LMFDB - Embedded newform 1334.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$10.6520436296$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.207184.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 2x^{2} + 7x - 1 $ x^5 - x^4 - 6x^3 + 2x^2 + 7*x - 1
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			1.2
Root			$-1.31977$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.17692 q^{3} +1.00000 q^{4} -3.87305 q^{5} +1.17692 q^{6} -1.06158 q^{7} -1.00000 q^{8} -1.61485 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.17692 q^{3} +1.00000 q^{4} -3.87305 q^{5} +1.17692 q^{6} -1.06158 q^{7} -1.00000 q^{8} -1.61485 q^{9} +3.87305 q^{10} +4.42632 q^{11} -1.17692 q^{12} +1.85336 q^{13} +1.06158 q^{14} +4.55828 q^{15} +1.00000 q^{16} +5.59235 q^{17} +1.61485 q^{18} +0.300083 q^{19} -3.87305 q^{20} +1.24940 q^{21} -4.42632 q^{22} +1.00000 q^{23} +1.17692 q^{24} +10.0005 q^{25} -1.85336 q^{26} +5.43133 q^{27} -1.06158 q^{28} +1.00000 q^{29} -4.55828 q^{30} -6.83518 q^{31} -1.00000 q^{32} -5.20944 q^{33} -5.59235 q^{34} +4.11155 q^{35} -1.61485 q^{36} -8.42253 q^{37} -0.300083 q^{38} -2.18126 q^{39} +3.87305 q^{40} +2.10807 q^{41} -1.24940 q^{42} -11.0265 q^{43} +4.42632 q^{44} +6.25440 q^{45} -1.00000 q^{46} +1.82808 q^{47} -1.17692 q^{48} -5.87305 q^{49} -10.0005 q^{50} -6.58176 q^{51} +1.85336 q^{52} +10.1355 q^{53} -5.43133 q^{54} -17.1433 q^{55} +1.06158 q^{56} -0.353174 q^{57} -1.00000 q^{58} -0.523572 q^{59} +4.55828 q^{60} -12.5301 q^{61} +6.83518 q^{62} +1.71430 q^{63} +1.00000 q^{64} -7.17814 q^{65} +5.20944 q^{66} -2.77306 q^{67} +5.59235 q^{68} -1.17692 q^{69} -4.11155 q^{70} -9.91865 q^{71} +1.61485 q^{72} +12.1020 q^{73} +8.42253 q^{74} -11.7698 q^{75} +0.300083 q^{76} -4.69889 q^{77} +2.18126 q^{78} +3.57208 q^{79} -3.87305 q^{80} -1.54769 q^{81} -2.10807 q^{82} +6.28919 q^{83} +1.24940 q^{84} -21.6594 q^{85} +11.0265 q^{86} -1.17692 q^{87} -4.42632 q^{88} -0.624227 q^{89} -6.25440 q^{90} -1.96749 q^{91} +1.00000 q^{92} +8.04448 q^{93} -1.82808 q^{94} -1.16224 q^{95} +1.17692 q^{96} -11.4351 q^{97} +5.87305 q^{98} -7.14786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + q^{3} + 5 q^{4} - 5 q^{5} - q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 + q^3 + 5 * q^4 - 5 * q^5 - q^6 - 2 * q^7 - 5 * q^8 + 2 * q^9	\( 5 q - 5 q^{2} + q^{3} + 5 q^{4} - 5 q^{5} - q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9} + 5 q^{10} + q^{11} + q^{12} - 11 q^{13} + 2 q^{14} + 5 q^{15} + 5 q^{16} + 4 q^{17} - 2 q^{18} - 12 q^{19} - 5 q^{20} - 8 q^{21} - q^{22} + 5 q^{23} - q^{24} - 4 q^{25} + 11 q^{26} - 5 q^{27} - 2 q^{28} + 5 q^{29} - 5 q^{30} - 5 q^{31} - 5 q^{32} - 11 q^{33} - 4 q^{34} - 4 q^{35} + 2 q^{36} + 12 q^{38} - 9 q^{39} + 5 q^{40} - 6 q^{41} + 8 q^{42} - 7 q^{43} + q^{44} + 6 q^{45} - 5 q^{46} + 5 q^{47} + q^{48} - 15 q^{49} + 4 q^{50} - 42 q^{51} - 11 q^{52} - q^{53} + 5 q^{54} - 31 q^{55} + 2 q^{56} - 4 q^{57} - 5 q^{58} - 12 q^{59} + 5 q^{60} - 20 q^{61} + 5 q^{62} + 10 q^{63} + 5 q^{64} + 3 q^{65} + 11 q^{66} - 4 q^{67} + 4 q^{68} + q^{69} + 4 q^{70} - 4 q^{71} - 2 q^{72} + 4 q^{73} - 12 q^{75} - 12 q^{76} + 14 q^{77} + 9 q^{78} - q^{79} - 5 q^{80} - 23 q^{81} + 6 q^{82} + 22 q^{83} - 8 q^{84} - 16 q^{85} + 7 q^{86} + q^{87} - q^{88} + 8 q^{89} - 6 q^{90} - 18 q^{91} + 5 q^{92} - 37 q^{93} - 5 q^{94} + 18 q^{95} - q^{96} - 46 q^{97} + 15 q^{98} - 24 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + q^3 + 5 * q^4 - 5 * q^5 - q^6 - 2 * q^7 - 5 * q^8 + 2 * q^9 + 5 * q^10 + q^11 + q^12 - 11 * q^13 + 2 * q^14 + 5 * q^15 + 5 * q^16 + 4 * q^17 - 2 * q^18 - 12 * q^19 - 5 * q^20 - 8 * q^21 - q^22 + 5 * q^23 - q^24 - 4 * q^25 + 11 * q^26 - 5 * q^27 - 2 * q^28 + 5 * q^29 - 5 * q^30 - 5 * q^31 - 5 * q^32 - 11 * q^33 - 4 * q^34 - 4 * q^35 + 2 * q^36 + 12 * q^38 - 9 * q^39 + 5 * q^40 - 6 * q^41 + 8 * q^42 - 7 * q^43 + q^44 + 6 * q^45 - 5 * q^46 + 5 * q^47 + q^48 - 15 * q^49 + 4 * q^50 - 42 * q^51 - 11 * q^52 - q^53 + 5 * q^54 - 31 * q^55 + 2 * q^56 - 4 * q^57 - 5 * q^58 - 12 * q^59 + 5 * q^60 - 20 * q^61 + 5 * q^62 + 10 * q^63 + 5 * q^64 + 3 * q^65 + 11 * q^66 - 4 * q^67 + 4 * q^68 + q^69 + 4 * q^70 - 4 * q^71 - 2 * q^72 + 4 * q^73 - 12 * q^75 - 12 * q^76 + 14 * q^77 + 9 * q^78 - q^79 - 5 * q^80 - 23 * q^81 + 6 * q^82 + 22 * q^83 - 8 * q^84 - 16 * q^85 + 7 * q^86 + q^87 - q^88 + 8 * q^89 - 6 * q^90 - 18 * q^91 + 5 * q^92 - 37 * q^93 - 5 * q^94 + 18 * q^95 - q^96 - 46 * q^97 + 15 * q^98 - 24 * 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
$3$	−1.17692	−0.679497	−0.339748	−	0.940516i	$-0.610342\pi$
$3$	−1.17692	−0.679497	−0.339748	+	0.940516i	$0.610342\pi$
$4$	1.00000	0.500000
$5$	−3.87305	−1.73208	−0.866040	−	0.499975i	$-0.833342\pi$
$5$	−3.87305	−1.73208	−0.866040	+	0.499975i	$0.833342\pi$
$6$	1.17692	0.480477
$7$	−1.06158	−0.401240	−0.200620	−	0.979669i	$-0.564296\pi$
$7$	−1.06158	−0.401240	−0.200620	+	0.979669i	$0.564296\pi$
$8$	−1.00000	−0.353553
$9$	−1.61485	−0.538284
$10$	3.87305	1.22477
$11$	4.42632	1.33459	0.667293	−	0.744795i	$-0.267453\pi$
$11$	4.42632	1.33459	0.667293	+	0.744795i	$0.267453\pi$
$12$	−1.17692	−0.339748
$13$	1.85336	0.514028	0.257014	−	0.966408i	$-0.417261\pi$
$13$	1.85336	0.514028	0.257014	+	0.966408i	$0.417261\pi$
$14$	1.06158	0.283719
$15$	4.55828	1.17694
$16$	1.00000	0.250000
$17$	5.59235	1.35634	0.678172	−	0.734903i	$-0.262773\pi$
$17$	5.59235	1.35634	0.678172	+	0.734903i	$0.262773\pi$
$18$	1.61485	0.380624
$19$	0.300083	0.0688438	0.0344219	−	0.999407i	$-0.489041\pi$
$19$	0.300083	0.0688438	0.0344219	+	0.999407i	$0.489041\pi$
$20$	−3.87305	−0.866040
$21$	1.24940	0.272641
$22$	−4.42632	−0.943695
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.17692	0.240238
$25$	10.0005	2.00010
$26$	−1.85336	−0.363473
$27$	5.43133	1.04526
$28$	−1.06158	−0.200620
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−4.55828	−0.832224
$31$	−6.83518	−1.22764	−0.613818	−	0.789448i	$-0.710367\pi$
$31$	−6.83518	−1.22764	−0.613818	+	0.789448i	$0.710367\pi$
$32$	−1.00000	−0.176777
$33$	−5.20944	−0.906847
$34$	−5.59235	−0.959080
$35$	4.11155	0.694979
$36$	−1.61485	−0.269142
$37$	−8.42253	−1.38466	−0.692328	−	0.721583i	$-0.743415\pi$
$37$	−8.42253	−1.38466	−0.692328	+	0.721583i	$0.743415\pi$
$38$	−0.300083	−0.0486799
$39$	−2.18126	−0.349281
$40$	3.87305	0.612383
$41$	2.10807	0.329225	0.164612	−	0.986358i	$-0.447363\pi$
$41$	2.10807	0.329225	0.164612	+	0.986358i	$0.447363\pi$
$42$	−1.24940	−0.192786
$43$	−11.0265	−1.68152	−0.840762	−	0.541405i	$-0.817892\pi$
$43$	−11.0265	−1.68152	−0.840762	+	0.541405i	$0.817892\pi$
$44$	4.42632	0.667293
$45$	6.25440	0.932351
$46$	−1.00000	−0.147442
$47$	1.82808	0.266653	0.133327	−	0.991072i	$-0.457434\pi$
$47$	1.82808	0.266653	0.133327	+	0.991072i	$0.457434\pi$
$48$	−1.17692	−0.169874
$49$	−5.87305	−0.839007
$50$	−10.0005	−1.41428
$51$	−6.58176	−0.921631
$52$	1.85336	0.257014
$53$	10.1355	1.39222	0.696111	−	0.717934i	$-0.254912\pi$
$53$	10.1355	1.39222	0.696111	+	0.717934i	$0.254912\pi$
$54$	−5.43133	−0.739110
$55$	−17.1433	−2.31161
$56$	1.06158	0.141860
$57$	−0.353174	−0.0467791
$58$	−1.00000	−0.131306
$59$	−0.523572	−0.0681632	−0.0340816	−	0.999419i	$-0.510851\pi$
$59$	−0.523572	−0.0681632	−0.0340816	+	0.999419i	$0.510851\pi$
$60$	4.55828	0.588471
$61$	−12.5301	−1.60431	−0.802154	−	0.597117i	$-0.796313\pi$
$61$	−12.5301	−1.60431	−0.802154	+	0.597117i	$0.796313\pi$
$62$	6.83518	0.868069
$63$	1.71430	0.215981
$64$	1.00000	0.125000
$65$	−7.17814	−0.890338
$66$	5.20944	0.641237
$67$	−2.77306	−0.338784	−0.169392	−	0.985549i	$-0.554180\pi$
$67$	−2.77306	−0.338784	−0.169392	+	0.985549i	$0.554180\pi$
$68$	5.59235	0.678172
$69$	−1.17692	−0.141685
$70$	−4.11155	−0.491424
$71$	−9.91865	−1.17713	−0.588564	−	0.808451i	$-0.700306\pi$
$71$	−9.91865	−1.17713	−0.588564	+	0.808451i	$0.700306\pi$
$72$	1.61485	0.190312
$73$	12.1020	1.41644	0.708218	−	0.705994i	$-0.249499\pi$
$73$	12.1020	1.41644	0.708218	+	0.705994i	$0.249499\pi$
$74$	8.42253	0.979099
$75$	−11.7698	−1.35906
$76$	0.300083	0.0344219
$77$	−4.69889	−0.535489
$78$	2.18126	0.246979
$79$	3.57208	0.401890	0.200945	−	0.979602i	$-0.435599\pi$
$79$	3.57208	0.401890	0.200945	+	0.979602i	$0.435599\pi$
$80$	−3.87305	−0.433020
$81$	−1.54769	−0.171966
$82$	−2.10807	−0.232797
$83$	6.28919	0.690328	0.345164	−	0.938542i	$-0.387823\pi$
$83$	6.28919	0.690328	0.345164	+	0.938542i	$0.387823\pi$
$84$	1.24940	0.136320
$85$	−21.6594	−2.34930
$86$	11.0265	1.18902
$87$	−1.17692	−0.126179
$88$	−4.42632	−0.471847
$89$	−0.624227	−0.0661679	−0.0330840	−	0.999453i	$-0.510533\pi$
$89$	−0.624227	−0.0661679	−0.0330840	+	0.999453i	$0.510533\pi$
$90$	−6.25440	−0.659272
$91$	−1.96749	−0.206249
$92$	1.00000	0.104257
$93$	8.04448	0.834174
$94$	−1.82808	−0.188552
$95$	−1.16224	−0.119243
$96$	1.17692	0.120119
$97$	−11.4351	−1.16106	−0.580530	−	0.814239i	$-0.697155\pi$
$97$	−11.4351	−1.16106	−0.580530	+	0.814239i	$0.697155\pi$
$98$	5.87305	0.593267
$99$	−7.14786	−0.718387
$100$	10.0005	1.00005
$101$	−16.4262	−1.63447	−0.817236	−	0.576303i	$-0.804495\pi$
$101$	−16.4262	−1.63447	−0.817236	+	0.576303i	$0.804495\pi$
$102$	6.58176	0.651691
$103$	6.86868	0.676791	0.338395	−	0.941004i	$-0.390116\pi$
$103$	6.86868	0.676791	0.338395	+	0.941004i	$0.390116\pi$
$104$	−1.85336	−0.181736
$105$	−4.83898	−0.472236
$106$	−10.1355	−0.984450
$107$	7.75172	0.749387	0.374694	−	0.927149i	$-0.377748\pi$
$107$	7.75172	0.749387	0.374694	+	0.927149i	$0.377748\pi$
$108$	5.43133	0.522630
$109$	20.7471	1.98721	0.993605	−	0.112908i	$-0.0360166\pi$
$109$	20.7471	1.98721	0.993605	+	0.112908i	$0.0360166\pi$
$110$	17.1433	1.63455
$111$	9.91266	0.940868
$112$	−1.06158	−0.100310
$113$	−2.54515	−0.239427	−0.119714	−	0.992808i	$-0.538198\pi$
$113$	−2.54515	−0.239427	−0.119714	+	0.992808i	$0.538198\pi$
$114$	0.353174	0.0330778
$115$	−3.87305	−0.361164
$116$	1.00000	0.0928477
$117$	−2.99290	−0.276693
$118$	0.523572	0.0481987
$119$	−5.93673	−0.544219
$120$	−4.55828	−0.416112
$121$	8.59231	0.781119
$122$	12.5301	1.13442
$123$	−2.48103	−0.223707
$124$	−6.83518	−0.613818
$125$	−19.3672	−1.73225
$126$	−1.71430	−0.152722
$127$	3.79549	0.336795	0.168398	−	0.985719i	$-0.446141\pi$
$127$	3.79549	0.336795	0.168398	+	0.985719i	$0.446141\pi$
$128$	−1.00000	−0.0883883
$129$	12.9773	1.14259
$130$	7.17814	0.629564
$131$	4.03461	0.352506	0.176253	−	0.984345i	$-0.443602\pi$
$131$	4.03461	0.352506	0.176253	+	0.984345i	$0.443602\pi$
$132$	−5.20944	−0.453423
$133$	−0.318562	−0.0276228
$134$	2.77306	0.239556
$135$	−21.0358	−1.81047
$136$	−5.59235	−0.479540
$137$	−1.95835	−0.167313	−0.0836564	−	0.996495i	$-0.526660\pi$
$137$	−1.95835	−0.167313	−0.0836564	+	0.996495i	$0.526660\pi$
$138$	1.17692	0.100186
$139$	−8.41485	−0.713738	−0.356869	−	0.934154i	$-0.616156\pi$
$139$	−8.41485	−0.713738	−0.356869	+	0.934154i	$0.616156\pi$
$140$	4.11155	0.347489
$141$	−2.15151	−0.181190
$142$	9.91865	0.832354
$143$	8.20355	0.686015
$144$	−1.61485	−0.134571
$145$	−3.87305	−0.321639
$146$	−12.1020	−1.00157
$147$	6.91212	0.570102
$148$	−8.42253	−0.692328
$149$	−17.6822	−1.44859	−0.724293	−	0.689492i	$-0.757834\pi$
$149$	−17.6822	−1.44859	−0.724293	+	0.689492i	$0.757834\pi$
$150$	11.7698	0.961001
$151$	−22.7142	−1.84846	−0.924228	−	0.381840i	$-0.875290\pi$
$151$	−22.7142	−1.84846	−0.924228	+	0.381840i	$0.875290\pi$
$152$	−0.300083	−0.0243399
$153$	−9.03082	−0.730099
$154$	4.69889	0.378648
$155$	26.4730	2.12636
$156$	−2.18126	−0.174640
$157$	−23.0201	−1.83720	−0.918602	−	0.395183i	$-0.870681\pi$
$157$	−23.0201	−1.83720	−0.918602	+	0.395183i	$0.870681\pi$
$158$	−3.57208	−0.284179
$159$	−11.9287	−0.946010
$160$	3.87305	0.306191
$161$	−1.06158	−0.0836642
$162$	1.54769	0.121598
$163$	3.11382	0.243893	0.121947	−	0.992537i	$-0.461086\pi$
$163$	3.11382	0.243893	0.121947	+	0.992537i	$0.461086\pi$
$164$	2.10807	0.164612
$165$	20.1764	1.57073
$166$	−6.28919	−0.488136
$167$	−14.0509	−1.08729	−0.543646	−	0.839314i	$-0.682957\pi$
$167$	−14.0509	−1.08729	−0.543646	+	0.839314i	$0.682957\pi$
$168$	−1.24940	−0.0963931
$169$	−9.56507	−0.735775
$170$	21.6594	1.66120
$171$	−0.484590	−0.0370575
$172$	−11.0265	−0.840762
$173$	0.151918	0.0115501	0.00577506	−	0.999983i	$-0.498162\pi$
$173$	0.151918	0.0115501	0.00577506	+	0.999983i	$0.498162\pi$
$174$	1.17692	0.0892223
$175$	−10.6163	−0.802519
$176$	4.42632	0.333646
$177$	0.616203	0.0463167
$178$	0.624227	0.0467878
$179$	−16.3982	−1.22566	−0.612831	−	0.790214i	$-0.709970\pi$
$179$	−16.3982	−1.22566	−0.612831	+	0.790214i	$0.709970\pi$
$180$	6.25440	0.466176
$181$	−2.05296	−0.152595	−0.0762975	−	0.997085i	$-0.524310\pi$
$181$	−2.05296	−0.152595	−0.0762975	+	0.997085i	$0.524310\pi$
$182$	1.96749	0.145840
$183$	14.7469	1.09012
$184$	−1.00000	−0.0737210
$185$	32.6209	2.39833
$186$	−8.04448	−0.589850
$187$	24.7535	1.81016
$188$	1.82808	0.133327
$189$	−5.76579	−0.419399
$190$	1.16224	0.0843174
$191$	15.3477	1.11052	0.555262	−	0.831676i	$-0.312618\pi$
$191$	15.3477	1.11052	0.555262	+	0.831676i	$0.312618\pi$
$192$	−1.17692	−0.0849371
$193$	21.9050	1.57676	0.788380	−	0.615189i	$-0.210920\pi$
$193$	21.9050	1.57676	0.788380	+	0.615189i	$0.210920\pi$
$194$	11.4351	0.820994
$195$	8.44811	0.604982
$196$	−5.87305	−0.419503
$197$	−23.0501	−1.64225	−0.821125	−	0.570749i	$-0.806653\pi$
$197$	−23.0501	−1.64225	−0.821125	+	0.570749i	$0.806653\pi$
$198$	7.14786	0.507976
$199$	−5.54301	−0.392934	−0.196467	−	0.980510i	$-0.562947\pi$
$199$	−5.54301	−0.392934	−0.196467	+	0.980510i	$0.562947\pi$
$200$	−10.0005	−0.707142
$201$	3.26368	0.230202
$202$	16.4262	1.15575
$203$	−1.06158	−0.0745083
$204$	−6.58176	−0.460815
$205$	−8.16464	−0.570243
$206$	−6.86868	−0.478563
$207$	−1.61485	−0.112240
$208$	1.85336	0.128507
$209$	1.32826	0.0918779
$210$	4.83898	0.333921
$211$	12.2622	0.844163	0.422082	−	0.906558i	$-0.361300\pi$
$211$	12.2622	0.844163	0.422082	+	0.906558i	$0.361300\pi$
$212$	10.1355	0.696111
$213$	11.6735	0.799854
$214$	−7.75172	−0.529897
$215$	42.7061	2.91253
$216$	−5.43133	−0.369555
$217$	7.25610	0.492576
$218$	−20.7471	−1.40517
$219$	−14.2432	−0.962464
$220$	−17.1433	−1.15580
$221$	10.3646	0.697199
$222$	−9.91266	−0.665294
$223$	12.1408	0.813011	0.406506	−	0.913648i	$-0.366747\pi$
$223$	12.1408	0.813011	0.406506	+	0.913648i	$0.366747\pi$
$224$	1.06158	0.0709298
$225$	−16.1493	−1.07662
$226$	2.54515	0.169301
$227$	−21.9961	−1.45993	−0.729966	−	0.683484i	$-0.760464\pi$
$227$	−21.9961	−1.45993	−0.729966	+	0.683484i	$0.760464\pi$
$228$	−0.353174	−0.0233896
$229$	−15.2770	−1.00953	−0.504766	−	0.863256i	$-0.668421\pi$
$229$	−15.2770	−1.00953	−0.504766	+	0.863256i	$0.668421\pi$
$230$	3.87305	0.255381
$231$	5.53023	0.363863
$232$	−1.00000	−0.0656532
$233$	8.76789	0.574403	0.287202	−	0.957870i	$-0.407275\pi$
$233$	8.76789	0.574403	0.287202	+	0.957870i	$0.407275\pi$
$234$	2.99290	0.195652
$235$	−7.08025	−0.461865
$236$	−0.523572	−0.0340816
$237$	−4.20406	−0.273083
$238$	5.93673	0.384821
$239$	25.3026	1.63669	0.818345	−	0.574728i	$-0.194892\pi$
$239$	25.3026	1.63669	0.818345	+	0.574728i	$0.194892\pi$
$240$	4.55828	0.294236
$241$	−19.3181	−1.24439	−0.622195	−	0.782862i	$-0.713759\pi$
$241$	−19.3181	−1.24439	−0.622195	+	0.782862i	$0.713759\pi$
$242$	−8.59231	−0.552335
$243$	−14.4725	−0.928409
$244$	−12.5301	−0.802154
$245$	22.7466	1.45323
$246$	2.48103	0.158185
$247$	0.556161	0.0353876
$248$	6.83518	0.434035
$249$	−7.40189	−0.469076
$250$	19.3672	1.22489
$251$	−0.420694	−0.0265540	−0.0132770	−	0.999912i	$-0.504226\pi$
$251$	−0.420694	−0.0265540	−0.0132770	+	0.999912i	$0.504226\pi$
$252$	1.71430	0.107990
$253$	4.42632	0.278280
$254$	−3.79549	−0.238150
$255$	25.4915	1.59634
$256$	1.00000	0.0625000
$257$	−23.4621	−1.46352	−0.731762	−	0.681561i	$-0.761302\pi$
$257$	−23.4621	−1.46352	−0.731762	+	0.681561i	$0.761302\pi$
$258$	−12.9773	−0.807933
$259$	8.94119	0.555578
$260$	−7.17814	−0.445169
$261$	−1.61485	−0.0999569
$262$	−4.03461	−0.249259
$263$	23.8357	1.46977	0.734887	−	0.678190i	$-0.237235\pi$
$263$	23.8357	1.46977	0.734887	+	0.678190i	$0.237235\pi$
$264$	5.20944	0.320619
$265$	−39.2554	−2.41144
$266$	0.318562	0.0195323
$267$	0.734667	0.0449609
$268$	−2.77306	−0.169392
$269$	−17.0462	−1.03933	−0.519663	−	0.854371i	$-0.673942\pi$
$269$	−17.0462	−1.03933	−0.519663	+	0.854371i	$0.673942\pi$
$270$	21.0358	1.28020
$271$	−7.73234	−0.469706	−0.234853	−	0.972031i	$-0.575461\pi$
$271$	−7.73234	−0.469706	−0.234853	+	0.972031i	$0.575461\pi$
$272$	5.59235	0.339086
$273$	2.31558	0.140145
$274$	1.95835	0.118308
$275$	44.2654	2.66930
$276$	−1.17692	−0.0708424
$277$	−0.523184	−0.0314351	−0.0157175	−	0.999876i	$-0.505003\pi$
$277$	−0.523184	−0.0314351	−0.0157175	+	0.999876i	$0.505003\pi$
$278$	8.41485	0.504689
$279$	11.0378	0.660817
$280$	−4.11155	−0.245712
$281$	1.26883	0.0756918	0.0378459	−	0.999284i	$-0.487950\pi$
$281$	1.26883	0.0756918	0.0378459	+	0.999284i	$0.487950\pi$
$282$	2.15151	0.128121
$283$	−8.58329	−0.510223	−0.255112	−	0.966912i	$-0.582112\pi$
$283$	−8.58329	−0.510223	−0.255112	+	0.966912i	$0.582112\pi$
$284$	−9.91865	−0.588564
$285$	1.36786	0.0810251
$286$	−8.20355	−0.485086
$287$	−2.23788	−0.132098
$288$	1.61485	0.0951561
$289$	14.2744	0.839668
$290$	3.87305	0.227433
$291$	13.4582	0.788937
$292$	12.1020	0.708218
$293$	−22.7894	−1.33137	−0.665686	−	0.746232i	$-0.731861\pi$
$293$	−22.7894	−1.33137	−0.665686	+	0.746232i	$0.731861\pi$
$294$	−6.91212	−0.403123
$295$	2.02782	0.118064
$296$	8.42253	0.489550
$297$	24.0408	1.39499
$298$	17.6822	1.02430
$299$	1.85336	0.107182
$300$	−11.7698	−0.679530
$301$	11.7055	0.674694
$302$	22.7142	1.30706
$303$	19.3324	1.11062
$304$	0.300083	0.0172109
$305$	48.5295	2.77879
$306$	9.03082	0.516258
$307$	5.18389	0.295860	0.147930	−	0.988998i	$-0.452739\pi$
$307$	5.18389	0.295860	0.147930	+	0.988998i	$0.452739\pi$
$308$	−4.69889	−0.267744
$309$	−8.08390	−0.459877
$310$	−26.4730	−1.50357
$311$	19.5799	1.11027	0.555136	−	0.831760i	$-0.312666\pi$
$311$	19.5799	1.11027	0.555136	+	0.831760i	$0.312666\pi$
$312$	2.18126	0.123489
$313$	−7.12294	−0.402613	−0.201306	−	0.979528i	$-0.564519\pi$
$313$	−7.12294	−0.402613	−0.201306	+	0.979528i	$0.564519\pi$
$314$	23.0201	1.29910
$315$	−6.63955	−0.374096
$316$	3.57208	0.200945
$317$	−19.4778	−1.09398	−0.546990	−	0.837139i	$-0.684227\pi$
$317$	−19.4778	−1.09398	−0.546990	+	0.837139i	$0.684227\pi$
$318$	11.9287	0.668930
$319$	4.42632	0.247826
$320$	−3.87305	−0.216510
$321$	−9.12318	−0.509206
$322$	1.06158	0.0591595
$323$	1.67817	0.0933758
$324$	−1.54769	−0.0859828
$325$	18.5345	1.02811
$326$	−3.11382	−0.172459
$327$	−24.4177	−1.35030
$328$	−2.10807	−0.116399
$329$	−1.94066	−0.106992
$330$	−20.1764	−1.11067
$331$	−14.0747	−0.773615	−0.386807	−	0.922161i	$-0.626422\pi$
$331$	−14.0747	−0.773615	−0.386807	+	0.922161i	$0.626422\pi$
$332$	6.28919	0.345164
$333$	13.6011	0.745338
$334$	14.0509	0.768832
$335$	10.7402	0.586800
$336$	1.24940	0.0681602
$337$	26.9446	1.46776	0.733882	−	0.679277i	$-0.237707\pi$
$337$	26.9446	1.46776	0.733882	+	0.679277i	$0.237707\pi$
$338$	9.56507	0.520271
$339$	2.99544	0.162690
$340$	−21.6594	−1.17465
$341$	−30.2547	−1.63838
$342$	0.484590	0.0262036
$343$	13.6658	0.737882
$344$	11.0265	0.594508
$345$	4.55828	0.245409
$346$	−0.151918	−0.00816716
$347$	31.7168	1.70265	0.851323	−	0.524642i	$-0.175801\pi$
$347$	31.7168	1.70265	0.851323	+	0.524642i	$0.175801\pi$
$348$	−1.17692	−0.0630897
$349$	3.43111	0.183663	0.0918315	−	0.995775i	$-0.470728\pi$
$349$	3.43111	0.183663	0.0918315	+	0.995775i	$0.470728\pi$
$350$	10.6163	0.567467
$351$	10.0662	0.537293
$352$	−4.42632	−0.235924
$353$	−8.61159	−0.458349	−0.229174	−	0.973385i	$-0.573603\pi$
$353$	−8.61159	−0.458349	−0.229174	+	0.973385i	$0.573603\pi$
$354$	−0.616203	−0.0327508
$355$	38.4154	2.03888
$356$	−0.624227	−0.0330840
$357$	6.98707	0.369795
$358$	16.3982	0.866674
$359$	3.05353	0.161159	0.0805797	−	0.996748i	$-0.474323\pi$
$359$	3.05353	0.161159	0.0805797	+	0.996748i	$0.474323\pi$
$360$	−6.25440	−0.329636
$361$	−18.9100	−0.995261
$362$	2.05296	0.107901
$363$	−10.1125	−0.530768
$364$	−1.96749	−0.103124
$365$	−46.8718	−2.45338
$366$	−14.7469	−0.770833
$367$	−15.6761	−0.818288	−0.409144	−	0.912470i	$-0.634173\pi$
$367$	−15.6761	−0.818288	−0.409144	+	0.912470i	$0.634173\pi$
$368$	1.00000	0.0521286
$369$	−3.40422	−0.177216
$370$	−32.6209	−1.69588
$371$	−10.7597	−0.558615
$372$	8.04448	0.417087
$373$	23.7103	1.22768	0.613838	−	0.789432i	$-0.289625\pi$
$373$	23.7103	1.22768	0.613838	+	0.789432i	$0.289625\pi$
$374$	−24.7535	−1.27997
$375$	22.7937	1.17706
$376$	−1.82808	−0.0942761
$377$	1.85336	0.0954527
$378$	5.76579	0.296560
$379$	6.79647	0.349111	0.174556	−	0.984647i	$-0.444151\pi$
$379$	6.79647	0.349111	0.174556	+	0.984647i	$0.444151\pi$
$380$	−1.16224	−0.0596214
$381$	−4.46700	−0.228851
$382$	−15.3477	−0.785259
$383$	−27.0871	−1.38409	−0.692044	−	0.721855i	$-0.743290\pi$
$383$	−27.0871	−1.38409	−0.692044	+	0.721855i	$0.743290\pi$
$384$	1.17692	0.0600596
$385$	18.1990	0.927509
$386$	−21.9050	−1.11494
$387$	17.8062	0.905138
$388$	−11.4351	−0.580530
$389$	−3.92583	−0.199048	−0.0995238	−	0.995035i	$-0.531732\pi$
$389$	−3.92583	−0.199048	−0.0995238	+	0.995035i	$0.531732\pi$
$390$	−8.44811	−0.427787
$391$	5.59235	0.282817
$392$	5.87305	0.296634
$393$	−4.74843	−0.239526
$394$	23.0501	1.16125
$395$	−13.8348	−0.696106
$396$	−7.14786	−0.359193
$397$	23.5375	1.18131	0.590657	−	0.806923i	$-0.298869\pi$
$397$	23.5375	1.18131	0.590657	+	0.806923i	$0.298869\pi$
$398$	5.54301	0.277846
$399$	0.374923	0.0187696
$400$	10.0005	0.500025
$401$	−25.7386	−1.28532	−0.642662	−	0.766150i	$-0.722170\pi$
$401$	−25.7386	−1.28532	−0.642662	+	0.766150i	$0.722170\pi$
$402$	−3.26368	−0.162778
$403$	−12.6680	−0.631040
$404$	−16.4262	−0.817236
$405$	5.99428	0.297858
$406$	1.06158	0.0526853
$407$	−37.2808	−1.84794
$408$	6.58176	0.325846
$409$	−10.2618	−0.507414	−0.253707	−	0.967281i	$-0.581650\pi$
$409$	−10.2618	−0.507414	−0.253707	+	0.967281i	$0.581650\pi$
$410$	8.16464	0.403223
$411$	2.30482	0.113688
$412$	6.86868	0.338395
$413$	0.555813	0.0273498
$414$	1.61485	0.0793657
$415$	−24.3583	−1.19570
$416$	−1.85336	−0.0908682
$417$	9.90363	0.484983
$418$	−1.32826	−0.0649675
$419$	10.9415	0.534528	0.267264	−	0.963623i	$-0.413880\pi$
$419$	10.9415	0.534528	0.267264	+	0.963623i	$0.413880\pi$
$420$	−4.83898	−0.236118
$421$	−14.2491	−0.694461	−0.347230	−	0.937780i	$-0.612878\pi$
$421$	−14.2491	−0.694461	−0.347230	+	0.937780i	$0.612878\pi$
$422$	−12.2622	−0.596913
$423$	−2.95208	−0.143535
$424$	−10.1355	−0.492225
$425$	55.9263	2.71282
$426$	−11.6735	−0.565582
$427$	13.3017	0.643712
$428$	7.75172	0.374694
$429$	−9.65494	−0.466145
$430$	−42.7061	−2.05947
$431$	32.3791	1.55964	0.779822	−	0.626001i	$-0.215309\pi$
$431$	32.3791	1.55964	0.779822	+	0.626001i	$0.215309\pi$
$432$	5.43133	0.261315
$433$	22.3305	1.07314	0.536568	−	0.843857i	$-0.319721\pi$
$433$	22.3305	1.07314	0.536568	+	0.843857i	$0.319721\pi$
$434$	−7.25610	−0.348304
$435$	4.55828	0.218553
$436$	20.7471	0.993605
$437$	0.300083	0.0143549
$438$	14.2432	0.680565
$439$	−28.5268	−1.36151	−0.680756	−	0.732510i	$-0.738349\pi$
$439$	−28.5268	−1.36151	−0.680756	+	0.732510i	$0.738349\pi$
$440$	17.1433	0.817277
$441$	9.48411	0.451624
$442$	−10.3646	−0.492994
$443$	22.1946	1.05450	0.527249	−	0.849711i	$-0.323224\pi$
$443$	22.1946	1.05450	0.527249	+	0.849711i	$0.323224\pi$
$444$	9.91266	0.470434
$445$	2.41766	0.114608
$446$	−12.1408	−0.574886
$447$	20.8106	0.984309
$448$	−1.06158	−0.0501549
$449$	−22.9324	−1.08225	−0.541123	−	0.840944i	$-0.682000\pi$
$449$	−22.9324	−1.08225	−0.541123	+	0.840944i	$0.682000\pi$
$450$	16.1493	0.761287
$451$	9.33098	0.439379
$452$	−2.54515	−0.119714
$453$	26.7329	1.25602
$454$	21.9961	1.03233
$455$	7.62017	0.357239
$456$	0.353174	0.0165389
$457$	16.7970	0.785731	0.392865	−	0.919596i	$-0.371484\pi$
$457$	16.7970	0.785731	0.392865	+	0.919596i	$0.371484\pi$
$458$	15.2770	0.713847
$459$	30.3739	1.41773
$460$	−3.87305	−0.180582
$461$	−21.0933	−0.982412	−0.491206	−	0.871043i	$-0.663444\pi$
$461$	−21.0933	−0.982412	−0.491206	+	0.871043i	$0.663444\pi$
$462$	−5.53023	−0.257290
$463$	−6.23615	−0.289819	−0.144909	−	0.989445i	$-0.546289\pi$
$463$	−6.23615	−0.289819	−0.144909	+	0.989445i	$0.546289\pi$
$464$	1.00000	0.0464238
$465$	−31.1567	−1.44486
$466$	−8.76789	−0.406164
$467$	−3.56114	−0.164790	−0.0823950	−	0.996600i	$-0.526257\pi$
$467$	−3.56114	−0.164790	−0.0823950	+	0.996600i	$0.526257\pi$
$468$	−2.99290	−0.138347
$469$	2.94383	0.135933
$470$	7.08025	0.326588
$471$	27.0929	1.24837
$472$	0.523572	0.0240993
$473$	−48.8068	−2.24414
$474$	4.20406	0.193099
$475$	3.00098	0.137694
$476$	−5.93673	−0.272109
$477$	−16.3674	−0.749411
$478$	−25.3026	−1.15731
$479$	−11.0866	−0.506558	−0.253279	−	0.967393i	$-0.581509\pi$
$479$	−11.0866	−0.506558	−0.253279	+	0.967393i	$0.581509\pi$
$480$	−4.55828	−0.208056
$481$	−15.6099	−0.711752
$482$	19.3181	0.879917
$483$	1.24940	0.0568496
$484$	8.59231	0.390560
$485$	44.2888	2.01105
$486$	14.4725	0.656484
$487$	16.6883	0.756220	0.378110	−	0.925761i	$-0.376574\pi$
$487$	16.6883	0.756220	0.378110	+	0.925761i	$0.376574\pi$
$488$	12.5301	0.567209
$489$	−3.66473	−0.165725
$490$	−22.7466	−1.02759
$491$	−33.0441	−1.49126	−0.745629	−	0.666361i	$-0.767851\pi$
$491$	−33.0441	−1.49126	−0.745629	+	0.666361i	$0.767851\pi$
$492$	−2.48103	−0.111854
$493$	5.59235	0.251867
$494$	−0.556161	−0.0250228
$495$	27.6840	1.24430
$496$	−6.83518	−0.306909
$497$	10.5294	0.472310
$498$	7.40189	0.331687
$499$	−30.8901	−1.38283	−0.691415	−	0.722458i	$-0.743012\pi$
$499$	−30.8901	−1.38283	−0.691415	+	0.722458i	$0.743012\pi$
$500$	−19.3672	−0.866126
$501$	16.5368	0.738812
$502$	0.420694	0.0187765
$503$	11.9862	0.534439	0.267219	−	0.963636i	$-0.413895\pi$
$503$	11.9862	0.534439	0.267219	+	0.963636i	$0.413895\pi$
$504$	−1.71430	−0.0763608
$505$	63.6196	2.83104
$506$	−4.42632	−0.196774
$507$	11.2574	0.499956
$508$	3.79549	0.168398
$509$	−19.4748	−0.863207	−0.431603	−	0.902064i	$-0.642052\pi$
$509$	−19.4748	−0.863207	−0.431603	+	0.902064i	$0.642052\pi$
$510$	−25.4915	−1.12878
$511$	−12.8473	−0.568330
$512$	−1.00000	−0.0441942
$513$	1.62985	0.0719596
$514$	23.4621	1.03487
$515$	−26.6027	−1.17226
$516$	12.9773	0.571295
$517$	8.09168	0.355872
$518$	−8.94119	−0.392853
$519$	−0.178796	−0.00784826
$520$	7.17814	0.314782
$521$	−2.45659	−0.107625	−0.0538127	−	0.998551i	$-0.517137\pi$
$521$	−2.45659	−0.107625	−0.0538127	+	0.998551i	$0.517137\pi$
$522$	1.61485	0.0706802
$523$	−28.2944	−1.23723	−0.618613	−	0.785696i	$-0.712305\pi$
$523$	−28.2944	−1.23723	−0.618613	+	0.785696i	$0.712305\pi$
$524$	4.03461	0.176253
$525$	12.4946	0.545309
$526$	−23.8357	−1.03929
$527$	−38.2247	−1.66510
$528$	−5.20944	−0.226712
$529$	1.00000	0.0434783
$530$	39.2554	1.70515
$531$	0.845491	0.0366912
$532$	−0.318562	−0.0138114
$533$	3.90700	0.169231
$534$	−0.734667	−0.0317922
$535$	−30.0228	−1.29800
$536$	2.77306	0.119778
$537$	19.2995	0.832834
$538$	17.0462	0.734914
$539$	−25.9960	−1.11973
$540$	−21.0358	−0.905236
$541$	−29.6973	−1.27679	−0.638393	−	0.769710i	$-0.720401\pi$
$541$	−29.6973	−1.27679	−0.638393	+	0.769710i	$0.720401\pi$
$542$	7.73234	0.332132
$543$	2.41617	0.103688
$544$	−5.59235	−0.239770
$545$	−80.3545	−3.44201
$546$	−2.31558	−0.0990976
$547$	−14.1727	−0.605982	−0.302991	−	0.952993i	$-0.597985\pi$
$547$	−14.1727	−0.605982	−0.302991	+	0.952993i	$0.597985\pi$
$548$	−1.95835	−0.0836564
$549$	20.2342	0.863574
$550$	−44.2654	−1.88748
$551$	0.300083	0.0127840
$552$	1.17692	0.0500932
$553$	−3.79205	−0.161254
$554$	0.523184	0.0222280
$555$	−38.3922	−1.62966
$556$	−8.41485	−0.356869
$557$	0.584143	0.0247509	0.0123755	−	0.999923i	$-0.496061\pi$
$557$	0.584143	0.0247509	0.0123755	+	0.999923i	$0.496061\pi$
$558$	−11.0378	−0.467268
$559$	−20.4360	−0.864351
$560$	4.11155	0.173745
$561$	−29.1330	−1.23000
$562$	−1.26883	−0.0535222
$563$	32.8544	1.38465	0.692325	−	0.721586i	$-0.256587\pi$
$563$	32.8544	1.38465	0.692325	+	0.721586i	$0.256587\pi$
$564$	−2.15151	−0.0905950
$565$	9.85748	0.414707
$566$	8.58329	0.360782
$567$	1.64300	0.0689994
$568$	9.91865	0.416177
$569$	3.08090	0.129158	0.0645790	−	0.997913i	$-0.479430\pi$
$569$	3.08090	0.129158	0.0645790	+	0.997913i	$0.479430\pi$
$570$	−1.36786	−0.0572934
$571$	22.3756	0.936391	0.468196	−	0.883625i	$-0.344904\pi$
$571$	22.3756	0.936391	0.468196	+	0.883625i	$0.344904\pi$
$572$	8.20355	0.343008
$573$	−18.0631	−0.754597
$574$	2.23788	0.0934074
$575$	10.0005	0.417050
$576$	−1.61485	−0.0672855
$577$	−26.6809	−1.11074	−0.555371	−	0.831603i	$-0.687424\pi$
$577$	−26.6809	−1.11074	−0.555371	+	0.831603i	$0.687424\pi$
$578$	−14.2744	−0.593735
$579$	−25.7805	−1.07140
$580$	−3.87305	−0.160820
$581$	−6.67648	−0.276987
$582$	−13.4582	−0.557862
$583$	44.8631	1.85804
$584$	−12.1020	−0.500786
$585$	11.5916	0.479255
$586$	22.7894	0.941422
$587$	−30.7941	−1.27101	−0.635504	−	0.772097i	$-0.719208\pi$
$587$	−30.7941	−1.27101	−0.635504	+	0.772097i	$0.719208\pi$
$588$	6.91212	0.285051
$589$	−2.05112	−0.0845150
$590$	−2.02782	−0.0834839
$591$	27.1281	1.11590
$592$	−8.42253	−0.346164
$593$	19.4388	0.798258	0.399129	−	0.916895i	$-0.369313\pi$
$593$	19.4388	0.798258	0.399129	+	0.916895i	$0.369313\pi$
$594$	−24.0408	−0.986405
$595$	22.9932	0.942630
$596$	−17.6822	−0.724293
$597$	6.52370	0.266997
$598$	−1.85336	−0.0757894
$599$	−26.9513	−1.10120	−0.550600	−	0.834769i	$-0.685601\pi$
$599$	−26.9513	−1.10120	−0.550600	+	0.834769i	$0.685601\pi$
$600$	11.7698	0.480501
$601$	−18.1651	−0.740970	−0.370485	−	0.928839i	$-0.620808\pi$
$601$	−18.1651	−0.740970	−0.370485	+	0.928839i	$0.620808\pi$
$602$	−11.7055	−0.477081
$603$	4.47809	0.182362
$604$	−22.7142	−0.924228
$605$	−33.2784	−1.35296
$606$	−19.3324	−0.785326
$607$	20.1012	0.815884	0.407942	−	0.913008i	$-0.366246\pi$
$607$	20.1012	0.815884	0.407942	+	0.913008i	$0.366246\pi$
$608$	−0.300083	−0.0121700
$609$	1.24940	0.0506282
$610$	−48.5295	−1.96490
$611$	3.38809	0.137067
$612$	−9.03082	−0.365049
$613$	−35.9082	−1.45032	−0.725158	−	0.688582i	$-0.758233\pi$
$613$	−35.9082	−1.45032	−0.725158	+	0.688582i	$0.758233\pi$
$614$	−5.18389	−0.209205
$615$	9.60915	0.387478
$616$	4.69889	0.189324
$617$	18.3275	0.737838	0.368919	−	0.929462i	$-0.379728\pi$
$617$	18.3275	0.737838	0.368919	+	0.929462i	$0.379728\pi$
$618$	8.08390	0.325182
$619$	−6.57698	−0.264351	−0.132176	−	0.991226i	$-0.542196\pi$
$619$	−6.57698	−0.264351	−0.132176	+	0.991226i	$0.542196\pi$
$620$	26.4730	1.06318
$621$	5.43133	0.217952
$622$	−19.5799	−0.785081
$623$	0.662667	0.0265492
$624$	−2.18126	−0.0873201
$625$	25.0075	1.00030
$626$	7.12294	0.284690
$627$	−1.56326	−0.0624307
$628$	−23.0201	−0.918602
$629$	−47.1017	−1.87807
$630$	6.63955	0.264526
$631$	32.2661	1.28449	0.642247	−	0.766498i	$-0.278002\pi$
$631$	32.2661	1.28449	0.642247	+	0.766498i	$0.278002\pi$
$632$	−3.57208	−0.142090
$633$	−14.4316	−0.573606
$634$	19.4778	0.773561
$635$	−14.7001	−0.583356
$636$	−11.9287	−0.473005
$637$	−10.8848	−0.431273
$638$	−4.42632	−0.175240
$639$	16.0172	0.633629
$640$	3.87305	0.153096
$641$	21.3957	0.845078	0.422539	−	0.906345i	$-0.361139\pi$
$641$	21.3957	0.845078	0.422539	+	0.906345i	$0.361139\pi$
$642$	9.12318	0.360063
$643$	−22.9350	−0.904468	−0.452234	−	0.891899i	$-0.649373\pi$
$643$	−22.9350	−0.904468	−0.452234	+	0.891899i	$0.649373\pi$
$644$	−1.06158	−0.0418321
$645$	−50.2618	−1.97906
$646$	−1.67817	−0.0660267
$647$	32.8818	1.29272	0.646358	−	0.763034i	$-0.276291\pi$
$647$	32.8818	1.29272	0.646358	+	0.763034i	$0.276291\pi$
$648$	1.54769	0.0607990
$649$	−2.31750	−0.0909697
$650$	−18.5345	−0.726982
$651$	−8.53986	−0.334704
$652$	3.11382	0.121947
$653$	−31.3807	−1.22802	−0.614010	−	0.789298i	$-0.710445\pi$
$653$	−31.3807	−1.22802	−0.614010	+	0.789298i	$0.710445\pi$
$654$	24.4177	0.954808
$655$	−15.6262	−0.610568
$656$	2.10807	0.0823062
$657$	−19.5430	−0.762446
$658$	1.94066	0.0756546
$659$	15.6397	0.609236	0.304618	−	0.952475i	$-0.401471\pi$
$659$	15.6397	0.609236	0.304618	+	0.952475i	$0.401471\pi$
$660$	20.1764	0.785365
$661$	−7.11571	−0.276769	−0.138385	−	0.990379i	$-0.544191\pi$
$661$	−7.11571	−0.276769	−0.138385	+	0.990379i	$0.544191\pi$
$662$	14.0747	0.547028
$663$	−12.1983	−0.473745
$664$	−6.28919	−0.244068
$665$	1.23381	0.0478450
$666$	−13.6011	−0.527034
$667$	1.00000	0.0387202
$668$	−14.0509	−0.543646
$669$	−14.2888	−0.552439
$670$	−10.7402	−0.414930
$671$	−55.4620	−2.14109
$672$	−1.24940	−0.0481966
$673$	−25.0278	−0.964751	−0.482375	−	0.875965i	$-0.660226\pi$
$673$	−25.0278	−0.964751	−0.482375	+	0.875965i	$0.660226\pi$
$674$	−26.9446	−1.03787
$675$	54.3160	2.09062
$676$	−9.56507	−0.367887
$677$	5.15763	0.198224	0.0991120	−	0.995076i	$-0.468400\pi$
$677$	5.15763	0.198224	0.0991120	+	0.995076i	$0.468400\pi$
$678$	−2.99544	−0.115039
$679$	12.1393	0.465863
$680$	21.6594	0.830601
$681$	25.8877	0.992018
$682$	30.2547	1.15851
$683$	15.2654	0.584113	0.292056	−	0.956401i	$-0.405661\pi$
$683$	15.2654	0.584113	0.292056	+	0.956401i	$0.405661\pi$
$684$	−0.484590	−0.0185288
$685$	7.58476	0.289799
$686$	−13.6658	−0.521762
$687$	17.9798	0.685974
$688$	−11.0265	−0.420381
$689$	18.7847	0.715642
$690$	−4.55828	−0.173531
$691$	11.0368	0.419860	0.209930	−	0.977716i	$-0.432676\pi$
$691$	11.0368	0.419860	0.209930	+	0.977716i	$0.432676\pi$
$692$	0.151918	0.00577506
$693$	7.58802	0.288245
$694$	−31.7168	−1.20395
$695$	32.5911	1.23625
$696$	1.17692	0.0446111
$697$	11.7890	0.446542
$698$	−3.43111	−0.129869
$699$	−10.3191	−0.390305
$700$	−10.6163	−0.401260
$701$	42.4627	1.60380	0.801898	−	0.597462i	$-0.203824\pi$
$701$	42.4627	1.60380	0.801898	+	0.597462i	$0.203824\pi$
$702$	−10.0662	−0.379923
$703$	−2.52746	−0.0953249
$704$	4.42632	0.166823
$705$	8.33291	0.313835
$706$	8.61159	0.324101
$707$	17.4378	0.655815
$708$	0.616203	0.0231583
$709$	−40.3961	−1.51711	−0.758553	−	0.651611i	$-0.774093\pi$
$709$	−40.3961	−1.51711	−0.758553	+	0.651611i	$0.774093\pi$
$710$	−38.4154	−1.44170
$711$	−5.76838	−0.216331
$712$	0.624227	0.0233939
$713$	−6.83518	−0.255980
$714$	−6.98707	−0.261484
$715$	−31.7727	−1.18823
$716$	−16.3982	−0.612831
$717$	−29.7792	−1.11212
$718$	−3.05353	−0.113957
$719$	−7.47961	−0.278942	−0.139471	−	0.990226i	$-0.544540\pi$
$719$	−7.47961	−0.278942	−0.139471	+	0.990226i	$0.544540\pi$
$720$	6.25440	0.233088
$721$	−7.29165	−0.271555
$722$	18.9100	0.703755
$723$	22.7359	0.845559
$724$	−2.05296	−0.0762975
$725$	10.0005	0.371409
$726$	10.1125	0.375310
$727$	−30.1563	−1.11843	−0.559217	−	0.829021i	$-0.688898\pi$
$727$	−30.1563	−1.11843	−0.559217	+	0.829021i	$0.688898\pi$
$728$	1.96749	0.0729199
$729$	21.6760	0.802816
$730$	46.8718	1.73480
$731$	−61.6640	−2.28072
$732$	14.7469	0.545061
$733$	−19.3985	−0.716501	−0.358250	−	0.933626i	$-0.616627\pi$
$733$	−19.3985	−0.716501	−0.358250	+	0.933626i	$0.616627\pi$
$734$	15.6761	0.578617
$735$	−26.7710	−0.987463
$736$	−1.00000	−0.0368605
$737$	−12.2745	−0.452136
$738$	3.40422	0.125311
$739$	41.9566	1.54340	0.771699	−	0.635988i	$-0.219407\pi$
$739$	41.9566	1.54340	0.771699	+	0.635988i	$0.219407\pi$
$740$	32.6209	1.19917
$741$	−0.654558	−0.0240458
$742$	10.7597	0.395000
$743$	−9.83403	−0.360775	−0.180388	−	0.983596i	$-0.557735\pi$
$743$	−9.83403	−0.360775	−0.180388	+	0.983596i	$0.557735\pi$
$744$	−8.04448	−0.294925
$745$	68.4842	2.50907
$746$	−23.7103	−0.868097
$747$	−10.1561	−0.371593
$748$	24.7535	0.905079
$749$	−8.22907	−0.300684
$750$	−22.7937	−0.832307
$751$	36.0333	1.31487	0.657437	−	0.753510i	$-0.271641\pi$
$751$	36.0333	1.31487	0.657437	+	0.753510i	$0.271641\pi$
$752$	1.82808	0.0666633
$753$	0.495125	0.0180434
$754$	−1.85336	−0.0674952
$755$	87.9732	3.20167
$756$	−5.76579	−0.209700
$757$	−36.9459	−1.34282	−0.671410	−	0.741086i	$-0.734311\pi$
$757$	−36.9459	−1.34282	−0.671410	+	0.741086i	$0.734311\pi$
$758$	−6.79647	−0.246859
$759$	−5.20944	−0.189091
$760$	1.16224	0.0421587
$761$	17.2441	0.625096	0.312548	−	0.949902i	$-0.398817\pi$
$761$	17.2441	0.625096	0.312548	+	0.949902i	$0.398817\pi$
$762$	4.46700	0.161822
$763$	−22.0247	−0.797348
$764$	15.3477	0.555262
$765$	34.9768	1.26459
$766$	27.0871	0.978698
$767$	−0.970364	−0.0350378
$768$	−1.17692	−0.0424685
$769$	22.0726	0.795959	0.397980	−	0.917394i	$-0.369712\pi$
$769$	22.0726	0.795959	0.397980	+	0.917394i	$0.369712\pi$
$770$	−18.1990	−0.655848
$771$	27.6130	0.994459
$772$	21.9050	0.788380
$773$	28.2046	1.01445	0.507224	−	0.861814i	$-0.330672\pi$
$773$	28.2046	1.01445	0.507224	+	0.861814i	$0.330672\pi$
$774$	−17.8062	−0.640029
$775$	−68.3553	−2.45539
$776$	11.4351	0.410497
$777$	−10.5231	−0.377514
$778$	3.92583	0.140748
$779$	0.632595	0.0226651
$780$	8.44811	0.302491
$781$	−43.9031	−1.57098
$782$	−5.59235	−0.199982
$783$	5.43133	0.194100
$784$	−5.87305	−0.209752
$785$	89.1580	3.18218
$786$	4.74843	0.169371
$787$	−36.2127	−1.29085	−0.645423	−	0.763826i	$-0.723319\pi$
$787$	−36.2127	−1.29085	−0.645423	+	0.763826i	$0.723319\pi$
$788$	−23.0501	−0.821125
$789$	−28.0528	−0.998706
$790$	13.8348	0.492221
$791$	2.70188	0.0960677
$792$	7.14786	0.253988
$793$	−23.2226	−0.824660
$794$	−23.5375	−0.835315
$795$	46.2006	1.63857
$796$	−5.54301	−0.196467
$797$	−27.3686	−0.969447	−0.484723	−	0.874668i	$-0.661080\pi$
$797$	−27.3686	−0.969447	−0.484723	+	0.874668i	$0.661080\pi$
$798$	−0.374923	−0.0132721
$799$	10.2233	0.361673
$800$	−10.0005	−0.353571
$801$	1.00803	0.0356172
$802$	25.7386	0.908862
$803$	53.5675	1.89036
$804$	3.26368	0.115101
$805$	4.11155	0.144913
$806$	12.6680	0.446212
$807$	20.0621	0.706219
$808$	16.4262	0.577873
$809$	−1.06074	−0.0372935	−0.0186467	−	0.999826i	$-0.505936\pi$
$809$	−1.06074	−0.0372935	−0.0186467	+	0.999826i	$0.505936\pi$
$810$	−5.99428	−0.210618
$811$	−32.5248	−1.14210	−0.571049	−	0.820916i	$-0.693463\pi$
$811$	−32.5248	−1.14210	−0.571049	+	0.820916i	$0.693463\pi$
$812$	−1.06158	−0.0372542
$813$	9.10036	0.319164
$814$	37.2808	1.30669
$815$	−12.0600	−0.422443
$816$	−6.58176	−0.230408
$817$	−3.30886	−0.115762
$818$	10.2618	0.358796
$819$	3.17720	0.111020
$820$	−8.16464	−0.285122
$821$	26.1021	0.910971	0.455486	−	0.890243i	$-0.349466\pi$
$821$	26.1021	0.910971	0.455486	+	0.890243i	$0.349466\pi$
$822$	−2.30482	−0.0803899
$823$	−35.1394	−1.22488	−0.612440	−	0.790517i	$-0.709812\pi$
$823$	−35.1394	−1.22488	−0.612440	+	0.790517i	$0.709812\pi$
$824$	−6.86868	−0.239282
$825$	−52.0970	−1.81378
$826$	−0.555813	−0.0193392
$827$	−17.9550	−0.624357	−0.312179	−	0.950023i	$-0.601059\pi$
$827$	−17.9550	−0.624357	−0.312179	+	0.950023i	$0.601059\pi$
$828$	−1.61485	−0.0561200
$829$	9.22883	0.320531	0.160265	−	0.987074i	$-0.448765\pi$
$829$	9.22883	0.320531	0.160265	+	0.987074i	$0.448765\pi$
$830$	24.3583	0.845490
$831$	0.615747	0.0213600
$832$	1.85336	0.0642536
$833$	−32.8441	−1.13798
$834$	−9.90363	−0.342935
$835$	54.4199	1.88328
$836$	1.32826	0.0459390
$837$	−37.1241	−1.28320
$838$	−10.9415	−0.377968
$839$	51.0432	1.76221	0.881103	−	0.472925i	$-0.156802\pi$
$839$	51.0432	1.76221	0.881103	+	0.472925i	$0.156802\pi$
$840$	4.83898	0.166961
$841$	1.00000	0.0344828
$842$	14.2491	0.491058
$843$	−1.49331	−0.0514323
$844$	12.2622	0.422082
$845$	37.0460	1.27442
$846$	2.95208	0.101495
$847$	−9.12143	−0.313416
$848$	10.1355	0.348056
$849$	10.1019	0.346695
$850$	−55.9263	−1.91826
$851$	−8.42253	−0.288721
$852$	11.6735	0.399927
$853$	33.6151	1.15096	0.575479	−	0.817816i	$-0.304815\pi$
$853$	33.6151	1.15096	0.575479	+	0.817816i	$0.304815\pi$
$854$	−13.3017	−0.455173
$855$	1.87684	0.0641866
$856$	−7.75172	−0.264948
$857$	53.5023	1.82760	0.913801	−	0.406162i	$-0.133133\pi$
$857$	53.5023	1.82760	0.913801	+	0.406162i	$0.133133\pi$
$858$	9.65494	0.329614
$859$	−25.2382	−0.861116	−0.430558	−	0.902563i	$-0.641683\pi$
$859$	−25.2382	−0.861116	−0.430558	+	0.902563i	$0.641683\pi$
$860$	42.7061	1.45627
$861$	2.63381	0.0897601
$862$	−32.3791	−1.10284
$863$	−57.9710	−1.97336	−0.986678	−	0.162686i	$-0.947984\pi$
$863$	−57.9710	−1.97336	−0.986678	+	0.162686i	$0.947984\pi$
$864$	−5.43133	−0.184777
$865$	−0.588386	−0.0200057
$866$	−22.3305	−0.758821
$867$	−16.7998	−0.570552
$868$	7.25610	0.246288
$869$	15.8112	0.536357
$870$	−4.55828	−0.154540
$871$	−5.13947	−0.174144
$872$	−20.7471	−0.702585
$873$	18.4660	0.624981
$874$	−0.300083	−0.0101505
$875$	20.5598	0.695048
$876$	−14.2432	−0.481232
$877$	13.6690	0.461570	0.230785	−	0.973005i	$-0.425871\pi$
$877$	13.6690	0.461570	0.230785	+	0.973005i	$0.425871\pi$
$878$	28.5268	0.962734
$879$	26.8214	0.904663
$880$	−17.1433	−0.577902
$881$	8.65754	0.291680	0.145840	−	0.989308i	$-0.453412\pi$
$881$	8.65754	0.291680	0.145840	+	0.989308i	$0.453412\pi$
$882$	−9.48411	−0.319347
$883$	−17.1147	−0.575956	−0.287978	−	0.957637i	$-0.592983\pi$
$883$	−17.1147	−0.575956	−0.287978	+	0.957637i	$0.592983\pi$
$884$	10.3646	0.348600
$885$	−2.38658	−0.0802242
$886$	−22.1946	−0.745643
$887$	18.2655	0.613297	0.306648	−	0.951823i	$-0.400792\pi$
$887$	18.2655	0.613297	0.306648	+	0.951823i	$0.400792\pi$
$888$	−9.91266	−0.332647
$889$	−4.02921	−0.135136
$890$	−2.41766	−0.0810402
$891$	−6.85058	−0.229503
$892$	12.1408	0.406506
$893$	0.548576	0.0183574
$894$	−20.8106	−0.696012
$895$	63.5112	2.12295
$896$	1.06158	0.0354649
$897$	−2.18126	−0.0728300
$898$	22.9324	0.765263
$899$	−6.83518	−0.227966
$900$	−16.1493	−0.538311
$901$	56.6814	1.88833
$902$	−9.33098	−0.310688
$903$	−13.7765	−0.458452
$904$	2.54515	0.0846503
$905$	7.95120	0.264307
$906$	−26.7329	−0.888140
$907$	−33.6720	−1.11806	−0.559030	−	0.829147i	$-0.688826\pi$
$907$	−33.6720	−1.11806	−0.559030	+	0.829147i	$0.688826\pi$
$908$	−21.9961	−0.729966
$909$	26.5260	0.879811
$910$	−7.62017	−0.252606
$911$	35.6379	1.18074	0.590368	−	0.807134i	$-0.298983\pi$
$911$	35.6379	1.18074	0.590368	+	0.807134i	$0.298983\pi$
$912$	−0.353174	−0.0116948
$913$	27.8380	0.921302
$914$	−16.7970	−0.555596
$915$	−57.1155	−1.88818
$916$	−15.2770	−0.504766
$917$	−4.28306	−0.141439
$918$	−30.3739	−1.00249
$919$	30.0777	0.992172	0.496086	−	0.868273i	$-0.334770\pi$
$919$	30.0777	0.992172	0.496086	+	0.868273i	$0.334770\pi$
$920$	3.87305	0.127691
$921$	−6.10104	−0.201036
$922$	21.0933	0.694670
$923$	−18.3828	−0.605077
$924$	5.53023	0.181931
$925$	−84.2295	−2.76945
$926$	6.23615	0.204933
$927$	−11.0919	−0.364306
$928$	−1.00000	−0.0328266
$929$	−37.2441	−1.22194	−0.610969	−	0.791655i	$-0.709220\pi$
$929$	−37.2441	−1.22194	−0.610969	+	0.791655i	$0.709220\pi$
$930$	31.1567	1.02167
$931$	−1.76240	−0.0577604
$932$	8.76789	0.287202
$933$	−23.0440	−0.754426
$934$	3.56114	0.116524
$935$	−95.8716	−3.13534
$936$	2.99290	0.0978259
$937$	56.4799	1.84512	0.922559	−	0.385855i	$-0.126094\pi$
$937$	56.4799	1.84512	0.922559	+	0.385855i	$0.126094\pi$
$938$	−2.94383	−0.0961194
$939$	8.38315	0.273574
$940$	−7.08025	−0.230932
$941$	−36.8722	−1.20200	−0.601000	−	0.799249i	$-0.705231\pi$
$941$	−36.8722	−1.20200	−0.601000	+	0.799249i	$0.705231\pi$
$942$	−27.0929	−0.882734
$943$	2.10807	0.0686481
$944$	−0.523572	−0.0170408
$945$	22.3312	0.726433
$946$	48.8068	1.58684
$947$	22.7339	0.738753	0.369376	−	0.929280i	$-0.379571\pi$
$947$	22.7339	0.738753	0.369376	+	0.929280i	$0.379571\pi$
$948$	−4.20406	−0.136542
$949$	22.4294	0.728089
$950$	−3.00098	−0.0973646
$951$	22.9238	0.743356
$952$	5.93673	0.192410
$953$	8.50840	0.275614	0.137807	−	0.990459i	$-0.455995\pi$
$953$	8.50840	0.275614	0.137807	+	0.990459i	$0.455995\pi$
$954$	16.3674	0.529914
$955$	−59.4425	−1.92351
$956$	25.3026	0.818345
$957$	−5.20944	−0.168397
$958$	11.0866	0.358190
$959$	2.07894	0.0671325
$960$	4.55828	0.147118
$961$	15.7198	0.507089
$962$	15.6099	0.503285
$963$	−12.5179	−0.403383
$964$	−19.3181	−0.622195
$965$	−84.8392	−2.73107
$966$	−1.24940	−0.0401987
$967$	−35.0782	−1.12804	−0.564019	−	0.825761i	$-0.690746\pi$
$967$	−35.0782	−1.12804	−0.564019	+	0.825761i	$0.690746\pi$
$968$	−8.59231	−0.276167
$969$	−1.97507	−0.0634485
$970$	−44.2888	−1.42203
$971$	−10.7257	−0.344204	−0.172102	−	0.985079i	$-0.555056\pi$
$971$	−10.7257	−0.344204	−0.172102	+	0.985079i	$0.555056\pi$
$972$	−14.4725	−0.464204
$973$	8.93304	0.286380
$974$	−16.6883	−0.534728
$975$	−21.8137	−0.698596
$976$	−12.5301	−0.401077
$977$	−6.53487	−0.209069	−0.104535	−	0.994521i	$-0.533335\pi$
$977$	−6.53487	−0.209069	−0.104535	+	0.994521i	$0.533335\pi$
$978$	3.66473	0.117185
$979$	−2.76303	−0.0883068
$980$	22.7466	0.726613
$981$	−33.5035	−1.06968
$982$	33.0441	1.05448
$983$	29.2414	0.932657	0.466329	−	0.884612i	$-0.345576\pi$
$983$	29.2414	0.932657	0.466329	+	0.884612i	$0.345576\pi$
$984$	2.48103	0.0790924
$985$	89.2740	2.84451
$986$	−5.59235	−0.178097
$987$	2.28400	0.0727006
$988$	0.556161	0.0176938
$989$	−11.0265	−0.350622
$990$	−27.6840	−0.879855
$991$	−7.57926	−0.240763	−0.120382	−	0.992728i	$-0.538412\pi$
$991$	−7.57926	−0.240763	−0.120382	+	0.992728i	$0.538412\pi$
$992$	6.83518	0.217017
$993$	16.5648	0.525668
$994$	−10.5294	−0.333974
$995$	21.4684	0.680593
$996$	−7.40189	−0.234538
$997$	−45.0631	−1.42716	−0.713582	−	0.700572i	$-0.752928\pi$
$997$	−45.0631	−1.42716	−0.713582	+	0.700572i	$0.752928\pi$
$998$	30.8901	0.977808
$999$	−45.7455	−1.44732

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.f.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.f.1.2	✓	5	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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.17692 q^{3} +1.00000 q^{4} -3.87305 q^{5} +1.17692 q^{6} -1.06158 q^{7} -1.00000 q^{8} -1.61485 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.17692 q^{3} +1.00000 q^{4} -3.87305 q^{5} +1.17692 q^{6} -1.06158 q^{7} -1.00000 q^{8} -1.61485 q^{9} +3.87305 q^{10} +4.42632 q^{11} -1.17692 q^{12} +1.85336 q^{13} +1.06158 q^{14} +4.55828 q^{15} +1.00000 q^{16} +5.59235 q^{17} +1.61485 q^{18} +0.300083 q^{19} -3.87305 q^{20} +1.24940 q^{21} -4.42632 q^{22} +1.00000 q^{23} +1.17692 q^{24} +10.0005 q^{25} -1.85336 q^{26} +5.43133 q^{27} -1.06158 q^{28} +1.00000 q^{29} -4.55828 q^{30} -6.83518 q^{31} -1.00000 q^{32} -5.20944 q^{33} -5.59235 q^{34} +4.11155 q^{35} -1.61485 q^{36} -8.42253 q^{37} -0.300083 q^{38} -2.18126 q^{39} +3.87305 q^{40} +2.10807 q^{41} -1.24940 q^{42} -11.0265 q^{43} +4.42632 q^{44} +6.25440 q^{45} -1.00000 q^{46} +1.82808 q^{47} -1.17692 q^{48} -5.87305 q^{49} -10.0005 q^{50} -6.58176 q^{51} +1.85336 q^{52} +10.1355 q^{53} -5.43133 q^{54} -17.1433 q^{55} +1.06158 q^{56} -0.353174 q^{57} -1.00000 q^{58} -0.523572 q^{59} +4.55828 q^{60} -12.5301 q^{61} +6.83518 q^{62} +1.71430 q^{63} +1.00000 q^{64} -7.17814 q^{65} +5.20944 q^{66} -2.77306 q^{67} +5.59235 q^{68} -1.17692 q^{69} -4.11155 q^{70} -9.91865 q^{71} +1.61485 q^{72} +12.1020 q^{73} +8.42253 q^{74} -11.7698 q^{75} +0.300083 q^{76} -4.69889 q^{77} +2.18126 q^{78} +3.57208 q^{79} -3.87305 q^{80} -1.54769 q^{81} -2.10807 q^{82} +6.28919 q^{83} +1.24940 q^{84} -21.6594 q^{85} +11.0265 q^{86} -1.17692 q^{87} -4.42632 q^{88} -0.624227 q^{89} -6.25440 q^{90} -1.96749 q^{91} +1.00000 q^{92} +8.04448 q^{93} -1.82808 q^{94} -1.16224 q^{95} +1.17692 q^{96} -11.4351 q^{97} +5.87305 q^{98} -7.14786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + q^{3} + 5 q^{4} - 5 q^{5} - q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 + q^3 + 5 * q^4 - 5 * q^5 - q^6 - 2 * q^7 - 5 * q^8 + 2 * q^9	\( 5 q - 5 q^{2} + q^{3} + 5 q^{4} - 5 q^{5} - q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9} + 5 q^{10} + q^{11} + q^{12} - 11 q^{13} + 2 q^{14} + 5 q^{15} + 5 q^{16} + 4 q^{17} - 2 q^{18} - 12 q^{19} - 5 q^{20} - 8 q^{21} - q^{22} + 5 q^{23} - q^{24} - 4 q^{25} + 11 q^{26} - 5 q^{27} - 2 q^{28} + 5 q^{29} - 5 q^{30} - 5 q^{31} - 5 q^{32} - 11 q^{33} - 4 q^{34} - 4 q^{35} + 2 q^{36} + 12 q^{38} - 9 q^{39} + 5 q^{40} - 6 q^{41} + 8 q^{42} - 7 q^{43} + q^{44} + 6 q^{45} - 5 q^{46} + 5 q^{47} + q^{48} - 15 q^{49} + 4 q^{50} - 42 q^{51} - 11 q^{52} - q^{53} + 5 q^{54} - 31 q^{55} + 2 q^{56} - 4 q^{57} - 5 q^{58} - 12 q^{59} + 5 q^{60} - 20 q^{61} + 5 q^{62} + 10 q^{63} + 5 q^{64} + 3 q^{65} + 11 q^{66} - 4 q^{67} + 4 q^{68} + q^{69} + 4 q^{70} - 4 q^{71} - 2 q^{72} + 4 q^{73} - 12 q^{75} - 12 q^{76} + 14 q^{77} + 9 q^{78} - q^{79} - 5 q^{80} - 23 q^{81} + 6 q^{82} + 22 q^{83} - 8 q^{84} - 16 q^{85} + 7 q^{86} + q^{87} - q^{88} + 8 q^{89} - 6 q^{90} - 18 q^{91} + 5 q^{92} - 37 q^{93} - 5 q^{94} + 18 q^{95} - q^{96} - 46 q^{97} + 15 q^{98} - 24 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + q^3 + 5 * q^4 - 5 * q^5 - q^6 - 2 * q^7 - 5 * q^8 + 2 * q^9 + 5 * q^10 + q^11 + q^12 - 11 * q^13 + 2 * q^14 + 5 * q^15 + 5 * q^16 + 4 * q^17 - 2 * q^18 - 12 * q^19 - 5 * q^20 - 8 * q^21 - q^22 + 5 * q^23 - q^24 - 4 * q^25 + 11 * q^26 - 5 * q^27 - 2 * q^28 + 5 * q^29 - 5 * q^30 - 5 * q^31 - 5 * q^32 - 11 * q^33 - 4 * q^34 - 4 * q^35 + 2 * q^36 + 12 * q^38 - 9 * q^39 + 5 * q^40 - 6 * q^41 + 8 * q^42 - 7 * q^43 + q^44 + 6 * q^45 - 5 * q^46 + 5 * q^47 + q^48 - 15 * q^49 + 4 * q^50 - 42 * q^51 - 11 * q^52 - q^53 + 5 * q^54 - 31 * q^55 + 2 * q^56 - 4 * q^57 - 5 * q^58 - 12 * q^59 + 5 * q^60 - 20 * q^61 + 5 * q^62 + 10 * q^63 + 5 * q^64 + 3 * q^65 + 11 * q^66 - 4 * q^67 + 4 * q^68 + q^69 + 4 * q^70 - 4 * q^71 - 2 * q^72 + 4 * q^73 - 12 * q^75 - 12 * q^76 + 14 * q^77 + 9 * q^78 - q^79 - 5 * q^80 - 23 * q^81 + 6 * q^82 + 22 * q^83 - 8 * q^84 - 16 * q^85 + 7 * q^86 + q^87 - q^88 + 8 * q^89 - 6 * q^90 - 18 * q^91 + 5 * q^92 - 37 * q^93 - 5 * q^94 + 18 * q^95 - q^96 - 46 * q^97 + 15 * q^98 - 24 * q^99

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