LMFDB - Embedded newform 6630.2.a.bk.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6630,2,Mod(1,6630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6630, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6630.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6630 = 2 \cdot 3 \cdot 5 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6630.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:	$52.9408165401$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.564.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x + 3 $ x^3 - x^2 - 5*x + 3
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			1.3
Root			$-2.08613$ of defining polynomial
Character	$\chi$	$=$	6630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +3.08613 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +3.08613 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +3.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} -3.08613 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -7.61033 q^{19} -1.00000 q^{20} +3.08613 q^{21} -3.00000 q^{22} -1.08613 q^{23} -1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{26} +1.00000 q^{27} +3.08613 q^{28} +8.17226 q^{29} +1.00000 q^{30} +3.05582 q^{31} -1.00000 q^{32} +3.00000 q^{33} -1.00000 q^{34} -3.08613 q^{35} +1.00000 q^{36} +3.82032 q^{37} +7.61033 q^{38} +1.00000 q^{39} +1.00000 q^{40} +7.08613 q^{41} -3.08613 q^{42} -9.87614 q^{43} +3.00000 q^{44} -1.00000 q^{45} +1.08613 q^{46} -7.31421 q^{47} +1.00000 q^{48} +2.52420 q^{49} -1.00000 q^{50} +1.00000 q^{51} +1.00000 q^{52} +9.96227 q^{53} -1.00000 q^{54} -3.00000 q^{55} -3.08613 q^{56} -7.61033 q^{57} -8.17226 q^{58} +7.79001 q^{59} -1.00000 q^{60} -5.43807 q^{61} -3.05582 q^{62} +3.08613 q^{63} +1.00000 q^{64} -1.00000 q^{65} -3.00000 q^{66} -1.03031 q^{67} +1.00000 q^{68} -1.08613 q^{69} +3.08613 q^{70} -13.2207 q^{71} -1.00000 q^{72} +16.0787 q^{73} -3.82032 q^{74} +1.00000 q^{75} -7.61033 q^{76} +9.25839 q^{77} -1.00000 q^{78} -0.969687 q^{79} -1.00000 q^{80} +1.00000 q^{81} -7.08613 q^{82} +15.5168 q^{83} +3.08613 q^{84} -1.00000 q^{85} +9.87614 q^{86} +8.17226 q^{87} -3.00000 q^{88} +9.99258 q^{89} +1.00000 q^{90} +3.08613 q^{91} -1.08613 q^{92} +3.05582 q^{93} +7.31421 q^{94} +7.61033 q^{95} -1.00000 q^{96} -5.56193 q^{97} -2.52420 q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 9 q^{11} + 3 q^{12} + 3 q^{13} - 2 q^{14} - 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} + q^{19} - 3 q^{20} + 2 q^{21} - 9 q^{22} + 4 q^{23} - 3 q^{24} + 3 q^{25} - 3 q^{26} + 3 q^{27} + 2 q^{28} + 10 q^{29} + 3 q^{30} + 3 q^{31} - 3 q^{32} + 9 q^{33} - 3 q^{34} - 2 q^{35} + 3 q^{36} - q^{37} - q^{38} + 3 q^{39} + 3 q^{40} + 14 q^{41} - 2 q^{42} - 11 q^{43} + 9 q^{44} - 3 q^{45} - 4 q^{46} + 6 q^{47} + 3 q^{48} - 9 q^{49} - 3 q^{50} + 3 q^{51} + 3 q^{52} + 4 q^{53} - 3 q^{54} - 9 q^{55} - 2 q^{56} + q^{57} - 10 q^{58} + 12 q^{59} - 3 q^{60} - 7 q^{61} - 3 q^{62} + 2 q^{63} + 3 q^{64} - 3 q^{65} - 9 q^{66} - 2 q^{67} + 3 q^{68} + 4 q^{69} + 2 q^{70} + 8 q^{71} - 3 q^{72} + 14 q^{73} + q^{74} + 3 q^{75} + q^{76} + 6 q^{77} - 3 q^{78} - 4 q^{79} - 3 q^{80} + 3 q^{81} - 14 q^{82} + 3 q^{83} + 2 q^{84} - 3 q^{85} + 11 q^{86} + 10 q^{87} - 9 q^{88} + 3 q^{89} + 3 q^{90} + 2 q^{91} + 4 q^{92} + 3 q^{93} - 6 q^{94} - q^{95} - 3 q^{96} - 26 q^{97} + 9 q^{98} + 9 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 9 * q^11 + 3 * q^12 + 3 * q^13 - 2 * q^14 - 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 + q^19 - 3 * q^20 + 2 * q^21 - 9 * q^22 + 4 * q^23 - 3 * q^24 + 3 * q^25 - 3 * q^26 + 3 * q^27 + 2 * q^28 + 10 * q^29 + 3 * q^30 + 3 * q^31 - 3 * q^32 + 9 * q^33 - 3 * q^34 - 2 * q^35 + 3 * q^36 - q^37 - q^38 + 3 * q^39 + 3 * q^40 + 14 * q^41 - 2 * q^42 - 11 * q^43 + 9 * q^44 - 3 * q^45 - 4 * q^46 + 6 * q^47 + 3 * q^48 - 9 * q^49 - 3 * q^50 + 3 * q^51 + 3 * q^52 + 4 * q^53 - 3 * q^54 - 9 * q^55 - 2 * q^56 + q^57 - 10 * q^58 + 12 * q^59 - 3 * q^60 - 7 * q^61 - 3 * q^62 + 2 * q^63 + 3 * q^64 - 3 * q^65 - 9 * q^66 - 2 * q^67 + 3 * q^68 + 4 * q^69 + 2 * q^70 + 8 * q^71 - 3 * q^72 + 14 * q^73 + q^74 + 3 * q^75 + q^76 + 6 * q^77 - 3 * q^78 - 4 * q^79 - 3 * q^80 + 3 * q^81 - 14 * q^82 + 3 * q^83 + 2 * q^84 - 3 * q^85 + 11 * q^86 + 10 * q^87 - 9 * q^88 + 3 * q^89 + 3 * q^90 + 2 * q^91 + 4 * q^92 + 3 * q^93 - 6 * q^94 - q^95 - 3 * q^96 - 26 * q^97 + 9 * q^98 + 9 * 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
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	3.08613	1.16645	0.583224	−	0.812312i	$-0.301791\pi$
$7$	3.08613	1.16645	0.583224	+	0.812312i	$0.301791\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−3.08613	−0.824803
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−7.61033	−1.74593	−0.872965	−	0.487783i	$-0.837806\pi$
$19$	−7.61033	−1.74593	−0.872965	+	0.487783i	$0.837806\pi$
$20$	−1.00000	−0.223607
$21$	3.08613	0.673449
$22$	−3.00000	−0.639602
$23$	−1.08613	−0.226474	−0.113237	−	0.993568i	$-0.536122\pi$
$23$	−1.08613	−0.226474	−0.113237	+	0.993568i	$0.536122\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	3.08613	0.583224
$29$	8.17226	1.51755	0.758775	−	0.651352i	$-0.225798\pi$
$29$	8.17226	1.51755	0.758775	+	0.651352i	$0.225798\pi$
$30$	1.00000	0.182574
$31$	3.05582	0.548841	0.274421	−	0.961610i	$-0.411514\pi$
$31$	3.05582	0.548841	0.274421	+	0.961610i	$0.411514\pi$
$32$	−1.00000	−0.176777
$33$	3.00000	0.522233
$34$	−1.00000	−0.171499
$35$	−3.08613	−0.521651
$36$	1.00000	0.166667
$37$	3.82032	0.628057	0.314028	−	0.949414i	$-0.398321\pi$
$37$	3.82032	0.628057	0.314028	+	0.949414i	$0.398321\pi$
$38$	7.61033	1.23456
$39$	1.00000	0.160128
$40$	1.00000	0.158114
$41$	7.08613	1.10667	0.553334	−	0.832960i	$-0.313355\pi$
$41$	7.08613	1.10667	0.553334	+	0.832960i	$0.313355\pi$
$42$	−3.08613	−0.476200
$43$	−9.87614	−1.50610	−0.753049	−	0.657965i	$-0.771417\pi$
$43$	−9.87614	−1.50610	−0.753049	+	0.657965i	$0.771417\pi$
$44$	3.00000	0.452267
$45$	−1.00000	−0.149071
$46$	1.08613	0.160141
$47$	−7.31421	−1.06689	−0.533443	−	0.845836i	$-0.679102\pi$
$47$	−7.31421	−1.06689	−0.533443	+	0.845836i	$0.679102\pi$
$48$	1.00000	0.144338
$49$	2.52420	0.360600
$50$	−1.00000	−0.141421
$51$	1.00000	0.140028
$52$	1.00000	0.138675
$53$	9.96227	1.36842	0.684211	−	0.729284i	$-0.260147\pi$
$53$	9.96227	1.36842	0.684211	+	0.729284i	$0.260147\pi$
$54$	−1.00000	−0.136083
$55$	−3.00000	−0.404520
$56$	−3.08613	−0.412401
$57$	−7.61033	−1.00801
$58$	−8.17226	−1.07307
$59$	7.79001	1.01417	0.507086	−	0.861895i	$-0.330723\pi$
$59$	7.79001	1.01417	0.507086	+	0.861895i	$0.330723\pi$
$60$	−1.00000	−0.129099
$61$	−5.43807	−0.696273	−0.348137	−	0.937444i	$-0.613186\pi$
$61$	−5.43807	−0.696273	−0.348137	+	0.937444i	$0.613186\pi$
$62$	−3.05582	−0.388089
$63$	3.08613	0.388816
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	−3.00000	−0.369274
$67$	−1.03031	−0.125873	−0.0629364	−	0.998018i	$-0.520047\pi$
$67$	−1.03031	−0.125873	−0.0629364	+	0.998018i	$0.520047\pi$
$68$	1.00000	0.121268
$69$	−1.08613	−0.130755
$70$	3.08613	0.368863
$71$	−13.2207	−1.56900	−0.784502	−	0.620127i	$-0.787081\pi$
$71$	−13.2207	−1.56900	−0.784502	+	0.620127i	$0.787081\pi$
$72$	−1.00000	−0.117851
$73$	16.0787	1.88187	0.940935	−	0.338586i	$-0.109949\pi$
$73$	16.0787	1.88187	0.940935	+	0.338586i	$0.109949\pi$
$74$	−3.82032	−0.444103
$75$	1.00000	0.115470
$76$	−7.61033	−0.872965
$77$	9.25839	1.05509
$78$	−1.00000	−0.113228
$79$	−0.969687	−0.109098	−0.0545492	−	0.998511i	$-0.517372\pi$
$79$	−0.969687	−0.109098	−0.0545492	+	0.998511i	$0.517372\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−7.08613	−0.782532
$83$	15.5168	1.70319	0.851594	−	0.524202i	$-0.175636\pi$
$83$	15.5168	1.70319	0.851594	+	0.524202i	$0.175636\pi$
$84$	3.08613	0.336724
$85$	−1.00000	−0.108465
$86$	9.87614	1.06497
$87$	8.17226	0.876158
$88$	−3.00000	−0.319801
$89$	9.99258	1.05921	0.529606	−	0.848244i	$-0.322340\pi$
$89$	9.99258	1.05921	0.529606	+	0.848244i	$0.322340\pi$
$90$	1.00000	0.105409
$91$	3.08613	0.323514
$92$	−1.08613	−0.113237
$93$	3.05582	0.316874
$94$	7.31421	0.754403
$95$	7.61033	0.780803
$96$	−1.00000	−0.102062
$97$	−5.56193	−0.564728	−0.282364	−	0.959307i	$-0.591119\pi$
$97$	−5.56193	−0.564728	−0.282364	+	0.959307i	$0.591119\pi$
$98$	−2.52420	−0.254983
$99$	3.00000	0.301511
$100$	1.00000	0.100000
$101$	9.00000	0.895533	0.447767	−	0.894150i	$-0.352219\pi$
$101$	9.00000	0.895533	0.447767	+	0.894150i	$0.352219\pi$
$102$	−1.00000	−0.0990148
$103$	2.70388	0.266421	0.133211	−	0.991088i	$-0.457471\pi$
$103$	2.70388	0.266421	0.133211	+	0.991088i	$0.457471\pi$
$104$	−1.00000	−0.0980581
$105$	−3.08613	−0.301175
$106$	−9.96227	−0.967621
$107$	−0.734191	−0.0709769	−0.0354885	−	0.999370i	$-0.511299\pi$
$107$	−0.734191	−0.0709769	−0.0354885	+	0.999370i	$0.511299\pi$
$108$	1.00000	0.0962250
$109$	19.7523	1.89193	0.945963	−	0.324276i	$-0.105121\pi$
$109$	19.7523	1.89193	0.945963	+	0.324276i	$0.105121\pi$
$110$	3.00000	0.286039
$111$	3.82032	0.362609
$112$	3.08613	0.291612
$113$	7.40776	0.696863	0.348432	−	0.937334i	$-0.386714\pi$
$113$	7.40776	0.696863	0.348432	+	0.937334i	$0.386714\pi$
$114$	7.61033	0.712773
$115$	1.08613	0.101282
$116$	8.17226	0.758775
$117$	1.00000	0.0924500
$118$	−7.79001	−0.717128
$119$	3.08613	0.282905
$120$	1.00000	0.0912871
$121$	−2.00000	−0.181818
$122$	5.43807	0.492340
$123$	7.08613	0.638935
$124$	3.05582	0.274421
$125$	−1.00000	−0.0894427
$126$	−3.08613	−0.274934
$127$	−13.6406	−1.21041	−0.605206	−	0.796069i	$-0.706909\pi$
$127$	−13.6406	−1.21041	−0.605206	+	0.796069i	$0.706909\pi$
$128$	−1.00000	−0.0883883
$129$	−9.87614	−0.869546
$130$	1.00000	0.0877058
$131$	−11.9065	−1.04027	−0.520136	−	0.854084i	$-0.674119\pi$
$131$	−11.9065	−1.04027	−0.520136	+	0.854084i	$0.674119\pi$
$132$	3.00000	0.261116
$133$	−23.4865	−2.03654
$134$	1.03031	0.0890055
$135$	−1.00000	−0.0860663
$136$	−1.00000	−0.0857493
$137$	7.14676	0.610589	0.305294	−	0.952258i	$-0.401245\pi$
$137$	7.14676	0.610589	0.305294	+	0.952258i	$0.401245\pi$
$138$	1.08613	0.0924575
$139$	−11.2839	−0.957088	−0.478544	−	0.878064i	$-0.658835\pi$
$139$	−11.2839	−0.957088	−0.478544	+	0.878064i	$0.658835\pi$
$140$	−3.08613	−0.260826
$141$	−7.31421	−0.615967
$142$	13.2207	1.10945
$143$	3.00000	0.250873
$144$	1.00000	0.0833333
$145$	−8.17226	−0.678669
$146$	−16.0787	−1.33068
$147$	2.52420	0.208192
$148$	3.82032	0.314028
$149$	−15.4865	−1.26870	−0.634350	−	0.773046i	$-0.718732\pi$
$149$	−15.4865	−1.26870	−0.634350	+	0.773046i	$0.718732\pi$
$150$	−1.00000	−0.0816497
$151$	−5.22066	−0.424851	−0.212426	−	0.977177i	$-0.568136\pi$
$151$	−5.22066	−0.424851	−0.212426	+	0.977177i	$0.568136\pi$
$152$	7.61033	0.617279
$153$	1.00000	0.0808452
$154$	−9.25839	−0.746062
$155$	−3.05582	−0.245449
$156$	1.00000	0.0800641
$157$	−4.73419	−0.377830	−0.188915	−	0.981993i	$-0.560497\pi$
$157$	−4.73419	−0.377830	−0.188915	+	0.981993i	$0.560497\pi$
$158$	0.969687	0.0771442
$159$	9.96227	0.790059
$160$	1.00000	0.0790569
$161$	−3.35194	−0.264170
$162$	−1.00000	−0.0785674
$163$	−13.6406	−1.06842	−0.534209	−	0.845353i	$-0.679390\pi$
$163$	−13.6406	−1.06842	−0.534209	+	0.845353i	$0.679390\pi$
$164$	7.08613	0.553334
$165$	−3.00000	−0.233550
$166$	−15.5168	−1.20434
$167$	−5.58482	−0.432167	−0.216083	−	0.976375i	$-0.569328\pi$
$167$	−5.58482	−0.432167	−0.216083	+	0.976375i	$0.569328\pi$
$168$	−3.08613	−0.238100
$169$	1.00000	0.0769231
$170$	1.00000	0.0766965
$171$	−7.61033	−0.581976
$172$	−9.87614	−0.753049
$173$	20.8129	1.58238	0.791188	−	0.611573i	$-0.209463\pi$
$173$	20.8129	1.58238	0.791188	+	0.611573i	$0.209463\pi$
$174$	−8.17226	−0.619537
$175$	3.08613	0.233290
$176$	3.00000	0.226134
$177$	7.79001	0.585533
$178$	−9.99258	−0.748976
$179$	6.19777	0.463243	0.231621	−	0.972806i	$-0.425597\pi$
$179$	6.19777	0.463243	0.231621	+	0.972806i	$0.425597\pi$
$180$	−1.00000	−0.0745356
$181$	10.8761	0.808417	0.404209	−	0.914667i	$-0.367547\pi$
$181$	10.8761	0.808417	0.404209	+	0.914667i	$0.367547\pi$
$182$	−3.08613	−0.228759
$183$	−5.43807	−0.401994
$184$	1.08613	0.0800706
$185$	−3.82032	−0.280876
$186$	−3.05582	−0.224063
$187$	3.00000	0.219382
$188$	−7.31421	−0.533443
$189$	3.08613	0.224483
$190$	−7.61033	−0.552111
$191$	21.9623	1.58913	0.794567	−	0.607176i	$-0.207698\pi$
$191$	21.9623	1.58913	0.794567	+	0.607176i	$0.207698\pi$
$192$	1.00000	0.0721688
$193$	14.4562	1.04058	0.520288	−	0.853991i	$-0.325824\pi$
$193$	14.4562	1.04058	0.520288	+	0.853991i	$0.325824\pi$
$194$	5.56193	0.399323
$195$	−1.00000	−0.0716115
$196$	2.52420	0.180300
$197$	−10.3445	−0.737017	−0.368508	−	0.929624i	$-0.620131\pi$
$197$	−10.3445	−0.737017	−0.368508	+	0.929624i	$0.620131\pi$
$198$	−3.00000	−0.213201
$199$	−11.4684	−0.812972	−0.406486	−	0.913657i	$-0.633246\pi$
$199$	−11.4684	−0.812972	−0.406486	+	0.913657i	$0.633246\pi$
$200$	−1.00000	−0.0707107
$201$	−1.03031	−0.0726726
$202$	−9.00000	−0.633238
$203$	25.2207	1.77014
$204$	1.00000	0.0700140
$205$	−7.08613	−0.494917
$206$	−2.70388	−0.188388
$207$	−1.08613	−0.0754913
$208$	1.00000	0.0693375
$209$	−22.8310	−1.57925
$210$	3.08613	0.212963
$211$	1.70869	0.117631	0.0588154	−	0.998269i	$-0.481268\pi$
$211$	1.70869	0.117631	0.0588154	+	0.998269i	$0.481268\pi$
$212$	9.96227	0.684211
$213$	−13.2207	−0.905865
$214$	0.734191	0.0501883
$215$	9.87614	0.673547
$216$	−1.00000	−0.0680414
$217$	9.43065	0.640194
$218$	−19.7523	−1.33779
$219$	16.0787	1.08650
$220$	−3.00000	−0.202260
$221$	1.00000	0.0672673
$222$	−3.82032	−0.256403
$223$	0.240304	0.0160919	0.00804597	−	0.999968i	$-0.497439\pi$
$223$	0.240304	0.0160919	0.00804597	+	0.999968i	$0.497439\pi$
$224$	−3.08613	−0.206201
$225$	1.00000	0.0666667
$226$	−7.40776	−0.492757
$227$	−6.83841	−0.453881	−0.226941	−	0.973909i	$-0.572872\pi$
$227$	−6.83841	−0.453881	−0.226941	+	0.973909i	$0.572872\pi$
$228$	−7.61033	−0.504006
$229$	−9.27648	−0.613007	−0.306503	−	0.951870i	$-0.599159\pi$
$229$	−9.27648	−0.613007	−0.306503	+	0.951870i	$0.599159\pi$
$230$	−1.08613	−0.0716173
$231$	9.25839	0.609157
$232$	−8.17226	−0.536535
$233$	6.67095	0.437029	0.218514	−	0.975834i	$-0.429879\pi$
$233$	6.67095	0.437029	0.218514	+	0.975834i	$0.429879\pi$
$234$	−1.00000	−0.0653720
$235$	7.31421	0.477126
$236$	7.79001	0.507086
$237$	−0.969687	−0.0629880
$238$	−3.08613	−0.200044
$239$	−4.79001	−0.309840	−0.154920	−	0.987927i	$-0.549512\pi$
$239$	−4.79001	−0.309840	−0.154920	+	0.987927i	$0.549512\pi$
$240$	−1.00000	−0.0645497
$241$	14.9016	0.959899	0.479950	−	0.877296i	$-0.340655\pi$
$241$	14.9016	0.959899	0.479950	+	0.877296i	$0.340655\pi$
$242$	2.00000	0.128565
$243$	1.00000	0.0641500
$244$	−5.43807	−0.348137
$245$	−2.52420	−0.161265
$246$	−7.08613	−0.451795
$247$	−7.61033	−0.484234
$248$	−3.05582	−0.194045
$249$	15.5168	0.983336
$250$	1.00000	0.0632456
$251$	4.53162	0.286033	0.143017	−	0.989720i	$-0.454320\pi$
$251$	4.53162	0.286033	0.143017	+	0.989720i	$0.454320\pi$
$252$	3.08613	0.194408
$253$	−3.25839	−0.204853
$254$	13.6406	0.855890
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	6.90164	0.430513	0.215256	−	0.976558i	$-0.430941\pi$
$257$	6.90164	0.430513	0.215256	+	0.976558i	$0.430941\pi$
$258$	9.87614	0.614862
$259$	11.7900	0.732595
$260$	−1.00000	−0.0620174
$261$	8.17226	0.505850
$262$	11.9065	0.735583
$263$	9.51678	0.586830	0.293415	−	0.955985i	$-0.405208\pi$
$263$	9.51678	0.586830	0.293415	+	0.955985i	$0.405208\pi$
$264$	−3.00000	−0.184637
$265$	−9.96227	−0.611977
$266$	23.4865	1.44005
$267$	9.99258	0.611536
$268$	−1.03031	−0.0629364
$269$	−14.3068	−0.872300	−0.436150	−	0.899874i	$-0.643658\pi$
$269$	−14.3068	−0.872300	−0.436150	+	0.899874i	$0.643658\pi$
$270$	1.00000	0.0608581
$271$	25.1090	1.52526	0.762632	−	0.646832i	$-0.223907\pi$
$271$	25.1090	1.52526	0.762632	+	0.646832i	$0.223907\pi$
$272$	1.00000	0.0606339
$273$	3.08613	0.186781
$274$	−7.14676	−0.431751
$275$	3.00000	0.180907
$276$	−1.08613	−0.0653774
$277$	−23.8310	−1.43187	−0.715933	−	0.698169i	$-0.753998\pi$
$277$	−23.8310	−1.43187	−0.715933	+	0.698169i	$0.753998\pi$
$278$	11.2839	0.676763
$279$	3.05582	0.182947
$280$	3.08613	0.184432
$281$	2.83516	0.169131	0.0845657	−	0.996418i	$-0.473050\pi$
$281$	2.83516	0.169131	0.0845657	+	0.996418i	$0.473050\pi$
$282$	7.31421	0.435555
$283$	−21.5046	−1.27831	−0.639157	−	0.769077i	$-0.720716\pi$
$283$	−21.5046	−1.27831	−0.639157	+	0.769077i	$0.720716\pi$
$284$	−13.2207	−0.784502
$285$	7.61033	0.450797
$286$	−3.00000	−0.177394
$287$	21.8687	1.29087
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	8.17226	0.479892
$291$	−5.56193	−0.326046
$292$	16.0787	0.940935
$293$	19.4381	1.13558	0.567792	−	0.823172i	$-0.307798\pi$
$293$	19.4381	1.13558	0.567792	+	0.823172i	$0.307798\pi$
$294$	−2.52420	−0.147214
$295$	−7.79001	−0.453552
$296$	−3.82032	−0.222052
$297$	3.00000	0.174078
$298$	15.4865	0.897107
$299$	−1.08613	−0.0628125
$300$	1.00000	0.0577350
$301$	−30.4791	−1.75678
$302$	5.22066	0.300415
$303$	9.00000	0.517036
$304$	−7.61033	−0.436482
$305$	5.43807	0.311383
$306$	−1.00000	−0.0571662
$307$	24.9878	1.42613	0.713064	−	0.701099i	$-0.247307\pi$
$307$	24.9878	1.42613	0.713064	+	0.701099i	$0.247307\pi$
$308$	9.25839	0.527546
$309$	2.70388	0.153818
$310$	3.05582	0.173559
$311$	−22.5094	−1.27639	−0.638194	−	0.769875i	$-0.720318\pi$
$311$	−22.5094	−1.27639	−0.638194	+	0.769875i	$0.720318\pi$
$312$	−1.00000	−0.0566139
$313$	−4.88836	−0.276307	−0.138153	−	0.990411i	$-0.544117\pi$
$313$	−4.88836	−0.276307	−0.138153	+	0.990411i	$0.544117\pi$
$314$	4.73419	0.267166
$315$	−3.08613	−0.173884
$316$	−0.969687	−0.0545492
$317$	−4.25097	−0.238758	−0.119379	−	0.992849i	$-0.538090\pi$
$317$	−4.25097	−0.238758	−0.119379	+	0.992849i	$0.538090\pi$
$318$	−9.96227	−0.558656
$319$	24.5168	1.37268
$320$	−1.00000	−0.0559017
$321$	−0.734191	−0.0409785
$322$	3.35194	0.186796
$323$	−7.61033	−0.423450
$324$	1.00000	0.0555556
$325$	1.00000	0.0554700
$326$	13.6406	0.755485
$327$	19.7523	1.09230
$328$	−7.08613	−0.391266
$329$	−22.5726	−1.24447
$330$	3.00000	0.165145
$331$	34.4413	1.89307	0.946533	−	0.322607i	$-0.104559\pi$
$331$	34.4413	1.89307	0.946533	+	0.322607i	$0.104559\pi$
$332$	15.5168	0.851594
$333$	3.82032	0.209352
$334$	5.58482	0.305588
$335$	1.03031	0.0562920
$336$	3.08613	0.168362
$337$	−30.9804	−1.68761	−0.843804	−	0.536652i	$-0.819689\pi$
$337$	−30.9804	−1.68761	−0.843804	+	0.536652i	$0.819689\pi$
$338$	−1.00000	−0.0543928
$339$	7.40776	0.402334
$340$	−1.00000	−0.0542326
$341$	9.16745	0.496445
$342$	7.61033	0.411520
$343$	−13.8129	−0.745827
$344$	9.87614	0.532486
$345$	1.08613	0.0584753
$346$	−20.8129	−1.11891
$347$	4.14676	0.222609	0.111305	−	0.993786i	$-0.464497\pi$
$347$	4.14676	0.222609	0.111305	+	0.993786i	$0.464497\pi$
$348$	8.17226	0.438079
$349$	−0.771922	−0.0413200	−0.0206600	−	0.999787i	$-0.506577\pi$
$349$	−0.771922	−0.0413200	−0.0206600	+	0.999787i	$0.506577\pi$
$350$	−3.08613	−0.164961
$351$	1.00000	0.0533761
$352$	−3.00000	−0.159901
$353$	−18.5168	−0.985549	−0.492774	−	0.870157i	$-0.664017\pi$
$353$	−18.5168	−0.985549	−0.492774	+	0.870157i	$0.664017\pi$
$354$	−7.79001	−0.414034
$355$	13.2207	0.701680
$356$	9.99258	0.529606
$357$	3.08613	0.163335
$358$	−6.19777	−0.327562
$359$	12.0000	0.633336	0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000	0.633336	0.316668	+	0.948536i	$0.397436\pi$
$360$	1.00000	0.0527046
$361$	38.9171	2.04827
$362$	−10.8761	−0.571637
$363$	−2.00000	−0.104973
$364$	3.08613	0.161757
$365$	−16.0787	−0.841598
$366$	5.43807	0.284252
$367$	28.9474	1.51104	0.755522	−	0.655123i	$-0.227383\pi$
$367$	28.9474	1.51104	0.755522	+	0.655123i	$0.227383\pi$
$368$	−1.08613	−0.0566185
$369$	7.08613	0.368889
$370$	3.82032	0.198609
$371$	30.7449	1.59619
$372$	3.05582	0.158437
$373$	30.3552	1.57173	0.785866	−	0.618397i	$-0.212218\pi$
$373$	30.3552	1.57173	0.785866	+	0.618397i	$0.212218\pi$
$374$	−3.00000	−0.155126
$375$	−1.00000	−0.0516398
$376$	7.31421	0.377201
$377$	8.17226	0.420893
$378$	−3.08613	−0.158733
$379$	−8.43807	−0.433435	−0.216717	−	0.976234i	$-0.569535\pi$
$379$	−8.43807	−0.433435	−0.216717	+	0.976234i	$0.569535\pi$
$380$	7.61033	0.390402
$381$	−13.6406	−0.698831
$382$	−21.9623	−1.12369
$383$	−30.8794	−1.57786	−0.788932	−	0.614481i	$-0.789365\pi$
$383$	−30.8794	−1.57786	−0.788932	+	0.614481i	$0.789365\pi$
$384$	−1.00000	−0.0510310
$385$	−9.25839	−0.471851
$386$	−14.4562	−0.735799
$387$	−9.87614	−0.502032
$388$	−5.56193	−0.282364
$389$	25.5120	1.29351	0.646754	−	0.762698i	$-0.276126\pi$
$389$	25.5120	1.29351	0.646754	+	0.762698i	$0.276126\pi$
$390$	1.00000	0.0506370
$391$	−1.08613	−0.0549280
$392$	−2.52420	−0.127491
$393$	−11.9065	−0.600601
$394$	10.3445	0.521149
$395$	0.969687	0.0487903
$396$	3.00000	0.150756
$397$	−19.8687	−0.997182	−0.498591	−	0.866837i	$-0.666149\pi$
$397$	−19.8687	−0.997182	−0.498591	+	0.866837i	$0.666149\pi$
$398$	11.4684	0.574858
$399$	−23.4865	−1.17579
$400$	1.00000	0.0500000
$401$	13.4684	0.672579	0.336289	−	0.941759i	$-0.390828\pi$
$401$	13.4684	0.672579	0.336289	+	0.941759i	$0.390828\pi$
$402$	1.03031	0.0513873
$403$	3.05582	0.152221
$404$	9.00000	0.447767
$405$	−1.00000	−0.0496904
$406$	−25.2207	−1.25168
$407$	11.4610	0.568099
$408$	−1.00000	−0.0495074
$409$	6.95485	0.343895	0.171948	−	0.985106i	$-0.444994\pi$
$409$	6.95485	0.343895	0.171948	+	0.985106i	$0.444994\pi$
$410$	7.08613	0.349959
$411$	7.14676	0.352523
$412$	2.70388	0.133211
$413$	24.0410	1.18298
$414$	1.08613	0.0533804
$415$	−15.5168	−0.761689
$416$	−1.00000	−0.0490290
$417$	−11.2839	−0.552575
$418$	22.8310	1.11670
$419$	31.0336	1.51609	0.758044	−	0.652203i	$-0.226155\pi$
$419$	31.0336	1.51609	0.758044	+	0.652203i	$0.226155\pi$
$420$	−3.08613	−0.150588
$421$	4.58482	0.223451	0.111725	−	0.993739i	$-0.464362\pi$
$421$	4.58482	0.223451	0.111725	+	0.993739i	$0.464362\pi$
$422$	−1.70869	−0.0831775
$423$	−7.31421	−0.355629
$424$	−9.96227	−0.483811
$425$	1.00000	0.0485071
$426$	13.2207	0.640543
$427$	−16.7826	−0.812166
$428$	−0.734191	−0.0354885
$429$	3.00000	0.144841
$430$	−9.87614	−0.476270
$431$	17.3897	0.837631	0.418815	−	0.908071i	$-0.362445\pi$
$431$	17.3897	0.837631	0.418815	+	0.908071i	$0.362445\pi$
$432$	1.00000	0.0481125
$433$	−17.4817	−0.840115	−0.420058	−	0.907497i	$-0.637990\pi$
$433$	−17.4817	−0.840115	−0.420058	+	0.907497i	$0.637990\pi$
$434$	−9.43065	−0.452686
$435$	−8.17226	−0.391830
$436$	19.7523	0.945963
$437$	8.26581	0.395407
$438$	−16.0787	−0.768271
$439$	−2.62517	−0.125292	−0.0626462	−	0.998036i	$-0.519954\pi$
$439$	−2.62517	−0.125292	−0.0626462	+	0.998036i	$0.519954\pi$
$440$	3.00000	0.143019
$441$	2.52420	0.120200
$442$	−1.00000	−0.0475651
$443$	−17.9065	−0.850761	−0.425381	−	0.905015i	$-0.639860\pi$
$443$	−17.9065	−0.850761	−0.425381	+	0.905015i	$0.639860\pi$
$444$	3.82032	0.181304
$445$	−9.99258	−0.473694
$446$	−0.240304	−0.0113787
$447$	−15.4865	−0.732485
$448$	3.08613	0.145806
$449$	13.4684	0.635612	0.317806	−	0.948156i	$-0.397054\pi$
$449$	13.4684	0.635612	0.317806	+	0.948156i	$0.397054\pi$
$450$	−1.00000	−0.0471405
$451$	21.2584	1.00102
$452$	7.40776	0.348432
$453$	−5.22066	−0.245288
$454$	6.83841	0.320942
$455$	−3.08613	−0.144680
$456$	7.61033	0.356386
$457$	−34.4562	−1.61179	−0.805895	−	0.592058i	$-0.798316\pi$
$457$	−34.4562	−1.61179	−0.805895	+	0.592058i	$0.798316\pi$
$458$	9.27648	0.433461
$459$	1.00000	0.0466760
$460$	1.08613	0.0506411
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	−9.25839	−0.430739
$463$	1.60708	0.0746873	0.0373437	−	0.999302i	$-0.488110\pi$
$463$	1.60708	0.0746873	0.0373437	+	0.999302i	$0.488110\pi$
$464$	8.17226	0.379388
$465$	−3.05582	−0.141710
$466$	−6.67095	−0.309026
$467$	−0.187097	−0.00865783	−0.00432891	−	0.999991i	$-0.501378\pi$
$467$	−0.187097	−0.00865783	−0.00432891	+	0.999991i	$0.501378\pi$
$468$	1.00000	0.0462250
$469$	−3.17968	−0.146824
$470$	−7.31421	−0.337379
$471$	−4.73419	−0.218140
$472$	−7.79001	−0.358564
$473$	−29.6284	−1.36232
$474$	0.969687	0.0445392
$475$	−7.61033	−0.349186
$476$	3.08613	0.141453
$477$	9.96227	0.456141
$478$	4.79001	0.219090
$479$	−2.78259	−0.127140	−0.0635699	−	0.997977i	$-0.520249\pi$
$479$	−2.78259	−0.127140	−0.0635699	+	0.997977i	$0.520249\pi$
$480$	1.00000	0.0456435
$481$	3.82032	0.174192
$482$	−14.9016	−0.678751
$483$	−3.35194	−0.152519
$484$	−2.00000	−0.0909091
$485$	5.56193	0.252554
$486$	−1.00000	−0.0453609
$487$	16.1116	0.730088	0.365044	−	0.930990i	$-0.381054\pi$
$487$	16.1116	0.730088	0.365044	+	0.930990i	$0.381054\pi$
$488$	5.43807	0.246170
$489$	−13.6406	−0.616851
$490$	2.52420	0.114032
$491$	12.5774	0.567610	0.283805	−	0.958882i	$-0.408403\pi$
$491$	12.5774	0.567610	0.283805	+	0.958882i	$0.408403\pi$
$492$	7.08613	0.319467
$493$	8.17226	0.368060
$494$	7.61033	0.342405
$495$	−3.00000	−0.134840
$496$	3.05582	0.137210
$497$	−40.8007	−1.83016
$498$	−15.5168	−0.695324
$499$	12.8613	0.575751	0.287875	−	0.957668i	$-0.407051\pi$
$499$	12.8613	0.575751	0.287875	+	0.957668i	$0.407051\pi$
$500$	−1.00000	−0.0447214
$501$	−5.58482	−0.249512
$502$	−4.53162	−0.202256
$503$	−32.4413	−1.44649	−0.723243	−	0.690593i	$-0.757350\pi$
$503$	−32.4413	−1.44649	−0.723243	+	0.690593i	$0.757350\pi$
$504$	−3.08613	−0.137467
$505$	−9.00000	−0.400495
$506$	3.25839	0.144853
$507$	1.00000	0.0444116
$508$	−13.6406	−0.605206
$509$	−3.03031	−0.134316	−0.0671581	−	0.997742i	$-0.521393\pi$
$509$	−3.03031	−0.134316	−0.0671581	+	0.997742i	$0.521393\pi$
$510$	1.00000	0.0442807
$511$	49.6210	2.19510
$512$	−1.00000	−0.0441942
$513$	−7.61033	−0.336004
$514$	−6.90164	−0.304418
$515$	−2.70388	−0.119147
$516$	−9.87614	−0.434773
$517$	−21.9426	−0.965036
$518$	−11.7900	−0.518023
$519$	20.8129	0.913585
$520$	1.00000	0.0438529
$521$	14.2329	0.623554	0.311777	−	0.950155i	$-0.399076\pi$
$521$	14.2329	0.623554	0.311777	+	0.950155i	$0.399076\pi$
$522$	−8.17226	−0.357690
$523$	−9.06804	−0.396518	−0.198259	−	0.980150i	$-0.563529\pi$
$523$	−9.06804	−0.396518	−0.198259	+	0.980150i	$0.563529\pi$
$524$	−11.9065	−0.520136
$525$	3.08613	0.134690
$526$	−9.51678	−0.414951
$527$	3.05582	0.133114
$528$	3.00000	0.130558
$529$	−21.8203	−0.948710
$530$	9.96227	0.432733
$531$	7.79001	0.338058
$532$	−23.4865	−1.01827
$533$	7.08613	0.306934
$534$	−9.99258	−0.432421
$535$	0.734191	0.0317418
$536$	1.03031	0.0445027
$537$	6.19777	0.267453
$538$	14.3068	0.616810
$539$	7.57260	0.326175
$540$	−1.00000	−0.0430331
$541$	14.7645	0.634776	0.317388	−	0.948296i	$-0.397194\pi$
$541$	14.7645	0.634776	0.317388	+	0.948296i	$0.397194\pi$
$542$	−25.1090	−1.07852
$543$	10.8761	0.466740
$544$	−1.00000	−0.0428746
$545$	−19.7523	−0.846095
$546$	−3.08613	−0.132074
$547$	15.3552	0.656540	0.328270	−	0.944584i	$-0.393534\pi$
$547$	15.3552	0.656540	0.328270	+	0.944584i	$0.393534\pi$
$548$	7.14676	0.305294
$549$	−5.43807	−0.232091
$550$	−3.00000	−0.127920
$551$	−62.1936	−2.64954
$552$	1.08613	0.0462288
$553$	−2.99258	−0.127258
$554$	23.8310	1.01248
$555$	−3.82032	−0.162164
$556$	−11.2839	−0.478544
$557$	15.5907	0.660599	0.330299	−	0.943876i	$-0.392850\pi$
$557$	15.5907	0.660599	0.330299	+	0.943876i	$0.392850\pi$
$558$	−3.05582	−0.129363
$559$	−9.87614	−0.417716
$560$	−3.08613	−0.130413
$561$	3.00000	0.126660
$562$	−2.83516	−0.119594
$563$	20.6613	0.870772	0.435386	−	0.900244i	$-0.356612\pi$
$563$	20.6613	0.870772	0.435386	+	0.900244i	$0.356612\pi$
$564$	−7.31421	−0.307984
$565$	−7.40776	−0.311647
$566$	21.5046	0.903904
$567$	3.08613	0.129605
$568$	13.2207	0.554727
$569$	−28.1574	−1.18042	−0.590210	−	0.807250i	$-0.700955\pi$
$569$	−28.1574	−1.18042	−0.590210	+	0.807250i	$0.700955\pi$
$570$	−7.61033	−0.318762
$571$	18.0558	0.755612	0.377806	−	0.925885i	$-0.376679\pi$
$571$	18.0558	0.755612	0.377806	+	0.925885i	$0.376679\pi$
$572$	3.00000	0.125436
$573$	21.9623	0.917487
$574$	−21.8687	−0.912783
$575$	−1.08613	−0.0452948
$576$	1.00000	0.0416667
$577$	46.9581	1.95489	0.977446	−	0.211187i	$-0.0677329\pi$
$577$	46.9581	1.95489	0.977446	+	0.211187i	$0.0677329\pi$
$578$	−1.00000	−0.0415945
$579$	14.4562	0.600777
$580$	−8.17226	−0.339335
$581$	47.8868	1.98668
$582$	5.56193	0.230549
$583$	29.8868	1.23779
$584$	−16.0787	−0.665342
$585$	−1.00000	−0.0413449
$586$	−19.4381	−0.802979
$587$	11.5874	0.478265	0.239132	−	0.970987i	$-0.423137\pi$
$587$	11.5874	0.478265	0.239132	+	0.970987i	$0.423137\pi$
$588$	2.52420	0.104096
$589$	−23.2558	−0.958238
$590$	7.79001	0.320710
$591$	−10.3445	−0.425517
$592$	3.82032	0.157014
$593$	−0.321627	−0.0132076	−0.00660381	−	0.999978i	$-0.502102\pi$
$593$	−0.321627	−0.0132076	−0.00660381	+	0.999978i	$0.502102\pi$
$594$	−3.00000	−0.123091
$595$	−3.08613	−0.126519
$596$	−15.4865	−0.634350
$597$	−11.4684	−0.469370
$598$	1.08613	0.0444152
$599$	−0.321627	−0.0131413	−0.00657065	−	0.999978i	$-0.502092\pi$
$599$	−0.321627	−0.0131413	−0.00657065	+	0.999978i	$0.502092\pi$
$600$	−1.00000	−0.0408248
$601$	43.8868	1.79018	0.895090	−	0.445885i	$-0.147111\pi$
$601$	43.8868	1.79018	0.895090	+	0.445885i	$0.147111\pi$
$602$	30.4791	1.24223
$603$	−1.03031	−0.0419576
$604$	−5.22066	−0.212426
$605$	2.00000	0.0813116
$606$	−9.00000	−0.365600
$607$	−38.5619	−1.56518	−0.782590	−	0.622537i	$-0.786102\pi$
$607$	−38.5619	−1.56518	−0.782590	+	0.622537i	$0.786102\pi$
$608$	7.61033	0.308640
$609$	25.2207	1.02199
$610$	−5.43807	−0.220181
$611$	−7.31421	−0.295901
$612$	1.00000	0.0404226
$613$	20.7039	0.836222	0.418111	−	0.908396i	$-0.362692\pi$
$613$	20.7039	0.836222	0.418111	+	0.908396i	$0.362692\pi$
$614$	−24.9878	−1.00842
$615$	−7.08613	−0.285740
$616$	−9.25839	−0.373031
$617$	13.0968	0.527257	0.263629	−	0.964624i	$-0.415081\pi$
$617$	13.0968	0.527257	0.263629	+	0.964624i	$0.415081\pi$
$618$	−2.70388	−0.108766
$619$	23.6736	0.951521	0.475760	−	0.879575i	$-0.342173\pi$
$619$	23.6736	0.951521	0.475760	+	0.879575i	$0.342173\pi$
$620$	−3.05582	−0.122725
$621$	−1.08613	−0.0435849
$622$	22.5094	0.902543
$623$	30.8384	1.23551
$624$	1.00000	0.0400320
$625$	1.00000	0.0400000
$626$	4.88836	0.195378
$627$	−22.8310	−0.911782
$628$	−4.73419	−0.188915
$629$	3.82032	0.152326
$630$	3.08613	0.122954
$631$	35.4535	1.41138	0.705692	−	0.708519i	$-0.250636\pi$
$631$	35.4535	1.41138	0.705692	+	0.708519i	$0.250636\pi$
$632$	0.969687	0.0385721
$633$	1.70869	0.0679142
$634$	4.25097	0.168828
$635$	13.6406	0.541312
$636$	9.96227	0.395030
$637$	2.52420	0.100012
$638$	−24.5168	−0.970629
$639$	−13.2207	−0.523001
$640$	1.00000	0.0395285
$641$	−28.8720	−1.14037	−0.570187	−	0.821515i	$-0.693129\pi$
$641$	−28.8720	−1.14037	−0.570187	+	0.821515i	$0.693129\pi$
$642$	0.734191	0.0289762
$643$	−11.6661	−0.460068	−0.230034	−	0.973183i	$-0.573884\pi$
$643$	−11.6661	−0.460068	−0.230034	+	0.973183i	$0.573884\pi$
$644$	−3.35194	−0.132085
$645$	9.87614	0.388873
$646$	7.61033	0.299424
$647$	−6.23069	−0.244954	−0.122477	−	0.992471i	$-0.539084\pi$
$647$	−6.23069	−0.244954	−0.122477	+	0.992471i	$0.539084\pi$
$648$	−1.00000	−0.0392837
$649$	23.3700	0.917354
$650$	−1.00000	−0.0392232
$651$	9.43065	0.369616
$652$	−13.6406	−0.534209
$653$	−27.7449	−1.08574	−0.542870	−	0.839817i	$-0.682662\pi$
$653$	−27.7449	−1.08574	−0.542870	+	0.839817i	$0.682662\pi$
$654$	−19.7523	−0.772375
$655$	11.9065	0.465224
$656$	7.08613	0.276667
$657$	16.0787	0.627290
$658$	22.5726	0.879972
$659$	−46.7045	−1.81935	−0.909675	−	0.415321i	$-0.863669\pi$
$659$	−46.7045	−1.81935	−0.909675	+	0.415321i	$0.863669\pi$
$660$	−3.00000	−0.116775
$661$	−24.7933	−0.964346	−0.482173	−	0.876076i	$-0.660152\pi$
$661$	−24.7933	−0.964346	−0.482173	+	0.876076i	$0.660152\pi$
$662$	−34.4413	−1.33860
$663$	1.00000	0.0388368
$664$	−15.5168	−0.602168
$665$	23.4865	0.910766
$666$	−3.82032	−0.148034
$667$	−8.87614	−0.343685
$668$	−5.58482	−0.216083
$669$	0.240304	0.00929069
$670$	−1.03031	−0.0398044
$671$	−16.3142	−0.629803
$672$	−3.08613	−0.119050
$673$	31.2159	1.20328	0.601641	−	0.798766i	$-0.294514\pi$
$673$	31.2159	1.20328	0.601641	+	0.798766i	$0.294514\pi$
$674$	30.9804	1.19332
$675$	1.00000	0.0384900
$676$	1.00000	0.0384615
$677$	−2.29612	−0.0882471	−0.0441236	−	0.999026i	$-0.514050\pi$
$677$	−2.29612	−0.0882471	−0.0441236	+	0.999026i	$0.514050\pi$
$678$	−7.40776	−0.284493
$679$	−17.1648	−0.658726
$680$	1.00000	0.0383482
$681$	−6.83841	−0.262048
$682$	−9.16745	−0.351040
$683$	18.4562	0.706205	0.353103	−	0.935585i	$-0.385127\pi$
$683$	18.4562	0.706205	0.353103	+	0.935585i	$0.385127\pi$
$684$	−7.61033	−0.290988
$685$	−7.14676	−0.273063
$686$	13.8129	0.527379
$687$	−9.27648	−0.353920
$688$	−9.87614	−0.376524
$689$	9.96227	0.379532
$690$	−1.08613	−0.0413483
$691$	−18.3478	−0.697982	−0.348991	−	0.937126i	$-0.613476\pi$
$691$	−18.3478	−0.697982	−0.348991	+	0.937126i	$0.613476\pi$
$692$	20.8129	0.791188
$693$	9.25839	0.351697
$694$	−4.14676	−0.157409
$695$	11.2839	0.428023
$696$	−8.17226	−0.309769
$697$	7.08613	0.268406
$698$	0.771922	0.0292177
$699$	6.67095	0.252319
$700$	3.08613	0.116645
$701$	−0.475800	−0.0179707	−0.00898537	−	0.999960i	$-0.502860\pi$
$701$	−0.475800	−0.0179707	−0.00898537	+	0.999960i	$0.502860\pi$
$702$	−1.00000	−0.0377426
$703$	−29.0739	−1.09654
$704$	3.00000	0.113067
$705$	7.31421	0.275469
$706$	18.5168	0.696888
$707$	27.7752	1.04459
$708$	7.79001	0.292766
$709$	−7.44549	−0.279621	−0.139811	−	0.990178i	$-0.544649\pi$
$709$	−7.44549	−0.279621	−0.139811	+	0.990178i	$0.544649\pi$
$710$	−13.2207	−0.496163
$711$	−0.969687	−0.0363661
$712$	−9.99258	−0.374488
$713$	−3.31902	−0.124298
$714$	−3.08613	−0.115496
$715$	−3.00000	−0.112194
$716$	6.19777	0.231621
$717$	−4.79001	−0.178886
$718$	−12.0000	−0.447836
$719$	37.0745	1.38265	0.691324	−	0.722545i	$-0.257028\pi$
$719$	37.0745	1.38265	0.691324	+	0.722545i	$0.257028\pi$
$720$	−1.00000	−0.0372678
$721$	8.34452	0.310766
$722$	−38.9171	−1.44835
$723$	14.9016	0.554198
$724$	10.8761	0.404209
$725$	8.17226	0.303510
$726$	2.00000	0.0742270
$727$	19.5981	0.726853	0.363427	−	0.931623i	$-0.381607\pi$
$727$	19.5981	0.726853	0.363427	+	0.931623i	$0.381607\pi$
$728$	−3.08613	−0.114380
$729$	1.00000	0.0370370
$730$	16.0787	0.595100
$731$	−9.87614	−0.365282
$732$	−5.43807	−0.200997
$733$	−13.9623	−0.515708	−0.257854	−	0.966184i	$-0.583015\pi$
$733$	−13.9623	−0.515708	−0.257854	+	0.966184i	$0.583015\pi$
$734$	−28.9474	−1.06847
$735$	−2.52420	−0.0931065
$736$	1.08613	0.0400353
$737$	−3.09094	−0.113856
$738$	−7.08613	−0.260844
$739$	25.9197	0.953473	0.476736	−	0.879046i	$-0.341820\pi$
$739$	25.9197	0.953473	0.476736	+	0.879046i	$0.341820\pi$
$740$	−3.82032	−0.140438
$741$	−7.61033	−0.279572
$742$	−30.7449	−1.12868
$743$	−1.14937	−0.0421662	−0.0210831	−	0.999778i	$-0.506711\pi$
$743$	−1.14937	−0.0421662	−0.0210831	+	0.999778i	$0.506711\pi$
$744$	−3.05582	−0.112032
$745$	15.4865	0.567380
$746$	−30.3552	−1.11138
$747$	15.5168	0.567729
$748$	3.00000	0.109691
$749$	−2.26581	−0.0827909
$750$	1.00000	0.0365148
$751$	−11.0336	−0.402620	−0.201310	−	0.979528i	$-0.564520\pi$
$751$	−11.0336	−0.402620	−0.201310	+	0.979528i	$0.564520\pi$
$752$	−7.31421	−0.266722
$753$	4.53162	0.165141
$754$	−8.17226	−0.297616
$755$	5.22066	0.189999
$756$	3.08613	0.112241
$757$	−33.5758	−1.22033	−0.610167	−	0.792272i	$-0.708898\pi$
$757$	−33.5758	−1.22033	−0.610167	+	0.792272i	$0.708898\pi$
$758$	8.43807	0.306484
$759$	−3.25839	−0.118272
$760$	−7.61033	−0.276056
$761$	−15.2084	−0.551305	−0.275653	−	0.961257i	$-0.588894\pi$
$761$	−15.2084	−0.551305	−0.275653	+	0.961257i	$0.588894\pi$
$762$	13.6406	0.494148
$763$	60.9581	2.20683
$764$	21.9623	0.794567
$765$	−1.00000	−0.0361551
$766$	30.8794	1.11572
$767$	7.79001	0.281281
$768$	1.00000	0.0360844
$769$	−24.9368	−0.899243	−0.449621	−	0.893219i	$-0.648441\pi$
$769$	−24.9368	−0.899243	−0.449621	+	0.893219i	$0.648441\pi$
$770$	9.25839	0.333649
$771$	6.90164	0.248557
$772$	14.4562	0.520288
$773$	19.1903	0.690229	0.345114	−	0.938561i	$-0.387840\pi$
$773$	19.1903	0.690229	0.345114	+	0.938561i	$0.387840\pi$
$774$	9.87614	0.354990
$775$	3.05582	0.109768
$776$	5.56193	0.199662
$777$	11.7900	0.422964
$778$	−25.5120	−0.914649
$779$	−53.9278	−1.93216
$780$	−1.00000	−0.0358057
$781$	−39.6620	−1.41922
$782$	1.08613	0.0388399
$783$	8.17226	0.292053
$784$	2.52420	0.0901500
$785$	4.73419	0.168971
$786$	11.9065	0.424689
$787$	1.58482	0.0564929	0.0282465	−	0.999601i	$-0.491008\pi$
$787$	1.58482	0.0564929	0.0282465	+	0.999601i	$0.491008\pi$
$788$	−10.3445	−0.368508
$789$	9.51678	0.338806
$790$	−0.969687	−0.0344999
$791$	22.8613	0.812854
$792$	−3.00000	−0.106600
$793$	−5.43807	−0.193112
$794$	19.8687	0.705115
$795$	−9.96227	−0.353325
$796$	−11.4684	−0.406486
$797$	20.6284	0.730696	0.365348	−	0.930871i	$-0.380950\pi$
$797$	20.6284	0.730696	0.365348	+	0.930871i	$0.380950\pi$
$798$	23.4865	0.831412
$799$	−7.31421	−0.258758
$800$	−1.00000	−0.0353553
$801$	9.99258	0.353071
$802$	−13.4684	−0.475585
$803$	48.2361	1.70222
$804$	−1.03031	−0.0363363
$805$	3.35194	0.118140
$806$	−3.05582	−0.107637
$807$	−14.3068	−0.503623
$808$	−9.00000	−0.316619
$809$	−48.4062	−1.70187	−0.850936	−	0.525270i	$-0.823964\pi$
$809$	−48.4062	−1.70187	−0.850936	+	0.525270i	$0.823964\pi$
$810$	1.00000	0.0351364
$811$	34.9581	1.22754	0.613772	−	0.789483i	$-0.289651\pi$
$811$	34.9581	1.22754	0.613772	+	0.789483i	$0.289651\pi$
$812$	25.2207	0.885072
$813$	25.1090	0.880612
$814$	−11.4610	−0.401707
$815$	13.6406	0.477811
$816$	1.00000	0.0350070
$817$	75.1607	2.62954
$818$	−6.95485	−0.243171
$819$	3.08613	0.107838
$820$	−7.08613	−0.247458
$821$	53.3674	1.86254	0.931268	−	0.364335i	$-0.118704\pi$
$821$	53.3674	1.86254	0.931268	+	0.364335i	$0.118704\pi$
$822$	−7.14676	−0.249272
$823$	−13.8081	−0.481320	−0.240660	−	0.970609i	$-0.577364\pi$
$823$	−13.8081	−0.481320	−0.240660	+	0.970609i	$0.577364\pi$
$824$	−2.70388	−0.0941941
$825$	3.00000	0.104447
$826$	−24.0410	−0.836493
$827$	−28.8613	−1.00361	−0.501803	−	0.864982i	$-0.667330\pi$
$827$	−28.8613	−1.00361	−0.501803	+	0.864982i	$0.667330\pi$
$828$	−1.08613	−0.0377456
$829$	28.8432	1.00177	0.500883	−	0.865515i	$-0.333009\pi$
$829$	28.8432	1.00177	0.500883	+	0.865515i	$0.333009\pi$
$830$	15.5168	0.538595
$831$	−23.8310	−0.826688
$832$	1.00000	0.0346688
$833$	2.52420	0.0874583
$834$	11.2839	0.390729
$835$	5.58482	0.193271
$836$	−22.8310	−0.789626
$837$	3.05582	0.105625
$838$	−31.0336	−1.07204
$839$	17.2632	0.595992	0.297996	−	0.954567i	$-0.403682\pi$
$839$	17.2632	0.595992	0.297996	+	0.954567i	$0.403682\pi$
$840$	3.08613	0.106482
$841$	37.7858	1.30296
$842$	−4.58482	−0.158003
$843$	2.83516	0.0976480
$844$	1.70869	0.0588154
$845$	−1.00000	−0.0344010
$846$	7.31421	0.251468
$847$	−6.17226	−0.212081
$848$	9.96227	0.342106
$849$	−21.5046	−0.738034
$850$	−1.00000	−0.0342997
$851$	−4.14937	−0.142238
$852$	−13.2207	−0.452932
$853$	6.52901	0.223549	0.111774	−	0.993734i	$-0.464347\pi$
$853$	6.52901	0.223549	0.111774	+	0.993734i	$0.464347\pi$
$854$	16.7826	0.574288
$855$	7.61033	0.260268
$856$	0.734191	0.0250941
$857$	−53.5929	−1.83070	−0.915349	−	0.402661i	$-0.868085\pi$
$857$	−53.5929	−1.83070	−0.915349	+	0.402661i	$0.868085\pi$
$858$	−3.00000	−0.102418
$859$	−19.9623	−0.681104	−0.340552	−	0.940226i	$-0.610614\pi$
$859$	−19.9623	−0.681104	−0.340552	+	0.940226i	$0.610614\pi$
$860$	9.87614	0.336774
$861$	21.8687	0.745284
$862$	−17.3897	−0.592295
$863$	10.2510	0.348947	0.174474	−	0.984662i	$-0.444178\pi$
$863$	10.2510	0.348947	0.174474	+	0.984662i	$0.444178\pi$
$864$	−1.00000	−0.0340207
$865$	−20.8129	−0.707660
$866$	17.4817	0.594051
$867$	1.00000	0.0339618
$868$	9.43065	0.320097
$869$	−2.90906	−0.0986832
$870$	8.17226	0.277066
$871$	−1.03031	−0.0349108
$872$	−19.7523	−0.668897
$873$	−5.56193	−0.188243
$874$	−8.26581	−0.279595
$875$	−3.08613	−0.104330
$876$	16.0787	0.543249
$877$	−32.0942	−1.08374	−0.541872	−	0.840461i	$-0.682284\pi$
$877$	−32.0942	−1.08374	−0.541872	+	0.840461i	$0.682284\pi$
$878$	2.62517	0.0885951
$879$	19.4381	0.655630
$880$	−3.00000	−0.101130
$881$	−9.67095	−0.325823	−0.162911	−	0.986641i	$-0.552088\pi$
$881$	−9.67095	−0.325823	−0.162911	+	0.986641i	$0.552088\pi$
$882$	−2.52420	−0.0849942
$883$	−48.7736	−1.64136	−0.820681	−	0.571386i	$-0.806406\pi$
$883$	−48.7736	−1.64136	−0.820681	+	0.571386i	$0.806406\pi$
$884$	1.00000	0.0336336
$885$	−7.79001	−0.261858
$886$	17.9065	0.601579
$887$	−34.9219	−1.17256	−0.586282	−	0.810107i	$-0.699409\pi$
$887$	−34.9219	−1.17256	−0.586282	+	0.810107i	$0.699409\pi$
$888$	−3.82032	−0.128202
$889$	−42.0968	−1.41188
$890$	9.99258	0.334952
$891$	3.00000	0.100504
$892$	0.240304	0.00804597
$893$	55.6635	1.86271
$894$	15.4865	0.517945
$895$	−6.19777	−0.207168
$896$	−3.08613	−0.103100
$897$	−1.08613	−0.0362648
$898$	−13.4684	−0.449446
$899$	24.9729	0.832894
$900$	1.00000	0.0333333
$901$	9.96227	0.331891
$902$	−21.2584	−0.707827
$903$	−30.4791	−1.01428
$904$	−7.40776	−0.246378
$905$	−10.8761	−0.361535
$906$	5.22066	0.173445
$907$	−45.8210	−1.52146	−0.760730	−	0.649068i	$-0.775159\pi$
$907$	−45.8210	−1.52146	−0.760730	+	0.649068i	$0.775159\pi$
$908$	−6.83841	−0.226941
$909$	9.00000	0.298511
$910$	3.08613	0.102304
$911$	−10.3419	−0.342643	−0.171321	−	0.985215i	$-0.554804\pi$
$911$	−10.3419	−0.342643	−0.171321	+	0.985215i	$0.554804\pi$
$912$	−7.61033	−0.252003
$913$	46.5503	1.54059
$914$	34.4562	1.13971
$915$	5.43807	0.179777
$916$	−9.27648	−0.306503
$917$	−36.7449	−1.21342
$918$	−1.00000	−0.0330049
$919$	−34.2797	−1.13078	−0.565392	−	0.824822i	$-0.691275\pi$
$919$	−34.2797	−1.13078	−0.565392	+	0.824822i	$0.691275\pi$
$920$	−1.08613	−0.0358087
$921$	24.9878	0.823375
$922$	0	0
$923$	−13.2207	−0.435163
$924$	9.25839	0.304579
$925$	3.82032	0.125611
$926$	−1.60708	−0.0528119
$927$	2.70388	0.0888070
$928$	−8.17226	−0.268268
$929$	55.4158	1.81813	0.909067	−	0.416650i	$-0.136796\pi$
$929$	55.4158	1.81813	0.909067	+	0.416650i	$0.136796\pi$
$930$	3.05582	0.100204
$931$	−19.2100	−0.629582
$932$	6.67095	0.218514
$933$	−22.5094	−0.736923
$934$	0.187097	0.00612201
$935$	−3.00000	−0.0981105
$936$	−1.00000	−0.0326860
$937$	−30.6284	−1.00059	−0.500293	−	0.865856i	$-0.666775\pi$
$937$	−30.6284	−1.00059	−0.500293	+	0.865856i	$0.666775\pi$
$938$	3.17968	0.103820
$939$	−4.88836	−0.159526
$940$	7.31421	0.238563
$941$	23.9091	0.779413	0.389707	−	0.920939i	$-0.372576\pi$
$941$	23.9091	0.779413	0.389707	+	0.920939i	$0.372576\pi$
$942$	4.73419	0.154248
$943$	−7.69646	−0.250631
$944$	7.79001	0.253543
$945$	−3.08613	−0.100392
$946$	29.6284	0.963303
$947$	−47.0484	−1.52887	−0.764434	−	0.644702i	$-0.776981\pi$
$947$	−47.0484	−1.52887	−0.764434	+	0.644702i	$0.776981\pi$
$948$	−0.969687	−0.0314940
$949$	16.0787	0.521937
$950$	7.61033	0.246912
$951$	−4.25097	−0.137847
$952$	−3.08613	−0.100022
$953$	21.0739	0.682651	0.341325	−	0.939945i	$-0.389124\pi$
$953$	21.0739	0.682651	0.341325	+	0.939945i	$0.389124\pi$
$954$	−9.96227	−0.322540
$955$	−21.9623	−0.710682
$956$	−4.79001	−0.154920
$957$	24.5168	0.792515
$958$	2.78259	0.0899014
$959$	22.0558	0.712219
$960$	−1.00000	−0.0322749
$961$	−21.6620	−0.698774
$962$	−3.82032	−0.123172
$963$	−0.734191	−0.0236590
$964$	14.9016	0.479950
$965$	−14.4562	−0.465360
$966$	3.35194	0.107847
$967$	23.4365	0.753667	0.376834	−	0.926281i	$-0.377013\pi$
$967$	23.4365	0.753667	0.376834	+	0.926281i	$0.377013\pi$
$968$	2.00000	0.0642824
$969$	−7.61033	−0.244479
$970$	−5.56193	−0.178583
$971$	57.8901	1.85778	0.928890	−	0.370355i	$-0.120764\pi$
$971$	57.8901	1.85778	0.928890	+	0.370355i	$0.120764\pi$
$972$	1.00000	0.0320750
$973$	−34.8236	−1.11639
$974$	−16.1116	−0.516250
$975$	1.00000	0.0320256
$976$	−5.43807	−0.174068
$977$	−32.9500	−1.05417	−0.527083	−	0.849814i	$-0.676714\pi$
$977$	−32.9500	−1.05417	−0.527083	+	0.849814i	$0.676714\pi$
$978$	13.6406	0.436180
$979$	29.9777	0.958093
$980$	−2.52420	−0.0806326
$981$	19.7523	0.630642
$982$	−12.5774	−0.401361
$983$	16.9878	0.541826	0.270913	−	0.962604i	$-0.412674\pi$
$983$	16.9878	0.541826	0.270913	+	0.962604i	$0.412674\pi$
$984$	−7.08613	−0.225898
$985$	10.3445	0.329604
$986$	−8.17226	−0.260258
$987$	−22.5726	−0.718494
$988$	−7.61033	−0.242117
$989$	10.7268	0.341092
$990$	3.00000	0.0953463
$991$	4.14456	0.131656	0.0658281	−	0.997831i	$-0.479031\pi$
$991$	4.14456	0.131656	0.0658281	+	0.997831i	$0.479031\pi$
$992$	−3.05582	−0.0970223
$993$	34.4413	1.09296
$994$	40.8007	1.29412
$995$	11.4684	0.363572
$996$	15.5168	0.491668
$997$	31.1090	0.985233	0.492616	−	0.870247i	$-0.336041\pi$
$997$	31.1090	0.985233	0.492616	+	0.870247i	$0.336041\pi$
$998$	−12.8613	−0.407117
$999$	3.82032	0.120870

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6630.2.a.bk.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6630.2.a.bk.1.3	✓	3	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:	\( N \)	\(=\)	\( 6630 = 2 \cdot 3 \cdot 5 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6630.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +3.08613 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +3.08613 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +3.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} -3.08613 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -7.61033 q^{19} -1.00000 q^{20} +3.08613 q^{21} -3.00000 q^{22} -1.08613 q^{23} -1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{26} +1.00000 q^{27} +3.08613 q^{28} +8.17226 q^{29} +1.00000 q^{30} +3.05582 q^{31} -1.00000 q^{32} +3.00000 q^{33} -1.00000 q^{34} -3.08613 q^{35} +1.00000 q^{36} +3.82032 q^{37} +7.61033 q^{38} +1.00000 q^{39} +1.00000 q^{40} +7.08613 q^{41} -3.08613 q^{42} -9.87614 q^{43} +3.00000 q^{44} -1.00000 q^{45} +1.08613 q^{46} -7.31421 q^{47} +1.00000 q^{48} +2.52420 q^{49} -1.00000 q^{50} +1.00000 q^{51} +1.00000 q^{52} +9.96227 q^{53} -1.00000 q^{54} -3.00000 q^{55} -3.08613 q^{56} -7.61033 q^{57} -8.17226 q^{58} +7.79001 q^{59} -1.00000 q^{60} -5.43807 q^{61} -3.05582 q^{62} +3.08613 q^{63} +1.00000 q^{64} -1.00000 q^{65} -3.00000 q^{66} -1.03031 q^{67} +1.00000 q^{68} -1.08613 q^{69} +3.08613 q^{70} -13.2207 q^{71} -1.00000 q^{72} +16.0787 q^{73} -3.82032 q^{74} +1.00000 q^{75} -7.61033 q^{76} +9.25839 q^{77} -1.00000 q^{78} -0.969687 q^{79} -1.00000 q^{80} +1.00000 q^{81} -7.08613 q^{82} +15.5168 q^{83} +3.08613 q^{84} -1.00000 q^{85} +9.87614 q^{86} +8.17226 q^{87} -3.00000 q^{88} +9.99258 q^{89} +1.00000 q^{90} +3.08613 q^{91} -1.08613 q^{92} +3.05582 q^{93} +7.31421 q^{94} +7.61033 q^{95} -1.00000 q^{96} -5.56193 q^{97} -2.52420 q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 9 q^{11} + 3 q^{12} + 3 q^{13} - 2 q^{14} - 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} + q^{19} - 3 q^{20} + 2 q^{21} - 9 q^{22} + 4 q^{23} - 3 q^{24} + 3 q^{25} - 3 q^{26} + 3 q^{27} + 2 q^{28} + 10 q^{29} + 3 q^{30} + 3 q^{31} - 3 q^{32} + 9 q^{33} - 3 q^{34} - 2 q^{35} + 3 q^{36} - q^{37} - q^{38} + 3 q^{39} + 3 q^{40} + 14 q^{41} - 2 q^{42} - 11 q^{43} + 9 q^{44} - 3 q^{45} - 4 q^{46} + 6 q^{47} + 3 q^{48} - 9 q^{49} - 3 q^{50} + 3 q^{51} + 3 q^{52} + 4 q^{53} - 3 q^{54} - 9 q^{55} - 2 q^{56} + q^{57} - 10 q^{58} + 12 q^{59} - 3 q^{60} - 7 q^{61} - 3 q^{62} + 2 q^{63} + 3 q^{64} - 3 q^{65} - 9 q^{66} - 2 q^{67} + 3 q^{68} + 4 q^{69} + 2 q^{70} + 8 q^{71} - 3 q^{72} + 14 q^{73} + q^{74} + 3 q^{75} + q^{76} + 6 q^{77} - 3 q^{78} - 4 q^{79} - 3 q^{80} + 3 q^{81} - 14 q^{82} + 3 q^{83} + 2 q^{84} - 3 q^{85} + 11 q^{86} + 10 q^{87} - 9 q^{88} + 3 q^{89} + 3 q^{90} + 2 q^{91} + 4 q^{92} + 3 q^{93} - 6 q^{94} - q^{95} - 3 q^{96} - 26 q^{97} + 9 q^{98} + 9 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 9 * q^11 + 3 * q^12 + 3 * q^13 - 2 * q^14 - 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 + q^19 - 3 * q^20 + 2 * q^21 - 9 * q^22 + 4 * q^23 - 3 * q^24 + 3 * q^25 - 3 * q^26 + 3 * q^27 + 2 * q^28 + 10 * q^29 + 3 * q^30 + 3 * q^31 - 3 * q^32 + 9 * q^33 - 3 * q^34 - 2 * q^35 + 3 * q^36 - q^37 - q^38 + 3 * q^39 + 3 * q^40 + 14 * q^41 - 2 * q^42 - 11 * q^43 + 9 * q^44 - 3 * q^45 - 4 * q^46 + 6 * q^47 + 3 * q^48 - 9 * q^49 - 3 * q^50 + 3 * q^51 + 3 * q^52 + 4 * q^53 - 3 * q^54 - 9 * q^55 - 2 * q^56 + q^57 - 10 * q^58 + 12 * q^59 - 3 * q^60 - 7 * q^61 - 3 * q^62 + 2 * q^63 + 3 * q^64 - 3 * q^65 - 9 * q^66 - 2 * q^67 + 3 * q^68 + 4 * q^69 + 2 * q^70 + 8 * q^71 - 3 * q^72 + 14 * q^73 + q^74 + 3 * q^75 + q^76 + 6 * q^77 - 3 * q^78 - 4 * q^79 - 3 * q^80 + 3 * q^81 - 14 * q^82 + 3 * q^83 + 2 * q^84 - 3 * q^85 + 11 * q^86 + 10 * q^87 - 9 * q^88 + 3 * q^89 + 3 * q^90 + 2 * q^91 + 4 * q^92 + 3 * q^93 - 6 * q^94 - q^95 - 3 * q^96 - 26 * q^97 + 9 * q^98 + 9 * q^99

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