855 q^{38} -5.40690 q^{39} -2.44064 q^{40} +0.953394 q^{41} +1.29982 q^{42} +8.60247 q^{43} -2.66317 q^{44} -14.6159 q^{45} -3.30111 q^{46} -5.12634 q^{47} +2.99809 q^{48} -6.81203 q^{49} +0.956705 q^{50} -9.94152 q^{51} -1.80345 q^{52} +10.1070 q^{53} +8.95993 q^{54} +6.49982 q^{55} +0.433551 q^{56} -8.42028 q^{57} -7.23750 q^{58} -1.99384 q^{59} -7.31725 q^{60} -7.73628 q^{61} -6.92416 q^{62} +2.59634 q^{63} +1.00000 q^{64} +4.40156 q^{65} -7.98442 q^{66} -5.20003 q^{67} -3.31595 q^{68} -9.89702 q^{69} -1.05814 q^{70} -1.76385 q^{71} +5.98855 q^{72} +12.1968 q^{73} -7.15663 q^{74} +2.86829 q^{75} -2.80855 q^{76} -1.15462 q^{77} -5.40690 q^{78} +8.31990 q^{79} -2.44064 q^{80} +8.89704 q^{81} +0.953394 q^{82} -3.61740 q^{83} +1.29982 q^{84} +8.09303 q^{85} +8.60247 q^{86} -21.6987 q^{87} -2.66317 q^{88} +5.01505 q^{89} -14.6159 q^{90} -0.781887 q^{91} -3.30111 q^{92} -20.7593 q^{93} -5.12634 q^{94} +6.85464 q^{95} +2.99809 q^{96} -2.79783 q^{97} -6.81203 q^{98} -15.9485 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9}+O(q^{10}) \) 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9	\( 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9} - 20 q^{10} - 13 q^{11} - 11 q^{12} - 51 q^{13} - 40 q^{14} - 31 q^{15} + 67 q^{16} - 34 q^{17} + 24 q^{18} - 33 q^{19} - 20 q^{20} - 39 q^{21} - 13 q^{22} - 43 q^{23} - 11 q^{24} - 9 q^{25} - 51 q^{26} - 29 q^{27} - 40 q^{28} - 63 q^{29} - 31 q^{30} - 43 q^{31} + 67 q^{32} - 49 q^{33} - 34 q^{34} - 20 q^{35} + 24 q^{36} - 77 q^{37} - 33 q^{38} - 40 q^{39} - 20 q^{40} - 50 q^{41} - 39 q^{42} - 56 q^{43} - 13 q^{44} - 48 q^{45} - 43 q^{46} - 48 q^{47} - 11 q^{48} + q^{49} - 9 q^{50} - 18 q^{51} - 51 q^{52} - 91 q^{53} - 29 q^{54} - 58 q^{55} - 40 q^{56} - 65 q^{57} - 63 q^{58} - 17 q^{59} - 31 q^{60} - 45 q^{61} - 43 q^{62} - 67 q^{63} + 67 q^{64} - 65 q^{65} - 49 q^{66} - 112 q^{67} - 34 q^{68} - 57 q^{69} - 20 q^{70} - 75 q^{71} + 24 q^{72} - 79 q^{73} - 77 q^{74} - 5 q^{75} - 33 q^{76} - 85 q^{77} - 40 q^{78} - 80 q^{79} - 20 q^{80} - 77 q^{81} - 50 q^{82} - 22 q^{83} - 39 q^{84} - 134 q^{85} - 56 q^{86} - 49 q^{87} - 13 q^{88} - 77 q^{89} - 48 q^{90} - 17 q^{91} - 43 q^{92} - 97 q^{93} - 48 q^{94} - 73 q^{95} - 11 q^{96} - 87 q^{97} + q^{98} - 44 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9 - 20 * q^10 - 13 * q^11 - 11 * q^12 - 51 * q^13 - 40 * q^14 - 31 * q^15 + 67 * q^16 - 34 * q^17 + 24 * q^18 - 33 * q^19 - 20 * q^20 - 39 * q^21 - 13 * q^22 - 43 * q^23 - 11 * q^24 - 9 * q^25 - 51 * q^26 - 29 * q^27 - 40 * q^28 - 63 * q^29 - 31 * q^30 - 43 * q^31 + 67 * q^32 - 49 * q^33 - 34 * q^34 - 20 * q^35 + 24 * q^36 - 77 * q^37 - 33 * q^38 - 40 * q^39 - 20 * q^40 - 50 * q^41 - 39 * q^42 - 56 * q^43 - 13 * q^44 - 48 * q^45 - 43 * q^46 - 48 * q^47 - 11 * q^48 + q^49 - 9 * q^50 - 18 * q^51 - 51 * q^52 - 91 * q^53 - 29 * q^54 - 58 * q^55 - 40 * q^56 - 65 * q^57 - 63 * q^58 - 17 * q^59 - 31 * q^60 - 45 * q^61 - 43 * q^62 - 67 * q^63 + 67 * q^64 - 65 * q^65 - 49 * q^66 - 112 * q^67 - 34 * q^68 - 57 * q^69 - 20 * q^70 - 75 * q^71 + 24 * q^72 - 79 * q^73 - 77 * q^74 - 5 * q^75 - 33 * q^76 - 85 * q^77 - 40 * q^78 - 80 * q^79 - 20 * q^80 - 77 * q^81 - 50 * q^82 - 22 * q^83 - 39 * q^84 - 134 * q^85 - 56 * q^86 - 49 * q^87 - 13 * q^88 - 77 * q^89 - 48 * q^90 - 17 * q^91 - 43 * q^92 - 97 * q^93 - 48 * q^94 - 73 * q^95 - 11 * q^96 - 87 * q^97 + q^98 - 44 * q^99

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