LMFDB - Embedded newform 1338.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1338,2,Mod(1,1338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1338, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1338.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1338 = 2 \cdot 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1338.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:	$10.6839837904$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.232773917.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 12x^{4} - x^{3} + 33x^{2} + 5x - 22 $ x^6 - 12x^4 - x^3 + 33x^2 + 5*x - 22
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.72012$ of defining polynomial
Character	$\chi$	$=$	1338.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.720124 q^{5} +1.00000 q^{6} -2.15975 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.720124 q^{5} +1.00000 q^{6} -2.15975 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.720124 q^{10} +0.190874 q^{11} +1.00000 q^{12} +5.68900 q^{13} -2.15975 q^{14} -0.720124 q^{15} +1.00000 q^{16} +1.47294 q^{17} +1.00000 q^{18} +3.39180 q^{19} -0.720124 q^{20} -2.15975 q^{21} +0.190874 q^{22} +4.79157 q^{23} +1.00000 q^{24} -4.48142 q^{25} +5.68900 q^{26} +1.00000 q^{27} -2.15975 q^{28} +6.73017 q^{29} -0.720124 q^{30} -5.71504 q^{31} +1.00000 q^{32} +0.190874 q^{33} +1.47294 q^{34} +1.55529 q^{35} +1.00000 q^{36} +1.29431 q^{37} +3.39180 q^{38} +5.68900 q^{39} -0.720124 q^{40} +6.26451 q^{41} -2.15975 q^{42} +6.06566 q^{43} +0.190874 q^{44} -0.720124 q^{45} +4.79157 q^{46} -6.16980 q^{47} +1.00000 q^{48} -2.33549 q^{49} -4.48142 q^{50} +1.47294 q^{51} +5.68900 q^{52} +4.33768 q^{53} +1.00000 q^{54} -0.137453 q^{55} -2.15975 q^{56} +3.39180 q^{57} +6.73017 q^{58} +2.58995 q^{59} -0.720124 q^{60} +6.98912 q^{61} -5.71504 q^{62} -2.15975 q^{63} +1.00000 q^{64} -4.09678 q^{65} +0.190874 q^{66} -7.00935 q^{67} +1.47294 q^{68} +4.79157 q^{69} +1.55529 q^{70} -13.2708 q^{71} +1.00000 q^{72} -6.23354 q^{73} +1.29431 q^{74} -4.48142 q^{75} +3.39180 q^{76} -0.412240 q^{77} +5.68900 q^{78} +5.25291 q^{79} -0.720124 q^{80} +1.00000 q^{81} +6.26451 q^{82} +2.12352 q^{83} -2.15975 q^{84} -1.06070 q^{85} +6.06566 q^{86} +6.73017 q^{87} +0.190874 q^{88} -12.9174 q^{89} -0.720124 q^{90} -12.2868 q^{91} +4.79157 q^{92} -5.71504 q^{93} -6.16980 q^{94} -2.44251 q^{95} +1.00000 q^{96} -2.68681 q^{97} -2.33549 q^{98} +0.190874 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} + 5 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 + 5 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} + 5 q^{7} + 6 q^{8} + 6 q^{9} + 6 q^{10} + q^{11} + 6 q^{12} + 6 q^{13} + 5 q^{14} + 6 q^{15} + 6 q^{16} + 10 q^{17} + 6 q^{18} - 4 q^{19} + 6 q^{20} + 5 q^{21} + q^{22} + 2 q^{23} + 6 q^{24} + 6 q^{26} + 6 q^{27} + 5 q^{28} + 6 q^{29} + 6 q^{30} - 5 q^{31} + 6 q^{32} + q^{33} + 10 q^{34} - 2 q^{35} + 6 q^{36} + q^{37} - 4 q^{38} + 6 q^{39} + 6 q^{40} + 12 q^{41} + 5 q^{42} - 11 q^{43} + q^{44} + 6 q^{45} + 2 q^{46} + 5 q^{47} + 6 q^{48} - q^{49} + 10 q^{51} + 6 q^{52} + 4 q^{53} + 6 q^{54} - 15 q^{55} + 5 q^{56} - 4 q^{57} + 6 q^{58} + q^{59} + 6 q^{60} - 8 q^{61} - 5 q^{62} + 5 q^{63} + 6 q^{64} + 5 q^{65} + q^{66} - 6 q^{67} + 10 q^{68} + 2 q^{69} - 2 q^{70} + q^{71} + 6 q^{72} - 10 q^{73} + q^{74} - 4 q^{76} - 8 q^{77} + 6 q^{78} - 10 q^{79} + 6 q^{80} + 6 q^{81} + 12 q^{82} - 6 q^{83} + 5 q^{84} - 2 q^{85} - 11 q^{86} + 6 q^{87} + q^{88} - 3 q^{89} + 6 q^{90} - 16 q^{91} + 2 q^{92} - 5 q^{93} + 5 q^{94} - 10 q^{95} + 6 q^{96} + 3 q^{97} - q^{98} + q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 + 5 * q^7 + 6 * q^8 + 6 * q^9 + 6 * q^10 + q^11 + 6 * q^12 + 6 * q^13 + 5 * q^14 + 6 * q^15 + 6 * q^16 + 10 * q^17 + 6 * q^18 - 4 * q^19 + 6 * q^20 + 5 * q^21 + q^22 + 2 * q^23 + 6 * q^24 + 6 * q^26 + 6 * q^27 + 5 * q^28 + 6 * q^29 + 6 * q^30 - 5 * q^31 + 6 * q^32 + q^33 + 10 * q^34 - 2 * q^35 + 6 * q^36 + q^37 - 4 * q^38 + 6 * q^39 + 6 * q^40 + 12 * q^41 + 5 * q^42 - 11 * q^43 + q^44 + 6 * q^45 + 2 * q^46 + 5 * q^47 + 6 * q^48 - q^49 + 10 * q^51 + 6 * q^52 + 4 * q^53 + 6 * q^54 - 15 * q^55 + 5 * q^56 - 4 * q^57 + 6 * q^58 + q^59 + 6 * q^60 - 8 * q^61 - 5 * q^62 + 5 * q^63 + 6 * q^64 + 5 * q^65 + q^66 - 6 * q^67 + 10 * q^68 + 2 * q^69 - 2 * q^70 + q^71 + 6 * q^72 - 10 * q^73 + q^74 - 4 * q^76 - 8 * q^77 + 6 * q^78 - 10 * q^79 + 6 * q^80 + 6 * q^81 + 12 * q^82 - 6 * q^83 + 5 * q^84 - 2 * q^85 - 11 * q^86 + 6 * q^87 + q^88 - 3 * q^89 + 6 * q^90 - 16 * q^91 + 2 * q^92 - 5 * q^93 + 5 * q^94 - 10 * q^95 + 6 * q^96 + 3 * 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
$5$	−0.720124	−0.322049	−0.161025	−	0.986950i	$-0.551480\pi$
$5$	−0.720124	−0.322049	−0.161025	+	0.986950i	$0.551480\pi$
$6$	1.00000	0.408248
$7$	−2.15975	−0.816308	−0.408154	−	0.912913i	$-0.633827\pi$
$7$	−2.15975	−0.816308	−0.408154	+	0.912913i	$0.633827\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.720124	−0.227723
$11$	0.190874	0.0575508	0.0287754	−	0.999586i	$-0.490839\pi$
$11$	0.190874	0.0575508	0.0287754	+	0.999586i	$0.490839\pi$
$12$	1.00000	0.288675
$13$	5.68900	1.57784	0.788922	−	0.614493i	$-0.210639\pi$
$13$	5.68900	1.57784	0.788922	+	0.614493i	$0.210639\pi$
$14$	−2.15975	−0.577217
$15$	−0.720124	−0.185935
$16$	1.00000	0.250000
$17$	1.47294	0.357240	0.178620	−	0.983918i	$-0.442837\pi$
$17$	1.47294	0.357240	0.178620	+	0.983918i	$0.442837\pi$
$18$	1.00000	0.235702
$19$	3.39180	0.778131	0.389066	−	0.921210i	$-0.372798\pi$
$19$	3.39180	0.778131	0.389066	+	0.921210i	$0.372798\pi$
$20$	−0.720124	−0.161025
$21$	−2.15975	−0.471296
$22$	0.190874	0.0406945
$23$	4.79157	0.999112	0.499556	−	0.866282i	$-0.333497\pi$
$23$	4.79157	0.999112	0.499556	+	0.866282i	$0.333497\pi$
$24$	1.00000	0.204124
$25$	−4.48142	−0.896284
$26$	5.68900	1.11570
$27$	1.00000	0.192450
$28$	−2.15975	−0.408154
$29$	6.73017	1.24976	0.624881	−	0.780720i	$-0.285148\pi$
$29$	6.73017	1.24976	0.624881	+	0.780720i	$0.285148\pi$
$30$	−0.720124	−0.131476
$31$	−5.71504	−1.02645	−0.513225	−	0.858254i	$-0.671549\pi$
$31$	−5.71504	−1.02645	−0.513225	+	0.858254i	$0.671549\pi$
$32$	1.00000	0.176777
$33$	0.190874	0.0332269
$34$	1.47294	0.252607
$35$	1.55529	0.262891
$36$	1.00000	0.166667
$37$	1.29431	0.212784	0.106392	−	0.994324i	$-0.466070\pi$
$37$	1.29431	0.212784	0.106392	+	0.994324i	$0.466070\pi$
$38$	3.39180	0.550222
$39$	5.68900	0.910969
$40$	−0.720124	−0.113862
$41$	6.26451	0.978352	0.489176	−	0.872185i	$-0.337298\pi$
$41$	6.26451	0.978352	0.489176	+	0.872185i	$0.337298\pi$
$42$	−2.15975	−0.333256
$43$	6.06566	0.925004	0.462502	−	0.886618i	$-0.346952\pi$
$43$	6.06566	0.925004	0.462502	+	0.886618i	$0.346952\pi$
$44$	0.190874	0.0287754
$45$	−0.720124	−0.107350
$46$	4.79157	0.706479
$47$	−6.16980	−0.899957	−0.449979	−	0.893039i	$-0.648568\pi$
$47$	−6.16980	−0.899957	−0.449979	+	0.893039i	$0.648568\pi$
$48$	1.00000	0.144338
$49$	−2.33549	−0.333641
$50$	−4.48142	−0.633769
$51$	1.47294	0.206253
$52$	5.68900	0.788922
$53$	4.33768	0.595825	0.297913	−	0.954593i	$-0.403710\pi$
$53$	4.33768	0.595825	0.297913	+	0.954593i	$0.403710\pi$
$54$	1.00000	0.136083
$55$	−0.137453	−0.0185342
$56$	−2.15975	−0.288609
$57$	3.39180	0.449254
$58$	6.73017	0.883715
$59$	2.58995	0.337183	0.168591	−	0.985686i	$-0.446078\pi$
$59$	2.58995	0.337183	0.168591	+	0.985686i	$0.446078\pi$
$60$	−0.720124	−0.0929676
$61$	6.98912	0.894865	0.447433	−	0.894318i	$-0.352338\pi$
$61$	6.98912	0.894865	0.447433	+	0.894318i	$0.352338\pi$
$62$	−5.71504	−0.725810
$63$	−2.15975	−0.272103
$64$	1.00000	0.125000
$65$	−4.09678	−0.508143
$66$	0.190874	0.0234950
$67$	−7.00935	−0.856328	−0.428164	−	0.903701i	$-0.640839\pi$
$67$	−7.00935	−0.856328	−0.428164	+	0.903701i	$0.640839\pi$
$68$	1.47294	0.178620
$69$	4.79157	0.576837
$70$	1.55529	0.185892
$71$	−13.2708	−1.57496	−0.787478	−	0.616343i	$-0.788614\pi$
$71$	−13.2708	−1.57496	−0.787478	+	0.616343i	$0.788614\pi$
$72$	1.00000	0.117851
$73$	−6.23354	−0.729580	−0.364790	−	0.931090i	$-0.618859\pi$
$73$	−6.23354	−0.729580	−0.364790	+	0.931090i	$0.618859\pi$
$74$	1.29431	0.150461
$75$	−4.48142	−0.517470
$76$	3.39180	0.389066
$77$	−0.412240	−0.0469792
$78$	5.68900	0.644152
$79$	5.25291	0.590999	0.295499	−	0.955343i	$-0.404514\pi$
$79$	5.25291	0.590999	0.295499	+	0.955343i	$0.404514\pi$
$80$	−0.720124	−0.0805123
$81$	1.00000	0.111111
$82$	6.26451	0.691799
$83$	2.12352	0.233087	0.116543	−	0.993186i	$-0.462819\pi$
$83$	2.12352	0.233087	0.116543	+	0.993186i	$0.462819\pi$
$84$	−2.15975	−0.235648
$85$	−1.06070	−0.115049
$86$	6.06566	0.654077
$87$	6.73017	0.721550
$88$	0.190874	0.0203473
$89$	−12.9174	−1.36925	−0.684623	−	0.728897i	$-0.740033\pi$
$89$	−12.9174	−1.36925	−0.684623	+	0.728897i	$0.740033\pi$
$90$	−0.720124	−0.0759077
$91$	−12.2868	−1.28801
$92$	4.79157	0.499556
$93$	−5.71504	−0.592622
$94$	−6.16980	−0.636366
$95$	−2.44251	−0.250597
$96$	1.00000	0.102062
$97$	−2.68681	−0.272804	−0.136402	−	0.990654i	$-0.543554\pi$
$97$	−2.68681	−0.272804	−0.136402	+	0.990654i	$0.543554\pi$
$98$	−2.33549	−0.235920
$99$	0.190874	0.0191836
$100$	−4.48142	−0.448142
$101$	9.61806	0.957032	0.478516	−	0.878079i	$-0.341175\pi$
$101$	9.61806	0.957032	0.478516	+	0.878079i	$0.341175\pi$
$102$	1.47294	0.145843
$103$	−5.35062	−0.527213	−0.263606	−	0.964630i	$-0.584912\pi$
$103$	−5.35062	−0.527213	−0.263606	+	0.964630i	$0.584912\pi$
$104$	5.68900	0.557852
$105$	1.55529	0.151780
$106$	4.33768	0.421312
$107$	−13.0692	−1.26345	−0.631723	−	0.775194i	$-0.717652\pi$
$107$	−13.0692	−1.26345	−0.631723	+	0.775194i	$0.717652\pi$
$108$	1.00000	0.0962250
$109$	−12.7771	−1.22382	−0.611911	−	0.790927i	$-0.709599\pi$
$109$	−12.7771	−1.22382	−0.611911	+	0.790927i	$0.709599\pi$
$110$	−0.137453	−0.0131056
$111$	1.29431	0.122851
$112$	−2.15975	−0.204077
$113$	9.85661	0.927231	0.463616	−	0.886036i	$-0.346552\pi$
$113$	9.85661	0.927231	0.463616	+	0.886036i	$0.346552\pi$
$114$	3.39180	0.317671
$115$	−3.45052	−0.321763
$116$	6.73017	0.624881
$117$	5.68900	0.525948
$118$	2.58995	0.238424
$119$	−3.18118	−0.291618
$120$	−0.720124	−0.0657380
$121$	−10.9636	−0.996688
$122$	6.98912	0.632765
$123$	6.26451	0.564852
$124$	−5.71504	−0.513225
$125$	6.82780	0.610697
$126$	−2.15975	−0.192406
$127$	−10.2948	−0.913514	−0.456757	−	0.889591i	$-0.650989\pi$
$127$	−10.2948	−0.913514	−0.456757	+	0.889591i	$0.650989\pi$
$128$	1.00000	0.0883883
$129$	6.06566	0.534051
$130$	−4.09678	−0.359312
$131$	−3.03891	−0.265511	−0.132755	−	0.991149i	$-0.542382\pi$
$131$	−3.03891	−0.265511	−0.132755	+	0.991149i	$0.542382\pi$
$132$	0.190874	0.0166135
$133$	−7.32543	−0.635195
$134$	−7.00935	−0.605515
$135$	−0.720124	−0.0619784
$136$	1.47294	0.126304
$137$	−9.30257	−0.794772	−0.397386	−	0.917652i	$-0.630083\pi$
$137$	−9.30257	−0.794772	−0.397386	+	0.917652i	$0.630083\pi$
$138$	4.79157	0.407886
$139$	−1.28426	−0.108930	−0.0544649	−	0.998516i	$-0.517345\pi$
$139$	−1.28426	−0.108930	−0.0544649	+	0.998516i	$0.517345\pi$
$140$	1.55529	0.131446
$141$	−6.16980	−0.519591
$142$	−13.2708	−1.11366
$143$	1.08588	0.0908061
$144$	1.00000	0.0833333
$145$	−4.84656	−0.402485
$146$	−6.23354	−0.515891
$147$	−2.33549	−0.192628
$148$	1.29431	0.106392
$149$	22.9484	1.88001	0.940004	−	0.341162i	$-0.110821\pi$
$149$	22.9484	1.88001	0.940004	+	0.341162i	$0.110821\pi$
$150$	−4.48142	−0.365907
$151$	1.16396	0.0947218	0.0473609	−	0.998878i	$-0.484919\pi$
$151$	1.16396	0.0947218	0.0473609	+	0.998878i	$0.484919\pi$
$152$	3.39180	0.275111
$153$	1.47294	0.119080
$154$	−0.412240	−0.0332193
$155$	4.11553	0.330568
$156$	5.68900	0.455484
$157$	−23.0958	−1.84325	−0.921625	−	0.388083i	$-0.873137\pi$
$157$	−23.0958	−1.84325	−0.921625	+	0.388083i	$0.873137\pi$
$158$	5.25291	0.417899
$159$	4.33768	0.344000
$160$	−0.720124	−0.0569308
$161$	−10.3486	−0.815583
$162$	1.00000	0.0785674
$163$	2.34483	0.183662	0.0918308	−	0.995775i	$-0.470728\pi$
$163$	2.34483	0.183662	0.0918308	+	0.995775i	$0.470728\pi$
$164$	6.26451	0.489176
$165$	−0.137453	−0.0107007
$166$	2.12352	0.164817
$167$	9.19583	0.711595	0.355797	−	0.934563i	$-0.384209\pi$
$167$	9.19583	0.711595	0.355797	+	0.934563i	$0.384209\pi$
$168$	−2.15975	−0.166628
$169$	19.3647	1.48959
$170$	−1.06070	−0.0813519
$171$	3.39180	0.259377
$172$	6.06566	0.462502
$173$	1.99140	0.151403	0.0757016	−	0.997131i	$-0.475880\pi$
$173$	1.99140	0.151403	0.0757016	+	0.997131i	$0.475880\pi$
$174$	6.73017	0.510213
$175$	9.67874	0.731644
$176$	0.190874	0.0143877
$177$	2.58995	0.194672
$178$	−12.9174	−0.968204
$179$	8.04049	0.600974	0.300487	−	0.953786i	$-0.402851\pi$
$179$	8.04049	0.600974	0.300487	+	0.953786i	$0.402851\pi$
$180$	−0.720124	−0.0536749
$181$	6.19065	0.460147	0.230074	−	0.973173i	$-0.426103\pi$
$181$	6.19065	0.460147	0.230074	+	0.973173i	$0.426103\pi$
$182$	−12.2868	−0.910759
$183$	6.98912	0.516651
$184$	4.79157	0.353239
$185$	−0.932065	−0.0685268
$186$	−5.71504	−0.419047
$187$	0.281146	0.0205594
$188$	−6.16980	−0.449979
$189$	−2.15975	−0.157099
$190$	−2.44251	−0.177199
$191$	−18.0212	−1.30397	−0.651985	−	0.758232i	$-0.726063\pi$
$191$	−18.0212	−1.30397	−0.651985	+	0.758232i	$0.726063\pi$
$192$	1.00000	0.0721688
$193$	−21.7993	−1.56915	−0.784575	−	0.620033i	$-0.787119\pi$
$193$	−21.7993	−1.56915	−0.784575	+	0.620033i	$0.787119\pi$
$194$	−2.68681	−0.192902
$195$	−4.09678	−0.293377
$196$	−2.33549	−0.166820
$197$	3.18861	0.227179	0.113589	−	0.993528i	$-0.463765\pi$
$197$	3.18861	0.227179	0.113589	+	0.993528i	$0.463765\pi$
$198$	0.190874	0.0135648
$199$	11.1529	0.790606	0.395303	−	0.918551i	$-0.370640\pi$
$199$	11.1529	0.790606	0.395303	+	0.918551i	$0.370640\pi$
$200$	−4.48142	−0.316884
$201$	−7.00935	−0.494401
$202$	9.61806	0.676724
$203$	−14.5355	−1.02019
$204$	1.47294	0.103126
$205$	−4.51122	−0.315078
$206$	−5.35062	−0.372796
$207$	4.79157	0.333037
$208$	5.68900	0.394461
$209$	0.647407	0.0447821
$210$	1.55529	0.107325
$211$	1.05765	0.0728114	0.0364057	−	0.999337i	$-0.488409\pi$
$211$	1.05765	0.0728114	0.0364057	+	0.999337i	$0.488409\pi$
$212$	4.33768	0.297913
$213$	−13.2708	−0.909301
$214$	−13.0692	−0.893392
$215$	−4.36803	−0.297897
$216$	1.00000	0.0680414
$217$	12.3430	0.837900
$218$	−12.7771	−0.865372
$219$	−6.23354	−0.421223
$220$	−0.137453	−0.00926709
$221$	8.37955	0.563669
$222$	1.29431	0.0868686
$223$	1.00000	0.0669650
$223$	1.00000	0.0669650
$224$	−2.15975	−0.144304
$225$	−4.48142	−0.298761
$226$	9.85661	0.655652
$227$	8.01392	0.531903	0.265951	−	0.963986i	$-0.414314\pi$
$227$	8.01392	0.531903	0.265951	+	0.963986i	$0.414314\pi$
$228$	3.39180	0.224627
$229$	−22.6459	−1.49648	−0.748242	−	0.663426i	$-0.769102\pi$
$229$	−22.6459	−1.49648	−0.748242	+	0.663426i	$0.769102\pi$
$230$	−3.45052	−0.227521
$231$	−0.412240	−0.0271234
$232$	6.73017	0.441857
$233$	5.44041	0.356413	0.178207	−	0.983993i	$-0.442970\pi$
$233$	5.44041	0.356413	0.178207	+	0.983993i	$0.442970\pi$
$234$	5.68900	0.371901
$235$	4.44302	0.289831
$236$	2.58995	0.168591
$237$	5.25291	0.341213
$238$	−3.18118	−0.206205
$239$	8.64211	0.559012	0.279506	−	0.960144i	$-0.409829\pi$
$239$	8.64211	0.559012	0.279506	+	0.960144i	$0.409829\pi$
$240$	−0.720124	−0.0464838
$241$	−2.02151	−0.130217	−0.0651084	−	0.997878i	$-0.520739\pi$
$241$	−2.02151	−0.130217	−0.0651084	+	0.997878i	$0.520739\pi$
$242$	−10.9636	−0.704765
$243$	1.00000	0.0641500
$244$	6.98912	0.447433
$245$	1.68184	0.107449
$246$	6.26451	0.399411
$247$	19.2959	1.22777
$248$	−5.71504	−0.362905
$249$	2.12352	0.134573
$250$	6.82780	0.431828
$251$	−1.93932	−0.122409	−0.0612045	−	0.998125i	$-0.519494\pi$
$251$	−1.93932	−0.122409	−0.0612045	+	0.998125i	$0.519494\pi$
$252$	−2.15975	−0.136051
$253$	0.914588	0.0574996
$254$	−10.2948	−0.645952
$255$	−1.06070	−0.0664235
$256$	1.00000	0.0625000
$257$	−1.39603	−0.0870821	−0.0435411	−	0.999052i	$-0.513864\pi$
$257$	−1.39603	−0.0870821	−0.0435411	+	0.999052i	$0.513864\pi$
$258$	6.06566	0.377631
$259$	−2.79539	−0.173697
$260$	−4.09678	−0.254072
$261$	6.73017	0.416587
$262$	−3.03891	−0.187744
$263$	−6.53132	−0.402738	−0.201369	−	0.979515i	$-0.564539\pi$
$263$	−6.53132	−0.402738	−0.201369	+	0.979515i	$0.564539\pi$
$264$	0.190874	0.0117475
$265$	−3.12366	−0.191885
$266$	−7.32543	−0.449151
$267$	−12.9174	−0.790535
$268$	−7.00935	−0.428164
$269$	4.46472	0.272219	0.136109	−	0.990694i	$-0.456540\pi$
$269$	4.46472	0.272219	0.136109	+	0.990694i	$0.456540\pi$
$270$	−0.720124	−0.0438253
$271$	−19.3438	−1.17505	−0.587527	−	0.809204i	$-0.699899\pi$
$271$	−19.3438	−1.17505	−0.587527	+	0.809204i	$0.699899\pi$
$272$	1.47294	0.0893101
$273$	−12.2868	−0.743631
$274$	−9.30257	−0.561989
$275$	−0.855388	−0.0515818
$276$	4.79157	0.288419
$277$	18.4637	1.10938	0.554689	−	0.832058i	$-0.312837\pi$
$277$	18.4637	1.10938	0.554689	+	0.832058i	$0.312837\pi$
$278$	−1.28426	−0.0770251
$279$	−5.71504	−0.342150
$280$	1.55529	0.0929462
$281$	12.5527	0.748832	0.374416	−	0.927261i	$-0.377843\pi$
$281$	12.5527	0.748832	0.374416	+	0.927261i	$0.377843\pi$
$282$	−6.16980	−0.367406
$283$	2.24527	0.133467	0.0667337	−	0.997771i	$-0.478742\pi$
$283$	2.24527	0.133467	0.0667337	+	0.997771i	$0.478742\pi$
$284$	−13.2708	−0.787478
$285$	−2.44251	−0.144682
$286$	1.08588	0.0642096
$287$	−13.5298	−0.798637
$288$	1.00000	0.0589256
$289$	−14.8304	−0.872379
$290$	−4.84656	−0.284600
$291$	−2.68681	−0.157504
$292$	−6.23354	−0.364790
$293$	27.3537	1.59802	0.799011	−	0.601317i	$-0.205357\pi$
$293$	27.3537	1.59802	0.799011	+	0.601317i	$0.205357\pi$
$294$	−2.33549	−0.136208
$295$	−1.86508	−0.108589
$296$	1.29431	0.0752304
$297$	0.190874	0.0110756
$298$	22.9484	1.32937
$299$	27.2592	1.57644
$300$	−4.48142	−0.258735
$301$	−13.1003	−0.755089
$302$	1.16396	0.0669784
$303$	9.61806	0.552543
$304$	3.39180	0.194533
$305$	−5.03303	−0.288191
$306$	1.47294	0.0842023
$307$	−24.7294	−1.41138	−0.705689	−	0.708521i	$-0.749363\pi$
$307$	−24.7294	−1.41138	−0.705689	+	0.708521i	$0.749363\pi$
$308$	−0.412240	−0.0234896
$309$	−5.35062	−0.304386
$310$	4.11553	0.233747
$311$	−9.40354	−0.533226	−0.266613	−	0.963804i	$-0.585905\pi$
$311$	−9.40354	−0.533226	−0.266613	+	0.963804i	$0.585905\pi$
$312$	5.68900	0.322076
$313$	16.2859	0.920531	0.460265	−	0.887781i	$-0.347754\pi$
$313$	16.2859	0.920531	0.460265	+	0.887781i	$0.347754\pi$
$314$	−23.0958	−1.30337
$315$	1.55529	0.0876305
$316$	5.25291	0.295499
$317$	−15.7134	−0.882550	−0.441275	−	0.897372i	$-0.645474\pi$
$317$	−15.7134	−0.882550	−0.441275	+	0.897372i	$0.645474\pi$
$318$	4.33768	0.243245
$319$	1.28462	0.0719247
$320$	−0.720124	−0.0402562
$321$	−13.0692	−0.729451
$322$	−10.3486	−0.576704
$323$	4.99591	0.277980
$324$	1.00000	0.0555556
$325$	−25.4948	−1.41420
$326$	2.34483	0.129868
$327$	−12.7771	−0.706574
$328$	6.26451	0.345900
$329$	13.3252	0.734643
$330$	−0.137453	−0.00756655
$331$	−21.8701	−1.20209	−0.601044	−	0.799216i	$-0.705248\pi$
$331$	−21.8701	−1.20209	−0.601044	+	0.799216i	$0.705248\pi$
$332$	2.12352	0.116543
$333$	1.29431	0.0709279
$334$	9.19583	0.503174
$335$	5.04760	0.275780
$336$	−2.15975	−0.117824
$337$	−7.15748	−0.389893	−0.194946	−	0.980814i	$-0.562453\pi$
$337$	−7.15748	−0.389893	−0.194946	+	0.980814i	$0.562453\pi$
$338$	19.3647	1.05330
$339$	9.85661	0.535337
$340$	−1.06070	−0.0575245
$341$	−1.09085	−0.0590730
$342$	3.39180	0.183407
$343$	20.1623	1.08866
$344$	6.06566	0.327038
$345$	−3.45052	−0.185770
$346$	1.99140	0.107058
$347$	−4.33587	−0.232762	−0.116381	−	0.993205i	$-0.537129\pi$
$347$	−4.33587	−0.232762	−0.116381	+	0.993205i	$0.537129\pi$
$348$	6.73017	0.360775
$349$	−20.3467	−1.08913	−0.544566	−	0.838718i	$-0.683306\pi$
$349$	−20.3467	−1.08913	−0.544566	+	0.838718i	$0.683306\pi$
$350$	9.67874	0.517351
$351$	5.68900	0.303656
$352$	0.190874	0.0101736
$353$	−15.9454	−0.848686	−0.424343	−	0.905501i	$-0.639495\pi$
$353$	−15.9454	−0.848686	−0.424343	+	0.905501i	$0.639495\pi$
$354$	2.58995	0.137654
$355$	9.55663	0.507213
$356$	−12.9174	−0.684623
$357$	−3.18118	−0.168366
$358$	8.04049	0.424953
$359$	23.9132	1.26209	0.631044	−	0.775747i	$-0.282627\pi$
$359$	23.9132	1.26209	0.631044	+	0.775747i	$0.282627\pi$
$360$	−0.720124	−0.0379539
$361$	−7.49572	−0.394511
$362$	6.19065	0.325373
$363$	−10.9636	−0.575438
$364$	−12.2868	−0.644004
$365$	4.48892	0.234961
$366$	6.98912	0.365327
$367$	10.6021	0.553427	0.276714	−	0.960952i	$-0.410755\pi$
$367$	10.6021	0.553427	0.276714	+	0.960952i	$0.410755\pi$
$368$	4.79157	0.249778
$369$	6.26451	0.326117
$370$	−0.932065	−0.0484558
$371$	−9.36829	−0.486377
$372$	−5.71504	−0.296311
$373$	18.1083	0.937614	0.468807	−	0.883301i	$-0.344684\pi$
$373$	18.1083	0.937614	0.468807	+	0.883301i	$0.344684\pi$
$374$	0.281146	0.0145377
$375$	6.82780	0.352586
$376$	−6.16980	−0.318183
$377$	38.2879	1.97193
$378$	−2.15975	−0.111085
$379$	−35.4047	−1.81862	−0.909309	−	0.416122i	$-0.863389\pi$
$379$	−35.4047	−1.81862	−0.909309	+	0.416122i	$0.863389\pi$
$380$	−2.44251	−0.125298
$381$	−10.2948	−0.527418
$382$	−18.0212	−0.922046
$383$	−32.1048	−1.64048	−0.820240	−	0.572019i	$-0.806160\pi$
$383$	−32.1048	−1.64048	−0.820240	+	0.572019i	$0.806160\pi$
$384$	1.00000	0.0510310
$385$	0.296864	0.0151296
$386$	−21.7993	−1.10956
$387$	6.06566	0.308335
$388$	−2.68681	−0.136402
$389$	32.7182	1.65888	0.829439	−	0.558597i	$-0.188660\pi$
$389$	32.7182	1.65888	0.829439	+	0.558597i	$0.188660\pi$
$390$	−4.09678	−0.207449
$391$	7.05769	0.356923
$392$	−2.33549	−0.117960
$393$	−3.03891	−0.153293
$394$	3.18861	0.160640
$395$	−3.78275	−0.190331
$396$	0.190874	0.00959179
$397$	32.0177	1.60692	0.803462	−	0.595356i	$-0.202989\pi$
$397$	32.0177	1.60692	0.803462	+	0.595356i	$0.202989\pi$
$398$	11.1529	0.559043
$399$	−7.32543	−0.366730
$400$	−4.48142	−0.224071
$401$	−7.57701	−0.378378	−0.189189	−	0.981941i	$-0.560586\pi$
$401$	−7.57701	−0.378378	−0.189189	+	0.981941i	$0.560586\pi$
$402$	−7.00935	−0.349594
$403$	−32.5128	−1.61958
$404$	9.61806	0.478516
$405$	−0.720124	−0.0357832
$406$	−14.5355	−0.721384
$407$	0.247051	0.0122459
$408$	1.47294	0.0729214
$409$	−16.7032	−0.825920	−0.412960	−	0.910749i	$-0.635505\pi$
$409$	−16.7032	−0.825920	−0.412960	+	0.910749i	$0.635505\pi$
$410$	−4.51122	−0.222793
$411$	−9.30257	−0.458862
$412$	−5.35062	−0.263606
$413$	−5.59364	−0.275245
$414$	4.79157	0.235493
$415$	−1.52920	−0.0750654
$416$	5.68900	0.278926
$417$	−1.28426	−0.0628907
$418$	0.647407	0.0316657
$419$	24.3492	1.18954	0.594768	−	0.803898i	$-0.297244\pi$
$419$	24.3492	1.18954	0.594768	+	0.803898i	$0.297244\pi$
$420$	1.55529	0.0758902
$421$	35.2333	1.71717	0.858583	−	0.512674i	$-0.171345\pi$
$421$	35.2333	1.71717	0.858583	+	0.512674i	$0.171345\pi$
$422$	1.05765	0.0514854
$423$	−6.16980	−0.299986
$424$	4.33768	0.210656
$425$	−6.60086	−0.320189
$426$	−13.2708	−0.642973
$427$	−15.0947	−0.730486
$428$	−13.0692	−0.631723
$429$	1.08588	0.0524269
$430$	−4.36803	−0.210645
$431$	5.36851	0.258592	0.129296	−	0.991606i	$-0.458728\pi$
$431$	5.36851	0.258592	0.129296	+	0.991606i	$0.458728\pi$
$432$	1.00000	0.0481125
$433$	−11.0259	−0.529872	−0.264936	−	0.964266i	$-0.585351\pi$
$433$	−11.0259	−0.529872	−0.264936	+	0.964266i	$0.585351\pi$
$434$	12.3430	0.592485
$435$	−4.84656	−0.232375
$436$	−12.7771	−0.611911
$437$	16.2520	0.777440
$438$	−6.23354	−0.297850
$439$	−14.9875	−0.715316	−0.357658	−	0.933853i	$-0.616425\pi$
$439$	−14.9875	−0.715316	−0.357658	+	0.933853i	$0.616425\pi$
$440$	−0.137453	−0.00655282
$441$	−2.33549	−0.111214
$442$	8.37955	0.398575
$443$	12.7430	0.605439	0.302719	−	0.953080i	$-0.402105\pi$
$443$	12.7430	0.605439	0.302719	+	0.953080i	$0.402105\pi$
$444$	1.29431	0.0614254
$445$	9.30216	0.440965
$446$	1.00000	0.0473514
$447$	22.9484	1.08542
$448$	−2.15975	−0.102039
$449$	−28.2186	−1.33172	−0.665860	−	0.746077i	$-0.731935\pi$
$449$	−28.2186	−1.33172	−0.665860	+	0.746077i	$0.731935\pi$
$450$	−4.48142	−0.211256
$451$	1.19573	0.0563049
$452$	9.85661	0.463616
$453$	1.16396	0.0546877
$454$	8.01392	0.376112
$455$	8.84802	0.414802
$456$	3.39180	0.158835
$457$	25.2255	1.18000	0.590000	−	0.807403i	$-0.299128\pi$
$457$	25.2255	1.18000	0.590000	+	0.807403i	$0.299128\pi$
$458$	−22.6459	−1.05817
$459$	1.47294	0.0687509
$460$	−3.45052	−0.160882
$461$	19.4256	0.904741	0.452371	−	0.891830i	$-0.350578\pi$
$461$	19.4256	0.904741	0.452371	+	0.891830i	$0.350578\pi$
$462$	−0.412240	−0.0191792
$463$	−17.2731	−0.802748	−0.401374	−	0.915914i	$-0.631467\pi$
$463$	−17.2731	−0.802748	−0.401374	+	0.915914i	$0.631467\pi$
$464$	6.73017	0.312440
$465$	4.11553	0.190853
$466$	5.44041	0.252022
$467$	−20.9309	−0.968566	−0.484283	−	0.874911i	$-0.660919\pi$
$467$	−20.9309	−0.968566	−0.484283	+	0.874911i	$0.660919\pi$
$468$	5.68900	0.262974
$469$	15.1384	0.699028
$470$	4.44302	0.204941
$471$	−23.0958	−1.06420
$472$	2.58995	0.119212
$473$	1.15778	0.0532347
$474$	5.25291	0.241274
$475$	−15.2001	−0.697427
$476$	−3.18118	−0.145809
$477$	4.33768	0.198608
$478$	8.64211	0.395281
$479$	−30.4422	−1.39094	−0.695470	−	0.718555i	$-0.744804\pi$
$479$	−30.4422	−1.39094	−0.695470	+	0.718555i	$0.744804\pi$
$480$	−0.720124	−0.0328690
$481$	7.36334	0.335739
$482$	−2.02151	−0.0920771
$483$	−10.3486	−0.470877
$484$	−10.9636	−0.498344
$485$	1.93484	0.0878564
$486$	1.00000	0.0453609
$487$	−11.4597	−0.519287	−0.259643	−	0.965705i	$-0.583605\pi$
$487$	−11.4597	−0.519287	−0.259643	+	0.965705i	$0.583605\pi$
$488$	6.98912	0.316383
$489$	2.34483	0.106037
$490$	1.68184	0.0759778
$491$	−33.5690	−1.51495	−0.757474	−	0.652865i	$-0.773567\pi$
$491$	−33.5690	−1.51495	−0.757474	+	0.652865i	$0.773567\pi$
$492$	6.26451	0.282426
$493$	9.91313	0.446465
$494$	19.2959	0.868165
$495$	−0.137453	−0.00617806
$496$	−5.71504	−0.256613
$497$	28.6616	1.28565
$498$	2.12352	0.0951573
$499$	−24.3218	−1.08880	−0.544398	−	0.838827i	$-0.683242\pi$
$499$	−24.3218	−1.08880	−0.544398	+	0.838827i	$0.683242\pi$
$500$	6.82780	0.305348
$501$	9.19583	0.410840
$502$	−1.93932	−0.0865563
$503$	15.3511	0.684471	0.342235	−	0.939614i	$-0.388816\pi$
$503$	15.3511	0.684471	0.342235	+	0.939614i	$0.388816\pi$
$504$	−2.15975	−0.0962028
$505$	−6.92619	−0.308211
$506$	0.914588	0.0406584
$507$	19.3647	0.860017
$508$	−10.2948	−0.456757
$509$	17.1445	0.759916	0.379958	−	0.925004i	$-0.375938\pi$
$509$	17.1445	0.759916	0.379958	+	0.925004i	$0.375938\pi$
$510$	−1.06070	−0.0469685
$511$	13.4629	0.595562
$512$	1.00000	0.0441942
$513$	3.39180	0.149751
$514$	−1.39603	−0.0615764
$515$	3.85311	0.169788
$516$	6.06566	0.267026
$517$	−1.17766	−0.0517932
$518$	−2.79539	−0.122822
$519$	1.99140	0.0874127
$520$	−4.09678	−0.179656
$521$	38.7232	1.69650	0.848248	−	0.529599i	$-0.177658\pi$
$521$	38.7232	1.69650	0.848248	+	0.529599i	$0.177658\pi$
$522$	6.73017	0.294572
$523$	3.94320	0.172424	0.0862120	−	0.996277i	$-0.472524\pi$
$523$	3.94320	0.172424	0.0862120	+	0.996277i	$0.472524\pi$
$524$	−3.03891	−0.132755
$525$	9.67874	0.422415
$526$	−6.53132	−0.284779
$527$	−8.41790	−0.366689
$528$	0.190874	0.00830674
$529$	−0.0408477	−0.00177599
$530$	−3.12366	−0.135683
$531$	2.58995	0.112394
$532$	−7.32543	−0.317598
$533$	35.6388	1.54369
$534$	−12.9174	−0.558993
$535$	9.41144	0.406892
$536$	−7.00935	−0.302758
$537$	8.04049	0.346973
$538$	4.46472	0.192488
$539$	−0.445784	−0.0192013
$540$	−0.720124	−0.0309892
$541$	3.41636	0.146881	0.0734405	−	0.997300i	$-0.476602\pi$
$541$	3.41636	0.146881	0.0734405	+	0.997300i	$0.476602\pi$
$542$	−19.3438	−0.830889
$543$	6.19065	0.265666
$544$	1.47294	0.0631518
$545$	9.20107	0.394131
$546$	−12.2868	−0.525827
$547$	13.3521	0.570894	0.285447	−	0.958395i	$-0.407858\pi$
$547$	13.3521	0.570894	0.285447	+	0.958395i	$0.407858\pi$
$548$	−9.30257	−0.397386
$549$	6.98912	0.298288
$550$	−0.855388	−0.0364739
$551$	22.8274	0.972479
$552$	4.79157	0.203943
$553$	−11.3450	−0.482437
$554$	18.4637	0.784449
$555$	−0.932065	−0.0395640
$556$	−1.28426	−0.0544649
$557$	−6.31642	−0.267635	−0.133818	−	0.991006i	$-0.542724\pi$
$557$	−6.31642	−0.267635	−0.133818	+	0.991006i	$0.542724\pi$
$558$	−5.71504	−0.241937
$559$	34.5075	1.45951
$560$	1.55529	0.0657229
$561$	0.281146	0.0118700
$562$	12.5527	0.529504
$563$	−25.0618	−1.05623	−0.528114	−	0.849173i	$-0.677101\pi$
$563$	−25.0618	−1.05623	−0.528114	+	0.849173i	$0.677101\pi$
$564$	−6.16980	−0.259795
$565$	−7.09798	−0.298614
$566$	2.24527	0.0943757
$567$	−2.15975	−0.0907009
$568$	−13.2708	−0.556831
$569$	4.38477	0.183819	0.0919095	−	0.995767i	$-0.470703\pi$
$569$	4.38477	0.183819	0.0919095	+	0.995767i	$0.470703\pi$
$570$	−2.44251	−0.102306
$571$	−8.85296	−0.370485	−0.185242	−	0.982693i	$-0.559307\pi$
$571$	−8.85296	−0.370485	−0.185242	+	0.982693i	$0.559307\pi$
$572$	1.08588	0.0454031
$573$	−18.0212	−0.752847
$574$	−13.5298	−0.564722
$575$	−21.4730	−0.895488
$576$	1.00000	0.0416667
$577$	40.2022	1.67364	0.836821	−	0.547477i	$-0.184412\pi$
$577$	40.2022	1.67364	0.836821	+	0.547477i	$0.184412\pi$
$578$	−14.8304	−0.616865
$579$	−21.7993	−0.905950
$580$	−4.84656	−0.201242
$581$	−4.58627	−0.190271
$582$	−2.68681	−0.111372
$583$	0.827951	0.0342902
$584$	−6.23354	−0.257946
$585$	−4.09678	−0.169381
$586$	27.3537	1.12997
$587$	28.4825	1.17560	0.587800	−	0.809006i	$-0.299994\pi$
$587$	28.4825	1.17560	0.587800	+	0.809006i	$0.299994\pi$
$588$	−2.33549	−0.0963138
$589$	−19.3842	−0.798714
$590$	−1.86508	−0.0767843
$591$	3.18861	0.131162
$592$	1.29431	0.0531959
$593$	18.9609	0.778632	0.389316	−	0.921104i	$-0.372711\pi$
$593$	18.9609	0.778632	0.389316	+	0.921104i	$0.372711\pi$
$594$	0.190874	0.00783167
$595$	2.29084	0.0939154
$596$	22.9484	0.940004
$597$	11.1529	0.456456
$598$	27.2592	1.11471
$599$	−2.15238	−0.0879440	−0.0439720	−	0.999033i	$-0.514001\pi$
$599$	−2.15238	−0.0879440	−0.0439720	+	0.999033i	$0.514001\pi$
$600$	−4.48142	−0.182953
$601$	−16.9616	−0.691876	−0.345938	−	0.938257i	$-0.612439\pi$
$601$	−16.9616	−0.691876	−0.345938	+	0.938257i	$0.612439\pi$
$602$	−13.1003	−0.533928
$603$	−7.00935	−0.285443
$604$	1.16396	0.0473609
$605$	7.89513	0.320983
$606$	9.61806	0.390707
$607$	31.6495	1.28461	0.642306	−	0.766448i	$-0.277978\pi$
$607$	31.6495	1.28461	0.642306	+	0.766448i	$0.277978\pi$
$608$	3.39180	0.137556
$609$	−14.5355	−0.589007
$610$	−5.03303	−0.203782
$611$	−35.1000	−1.41999
$612$	1.47294	0.0595400
$613$	36.0887	1.45761	0.728804	−	0.684723i	$-0.240077\pi$
$613$	36.0887	1.45761	0.728804	+	0.684723i	$0.240077\pi$
$614$	−24.7294	−0.997996
$615$	−4.51122	−0.181910
$616$	−0.412240	−0.0166096
$617$	−15.2008	−0.611960	−0.305980	−	0.952038i	$-0.598984\pi$
$617$	−15.2008	−0.611960	−0.305980	+	0.952038i	$0.598984\pi$
$618$	−5.35062	−0.215234
$619$	−31.4228	−1.26299	−0.631494	−	0.775381i	$-0.717558\pi$
$619$	−31.4228	−1.26299	−0.631494	+	0.775381i	$0.717558\pi$
$620$	4.11553	0.165284
$621$	4.79157	0.192279
$622$	−9.40354	−0.377048
$623$	27.8984	1.11773
$624$	5.68900	0.227742
$625$	17.4902	0.699610
$626$	16.2859	0.650914
$627$	0.647407	0.0258549
$628$	−23.0958	−0.921625
$629$	1.90644	0.0760149
$630$	1.55529	0.0619641
$631$	15.8955	0.632790	0.316395	−	0.948628i	$-0.397528\pi$
$631$	15.8955	0.632790	0.316395	+	0.948628i	$0.397528\pi$
$632$	5.25291	0.208950
$633$	1.05765	0.0420377
$634$	−15.7134	−0.624057
$635$	7.41352	0.294197
$636$	4.33768	0.172000
$637$	−13.2866	−0.526433
$638$	1.28462	0.0508585
$639$	−13.2708	−0.524985
$640$	−0.720124	−0.0284654
$641$	−18.3511	−0.724826	−0.362413	−	0.932018i	$-0.618047\pi$
$641$	−18.3511	−0.724826	−0.362413	+	0.932018i	$0.618047\pi$
$642$	−13.0692	−0.515800
$643$	−17.9599	−0.708270	−0.354135	−	0.935194i	$-0.615225\pi$
$643$	−17.9599	−0.708270	−0.354135	+	0.935194i	$0.615225\pi$
$644$	−10.3486	−0.407792
$645$	−4.36803	−0.171991
$646$	4.99591	0.196561
$647$	47.3100	1.85995	0.929974	−	0.367626i	$-0.119829\pi$
$647$	47.3100	1.85995	0.929974	+	0.367626i	$0.119829\pi$
$648$	1.00000	0.0392837
$649$	0.494355	0.0194051
$650$	−25.4948	−0.999988
$651$	12.3430	0.483762
$652$	2.34483	0.0918308
$653$	−16.9899	−0.664868	−0.332434	−	0.943127i	$-0.607870\pi$
$653$	−16.9899	−0.664868	−0.332434	+	0.943127i	$0.607870\pi$
$654$	−12.7771	−0.499623
$655$	2.18839	0.0855075
$656$	6.26451	0.244588
$657$	−6.23354	−0.243193
$658$	13.3252	0.519471
$659$	−7.23982	−0.282023	−0.141012	−	0.990008i	$-0.545036\pi$
$659$	−7.23982	−0.282023	−0.141012	+	0.990008i	$0.545036\pi$
$660$	−0.137453	−0.00535036
$661$	−37.5625	−1.46101	−0.730506	−	0.682906i	$-0.760716\pi$
$661$	−37.5625	−1.46101	−0.730506	+	0.682906i	$0.760716\pi$
$662$	−21.8701	−0.850004
$663$	8.37955	0.325435
$664$	2.12352	0.0824086
$665$	5.27522	0.204564
$666$	1.29431	0.0501536
$667$	32.2481	1.24865
$668$	9.19583	0.355797
$669$	1.00000	0.0386622
$670$	5.04760	0.195006
$671$	1.33404	0.0515002
$672$	−2.15975	−0.0833141
$673$	1.19339	0.0460019	0.0230010	−	0.999735i	$-0.492678\pi$
$673$	1.19339	0.0460019	0.0230010	+	0.999735i	$0.492678\pi$
$674$	−7.15748	−0.275696
$675$	−4.48142	−0.172490
$676$	19.3647	0.744796
$677$	16.7960	0.645522	0.322761	−	0.946480i	$-0.395389\pi$
$677$	16.7960	0.645522	0.322761	+	0.946480i	$0.395389\pi$
$678$	9.85661	0.378541
$679$	5.80283	0.222692
$680$	−1.06070	−0.0406759
$681$	8.01392	0.307094
$682$	−1.09085	−0.0417709
$683$	−17.5686	−0.672244	−0.336122	−	0.941818i	$-0.609116\pi$
$683$	−17.5686	−0.672244	−0.336122	+	0.941818i	$0.609116\pi$
$684$	3.39180	0.129689
$685$	6.69900	0.255956
$686$	20.1623	0.769800
$687$	−22.6459	−0.863995
$688$	6.06566	0.231251
$689$	24.6770	0.940120
$690$	−3.45052	−0.131359
$691$	34.7714	1.32277	0.661383	−	0.750048i	$-0.269970\pi$
$691$	34.7714	1.32277	0.661383	+	0.750048i	$0.269970\pi$
$692$	1.99140	0.0757016
$693$	−0.412240	−0.0156597
$694$	−4.33587	−0.164587
$695$	0.924830	0.0350808
$696$	6.73017	0.255107
$697$	9.22724	0.349507
$698$	−20.3467	−0.770133
$699$	5.44041	0.205775
$700$	9.67874	0.365822
$701$	−42.3398	−1.59915	−0.799575	−	0.600566i	$-0.794942\pi$
$701$	−42.3398	−1.59915	−0.799575	+	0.600566i	$0.794942\pi$
$702$	5.68900	0.214717
$703$	4.39004	0.165574
$704$	0.190874	0.00719385
$705$	4.44302	0.167334
$706$	−15.9454	−0.600112
$707$	−20.7726	−0.781233
$708$	2.58995	0.0973362
$709$	26.3375	0.989125	0.494562	−	0.869142i	$-0.335328\pi$
$709$	26.3375	0.989125	0.494562	+	0.869142i	$0.335328\pi$
$710$	9.55663	0.358654
$711$	5.25291	0.197000
$712$	−12.9174	−0.484102
$713$	−27.3840	−1.02554
$714$	−3.18118	−0.119053
$715$	−0.781971	−0.0292440
$716$	8.04049	0.300487
$717$	8.64211	0.322746
$718$	23.9132	0.892431
$719$	−16.3033	−0.608012	−0.304006	−	0.952670i	$-0.598324\pi$
$719$	−16.3033	−0.608012	−0.304006	+	0.952670i	$0.598324\pi$
$720$	−0.720124	−0.0268374
$721$	11.5560	0.430368
$722$	−7.49572	−0.278962
$723$	−2.02151	−0.0751807
$724$	6.19065	0.230074
$725$	−30.1607	−1.12014
$726$	−10.9636	−0.406896
$727$	4.99784	0.185360	0.0926799	−	0.995696i	$-0.470457\pi$
$727$	4.99784	0.185360	0.0926799	+	0.995696i	$0.470457\pi$
$728$	−12.2868	−0.455379
$729$	1.00000	0.0370370
$730$	4.48892	0.166142
$731$	8.93435	0.330449
$732$	6.98912	0.258325
$733$	44.9853	1.66157	0.830784	−	0.556594i	$-0.187892\pi$
$733$	44.9853	1.66157	0.830784	+	0.556594i	$0.187892\pi$
$734$	10.6021	0.391332
$735$	1.68184	0.0620356
$736$	4.79157	0.176620
$737$	−1.33790	−0.0492823
$738$	6.26451	0.230600
$739$	5.31268	0.195430	0.0977150	−	0.995214i	$-0.468847\pi$
$739$	5.31268	0.195430	0.0977150	+	0.995214i	$0.468847\pi$
$740$	−0.932065	−0.0342634
$741$	19.2959	0.708853
$742$	−9.36829	−0.343921
$743$	−32.8810	−1.20629	−0.603144	−	0.797632i	$-0.706086\pi$
$743$	−32.8810	−1.20629	−0.603144	+	0.797632i	$0.706086\pi$
$744$	−5.71504	−0.209523
$745$	−16.5257	−0.605455
$746$	18.1083	0.662993
$747$	2.12352	0.0776956
$748$	0.281146	0.0102797
$749$	28.2262	1.03136
$750$	6.82780	0.249316
$751$	12.4460	0.454162	0.227081	−	0.973876i	$-0.427082\pi$
$751$	12.4460	0.454162	0.227081	+	0.973876i	$0.427082\pi$
$752$	−6.16980	−0.224989
$753$	−1.93932	−0.0706729
$754$	38.2879	1.39436
$755$	−0.838196	−0.0305051
$756$	−2.15975	−0.0785493
$757$	5.10450	0.185526	0.0927630	−	0.995688i	$-0.470430\pi$
$757$	5.10450	0.185526	0.0927630	+	0.995688i	$0.470430\pi$
$758$	−35.4047	−1.28596
$759$	0.914588	0.0331974
$760$	−2.44251	−0.0885993
$761$	28.6499	1.03856	0.519280	−	0.854604i	$-0.326200\pi$
$761$	28.6499	1.03856	0.519280	+	0.854604i	$0.326200\pi$
$762$	−10.2948	−0.372941
$763$	27.5953	0.999015
$764$	−18.0212	−0.651985
$765$	−1.06070	−0.0383496
$766$	−32.1048	−1.16000
$767$	14.7342	0.532022
$768$	1.00000	0.0360844
$769$	28.6270	1.03232	0.516158	−	0.856494i	$-0.327362\pi$
$769$	28.6270	1.03232	0.516158	+	0.856494i	$0.327362\pi$
$770$	0.296864	0.0106982
$771$	−1.39603	−0.0502769
$772$	−21.7993	−0.784575
$773$	−31.3331	−1.12697	−0.563487	−	0.826125i	$-0.690541\pi$
$773$	−31.3331	−1.12697	−0.563487	+	0.826125i	$0.690541\pi$
$774$	6.06566	0.218026
$775$	25.6115	0.919992
$776$	−2.68681	−0.0964508
$777$	−2.79539	−0.100284
$778$	32.7182	1.17300
$779$	21.2479	0.761287
$780$	−4.09678	−0.146688
$781$	−2.53306	−0.0906399
$782$	7.05769	0.252383
$783$	6.73017	0.240517
$784$	−2.33549	−0.0834102
$785$	16.6319	0.593617
$786$	−3.03891	−0.108394
$787$	42.5300	1.51603	0.758015	−	0.652237i	$-0.226169\pi$
$787$	42.5300	1.51603	0.758015	+	0.652237i	$0.226169\pi$
$788$	3.18861	0.113589
$789$	−6.53132	−0.232521
$790$	−3.78275	−0.134584
$791$	−21.2878	−0.756907
$792$	0.190874	0.00678242
$793$	39.7611	1.41196
$794$	32.0177	1.13627
$795$	−3.12366	−0.110785
$796$	11.1529	0.395303
$797$	24.0007	0.850149	0.425074	−	0.905158i	$-0.360248\pi$
$797$	24.0007	0.850149	0.425074	+	0.905158i	$0.360248\pi$
$798$	−7.32543	−0.259317
$799$	−9.08774	−0.321501
$800$	−4.48142	−0.158442
$801$	−12.9174	−0.456416
$802$	−7.57701	−0.267554
$803$	−1.18982	−0.0419879
$804$	−7.00935	−0.247201
$805$	7.45227	0.262658
$806$	−32.5128	−1.14522
$807$	4.46472	0.157166
$808$	9.61806	0.338362
$809$	−41.5631	−1.46128	−0.730640	−	0.682763i	$-0.760778\pi$
$809$	−41.5631	−1.46128	−0.730640	+	0.682763i	$0.760778\pi$
$810$	−0.720124	−0.0253026
$811$	23.6000	0.828707	0.414354	−	0.910116i	$-0.364008\pi$
$811$	23.6000	0.828707	0.414354	+	0.910116i	$0.364008\pi$
$812$	−14.5355	−0.510095
$813$	−19.3438	−0.678418
$814$	0.247051	0.00865913
$815$	−1.68857	−0.0591481
$816$	1.47294	0.0515632
$817$	20.5735	0.719775
$818$	−16.7032	−0.584014
$819$	−12.2868	−0.429336
$820$	−4.51122	−0.157539
$821$	52.8820	1.84559	0.922797	−	0.385286i	$-0.125897\pi$
$821$	52.8820	1.84559	0.922797	+	0.385286i	$0.125897\pi$
$822$	−9.30257	−0.324464
$823$	−13.2767	−0.462797	−0.231398	−	0.972859i	$-0.574330\pi$
$823$	−13.2767	−0.462797	−0.231398	+	0.972859i	$0.574330\pi$
$824$	−5.35062	−0.186398
$825$	−0.855388	−0.0297808
$826$	−5.59364	−0.194628
$827$	17.6180	0.612637	0.306318	−	0.951929i	$-0.400903\pi$
$827$	17.6180	0.612637	0.306318	+	0.951929i	$0.400903\pi$
$828$	4.79157	0.166519
$829$	−6.06705	−0.210717	−0.105359	−	0.994434i	$-0.533599\pi$
$829$	−6.06705	−0.210717	−0.105359	+	0.994434i	$0.533599\pi$
$830$	−1.52920	−0.0530792
$831$	18.4637	0.640500
$832$	5.68900	0.197231
$833$	−3.44003	−0.119190
$834$	−1.28426	−0.0444704
$835$	−6.62214	−0.229169
$836$	0.647407	0.0223910
$837$	−5.71504	−0.197541
$838$	24.3492	0.841129
$839$	38.1492	1.31706	0.658529	−	0.752555i	$-0.271179\pi$
$839$	38.1492	1.31706	0.658529	+	0.752555i	$0.271179\pi$
$840$	1.55529	0.0536625
$841$	16.2952	0.561904
$842$	35.2333	1.21422
$843$	12.5527	0.432339
$844$	1.05765	0.0364057
$845$	−13.9450	−0.479722
$846$	−6.16980	−0.212122
$847$	23.6785	0.813605
$848$	4.33768	0.148956
$849$	2.24527	0.0770574
$850$	−6.60086	−0.226408
$851$	6.20179	0.212595
$852$	−13.2708	−0.454651
$853$	10.6807	0.365700	0.182850	−	0.983141i	$-0.441468\pi$
$853$	10.6807	0.365700	0.182850	+	0.983141i	$0.441468\pi$
$854$	−15.0947	−0.516532
$855$	−2.44251	−0.0835322
$856$	−13.0692	−0.446696
$857$	−24.5920	−0.840046	−0.420023	−	0.907513i	$-0.637978\pi$
$857$	−24.5920	−0.840046	−0.420023	+	0.907513i	$0.637978\pi$
$858$	1.08588	0.0370715
$859$	−22.2297	−0.758468	−0.379234	−	0.925301i	$-0.623812\pi$
$859$	−22.2297	−0.758468	−0.379234	+	0.925301i	$0.623812\pi$
$860$	−4.36803	−0.148948
$861$	−13.5298	−0.461093
$862$	5.36851	0.182852
$863$	6.52908	0.222253	0.111126	−	0.993806i	$-0.464554\pi$
$863$	6.52908	0.222253	0.111126	+	0.993806i	$0.464554\pi$
$864$	1.00000	0.0340207
$865$	−1.43405	−0.0487593
$866$	−11.0259	−0.374676
$867$	−14.8304	−0.503668
$868$	12.3430	0.418950
$869$	1.00265	0.0340124
$870$	−4.84656	−0.164314
$871$	−39.8762	−1.35115
$872$	−12.7771	−0.432686
$873$	−2.68681	−0.0909347
$874$	16.2520	0.549733
$875$	−14.7463	−0.498517
$876$	−6.23354	−0.210612
$877$	−27.8046	−0.938895	−0.469447	−	0.882960i	$-0.655547\pi$
$877$	−27.8046	−0.938895	−0.469447	+	0.882960i	$0.655547\pi$
$878$	−14.9875	−0.505805
$879$	27.3537	0.922618
$880$	−0.137453	−0.00463354
$881$	26.5940	0.895976	0.447988	−	0.894040i	$-0.352141\pi$
$881$	26.5940	0.895976	0.447988	+	0.894040i	$0.352141\pi$
$882$	−2.33549	−0.0786399
$883$	−43.9447	−1.47886	−0.739429	−	0.673235i	$-0.764904\pi$
$883$	−43.9447	−1.47886	−0.739429	+	0.673235i	$0.764904\pi$
$884$	8.37955	0.281835
$885$	−1.86508	−0.0626941
$886$	12.7430	0.428110
$887$	11.9452	0.401080	0.200540	−	0.979686i	$-0.435730\pi$
$887$	11.9452	0.401080	0.200540	+	0.979686i	$0.435730\pi$
$888$	1.29431	0.0434343
$889$	22.2341	0.745709
$890$	9.30216	0.311809
$891$	0.190874	0.00639453
$892$	1.00000	0.0334825
$893$	−20.9267	−0.700285
$894$	22.9484	0.767510
$895$	−5.79015	−0.193543
$896$	−2.15975	−0.0721521
$897$	27.2592	0.910159
$898$	−28.2186	−0.941668
$899$	−38.4632	−1.28282
$900$	−4.48142	−0.149381
$901$	6.38913	0.212853
$902$	1.19573	0.0398136
$903$	−13.1003	−0.435951
$904$	9.85661	0.327826
$905$	−4.45803	−0.148190
$906$	1.16396	0.0386700
$907$	37.4317	1.24290	0.621449	−	0.783455i	$-0.286544\pi$
$907$	37.4317	1.24290	0.621449	+	0.783455i	$0.286544\pi$
$908$	8.01392	0.265951
$909$	9.61806	0.319011
$910$	8.84802	0.293309
$911$	−14.9654	−0.495825	−0.247912	−	0.968782i	$-0.579744\pi$
$911$	−14.9654	−0.495825	−0.247912	+	0.968782i	$0.579744\pi$
$912$	3.39180	0.112314
$913$	0.405326	0.0134143
$914$	25.2255	0.834386
$915$	−5.03303	−0.166387
$916$	−22.6459	−0.748242
$917$	6.56328	0.216738
$918$	1.47294	0.0486142
$919$	−35.2310	−1.16216	−0.581081	−	0.813846i	$-0.697370\pi$
$919$	−35.2310	−1.16216	−0.581081	+	0.813846i	$0.697370\pi$
$920$	−3.45052	−0.113760
$921$	−24.7294	−0.814860
$922$	19.4256	0.639749
$923$	−75.4977	−2.48504
$924$	−0.412240	−0.0135617
$925$	−5.80036	−0.190715
$926$	−17.2731	−0.567629
$927$	−5.35062	−0.175738
$928$	6.73017	0.220929
$929$	22.6674	0.743694	0.371847	−	0.928294i	$-0.378725\pi$
$929$	22.6674	0.743694	0.371847	+	0.928294i	$0.378725\pi$
$930$	4.11553	0.134954
$931$	−7.92149	−0.259616
$932$	5.44041	0.178207
$933$	−9.40354	−0.307858
$934$	−20.9309	−0.684880
$935$	−0.202460	−0.00662115
$936$	5.68900	0.185951
$937$	−54.1789	−1.76995	−0.884974	−	0.465640i	$-0.845824\pi$
$937$	−54.1789	−1.76995	−0.884974	+	0.465640i	$0.845824\pi$
$938$	15.1384	0.494287
$939$	16.2859	0.531469
$940$	4.44302	0.144915
$941$	−46.8129	−1.52606	−0.763029	−	0.646365i	$-0.776288\pi$
$941$	−46.8129	−1.52606	−0.763029	+	0.646365i	$0.776288\pi$
$942$	−23.0958	−0.752503
$943$	30.0168	0.977483
$944$	2.58995	0.0842956
$945$	1.55529	0.0505935
$946$	1.15778	0.0376426
$947$	−15.1111	−0.491044	−0.245522	−	0.969391i	$-0.578959\pi$
$947$	−15.1111	−0.491044	−0.245522	+	0.969391i	$0.578959\pi$
$948$	5.25291	0.170607
$949$	−35.4626	−1.15116
$950$	−15.2001	−0.493155
$951$	−15.7134	−0.509540
$952$	−3.18118	−0.103103
$953$	−15.7453	−0.510041	−0.255020	−	0.966936i	$-0.582082\pi$
$953$	−15.7453	−0.510041	−0.255020	+	0.966936i	$0.582082\pi$
$954$	4.33768	0.140437
$955$	12.9775	0.419942
$956$	8.64211	0.279506
$957$	1.28462	0.0415258
$958$	−30.4422	−0.983543
$959$	20.0912	0.648779
$960$	−0.720124	−0.0232419
$961$	1.66163	0.0536009
$962$	7.36334	0.237404
$963$	−13.0692	−0.421149
$964$	−2.02151	−0.0651084
$965$	15.6982	0.505344
$966$	−10.3486	−0.332960
$967$	−25.7901	−0.829353	−0.414676	−	0.909969i	$-0.636105\pi$
$967$	−25.7901	−0.829353	−0.414676	+	0.909969i	$0.636105\pi$
$968$	−10.9636	−0.352382
$969$	4.99591	0.160492
$970$	1.93484	0.0621238
$971$	47.8921	1.53693	0.768466	−	0.639891i	$-0.221020\pi$
$971$	47.8921	1.53693	0.768466	+	0.639891i	$0.221020\pi$
$972$	1.00000	0.0320750
$973$	2.77369	0.0889204
$974$	−11.4597	−0.367191
$975$	−25.4948	−0.816487
$976$	6.98912	0.223716
$977$	−19.6784	−0.629566	−0.314783	−	0.949164i	$-0.601932\pi$
$977$	−19.6784	−0.629566	−0.314783	+	0.949164i	$0.601932\pi$
$978$	2.34483	0.0749795
$979$	−2.46561	−0.0788012
$980$	1.68184	0.0537244
$981$	−12.7771	−0.407940
$982$	−33.5690	−1.07123
$983$	12.4349	0.396610	0.198305	−	0.980140i	$-0.436456\pi$
$983$	12.4349	0.396610	0.198305	+	0.980140i	$0.436456\pi$
$984$	6.26451	0.199705
$985$	−2.29619	−0.0731628
$986$	9.91313	0.315699
$987$	13.3252	0.424146
$988$	19.2959	0.613885
$989$	29.0640	0.924182
$990$	−0.137453	−0.00436855
$991$	−0.215106	−0.00683306	−0.00341653	−	0.999994i	$-0.501088\pi$
$991$	−0.215106	−0.00683306	−0.00341653	+	0.999994i	$0.501088\pi$
$992$	−5.71504	−0.181453
$993$	−21.8701	−0.694026
$994$	28.6616	0.909092
$995$	−8.03144	−0.254614
$996$	2.12352	0.0672863
$997$	60.4304	1.91385	0.956926	−	0.290333i	$-0.0937661\pi$
$997$	60.4304	1.91385	0.956926	+	0.290333i	$0.0937661\pi$
$998$	−24.3218	−0.769894
$999$	1.29431	0.0409502

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1338.2.a.i.1.2	✓	6
3.2	odd	2		4014.2.a.s.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1338.2.a.i.1.2	✓	6	1.1	even	1	trivial
4014.2.a.s.1.5		6	3.2	odd	2

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:	\( N \)	\(=\)	\( 1338 = 2 \cdot 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1338.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.720124 q^{5} +1.00000 q^{6} -2.15975 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.720124 q^{5} +1.00000 q^{6} -2.15975 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.720124 q^{10} +0.190874 q^{11} +1.00000 q^{12} +5.68900 q^{13} -2.15975 q^{14} -0.720124 q^{15} +1.00000 q^{16} +1.47294 q^{17} +1.00000 q^{18} +3.39180 q^{19} -0.720124 q^{20} -2.15975 q^{21} +0.190874 q^{22} +4.79157 q^{23} +1.00000 q^{24} -4.48142 q^{25} +5.68900 q^{26} +1.00000 q^{27} -2.15975 q^{28} +6.73017 q^{29} -0.720124 q^{30} -5.71504 q^{31} +1.00000 q^{32} +0.190874 q^{33} +1.47294 q^{34} +1.55529 q^{35} +1.00000 q^{36} +1.29431 q^{37} +3.39180 q^{38} +5.68900 q^{39} -0.720124 q^{40} +6.26451 q^{41} -2.15975 q^{42} +6.06566 q^{43} +0.190874 q^{44} -0.720124 q^{45} +4.79157 q^{46} -6.16980 q^{47} +1.00000 q^{48} -2.33549 q^{49} -4.48142 q^{50} +1.47294 q^{51} +5.68900 q^{52} +4.33768 q^{53} +1.00000 q^{54} -0.137453 q^{55} -2.15975 q^{56} +3.39180 q^{57} +6.73017 q^{58} +2.58995 q^{59} -0.720124 q^{60} +6.98912 q^{61} -5.71504 q^{62} -2.15975 q^{63} +1.00000 q^{64} -4.09678 q^{65} +0.190874 q^{66} -7.00935 q^{67} +1.47294 q^{68} +4.79157 q^{69} +1.55529 q^{70} -13.2708 q^{71} +1.00000 q^{72} -6.23354 q^{73} +1.29431 q^{74} -4.48142 q^{75} +3.39180 q^{76} -0.412240 q^{77} +5.68900 q^{78} +5.25291 q^{79} -0.720124 q^{80} +1.00000 q^{81} +6.26451 q^{82} +2.12352 q^{83} -2.15975 q^{84} -1.06070 q^{85} +6.06566 q^{86} +6.73017 q^{87} +0.190874 q^{88} -12.9174 q^{89} -0.720124 q^{90} -12.2868 q^{91} +4.79157 q^{92} -5.71504 q^{93} -6.16980 q^{94} -2.44251 q^{95} +1.00000 q^{96} -2.68681 q^{97} -2.33549 q^{98} +0.190874 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} + 5 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 + 5 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} + 5 q^{7} + 6 q^{8} + 6 q^{9} + 6 q^{10} + q^{11} + 6 q^{12} + 6 q^{13} + 5 q^{14} + 6 q^{15} + 6 q^{16} + 10 q^{17} + 6 q^{18} - 4 q^{19} + 6 q^{20} + 5 q^{21} + q^{22} + 2 q^{23} + 6 q^{24} + 6 q^{26} + 6 q^{27} + 5 q^{28} + 6 q^{29} + 6 q^{30} - 5 q^{31} + 6 q^{32} + q^{33} + 10 q^{34} - 2 q^{35} + 6 q^{36} + q^{37} - 4 q^{38} + 6 q^{39} + 6 q^{40} + 12 q^{41} + 5 q^{42} - 11 q^{43} + q^{44} + 6 q^{45} + 2 q^{46} + 5 q^{47} + 6 q^{48} - q^{49} + 10 q^{51} + 6 q^{52} + 4 q^{53} + 6 q^{54} - 15 q^{55} + 5 q^{56} - 4 q^{57} + 6 q^{58} + q^{59} + 6 q^{60} - 8 q^{61} - 5 q^{62} + 5 q^{63} + 6 q^{64} + 5 q^{65} + q^{66} - 6 q^{67} + 10 q^{68} + 2 q^{69} - 2 q^{70} + q^{71} + 6 q^{72} - 10 q^{73} + q^{74} - 4 q^{76} - 8 q^{77} + 6 q^{78} - 10 q^{79} + 6 q^{80} + 6 q^{81} + 12 q^{82} - 6 q^{83} + 5 q^{84} - 2 q^{85} - 11 q^{86} + 6 q^{87} + q^{88} - 3 q^{89} + 6 q^{90} - 16 q^{91} + 2 q^{92} - 5 q^{93} + 5 q^{94} - 10 q^{95} + 6 q^{96} + 3 q^{97} - q^{98} + q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 + 5 * q^7 + 6 * q^8 + 6 * q^9 + 6 * q^10 + q^11 + 6 * q^12 + 6 * q^13 + 5 * q^14 + 6 * q^15 + 6 * q^16 + 10 * q^17 + 6 * q^18 - 4 * q^19 + 6 * q^20 + 5 * q^21 + q^22 + 2 * q^23 + 6 * q^24 + 6 * q^26 + 6 * q^27 + 5 * q^28 + 6 * q^29 + 6 * q^30 - 5 * q^31 + 6 * q^32 + q^33 + 10 * q^34 - 2 * q^35 + 6 * q^36 + q^37 - 4 * q^38 + 6 * q^39 + 6 * q^40 + 12 * q^41 + 5 * q^42 - 11 * q^43 + q^44 + 6 * q^45 + 2 * q^46 + 5 * q^47 + 6 * q^48 - q^49 + 10 * q^51 + 6 * q^52 + 4 * q^53 + 6 * q^54 - 15 * q^55 + 5 * q^56 - 4 * q^57 + 6 * q^58 + q^59 + 6 * q^60 - 8 * q^61 - 5 * q^62 + 5 * q^63 + 6 * q^64 + 5 * q^65 + q^66 - 6 * q^67 + 10 * q^68 + 2 * q^69 - 2 * q^70 + q^71 + 6 * q^72 - 10 * q^73 + q^74 - 4 * q^76 - 8 * q^77 + 6 * q^78 - 10 * q^79 + 6 * q^80 + 6 * q^81 + 12 * q^82 - 6 * q^83 + 5 * q^84 - 2 * q^85 - 11 * q^86 + 6 * q^87 + q^88 - 3 * q^89 + 6 * q^90 - 16 * q^91 + 2 * q^92 - 5 * q^93 + 5 * q^94 - 10 * q^95 + 6 * q^96 + 3 * q^97 - q^98 + q^99

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