LMFDB - Embedded newform 8034.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.56155$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{6} -0.561553 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{6} -0.561553 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{10} -2.56155 q^{11} -1.00000 q^{12} -1.00000 q^{13} +0.561553 q^{14} +2.00000 q^{15} +1.00000 q^{16} +3.43845 q^{17} -1.00000 q^{18} -2.00000 q^{19} -2.00000 q^{20} +0.561553 q^{21} +2.56155 q^{22} +3.12311 q^{23} +1.00000 q^{24} -1.00000 q^{25} +1.00000 q^{26} -1.00000 q^{27} -0.561553 q^{28} +6.00000 q^{29} -2.00000 q^{30} +1.12311 q^{31} -1.00000 q^{32} +2.56155 q^{33} -3.43845 q^{34} +1.12311 q^{35} +1.00000 q^{36} -9.12311 q^{37} +2.00000 q^{38} +1.00000 q^{39} +2.00000 q^{40} +2.00000 q^{41} -0.561553 q^{42} +1.12311 q^{43} -2.56155 q^{44} -2.00000 q^{45} -3.12311 q^{46} -10.2462 q^{47} -1.00000 q^{48} -6.68466 q^{49} +1.00000 q^{50} -3.43845 q^{51} -1.00000 q^{52} +6.56155 q^{53} +1.00000 q^{54} +5.12311 q^{55} +0.561553 q^{56} +2.00000 q^{57} -6.00000 q^{58} -8.00000 q^{59} +2.00000 q^{60} +11.1231 q^{61} -1.12311 q^{62} -0.561553 q^{63} +1.00000 q^{64} +2.00000 q^{65} -2.56155 q^{66} +11.6847 q^{67} +3.43845 q^{68} -3.12311 q^{69} -1.12311 q^{70} +2.24621 q^{71} -1.00000 q^{72} +3.68466 q^{73} +9.12311 q^{74} +1.00000 q^{75} -2.00000 q^{76} +1.43845 q^{77} -1.00000 q^{78} +7.36932 q^{79} -2.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} +11.3693 q^{83} +0.561553 q^{84} -6.87689 q^{85} -1.12311 q^{86} -6.00000 q^{87} +2.56155 q^{88} +2.00000 q^{89} +2.00000 q^{90} +0.561553 q^{91} +3.12311 q^{92} -1.12311 q^{93} +10.2462 q^{94} +4.00000 q^{95} +1.00000 q^{96} +4.24621 q^{97} +6.68466 q^{98} -2.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} + 3 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 + 2 * q^6 + 3 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} + 3 q^{7} - 2 q^{8} + 2 q^{9} + 4 q^{10} - q^{11} - 2 q^{12} - 2 q^{13} - 3 q^{14} + 4 q^{15} + 2 q^{16} + 11 q^{17} - 2 q^{18} - 4 q^{19} - 4 q^{20} - 3 q^{21} + q^{22} - 2 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26} - 2 q^{27} + 3 q^{28} + 12 q^{29} - 4 q^{30} - 6 q^{31} - 2 q^{32} + q^{33} - 11 q^{34} - 6 q^{35} + 2 q^{36} - 10 q^{37} + 4 q^{38} + 2 q^{39} + 4 q^{40} + 4 q^{41} + 3 q^{42} - 6 q^{43} - q^{44} - 4 q^{45} + 2 q^{46} - 4 q^{47} - 2 q^{48} - q^{49} + 2 q^{50} - 11 q^{51} - 2 q^{52} + 9 q^{53} + 2 q^{54} + 2 q^{55} - 3 q^{56} + 4 q^{57} - 12 q^{58} - 16 q^{59} + 4 q^{60} + 14 q^{61} + 6 q^{62} + 3 q^{63} + 2 q^{64} + 4 q^{65} - q^{66} + 11 q^{67} + 11 q^{68} + 2 q^{69} + 6 q^{70} - 12 q^{71} - 2 q^{72} - 5 q^{73} + 10 q^{74} + 2 q^{75} - 4 q^{76} + 7 q^{77} - 2 q^{78} - 10 q^{79} - 4 q^{80} + 2 q^{81} - 4 q^{82} - 2 q^{83} - 3 q^{84} - 22 q^{85} + 6 q^{86} - 12 q^{87} + q^{88} + 4 q^{89} + 4 q^{90} - 3 q^{91} - 2 q^{92} + 6 q^{93} + 4 q^{94} + 8 q^{95} + 2 q^{96} - 8 q^{97} + q^{98} - q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 + 2 * q^6 + 3 * q^7 - 2 * q^8 + 2 * q^9 + 4 * q^10 - q^11 - 2 * q^12 - 2 * q^13 - 3 * q^14 + 4 * q^15 + 2 * q^16 + 11 * q^17 - 2 * q^18 - 4 * q^19 - 4 * q^20 - 3 * q^21 + q^22 - 2 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 - 2 * q^27 + 3 * q^28 + 12 * q^29 - 4 * q^30 - 6 * q^31 - 2 * q^32 + q^33 - 11 * q^34 - 6 * q^35 + 2 * q^36 - 10 * q^37 + 4 * q^38 + 2 * q^39 + 4 * q^40 + 4 * q^41 + 3 * q^42 - 6 * q^43 - q^44 - 4 * q^45 + 2 * q^46 - 4 * q^47 - 2 * q^48 - q^49 + 2 * q^50 - 11 * q^51 - 2 * q^52 + 9 * q^53 + 2 * q^54 + 2 * q^55 - 3 * q^56 + 4 * q^57 - 12 * q^58 - 16 * q^59 + 4 * q^60 + 14 * q^61 + 6 * q^62 + 3 * q^63 + 2 * q^64 + 4 * q^65 - q^66 + 11 * q^67 + 11 * q^68 + 2 * q^69 + 6 * q^70 - 12 * q^71 - 2 * q^72 - 5 * q^73 + 10 * q^74 + 2 * q^75 - 4 * q^76 + 7 * q^77 - 2 * q^78 - 10 * q^79 - 4 * q^80 + 2 * q^81 - 4 * q^82 - 2 * q^83 - 3 * q^84 - 22 * q^85 + 6 * q^86 - 12 * q^87 + q^88 + 4 * q^89 + 4 * q^90 - 3 * q^91 - 2 * q^92 + 6 * q^93 + 4 * q^94 + 8 * q^95 + 2 * q^96 - 8 * q^97 + q^98 - 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	1.00000	0.408248
$7$	−0.561553	−0.212247	−0.106124	−	0.994353i	$-0.533844\pi$
$7$	−0.561553	−0.212247	−0.106124	+	0.994353i	$0.533844\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.00000	0.632456
$11$	−2.56155	−0.772337	−0.386169	−	0.922428i	$-0.626202\pi$
$11$	−2.56155	−0.772337	−0.386169	+	0.922428i	$0.626202\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.561553	0.150081
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	3.43845	0.833946	0.416973	−	0.908919i	$-0.363091\pi$
$17$	3.43845	0.833946	0.416973	+	0.908919i	$0.363091\pi$
$18$	−1.00000	−0.235702
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	−2.00000	−0.447214
$21$	0.561553	0.122541
$22$	2.56155	0.546125
$23$	3.12311	0.651213	0.325606	−	0.945505i	$-0.394432\pi$
$23$	3.12311	0.651213	0.325606	+	0.945505i	$0.394432\pi$
$24$	1.00000	0.204124
$25$	−1.00000	−0.200000
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	−0.561553	−0.106124
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	−2.00000	−0.365148
$31$	1.12311	0.201716	0.100858	−	0.994901i	$-0.467841\pi$
$31$	1.12311	0.201716	0.100858	+	0.994901i	$0.467841\pi$
$32$	−1.00000	−0.176777
$33$	2.56155	0.445909
$34$	−3.43845	−0.589689
$35$	1.12311	0.189839
$36$	1.00000	0.166667
$37$	−9.12311	−1.49983	−0.749915	−	0.661535i	$-0.769905\pi$
$37$	−9.12311	−1.49983	−0.749915	+	0.661535i	$0.769905\pi$
$38$	2.00000	0.324443
$39$	1.00000	0.160128
$40$	2.00000	0.316228
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	−0.561553	−0.0866495
$43$	1.12311	0.171272	0.0856360	−	0.996326i	$-0.472708\pi$
$43$	1.12311	0.171272	0.0856360	+	0.996326i	$0.472708\pi$
$44$	−2.56155	−0.386169
$45$	−2.00000	−0.298142
$46$	−3.12311	−0.460477
$47$	−10.2462	−1.49456	−0.747282	−	0.664507i	$-0.768641\pi$
$47$	−10.2462	−1.49456	−0.747282	+	0.664507i	$0.768641\pi$
$48$	−1.00000	−0.144338
$49$	−6.68466	−0.954951
$50$	1.00000	0.141421
$51$	−3.43845	−0.481479
$52$	−1.00000	−0.138675
$53$	6.56155	0.901299	0.450649	−	0.892701i	$-0.351193\pi$
$53$	6.56155	0.901299	0.450649	+	0.892701i	$0.351193\pi$
$54$	1.00000	0.136083
$55$	5.12311	0.690799
$56$	0.561553	0.0750407
$57$	2.00000	0.264906
$58$	−6.00000	−0.787839
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	2.00000	0.258199
$61$	11.1231	1.42417	0.712084	−	0.702094i	$-0.247752\pi$
$61$	11.1231	1.42417	0.712084	+	0.702094i	$0.247752\pi$
$62$	−1.12311	−0.142635
$63$	−0.561553	−0.0707490
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	−2.56155	−0.315305
$67$	11.6847	1.42751	0.713754	−	0.700396i	$-0.246993\pi$
$67$	11.6847	1.42751	0.713754	+	0.700396i	$0.246993\pi$
$68$	3.43845	0.416973
$69$	−3.12311	−0.375978
$70$	−1.12311	−0.134237
$71$	2.24621	0.266576	0.133288	−	0.991077i	$-0.457446\pi$
$71$	2.24621	0.266576	0.133288	+	0.991077i	$0.457446\pi$
$72$	−1.00000	−0.117851
$73$	3.68466	0.431257	0.215628	−	0.976476i	$-0.430820\pi$
$73$	3.68466	0.431257	0.215628	+	0.976476i	$0.430820\pi$
$74$	9.12311	1.06054
$75$	1.00000	0.115470
$76$	−2.00000	−0.229416
$77$	1.43845	0.163926
$78$	−1.00000	−0.113228
$79$	7.36932	0.829113	0.414556	−	0.910024i	$-0.363937\pi$
$79$	7.36932	0.829113	0.414556	+	0.910024i	$0.363937\pi$
$80$	−2.00000	−0.223607
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	11.3693	1.24794	0.623972	−	0.781446i	$-0.285518\pi$
$83$	11.3693	1.24794	0.623972	+	0.781446i	$0.285518\pi$
$84$	0.561553	0.0612704
$85$	−6.87689	−0.745904
$86$	−1.12311	−0.121108
$87$	−6.00000	−0.643268
$88$	2.56155	0.273062
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	2.00000	0.210819
$91$	0.561553	0.0588667
$92$	3.12311	0.325606
$93$	−1.12311	−0.116461
$94$	10.2462	1.05682
$95$	4.00000	0.410391
$96$	1.00000	0.102062
$97$	4.24621	0.431137	0.215569	−	0.976489i	$-0.430839\pi$
$97$	4.24621	0.431137	0.215569	+	0.976489i	$0.430839\pi$
$98$	6.68466	0.675252
$99$	−2.56155	−0.257446
$100$	−1.00000	−0.100000
$101$	−3.68466	−0.366637	−0.183319	−	0.983054i	$-0.558684\pi$
$101$	−3.68466	−0.366637	−0.183319	+	0.983054i	$0.558684\pi$
$102$	3.43845	0.340457
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	−1.12311	−0.109604
$106$	−6.56155	−0.637314
$107$	8.56155	0.827677	0.413838	−	0.910350i	$-0.364188\pi$
$107$	8.56155	0.827677	0.413838	+	0.910350i	$0.364188\pi$
$108$	−1.00000	−0.0962250
$109$	−6.24621	−0.598279	−0.299139	−	0.954209i	$-0.596700\pi$
$109$	−6.24621	−0.598279	−0.299139	+	0.954209i	$0.596700\pi$
$110$	−5.12311	−0.488469
$111$	9.12311	0.865927
$112$	−0.561553	−0.0530618
$113$	4.00000	0.376288	0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000	0.376288	0.188144	+	0.982141i	$0.439753\pi$
$114$	−2.00000	−0.187317
$115$	−6.24621	−0.582462
$116$	6.00000	0.557086
$117$	−1.00000	−0.0924500
$118$	8.00000	0.736460
$119$	−1.93087	−0.177003
$120$	−2.00000	−0.182574
$121$	−4.43845	−0.403495
$122$	−11.1231	−1.00704
$123$	−2.00000	−0.180334
$124$	1.12311	0.100858
$125$	12.0000	1.07331
$126$	0.561553	0.0500271
$127$	−11.6847	−1.03685	−0.518423	−	0.855124i	$-0.673481\pi$
$127$	−11.6847	−1.03685	−0.518423	+	0.855124i	$0.673481\pi$
$128$	−1.00000	−0.0883883
$129$	−1.12311	−0.0988839
$130$	−2.00000	−0.175412
$131$	21.3693	1.86705	0.933523	−	0.358518i	$-0.116718\pi$
$131$	21.3693	1.86705	0.933523	+	0.358518i	$0.116718\pi$
$132$	2.56155	0.222955
$133$	1.12311	0.0973856
$134$	−11.6847	−1.00940
$135$	2.00000	0.172133
$136$	−3.43845	−0.294844
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	3.12311	0.265856
$139$	−12.8078	−1.08634	−0.543170	−	0.839623i	$-0.682776\pi$
$139$	−12.8078	−1.08634	−0.543170	+	0.839623i	$0.682776\pi$
$140$	1.12311	0.0949197
$141$	10.2462	0.862887
$142$	−2.24621	−0.188498
$143$	2.56155	0.214208
$144$	1.00000	0.0833333
$145$	−12.0000	−0.996546
$146$	−3.68466	−0.304945
$147$	6.68466	0.551341
$148$	−9.12311	−0.749915
$149$	6.31534	0.517373	0.258686	−	0.965961i	$-0.416710\pi$
$149$	6.31534	0.517373	0.258686	+	0.965961i	$0.416710\pi$
$150$	−1.00000	−0.0816497
$151$	−7.36932	−0.599707	−0.299853	−	0.953985i	$-0.596938\pi$
$151$	−7.36932	−0.599707	−0.299853	+	0.953985i	$0.596938\pi$
$152$	2.00000	0.162221
$153$	3.43845	0.277982
$154$	−1.43845	−0.115913
$155$	−2.24621	−0.180420
$156$	1.00000	0.0800641
$157$	−6.80776	−0.543319	−0.271659	−	0.962393i	$-0.587572\pi$
$157$	−6.80776	−0.543319	−0.271659	+	0.962393i	$0.587572\pi$
$158$	−7.36932	−0.586271
$159$	−6.56155	−0.520365
$160$	2.00000	0.158114
$161$	−1.75379	−0.138218
$162$	−1.00000	−0.0785674
$163$	−22.4924	−1.76174	−0.880871	−	0.473356i	$-0.843042\pi$
$163$	−22.4924	−1.76174	−0.880871	+	0.473356i	$0.843042\pi$
$164$	2.00000	0.156174
$165$	−5.12311	−0.398833
$166$	−11.3693	−0.882430
$167$	−3.19224	−0.247023	−0.123511	−	0.992343i	$-0.539416\pi$
$167$	−3.19224	−0.247023	−0.123511	+	0.992343i	$0.539416\pi$
$168$	−0.561553	−0.0433247
$169$	1.00000	0.0769231
$170$	6.87689	0.527434
$171$	−2.00000	−0.152944
$172$	1.12311	0.0856360
$173$	20.8078	1.58199	0.790993	−	0.611826i	$-0.209565\pi$
$173$	20.8078	1.58199	0.790993	+	0.611826i	$0.209565\pi$
$174$	6.00000	0.454859
$175$	0.561553	0.0424494
$176$	−2.56155	−0.193084
$177$	8.00000	0.601317
$178$	−2.00000	−0.149906
$179$	−10.8078	−0.807810	−0.403905	−	0.914801i	$-0.632347\pi$
$179$	−10.8078	−0.807810	−0.403905	+	0.914801i	$0.632347\pi$
$180$	−2.00000	−0.149071
$181$	15.9309	1.18413	0.592066	−	0.805889i	$-0.298312\pi$
$181$	15.9309	1.18413	0.592066	+	0.805889i	$0.298312\pi$
$182$	−0.561553	−0.0416251
$183$	−11.1231	−0.822244
$184$	−3.12311	−0.230238
$185$	18.2462	1.34149
$186$	1.12311	0.0823501
$187$	−8.80776	−0.644087
$188$	−10.2462	−0.747282
$189$	0.561553	0.0408470
$190$	−4.00000	−0.290191
$191$	−3.68466	−0.266613	−0.133306	−	0.991075i	$-0.542559\pi$
$191$	−3.68466	−0.266613	−0.133306	+	0.991075i	$0.542559\pi$
$192$	−1.00000	−0.0721688
$193$	−0.630683	−0.0453976	−0.0226988	−	0.999742i	$-0.507226\pi$
$193$	−0.630683	−0.0453976	−0.0226988	+	0.999742i	$0.507226\pi$
$194$	−4.24621	−0.304860
$195$	−2.00000	−0.143223
$196$	−6.68466	−0.477476
$197$	18.4924	1.31753	0.658765	−	0.752349i	$-0.271079\pi$
$197$	18.4924	1.31753	0.658765	+	0.752349i	$0.271079\pi$
$198$	2.56155	0.182042
$199$	−19.6847	−1.39541	−0.697704	−	0.716386i	$-0.745795\pi$
$199$	−19.6847	−1.39541	−0.697704	+	0.716386i	$0.745795\pi$
$200$	1.00000	0.0707107
$201$	−11.6847	−0.824172
$202$	3.68466	0.259252
$203$	−3.36932	−0.236480
$204$	−3.43845	−0.240739
$205$	−4.00000	−0.279372
$206$	1.00000	0.0696733
$207$	3.12311	0.217071
$208$	−1.00000	−0.0693375
$209$	5.12311	0.354373
$210$	1.12311	0.0775017
$211$	8.49242	0.584642	0.292321	−	0.956320i	$-0.405572\pi$
$211$	8.49242	0.584642	0.292321	+	0.956320i	$0.405572\pi$
$212$	6.56155	0.450649
$213$	−2.24621	−0.153908
$214$	−8.56155	−0.585256
$215$	−2.24621	−0.153190
$216$	1.00000	0.0680414
$217$	−0.630683	−0.0428136
$218$	6.24621	0.423047
$219$	−3.68466	−0.248986
$220$	5.12311	0.345400
$221$	−3.43845	−0.231295
$222$	−9.12311	−0.612303
$223$	−5.68466	−0.380673	−0.190336	−	0.981719i	$-0.560958\pi$
$223$	−5.68466	−0.380673	−0.190336	+	0.981719i	$0.560958\pi$
$224$	0.561553	0.0375203
$225$	−1.00000	−0.0666667
$226$	−4.00000	−0.266076
$227$	−4.80776	−0.319103	−0.159551	−	0.987190i	$-0.551005\pi$
$227$	−4.80776	−0.319103	−0.159551	+	0.987190i	$0.551005\pi$
$228$	2.00000	0.132453
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	6.24621	0.411863
$231$	−1.43845	−0.0946429
$232$	−6.00000	−0.393919
$233$	24.4924	1.60455	0.802276	−	0.596953i	$-0.203622\pi$
$233$	24.4924	1.60455	0.802276	+	0.596953i	$0.203622\pi$
$234$	1.00000	0.0653720
$235$	20.4924	1.33678
$236$	−8.00000	−0.520756
$237$	−7.36932	−0.478689
$238$	1.93087	0.125160
$239$	−2.56155	−0.165693	−0.0828465	−	0.996562i	$-0.526401\pi$
$239$	−2.56155	−0.165693	−0.0828465	+	0.996562i	$0.526401\pi$
$240$	2.00000	0.129099
$241$	−8.31534	−0.535638	−0.267819	−	0.963469i	$-0.586303\pi$
$241$	−8.31534	−0.535638	−0.267819	+	0.963469i	$0.586303\pi$
$242$	4.43845	0.285314
$243$	−1.00000	−0.0641500
$244$	11.1231	0.712084
$245$	13.3693	0.854134
$246$	2.00000	0.127515
$247$	2.00000	0.127257
$248$	−1.12311	−0.0713173
$249$	−11.3693	−0.720501
$250$	−12.0000	−0.758947
$251$	5.75379	0.363176	0.181588	−	0.983375i	$-0.441876\pi$
$251$	5.75379	0.363176	0.181588	+	0.983375i	$0.441876\pi$
$252$	−0.561553	−0.0353745
$253$	−8.00000	−0.502956
$254$	11.6847	0.733161
$255$	6.87689	0.430648
$256$	1.00000	0.0625000
$257$	21.1231	1.31762	0.658812	−	0.752308i	$-0.271059\pi$
$257$	21.1231	1.31762	0.658812	+	0.752308i	$0.271059\pi$
$258$	1.12311	0.0699215
$259$	5.12311	0.318334
$260$	2.00000	0.124035
$261$	6.00000	0.371391
$262$	−21.3693	−1.32020
$263$	0.315342	0.0194448	0.00972240	−	0.999953i	$-0.496905\pi$
$263$	0.315342	0.0194448	0.00972240	+	0.999953i	$0.496905\pi$
$264$	−2.56155	−0.157653
$265$	−13.1231	−0.806146
$266$	−1.12311	−0.0688620
$267$	−2.00000	−0.122398
$268$	11.6847	0.713754
$269$	−11.7538	−0.716641	−0.358321	−	0.933599i	$-0.616651\pi$
$269$	−11.7538	−0.716641	−0.358321	+	0.933599i	$0.616651\pi$
$270$	−2.00000	−0.121716
$271$	−11.3693	−0.690637	−0.345318	−	0.938486i	$-0.612229\pi$
$271$	−11.3693	−0.690637	−0.345318	+	0.938486i	$0.612229\pi$
$272$	3.43845	0.208486
$273$	−0.561553	−0.0339867
$274$	6.00000	0.362473
$275$	2.56155	0.154467
$276$	−3.12311	−0.187989
$277$	6.00000	0.360505	0.180253	−	0.983620i	$-0.442309\pi$
$277$	6.00000	0.360505	0.180253	+	0.983620i	$0.442309\pi$
$278$	12.8078	0.768159
$279$	1.12311	0.0672386
$280$	−1.12311	−0.0671184
$281$	−22.4924	−1.34179	−0.670893	−	0.741554i	$-0.734089\pi$
$281$	−22.4924	−1.34179	−0.670893	+	0.741554i	$0.734089\pi$
$282$	−10.2462	−0.610153
$283$	21.6155	1.28491	0.642455	−	0.766324i	$-0.277916\pi$
$283$	21.6155	1.28491	0.642455	+	0.766324i	$0.277916\pi$
$284$	2.24621	0.133288
$285$	−4.00000	−0.236940
$286$	−2.56155	−0.151468
$287$	−1.12311	−0.0662948
$288$	−1.00000	−0.0589256
$289$	−5.17708	−0.304534
$290$	12.0000	0.704664
$291$	−4.24621	−0.248917
$292$	3.68466	0.215628
$293$	−7.61553	−0.444904	−0.222452	−	0.974944i	$-0.571406\pi$
$293$	−7.61553	−0.444904	−0.222452	+	0.974944i	$0.571406\pi$
$294$	−6.68466	−0.389857
$295$	16.0000	0.931556
$296$	9.12311	0.530270
$297$	2.56155	0.148636
$298$	−6.31534	−0.365838
$299$	−3.12311	−0.180614
$300$	1.00000	0.0577350
$301$	−0.630683	−0.0363520
$302$	7.36932	0.424057
$303$	3.68466	0.211678
$304$	−2.00000	−0.114708
$305$	−22.2462	−1.27381
$306$	−3.43845	−0.196563
$307$	21.4384	1.22356	0.611778	−	0.791029i	$-0.290454\pi$
$307$	21.4384	1.22356	0.611778	+	0.791029i	$0.290454\pi$
$308$	1.43845	0.0819631
$309$	1.00000	0.0568880
$310$	2.24621	0.127576
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	−1.00000	−0.0566139
$313$	−16.2462	−0.918290	−0.459145	−	0.888361i	$-0.651844\pi$
$313$	−16.2462	−0.918290	−0.459145	+	0.888361i	$0.651844\pi$
$314$	6.80776	0.384184
$315$	1.12311	0.0632798
$316$	7.36932	0.414556
$317$	−13.0540	−0.733184	−0.366592	−	0.930382i	$-0.619476\pi$
$317$	−13.0540	−0.733184	−0.366592	+	0.930382i	$0.619476\pi$
$318$	6.56155	0.367954
$319$	−15.3693	−0.860517
$320$	−2.00000	−0.111803
$321$	−8.56155	−0.477859
$322$	1.75379	0.0977348
$323$	−6.87689	−0.382641
$324$	1.00000	0.0555556
$325$	1.00000	0.0554700
$326$	22.4924	1.24574
$327$	6.24621	0.345416
$328$	−2.00000	−0.110432
$329$	5.75379	0.317217
$330$	5.12311	0.282018
$331$	21.9309	1.20543	0.602715	−	0.797957i	$-0.294086\pi$
$331$	21.9309	1.20543	0.602715	+	0.797957i	$0.294086\pi$
$332$	11.3693	0.623972
$333$	−9.12311	−0.499943
$334$	3.19224	0.174671
$335$	−23.3693	−1.27680
$336$	0.561553	0.0306352
$337$	−27.9309	−1.52149	−0.760746	−	0.649050i	$-0.775167\pi$
$337$	−27.9309	−1.52149	−0.760746	+	0.649050i	$0.775167\pi$
$338$	−1.00000	−0.0543928
$339$	−4.00000	−0.217250
$340$	−6.87689	−0.372952
$341$	−2.87689	−0.155793
$342$	2.00000	0.108148
$343$	7.68466	0.414933
$344$	−1.12311	−0.0605538
$345$	6.24621	0.336285
$346$	−20.8078	−1.11863
$347$	−16.8769	−0.905999	−0.453000	−	0.891511i	$-0.649646\pi$
$347$	−16.8769	−0.905999	−0.453000	+	0.891511i	$0.649646\pi$
$348$	−6.00000	−0.321634
$349$	1.75379	0.0938782	0.0469391	−	0.998898i	$-0.485053\pi$
$349$	1.75379	0.0938782	0.0469391	+	0.998898i	$0.485053\pi$
$350$	−0.561553	−0.0300163
$351$	1.00000	0.0533761
$352$	2.56155	0.136531
$353$	−14.3153	−0.761929	−0.380964	−	0.924590i	$-0.624408\pi$
$353$	−14.3153	−0.761929	−0.380964	+	0.924590i	$0.624408\pi$
$354$	−8.00000	−0.425195
$355$	−4.49242	−0.238433
$356$	2.00000	0.106000
$357$	1.93087	0.102192
$358$	10.8078	0.571208
$359$	19.0540	1.00563	0.502815	−	0.864394i	$-0.332298\pi$
$359$	19.0540	1.00563	0.502815	+	0.864394i	$0.332298\pi$
$360$	2.00000	0.105409
$361$	−15.0000	−0.789474
$362$	−15.9309	−0.837308
$363$	4.43845	0.232958
$364$	0.561553	0.0294334
$365$	−7.36932	−0.385728
$366$	11.1231	0.581414
$367$	−13.7538	−0.717942	−0.358971	−	0.933349i	$-0.616872\pi$
$367$	−13.7538	−0.717942	−0.358971	+	0.933349i	$0.616872\pi$
$368$	3.12311	0.162803
$369$	2.00000	0.104116
$370$	−18.2462	−0.948575
$371$	−3.68466	−0.191298
$372$	−1.12311	−0.0582303
$373$	−29.3693	−1.52069	−0.760343	−	0.649522i	$-0.774969\pi$
$373$	−29.3693	−1.52069	−0.760343	+	0.649522i	$0.774969\pi$
$374$	8.80776	0.455439
$375$	−12.0000	−0.619677
$376$	10.2462	0.528408
$377$	−6.00000	−0.309016
$378$	−0.561553	−0.0288832
$379$	−12.8078	−0.657891	−0.328945	−	0.944349i	$-0.606693\pi$
$379$	−12.8078	−0.657891	−0.328945	+	0.944349i	$0.606693\pi$
$380$	4.00000	0.205196
$381$	11.6847	0.598623
$382$	3.68466	0.188524
$383$	4.49242	0.229552	0.114776	−	0.993391i	$-0.463385\pi$
$383$	4.49242	0.229552	0.114776	+	0.993391i	$0.463385\pi$
$384$	1.00000	0.0510310
$385$	−2.87689	−0.146620
$386$	0.630683	0.0321009
$387$	1.12311	0.0570907
$388$	4.24621	0.215569
$389$	2.56155	0.129876	0.0649379	−	0.997889i	$-0.479315\pi$
$389$	2.56155	0.129876	0.0649379	+	0.997889i	$0.479315\pi$
$390$	2.00000	0.101274
$391$	10.7386	0.543076
$392$	6.68466	0.337626
$393$	−21.3693	−1.07794
$394$	−18.4924	−0.931635
$395$	−14.7386	−0.741581
$396$	−2.56155	−0.128723
$397$	17.6155	0.884098	0.442049	−	0.896991i	$-0.354252\pi$
$397$	17.6155	0.884098	0.442049	+	0.896991i	$0.354252\pi$
$398$	19.6847	0.986703
$399$	−1.12311	−0.0562256
$400$	−1.00000	−0.0500000
$401$	5.36932	0.268131	0.134065	−	0.990972i	$-0.457197\pi$
$401$	5.36932	0.268131	0.134065	+	0.990972i	$0.457197\pi$
$402$	11.6847	0.582778
$403$	−1.12311	−0.0559459
$404$	−3.68466	−0.183319
$405$	−2.00000	−0.0993808
$406$	3.36932	0.167216
$407$	23.3693	1.15837
$408$	3.43845	0.170229
$409$	21.3693	1.05664	0.528322	−	0.849044i	$-0.322821\pi$
$409$	21.3693	1.05664	0.528322	+	0.849044i	$0.322821\pi$
$410$	4.00000	0.197546
$411$	6.00000	0.295958
$412$	−1.00000	−0.0492665
$413$	4.49242	0.221058
$414$	−3.12311	−0.153492
$415$	−22.7386	−1.11620
$416$	1.00000	0.0490290
$417$	12.8078	0.627199
$418$	−5.12311	−0.250579
$419$	−19.9309	−0.973687	−0.486843	−	0.873489i	$-0.661852\pi$
$419$	−19.9309	−0.973687	−0.486843	+	0.873489i	$0.661852\pi$
$420$	−1.12311	−0.0548019
$421$	17.0540	0.831160	0.415580	−	0.909557i	$-0.363579\pi$
$421$	17.0540	0.831160	0.415580	+	0.909557i	$0.363579\pi$
$422$	−8.49242	−0.413405
$423$	−10.2462	−0.498188
$424$	−6.56155	−0.318657
$425$	−3.43845	−0.166789
$426$	2.24621	0.108829
$427$	−6.24621	−0.302275
$428$	8.56155	0.413838
$429$	−2.56155	−0.123673
$430$	2.24621	0.108322
$431$	−32.0000	−1.54139	−0.770693	−	0.637207i	$-0.780090\pi$
$431$	−32.0000	−1.54139	−0.770693	+	0.637207i	$0.780090\pi$
$432$	−1.00000	−0.0481125
$433$	−22.4924	−1.08092	−0.540458	−	0.841371i	$-0.681749\pi$
$433$	−22.4924	−1.08092	−0.540458	+	0.841371i	$0.681749\pi$
$434$	0.630683	0.0302738
$435$	12.0000	0.575356
$436$	−6.24621	−0.299139
$437$	−6.24621	−0.298797
$438$	3.68466	0.176060
$439$	−11.0540	−0.527577	−0.263789	−	0.964580i	$-0.584972\pi$
$439$	−11.0540	−0.527577	−0.263789	+	0.964580i	$0.584972\pi$
$440$	−5.12311	−0.244234
$441$	−6.68466	−0.318317
$442$	3.43845	0.163550
$443$	−12.4924	−0.593533	−0.296766	−	0.954950i	$-0.595908\pi$
$443$	−12.4924	−0.593533	−0.296766	+	0.954950i	$0.595908\pi$
$444$	9.12311	0.432963
$445$	−4.00000	−0.189618
$446$	5.68466	0.269176
$447$	−6.31534	−0.298705
$448$	−0.561553	−0.0265309
$449$	−26.3153	−1.24190	−0.620949	−	0.783851i	$-0.713253\pi$
$449$	−26.3153	−1.24190	−0.620949	+	0.783851i	$0.713253\pi$
$450$	1.00000	0.0471405
$451$	−5.12311	−0.241238
$452$	4.00000	0.188144
$453$	7.36932	0.346241
$454$	4.80776	0.225640
$455$	−1.12311	−0.0526520
$456$	−2.00000	−0.0936586
$457$	8.63068	0.403726	0.201863	−	0.979414i	$-0.435300\pi$
$457$	8.63068	0.403726	0.201863	+	0.979414i	$0.435300\pi$
$458$	6.00000	0.280362
$459$	−3.43845	−0.160493
$460$	−6.24621	−0.291231
$461$	8.24621	0.384064	0.192032	−	0.981389i	$-0.438492\pi$
$461$	8.24621	0.384064	0.192032	+	0.981389i	$0.438492\pi$
$462$	1.43845	0.0669226
$463$	13.1231	0.609882	0.304941	−	0.952371i	$-0.401363\pi$
$463$	13.1231	0.609882	0.304941	+	0.952371i	$0.401363\pi$
$464$	6.00000	0.278543
$465$	2.24621	0.104166
$466$	−24.4924	−1.13459
$467$	−38.1771	−1.76662	−0.883312	−	0.468785i	$-0.844692\pi$
$467$	−38.1771	−1.76662	−0.883312	+	0.468785i	$0.844692\pi$
$468$	−1.00000	−0.0462250
$469$	−6.56155	−0.302984
$470$	−20.4924	−0.945245
$471$	6.80776	0.313685
$472$	8.00000	0.368230
$473$	−2.87689	−0.132280
$474$	7.36932	0.338484
$475$	2.00000	0.0917663
$476$	−1.93087	−0.0885013
$477$	6.56155	0.300433
$478$	2.56155	0.117163
$479$	−5.12311	−0.234081	−0.117040	−	0.993127i	$-0.537341\pi$
$479$	−5.12311	−0.234081	−0.117040	+	0.993127i	$0.537341\pi$
$480$	−2.00000	−0.0912871
$481$	9.12311	0.415978
$482$	8.31534	0.378753
$483$	1.75379	0.0798002
$484$	−4.43845	−0.201748
$485$	−8.49242	−0.385621
$486$	1.00000	0.0453609
$487$	5.61553	0.254464	0.127232	−	0.991873i	$-0.459391\pi$
$487$	5.61553	0.254464	0.127232	+	0.991873i	$0.459391\pi$
$488$	−11.1231	−0.503519
$489$	22.4924	1.01714
$490$	−13.3693	−0.603964
$491$	15.4384	0.696727	0.348364	−	0.937359i	$-0.386737\pi$
$491$	15.4384	0.696727	0.348364	+	0.937359i	$0.386737\pi$
$492$	−2.00000	−0.0901670
$493$	20.6307	0.929159
$494$	−2.00000	−0.0899843
$495$	5.12311	0.230266
$496$	1.12311	0.0504289
$497$	−1.26137	−0.0565800
$498$	11.3693	0.509471
$499$	22.7386	1.01792	0.508961	−	0.860790i	$-0.330030\pi$
$499$	22.7386	1.01792	0.508961	+	0.860790i	$0.330030\pi$
$500$	12.0000	0.536656
$501$	3.19224	0.142619
$502$	−5.75379	−0.256804
$503$	−10.6307	−0.473999	−0.236999	−	0.971510i	$-0.576164\pi$
$503$	−10.6307	−0.473999	−0.236999	+	0.971510i	$0.576164\pi$
$504$	0.561553	0.0250136
$505$	7.36932	0.327930
$506$	8.00000	0.355643
$507$	−1.00000	−0.0444116
$508$	−11.6847	−0.518423
$509$	7.93087	0.351530	0.175765	−	0.984432i	$-0.443760\pi$
$509$	7.93087	0.351530	0.175765	+	0.984432i	$0.443760\pi$
$510$	−6.87689	−0.304514
$511$	−2.06913	−0.0915329
$512$	−1.00000	−0.0441942
$513$	2.00000	0.0883022
$514$	−21.1231	−0.931700
$515$	2.00000	0.0881305
$516$	−1.12311	−0.0494420
$517$	26.2462	1.15431
$518$	−5.12311	−0.225096
$519$	−20.8078	−0.913359
$520$	−2.00000	−0.0877058
$521$	6.87689	0.301282	0.150641	−	0.988589i	$-0.451866\pi$
$521$	6.87689	0.301282	0.150641	+	0.988589i	$0.451866\pi$
$522$	−6.00000	−0.262613
$523$	−26.5616	−1.16146	−0.580728	−	0.814098i	$-0.697232\pi$
$523$	−26.5616	−1.16146	−0.580728	+	0.814098i	$0.697232\pi$
$524$	21.3693	0.933523
$525$	−0.561553	−0.0245082
$526$	−0.315342	−0.0137495
$527$	3.86174	0.168220
$528$	2.56155	0.111477
$529$	−13.2462	−0.575922
$530$	13.1231	0.570031
$531$	−8.00000	−0.347170
$532$	1.12311	0.0486928
$533$	−2.00000	−0.0866296
$534$	2.00000	0.0865485
$535$	−17.1231	−0.740296
$536$	−11.6847	−0.504700
$537$	10.8078	0.466389
$538$	11.7538	0.506742
$539$	17.1231	0.737544
$540$	2.00000	0.0860663
$541$	−16.5616	−0.712037	−0.356018	−	0.934479i	$-0.615866\pi$
$541$	−16.5616	−0.712037	−0.356018	+	0.934479i	$0.615866\pi$
$542$	11.3693	0.488354
$543$	−15.9309	−0.683659
$544$	−3.43845	−0.147422
$545$	12.4924	0.535117
$546$	0.561553	0.0240322
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	−6.00000	−0.256307
$549$	11.1231	0.474723
$550$	−2.56155	−0.109225
$551$	−12.0000	−0.511217
$552$	3.12311	0.132928
$553$	−4.13826	−0.175977
$554$	−6.00000	−0.254916
$555$	−18.2462	−0.774509
$556$	−12.8078	−0.543170
$557$	4.87689	0.206641	0.103320	−	0.994648i	$-0.467053\pi$
$557$	4.87689	0.206641	0.103320	+	0.994648i	$0.467053\pi$
$558$	−1.12311	−0.0475449
$559$	−1.12311	−0.0475023
$560$	1.12311	0.0474599
$561$	8.80776	0.371864
$562$	22.4924	0.948786
$563$	33.6155	1.41673	0.708363	−	0.705849i	$-0.249434\pi$
$563$	33.6155	1.41673	0.708363	+	0.705849i	$0.249434\pi$
$564$	10.2462	0.431443
$565$	−8.00000	−0.336563
$566$	−21.6155	−0.908568
$567$	−0.561553	−0.0235830
$568$	−2.24621	−0.0942489
$569$	0.630683	0.0264396	0.0132198	−	0.999913i	$-0.495792\pi$
$569$	0.630683	0.0264396	0.0132198	+	0.999913i	$0.495792\pi$
$570$	4.00000	0.167542
$571$	−26.2462	−1.09837	−0.549185	−	0.835701i	$-0.685062\pi$
$571$	−26.2462	−1.09837	−0.549185	+	0.835701i	$0.685062\pi$
$572$	2.56155	0.107104
$573$	3.68466	0.153929
$574$	1.12311	0.0468775
$575$	−3.12311	−0.130243
$576$	1.00000	0.0416667
$577$	−20.8078	−0.866239	−0.433119	−	0.901337i	$-0.642587\pi$
$577$	−20.8078	−0.866239	−0.433119	+	0.901337i	$0.642587\pi$
$578$	5.17708	0.215338
$579$	0.630683	0.0262103
$580$	−12.0000	−0.498273
$581$	−6.38447	−0.264873
$582$	4.24621	0.176011
$583$	−16.8078	−0.696106
$584$	−3.68466	−0.152472
$585$	2.00000	0.0826898
$586$	7.61553	0.314595
$587$	−36.4924	−1.50620	−0.753102	−	0.657904i	$-0.771443\pi$
$587$	−36.4924	−1.50620	−0.753102	+	0.657904i	$0.771443\pi$
$588$	6.68466	0.275671
$589$	−2.24621	−0.0925535
$590$	−16.0000	−0.658710
$591$	−18.4924	−0.760677
$592$	−9.12311	−0.374957
$593$	13.6847	0.561962	0.280981	−	0.959713i	$-0.409340\pi$
$593$	13.6847	0.561962	0.280981	+	0.959713i	$0.409340\pi$
$594$	−2.56155	−0.105102
$595$	3.86174	0.158316
$596$	6.31534	0.258686
$597$	19.6847	0.805639
$598$	3.12311	0.127713
$599$	9.93087	0.405764	0.202882	−	0.979203i	$-0.434969\pi$
$599$	9.93087	0.405764	0.202882	+	0.979203i	$0.434969\pi$
$600$	−1.00000	−0.0408248
$601$	3.75379	0.153120	0.0765601	−	0.997065i	$-0.475606\pi$
$601$	3.75379	0.153120	0.0765601	+	0.997065i	$0.475606\pi$
$602$	0.630683	0.0257047
$603$	11.6847	0.475836
$604$	−7.36932	−0.299853
$605$	8.87689	0.360897
$606$	−3.68466	−0.149679
$607$	−14.8769	−0.603835	−0.301917	−	0.953334i	$-0.597627\pi$
$607$	−14.8769	−0.603835	−0.301917	+	0.953334i	$0.597627\pi$
$608$	2.00000	0.0811107
$609$	3.36932	0.136532
$610$	22.2462	0.900723
$611$	10.2462	0.414517
$612$	3.43845	0.138991
$613$	−43.7926	−1.76877	−0.884383	−	0.466761i	$-0.845421\pi$
$613$	−43.7926	−1.76877	−0.884383	+	0.466761i	$0.845421\pi$
$614$	−21.4384	−0.865185
$615$	4.00000	0.161296
$616$	−1.43845	−0.0579567
$617$	−12.2462	−0.493014	−0.246507	−	0.969141i	$-0.579283\pi$
$617$	−12.2462	−0.493014	−0.246507	+	0.969141i	$0.579283\pi$
$618$	−1.00000	−0.0402259
$619$	−6.49242	−0.260952	−0.130476	−	0.991451i	$-0.541651\pi$
$619$	−6.49242	−0.260952	−0.130476	+	0.991451i	$0.541651\pi$
$620$	−2.24621	−0.0902100
$621$	−3.12311	−0.125326
$622$	18.0000	0.721734
$623$	−1.12311	−0.0449963
$624$	1.00000	0.0400320
$625$	−19.0000	−0.760000
$626$	16.2462	0.649329
$627$	−5.12311	−0.204597
$628$	−6.80776	−0.271659
$629$	−31.3693	−1.25078
$630$	−1.12311	−0.0447456
$631$	−37.0540	−1.47510	−0.737548	−	0.675295i	$-0.764016\pi$
$631$	−37.0540	−1.47510	−0.737548	+	0.675295i	$0.764016\pi$
$632$	−7.36932	−0.293136
$633$	−8.49242	−0.337543
$634$	13.0540	0.518440
$635$	23.3693	0.927383
$636$	−6.56155	−0.260182
$637$	6.68466	0.264856
$638$	15.3693	0.608477
$639$	2.24621	0.0888587
$640$	2.00000	0.0790569
$641$	−38.8078	−1.53281	−0.766407	−	0.642355i	$-0.777958\pi$
$641$	−38.8078	−1.53281	−0.766407	+	0.642355i	$0.777958\pi$
$642$	8.56155	0.337898
$643$	−24.7386	−0.975596	−0.487798	−	0.872956i	$-0.662200\pi$
$643$	−24.7386	−0.975596	−0.487798	+	0.872956i	$0.662200\pi$
$644$	−1.75379	−0.0691090
$645$	2.24621	0.0884445
$646$	6.87689	0.270568
$647$	−8.24621	−0.324192	−0.162096	−	0.986775i	$-0.551825\pi$
$647$	−8.24621	−0.324192	−0.162096	+	0.986775i	$0.551825\pi$
$648$	−1.00000	−0.0392837
$649$	20.4924	0.804398
$650$	−1.00000	−0.0392232
$651$	0.630683	0.0247184
$652$	−22.4924	−0.880871
$653$	18.8769	0.738710	0.369355	−	0.929288i	$-0.379579\pi$
$653$	18.8769	0.738710	0.369355	+	0.929288i	$0.379579\pi$
$654$	−6.24621	−0.244246
$655$	−42.7386	−1.66994
$656$	2.00000	0.0780869
$657$	3.68466	0.143752
$658$	−5.75379	−0.224306
$659$	21.5464	0.839328	0.419664	−	0.907679i	$-0.362148\pi$
$659$	21.5464	0.839328	0.419664	+	0.907679i	$0.362148\pi$
$660$	−5.12311	−0.199417
$661$	−18.2462	−0.709695	−0.354848	−	0.934924i	$-0.615467\pi$
$661$	−18.2462	−0.709695	−0.354848	+	0.934924i	$0.615467\pi$
$662$	−21.9309	−0.852367
$663$	3.43845	0.133538
$664$	−11.3693	−0.441215
$665$	−2.24621	−0.0871043
$666$	9.12311	0.353513
$667$	18.7386	0.725563
$668$	−3.19224	−0.123511
$669$	5.68466	0.219782
$670$	23.3693	0.902835
$671$	−28.4924	−1.09994
$672$	−0.561553	−0.0216624
$673$	−1.68466	−0.0649388	−0.0324694	−	0.999473i	$-0.510337\pi$
$673$	−1.68466	−0.0649388	−0.0324694	+	0.999473i	$0.510337\pi$
$674$	27.9309	1.07586
$675$	1.00000	0.0384900
$676$	1.00000	0.0384615
$677$	−24.2462	−0.931858	−0.465929	−	0.884822i	$-0.654280\pi$
$677$	−24.2462	−0.931858	−0.465929	+	0.884822i	$0.654280\pi$
$678$	4.00000	0.153619
$679$	−2.38447	−0.0915076
$680$	6.87689	0.263717
$681$	4.80776	0.184234
$682$	2.87689	0.110162
$683$	5.43845	0.208096	0.104048	−	0.994572i	$-0.466820\pi$
$683$	5.43845	0.208096	0.104048	+	0.994572i	$0.466820\pi$
$684$	−2.00000	−0.0764719
$685$	12.0000	0.458496
$686$	−7.68466	−0.293402
$687$	6.00000	0.228914
$688$	1.12311	0.0428180
$689$	−6.56155	−0.249975
$690$	−6.24621	−0.237789
$691$	−21.7538	−0.827553	−0.413777	−	0.910378i	$-0.635791\pi$
$691$	−21.7538	−0.827553	−0.413777	+	0.910378i	$0.635791\pi$
$692$	20.8078	0.790993
$693$	1.43845	0.0546421
$694$	16.8769	0.640638
$695$	25.6155	0.971652
$696$	6.00000	0.227429
$697$	6.87689	0.260481
$698$	−1.75379	−0.0663819
$699$	−24.4924	−0.926388
$700$	0.561553	0.0212247
$701$	−17.3693	−0.656030	−0.328015	−	0.944673i	$-0.606380\pi$
$701$	−17.3693	−0.656030	−0.328015	+	0.944673i	$0.606380\pi$
$702$	−1.00000	−0.0377426
$703$	18.2462	0.688169
$704$	−2.56155	−0.0965422
$705$	−20.4924	−0.771789
$706$	14.3153	0.538765
$707$	2.06913	0.0778177
$708$	8.00000	0.300658
$709$	8.73863	0.328186	0.164093	−	0.986445i	$-0.447530\pi$
$709$	8.73863	0.328186	0.164093	+	0.986445i	$0.447530\pi$
$710$	4.49242	0.168598
$711$	7.36932	0.276371
$712$	−2.00000	−0.0749532
$713$	3.50758	0.131360
$714$	−1.93087	−0.0722610
$715$	−5.12311	−0.191593
$716$	−10.8078	−0.403905
$717$	2.56155	0.0956629
$718$	−19.0540	−0.711088
$719$	11.1922	0.417400	0.208700	−	0.977980i	$-0.433077\pi$
$719$	11.1922	0.417400	0.208700	+	0.977980i	$0.433077\pi$
$720$	−2.00000	−0.0745356
$721$	0.561553	0.0209133
$722$	15.0000	0.558242
$723$	8.31534	0.309251
$724$	15.9309	0.592066
$725$	−6.00000	−0.222834
$726$	−4.43845	−0.164726
$727$	−21.9309	−0.813371	−0.406685	−	0.913568i	$-0.633316\pi$
$727$	−21.9309	−0.813371	−0.406685	+	0.913568i	$0.633316\pi$
$728$	−0.561553	−0.0208125
$729$	1.00000	0.0370370
$730$	7.36932	0.272751
$731$	3.86174	0.142832
$732$	−11.1231	−0.411122
$733$	46.1080	1.70304	0.851518	−	0.524325i	$-0.175682\pi$
$733$	46.1080	1.70304	0.851518	+	0.524325i	$0.175682\pi$
$734$	13.7538	0.507662
$735$	−13.3693	−0.493135
$736$	−3.12311	−0.115119
$737$	−29.9309	−1.10252
$738$	−2.00000	−0.0736210
$739$	−25.3693	−0.933225	−0.466613	−	0.884462i	$-0.654526\pi$
$739$	−25.3693	−0.933225	−0.466613	+	0.884462i	$0.654526\pi$
$740$	18.2462	0.670744
$741$	−2.00000	−0.0734718
$742$	3.68466	0.135268
$743$	6.73863	0.247216	0.123608	−	0.992331i	$-0.460553\pi$
$743$	6.73863	0.247216	0.123608	+	0.992331i	$0.460553\pi$
$744$	1.12311	0.0411750
$745$	−12.6307	−0.462752
$746$	29.3693	1.07529
$747$	11.3693	0.415982
$748$	−8.80776	−0.322044
$749$	−4.80776	−0.175672
$750$	12.0000	0.438178
$751$	−18.7386	−0.683782	−0.341891	−	0.939740i	$-0.611067\pi$
$751$	−18.7386	−0.683782	−0.341891	+	0.939740i	$0.611067\pi$
$752$	−10.2462	−0.373641
$753$	−5.75379	−0.209680
$754$	6.00000	0.218507
$755$	14.7386	0.536394
$756$	0.561553	0.0204235
$757$	−1.50758	−0.0547938	−0.0273969	−	0.999625i	$-0.508722\pi$
$757$	−1.50758	−0.0547938	−0.0273969	+	0.999625i	$0.508722\pi$
$758$	12.8078	0.465199
$759$	8.00000	0.290382
$760$	−4.00000	−0.145095
$761$	−20.2462	−0.733925	−0.366962	−	0.930236i	$-0.619602\pi$
$761$	−20.2462	−0.733925	−0.366962	+	0.930236i	$0.619602\pi$
$762$	−11.6847	−0.423291
$763$	3.50758	0.126983
$764$	−3.68466	−0.133306
$765$	−6.87689	−0.248635
$766$	−4.49242	−0.162318
$767$	8.00000	0.288863
$768$	−1.00000	−0.0360844
$769$	5.93087	0.213873	0.106936	−	0.994266i	$-0.465896\pi$
$769$	5.93087	0.213873	0.106936	+	0.994266i	$0.465896\pi$
$770$	2.87689	0.103676
$771$	−21.1231	−0.760730
$772$	−0.630683	−0.0226988
$773$	−45.0540	−1.62048	−0.810239	−	0.586099i	$-0.800663\pi$
$773$	−45.0540	−1.62048	−0.810239	+	0.586099i	$0.800663\pi$
$774$	−1.12311	−0.0403692
$775$	−1.12311	−0.0403431
$776$	−4.24621	−0.152430
$777$	−5.12311	−0.183790
$778$	−2.56155	−0.0918361
$779$	−4.00000	−0.143315
$780$	−2.00000	−0.0716115
$781$	−5.75379	−0.205887
$782$	−10.7386	−0.384013
$783$	−6.00000	−0.214423
$784$	−6.68466	−0.238738
$785$	13.6155	0.485959
$786$	21.3693	0.762218
$787$	45.8617	1.63479	0.817397	−	0.576074i	$-0.195416\pi$
$787$	45.8617	1.63479	0.817397	+	0.576074i	$0.195416\pi$
$788$	18.4924	0.658765
$789$	−0.315342	−0.0112265
$790$	14.7386	0.524377
$791$	−2.24621	−0.0798661
$792$	2.56155	0.0910208
$793$	−11.1231	−0.394993
$794$	−17.6155	−0.625152
$795$	13.1231	0.465429
$796$	−19.6847	−0.697704
$797$	32.7386	1.15966	0.579831	−	0.814737i	$-0.303119\pi$
$797$	32.7386	1.15966	0.579831	+	0.814737i	$0.303119\pi$
$798$	1.12311	0.0397575
$799$	−35.2311	−1.24639
$800$	1.00000	0.0353553
$801$	2.00000	0.0706665
$802$	−5.36932	−0.189597
$803$	−9.43845	−0.333076
$804$	−11.6847	−0.412086
$805$	3.50758	0.123626
$806$	1.12311	0.0395597
$807$	11.7538	0.413753
$808$	3.68466	0.129626
$809$	−23.3693	−0.821621	−0.410811	−	0.911721i	$-0.634754\pi$
$809$	−23.3693	−0.821621	−0.410811	+	0.911721i	$0.634754\pi$
$810$	2.00000	0.0702728
$811$	−39.2311	−1.37759	−0.688794	−	0.724957i	$-0.741860\pi$
$811$	−39.2311	−1.37759	−0.688794	+	0.724957i	$0.741860\pi$
$812$	−3.36932	−0.118240
$813$	11.3693	0.398739
$814$	−23.3693	−0.819094
$815$	44.9848	1.57575
$816$	−3.43845	−0.120370
$817$	−2.24621	−0.0785850
$818$	−21.3693	−0.747161
$819$	0.561553	0.0196222
$820$	−4.00000	−0.139686
$821$	2.17708	0.0759806	0.0379903	−	0.999278i	$-0.487904\pi$
$821$	2.17708	0.0759806	0.0379903	+	0.999278i	$0.487904\pi$
$822$	−6.00000	−0.209274
$823$	8.00000	0.278862	0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000	0.278862	0.139431	+	0.990232i	$0.455473\pi$
$824$	1.00000	0.0348367
$825$	−2.56155	−0.0891818
$826$	−4.49242	−0.156311
$827$	1.75379	0.0609852	0.0304926	−	0.999535i	$-0.490292\pi$
$827$	1.75379	0.0609852	0.0304926	+	0.999535i	$0.490292\pi$
$828$	3.12311	0.108535
$829$	49.2311	1.70987	0.854933	−	0.518739i	$-0.173598\pi$
$829$	49.2311	1.70987	0.854933	+	0.518739i	$0.173598\pi$
$830$	22.7386	0.789269
$831$	−6.00000	−0.208138
$832$	−1.00000	−0.0346688
$833$	−22.9848	−0.796378
$834$	−12.8078	−0.443497
$835$	6.38447	0.220944
$836$	5.12311	0.177186
$837$	−1.12311	−0.0388202
$838$	19.9309	0.688500
$839$	−46.2462	−1.59660	−0.798298	−	0.602262i	$-0.794266\pi$
$839$	−46.2462	−1.59660	−0.798298	+	0.602262i	$0.794266\pi$
$840$	1.12311	0.0387508
$841$	7.00000	0.241379
$842$	−17.0540	−0.587719
$843$	22.4924	0.774680
$844$	8.49242	0.292321
$845$	−2.00000	−0.0688021
$846$	10.2462	0.352272
$847$	2.49242	0.0856407
$848$	6.56155	0.225325
$849$	−21.6155	−0.741843
$850$	3.43845	0.117938
$851$	−28.4924	−0.976708
$852$	−2.24621	−0.0769539
$853$	23.3002	0.797783	0.398892	−	0.916998i	$-0.369395\pi$
$853$	23.3002	0.797783	0.398892	+	0.916998i	$0.369395\pi$
$854$	6.24621	0.213741
$855$	4.00000	0.136797
$856$	−8.56155	−0.292628
$857$	35.9309	1.22738	0.613688	−	0.789549i	$-0.289685\pi$
$857$	35.9309	1.22738	0.613688	+	0.789549i	$0.289685\pi$
$858$	2.56155	0.0874500
$859$	5.61553	0.191599	0.0957997	−	0.995401i	$-0.469459\pi$
$859$	5.61553	0.191599	0.0957997	+	0.995401i	$0.469459\pi$
$860$	−2.24621	−0.0765952
$861$	1.12311	0.0382753
$862$	32.0000	1.08992
$863$	−29.7538	−1.01283	−0.506415	−	0.862290i	$-0.669030\pi$
$863$	−29.7538	−1.01283	−0.506415	+	0.862290i	$0.669030\pi$
$864$	1.00000	0.0340207
$865$	−41.6155	−1.41497
$866$	22.4924	0.764324
$867$	5.17708	0.175823
$868$	−0.630683	−0.0214068
$869$	−18.8769	−0.640355
$870$	−12.0000	−0.406838
$871$	−11.6847	−0.395920
$872$	6.24621	0.211523
$873$	4.24621	0.143712
$874$	6.24621	0.211281
$875$	−6.73863	−0.227807
$876$	−3.68466	−0.124493
$877$	−36.9848	−1.24889	−0.624445	−	0.781069i	$-0.714675\pi$
$877$	−36.9848	−1.24889	−0.624445	+	0.781069i	$0.714675\pi$
$878$	11.0540	0.373054
$879$	7.61553	0.256865
$880$	5.12311	0.172700
$881$	2.73863	0.0922669	0.0461335	−	0.998935i	$-0.485310\pi$
$881$	2.73863	0.0922669	0.0461335	+	0.998935i	$0.485310\pi$
$882$	6.68466	0.225084
$883$	−38.9157	−1.30962	−0.654809	−	0.755794i	$-0.727251\pi$
$883$	−38.9157	−1.30962	−0.654809	+	0.755794i	$0.727251\pi$
$884$	−3.43845	−0.115647
$885$	−16.0000	−0.537834
$886$	12.4924	0.419691
$887$	31.1231	1.04501	0.522506	−	0.852636i	$-0.324997\pi$
$887$	31.1231	1.04501	0.522506	+	0.852636i	$0.324997\pi$
$888$	−9.12311	−0.306151
$889$	6.56155	0.220067
$890$	4.00000	0.134080
$891$	−2.56155	−0.0858152
$892$	−5.68466	−0.190336
$893$	20.4924	0.685753
$894$	6.31534	0.211217
$895$	21.6155	0.722527
$896$	0.561553	0.0187602
$897$	3.12311	0.104277
$898$	26.3153	0.878154
$899$	6.73863	0.224746
$900$	−1.00000	−0.0333333
$901$	22.5616	0.751634
$902$	5.12311	0.170581
$903$	0.630683	0.0209878
$904$	−4.00000	−0.133038
$905$	−31.8617	−1.05912
$906$	−7.36932	−0.244829
$907$	−55.5464	−1.84439	−0.922194	−	0.386728i	$-0.873605\pi$
$907$	−55.5464	−1.84439	−0.922194	+	0.386728i	$0.873605\pi$
$908$	−4.80776	−0.159551
$909$	−3.68466	−0.122212
$910$	1.12311	0.0372306
$911$	10.7386	0.355787	0.177893	−	0.984050i	$-0.443072\pi$
$911$	10.7386	0.355787	0.177893	+	0.984050i	$0.443072\pi$
$912$	2.00000	0.0662266
$913$	−29.1231	−0.963834
$914$	−8.63068	−0.285478
$915$	22.2462	0.735437
$916$	−6.00000	−0.198246
$917$	−12.0000	−0.396275
$918$	3.43845	0.113486
$919$	−32.8078	−1.08223	−0.541114	−	0.840949i	$-0.681997\pi$
$919$	−32.8078	−1.08223	−0.541114	+	0.840949i	$0.681997\pi$
$920$	6.24621	0.205931
$921$	−21.4384	−0.706421
$922$	−8.24621	−0.271575
$923$	−2.24621	−0.0739349
$924$	−1.43845	−0.0473214
$925$	9.12311	0.299966
$926$	−13.1231	−0.431252
$927$	−1.00000	−0.0328443
$928$	−6.00000	−0.196960
$929$	0.384472	0.0126141	0.00630706	−	0.999980i	$-0.497992\pi$
$929$	0.384472	0.0126141	0.00630706	+	0.999980i	$0.497992\pi$
$930$	−2.24621	−0.0736562
$931$	13.3693	0.438162
$932$	24.4924	0.802276
$933$	18.0000	0.589294
$934$	38.1771	1.24919
$935$	17.6155	0.576089
$936$	1.00000	0.0326860
$937$	48.7386	1.59222	0.796111	−	0.605151i	$-0.206887\pi$
$937$	48.7386	1.59222	0.796111	+	0.605151i	$0.206887\pi$
$938$	6.56155	0.214242
$939$	16.2462	0.530175
$940$	20.4924	0.668389
$941$	−19.4384	−0.633675	−0.316838	−	0.948480i	$-0.602621\pi$
$941$	−19.4384	−0.633675	−0.316838	+	0.948480i	$0.602621\pi$
$942$	−6.80776	−0.221809
$943$	6.24621	0.203405
$944$	−8.00000	−0.260378
$945$	−1.12311	−0.0365346
$946$	2.87689	0.0935359
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	−7.36932	−0.239344
$949$	−3.68466	−0.119609
$950$	−2.00000	−0.0648886
$951$	13.0540	0.423304
$952$	1.93087	0.0625798
$953$	13.1922	0.427338	0.213669	−	0.976906i	$-0.431459\pi$
$953$	13.1922	0.427338	0.213669	+	0.976906i	$0.431459\pi$
$954$	−6.56155	−0.212438
$955$	7.36932	0.238465
$956$	−2.56155	−0.0828465
$957$	15.3693	0.496819
$958$	5.12311	0.165520
$959$	3.36932	0.108801
$960$	2.00000	0.0645497
$961$	−29.7386	−0.959311
$962$	−9.12311	−0.294141
$963$	8.56155	0.275892
$964$	−8.31534	−0.267819
$965$	1.26137	0.0406048
$966$	−1.75379	−0.0564272
$967$	17.1231	0.550642	0.275321	−	0.961352i	$-0.411216\pi$
$967$	17.1231	0.550642	0.275321	+	0.961352i	$0.411216\pi$
$968$	4.43845	0.142657
$969$	6.87689	0.220918
$970$	8.49242	0.272675
$971$	13.6155	0.436943	0.218472	−	0.975843i	$-0.429893\pi$
$971$	13.6155	0.436943	0.218472	+	0.975843i	$0.429893\pi$
$972$	−1.00000	−0.0320750
$973$	7.19224	0.230572
$974$	−5.61553	−0.179933
$975$	−1.00000	−0.0320256
$976$	11.1231	0.356042
$977$	−15.1231	−0.483831	−0.241916	−	0.970297i	$-0.577776\pi$
$977$	−15.1231	−0.483831	−0.241916	+	0.970297i	$0.577776\pi$
$978$	−22.4924	−0.719228
$979$	−5.12311	−0.163735
$980$	13.3693	0.427067
$981$	−6.24621	−0.199426
$982$	−15.4384	−0.492661
$983$	20.8078	0.663665	0.331832	−	0.943338i	$-0.392333\pi$
$983$	20.8078	0.663665	0.331832	+	0.943338i	$0.392333\pi$
$984$	2.00000	0.0637577
$985$	−36.9848	−1.17844
$986$	−20.6307	−0.657015
$987$	−5.75379	−0.183145
$988$	2.00000	0.0636285
$989$	3.50758	0.111534
$990$	−5.12311	−0.162823
$991$	−55.8617	−1.77451	−0.887253	−	0.461283i	$-0.847389\pi$
$991$	−55.8617	−1.77451	−0.887253	+	0.461283i	$0.847389\pi$
$992$	−1.12311	−0.0356586
$993$	−21.9309	−0.695955
$994$	1.26137	0.0400081
$995$	39.3693	1.24809
$996$	−11.3693	−0.360251
$997$	50.4924	1.59911	0.799556	−	0.600592i	$-0.205068\pi$
$997$	50.4924	1.59911	0.799556	+	0.600592i	$0.205068\pi$
$998$	−22.7386	−0.719779
$999$	9.12311	0.288642

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.l.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.l.1.1	✓	2	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{6} -0.561553 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{6} -0.561553 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{10} -2.56155 q^{11} -1.00000 q^{12} -1.00000 q^{13} +0.561553 q^{14} +2.00000 q^{15} +1.00000 q^{16} +3.43845 q^{17} -1.00000 q^{18} -2.00000 q^{19} -2.00000 q^{20} +0.561553 q^{21} +2.56155 q^{22} +3.12311 q^{23} +1.00000 q^{24} -1.00000 q^{25} +1.00000 q^{26} -1.00000 q^{27} -0.561553 q^{28} +6.00000 q^{29} -2.00000 q^{30} +1.12311 q^{31} -1.00000 q^{32} +2.56155 q^{33} -3.43845 q^{34} +1.12311 q^{35} +1.00000 q^{36} -9.12311 q^{37} +2.00000 q^{38} +1.00000 q^{39} +2.00000 q^{40} +2.00000 q^{41} -0.561553 q^{42} +1.12311 q^{43} -2.56155 q^{44} -2.00000 q^{45} -3.12311 q^{46} -10.2462 q^{47} -1.00000 q^{48} -6.68466 q^{49} +1.00000 q^{50} -3.43845 q^{51} -1.00000 q^{52} +6.56155 q^{53} +1.00000 q^{54} +5.12311 q^{55} +0.561553 q^{56} +2.00000 q^{57} -6.00000 q^{58} -8.00000 q^{59} +2.00000 q^{60} +11.1231 q^{61} -1.12311 q^{62} -0.561553 q^{63} +1.00000 q^{64} +2.00000 q^{65} -2.56155 q^{66} +11.6847 q^{67} +3.43845 q^{68} -3.12311 q^{69} -1.12311 q^{70} +2.24621 q^{71} -1.00000 q^{72} +3.68466 q^{73} +9.12311 q^{74} +1.00000 q^{75} -2.00000 q^{76} +1.43845 q^{77} -1.00000 q^{78} +7.36932 q^{79} -2.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} +11.3693 q^{83} +0.561553 q^{84} -6.87689 q^{85} -1.12311 q^{86} -6.00000 q^{87} +2.56155 q^{88} +2.00000 q^{89} +2.00000 q^{90} +0.561553 q^{91} +3.12311 q^{92} -1.12311 q^{93} +10.2462 q^{94} +4.00000 q^{95} +1.00000 q^{96} +4.24621 q^{97} +6.68466 q^{98} -2.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} + 3 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 + 2 * q^6 + 3 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} + 3 q^{7} - 2 q^{8} + 2 q^{9} + 4 q^{10} - q^{11} - 2 q^{12} - 2 q^{13} - 3 q^{14} + 4 q^{15} + 2 q^{16} + 11 q^{17} - 2 q^{18} - 4 q^{19} - 4 q^{20} - 3 q^{21} + q^{22} - 2 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26} - 2 q^{27} + 3 q^{28} + 12 q^{29} - 4 q^{30} - 6 q^{31} - 2 q^{32} + q^{33} - 11 q^{34} - 6 q^{35} + 2 q^{36} - 10 q^{37} + 4 q^{38} + 2 q^{39} + 4 q^{40} + 4 q^{41} + 3 q^{42} - 6 q^{43} - q^{44} - 4 q^{45} + 2 q^{46} - 4 q^{47} - 2 q^{48} - q^{49} + 2 q^{50} - 11 q^{51} - 2 q^{52} + 9 q^{53} + 2 q^{54} + 2 q^{55} - 3 q^{56} + 4 q^{57} - 12 q^{58} - 16 q^{59} + 4 q^{60} + 14 q^{61} + 6 q^{62} + 3 q^{63} + 2 q^{64} + 4 q^{65} - q^{66} + 11 q^{67} + 11 q^{68} + 2 q^{69} + 6 q^{70} - 12 q^{71} - 2 q^{72} - 5 q^{73} + 10 q^{74} + 2 q^{75} - 4 q^{76} + 7 q^{77} - 2 q^{78} - 10 q^{79} - 4 q^{80} + 2 q^{81} - 4 q^{82} - 2 q^{83} - 3 q^{84} - 22 q^{85} + 6 q^{86} - 12 q^{87} + q^{88} + 4 q^{89} + 4 q^{90} - 3 q^{91} - 2 q^{92} + 6 q^{93} + 4 q^{94} + 8 q^{95} + 2 q^{96} - 8 q^{97} + q^{98} - q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 + 2 * q^6 + 3 * q^7 - 2 * q^8 + 2 * q^9 + 4 * q^10 - q^11 - 2 * q^12 - 2 * q^13 - 3 * q^14 + 4 * q^15 + 2 * q^16 + 11 * q^17 - 2 * q^18 - 4 * q^19 - 4 * q^20 - 3 * q^21 + q^22 - 2 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 - 2 * q^27 + 3 * q^28 + 12 * q^29 - 4 * q^30 - 6 * q^31 - 2 * q^32 + q^33 - 11 * q^34 - 6 * q^35 + 2 * q^36 - 10 * q^37 + 4 * q^38 + 2 * q^39 + 4 * q^40 + 4 * q^41 + 3 * q^42 - 6 * q^43 - q^44 - 4 * q^45 + 2 * q^46 - 4 * q^47 - 2 * q^48 - q^49 + 2 * q^50 - 11 * q^51 - 2 * q^52 + 9 * q^53 + 2 * q^54 + 2 * q^55 - 3 * q^56 + 4 * q^57 - 12 * q^58 - 16 * q^59 + 4 * q^60 + 14 * q^61 + 6 * q^62 + 3 * q^63 + 2 * q^64 + 4 * q^65 - q^66 + 11 * q^67 + 11 * q^68 + 2 * q^69 + 6 * q^70 - 12 * q^71 - 2 * q^72 - 5 * q^73 + 10 * q^74 + 2 * q^75 - 4 * q^76 + 7 * q^77 - 2 * q^78 - 10 * q^79 - 4 * q^80 + 2 * q^81 - 4 * q^82 - 2 * q^83 - 3 * q^84 - 22 * q^85 + 6 * q^86 - 12 * q^87 + q^88 + 4 * q^89 + 4 * q^90 - 3 * q^91 - 2 * q^92 + 6 * q^93 + 4 * q^94 + 8 * q^95 + 2 * q^96 - 8 * q^97 + q^98 - q^99

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