LMFDB - Embedded newform 8022.2.a.q.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8022,2,Mod(1,8022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8022, 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("8022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8022 = 2 \cdot 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8022.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0559925015$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 11x^{7} + 36x^{6} + 50x^{5} - 70x^{4} - 73x^{3} + 14x^{2} + 22x + 4 $ x^9 - 4x^8 - 11x^7 + 36x^6 + 50x^5 - 70x^4 - 73x^3 + 14x^2 + 22x + 4
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			1.9
Root			$-0.716055$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.34081 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.34081 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.34081 q^{10} -5.19543 q^{11} -1.00000 q^{12} +1.61292 q^{13} -1.00000 q^{14} -4.34081 q^{15} +1.00000 q^{16} -5.89131 q^{17} +1.00000 q^{18} -8.17378 q^{19} +4.34081 q^{20} +1.00000 q^{21} -5.19543 q^{22} -2.11779 q^{23} -1.00000 q^{24} +13.8427 q^{25} +1.61292 q^{26} -1.00000 q^{27} -1.00000 q^{28} -2.86456 q^{29} -4.34081 q^{30} +9.30033 q^{31} +1.00000 q^{32} +5.19543 q^{33} -5.89131 q^{34} -4.34081 q^{35} +1.00000 q^{36} -7.82341 q^{37} -8.17378 q^{38} -1.61292 q^{39} +4.34081 q^{40} -5.82591 q^{41} +1.00000 q^{42} +4.33174 q^{43} -5.19543 q^{44} +4.34081 q^{45} -2.11779 q^{46} -0.173059 q^{47} -1.00000 q^{48} +1.00000 q^{49} +13.8427 q^{50} +5.89131 q^{51} +1.61292 q^{52} -3.17696 q^{53} -1.00000 q^{54} -22.5524 q^{55} -1.00000 q^{56} +8.17378 q^{57} -2.86456 q^{58} -2.76129 q^{59} -4.34081 q^{60} +12.1928 q^{61} +9.30033 q^{62} -1.00000 q^{63} +1.00000 q^{64} +7.00139 q^{65} +5.19543 q^{66} -12.5190 q^{67} -5.89131 q^{68} +2.11779 q^{69} -4.34081 q^{70} -8.87043 q^{71} +1.00000 q^{72} +3.52000 q^{73} -7.82341 q^{74} -13.8427 q^{75} -8.17378 q^{76} +5.19543 q^{77} -1.61292 q^{78} +11.1020 q^{79} +4.34081 q^{80} +1.00000 q^{81} -5.82591 q^{82} -17.4349 q^{83} +1.00000 q^{84} -25.5731 q^{85} +4.33174 q^{86} +2.86456 q^{87} -5.19543 q^{88} -6.10744 q^{89} +4.34081 q^{90} -1.61292 q^{91} -2.11779 q^{92} -9.30033 q^{93} -0.173059 q^{94} -35.4809 q^{95} -1.00000 q^{96} -3.65698 q^{97} +1.00000 q^{98} -5.19543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} - 9 q^{6} - 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 - 9 * q^6 - 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} - 9 q^{6} - 9 q^{7} + 9 q^{8} + 9 q^{9} + 6 q^{10} - 7 q^{11} - 9 q^{12} - q^{13} - 9 q^{14} - 6 q^{15} + 9 q^{16} - 10 q^{17} + 9 q^{18} + 6 q^{20} + 9 q^{21} - 7 q^{22} - 19 q^{23} - 9 q^{24} + 5 q^{25} - q^{26} - 9 q^{27} - 9 q^{28} - 21 q^{29} - 6 q^{30} + 6 q^{31} + 9 q^{32} + 7 q^{33} - 10 q^{34} - 6 q^{35} + 9 q^{36} - 14 q^{37} + q^{39} + 6 q^{40} + 12 q^{41} + 9 q^{42} - 17 q^{43} - 7 q^{44} + 6 q^{45} - 19 q^{46} - 11 q^{47} - 9 q^{48} + 9 q^{49} + 5 q^{50} + 10 q^{51} - q^{52} - 12 q^{53} - 9 q^{54} - 21 q^{55} - 9 q^{56} - 21 q^{58} - 8 q^{59} - 6 q^{60} + q^{61} + 6 q^{62} - 9 q^{63} + 9 q^{64} - 8 q^{65} + 7 q^{66} - 31 q^{67} - 10 q^{68} + 19 q^{69} - 6 q^{70} - 41 q^{71} + 9 q^{72} - q^{73} - 14 q^{74} - 5 q^{75} + 7 q^{77} + q^{78} - 17 q^{79} + 6 q^{80} + 9 q^{81} + 12 q^{82} - 36 q^{83} + 9 q^{84} - 30 q^{85} - 17 q^{86} + 21 q^{87} - 7 q^{88} - 17 q^{89} + 6 q^{90} + q^{91} - 19 q^{92} - 6 q^{93} - 11 q^{94} - 50 q^{95} - 9 q^{96} - 14 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 - 9 * q^6 - 9 * q^7 + 9 * q^8 + 9 * q^9 + 6 * q^10 - 7 * q^11 - 9 * q^12 - q^13 - 9 * q^14 - 6 * q^15 + 9 * q^16 - 10 * q^17 + 9 * q^18 + 6 * q^20 + 9 * q^21 - 7 * q^22 - 19 * q^23 - 9 * q^24 + 5 * q^25 - q^26 - 9 * q^27 - 9 * q^28 - 21 * q^29 - 6 * q^30 + 6 * q^31 + 9 * q^32 + 7 * q^33 - 10 * q^34 - 6 * q^35 + 9 * q^36 - 14 * q^37 + q^39 + 6 * q^40 + 12 * q^41 + 9 * q^42 - 17 * q^43 - 7 * q^44 + 6 * q^45 - 19 * q^46 - 11 * q^47 - 9 * q^48 + 9 * q^49 + 5 * q^50 + 10 * q^51 - q^52 - 12 * q^53 - 9 * q^54 - 21 * q^55 - 9 * q^56 - 21 * q^58 - 8 * q^59 - 6 * q^60 + q^61 + 6 * q^62 - 9 * q^63 + 9 * q^64 - 8 * q^65 + 7 * q^66 - 31 * q^67 - 10 * q^68 + 19 * q^69 - 6 * q^70 - 41 * q^71 + 9 * q^72 - q^73 - 14 * q^74 - 5 * q^75 + 7 * q^77 + q^78 - 17 * q^79 + 6 * q^80 + 9 * q^81 + 12 * q^82 - 36 * q^83 + 9 * q^84 - 30 * q^85 - 17 * q^86 + 21 * q^87 - 7 * q^88 - 17 * q^89 + 6 * q^90 + q^91 - 19 * q^92 - 6 * q^93 - 11 * q^94 - 50 * q^95 - 9 * q^96 - 14 * q^97 + 9 * q^98 - 7 * 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
$5$	4.34081	1.94127	0.970636	−	0.240554i	$-0.0773292\pi$
$5$	4.34081	1.94127	0.970636	+	0.240554i	$0.0773292\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	4.34081	1.37269
$11$	−5.19543	−1.56648	−0.783240	−	0.621719i	$-0.786435\pi$
$11$	−5.19543	−1.56648	−0.783240	+	0.621719i	$0.786435\pi$
$12$	−1.00000	−0.288675
$13$	1.61292	0.447344	0.223672	−	0.974664i	$-0.428196\pi$
$13$	1.61292	0.447344	0.223672	+	0.974664i	$0.428196\pi$
$14$	−1.00000	−0.267261
$15$	−4.34081	−1.12079
$16$	1.00000	0.250000
$17$	−5.89131	−1.42885	−0.714426	−	0.699711i	$-0.753312\pi$
$17$	−5.89131	−1.42885	−0.714426	+	0.699711i	$0.753312\pi$
$18$	1.00000	0.235702
$19$	−8.17378	−1.87519	−0.937597	−	0.347725i	$-0.886954\pi$
$19$	−8.17378	−1.87519	−0.937597	+	0.347725i	$0.886954\pi$
$20$	4.34081	0.970636
$21$	1.00000	0.218218
$22$	−5.19543	−1.10767
$23$	−2.11779	−0.441591	−0.220795	−	0.975320i	$-0.570865\pi$
$23$	−2.11779	−0.441591	−0.220795	+	0.975320i	$0.570865\pi$
$24$	−1.00000	−0.204124
$25$	13.8427	2.76853
$26$	1.61292	0.316320
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	−2.86456	−0.531936	−0.265968	−	0.963982i	$-0.585692\pi$
$29$	−2.86456	−0.531936	−0.265968	+	0.963982i	$0.585692\pi$
$30$	−4.34081	−0.792521
$31$	9.30033	1.67039	0.835194	−	0.549955i	$-0.185355\pi$
$31$	9.30033	1.67039	0.835194	+	0.549955i	$0.185355\pi$
$32$	1.00000	0.176777
$33$	5.19543	0.904408
$34$	−5.89131	−1.01035
$35$	−4.34081	−0.733732
$36$	1.00000	0.166667
$37$	−7.82341	−1.28616	−0.643080	−	0.765799i	$-0.722344\pi$
$37$	−7.82341	−1.28616	−0.643080	+	0.765799i	$0.722344\pi$
$38$	−8.17378	−1.32596
$39$	−1.61292	−0.258274
$40$	4.34081	0.686343
$41$	−5.82591	−0.909854	−0.454927	−	0.890529i	$-0.650335\pi$
$41$	−5.82591	−0.909854	−0.454927	+	0.890529i	$0.650335\pi$
$42$	1.00000	0.154303
$43$	4.33174	0.660584	0.330292	−	0.943879i	$-0.392853\pi$
$43$	4.33174	0.660584	0.330292	+	0.943879i	$0.392853\pi$
$44$	−5.19543	−0.783240
$45$	4.34081	0.647090
$46$	−2.11779	−0.312252
$47$	−0.173059	−0.0252432	−0.0126216	−	0.999920i	$-0.504018\pi$
$47$	−0.173059	−0.0252432	−0.0126216	+	0.999920i	$0.504018\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	13.8427	1.95765
$51$	5.89131	0.824949
$52$	1.61292	0.223672
$53$	−3.17696	−0.436388	−0.218194	−	0.975905i	$-0.570017\pi$
$53$	−3.17696	−0.436388	−0.218194	+	0.975905i	$0.570017\pi$
$54$	−1.00000	−0.136083
$55$	−22.5524	−3.04096
$56$	−1.00000	−0.133631
$57$	8.17378	1.08264
$58$	−2.86456	−0.376135
$59$	−2.76129	−0.359489	−0.179744	−	0.983713i	$-0.557527\pi$
$59$	−2.76129	−0.359489	−0.179744	+	0.983713i	$0.557527\pi$
$60$	−4.34081	−0.560397
$61$	12.1928	1.56113	0.780564	−	0.625076i	$-0.214932\pi$
$61$	12.1928	1.56113	0.780564	+	0.625076i	$0.214932\pi$
$62$	9.30033	1.18114
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	7.00139	0.868416
$66$	5.19543	0.639513
$67$	−12.5190	−1.52944	−0.764718	−	0.644365i	$-0.777122\pi$
$67$	−12.5190	−1.52944	−0.764718	+	0.644365i	$0.777122\pi$
$68$	−5.89131	−0.714426
$69$	2.11779	0.254952
$70$	−4.34081	−0.518827
$71$	−8.87043	−1.05273	−0.526363	−	0.850260i	$-0.676445\pi$
$71$	−8.87043	−1.05273	−0.526363	+	0.850260i	$0.676445\pi$
$72$	1.00000	0.117851
$73$	3.52000	0.411985	0.205992	−	0.978554i	$-0.433958\pi$
$73$	3.52000	0.411985	0.205992	+	0.978554i	$0.433958\pi$
$74$	−7.82341	−0.909452
$75$	−13.8427	−1.59841
$76$	−8.17378	−0.937597
$77$	5.19543	0.592074
$78$	−1.61292	−0.182627
$79$	11.1020	1.24907	0.624536	−	0.780996i	$-0.285288\pi$
$79$	11.1020	1.24907	0.624536	+	0.780996i	$0.285288\pi$
$80$	4.34081	0.485318
$81$	1.00000	0.111111
$82$	−5.82591	−0.643364
$83$	−17.4349	−1.91373	−0.956863	−	0.290538i	$-0.906166\pi$
$83$	−17.4349	−1.91373	−0.956863	+	0.290538i	$0.906166\pi$
$84$	1.00000	0.109109
$85$	−25.5731	−2.77379
$86$	4.33174	0.467103
$87$	2.86456	0.307113
$88$	−5.19543	−0.553835
$89$	−6.10744	−0.647388	−0.323694	−	0.946162i	$-0.604925\pi$
$89$	−6.10744	−0.647388	−0.323694	+	0.946162i	$0.604925\pi$
$90$	4.34081	0.457562
$91$	−1.61292	−0.169080
$92$	−2.11779	−0.220795
$93$	−9.30033	−0.964399
$94$	−0.173059	−0.0178497
$95$	−35.4809	−3.64026
$96$	−1.00000	−0.102062
$97$	−3.65698	−0.371310	−0.185655	−	0.982615i	$-0.559441\pi$
$97$	−3.65698	−0.371310	−0.185655	+	0.982615i	$0.559441\pi$
$98$	1.00000	0.101015
$99$	−5.19543	−0.522160
$100$	13.8427	1.38427
$101$	−17.6653	−1.75776	−0.878881	−	0.477041i	$-0.841709\pi$
$101$	−17.6653	−1.75776	−0.878881	+	0.477041i	$0.841709\pi$
$102$	5.89131	0.583327
$103$	−3.13269	−0.308673	−0.154337	−	0.988018i	$-0.549324\pi$
$103$	−3.13269	−0.308673	−0.154337	+	0.988018i	$0.549324\pi$
$104$	1.61292	0.158160
$105$	4.34081	0.423620
$106$	−3.17696	−0.308573
$107$	−2.38531	−0.230597	−0.115298	−	0.993331i	$-0.536782\pi$
$107$	−2.38531	−0.230597	−0.115298	+	0.993331i	$0.536782\pi$
$108$	−1.00000	−0.0962250
$109$	11.7876	1.12904	0.564521	−	0.825418i	$-0.309061\pi$
$109$	11.7876	1.12904	0.564521	+	0.825418i	$0.309061\pi$
$110$	−22.5524	−2.15029
$111$	7.82341	0.742565
$112$	−1.00000	−0.0944911
$113$	−10.4172	−0.979964	−0.489982	−	0.871733i	$-0.662997\pi$
$113$	−10.4172	−0.979964	−0.489982	+	0.871733i	$0.662997\pi$
$114$	8.17378	0.765544
$115$	−9.19295	−0.857247
$116$	−2.86456	−0.265968
$117$	1.61292	0.149115
$118$	−2.76129	−0.254197
$119$	5.89131	0.540056
$120$	−4.34081	−0.396260
$121$	15.9925	1.45386
$122$	12.1928	1.10388
$123$	5.82591	0.525305
$124$	9.30033	0.835194
$125$	38.3844	3.43321
$126$	−1.00000	−0.0890871
$127$	−12.6690	−1.12419	−0.562094	−	0.827073i	$-0.690004\pi$
$127$	−12.6690	−1.12419	−0.562094	+	0.827073i	$0.690004\pi$
$128$	1.00000	0.0883883
$129$	−4.33174	−0.381388
$130$	7.00139	0.614063
$131$	−4.93578	−0.431241	−0.215620	−	0.976477i	$-0.569177\pi$
$131$	−4.93578	−0.431241	−0.215620	+	0.976477i	$0.569177\pi$
$132$	5.19543	0.452204
$133$	8.17378	0.708756
$134$	−12.5190	−1.08147
$135$	−4.34081	−0.373598
$136$	−5.89131	−0.505176
$137$	−8.86611	−0.757483	−0.378741	−	0.925503i	$-0.623643\pi$
$137$	−8.86611	−0.757483	−0.378741	+	0.925503i	$0.623643\pi$
$138$	2.11779	0.180279
$139$	0.819394	0.0695001	0.0347500	−	0.999396i	$-0.488936\pi$
$139$	0.819394	0.0695001	0.0347500	+	0.999396i	$0.488936\pi$
$140$	−4.34081	−0.366866
$141$	0.173059	0.0145742
$142$	−8.87043	−0.744390
$143$	−8.37982	−0.700755
$144$	1.00000	0.0833333
$145$	−12.4345	−1.03263
$146$	3.52000	0.291317
$147$	−1.00000	−0.0824786
$148$	−7.82341	−0.643080
$149$	21.1669	1.73406	0.867028	−	0.498259i	$-0.166027\pi$
$149$	21.1669	1.73406	0.867028	+	0.498259i	$0.166027\pi$
$150$	−13.8427	−1.13025
$151$	2.76036	0.224635	0.112318	−	0.993672i	$-0.464173\pi$
$151$	2.76036	0.224635	0.112318	+	0.993672i	$0.464173\pi$
$152$	−8.17378	−0.662981
$153$	−5.89131	−0.476284
$154$	5.19543	0.418660
$155$	40.3710	3.24268
$156$	−1.61292	−0.129137
$157$	5.71955	0.456470	0.228235	−	0.973606i	$-0.426705\pi$
$157$	5.71955	0.456470	0.228235	+	0.973606i	$0.426705\pi$
$158$	11.1020	0.883227
$159$	3.17696	0.251949
$160$	4.34081	0.343172
$161$	2.11779	0.166906
$162$	1.00000	0.0785674
$163$	−6.48964	−0.508308	−0.254154	−	0.967164i	$-0.581797\pi$
$163$	−6.48964	−0.508308	−0.254154	+	0.967164i	$0.581797\pi$
$164$	−5.82591	−0.454927
$165$	22.5524	1.75570
$166$	−17.4349	−1.35321
$167$	−8.01172	−0.619965	−0.309983	−	0.950742i	$-0.600323\pi$
$167$	−8.01172	−0.619965	−0.309983	+	0.950742i	$0.600323\pi$
$168$	1.00000	0.0771517
$169$	−10.3985	−0.799883
$170$	−25.5731	−1.96137
$171$	−8.17378	−0.625064
$172$	4.33174	0.330292
$173$	−24.7803	−1.88401	−0.942005	−	0.335599i	$-0.891061\pi$
$173$	−24.7803	−1.88401	−0.942005	+	0.335599i	$0.891061\pi$
$174$	2.86456	0.217162
$175$	−13.8427	−1.04641
$176$	−5.19543	−0.391620
$177$	2.76129	0.207551
$178$	−6.10744	−0.457772
$179$	17.8065	1.33092	0.665461	−	0.746433i	$-0.268235\pi$
$179$	17.8065	1.33092	0.665461	+	0.746433i	$0.268235\pi$
$180$	4.34081	0.323545
$181$	−5.17711	−0.384811	−0.192406	−	0.981315i	$-0.561629\pi$
$181$	−5.17711	−0.384811	−0.192406	+	0.981315i	$0.561629\pi$
$182$	−1.61292	−0.119558
$183$	−12.1928	−0.901317
$184$	−2.11779	−0.156126
$185$	−33.9600	−2.49679
$186$	−9.30033	−0.681933
$187$	30.6079	2.23827
$188$	−0.173059	−0.0126216
$189$	1.00000	0.0727393
$190$	−35.4809	−2.57405
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	−1.00000	−0.0721688
$193$	−19.7507	−1.42169	−0.710844	−	0.703349i	$-0.751687\pi$
$193$	−19.7507	−1.42169	−0.710844	+	0.703349i	$0.751687\pi$
$194$	−3.65698	−0.262556
$195$	−7.00139	−0.501380
$196$	1.00000	0.0714286
$197$	15.4630	1.10169	0.550847	−	0.834606i	$-0.314305\pi$
$197$	15.4630	1.10169	0.550847	+	0.834606i	$0.314305\pi$
$198$	−5.19543	−0.369223
$199$	1.32577	0.0939815	0.0469907	−	0.998895i	$-0.485037\pi$
$199$	1.32577	0.0939815	0.0469907	+	0.998895i	$0.485037\pi$
$200$	13.8427	0.978825
$201$	12.5190	0.883020
$202$	−17.6653	−1.24293
$203$	2.86456	0.201053
$204$	5.89131	0.412474
$205$	−25.2892	−1.76627
$206$	−3.13269	−0.218265
$207$	−2.11779	−0.147197
$208$	1.61292	0.111836
$209$	42.4663	2.93745
$210$	4.34081	0.299545
$211$	−0.640129	−0.0440683	−0.0220341	−	0.999757i	$-0.507014\pi$
$211$	−0.640129	−0.0440683	−0.0220341	+	0.999757i	$0.507014\pi$
$212$	−3.17696	−0.218194
$213$	8.87043	0.607792
$214$	−2.38531	−0.163056
$215$	18.8033	1.28237
$216$	−1.00000	−0.0680414
$217$	−9.30033	−0.631348
$218$	11.7876	0.798354
$219$	−3.52000	−0.237859
$220$	−22.5524	−1.52048
$221$	−9.50222	−0.639188
$222$	7.82341	0.525073
$223$	18.0140	1.20631	0.603155	−	0.797624i	$-0.293910\pi$
$223$	18.0140	1.20631	0.603155	+	0.797624i	$0.293910\pi$
$224$	−1.00000	−0.0668153
$225$	13.8427	0.922845
$226$	−10.4172	−0.692939
$227$	−3.09131	−0.205177	−0.102589	−	0.994724i	$-0.532713\pi$
$227$	−3.09131	−0.205177	−0.102589	+	0.994724i	$0.532713\pi$
$228$	8.17378	0.541322
$229$	5.02521	0.332075	0.166038	−	0.986119i	$-0.446903\pi$
$229$	5.02521	0.332075	0.166038	+	0.986119i	$0.446903\pi$
$230$	−9.19295	−0.606165
$231$	−5.19543	−0.341834
$232$	−2.86456	−0.188068
$233$	16.1692	1.05928	0.529640	−	0.848223i	$-0.322327\pi$
$233$	16.1692	1.05928	0.529640	+	0.848223i	$0.322327\pi$
$234$	1.61292	0.105440
$235$	−0.751217	−0.0490040
$236$	−2.76129	−0.179744
$237$	−11.1020	−0.721152
$238$	5.89131	0.381877
$239$	−6.70777	−0.433890	−0.216945	−	0.976184i	$-0.569609\pi$
$239$	−6.70777	−0.433890	−0.216945	+	0.976184i	$0.569609\pi$
$240$	−4.34081	−0.280198
$241$	−5.68401	−0.366139	−0.183070	−	0.983100i	$-0.558603\pi$
$241$	−5.68401	−0.366139	−0.183070	+	0.983100i	$0.558603\pi$
$242$	15.9925	1.02804
$243$	−1.00000	−0.0641500
$244$	12.1928	0.780564
$245$	4.34081	0.277324
$246$	5.82591	0.371446
$247$	−13.1837	−0.838856
$248$	9.30033	0.590572
$249$	17.4349	1.10489
$250$	38.3844	2.42764
$251$	−19.7316	−1.24545	−0.622724	−	0.782441i	$-0.713974\pi$
$251$	−19.7316	−1.24545	−0.622724	+	0.782441i	$0.713974\pi$
$252$	−1.00000	−0.0629941
$253$	11.0028	0.691743
$254$	−12.6690	−0.794921
$255$	25.5731	1.60145
$256$	1.00000	0.0625000
$257$	21.6663	1.35150	0.675752	−	0.737129i	$-0.263819\pi$
$257$	21.6663	1.35150	0.675752	+	0.737129i	$0.263819\pi$
$258$	−4.33174	−0.269682
$259$	7.82341	0.486123
$260$	7.00139	0.434208
$261$	−2.86456	−0.177312
$262$	−4.93578	−0.304933
$263$	1.27319	0.0785085	0.0392542	−	0.999229i	$-0.487502\pi$
$263$	1.27319	0.0785085	0.0392542	+	0.999229i	$0.487502\pi$
$264$	5.19543	0.319757
$265$	−13.7906	−0.847148
$266$	8.17378	0.501166
$267$	6.10744	0.373770
$268$	−12.5190	−0.764718
$269$	26.9063	1.64051	0.820253	−	0.572001i	$-0.193832\pi$
$269$	26.9063	1.64051	0.820253	+	0.572001i	$0.193832\pi$
$270$	−4.34081	−0.264174
$271$	−5.37947	−0.326780	−0.163390	−	0.986562i	$-0.552243\pi$
$271$	−5.37947	−0.326780	−0.163390	+	0.986562i	$0.552243\pi$
$272$	−5.89131	−0.357213
$273$	1.61292	0.0976184
$274$	−8.86611	−0.535621
$275$	−71.9186	−4.33686
$276$	2.11779	0.127476
$277$	20.2251	1.21521	0.607606	−	0.794239i	$-0.292130\pi$
$277$	20.2251	1.21521	0.607606	+	0.794239i	$0.292130\pi$
$278$	0.819394	0.0491440
$279$	9.30033	0.556796
$280$	−4.34081	−0.259413
$281$	−17.1869	−1.02528	−0.512642	−	0.858602i	$-0.671333\pi$
$281$	−17.1869	−1.02528	−0.512642	+	0.858602i	$0.671333\pi$
$282$	0.173059	0.0103055
$283$	−3.48521	−0.207174	−0.103587	−	0.994620i	$-0.533032\pi$
$283$	−3.48521	−0.207174	−0.103587	+	0.994620i	$0.533032\pi$
$284$	−8.87043	−0.526363
$285$	35.4809	2.10170
$286$	−8.37982	−0.495509
$287$	5.82591	0.343893
$288$	1.00000	0.0589256
$289$	17.7075	1.04162
$290$	−12.4345	−0.730181
$291$	3.65698	0.214376
$292$	3.52000	0.205992
$293$	9.63755	0.563031	0.281516	−	0.959557i	$-0.409163\pi$
$293$	9.63755	0.563031	0.281516	+	0.959557i	$0.409163\pi$
$294$	−1.00000	−0.0583212
$295$	−11.9862	−0.697866
$296$	−7.82341	−0.454726
$297$	5.19543	0.301469
$298$	21.1669	1.22616
$299$	−3.41583	−0.197543
$300$	−13.8427	−0.799207
$301$	−4.33174	−0.249677
$302$	2.76036	0.158841
$303$	17.6653	1.01484
$304$	−8.17378	−0.468798
$305$	52.9267	3.03057
$306$	−5.89131	−0.336784
$307$	6.00865	0.342932	0.171466	−	0.985190i	$-0.445150\pi$
$307$	6.00865	0.342932	0.171466	+	0.985190i	$0.445150\pi$
$308$	5.19543	0.296037
$309$	3.13269	0.178212
$310$	40.3710	2.29292
$311$	−3.41392	−0.193586	−0.0967928	−	0.995305i	$-0.530858\pi$
$311$	−3.41392	−0.193586	−0.0967928	+	0.995305i	$0.530858\pi$
$312$	−1.61292	−0.0913137
$313$	−16.9242	−0.956611	−0.478305	−	0.878194i	$-0.658749\pi$
$313$	−16.9242	−0.956611	−0.478305	+	0.878194i	$0.658749\pi$
$314$	5.71955	0.322773
$315$	−4.34081	−0.244577
$316$	11.1020	0.624536
$317$	16.7195	0.939062	0.469531	−	0.882916i	$-0.344423\pi$
$317$	16.7195	0.939062	0.469531	+	0.882916i	$0.344423\pi$
$318$	3.17696	0.178155
$319$	14.8826	0.833267
$320$	4.34081	0.242659
$321$	2.38531	0.133135
$322$	2.11779	0.118020
$323$	48.1543	2.67937
$324$	1.00000	0.0555556
$325$	22.3271	1.23849
$326$	−6.48964	−0.359428
$327$	−11.7876	−0.651853
$328$	−5.82591	−0.321682
$329$	0.173059	0.00954105
$330$	22.5524	1.24147
$331$	−1.53715	−0.0844892	−0.0422446	−	0.999107i	$-0.513451\pi$
$331$	−1.53715	−0.0844892	−0.0422446	+	0.999107i	$0.513451\pi$
$332$	−17.4349	−0.956863
$333$	−7.82341	−0.428720
$334$	−8.01172	−0.438382
$335$	−54.3425	−2.96905
$336$	1.00000	0.0545545
$337$	−17.4065	−0.948194	−0.474097	−	0.880473i	$-0.657225\pi$
$337$	−17.4065	−0.948194	−0.474097	+	0.880473i	$0.657225\pi$
$338$	−10.3985	−0.565603
$339$	10.4172	0.565783
$340$	−25.5731	−1.38690
$341$	−48.3192	−2.61663
$342$	−8.17378	−0.441987
$343$	−1.00000	−0.0539949
$344$	4.33174	0.233552
$345$	9.19295	0.494932
$346$	−24.7803	−1.33220
$347$	15.8773	0.852338	0.426169	−	0.904644i	$-0.359863\pi$
$347$	15.8773	0.852338	0.426169	+	0.904644i	$0.359863\pi$
$348$	2.86456	0.153557
$349$	−9.27584	−0.496524	−0.248262	−	0.968693i	$-0.579859\pi$
$349$	−9.27584	−0.496524	−0.248262	+	0.968693i	$0.579859\pi$
$350$	−13.8427	−0.739922
$351$	−1.61292	−0.0860914
$352$	−5.19543	−0.276917
$353$	34.7861	1.85148	0.925739	−	0.378163i	$-0.123444\pi$
$353$	34.7861	1.85148	0.925739	+	0.378163i	$0.123444\pi$
$354$	2.76129	0.146761
$355$	−38.5049	−2.04363
$356$	−6.10744	−0.323694
$357$	−5.89131	−0.311801
$358$	17.8065	0.941103
$359$	−8.15083	−0.430185	−0.215092	−	0.976594i	$-0.569005\pi$
$359$	−8.15083	−0.430185	−0.215092	+	0.976594i	$0.569005\pi$
$360$	4.34081	0.228781
$361$	47.8106	2.51635
$362$	−5.17711	−0.272103
$363$	−15.9925	−0.839387
$364$	−1.61292	−0.0845400
$365$	15.2797	0.799774
$366$	−12.1928	−0.637327
$367$	14.2199	0.742275	0.371137	−	0.928578i	$-0.378968\pi$
$367$	14.2199	0.742275	0.371137	+	0.928578i	$0.378968\pi$
$368$	−2.11779	−0.110398
$369$	−5.82591	−0.303285
$370$	−33.9600	−1.76549
$371$	3.17696	0.164939
$372$	−9.30033	−0.482200
$373$	25.3381	1.31196	0.655980	−	0.754778i	$-0.272256\pi$
$373$	25.3381	1.31196	0.655980	+	0.754778i	$0.272256\pi$
$374$	30.6079	1.58270
$375$	−38.3844	−1.98216
$376$	−0.173059	−0.00892484
$377$	−4.62031	−0.237958
$378$	1.00000	0.0514344
$379$	−37.7886	−1.94107	−0.970536	−	0.240957i	$-0.922539\pi$
$379$	−37.7886	−1.94107	−0.970536	+	0.240957i	$0.922539\pi$
$380$	−35.4809	−1.82013
$381$	12.6690	0.649050
$382$	1.00000	0.0511645
$383$	−32.3908	−1.65509	−0.827545	−	0.561399i	$-0.810263\pi$
$383$	−32.3908	−1.65509	−0.827545	+	0.561399i	$0.810263\pi$
$384$	−1.00000	−0.0510310
$385$	22.5524	1.14938
$386$	−19.7507	−1.00529
$387$	4.33174	0.220195
$388$	−3.65698	−0.185655
$389$	−3.69940	−0.187567	−0.0937835	−	0.995593i	$-0.529896\pi$
$389$	−3.69940	−0.187567	−0.0937835	+	0.995593i	$0.529896\pi$
$390$	−7.00139	−0.354529
$391$	12.4766	0.630968
$392$	1.00000	0.0505076
$393$	4.93578	0.248977
$394$	15.4630	0.779016
$395$	48.1917	2.42479
$396$	−5.19543	−0.261080
$397$	22.6354	1.13604	0.568019	−	0.823015i	$-0.307710\pi$
$397$	22.6354	1.13604	0.568019	+	0.823015i	$0.307710\pi$
$398$	1.32577	0.0664549
$399$	−8.17378	−0.409201
$400$	13.8427	0.692134
$401$	−7.36135	−0.367608	−0.183804	−	0.982963i	$-0.558841\pi$
$401$	−7.36135	−0.367608	−0.183804	+	0.982963i	$0.558841\pi$
$402$	12.5190	0.624390
$403$	15.0007	0.747238
$404$	−17.6653	−0.878881
$405$	4.34081	0.215697
$406$	2.86456	0.142166
$407$	40.6459	2.01474
$408$	5.89131	0.291663
$409$	−29.9077	−1.47884	−0.739420	−	0.673244i	$-0.764900\pi$
$409$	−29.9077	−1.47884	−0.739420	+	0.673244i	$0.764900\pi$
$410$	−25.2892	−1.24894
$411$	8.86611	0.437333
$412$	−3.13269	−0.154337
$413$	2.76129	0.135874
$414$	−2.11779	−0.104084
$415$	−75.6816	−3.71506
$416$	1.61292	0.0790800
$417$	−0.819394	−0.0401259
$418$	42.4663	2.07709
$419$	6.81214	0.332795	0.166397	−	0.986059i	$-0.446787\pi$
$419$	6.81214	0.332795	0.166397	+	0.986059i	$0.446787\pi$
$420$	4.34081	0.211810
$421$	−4.32673	−0.210872	−0.105436	−	0.994426i	$-0.533624\pi$
$421$	−4.32673	−0.210872	−0.105436	+	0.994426i	$0.533624\pi$
$422$	−0.640129	−0.0311610
$423$	−0.173059	−0.00841442
$424$	−3.17696	−0.154287
$425$	−81.5515	−3.95583
$426$	8.87043	0.429774
$427$	−12.1928	−0.590051
$428$	−2.38531	−0.115298
$429$	8.37982	0.404581
$430$	18.8033	0.906774
$431$	−41.4801	−1.99803	−0.999014	−	0.0444035i	$-0.985861\pi$
$431$	−41.4801	−1.99803	−0.999014	+	0.0444035i	$0.985861\pi$
$432$	−1.00000	−0.0481125
$433$	33.7144	1.62021	0.810106	−	0.586284i	$-0.199410\pi$
$433$	33.7144	1.62021	0.810106	+	0.586284i	$0.199410\pi$
$434$	−9.30033	−0.446430
$435$	12.4345	0.596190
$436$	11.7876	0.564521
$437$	17.3104	0.828068
$438$	−3.52000	−0.168192
$439$	7.79608	0.372087	0.186043	−	0.982542i	$-0.440434\pi$
$439$	7.79608	0.372087	0.186043	+	0.982542i	$0.440434\pi$
$440$	−22.5524	−1.07514
$441$	1.00000	0.0476190
$442$	−9.50222	−0.451975
$443$	4.61865	0.219439	0.109719	−	0.993963i	$-0.465005\pi$
$443$	4.61865	0.219439	0.109719	+	0.993963i	$0.465005\pi$
$444$	7.82341	0.371282
$445$	−26.5113	−1.25676
$446$	18.0140	0.852990
$447$	−21.1669	−1.00116
$448$	−1.00000	−0.0472456
$449$	4.91807	0.232098	0.116049	−	0.993243i	$-0.462977\pi$
$449$	4.91807	0.232098	0.116049	+	0.993243i	$0.462977\pi$
$450$	13.8427	0.652550
$451$	30.2681	1.42527
$452$	−10.4172	−0.489982
$453$	−2.76036	−0.129693
$454$	−3.09131	−0.145082
$455$	−7.00139	−0.328230
$456$	8.17378	0.382772
$457$	−24.5936	−1.15044	−0.575220	−	0.817999i	$-0.695083\pi$
$457$	−24.5936	−1.15044	−0.575220	+	0.817999i	$0.695083\pi$
$458$	5.02521	0.234813
$459$	5.89131	0.274983
$460$	−9.19295	−0.428624
$461$	31.1500	1.45080	0.725400	−	0.688327i	$-0.241655\pi$
$461$	31.1500	1.45080	0.725400	+	0.688327i	$0.241655\pi$
$462$	−5.19543	−0.241713
$463$	−22.2869	−1.03576	−0.517881	−	0.855453i	$-0.673279\pi$
$463$	−22.2869	−1.03576	−0.517881	+	0.855453i	$0.673279\pi$
$464$	−2.86456	−0.132984
$465$	−40.3710	−1.87216
$466$	16.1692	0.749024
$467$	2.32091	0.107399	0.0536995	−	0.998557i	$-0.482899\pi$
$467$	2.32091	0.107399	0.0536995	+	0.998557i	$0.482899\pi$
$468$	1.61292	0.0745573
$469$	12.5190	0.578072
$470$	−0.751217	−0.0346511
$471$	−5.71955	−0.263543
$472$	−2.76129	−0.127099
$473$	−22.5052	−1.03479
$474$	−11.1020	−0.509931
$475$	−113.147	−5.19154
$476$	5.89131	0.270028
$477$	−3.17696	−0.145463
$478$	−6.70777	−0.306806
$479$	25.7647	1.17722	0.588609	−	0.808418i	$-0.299676\pi$
$479$	25.7647	1.17722	0.588609	+	0.808418i	$0.299676\pi$
$480$	−4.34081	−0.198130
$481$	−12.6185	−0.575356
$482$	−5.68401	−0.258899
$483$	−2.11779	−0.0963630
$484$	15.9925	0.726931
$485$	−15.8743	−0.720814
$486$	−1.00000	−0.0453609
$487$	−13.2378	−0.599861	−0.299931	−	0.953961i	$-0.596964\pi$
$487$	−13.2378	−0.599861	−0.299931	+	0.953961i	$0.596964\pi$
$488$	12.1928	0.551942
$489$	6.48964	0.293472
$490$	4.34081	0.196098
$491$	−6.94398	−0.313377	−0.156689	−	0.987648i	$-0.550082\pi$
$491$	−6.94398	−0.313377	−0.156689	+	0.987648i	$0.550082\pi$
$492$	5.82591	0.262652
$493$	16.8760	0.760058
$494$	−13.1837	−0.593161
$495$	−22.5524	−1.01365
$496$	9.30033	0.417597
$497$	8.87043	0.397893
$498$	17.4349	0.781276
$499$	0.189643	0.00848960	0.00424480	−	0.999991i	$-0.498649\pi$
$499$	0.189643	0.00848960	0.00424480	+	0.999991i	$0.498649\pi$
$500$	38.3844	1.71660
$501$	8.01172	0.357937
$502$	−19.7316	−0.880665
$503$	−6.69834	−0.298664	−0.149332	−	0.988787i	$-0.547712\pi$
$503$	−6.69834	−0.298664	−0.149332	+	0.988787i	$0.547712\pi$
$504$	−1.00000	−0.0445435
$505$	−76.6817	−3.41229
$506$	11.0028	0.489136
$507$	10.3985	0.461813
$508$	−12.6690	−0.562094
$509$	6.21388	0.275425	0.137713	−	0.990472i	$-0.456025\pi$
$509$	6.21388	0.275425	0.137713	+	0.990472i	$0.456025\pi$
$510$	25.5731	1.13240
$511$	−3.52000	−0.155716
$512$	1.00000	0.0441942
$513$	8.17378	0.360881
$514$	21.6663	0.955658
$515$	−13.5984	−0.599218
$516$	−4.33174	−0.190694
$517$	0.899116	0.0395431
$518$	7.82341	0.343741
$519$	24.7803	1.08773
$520$	7.00139	0.307031
$521$	−24.4823	−1.07259	−0.536294	−	0.844031i	$-0.680176\pi$
$521$	−24.4823	−1.07259	−0.536294	+	0.844031i	$0.680176\pi$
$522$	−2.86456	−0.125378
$523$	−17.4815	−0.764411	−0.382205	−	0.924077i	$-0.624835\pi$
$523$	−17.4815	−0.764411	−0.382205	+	0.924077i	$0.624835\pi$
$524$	−4.93578	−0.215620
$525$	13.8427	0.604144
$526$	1.27319	0.0555139
$527$	−54.7911	−2.38674
$528$	5.19543	0.226102
$529$	−18.5149	−0.804998
$530$	−13.7906	−0.599024
$531$	−2.76129	−0.119830
$532$	8.17378	0.354378
$533$	−9.39673	−0.407018
$534$	6.10744	0.264295
$535$	−10.3542	−0.447651
$536$	−12.5190	−0.540737
$537$	−17.8065	−0.768408
$538$	26.9063	1.16001
$539$	−5.19543	−0.223783
$540$	−4.34081	−0.186799
$541$	−4.19283	−0.180264	−0.0901319	−	0.995930i	$-0.528729\pi$
$541$	−4.19283	−0.180264	−0.0901319	+	0.995930i	$0.528729\pi$
$542$	−5.37947	−0.231068
$543$	5.17711	0.222171
$544$	−5.89131	−0.252588
$545$	51.1676	2.19178
$546$	1.61292	0.0690267
$547$	−8.49981	−0.363426	−0.181713	−	0.983352i	$-0.558164\pi$
$547$	−8.49981	−0.363426	−0.181713	+	0.983352i	$0.558164\pi$
$548$	−8.86611	−0.378741
$549$	12.1928	0.520376
$550$	−71.9186	−3.06662
$551$	23.4143	0.997482
$552$	2.11779	0.0901393
$553$	−11.1020	−0.472105
$554$	20.2251	0.859284
$555$	33.9600	1.44152
$556$	0.819394	0.0347500
$557$	40.4637	1.71450	0.857251	−	0.514898i	$-0.172170\pi$
$557$	40.4637	1.71450	0.857251	+	0.514898i	$0.172170\pi$
$558$	9.30033	0.393714
$559$	6.98675	0.295508
$560$	−4.34081	−0.183433
$561$	−30.6079	−1.29227
$562$	−17.1869	−0.724985
$563$	8.64080	0.364166	0.182083	−	0.983283i	$-0.441716\pi$
$563$	8.64080	0.364166	0.182083	+	0.983283i	$0.441716\pi$
$564$	0.173059	0.00728710
$565$	−45.2190	−1.90238
$566$	−3.48521	−0.146494
$567$	−1.00000	−0.0419961
$568$	−8.87043	−0.372195
$569$	1.62655	0.0681886	0.0340943	−	0.999419i	$-0.489145\pi$
$569$	1.62655	0.0681886	0.0340943	+	0.999419i	$0.489145\pi$
$570$	35.4809	1.48613
$571$	−29.4986	−1.23448	−0.617238	−	0.786776i	$-0.711749\pi$
$571$	−29.4986	−1.23448	−0.617238	+	0.786776i	$0.711749\pi$
$572$	−8.37982	−0.350378
$573$	−1.00000	−0.0417756
$574$	5.82591	0.243169
$575$	−29.3159	−1.22256
$576$	1.00000	0.0416667
$577$	31.5545	1.31363	0.656816	−	0.754051i	$-0.271903\pi$
$577$	31.5545	1.31363	0.656816	+	0.754051i	$0.271903\pi$
$578$	17.7075	0.736537
$579$	19.7507	0.820812
$580$	−12.4345	−0.516316
$581$	17.4349	0.723321
$582$	3.65698	0.151587
$583$	16.5056	0.683594
$584$	3.52000	0.145659
$585$	7.00139	0.289472
$586$	9.63755	0.398123
$587$	27.6607	1.14168	0.570840	−	0.821061i	$-0.306617\pi$
$587$	27.6607	1.14168	0.570840	+	0.821061i	$0.306617\pi$
$588$	−1.00000	−0.0412393
$589$	−76.0188	−3.13230
$590$	−11.9862	−0.493465
$591$	−15.4630	−0.636064
$592$	−7.82341	−0.321540
$593$	−33.1354	−1.36071	−0.680353	−	0.732884i	$-0.738174\pi$
$593$	−33.1354	−1.36071	−0.680353	+	0.732884i	$0.738174\pi$
$594$	5.19543	0.213171
$595$	25.5731	1.04839
$596$	21.1669	0.867028
$597$	−1.32577	−0.0542602
$598$	−3.41583	−0.139684
$599$	−28.7009	−1.17269	−0.586343	−	0.810063i	$-0.699433\pi$
$599$	−28.7009	−1.17269	−0.586343	+	0.810063i	$0.699433\pi$
$600$	−13.8427	−0.565125
$601$	−9.16090	−0.373681	−0.186840	−	0.982390i	$-0.559825\pi$
$601$	−9.16090	−0.373681	−0.186840	+	0.982390i	$0.559825\pi$
$602$	−4.33174	−0.176548
$603$	−12.5190	−0.509812
$604$	2.76036	0.112318
$605$	69.4204	2.82234
$606$	17.6653	0.717603
$607$	−3.88191	−0.157562	−0.0787810	−	0.996892i	$-0.525103\pi$
$607$	−3.88191	−0.157562	−0.0787810	+	0.996892i	$0.525103\pi$
$608$	−8.17378	−0.331490
$609$	−2.86456	−0.116078
$610$	52.9267	2.14294
$611$	−0.279131	−0.0112924
$612$	−5.89131	−0.238142
$613$	1.73802	0.0701980	0.0350990	−	0.999384i	$-0.488825\pi$
$613$	1.73802	0.0701980	0.0350990	+	0.999384i	$0.488825\pi$
$614$	6.00865	0.242489
$615$	25.2892	1.01976
$616$	5.19543	0.209330
$617$	19.3185	0.777734	0.388867	−	0.921294i	$-0.372867\pi$
$617$	19.3185	0.777734	0.388867	+	0.921294i	$0.372867\pi$
$618$	3.13269	0.126015
$619$	47.7955	1.92106	0.960532	−	0.278168i	$-0.0897272\pi$
$619$	47.7955	1.92106	0.960532	+	0.278168i	$0.0897272\pi$
$620$	40.3710	1.62134
$621$	2.11779	0.0849841
$622$	−3.41392	−0.136886
$623$	6.10744	0.244690
$624$	−1.61292	−0.0645685
$625$	97.4062	3.89625
$626$	−16.9242	−0.676426
$627$	−42.4663	−1.69594
$628$	5.71955	0.228235
$629$	46.0901	1.83773
$630$	−4.34081	−0.172942
$631$	21.9541	0.873980	0.436990	−	0.899466i	$-0.356044\pi$
$631$	21.9541	0.873980	0.436990	+	0.899466i	$0.356044\pi$
$632$	11.1020	0.441614
$633$	0.640129	0.0254428
$634$	16.7195	0.664017
$635$	−54.9936	−2.18235
$636$	3.17696	0.125974
$637$	1.61292	0.0639063
$638$	14.8826	0.589209
$639$	−8.87043	−0.350909
$640$	4.34081	0.171586
$641$	3.96485	0.156602	0.0783010	−	0.996930i	$-0.475050\pi$
$641$	3.96485	0.156602	0.0783010	+	0.996930i	$0.475050\pi$
$642$	2.38531	0.0941407
$643$	29.6431	1.16901	0.584505	−	0.811390i	$-0.301289\pi$
$643$	29.6431	1.16901	0.584505	+	0.811390i	$0.301289\pi$
$644$	2.11779	0.0834528
$645$	−18.8033	−0.740378
$646$	48.1543	1.89460
$647$	−16.5851	−0.652028	−0.326014	−	0.945365i	$-0.605706\pi$
$647$	−16.5851	−0.652028	−0.326014	+	0.945365i	$0.605706\pi$
$648$	1.00000	0.0392837
$649$	14.3461	0.563132
$650$	22.3271	0.875743
$651$	9.30033	0.364509
$652$	−6.48964	−0.254154
$653$	−31.7807	−1.24368	−0.621838	−	0.783146i	$-0.713614\pi$
$653$	−31.7807	−1.24368	−0.621838	+	0.783146i	$0.713614\pi$
$654$	−11.7876	−0.460930
$655$	−21.4253	−0.837156
$656$	−5.82591	−0.227464
$657$	3.52000	0.137328
$658$	0.173059	0.00674654
$659$	39.3149	1.53149	0.765746	−	0.643143i	$-0.222370\pi$
$659$	39.3149	1.53149	0.765746	+	0.643143i	$0.222370\pi$
$660$	22.5524	0.877851
$661$	41.5181	1.61487	0.807434	−	0.589957i	$-0.200855\pi$
$661$	41.5181	1.61487	0.807434	+	0.589957i	$0.200855\pi$
$662$	−1.53715	−0.0597429
$663$	9.50222	0.369036
$664$	−17.4349	−0.676605
$665$	35.4809	1.37589
$666$	−7.82341	−0.303151
$667$	6.06655	0.234898
$668$	−8.01172	−0.309983
$669$	−18.0140	−0.696463
$670$	−54.3425	−2.09944
$671$	−63.3468	−2.44548
$672$	1.00000	0.0385758
$673$	−5.19912	−0.200411	−0.100206	−	0.994967i	$-0.531950\pi$
$673$	−5.19912	−0.200411	−0.100206	+	0.994967i	$0.531950\pi$
$674$	−17.4065	−0.670475
$675$	−13.8427	−0.532805
$676$	−10.3985	−0.399942
$677$	−30.2136	−1.16120	−0.580602	−	0.814187i	$-0.697183\pi$
$677$	−30.2136	−1.16120	−0.580602	+	0.814187i	$0.697183\pi$
$678$	10.4172	0.400069
$679$	3.65698	0.140342
$680$	−25.5731	−0.980683
$681$	3.09131	0.118459
$682$	−48.3192	−1.85024
$683$	18.6517	0.713689	0.356844	−	0.934164i	$-0.383853\pi$
$683$	18.6517	0.713689	0.356844	+	0.934164i	$0.383853\pi$
$684$	−8.17378	−0.312532
$685$	−38.4861	−1.47048
$686$	−1.00000	−0.0381802
$687$	−5.02521	−0.191724
$688$	4.33174	0.165146
$689$	−5.12418	−0.195216
$690$	9.19295	0.349970
$691$	−24.1420	−0.918405	−0.459202	−	0.888332i	$-0.651865\pi$
$691$	−24.1420	−0.918405	−0.459202	+	0.888332i	$0.651865\pi$
$692$	−24.7803	−0.942005
$693$	5.19543	0.197358
$694$	15.8773	0.602694
$695$	3.55684	0.134918
$696$	2.86456	0.108581
$697$	34.3222	1.30005
$698$	−9.27584	−0.351096
$699$	−16.1692	−0.611575
$700$	−13.8427	−0.523204
$701$	−11.8991	−0.449424	−0.224712	−	0.974425i	$-0.572144\pi$
$701$	−11.8991	−0.449424	−0.224712	+	0.974425i	$0.572144\pi$
$702$	−1.61292	−0.0608758
$703$	63.9468	2.41180
$704$	−5.19543	−0.195810
$705$	0.751217	0.0282925
$706$	34.7861	1.30919
$707$	17.6653	0.664372
$708$	2.76129	0.103776
$709$	−27.3739	−1.02805	−0.514024	−	0.857776i	$-0.671846\pi$
$709$	−27.3739	−1.02805	−0.514024	+	0.857776i	$0.671846\pi$
$710$	−38.5049	−1.44506
$711$	11.1020	0.416357
$712$	−6.10744	−0.228886
$713$	−19.6962	−0.737628
$714$	−5.89131	−0.220477
$715$	−36.3752	−1.36036
$716$	17.8065	0.665461
$717$	6.70777	0.250506
$718$	−8.15083	−0.304186
$719$	−27.4346	−1.02314	−0.511570	−	0.859242i	$-0.670936\pi$
$719$	−27.4346	−1.02314	−0.511570	+	0.859242i	$0.670936\pi$
$720$	4.34081	0.161773
$721$	3.13269	0.116667
$722$	47.8106	1.77933
$723$	5.68401	0.211390
$724$	−5.17711	−0.192406
$725$	−39.6532	−1.47268
$726$	−15.9925	−0.593537
$727$	21.0753	0.781640	0.390820	−	0.920467i	$-0.372191\pi$
$727$	21.0753	0.781640	0.390820	+	0.920467i	$0.372191\pi$
$728$	−1.61292	−0.0597788
$729$	1.00000	0.0370370
$730$	15.2797	0.565526
$731$	−25.5196	−0.943877
$732$	−12.1928	−0.450659
$733$	−42.0637	−1.55366	−0.776829	−	0.629712i	$-0.783173\pi$
$733$	−42.0637	−1.55366	−0.776829	+	0.629712i	$0.783173\pi$
$734$	14.2199	0.524867
$735$	−4.34081	−0.160113
$736$	−2.11779	−0.0780629
$737$	65.0414	2.39583
$738$	−5.82591	−0.214455
$739$	8.32668	0.306302	0.153151	−	0.988203i	$-0.451058\pi$
$739$	8.32668	0.306302	0.153151	+	0.988203i	$0.451058\pi$
$740$	−33.9600	−1.24839
$741$	13.1837	0.484314
$742$	3.17696	0.116630
$743$	−18.5676	−0.681179	−0.340589	−	0.940212i	$-0.610627\pi$
$743$	−18.5676	−0.681179	−0.340589	+	0.940212i	$0.610627\pi$
$744$	−9.30033	−0.340967
$745$	91.8814	3.36627
$746$	25.3381	0.927695
$747$	−17.4349	−0.637909
$748$	30.6079	1.11914
$749$	2.38531	0.0871573
$750$	−38.3844	−1.40160
$751$	−5.15236	−0.188012	−0.0940061	−	0.995572i	$-0.529967\pi$
$751$	−5.15236	−0.188012	−0.0940061	+	0.995572i	$0.529967\pi$
$752$	−0.173059	−0.00631081
$753$	19.7316	0.719060
$754$	−4.62031	−0.168262
$755$	11.9822	0.436078
$756$	1.00000	0.0363696
$757$	−11.3263	−0.411660	−0.205830	−	0.978588i	$-0.565989\pi$
$757$	−11.3263	−0.411660	−0.205830	+	0.978588i	$0.565989\pi$
$758$	−37.7886	−1.37254
$759$	−11.0028	−0.399378
$760$	−35.4809	−1.28703
$761$	31.7264	1.15008	0.575040	−	0.818125i	$-0.304986\pi$
$761$	31.7264	1.15008	0.575040	+	0.818125i	$0.304986\pi$
$762$	12.6690	0.458948
$763$	−11.7876	−0.426738
$764$	1.00000	0.0361787
$765$	−25.5731	−0.924597
$766$	−32.3908	−1.17033
$767$	−4.45374	−0.160815
$768$	−1.00000	−0.0360844
$769$	−4.63690	−0.167211	−0.0836055	−	0.996499i	$-0.526644\pi$
$769$	−4.63690	−0.167211	−0.0836055	+	0.996499i	$0.526644\pi$
$770$	22.5524	0.812732
$771$	−21.6663	−0.780291
$772$	−19.7507	−0.710844
$773$	34.4989	1.24084	0.620419	−	0.784270i	$-0.286962\pi$
$773$	34.4989	1.24084	0.620419	+	0.784270i	$0.286962\pi$
$774$	4.33174	0.155701
$775$	128.741	4.62453
$776$	−3.65698	−0.131278
$777$	−7.82341	−0.280663
$778$	−3.69940	−0.132630
$779$	47.6197	1.70615
$780$	−7.00139	−0.250690
$781$	46.0857	1.64908
$782$	12.4766	0.446162
$783$	2.86456	0.102371
$784$	1.00000	0.0357143
$785$	24.8275	0.886132
$786$	4.93578	0.176053
$787$	−10.1542	−0.361958	−0.180979	−	0.983487i	$-0.557927\pi$
$787$	−10.1542	−0.361958	−0.180979	+	0.983487i	$0.557927\pi$
$788$	15.4630	0.550847
$789$	−1.27319	−0.0453269
$790$	48.1917	1.71458
$791$	10.4172	0.370392
$792$	−5.19543	−0.184612
$793$	19.6660	0.698361
$794$	22.6354	0.803300
$795$	13.7906	0.489101
$796$	1.32577	0.0469907
$797$	−48.4027	−1.71451	−0.857256	−	0.514890i	$-0.827833\pi$
$797$	−48.4027	−1.71451	−0.857256	+	0.514890i	$0.827833\pi$
$798$	−8.17378	−0.289349
$799$	1.01954	0.0360689
$800$	13.8427	0.489412
$801$	−6.10744	−0.215796
$802$	−7.36135	−0.259938
$803$	−18.2879	−0.645366
$804$	12.5190	0.441510
$805$	9.19295	0.324009
$806$	15.0007	0.528377
$807$	−26.9063	−0.947147
$808$	−17.6653	−0.621463
$809$	−1.69666	−0.0596515	−0.0298258	−	0.999555i	$-0.509495\pi$
$809$	−1.69666	−0.0596515	−0.0298258	+	0.999555i	$0.509495\pi$
$810$	4.34081	0.152521
$811$	8.26745	0.290309	0.145155	−	0.989409i	$-0.453632\pi$
$811$	8.26745	0.290309	0.145155	+	0.989409i	$0.453632\pi$
$812$	2.86456	0.100526
$813$	5.37947	0.188666
$814$	40.6459	1.42464
$815$	−28.1703	−0.986763
$816$	5.89131	0.206237
$817$	−35.4067	−1.23872
$818$	−29.9077	−1.04570
$819$	−1.61292	−0.0563600
$820$	−25.2892	−0.883137
$821$	−39.6026	−1.38214	−0.691071	−	0.722787i	$-0.742861\pi$
$821$	−39.6026	−1.38214	−0.691071	+	0.722787i	$0.742861\pi$
$822$	8.86611	0.309241
$823$	31.2756	1.09020	0.545100	−	0.838371i	$-0.316492\pi$
$823$	31.2756	1.09020	0.545100	+	0.838371i	$0.316492\pi$
$824$	−3.13269	−0.109132
$825$	71.9186	2.50389
$826$	2.76129	0.0960775
$827$	41.1369	1.43047	0.715235	−	0.698885i	$-0.246320\pi$
$827$	41.1369	1.43047	0.715235	+	0.698885i	$0.246320\pi$
$828$	−2.11779	−0.0735984
$829$	43.3232	1.50468	0.752338	−	0.658777i	$-0.228926\pi$
$829$	43.3232	1.50468	0.752338	+	0.658777i	$0.228926\pi$
$830$	−75.6816	−2.62695
$831$	−20.2251	−0.701603
$832$	1.61292	0.0559180
$833$	−5.89131	−0.204122
$834$	−0.819394	−0.0283733
$835$	−34.7774	−1.20352
$836$	42.4663	1.46873
$837$	−9.30033	−0.321466
$838$	6.81214	0.235321
$839$	−57.1008	−1.97134	−0.985670	−	0.168687i	$-0.946047\pi$
$839$	−57.1008	−1.97134	−0.985670	+	0.168687i	$0.946047\pi$
$840$	4.34081	0.149772
$841$	−20.7943	−0.717044
$842$	−4.32673	−0.149109
$843$	17.1869	0.591948
$844$	−0.640129	−0.0220341
$845$	−45.1379	−1.55279
$846$	−0.173059	−0.00594989
$847$	−15.9925	−0.549508
$848$	−3.17696	−0.109097
$849$	3.48521	0.119612
$850$	−81.5515	−2.79719
$851$	16.5684	0.567956
$852$	8.87043	0.303896
$853$	−30.1895	−1.03367	−0.516834	−	0.856086i	$-0.672890\pi$
$853$	−30.1895	−1.03367	−0.516834	+	0.856086i	$0.672890\pi$
$854$	−12.1928	−0.417229
$855$	−35.4809	−1.21342
$856$	−2.38531	−0.0815282
$857$	−6.62907	−0.226445	−0.113222	−	0.993570i	$-0.536117\pi$
$857$	−6.62907	−0.226445	−0.113222	+	0.993570i	$0.536117\pi$
$858$	8.37982	0.286082
$859$	51.0364	1.74134	0.870670	−	0.491867i	$-0.163685\pi$
$859$	51.0364	1.74134	0.870670	+	0.491867i	$0.163685\pi$
$860$	18.8033	0.641186
$861$	−5.82591	−0.198546
$862$	−41.4801	−1.41282
$863$	11.4267	0.388970	0.194485	−	0.980906i	$-0.437696\pi$
$863$	11.4267	0.388970	0.194485	+	0.980906i	$0.437696\pi$
$864$	−1.00000	−0.0340207
$865$	−107.567	−3.65737
$866$	33.7144	1.14566
$867$	−17.7075	−0.601380
$868$	−9.30033	−0.315674
$869$	−57.6796	−1.95665
$870$	12.4345	0.421570
$871$	−20.1921	−0.684184
$872$	11.7876	0.399177
$873$	−3.65698	−0.123770
$874$	17.3104	0.585532
$875$	−38.3844	−1.29763
$876$	−3.52000	−0.118930
$877$	7.80037	0.263400	0.131700	−	0.991290i	$-0.457956\pi$
$877$	7.80037	0.263400	0.131700	+	0.991290i	$0.457956\pi$
$878$	7.79608	0.263105
$879$	−9.63755	−0.325066
$880$	−22.5524	−0.760241
$881$	−41.6883	−1.40451	−0.702257	−	0.711923i	$-0.747824\pi$
$881$	−41.6883	−1.40451	−0.702257	+	0.711923i	$0.747824\pi$
$882$	1.00000	0.0336718
$883$	−8.05475	−0.271064	−0.135532	−	0.990773i	$-0.543274\pi$
$883$	−8.05475	−0.271064	−0.135532	+	0.990773i	$0.543274\pi$
$884$	−9.50222	−0.319594
$885$	11.9862	0.402913
$886$	4.61865	0.155167
$887$	34.5199	1.15906	0.579532	−	0.814949i	$-0.303235\pi$
$887$	34.5199	1.15906	0.579532	+	0.814949i	$0.303235\pi$
$888$	7.82341	0.262536
$889$	12.6690	0.424903
$890$	−26.5113	−0.888660
$891$	−5.19543	−0.174053
$892$	18.0140	0.603155
$893$	1.41455	0.0473360
$894$	−21.1669	−0.707926
$895$	77.2948	2.58368
$896$	−1.00000	−0.0334077
$897$	3.41583	0.114051
$898$	4.91807	0.164118
$899$	−26.6414	−0.888540
$900$	13.8427	0.461422
$901$	18.7164	0.623535
$902$	30.2681	1.00782
$903$	4.33174	0.144151
$904$	−10.4172	−0.346470
$905$	−22.4729	−0.747023
$906$	−2.76036	−0.0917069
$907$	−4.45015	−0.147765	−0.0738824	−	0.997267i	$-0.523539\pi$
$907$	−4.45015	−0.147765	−0.0738824	+	0.997267i	$0.523539\pi$
$908$	−3.09131	−0.102589
$909$	−17.6653	−0.585921
$910$	−7.00139	−0.232094
$911$	−41.6853	−1.38110	−0.690548	−	0.723287i	$-0.742630\pi$
$911$	−41.6853	−1.38110	−0.690548	+	0.723287i	$0.742630\pi$
$912$	8.17378	0.270661
$913$	90.5817	2.99782
$914$	−24.5936	−0.813483
$915$	−52.9267	−1.74970
$916$	5.02521	0.166038
$917$	4.93578	0.162994
$918$	5.89131	0.194442
$919$	−16.6392	−0.548876	−0.274438	−	0.961605i	$-0.588492\pi$
$919$	−16.6392	−0.548876	−0.274438	+	0.961605i	$0.588492\pi$
$920$	−9.19295	−0.303083
$921$	−6.00865	−0.197992
$922$	31.1500	1.02587
$923$	−14.3073	−0.470931
$924$	−5.19543	−0.170917
$925$	−108.297	−3.56078
$926$	−22.2869	−0.732394
$927$	−3.13269	−0.102891
$928$	−2.86456	−0.0940338
$929$	37.5313	1.23136	0.615681	−	0.787996i	$-0.288881\pi$
$929$	37.5313	1.23136	0.615681	+	0.787996i	$0.288881\pi$
$930$	−40.3710	−1.32382
$931$	−8.17378	−0.267885
$932$	16.1692	0.529640
$933$	3.41392	0.111767
$934$	2.32091	0.0759425
$935$	132.863	4.34509
$936$	1.61292	0.0527200
$937$	34.1127	1.11441	0.557206	−	0.830374i	$-0.311873\pi$
$937$	34.1127	1.11441	0.557206	+	0.830374i	$0.311873\pi$
$938$	12.5190	0.408759
$939$	16.9242	0.552299
$940$	−0.751217	−0.0245020
$941$	24.2465	0.790413	0.395207	−	0.918592i	$-0.370673\pi$
$941$	24.2465	0.790413	0.395207	+	0.918592i	$0.370673\pi$
$942$	−5.71955	−0.186353
$943$	12.3381	0.401783
$944$	−2.76129	−0.0898722
$945$	4.34081	0.141207
$946$	−22.5052	−0.731708
$947$	29.3777	0.954646	0.477323	−	0.878728i	$-0.341607\pi$
$947$	29.3777	0.954646	0.477323	+	0.878728i	$0.341607\pi$
$948$	−11.1020	−0.360576
$949$	5.67748	0.184299
$950$	−113.147	−3.67097
$951$	−16.7195	−0.542168
$952$	5.89131	0.190938
$953$	−18.5193	−0.599898	−0.299949	−	0.953955i	$-0.596970\pi$
$953$	−18.5193	−0.599898	−0.299949	+	0.953955i	$0.596970\pi$
$954$	−3.17696	−0.102858
$955$	4.34081	0.140465
$956$	−6.70777	−0.216945
$957$	−14.8826	−0.481087
$958$	25.7647	0.832419
$959$	8.86611	0.286301
$960$	−4.34081	−0.140099
$961$	55.4962	1.79020
$962$	−12.6185	−0.406838
$963$	−2.38531	−0.0768655
$964$	−5.68401	−0.183070
$965$	−85.7343	−2.75988
$966$	−2.11779	−0.0681389
$967$	36.2141	1.16457	0.582284	−	0.812986i	$-0.302159\pi$
$967$	36.2141	1.16457	0.582284	+	0.812986i	$0.302159\pi$
$968$	15.9925	0.514018
$969$	−48.1543	−1.54694
$970$	−15.8743	−0.509693
$971$	38.8442	1.24657	0.623285	−	0.781995i	$-0.285798\pi$
$971$	38.8442	1.24657	0.623285	+	0.781995i	$0.285798\pi$
$972$	−1.00000	−0.0320750
$973$	−0.819394	−0.0262686
$974$	−13.2378	−0.424166
$975$	−22.3271	−0.715041
$976$	12.1928	0.390282
$977$	−57.1347	−1.82790	−0.913950	−	0.405826i	$-0.866984\pi$
$977$	−57.1347	−1.82790	−0.913950	+	0.405826i	$0.866984\pi$
$978$	6.48964	0.207516
$979$	31.7308	1.01412
$980$	4.34081	0.138662
$981$	11.7876	0.376348
$982$	−6.94398	−0.221591
$983$	41.6504	1.32844	0.664221	−	0.747536i	$-0.268763\pi$
$983$	41.6504	1.32844	0.664221	+	0.747536i	$0.268763\pi$
$984$	5.82591	0.185723
$985$	67.1221	2.13869
$986$	16.8760	0.537442
$987$	−0.173059	−0.00550853
$988$	−13.1837	−0.419428
$989$	−9.17373	−0.291708
$990$	−22.5524	−0.716762
$991$	9.60906	0.305242	0.152621	−	0.988285i	$-0.451229\pi$
$991$	9.60906	0.305242	0.152621	+	0.988285i	$0.451229\pi$
$992$	9.30033	0.295286
$993$	1.53715	0.0487798
$994$	8.87043	0.281353
$995$	5.75493	0.182444
$996$	17.4349	0.552445
$997$	−53.5901	−1.69722	−0.848608	−	0.529022i	$-0.822559\pi$
$997$	−53.5901	−1.69722	−0.848608	+	0.529022i	$0.822559\pi$
$998$	0.189643	0.00600305
$999$	7.82341	0.247522

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.q.1.9	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.q.1.9	✓	9	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:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.34081 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.34081 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.34081 q^{10} -5.19543 q^{11} -1.00000 q^{12} +1.61292 q^{13} -1.00000 q^{14} -4.34081 q^{15} +1.00000 q^{16} -5.89131 q^{17} +1.00000 q^{18} -8.17378 q^{19} +4.34081 q^{20} +1.00000 q^{21} -5.19543 q^{22} -2.11779 q^{23} -1.00000 q^{24} +13.8427 q^{25} +1.61292 q^{26} -1.00000 q^{27} -1.00000 q^{28} -2.86456 q^{29} -4.34081 q^{30} +9.30033 q^{31} +1.00000 q^{32} +5.19543 q^{33} -5.89131 q^{34} -4.34081 q^{35} +1.00000 q^{36} -7.82341 q^{37} -8.17378 q^{38} -1.61292 q^{39} +4.34081 q^{40} -5.82591 q^{41} +1.00000 q^{42} +4.33174 q^{43} -5.19543 q^{44} +4.34081 q^{45} -2.11779 q^{46} -0.173059 q^{47} -1.00000 q^{48} +1.00000 q^{49} +13.8427 q^{50} +5.89131 q^{51} +1.61292 q^{52} -3.17696 q^{53} -1.00000 q^{54} -22.5524 q^{55} -1.00000 q^{56} +8.17378 q^{57} -2.86456 q^{58} -2.76129 q^{59} -4.34081 q^{60} +12.1928 q^{61} +9.30033 q^{62} -1.00000 q^{63} +1.00000 q^{64} +7.00139 q^{65} +5.19543 q^{66} -12.5190 q^{67} -5.89131 q^{68} +2.11779 q^{69} -4.34081 q^{70} -8.87043 q^{71} +1.00000 q^{72} +3.52000 q^{73} -7.82341 q^{74} -13.8427 q^{75} -8.17378 q^{76} +5.19543 q^{77} -1.61292 q^{78} +11.1020 q^{79} +4.34081 q^{80} +1.00000 q^{81} -5.82591 q^{82} -17.4349 q^{83} +1.00000 q^{84} -25.5731 q^{85} +4.33174 q^{86} +2.86456 q^{87} -5.19543 q^{88} -6.10744 q^{89} +4.34081 q^{90} -1.61292 q^{91} -2.11779 q^{92} -9.30033 q^{93} -0.173059 q^{94} -35.4809 q^{95} -1.00000 q^{96} -3.65698 q^{97} +1.00000 q^{98} -5.19543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} - 9 q^{6} - 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 - 9 * q^6 - 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} - 9 q^{6} - 9 q^{7} + 9 q^{8} + 9 q^{9} + 6 q^{10} - 7 q^{11} - 9 q^{12} - q^{13} - 9 q^{14} - 6 q^{15} + 9 q^{16} - 10 q^{17} + 9 q^{18} + 6 q^{20} + 9 q^{21} - 7 q^{22} - 19 q^{23} - 9 q^{24} + 5 q^{25} - q^{26} - 9 q^{27} - 9 q^{28} - 21 q^{29} - 6 q^{30} + 6 q^{31} + 9 q^{32} + 7 q^{33} - 10 q^{34} - 6 q^{35} + 9 q^{36} - 14 q^{37} + q^{39} + 6 q^{40} + 12 q^{41} + 9 q^{42} - 17 q^{43} - 7 q^{44} + 6 q^{45} - 19 q^{46} - 11 q^{47} - 9 q^{48} + 9 q^{49} + 5 q^{50} + 10 q^{51} - q^{52} - 12 q^{53} - 9 q^{54} - 21 q^{55} - 9 q^{56} - 21 q^{58} - 8 q^{59} - 6 q^{60} + q^{61} + 6 q^{62} - 9 q^{63} + 9 q^{64} - 8 q^{65} + 7 q^{66} - 31 q^{67} - 10 q^{68} + 19 q^{69} - 6 q^{70} - 41 q^{71} + 9 q^{72} - q^{73} - 14 q^{74} - 5 q^{75} + 7 q^{77} + q^{78} - 17 q^{79} + 6 q^{80} + 9 q^{81} + 12 q^{82} - 36 q^{83} + 9 q^{84} - 30 q^{85} - 17 q^{86} + 21 q^{87} - 7 q^{88} - 17 q^{89} + 6 q^{90} + q^{91} - 19 q^{92} - 6 q^{93} - 11 q^{94} - 50 q^{95} - 9 q^{96} - 14 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 - 9 * q^6 - 9 * q^7 + 9 * q^8 + 9 * q^9 + 6 * q^10 - 7 * q^11 - 9 * q^12 - q^13 - 9 * q^14 - 6 * q^15 + 9 * q^16 - 10 * q^17 + 9 * q^18 + 6 * q^20 + 9 * q^21 - 7 * q^22 - 19 * q^23 - 9 * q^24 + 5 * q^25 - q^26 - 9 * q^27 - 9 * q^28 - 21 * q^29 - 6 * q^30 + 6 * q^31 + 9 * q^32 + 7 * q^33 - 10 * q^34 - 6 * q^35 + 9 * q^36 - 14 * q^37 + q^39 + 6 * q^40 + 12 * q^41 + 9 * q^42 - 17 * q^43 - 7 * q^44 + 6 * q^45 - 19 * q^46 - 11 * q^47 - 9 * q^48 + 9 * q^49 + 5 * q^50 + 10 * q^51 - q^52 - 12 * q^53 - 9 * q^54 - 21 * q^55 - 9 * q^56 - 21 * q^58 - 8 * q^59 - 6 * q^60 + q^61 + 6 * q^62 - 9 * q^63 + 9 * q^64 - 8 * q^65 + 7 * q^66 - 31 * q^67 - 10 * q^68 + 19 * q^69 - 6 * q^70 - 41 * q^71 + 9 * q^72 - q^73 - 14 * q^74 - 5 * q^75 + 7 * q^77 + q^78 - 17 * q^79 + 6 * q^80 + 9 * q^81 + 12 * q^82 - 36 * q^83 + 9 * q^84 - 30 * q^85 - 17 * q^86 + 21 * q^87 - 7 * q^88 - 17 * q^89 + 6 * q^90 + q^91 - 19 * q^92 - 6 * q^93 - 11 * q^94 - 50 * q^95 - 9 * q^96 - 14 * q^97 + 9 * q^98 - 7 * q^99

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