LMFDB - Embedded newform 6018.2.a.z.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4 x^{10} - 27 x^{9} + 117 x^{8} + 200 x^{7} - 1023 x^{6} - 484 x^{5} + 3403 x^{4} + 562 x^{3} + \cdots + 1200 $ x^11 - 4x^10 - 27x^9 + 117x^8 + 200x^7 - 1023x^6 - 484x^5 + 3403x^4 + 562x^3 - 4372x^2 - 692x + 1200
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-4.08681$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.08681 q^{5} -1.00000 q^{6} -0.153752 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.08681 q^{5} -1.00000 q^{6} -0.153752 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.08681 q^{10} +4.40099 q^{11} -1.00000 q^{12} +0.950947 q^{13} -0.153752 q^{14} +4.08681 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -3.15599 q^{19} -4.08681 q^{20} +0.153752 q^{21} +4.40099 q^{22} +0.350961 q^{23} -1.00000 q^{24} +11.7020 q^{25} +0.950947 q^{26} -1.00000 q^{27} -0.153752 q^{28} +5.57627 q^{29} +4.08681 q^{30} -4.44408 q^{31} +1.00000 q^{32} -4.40099 q^{33} -1.00000 q^{34} +0.628354 q^{35} +1.00000 q^{36} +0.0233567 q^{37} -3.15599 q^{38} -0.950947 q^{39} -4.08681 q^{40} -3.30306 q^{41} +0.153752 q^{42} -7.47395 q^{43} +4.40099 q^{44} -4.08681 q^{45} +0.350961 q^{46} -6.21010 q^{47} -1.00000 q^{48} -6.97636 q^{49} +11.7020 q^{50} +1.00000 q^{51} +0.950947 q^{52} -4.18834 q^{53} -1.00000 q^{54} -17.9860 q^{55} -0.153752 q^{56} +3.15599 q^{57} +5.57627 q^{58} -1.00000 q^{59} +4.08681 q^{60} -3.20062 q^{61} -4.44408 q^{62} -0.153752 q^{63} +1.00000 q^{64} -3.88634 q^{65} -4.40099 q^{66} +12.6667 q^{67} -1.00000 q^{68} -0.350961 q^{69} +0.628354 q^{70} +8.12990 q^{71} +1.00000 q^{72} +12.5620 q^{73} +0.0233567 q^{74} -11.7020 q^{75} -3.15599 q^{76} -0.676660 q^{77} -0.950947 q^{78} +2.48459 q^{79} -4.08681 q^{80} +1.00000 q^{81} -3.30306 q^{82} -15.3670 q^{83} +0.153752 q^{84} +4.08681 q^{85} -7.47395 q^{86} -5.57627 q^{87} +4.40099 q^{88} -7.84188 q^{89} -4.08681 q^{90} -0.146210 q^{91} +0.350961 q^{92} +4.44408 q^{93} -6.21010 q^{94} +12.8979 q^{95} -1.00000 q^{96} +14.1034 q^{97} -6.97636 q^{98} +4.40099 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9} + 4 q^{10} + 9 q^{11} - 11 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 11 q^{16} - 11 q^{17} + 11 q^{18} - q^{19} + 4 q^{20} - 3 q^{21} + 9 q^{22} + 10 q^{23} - 11 q^{24} + 15 q^{25} + 6 q^{26} - 11 q^{27} + 3 q^{28} + 14 q^{29} - 4 q^{30} + 17 q^{31} + 11 q^{32} - 9 q^{33} - 11 q^{34} + 8 q^{35} + 11 q^{36} + 30 q^{37} - q^{38} - 6 q^{39} + 4 q^{40} + 10 q^{41} - 3 q^{42} + 11 q^{43} + 9 q^{44} + 4 q^{45} + 10 q^{46} - 6 q^{47} - 11 q^{48} + 18 q^{49} + 15 q^{50} + 11 q^{51} + 6 q^{52} + 10 q^{53} - 11 q^{54} - 11 q^{55} + 3 q^{56} + q^{57} + 14 q^{58} - 11 q^{59} - 4 q^{60} + 13 q^{61} + 17 q^{62} + 3 q^{63} + 11 q^{64} + 32 q^{65} - 9 q^{66} + 26 q^{67} - 11 q^{68} - 10 q^{69} + 8 q^{70} + 14 q^{71} + 11 q^{72} + 20 q^{73} + 30 q^{74} - 15 q^{75} - q^{76} + 26 q^{77} - 6 q^{78} + 15 q^{79} + 4 q^{80} + 11 q^{81} + 10 q^{82} + 2 q^{83} - 3 q^{84} - 4 q^{85} + 11 q^{86} - 14 q^{87} + 9 q^{88} + q^{89} + 4 q^{90} + 17 q^{91} + 10 q^{92} - 17 q^{93} - 6 q^{94} + 3 q^{95} - 11 q^{96} + 33 q^{97} + 18 q^{98} + 9 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9 + 4 * q^10 + 9 * q^11 - 11 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 11 * q^16 - 11 * q^17 + 11 * q^18 - q^19 + 4 * q^20 - 3 * q^21 + 9 * q^22 + 10 * q^23 - 11 * q^24 + 15 * q^25 + 6 * q^26 - 11 * q^27 + 3 * q^28 + 14 * q^29 - 4 * q^30 + 17 * q^31 + 11 * q^32 - 9 * q^33 - 11 * q^34 + 8 * q^35 + 11 * q^36 + 30 * q^37 - q^38 - 6 * q^39 + 4 * q^40 + 10 * q^41 - 3 * q^42 + 11 * q^43 + 9 * q^44 + 4 * q^45 + 10 * q^46 - 6 * q^47 - 11 * q^48 + 18 * q^49 + 15 * q^50 + 11 * q^51 + 6 * q^52 + 10 * q^53 - 11 * q^54 - 11 * q^55 + 3 * q^56 + q^57 + 14 * q^58 - 11 * q^59 - 4 * q^60 + 13 * q^61 + 17 * q^62 + 3 * q^63 + 11 * q^64 + 32 * q^65 - 9 * q^66 + 26 * q^67 - 11 * q^68 - 10 * q^69 + 8 * q^70 + 14 * q^71 + 11 * q^72 + 20 * q^73 + 30 * q^74 - 15 * q^75 - q^76 + 26 * q^77 - 6 * q^78 + 15 * q^79 + 4 * q^80 + 11 * q^81 + 10 * q^82 + 2 * q^83 - 3 * q^84 - 4 * q^85 + 11 * q^86 - 14 * q^87 + 9 * q^88 + q^89 + 4 * q^90 + 17 * q^91 + 10 * q^92 - 17 * q^93 - 6 * q^94 + 3 * q^95 - 11 * q^96 + 33 * q^97 + 18 * 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
$5$	−4.08681	−1.82768	−0.913839	−	0.406078i	$-0.866896\pi$
$5$	−4.08681	−1.82768	−0.913839	+	0.406078i	$0.866896\pi$
$6$	−1.00000	−0.408248
$7$	−0.153752	−0.0581127	−0.0290563	−	0.999578i	$-0.509250\pi$
$7$	−0.153752	−0.0581127	−0.0290563	+	0.999578i	$0.509250\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−4.08681	−1.29236
$11$	4.40099	1.32695	0.663475	−	0.748199i	$-0.269081\pi$
$11$	4.40099	1.32695	0.663475	+	0.748199i	$0.269081\pi$
$12$	−1.00000	−0.288675
$13$	0.950947	0.263745	0.131873	−	0.991267i	$-0.457901\pi$
$13$	0.950947	0.263745	0.131873	+	0.991267i	$0.457901\pi$
$14$	−0.153752	−0.0410919
$15$	4.08681	1.05521
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−3.15599	−0.724034	−0.362017	−	0.932171i	$-0.617912\pi$
$19$	−3.15599	−0.724034	−0.362017	+	0.932171i	$0.617912\pi$
$20$	−4.08681	−0.913839
$21$	0.153752	0.0335514
$22$	4.40099	0.938295
$23$	0.350961	0.0731804	0.0365902	−	0.999330i	$-0.488350\pi$
$23$	0.350961	0.0731804	0.0365902	+	0.999330i	$0.488350\pi$
$24$	−1.00000	−0.204124
$25$	11.7020	2.34040
$26$	0.950947	0.186496
$27$	−1.00000	−0.192450
$28$	−0.153752	−0.0290563
$29$	5.57627	1.03549	0.517743	−	0.855536i	$-0.326772\pi$
$29$	5.57627	1.03549	0.517743	+	0.855536i	$0.326772\pi$
$30$	4.08681	0.746146
$31$	−4.44408	−0.798180	−0.399090	−	0.916912i	$-0.630674\pi$
$31$	−4.44408	−0.798180	−0.399090	+	0.916912i	$0.630674\pi$
$32$	1.00000	0.176777
$33$	−4.40099	−0.766115
$34$	−1.00000	−0.171499
$35$	0.628354	0.106211
$36$	1.00000	0.166667
$37$	0.0233567	0.00383982	0.00191991	−	0.999998i	$-0.499389\pi$
$37$	0.0233567	0.00383982	0.00191991	+	0.999998i	$0.499389\pi$
$38$	−3.15599	−0.511970
$39$	−0.950947	−0.152273
$40$	−4.08681	−0.646181
$41$	−3.30306	−0.515852	−0.257926	−	0.966165i	$-0.583039\pi$
$41$	−3.30306	−0.515852	−0.257926	+	0.966165i	$0.583039\pi$
$42$	0.153752	0.0237244
$43$	−7.47395	−1.13977	−0.569883	−	0.821726i	$-0.693012\pi$
$43$	−7.47395	−1.13977	−0.569883	+	0.821726i	$0.693012\pi$
$44$	4.40099	0.663475
$45$	−4.08681	−0.609226
$46$	0.350961	0.0517464
$47$	−6.21010	−0.905836	−0.452918	−	0.891552i	$-0.649617\pi$
$47$	−6.21010	−0.905836	−0.452918	+	0.891552i	$0.649617\pi$
$48$	−1.00000	−0.144338
$49$	−6.97636	−0.996623
$50$	11.7020	1.65492
$51$	1.00000	0.140028
$52$	0.950947	0.131873
$53$	−4.18834	−0.575313	−0.287657	−	0.957734i	$-0.592876\pi$
$53$	−4.18834	−0.575313	−0.287657	+	0.957734i	$0.592876\pi$
$54$	−1.00000	−0.136083
$55$	−17.9860	−2.42524
$56$	−0.153752	−0.0205459
$57$	3.15599	0.418021
$58$	5.57627	0.732200
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	4.08681	0.527605
$61$	−3.20062	−0.409797	−0.204899	−	0.978783i	$-0.565686\pi$
$61$	−3.20062	−0.409797	−0.204899	+	0.978783i	$0.565686\pi$
$62$	−4.44408	−0.564399
$63$	−0.153752	−0.0193709
$64$	1.00000	0.125000
$65$	−3.88634	−0.482041
$66$	−4.40099	−0.541725
$67$	12.6667	1.54749	0.773743	−	0.633500i	$-0.218382\pi$
$67$	12.6667	1.54749	0.773743	+	0.633500i	$0.218382\pi$
$68$	−1.00000	−0.121268
$69$	−0.350961	−0.0422507
$70$	0.628354	0.0751026
$71$	8.12990	0.964841	0.482421	−	0.875940i	$-0.339758\pi$
$71$	8.12990	0.964841	0.482421	+	0.875940i	$0.339758\pi$
$72$	1.00000	0.117851
$73$	12.5620	1.47027	0.735134	−	0.677921i	$-0.237119\pi$
$73$	12.5620	1.47027	0.735134	+	0.677921i	$0.237119\pi$
$74$	0.0233567	0.00271516
$75$	−11.7020	−1.35123
$76$	−3.15599	−0.362017
$77$	−0.676660	−0.0771126
$78$	−0.950947	−0.107674
$79$	2.48459	0.279538	0.139769	−	0.990184i	$-0.455364\pi$
$79$	2.48459	0.279538	0.139769	+	0.990184i	$0.455364\pi$
$80$	−4.08681	−0.456919
$81$	1.00000	0.111111
$82$	−3.30306	−0.364762
$83$	−15.3670	−1.68675	−0.843373	−	0.537328i	$-0.819434\pi$
$83$	−15.3670	−1.68675	−0.843373	+	0.537328i	$0.819434\pi$
$84$	0.153752	0.0167757
$85$	4.08681	0.443277
$86$	−7.47395	−0.805937
$87$	−5.57627	−0.597839
$88$	4.40099	0.469148
$89$	−7.84188	−0.831238	−0.415619	−	0.909539i	$-0.636435\pi$
$89$	−7.84188	−0.831238	−0.415619	+	0.909539i	$0.636435\pi$
$90$	−4.08681	−0.430788
$91$	−0.146210	−0.0153269
$92$	0.350961	0.0365902
$93$	4.44408	0.460830
$94$	−6.21010	−0.640523
$95$	12.8979	1.32330
$96$	−1.00000	−0.102062
$97$	14.1034	1.43199	0.715993	−	0.698107i	$-0.245974\pi$
$97$	14.1034	1.43199	0.715993	+	0.698107i	$0.245974\pi$
$98$	−6.97636	−0.704719
$99$	4.40099	0.442317
$100$	11.7020	1.17020
$101$	7.73723	0.769883	0.384941	−	0.922941i	$-0.374222\pi$
$101$	7.73723	0.769883	0.384941	+	0.922941i	$0.374222\pi$
$102$	1.00000	0.0990148
$103$	9.91079	0.976540	0.488270	−	0.872693i	$-0.337628\pi$
$103$	9.91079	0.976540	0.488270	+	0.872693i	$0.337628\pi$
$104$	0.950947	0.0932480
$105$	−0.628354	−0.0613210
$106$	−4.18834	−0.406808
$107$	9.70267	0.937992	0.468996	−	0.883200i	$-0.344616\pi$
$107$	9.70267	0.937992	0.468996	+	0.883200i	$0.344616\pi$
$108$	−1.00000	−0.0962250
$109$	11.1018	1.06336	0.531681	−	0.846945i	$-0.321561\pi$
$109$	11.1018	1.06336	0.531681	+	0.846945i	$0.321561\pi$
$110$	−17.9860	−1.71490
$111$	−0.0233567	−0.00221692
$112$	−0.153752	−0.0145282
$113$	14.0732	1.32389	0.661946	−	0.749552i	$-0.269731\pi$
$113$	14.0732	1.32389	0.661946	+	0.749552i	$0.269731\pi$
$114$	3.15599	0.295586
$115$	−1.43431	−0.133750
$116$	5.57627	0.517743
$117$	0.950947	0.0879151
$118$	−1.00000	−0.0920575
$119$	0.153752	0.0140944
$120$	4.08681	0.373073
$121$	8.36875	0.760795
$122$	−3.20062	−0.289770
$123$	3.30306	0.297827
$124$	−4.44408	−0.399090
$125$	−27.3899	−2.44982
$126$	−0.153752	−0.0136973
$127$	5.50750	0.488712	0.244356	−	0.969686i	$-0.421423\pi$
$127$	5.50750	0.488712	0.244356	+	0.969686i	$0.421423\pi$
$128$	1.00000	0.0883883
$129$	7.47395	0.658045
$130$	−3.88634	−0.340855
$131$	12.6218	1.10277	0.551385	−	0.834251i	$-0.314100\pi$
$131$	12.6218	1.10277	0.551385	+	0.834251i	$0.314100\pi$
$132$	−4.40099	−0.383057
$133$	0.485239	0.0420756
$134$	12.6667	1.09424
$135$	4.08681	0.351737
$136$	−1.00000	−0.0857493
$137$	0.932092	0.0796340	0.0398170	−	0.999207i	$-0.487323\pi$
$137$	0.932092	0.0796340	0.0398170	+	0.999207i	$0.487323\pi$
$138$	−0.350961	−0.0298758
$139$	7.63886	0.647920	0.323960	−	0.946071i	$-0.394986\pi$
$139$	7.63886	0.647920	0.323960	+	0.946071i	$0.394986\pi$
$140$	0.628354	0.0531056
$141$	6.21010	0.522985
$142$	8.12990	0.682246
$143$	4.18511	0.349977
$144$	1.00000	0.0833333
$145$	−22.7891	−1.89254
$146$	12.5620	1.03964
$147$	6.97636	0.575401
$148$	0.0233567	0.00191991
$149$	−1.29790	−0.106329	−0.0531643	−	0.998586i	$-0.516931\pi$
$149$	−1.29790	−0.106329	−0.0531643	+	0.998586i	$0.516931\pi$
$150$	−11.7020	−0.955466
$151$	15.1909	1.23622	0.618111	−	0.786091i	$-0.287898\pi$
$151$	15.1909	1.23622	0.618111	+	0.786091i	$0.287898\pi$
$152$	−3.15599	−0.255985
$153$	−1.00000	−0.0808452
$154$	−0.676660	−0.0545268
$155$	18.1621	1.45882
$156$	−0.950947	−0.0761367
$157$	15.1425	1.20850	0.604251	−	0.796794i	$-0.293472\pi$
$157$	15.1425	1.20850	0.604251	+	0.796794i	$0.293472\pi$
$158$	2.48459	0.197663
$159$	4.18834	0.332157
$160$	−4.08681	−0.323091
$161$	−0.0539608	−0.00425271
$162$	1.00000	0.0785674
$163$	20.3422	1.59332	0.796662	−	0.604424i	$-0.206597\pi$
$163$	20.3422	1.59332	0.796662	+	0.604424i	$0.206597\pi$
$164$	−3.30306	−0.257926
$165$	17.9860	1.40021
$166$	−15.3670	−1.19271
$167$	3.85482	0.298295	0.149148	−	0.988815i	$-0.452347\pi$
$167$	3.85482	0.298295	0.149148	+	0.988815i	$0.452347\pi$
$168$	0.153752	0.0118622
$169$	−12.0957	−0.930438
$170$	4.08681	0.313444
$171$	−3.15599	−0.241345
$172$	−7.47395	−0.569883
$173$	−2.16625	−0.164697	−0.0823483	−	0.996604i	$-0.526242\pi$
$173$	−2.16625	−0.164697	−0.0823483	+	0.996604i	$0.526242\pi$
$174$	−5.57627	−0.422736
$175$	−1.79920	−0.136007
$176$	4.40099	0.331737
$177$	1.00000	0.0751646
$178$	−7.84188	−0.587774
$179$	24.4934	1.83072	0.915361	−	0.402634i	$-0.131905\pi$
$179$	24.4934	1.83072	0.915361	+	0.402634i	$0.131905\pi$
$180$	−4.08681	−0.304613
$181$	7.26868	0.540277	0.270138	−	0.962822i	$-0.412931\pi$
$181$	7.26868	0.540277	0.270138	+	0.962822i	$0.412931\pi$
$182$	−0.146210	−0.0108378
$183$	3.20062	0.236597
$184$	0.350961	0.0258732
$185$	−0.0954545	−0.00701795
$186$	4.44408	0.325856
$187$	−4.40099	−0.321833
$188$	−6.21010	−0.452918
$189$	0.153752	0.0111838
$190$	12.8979	0.935715
$191$	−21.4030	−1.54866	−0.774332	−	0.632779i	$-0.781914\pi$
$191$	−21.4030	−1.54866	−0.774332	+	0.632779i	$0.781914\pi$
$192$	−1.00000	−0.0721688
$193$	5.22947	0.376425	0.188213	−	0.982128i	$-0.439731\pi$
$193$	5.22947	0.376425	0.188213	+	0.982128i	$0.439731\pi$
$194$	14.1034	1.01257
$195$	3.88634	0.278307
$196$	−6.97636	−0.498311
$197$	−8.39960	−0.598447	−0.299223	−	0.954183i	$-0.596728\pi$
$197$	−8.39960	−0.598447	−0.299223	+	0.954183i	$0.596728\pi$
$198$	4.40099	0.312765
$199$	−17.0530	−1.20885	−0.604427	−	0.796661i	$-0.706598\pi$
$199$	−17.0530	−1.20885	−0.604427	+	0.796661i	$0.706598\pi$
$200$	11.7020	0.827458
$201$	−12.6667	−0.893441
$202$	7.73723	0.544389
$203$	−0.857360	−0.0601749
$204$	1.00000	0.0700140
$205$	13.4990	0.942810
$206$	9.91079	0.690518
$207$	0.350961	0.0243935
$208$	0.950947	0.0659363
$209$	−13.8895	−0.960757
$210$	−0.628354	−0.0433605
$211$	−4.04577	−0.278522	−0.139261	−	0.990256i	$-0.544473\pi$
$211$	−4.04577	−0.278522	−0.139261	+	0.990256i	$0.544473\pi$
$212$	−4.18834	−0.287657
$213$	−8.12990	−0.557051
$214$	9.70267	0.663261
$215$	30.5446	2.08313
$216$	−1.00000	−0.0680414
$217$	0.683284	0.0463844
$218$	11.1018	0.751910
$219$	−12.5620	−0.848860
$220$	−17.9860	−1.21262
$221$	−0.950947	−0.0639676
$222$	−0.0233567	−0.00156760
$223$	−17.4348	−1.16752	−0.583761	−	0.811925i	$-0.698420\pi$
$223$	−17.4348	−1.16752	−0.583761	+	0.811925i	$0.698420\pi$
$224$	−0.153752	−0.0102730
$225$	11.7020	0.780134
$226$	14.0732	0.936133
$227$	−18.1926	−1.20749	−0.603744	−	0.797179i	$-0.706325\pi$
$227$	−18.1926	−1.20749	−0.603744	+	0.797179i	$0.706325\pi$
$228$	3.15599	0.209011
$229$	−18.0306	−1.19149	−0.595747	−	0.803172i	$-0.703144\pi$
$229$	−18.0306	−1.19149	−0.595747	+	0.803172i	$0.703144\pi$
$230$	−1.43431	−0.0945756
$231$	0.676660	0.0445210
$232$	5.57627	0.366100
$233$	−27.1457	−1.77838	−0.889188	−	0.457543i	$-0.848730\pi$
$233$	−27.1457	−1.77838	−0.889188	+	0.457543i	$0.848730\pi$
$234$	0.950947	0.0621653
$235$	25.3795	1.65558
$236$	−1.00000	−0.0650945
$237$	−2.48459	−0.161391
$238$	0.153752	0.00996624
$239$	−3.88953	−0.251593	−0.125796	−	0.992056i	$-0.540149\pi$
$239$	−3.88953	−0.251593	−0.125796	+	0.992056i	$0.540149\pi$
$240$	4.08681	0.263802
$241$	13.0664	0.841680	0.420840	−	0.907135i	$-0.361735\pi$
$241$	13.0664	0.841680	0.420840	+	0.907135i	$0.361735\pi$
$242$	8.36875	0.537963
$243$	−1.00000	−0.0641500
$244$	−3.20062	−0.204899
$245$	28.5111	1.82150
$246$	3.30306	0.210596
$247$	−3.00118	−0.190961
$248$	−4.44408	−0.282199
$249$	15.3670	0.973843
$250$	−27.3899	−1.73229
$251$	13.4335	0.847913	0.423956	−	0.905683i	$-0.360641\pi$
$251$	13.4335	0.847913	0.423956	+	0.905683i	$0.360641\pi$
$252$	−0.153752	−0.00968544
$253$	1.54458	0.0971067
$254$	5.50750	0.345572
$255$	−4.08681	−0.255926
$256$	1.00000	0.0625000
$257$	−0.321237	−0.0200382	−0.0100191	−	0.999950i	$-0.503189\pi$
$257$	−0.321237	−0.0200382	−0.0100191	+	0.999950i	$0.503189\pi$
$258$	7.47395	0.465308
$259$	−0.00359113	−0.000223142 0
$260$	−3.88634	−0.241021
$261$	5.57627	0.345162
$262$	12.6218	0.779776
$263$	−16.1409	−0.995289	−0.497645	−	0.867381i	$-0.665802\pi$
$263$	−16.1409	−0.995289	−0.497645	+	0.867381i	$0.665802\pi$
$264$	−4.40099	−0.270862
$265$	17.1170	1.05149
$266$	0.485239	0.0297519
$267$	7.84188	0.479915
$268$	12.6667	0.773743
$269$	−2.76824	−0.168783	−0.0843914	−	0.996433i	$-0.526895\pi$
$269$	−2.76824	−0.168783	−0.0843914	+	0.996433i	$0.526895\pi$
$270$	4.08681	0.248715
$271$	25.8825	1.57225	0.786124	−	0.618068i	$-0.212085\pi$
$271$	25.8825	1.57225	0.786124	+	0.618068i	$0.212085\pi$
$272$	−1.00000	−0.0606339
$273$	0.146210	0.00884901
$274$	0.932092	0.0563098
$275$	51.5005	3.10560
$276$	−0.350961	−0.0211254
$277$	29.0931	1.74803	0.874017	−	0.485895i	$-0.161506\pi$
$277$	29.0931	1.74803	0.874017	+	0.485895i	$0.161506\pi$
$278$	7.63886	0.458148
$279$	−4.44408	−0.266060
$280$	0.628354	0.0375513
$281$	−26.2373	−1.56519	−0.782594	−	0.622533i	$-0.786104\pi$
$281$	−26.2373	−1.56519	−0.782594	+	0.622533i	$0.786104\pi$
$282$	6.21010	0.369806
$283$	15.5191	0.922517	0.461258	−	0.887266i	$-0.347398\pi$
$283$	15.5191	0.922517	0.461258	+	0.887266i	$0.347398\pi$
$284$	8.12990	0.482421
$285$	−12.8979	−0.764008
$286$	4.18511	0.247471
$287$	0.507851	0.0299775
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−22.7891	−1.33822
$291$	−14.1034	−0.826758
$292$	12.5620	0.735134
$293$	−4.78468	−0.279524	−0.139762	−	0.990185i	$-0.544634\pi$
$293$	−4.78468	−0.279524	−0.139762	+	0.990185i	$0.544634\pi$
$294$	6.97636	0.406870
$295$	4.08681	0.237943
$296$	0.0233567	0.00135758
$297$	−4.40099	−0.255372
$298$	−1.29790	−0.0751856
$299$	0.333745	0.0193010
$300$	−11.7020	−0.675616
$301$	1.14913	0.0662349
$302$	15.1909	0.874141
$303$	−7.73723	−0.444492
$304$	−3.15599	−0.181009
$305$	13.0803	0.748977
$306$	−1.00000	−0.0571662
$307$	28.8566	1.64693	0.823466	−	0.567366i	$-0.192038\pi$
$307$	28.8566	1.64693	0.823466	+	0.567366i	$0.192038\pi$
$308$	−0.676660	−0.0385563
$309$	−9.91079	−0.563805
$310$	18.1621	1.03154
$311$	11.3419	0.643143	0.321571	−	0.946885i	$-0.395789\pi$
$311$	11.3419	0.643143	0.321571	+	0.946885i	$0.395789\pi$
$312$	−0.950947	−0.0538368
$313$	32.8804	1.85851	0.929256	−	0.369438i	$-0.120450\pi$
$313$	32.8804	1.85851	0.929256	+	0.369438i	$0.120450\pi$
$314$	15.1425	0.854540
$315$	0.628354	0.0354037
$316$	2.48459	0.139769
$317$	10.5564	0.592904	0.296452	−	0.955048i	$-0.404196\pi$
$317$	10.5564	0.592904	0.296452	+	0.955048i	$0.404196\pi$
$318$	4.18834	0.234871
$319$	24.5411	1.37404
$320$	−4.08681	−0.228460
$321$	−9.70267	−0.541550
$322$	−0.0539608	−0.00300712
$323$	3.15599	0.175604
$324$	1.00000	0.0555556
$325$	11.1280	0.617270
$326$	20.3422	1.12665
$327$	−11.1018	−0.613932
$328$	−3.30306	−0.182381
$329$	0.954813	0.0526406
$330$	17.9860	0.990098
$331$	−3.36394	−0.184899	−0.0924495	−	0.995717i	$-0.529470\pi$
$331$	−3.36394	−0.184899	−0.0924495	+	0.995717i	$0.529470\pi$
$332$	−15.3670	−0.843373
$333$	0.0233567	0.00127994
$334$	3.85482	0.210927
$335$	−51.7665	−2.82830
$336$	0.153752	0.00838784
$337$	2.47709	0.134936	0.0674680	−	0.997721i	$-0.478508\pi$
$337$	2.47709	0.134936	0.0674680	+	0.997721i	$0.478508\pi$
$338$	−12.0957	−0.657919
$339$	−14.0732	−0.764349
$340$	4.08681	0.221638
$341$	−19.5584	−1.05914
$342$	−3.15599	−0.170657
$343$	2.14889	0.116029
$344$	−7.47395	−0.402968
$345$	1.43431	0.0772207
$346$	−2.16625	−0.116458
$347$	1.75546	0.0942381	0.0471190	−	0.998889i	$-0.484996\pi$
$347$	1.75546	0.0942381	0.0471190	+	0.998889i	$0.484996\pi$
$348$	−5.57627	−0.298919
$349$	29.8063	1.59550	0.797748	−	0.602991i	$-0.206025\pi$
$349$	29.8063	1.59550	0.797748	+	0.602991i	$0.206025\pi$
$350$	−1.79920	−0.0961715
$351$	−0.950947	−0.0507578
$352$	4.40099	0.234574
$353$	23.7496	1.26406	0.632031	−	0.774943i	$-0.282221\pi$
$353$	23.7496	1.26406	0.632031	+	0.774943i	$0.282221\pi$
$354$	1.00000	0.0531494
$355$	−33.2253	−1.76342
$356$	−7.84188	−0.415619
$357$	−0.153752	−0.00813740
$358$	24.4934	1.29452
$359$	7.27767	0.384101	0.192050	−	0.981385i	$-0.438486\pi$
$359$	7.27767	0.384101	0.192050	+	0.981385i	$0.438486\pi$
$360$	−4.08681	−0.215394
$361$	−9.03971	−0.475774
$362$	7.26868	0.382033
$363$	−8.36875	−0.439245
$364$	−0.146210	−0.00766347
$365$	−51.3384	−2.68718
$366$	3.20062	0.167299
$367$	−10.0167	−0.522869	−0.261435	−	0.965221i	$-0.584196\pi$
$367$	−10.0167	−0.522869	−0.261435	+	0.965221i	$0.584196\pi$
$368$	0.350961	0.0182951
$369$	−3.30306	−0.171951
$370$	−0.0954545	−0.00496244
$371$	0.643965	0.0334330
$372$	4.44408	0.230415
$373$	−10.6068	−0.549202	−0.274601	−	0.961558i	$-0.588546\pi$
$373$	−10.6068	−0.549202	−0.274601	+	0.961558i	$0.588546\pi$
$374$	−4.40099	−0.227570
$375$	27.3899	1.41441
$376$	−6.21010	−0.320262
$377$	5.30273	0.273105
$378$	0.153752	0.00790813
$379$	2.22887	0.114490	0.0572448	−	0.998360i	$-0.481768\pi$
$379$	2.22887	0.114490	0.0572448	+	0.998360i	$0.481768\pi$
$380$	12.8979	0.661651
$381$	−5.50750	−0.282158
$382$	−21.4030	−1.09507
$383$	34.0760	1.74120	0.870601	−	0.491990i	$-0.163730\pi$
$383$	34.0760	1.74120	0.870601	+	0.491990i	$0.163730\pi$
$384$	−1.00000	−0.0510310
$385$	2.76538	0.140937
$386$	5.22947	0.266173
$387$	−7.47395	−0.379922
$388$	14.1034	0.715993
$389$	−24.4150	−1.23789	−0.618944	−	0.785435i	$-0.712439\pi$
$389$	−24.4150	−1.23789	−0.618944	+	0.785435i	$0.712439\pi$
$390$	3.88634	0.196792
$391$	−0.350961	−0.0177489
$392$	−6.97636	−0.352359
$393$	−12.6218	−0.636685
$394$	−8.39960	−0.423166
$395$	−10.1540	−0.510906
$396$	4.40099	0.221158
$397$	28.6501	1.43791	0.718953	−	0.695059i	$-0.244622\pi$
$397$	28.6501	1.43791	0.718953	+	0.695059i	$0.244622\pi$
$398$	−17.0530	−0.854788
$399$	−0.485239	−0.0242923
$400$	11.7020	0.585101
$401$	−4.98428	−0.248903	−0.124452	−	0.992226i	$-0.539717\pi$
$401$	−4.98428	−0.248903	−0.124452	+	0.992226i	$0.539717\pi$
$402$	−12.6667	−0.631758
$403$	−4.22608	−0.210516
$404$	7.73723	0.384941
$405$	−4.08681	−0.203075
$406$	−0.857360	−0.0425501
$407$	0.102793	0.00509525
$408$	1.00000	0.0495074
$409$	24.2786	1.20050	0.600250	−	0.799812i	$-0.295068\pi$
$409$	24.2786	1.20050	0.600250	+	0.799812i	$0.295068\pi$
$410$	13.4990	0.666667
$411$	−0.932092	−0.0459767
$412$	9.91079	0.488270
$413$	0.153752	0.00756562
$414$	0.350961	0.0172488
$415$	62.8020	3.08283
$416$	0.950947	0.0466240
$417$	−7.63886	−0.374077
$418$	−13.8895	−0.679358
$419$	1.72464	0.0842542	0.0421271	−	0.999112i	$-0.486587\pi$
$419$	1.72464	0.0842542	0.0421271	+	0.999112i	$0.486587\pi$
$420$	−0.628354	−0.0306605
$421$	−22.6518	−1.10398	−0.551990	−	0.833851i	$-0.686131\pi$
$421$	−22.6518	−1.10398	−0.551990	+	0.833851i	$0.686131\pi$
$422$	−4.04577	−0.196945
$423$	−6.21010	−0.301945
$424$	−4.18834	−0.203404
$425$	−11.7020	−0.567631
$426$	−8.12990	−0.393895
$427$	0.492100	0.0238144
$428$	9.70267	0.468996
$429$	−4.18511	−0.202059
$430$	30.5446	1.47299
$431$	−25.0669	−1.20743	−0.603716	−	0.797200i	$-0.706314\pi$
$431$	−25.0669	−1.20743	−0.603716	+	0.797200i	$0.706314\pi$
$432$	−1.00000	−0.0481125
$433$	25.1528	1.20877	0.604384	−	0.796693i	$-0.293419\pi$
$433$	25.1528	1.20877	0.604384	+	0.796693i	$0.293419\pi$
$434$	0.683284	0.0327987
$435$	22.7891	1.09266
$436$	11.1018	0.531681
$437$	−1.10763	−0.0529851
$438$	−12.5620	−0.600235
$439$	9.14173	0.436311	0.218155	−	0.975914i	$-0.429996\pi$
$439$	9.14173	0.436311	0.218155	+	0.975914i	$0.429996\pi$
$440$	−17.9860	−0.857450
$441$	−6.97636	−0.332208
$442$	−0.950947	−0.0452319
$443$	2.52015	0.119736	0.0598679	−	0.998206i	$-0.480932\pi$
$443$	2.52015	0.119736	0.0598679	+	0.998206i	$0.480932\pi$
$444$	−0.0233567	−0.00110846
$445$	32.0483	1.51923
$446$	−17.4348	−0.825563
$447$	1.29790	0.0613888
$448$	−0.153752	−0.00726408
$449$	13.9313	0.657459	0.328730	−	0.944424i	$-0.393380\pi$
$449$	13.9313	0.657459	0.328730	+	0.944424i	$0.393380\pi$
$450$	11.7020	0.551638
$451$	−14.5368	−0.684509
$452$	14.0732	0.661946
$453$	−15.1909	−0.713733
$454$	−18.1926	−0.853822
$455$	0.597531	0.0280127
$456$	3.15599	0.147793
$457$	−25.3925	−1.18781	−0.593905	−	0.804535i	$-0.702414\pi$
$457$	−25.3925	−1.18781	−0.593905	+	0.804535i	$0.702414\pi$
$458$	−18.0306	−0.842513
$459$	1.00000	0.0466760
$460$	−1.43431	−0.0668751
$461$	19.3001	0.898896	0.449448	−	0.893307i	$-0.351621\pi$
$461$	19.3001	0.898896	0.449448	+	0.893307i	$0.351621\pi$
$462$	0.676660	0.0314811
$463$	−10.5115	−0.488513	−0.244256	−	0.969711i	$-0.578544\pi$
$463$	−10.5115	−0.488513	−0.244256	+	0.969711i	$0.578544\pi$
$464$	5.57627	0.258872
$465$	−18.1621	−0.842247
$466$	−27.1457	−1.25750
$467$	19.8694	0.919445	0.459723	−	0.888063i	$-0.347949\pi$
$467$	19.8694	0.919445	0.459723	+	0.888063i	$0.347949\pi$
$468$	0.950947	0.0439575
$469$	−1.94753	−0.0899285
$470$	25.3795	1.17067
$471$	−15.1425	−0.697729
$472$	−1.00000	−0.0460287
$473$	−32.8928	−1.51241
$474$	−2.48459	−0.114121
$475$	−36.9315	−1.69453
$476$	0.153752	0.00704719
$477$	−4.18834	−0.191771
$478$	−3.88953	−0.177903
$479$	−33.9625	−1.55179	−0.775893	−	0.630865i	$-0.782700\pi$
$479$	−33.9625	−1.55179	−0.775893	+	0.630865i	$0.782700\pi$
$480$	4.08681	0.186537
$481$	0.0222110	0.00101273
$482$	13.0664	0.595158
$483$	0.0539608	0.00245530
$484$	8.36875	0.380398
$485$	−57.6380	−2.61721
$486$	−1.00000	−0.0453609
$487$	2.36077	0.106977	0.0534883	−	0.998568i	$-0.482966\pi$
$487$	2.36077	0.106977	0.0534883	+	0.998568i	$0.482966\pi$
$488$	−3.20062	−0.144885
$489$	−20.3422	−0.919907
$490$	28.5111	1.28800
$491$	42.5737	1.92133	0.960663	−	0.277718i	$-0.0895782\pi$
$491$	42.5737	1.92133	0.960663	+	0.277718i	$0.0895782\pi$
$492$	3.30306	0.148914
$493$	−5.57627	−0.251142
$494$	−3.00118	−0.135030
$495$	−17.9860	−0.808412
$496$	−4.44408	−0.199545
$497$	−1.24998	−0.0560695
$498$	15.3670	0.688611
$499$	−5.00957	−0.224259	−0.112130	−	0.993694i	$-0.535767\pi$
$499$	−5.00957	−0.224259	−0.112130	+	0.993694i	$0.535767\pi$
$500$	−27.3899	−1.22491
$501$	−3.85482	−0.172221
$502$	13.4335	0.599565
$503$	−5.70501	−0.254374	−0.127187	−	0.991879i	$-0.540595\pi$
$503$	−5.70501	−0.254374	−0.127187	+	0.991879i	$0.540595\pi$
$504$	−0.153752	−0.00684864
$505$	−31.6206	−1.40710
$506$	1.54458	0.0686648
$507$	12.0957	0.537189
$508$	5.50750	0.244356
$509$	−24.5698	−1.08904	−0.544518	−	0.838749i	$-0.683287\pi$
$509$	−24.5698	−1.08904	−0.544518	+	0.838749i	$0.683287\pi$
$510$	−4.08681	−0.180967
$511$	−1.93143	−0.0854412
$512$	1.00000	0.0441942
$513$	3.15599	0.139340
$514$	−0.321237	−0.0141691
$515$	−40.5035	−1.78480
$516$	7.47395	0.329022
$517$	−27.3306	−1.20200
$518$	−0.00359113	−0.000157785 0
$519$	2.16625	0.0950877
$520$	−3.88634	−0.170427
$521$	32.7416	1.43443	0.717217	−	0.696849i	$-0.245415\pi$
$521$	32.7416	1.43443	0.717217	+	0.696849i	$0.245415\pi$
$522$	5.57627	0.244067
$523$	29.3707	1.28429	0.642145	−	0.766584i	$-0.278045\pi$
$523$	29.3707	1.28429	0.642145	+	0.766584i	$0.278045\pi$
$524$	12.6218	0.551385
$525$	1.79920	0.0785237
$526$	−16.1409	−0.703776
$527$	4.44408	0.193587
$528$	−4.40099	−0.191529
$529$	−22.8768	−0.994645
$530$	17.1170	0.743513
$531$	−1.00000	−0.0433963
$532$	0.485239	0.0210378
$533$	−3.14104	−0.136053
$534$	7.84188	0.339351
$535$	−39.6530	−1.71435
$536$	12.6667	0.547119
$537$	−24.4934	−1.05697
$538$	−2.76824	−0.119347
$539$	−30.7029	−1.32247
$540$	4.08681	0.175868
$541$	−16.5372	−0.710989	−0.355494	−	0.934678i	$-0.615687\pi$
$541$	−16.5372	−0.710989	−0.355494	+	0.934678i	$0.615687\pi$
$542$	25.8825	1.11175
$543$	−7.26868	−0.311929
$544$	−1.00000	−0.0428746
$545$	−45.3710	−1.94348
$546$	0.146210	0.00625720
$547$	−5.26212	−0.224992	−0.112496	−	0.993652i	$-0.535885\pi$
$547$	−5.26212	−0.224992	−0.112496	+	0.993652i	$0.535885\pi$
$548$	0.932092	0.0398170
$549$	−3.20062	−0.136599
$550$	51.5005	2.19599
$551$	−17.5987	−0.749728
$552$	−0.350961	−0.0149379
$553$	−0.382010	−0.0162447
$554$	29.0931	1.23605
$555$	0.0954545	0.00405182
$556$	7.63886	0.323960
$557$	−30.9554	−1.31162	−0.655811	−	0.754925i	$-0.727673\pi$
$557$	−30.9554	−1.31162	−0.655811	+	0.754925i	$0.727673\pi$
$558$	−4.44408	−0.188133
$559$	−7.10733	−0.300608
$560$	0.628354	0.0265528
$561$	4.40099	0.185810
$562$	−26.2373	−1.10675
$563$	7.35847	0.310122	0.155061	−	0.987905i	$-0.450443\pi$
$563$	7.35847	0.310122	0.155061	+	0.987905i	$0.450443\pi$
$564$	6.21010	0.261492
$565$	−57.5143	−2.41965
$566$	15.5191	0.652318
$567$	−0.153752	−0.00645696
$568$	8.12990	0.341123
$569$	6.32302	0.265075	0.132537	−	0.991178i	$-0.457688\pi$
$569$	6.32302	0.265075	0.132537	+	0.991178i	$0.457688\pi$
$570$	−12.8979	−0.540235
$571$	−17.0062	−0.711689	−0.355844	−	0.934545i	$-0.615807\pi$
$571$	−17.0062	−0.711689	−0.355844	+	0.934545i	$0.615807\pi$
$572$	4.18511	0.174988
$573$	21.4030	0.894122
$574$	0.507851	0.0211973
$575$	4.10695	0.171272
$576$	1.00000	0.0416667
$577$	37.3899	1.55656	0.778282	−	0.627915i	$-0.216091\pi$
$577$	37.3899	1.55656	0.778282	+	0.627915i	$0.216091\pi$
$578$	1.00000	0.0415945
$579$	−5.22947	−0.217329
$580$	−22.7891	−0.946268
$581$	2.36270	0.0980213
$582$	−14.1034	−0.584606
$583$	−18.4329	−0.763411
$584$	12.5620	0.519819
$585$	−3.88634	−0.160680
$586$	−4.78468	−0.197653
$587$	−28.0381	−1.15726	−0.578628	−	0.815592i	$-0.696412\pi$
$587$	−28.0381	−1.15726	−0.578628	+	0.815592i	$0.696412\pi$
$588$	6.97636	0.287700
$589$	14.0255	0.577910
$590$	4.08681	0.168251
$591$	8.39960	0.345514
$592$	0.0233567	0.000959955 0
$593$	22.9361	0.941875	0.470937	−	0.882167i	$-0.343916\pi$
$593$	22.9361	0.941875	0.470937	+	0.882167i	$0.343916\pi$
$594$	−4.40099	−0.180575
$595$	−0.628354	−0.0257600
$596$	−1.29790	−0.0531643
$597$	17.0530	0.697932
$598$	0.333745	0.0136479
$599$	26.9872	1.10267	0.551334	−	0.834284i	$-0.314119\pi$
$599$	26.9872	1.10267	0.551334	+	0.834284i	$0.314119\pi$
$600$	−11.7020	−0.477733
$601$	−16.2049	−0.661010	−0.330505	−	0.943804i	$-0.607219\pi$
$601$	−16.2049	−0.661010	−0.330505	+	0.943804i	$0.607219\pi$
$602$	1.14913	0.0468351
$603$	12.6667	0.515829
$604$	15.1909	0.618111
$605$	−34.2015	−1.39049
$606$	−7.73723	−0.314303
$607$	−18.4488	−0.748814	−0.374407	−	0.927265i	$-0.622154\pi$
$607$	−18.4488	−0.748814	−0.374407	+	0.927265i	$0.622154\pi$
$608$	−3.15599	−0.127992
$609$	0.857360	0.0347420
$610$	13.0803	0.529607
$611$	−5.90548	−0.238910
$612$	−1.00000	−0.0404226
$613$	45.1782	1.82473	0.912366	−	0.409376i	$-0.134253\pi$
$613$	45.1782	1.82473	0.912366	+	0.409376i	$0.134253\pi$
$614$	28.8566	1.16456
$615$	−13.4990	−0.544332
$616$	−0.676660	−0.0272634
$617$	1.79342	0.0722002	0.0361001	−	0.999348i	$-0.488506\pi$
$617$	1.79342	0.0722002	0.0361001	+	0.999348i	$0.488506\pi$
$618$	−9.91079	−0.398671
$619$	4.11036	0.165209	0.0826046	−	0.996582i	$-0.473676\pi$
$619$	4.11036	0.165209	0.0826046	+	0.996582i	$0.473676\pi$
$620$	18.1621	0.729408
$621$	−0.350961	−0.0140836
$622$	11.3419	0.454771
$623$	1.20570	0.0483054
$624$	−0.950947	−0.0380683
$625$	53.4271	2.13708
$626$	32.8804	1.31417
$627$	13.8895	0.554693
$628$	15.1425	0.604251
$629$	−0.0233567	−0.000931293 0
$630$	0.628354	0.0250342
$631$	6.86062	0.273117	0.136559	−	0.990632i	$-0.456396\pi$
$631$	6.86062	0.273117	0.136559	+	0.990632i	$0.456396\pi$
$632$	2.48459	0.0988317
$633$	4.04577	0.160805
$634$	10.5564	0.419247
$635$	−22.5081	−0.893208
$636$	4.18834	0.166079
$637$	−6.63415	−0.262855
$638$	24.5411	0.971592
$639$	8.12990	0.321614
$640$	−4.08681	−0.161545
$641$	−36.9389	−1.45900	−0.729498	−	0.683982i	$-0.760246\pi$
$641$	−36.9389	−1.45900	−0.729498	+	0.683982i	$0.760246\pi$
$642$	−9.70267	−0.382934
$643$	−18.0082	−0.710175	−0.355087	−	0.934833i	$-0.615549\pi$
$643$	−18.0082	−0.710175	−0.355087	+	0.934833i	$0.615549\pi$
$644$	−0.0539608	−0.00212635
$645$	−30.5446	−1.20269
$646$	3.15599	0.124171
$647$	29.3041	1.15206	0.576031	−	0.817428i	$-0.304601\pi$
$647$	29.3041	1.15206	0.576031	+	0.817428i	$0.304601\pi$
$648$	1.00000	0.0392837
$649$	−4.40099	−0.172754
$650$	11.1280	0.436476
$651$	−0.683284	−0.0267800
$652$	20.3422	0.796662
$653$	37.2445	1.45749	0.728744	−	0.684786i	$-0.240104\pi$
$653$	37.2445	1.45749	0.728744	+	0.684786i	$0.240104\pi$
$654$	−11.1018	−0.434115
$655$	−51.5828	−2.01551
$656$	−3.30306	−0.128963
$657$	12.5620	0.490090
$658$	0.954813	0.0372225
$659$	24.2875	0.946108	0.473054	−	0.881033i	$-0.343152\pi$
$659$	24.2875	0.946108	0.473054	+	0.881033i	$0.343152\pi$
$660$	17.9860	0.700105
$661$	32.5584	1.26637	0.633187	−	0.773999i	$-0.281746\pi$
$661$	32.5584	1.26637	0.633187	+	0.773999i	$0.281746\pi$
$662$	−3.36394	−0.130743
$663$	0.950947	0.0369317
$664$	−15.3670	−0.596355
$665$	−1.98308	−0.0769005
$666$	0.0233567	0.000905054 0
$667$	1.95705	0.0757773
$668$	3.85482	0.149148
$669$	17.4348	0.674070
$670$	−51.7665	−1.99991
$671$	−14.0859	−0.543780
$672$	0.153752	0.00593110
$673$	−5.59097	−0.215516	−0.107758	−	0.994177i	$-0.534367\pi$
$673$	−5.59097	−0.215516	−0.107758	+	0.994177i	$0.534367\pi$
$674$	2.47709	0.0954141
$675$	−11.7020	−0.450411
$676$	−12.0957	−0.465219
$677$	−1.46076	−0.0561416	−0.0280708	−	0.999606i	$-0.508936\pi$
$677$	−1.46076	−0.0561416	−0.0280708	+	0.999606i	$0.508936\pi$
$678$	−14.0732	−0.540477
$679$	−2.16843	−0.0832165
$680$	4.08681	0.156722
$681$	18.1926	0.697143
$682$	−19.5584	−0.748928
$683$	−31.5330	−1.20658	−0.603288	−	0.797523i	$-0.706143\pi$
$683$	−31.5330	−1.20658	−0.603288	+	0.797523i	$0.706143\pi$
$684$	−3.15599	−0.120672
$685$	−3.80928	−0.145545
$686$	2.14889	0.0820449
$687$	18.0306	0.687909
$688$	−7.47395	−0.284942
$689$	−3.98289	−0.151736
$690$	1.43431	0.0546033
$691$	−5.98773	−0.227784	−0.113892	−	0.993493i	$-0.536332\pi$
$691$	−5.98773	−0.227784	−0.113892	+	0.993493i	$0.536332\pi$
$692$	−2.16625	−0.0823483
$693$	−0.676660	−0.0257042
$694$	1.75546	0.0666364
$695$	−31.2186	−1.18419
$696$	−5.57627	−0.211368
$697$	3.30306	0.125112
$698$	29.8063	1.12819
$699$	27.1457	1.02675
$700$	−1.79920	−0.0680035
$701$	−9.25526	−0.349566	−0.174783	−	0.984607i	$-0.555922\pi$
$701$	−9.25526	−0.349566	−0.174783	+	0.984607i	$0.555922\pi$
$702$	−0.950947	−0.0358912
$703$	−0.0737136	−0.00278016
$704$	4.40099	0.165869
$705$	−25.3795	−0.955847
$706$	23.7496	0.893828
$707$	−1.18961	−0.0447399
$708$	1.00000	0.0375823
$709$	1.72759	0.0648811	0.0324405	−	0.999474i	$-0.489672\pi$
$709$	1.72759	0.0648811	0.0324405	+	0.999474i	$0.489672\pi$
$710$	−33.2253	−1.24692
$711$	2.48459	0.0931794
$712$	−7.84188	−0.293887
$713$	−1.55970	−0.0584111
$714$	−0.153752	−0.00575401
$715$	−17.1038	−0.639644
$716$	24.4934	0.915361
$717$	3.88953	0.145257
$718$	7.27767	0.271600
$719$	−7.69522	−0.286983	−0.143492	−	0.989652i	$-0.545833\pi$
$719$	−7.69522	−0.286983	−0.143492	+	0.989652i	$0.545833\pi$
$720$	−4.08681	−0.152306
$721$	−1.52380	−0.0567493
$722$	−9.03971	−0.336423
$723$	−13.0664	−0.485944
$724$	7.26868	0.270138
$725$	65.2536	2.42346
$726$	−8.36875	−0.310593
$727$	−41.3871	−1.53496	−0.767481	−	0.641072i	$-0.778490\pi$
$727$	−41.3871	−1.53496	−0.767481	+	0.641072i	$0.778490\pi$
$728$	−0.146210	−0.00541889
$729$	1.00000	0.0370370
$730$	−51.3384	−1.90012
$731$	7.47395	0.276434
$732$	3.20062	0.118298
$733$	35.1573	1.29856	0.649282	−	0.760547i	$-0.275069\pi$
$733$	35.1573	1.29856	0.649282	+	0.760547i	$0.275069\pi$
$734$	−10.0167	−0.369724
$735$	−28.5111	−1.05165
$736$	0.350961	0.0129366
$737$	55.7461	2.05344
$738$	−3.30306	−0.121587
$739$	−16.2275	−0.596940	−0.298470	−	0.954419i	$-0.596476\pi$
$739$	−16.2275	−0.596940	−0.298470	+	0.954419i	$0.596476\pi$
$740$	−0.0954545	−0.00350898
$741$	3.00118	0.110251
$742$	0.643965	0.0236407
$743$	7.54508	0.276802	0.138401	−	0.990376i	$-0.455804\pi$
$743$	7.54508	0.276802	0.138401	+	0.990376i	$0.455804\pi$
$744$	4.44408	0.162928
$745$	5.30429	0.194334
$746$	−10.6068	−0.388344
$747$	−15.3670	−0.562249
$748$	−4.40099	−0.160916
$749$	−1.49180	−0.0545092
$750$	27.3899	1.00014
$751$	13.6774	0.499095	0.249547	−	0.968363i	$-0.419718\pi$
$751$	13.6774	0.499095	0.249547	+	0.968363i	$0.419718\pi$
$752$	−6.21010	−0.226459
$753$	−13.4335	−0.489543
$754$	5.30273	0.193114
$755$	−62.0825	−2.25941
$756$	0.153752	0.00559189
$757$	0.616942	0.0224231	0.0112116	−	0.999937i	$-0.496431\pi$
$757$	0.616942	0.0224231	0.0112116	+	0.999937i	$0.496431\pi$
$758$	2.22887	0.0809564
$759$	−1.54458	−0.0560646
$760$	12.8979	0.467858
$761$	−11.1325	−0.403554	−0.201777	−	0.979431i	$-0.564672\pi$
$761$	−11.1325	−0.403554	−0.201777	+	0.979431i	$0.564672\pi$
$762$	−5.50750	−0.199516
$763$	−1.70692	−0.0617948
$764$	−21.4030	−0.774332
$765$	4.08681	0.147759
$766$	34.0760	1.23122
$767$	−0.950947	−0.0343367
$768$	−1.00000	−0.0360844
$769$	−47.6460	−1.71816	−0.859079	−	0.511844i	$-0.828963\pi$
$769$	−47.6460	−1.71816	−0.859079	+	0.511844i	$0.828963\pi$
$770$	2.76538	0.0996574
$771$	0.321237	0.0115691
$772$	5.22947	0.188213
$773$	−23.8549	−0.858000	−0.429000	−	0.903305i	$-0.641134\pi$
$773$	−23.8549	−0.858000	−0.429000	+	0.903305i	$0.641134\pi$
$774$	−7.47395	−0.268646
$775$	−52.0047	−1.86806
$776$	14.1034	0.506284
$777$	0.00359113	0.000128831 0
$778$	−24.4150	−0.875319
$779$	10.4244	0.373494
$780$	3.88634	0.139153
$781$	35.7796	1.28030
$782$	−0.350961	−0.0125503
$783$	−5.57627	−0.199280
$784$	−6.97636	−0.249156
$785$	−61.8845	−2.20875
$786$	−12.6218	−0.450204
$787$	14.9679	0.533546	0.266773	−	0.963759i	$-0.414043\pi$
$787$	14.9679	0.533546	0.266773	+	0.963759i	$0.414043\pi$
$788$	−8.39960	−0.299223
$789$	16.1409	0.574630
$790$	−10.1540	−0.361265
$791$	−2.16377	−0.0769349
$792$	4.40099	0.156383
$793$	−3.04362	−0.108082
$794$	28.6501	1.01675
$795$	−17.1170	−0.607076
$796$	−17.0530	−0.604427
$797$	13.5595	0.480303	0.240151	−	0.970735i	$-0.422803\pi$
$797$	13.5595	0.480303	0.240151	+	0.970735i	$0.422803\pi$
$798$	−0.485239	−0.0171773
$799$	6.21010	0.219698
$800$	11.7020	0.413729
$801$	−7.84188	−0.277079
$802$	−4.98428	−0.176001
$803$	55.2852	1.95097
$804$	−12.6667	−0.446721
$805$	0.220528	0.00777258
$806$	−4.22608	−0.148857
$807$	2.76824	0.0974468
$808$	7.73723	0.272195
$809$	41.6224	1.46337	0.731684	−	0.681644i	$-0.238735\pi$
$809$	41.6224	1.46337	0.731684	+	0.681644i	$0.238735\pi$
$810$	−4.08681	−0.143596
$811$	8.10415	0.284575	0.142288	−	0.989825i	$-0.454554\pi$
$811$	8.10415	0.284575	0.142288	+	0.989825i	$0.454554\pi$
$812$	−0.857360	−0.0300874
$813$	−25.8825	−0.907738
$814$	0.102793	0.00360288
$815$	−83.1348	−2.91208
$816$	1.00000	0.0350070
$817$	23.5877	0.825230
$818$	24.2786	0.848882
$819$	−0.146210	−0.00510898
$820$	13.4990	0.471405
$821$	−28.9255	−1.00951	−0.504753	−	0.863264i	$-0.668416\pi$
$821$	−28.9255	−1.00951	−0.504753	+	0.863264i	$0.668416\pi$
$822$	−0.932092	−0.0325105
$823$	−42.6437	−1.48647	−0.743233	−	0.669033i	$-0.766708\pi$
$823$	−42.6437	−1.48647	−0.743233	+	0.669033i	$0.766708\pi$
$824$	9.91079	0.345259
$825$	−51.5005	−1.79302
$826$	0.153752	0.00534970
$827$	3.07217	0.106830	0.0534149	−	0.998572i	$-0.482989\pi$
$827$	3.07217	0.106830	0.0534149	+	0.998572i	$0.482989\pi$
$828$	0.350961	0.0121967
$829$	14.3826	0.499530	0.249765	−	0.968307i	$-0.419647\pi$
$829$	14.3826	0.499530	0.249765	+	0.968307i	$0.419647\pi$
$830$	62.8020	2.17989
$831$	−29.0931	−1.00923
$832$	0.950947	0.0329682
$833$	6.97636	0.241717
$834$	−7.63886	−0.264512
$835$	−15.7539	−0.545187
$836$	−13.8895	−0.480379
$837$	4.44408	0.153610
$838$	1.72464	0.0595767
$839$	46.9542	1.62104	0.810520	−	0.585711i	$-0.199185\pi$
$839$	46.9542	1.62104	0.810520	+	0.585711i	$0.199185\pi$
$840$	−0.628354	−0.0216803
$841$	2.09476	0.0722330
$842$	−22.6518	−0.780632
$843$	26.2373	0.903661
$844$	−4.04577	−0.139261
$845$	49.4328	1.70054
$846$	−6.21010	−0.213508
$847$	−1.28671	−0.0442118
$848$	−4.18834	−0.143828
$849$	−15.5191	−0.532615
$850$	−11.7020	−0.401376
$851$	0.00819729	0.000281000 0
$852$	−8.12990	−0.278526
$853$	−37.4179	−1.28116	−0.640582	−	0.767890i	$-0.721307\pi$
$853$	−37.4179	−1.28116	−0.640582	+	0.767890i	$0.721307\pi$
$854$	0.492100	0.0168393
$855$	12.8979	0.441100
$856$	9.70267	0.331630
$857$	13.8732	0.473901	0.236951	−	0.971522i	$-0.423852\pi$
$857$	13.8732	0.473901	0.236951	+	0.971522i	$0.423852\pi$
$858$	−4.18511	−0.142877
$859$	−25.3523	−0.865010	−0.432505	−	0.901632i	$-0.642370\pi$
$859$	−25.3523	−0.865010	−0.432505	+	0.901632i	$0.642370\pi$
$860$	30.5446	1.04156
$861$	−0.507851	−0.0173075
$862$	−25.0669	−0.853783
$863$	−13.2406	−0.450716	−0.225358	−	0.974276i	$-0.572355\pi$
$863$	−13.2406	−0.450716	−0.225358	+	0.974276i	$0.572355\pi$
$864$	−1.00000	−0.0340207
$865$	8.85304	0.301012
$866$	25.1528	0.854728
$867$	−1.00000	−0.0339618
$868$	0.683284	0.0231922
$869$	10.9347	0.370933
$870$	22.7891	0.772624
$871$	12.0454	0.408142
$872$	11.1018	0.375955
$873$	14.1034	0.477329
$874$	−1.10763	−0.0374661
$875$	4.21124	0.142366
$876$	−12.5620	−0.424430
$877$	43.6902	1.47531	0.737657	−	0.675176i	$-0.235932\pi$
$877$	43.6902	1.47531	0.737657	+	0.675176i	$0.235932\pi$
$878$	9.14173	0.308518
$879$	4.78468	0.161383
$880$	−17.9860	−0.606309
$881$	−17.2779	−0.582106	−0.291053	−	0.956707i	$-0.594006\pi$
$881$	−17.2779	−0.582106	−0.291053	+	0.956707i	$0.594006\pi$
$882$	−6.97636	−0.234906
$883$	−3.38449	−0.113897	−0.0569486	−	0.998377i	$-0.518137\pi$
$883$	−3.38449	−0.113897	−0.0569486	+	0.998377i	$0.518137\pi$
$884$	−0.950947	−0.0319838
$885$	−4.08681	−0.137377
$886$	2.52015	0.0846660
$887$	6.29205	0.211266	0.105633	−	0.994405i	$-0.466313\pi$
$887$	6.29205	0.211266	0.105633	+	0.994405i	$0.466313\pi$
$888$	−0.0233567	−0.000783800 0
$889$	−0.846788	−0.0284004
$890$	32.0483	1.07426
$891$	4.40099	0.147439
$892$	−17.4348	−0.583761
$893$	19.5990	0.655857
$894$	1.29790	0.0434084
$895$	−100.100	−3.34597
$896$	−0.153752	−0.00513648
$897$	−0.333745	−0.0111434
$898$	13.9313	0.464894
$899$	−24.7814	−0.826505
$900$	11.7020	0.390067
$901$	4.18834	0.139534
$902$	−14.5368	−0.484021
$903$	−1.14913	−0.0382407
$904$	14.0732	0.468066
$905$	−29.7057	−0.987451
$906$	−15.1909	−0.504685
$907$	51.5799	1.71268	0.856341	−	0.516410i	$-0.172732\pi$
$907$	51.5799	1.71268	0.856341	+	0.516410i	$0.172732\pi$
$908$	−18.1926	−0.603744
$909$	7.73723	0.256628
$910$	0.597531	0.0198080
$911$	−27.7278	−0.918662	−0.459331	−	0.888265i	$-0.651911\pi$
$911$	−27.7278	−0.918662	−0.459331	+	0.888265i	$0.651911\pi$
$912$	3.15599	0.104505
$913$	−67.6300	−2.23823
$914$	−25.3925	−0.839908
$915$	−13.0803	−0.432422
$916$	−18.0306	−0.595747
$917$	−1.94062	−0.0640849
$918$	1.00000	0.0330049
$919$	−25.9614	−0.856388	−0.428194	−	0.903687i	$-0.640850\pi$
$919$	−25.9614	−0.856388	−0.428194	+	0.903687i	$0.640850\pi$
$920$	−1.43431	−0.0472878
$921$	−28.8566	−0.950856
$922$	19.3001	0.635615
$923$	7.73110	0.254472
$924$	0.676660	0.0222605
$925$	0.273321	0.00898673
$926$	−10.5115	−0.345431
$927$	9.91079	0.325513
$928$	5.57627	0.183050
$929$	54.3725	1.78390	0.891952	−	0.452131i	$-0.149336\pi$
$929$	54.3725	1.78390	0.891952	+	0.452131i	$0.149336\pi$
$930$	−18.1621	−0.595559
$931$	22.0173	0.721589
$932$	−27.1457	−0.889188
$933$	−11.3419	−0.371319
$934$	19.8694	0.650146
$935$	17.9860	0.588206
$936$	0.950947	0.0310827
$937$	−6.88282	−0.224852	−0.112426	−	0.993660i	$-0.535862\pi$
$937$	−6.88282	−0.224852	−0.112426	+	0.993660i	$0.535862\pi$
$938$	−1.94753	−0.0635891
$939$	−32.8804	−1.07301
$940$	25.3795	0.827788
$941$	4.64621	0.151462	0.0757310	−	0.997128i	$-0.475871\pi$
$941$	4.64621	0.151462	0.0757310	+	0.997128i	$0.475871\pi$
$942$	−15.1425	−0.493369
$943$	−1.15925	−0.0377502
$944$	−1.00000	−0.0325472
$945$	−0.628354	−0.0204403
$946$	−32.8928	−1.06944
$947$	−30.2275	−0.982263	−0.491131	−	0.871086i	$-0.663416\pi$
$947$	−30.2275	−0.982263	−0.491131	+	0.871086i	$0.663416\pi$
$948$	−2.48459	−0.0806957
$949$	11.9458	0.387776
$950$	−36.9315	−1.19822
$951$	−10.5564	−0.342313
$952$	0.153752	0.00498312
$953$	14.9430	0.484050	0.242025	−	0.970270i	$-0.422188\pi$
$953$	14.9430	0.484050	0.242025	+	0.970270i	$0.422188\pi$
$954$	−4.18834	−0.135603
$955$	87.4699	2.83046
$956$	−3.88953	−0.125796
$957$	−24.5411	−0.793302
$958$	−33.9625	−1.09728
$959$	−0.143311	−0.00462774
$960$	4.08681	0.131901
$961$	−11.2502	−0.362909
$962$	0.0222110	0.000716111 0
$963$	9.70267	0.312664
$964$	13.0664	0.420840
$965$	−21.3718	−0.687984
$966$	0.0539608	0.00173616
$967$	−10.2301	−0.328978	−0.164489	−	0.986379i	$-0.552598\pi$
$967$	−10.2301	−0.328978	−0.164489	+	0.986379i	$0.552598\pi$
$968$	8.36875	0.268982
$969$	−3.15599	−0.101385
$970$	−57.6380	−1.85065
$971$	18.1197	0.581490	0.290745	−	0.956801i	$-0.406097\pi$
$971$	18.1197	0.581490	0.290745	+	0.956801i	$0.406097\pi$
$972$	−1.00000	−0.0320750
$973$	−1.17449	−0.0376523
$974$	2.36077	0.0756439
$975$	−11.1280	−0.356381
$976$	−3.20062	−0.102449
$977$	31.6595	1.01288	0.506439	−	0.862276i	$-0.330962\pi$
$977$	31.6595	1.01288	0.506439	+	0.862276i	$0.330962\pi$
$978$	−20.3422	−0.650472
$979$	−34.5121	−1.10301
$980$	28.5111	0.910752
$981$	11.1018	0.354454
$982$	42.5737	1.35858
$983$	−24.2333	−0.772922	−0.386461	−	0.922306i	$-0.626303\pi$
$983$	−24.2333	−0.772922	−0.386461	+	0.922306i	$0.626303\pi$
$984$	3.30306	0.105298
$985$	34.3276	1.09377
$986$	−5.57627	−0.177585
$987$	−0.954813	−0.0303920
$988$	−3.00118	−0.0954803
$989$	−2.62306	−0.0834086
$990$	−17.9860	−0.571633
$991$	−44.3024	−1.40731	−0.703655	−	0.710541i	$-0.748450\pi$
$991$	−44.3024	−1.40731	−0.703655	+	0.710541i	$0.748450\pi$
$992$	−4.44408	−0.141100
$993$	3.36394	0.106752
$994$	−1.24998	−0.0396471
$995$	69.6923	2.20939
$996$	15.3670	0.486922
$997$	−36.1340	−1.14437	−0.572187	−	0.820123i	$-0.693905\pi$
$997$	−36.1340	−1.14437	−0.572187	+	0.820123i	$0.693905\pi$
$998$	−5.00957	−0.158575
$999$	−0.0233567	−0.000738974 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.z.1.1	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.z.1.1	✓	11	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.08681 q^{5} -1.00000 q^{6} -0.153752 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.08681 q^{5} -1.00000 q^{6} -0.153752 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.08681 q^{10} +4.40099 q^{11} -1.00000 q^{12} +0.950947 q^{13} -0.153752 q^{14} +4.08681 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -3.15599 q^{19} -4.08681 q^{20} +0.153752 q^{21} +4.40099 q^{22} +0.350961 q^{23} -1.00000 q^{24} +11.7020 q^{25} +0.950947 q^{26} -1.00000 q^{27} -0.153752 q^{28} +5.57627 q^{29} +4.08681 q^{30} -4.44408 q^{31} +1.00000 q^{32} -4.40099 q^{33} -1.00000 q^{34} +0.628354 q^{35} +1.00000 q^{36} +0.0233567 q^{37} -3.15599 q^{38} -0.950947 q^{39} -4.08681 q^{40} -3.30306 q^{41} +0.153752 q^{42} -7.47395 q^{43} +4.40099 q^{44} -4.08681 q^{45} +0.350961 q^{46} -6.21010 q^{47} -1.00000 q^{48} -6.97636 q^{49} +11.7020 q^{50} +1.00000 q^{51} +0.950947 q^{52} -4.18834 q^{53} -1.00000 q^{54} -17.9860 q^{55} -0.153752 q^{56} +3.15599 q^{57} +5.57627 q^{58} -1.00000 q^{59} +4.08681 q^{60} -3.20062 q^{61} -4.44408 q^{62} -0.153752 q^{63} +1.00000 q^{64} -3.88634 q^{65} -4.40099 q^{66} +12.6667 q^{67} -1.00000 q^{68} -0.350961 q^{69} +0.628354 q^{70} +8.12990 q^{71} +1.00000 q^{72} +12.5620 q^{73} +0.0233567 q^{74} -11.7020 q^{75} -3.15599 q^{76} -0.676660 q^{77} -0.950947 q^{78} +2.48459 q^{79} -4.08681 q^{80} +1.00000 q^{81} -3.30306 q^{82} -15.3670 q^{83} +0.153752 q^{84} +4.08681 q^{85} -7.47395 q^{86} -5.57627 q^{87} +4.40099 q^{88} -7.84188 q^{89} -4.08681 q^{90} -0.146210 q^{91} +0.350961 q^{92} +4.44408 q^{93} -6.21010 q^{94} +12.8979 q^{95} -1.00000 q^{96} +14.1034 q^{97} -6.97636 q^{98} +4.40099 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9} + 4 q^{10} + 9 q^{11} - 11 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 11 q^{16} - 11 q^{17} + 11 q^{18} - q^{19} + 4 q^{20} - 3 q^{21} + 9 q^{22} + 10 q^{23} - 11 q^{24} + 15 q^{25} + 6 q^{26} - 11 q^{27} + 3 q^{28} + 14 q^{29} - 4 q^{30} + 17 q^{31} + 11 q^{32} - 9 q^{33} - 11 q^{34} + 8 q^{35} + 11 q^{36} + 30 q^{37} - q^{38} - 6 q^{39} + 4 q^{40} + 10 q^{41} - 3 q^{42} + 11 q^{43} + 9 q^{44} + 4 q^{45} + 10 q^{46} - 6 q^{47} - 11 q^{48} + 18 q^{49} + 15 q^{50} + 11 q^{51} + 6 q^{52} + 10 q^{53} - 11 q^{54} - 11 q^{55} + 3 q^{56} + q^{57} + 14 q^{58} - 11 q^{59} - 4 q^{60} + 13 q^{61} + 17 q^{62} + 3 q^{63} + 11 q^{64} + 32 q^{65} - 9 q^{66} + 26 q^{67} - 11 q^{68} - 10 q^{69} + 8 q^{70} + 14 q^{71} + 11 q^{72} + 20 q^{73} + 30 q^{74} - 15 q^{75} - q^{76} + 26 q^{77} - 6 q^{78} + 15 q^{79} + 4 q^{80} + 11 q^{81} + 10 q^{82} + 2 q^{83} - 3 q^{84} - 4 q^{85} + 11 q^{86} - 14 q^{87} + 9 q^{88} + q^{89} + 4 q^{90} + 17 q^{91} + 10 q^{92} - 17 q^{93} - 6 q^{94} + 3 q^{95} - 11 q^{96} + 33 q^{97} + 18 q^{98} + 9 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9 + 4 * q^10 + 9 * q^11 - 11 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 11 * q^16 - 11 * q^17 + 11 * q^18 - q^19 + 4 * q^20 - 3 * q^21 + 9 * q^22 + 10 * q^23 - 11 * q^24 + 15 * q^25 + 6 * q^26 - 11 * q^27 + 3 * q^28 + 14 * q^29 - 4 * q^30 + 17 * q^31 + 11 * q^32 - 9 * q^33 - 11 * q^34 + 8 * q^35 + 11 * q^36 + 30 * q^37 - q^38 - 6 * q^39 + 4 * q^40 + 10 * q^41 - 3 * q^42 + 11 * q^43 + 9 * q^44 + 4 * q^45 + 10 * q^46 - 6 * q^47 - 11 * q^48 + 18 * q^49 + 15 * q^50 + 11 * q^51 + 6 * q^52 + 10 * q^53 - 11 * q^54 - 11 * q^55 + 3 * q^56 + q^57 + 14 * q^58 - 11 * q^59 - 4 * q^60 + 13 * q^61 + 17 * q^62 + 3 * q^63 + 11 * q^64 + 32 * q^65 - 9 * q^66 + 26 * q^67 - 11 * q^68 - 10 * q^69 + 8 * q^70 + 14 * q^71 + 11 * q^72 + 20 * q^73 + 30 * q^74 - 15 * q^75 - q^76 + 26 * q^77 - 6 * q^78 + 15 * q^79 + 4 * q^80 + 11 * q^81 + 10 * q^82 + 2 * q^83 - 3 * q^84 - 4 * q^85 + 11 * q^86 - 14 * q^87 + 9 * q^88 + q^89 + 4 * q^90 + 17 * q^91 + 10 * q^92 - 17 * q^93 - 6 * q^94 + 3 * q^95 - 11 * q^96 + 33 * q^97 + 18 * q^98 + 9 * q^99

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