LMFDB - Embedded newform 4026.2.a.u.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.9176805.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 12x^{3} + 7x^{2} + 30x - 20 $ x^5 - x^4 - 12x^3 + 7x^2 + 30*x - 20
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			$1.62906$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.62906 q^{5} -1.00000 q^{6} -4.09482 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.62906 q^{5} -1.00000 q^{6} -4.09482 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.62906 q^{10} -1.00000 q^{11} +1.00000 q^{12} +2.05318 q^{13} +4.09482 q^{14} -1.62906 q^{15} +1.00000 q^{16} -6.07005 q^{17} -1.00000 q^{18} +8.57070 q^{19} -1.62906 q^{20} -4.09482 q^{21} +1.00000 q^{22} -8.01687 q^{23} -1.00000 q^{24} -2.34617 q^{25} -2.05318 q^{26} +1.00000 q^{27} -4.09482 q^{28} +1.71712 q^{29} +1.62906 q^{30} -4.38782 q^{31} -1.00000 q^{32} -1.00000 q^{33} +6.07005 q^{34} +6.67070 q^{35} +1.00000 q^{36} +3.63917 q^{37} -8.57070 q^{38} +2.05318 q^{39} +1.62906 q^{40} +2.67070 q^{41} +4.09482 q^{42} -1.73399 q^{43} -1.00000 q^{44} -1.62906 q^{45} +8.01687 q^{46} +9.02841 q^{47} +1.00000 q^{48} +9.76758 q^{49} +2.34617 q^{50} -6.07005 q^{51} +2.05318 q^{52} -8.44100 q^{53} -1.00000 q^{54} +1.62906 q^{55} +4.09482 q^{56} +8.57070 q^{57} -1.71712 q^{58} +6.78574 q^{59} -1.62906 q^{60} -1.00000 q^{61} +4.38782 q^{62} -4.09482 q^{63} +1.00000 q^{64} -3.34475 q^{65} +1.00000 q^{66} -8.71870 q^{67} -6.07005 q^{68} -8.01687 q^{69} -6.67070 q^{70} -4.87030 q^{71} -1.00000 q^{72} -13.8572 q^{73} -3.63917 q^{74} -2.34617 q^{75} +8.57070 q^{76} +4.09482 q^{77} -2.05318 q^{78} +15.9806 q^{79} -1.62906 q^{80} +1.00000 q^{81} -2.67070 q^{82} -14.6824 q^{83} -4.09482 q^{84} +9.88846 q^{85} +1.73399 q^{86} +1.71712 q^{87} +1.00000 q^{88} +11.8389 q^{89} +1.62906 q^{90} -8.40741 q^{91} -8.01687 q^{92} -4.38782 q^{93} -9.02841 q^{94} -13.9622 q^{95} -1.00000 q^{96} +4.94164 q^{97} -9.76758 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - 3 q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - 3 * q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - 3 q^{7} - 5 q^{8} + 5 q^{9} + q^{10} - 5 q^{11} + 5 q^{12} + 2 q^{13} + 3 q^{14} - q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} + 7 q^{19} - q^{20} - 3 q^{21} + 5 q^{22} - 12 q^{23} - 5 q^{24} - 2 q^{26} + 5 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} - q^{31} - 5 q^{32} - 5 q^{33} - 6 q^{34} + 17 q^{35} + 5 q^{36} + 3 q^{37} - 7 q^{38} + 2 q^{39} + q^{40} - 3 q^{41} + 3 q^{42} + 24 q^{43} - 5 q^{44} - q^{45} + 12 q^{46} + 18 q^{47} + 5 q^{48} + 26 q^{49} + 6 q^{51} + 2 q^{52} - 13 q^{53} - 5 q^{54} + q^{55} + 3 q^{56} + 7 q^{57} - 4 q^{58} - 16 q^{59} - q^{60} - 5 q^{61} + q^{62} - 3 q^{63} + 5 q^{64} + 4 q^{65} + 5 q^{66} + 18 q^{67} + 6 q^{68} - 12 q^{69} - 17 q^{70} - 31 q^{71} - 5 q^{72} + 8 q^{73} - 3 q^{74} + 7 q^{76} + 3 q^{77} - 2 q^{78} + 32 q^{79} - q^{80} + 5 q^{81} + 3 q^{82} + 8 q^{83} - 3 q^{84} + 29 q^{85} - 24 q^{86} + 4 q^{87} + 5 q^{88} + q^{89} + q^{90} - 3 q^{91} - 12 q^{92} - q^{93} - 18 q^{94} + 33 q^{95} - 5 q^{96} - 4 q^{97} - 26 q^{98} - 5 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - 3 * q^7 - 5 * q^8 + 5 * q^9 + q^10 - 5 * q^11 + 5 * q^12 + 2 * q^13 + 3 * q^14 - q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 + 7 * q^19 - q^20 - 3 * q^21 + 5 * q^22 - 12 * q^23 - 5 * q^24 - 2 * q^26 + 5 * q^27 - 3 * q^28 + 4 * q^29 + q^30 - q^31 - 5 * q^32 - 5 * q^33 - 6 * q^34 + 17 * q^35 + 5 * q^36 + 3 * q^37 - 7 * q^38 + 2 * q^39 + q^40 - 3 * q^41 + 3 * q^42 + 24 * q^43 - 5 * q^44 - q^45 + 12 * q^46 + 18 * q^47 + 5 * q^48 + 26 * q^49 + 6 * q^51 + 2 * q^52 - 13 * q^53 - 5 * q^54 + q^55 + 3 * q^56 + 7 * q^57 - 4 * q^58 - 16 * q^59 - q^60 - 5 * q^61 + q^62 - 3 * q^63 + 5 * q^64 + 4 * q^65 + 5 * q^66 + 18 * q^67 + 6 * q^68 - 12 * q^69 - 17 * q^70 - 31 * q^71 - 5 * q^72 + 8 * q^73 - 3 * q^74 + 7 * q^76 + 3 * q^77 - 2 * q^78 + 32 * q^79 - q^80 + 5 * q^81 + 3 * q^82 + 8 * q^83 - 3 * q^84 + 29 * q^85 - 24 * q^86 + 4 * q^87 + 5 * q^88 + q^89 + q^90 - 3 * q^91 - 12 * q^92 - q^93 - 18 * q^94 + 33 * q^95 - 5 * q^96 - 4 * q^97 - 26 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.62906	−0.728536	−0.364268	−	0.931294i	$-0.618681\pi$
$5$	−1.62906	−0.728536	−0.364268	+	0.931294i	$0.618681\pi$
$6$	−1.00000	−0.408248
$7$	−4.09482	−1.54770	−0.773849	−	0.633370i	$-0.781671\pi$
$7$	−4.09482	−1.54770	−0.773849	+	0.633370i	$0.781671\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.62906	0.515153
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	2.05318	0.569450	0.284725	−	0.958609i	$-0.408098\pi$
$13$	2.05318	0.569450	0.284725	+	0.958609i	$0.408098\pi$
$14$	4.09482	1.09439
$15$	−1.62906	−0.420621
$16$	1.00000	0.250000
$17$	−6.07005	−1.47220	−0.736102	−	0.676870i	$-0.763336\pi$
$17$	−6.07005	−1.47220	−0.736102	+	0.676870i	$0.763336\pi$
$18$	−1.00000	−0.235702
$19$	8.57070	1.96625	0.983127	−	0.182926i	$-0.0585568\pi$
$19$	8.57070	1.96625	0.983127	+	0.182926i	$0.0585568\pi$
$20$	−1.62906	−0.364268
$21$	−4.09482	−0.893564
$22$	1.00000	0.213201
$23$	−8.01687	−1.67163	−0.835817	−	0.549008i	$-0.815006\pi$
$23$	−8.01687	−1.67163	−0.835817	+	0.549008i	$0.815006\pi$
$24$	−1.00000	−0.204124
$25$	−2.34617	−0.469235
$26$	−2.05318	−0.402662
$27$	1.00000	0.192450
$28$	−4.09482	−0.773849
$29$	1.71712	0.318861	0.159430	−	0.987209i	$-0.449034\pi$
$29$	1.71712	0.318861	0.159430	+	0.987209i	$0.449034\pi$
$30$	1.62906	0.297424
$31$	−4.38782	−0.788075	−0.394038	−	0.919094i	$-0.628922\pi$
$31$	−4.38782	−0.788075	−0.394038	+	0.919094i	$0.628922\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	6.07005	1.04101
$35$	6.67070	1.12755
$36$	1.00000	0.166667
$37$	3.63917	0.598275	0.299138	−	0.954210i	$-0.403301\pi$
$37$	3.63917	0.598275	0.299138	+	0.954210i	$0.403301\pi$
$38$	−8.57070	−1.39035
$39$	2.05318	0.328772
$40$	1.62906	0.257577
$41$	2.67070	0.417093	0.208547	−	0.978012i	$-0.433127\pi$
$41$	2.67070	0.417093	0.208547	+	0.978012i	$0.433127\pi$
$42$	4.09482	0.631845
$43$	−1.73399	−0.264431	−0.132216	−	0.991221i	$-0.542209\pi$
$43$	−1.73399	−0.264431	−0.132216	+	0.991221i	$0.542209\pi$
$44$	−1.00000	−0.150756
$45$	−1.62906	−0.242845
$46$	8.01687	1.18202
$47$	9.02841	1.31693	0.658465	−	0.752612i	$-0.271206\pi$
$47$	9.02841	1.31693	0.658465	+	0.752612i	$0.271206\pi$
$48$	1.00000	0.144338
$49$	9.76758	1.39537
$50$	2.34617	0.331799
$51$	−6.07005	−0.849978
$52$	2.05318	0.284725
$53$	−8.44100	−1.15946	−0.579730	−	0.814809i	$-0.696842\pi$
$53$	−8.44100	−1.15946	−0.579730	+	0.814809i	$0.696842\pi$
$54$	−1.00000	−0.136083
$55$	1.62906	0.219662
$56$	4.09482	0.547194
$57$	8.57070	1.13522
$58$	−1.71712	−0.225468
$59$	6.78574	0.883429	0.441714	−	0.897156i	$-0.354370\pi$
$59$	6.78574	0.883429	0.441714	+	0.897156i	$0.354370\pi$
$60$	−1.62906	−0.210310
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	4.38782	0.557253
$63$	−4.09482	−0.515899
$64$	1.00000	0.125000
$65$	−3.34475	−0.414865
$66$	1.00000	0.123091
$67$	−8.71870	−1.06516	−0.532580	−	0.846380i	$-0.678777\pi$
$67$	−8.71870	−1.06516	−0.532580	+	0.846380i	$0.678777\pi$
$68$	−6.07005	−0.736102
$69$	−8.01687	−0.965118
$70$	−6.67070	−0.797301
$71$	−4.87030	−0.577998	−0.288999	−	0.957329i	$-0.593322\pi$
$71$	−4.87030	−0.577998	−0.288999	+	0.957329i	$0.593322\pi$
$72$	−1.00000	−0.117851
$73$	−13.8572	−1.62187	−0.810933	−	0.585139i	$-0.801040\pi$
$73$	−13.8572	−1.62187	−0.810933	+	0.585139i	$0.801040\pi$
$74$	−3.63917	−0.423045
$75$	−2.34617	−0.270913
$76$	8.57070	0.983127
$77$	4.09482	0.466648
$78$	−2.05318	−0.232477
$79$	15.9806	1.79795	0.898977	−	0.437996i	$-0.144311\pi$
$79$	15.9806	1.79795	0.898977	+	0.437996i	$0.144311\pi$
$80$	−1.62906	−0.182134
$81$	1.00000	0.111111
$82$	−2.67070	−0.294929
$83$	−14.6824	−1.61160	−0.805801	−	0.592186i	$-0.798265\pi$
$83$	−14.6824	−1.61160	−0.805801	+	0.592186i	$0.798265\pi$
$84$	−4.09482	−0.446782
$85$	9.88846	1.07255
$86$	1.73399	0.186981
$87$	1.71712	0.184094
$88$	1.00000	0.106600
$89$	11.8389	1.25492	0.627462	−	0.778647i	$-0.284094\pi$
$89$	11.8389	1.25492	0.627462	+	0.778647i	$0.284094\pi$
$90$	1.62906	0.171718
$91$	−8.40741	−0.881336
$92$	−8.01687	−0.835817
$93$	−4.38782	−0.454995
$94$	−9.02841	−0.931209
$95$	−13.9622	−1.43249
$96$	−1.00000	−0.102062
$97$	4.94164	0.501748	0.250874	−	0.968020i	$-0.419282\pi$
$97$	4.94164	0.501748	0.250874	+	0.968020i	$0.419282\pi$
$98$	−9.76758	−0.986674
$99$	−1.00000	−0.100504
$100$	−2.34617	−0.234617
$101$	8.66695	0.862394	0.431197	−	0.902258i	$-0.358091\pi$
$101$	8.66695	0.862394	0.431197	+	0.902258i	$0.358091\pi$
$102$	6.07005	0.601025
$103$	2.92477	0.288186	0.144093	−	0.989564i	$-0.453974\pi$
$103$	2.92477	0.288186	0.144093	+	0.989564i	$0.453974\pi$
$104$	−2.05318	−0.201331
$105$	6.67070	0.650994
$106$	8.44100	0.819862
$107$	11.9162	1.15199	0.575993	−	0.817454i	$-0.304615\pi$
$107$	11.9162	1.15199	0.575993	+	0.817454i	$0.304615\pi$
$108$	1.00000	0.0962250
$109$	15.1581	1.45188	0.725942	−	0.687756i	$-0.241404\pi$
$109$	15.1581	1.45188	0.725942	+	0.687756i	$0.241404\pi$
$110$	−1.62906	−0.155324
$111$	3.63917	0.345414
$112$	−4.09482	−0.386924
$113$	15.9090	1.49659	0.748295	−	0.663366i	$-0.230873\pi$
$113$	15.9090	1.49659	0.748295	+	0.663366i	$0.230873\pi$
$114$	−8.57070	−0.802720
$115$	13.0599	1.21785
$116$	1.71712	0.159430
$117$	2.05318	0.189817
$118$	−6.78574	−0.624678
$119$	24.8558	2.27853
$120$	1.62906	0.148712
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	2.67070	0.240809
$124$	−4.38782	−0.394038
$125$	11.9673	1.07039
$126$	4.09482	0.364796
$127$	12.6938	1.12639	0.563195	−	0.826324i	$-0.309572\pi$
$127$	12.6938	1.12639	0.563195	+	0.826324i	$0.309572\pi$
$128$	−1.00000	−0.0883883
$129$	−1.73399	−0.152669
$130$	3.34475	0.293354
$131$	−10.9774	−0.959104	−0.479552	−	0.877514i	$-0.659201\pi$
$131$	−10.9774	−0.959104	−0.479552	+	0.877514i	$0.659201\pi$
$132$	−1.00000	−0.0870388
$133$	−35.0955	−3.04317
$134$	8.71870	0.753181
$135$	−1.62906	−0.140207
$136$	6.07005	0.520503
$137$	−2.77547	−0.237125	−0.118562	−	0.992947i	$-0.537829\pi$
$137$	−2.77547	−0.237125	−0.118562	+	0.992947i	$0.537829\pi$
$138$	8.01687	0.682442
$139$	17.0533	1.44645	0.723223	−	0.690615i	$-0.242660\pi$
$139$	17.0533	1.44645	0.723223	+	0.690615i	$0.242660\pi$
$140$	6.67070	0.563777
$141$	9.02841	0.760329
$142$	4.87030	0.408706
$143$	−2.05318	−0.171696
$144$	1.00000	0.0833333
$145$	−2.79728	−0.232302
$146$	13.8572	1.14683
$147$	9.76758	0.805616
$148$	3.63917	0.299138
$149$	−0.367193	−0.0300816	−0.0150408	−	0.999887i	$-0.504788\pi$
$149$	−0.367193	−0.0300816	−0.0150408	+	0.999887i	$0.504788\pi$
$150$	2.34617	0.191564
$151$	−2.81051	−0.228716	−0.114358	−	0.993440i	$-0.536481\pi$
$151$	−2.81051	−0.228716	−0.114358	+	0.993440i	$0.536481\pi$
$152$	−8.57070	−0.695176
$153$	−6.07005	−0.490735
$154$	−4.09482	−0.329970
$155$	7.14800	0.574141
$156$	2.05318	0.164386
$157$	−2.35423	−0.187888	−0.0939440	−	0.995577i	$-0.529947\pi$
$157$	−2.35423	−0.187888	−0.0939440	+	0.995577i	$0.529947\pi$
$158$	−15.9806	−1.27135
$159$	−8.44100	−0.669415
$160$	1.62906	0.128788
$161$	32.8277	2.58718
$162$	−1.00000	−0.0785674
$163$	23.6811	1.85485	0.927424	−	0.374013i	$-0.122018\pi$
$163$	23.6811	1.85485	0.927424	+	0.374013i	$0.122018\pi$
$164$	2.67070	0.208547
$165$	1.62906	0.126822
$166$	14.6824	1.13958
$167$	1.19754	0.0926686	0.0463343	−	0.998926i	$-0.485246\pi$
$167$	1.19754	0.0926686	0.0463343	+	0.998926i	$0.485246\pi$
$168$	4.09482	0.315922
$169$	−8.78445	−0.675727
$170$	−9.88846	−0.758410
$171$	8.57070	0.655418
$172$	−1.73399	−0.132216
$173$	3.99416	0.303670	0.151835	−	0.988406i	$-0.451482\pi$
$173$	3.99416	0.303670	0.151835	+	0.988406i	$0.451482\pi$
$174$	−1.71712	−0.130174
$175$	9.60717	0.726234
$176$	−1.00000	−0.0753778
$177$	6.78574	0.510048
$178$	−11.8389	−0.887365
$179$	−10.2150	−0.763508	−0.381754	−	0.924264i	$-0.624680\pi$
$179$	−10.2150	−0.763508	−0.381754	+	0.924264i	$0.624680\pi$
$180$	−1.62906	−0.121423
$181$	−9.65733	−0.717824	−0.358912	−	0.933371i	$-0.616852\pi$
$181$	−9.65733	−0.717824	−0.358912	+	0.933371i	$0.616852\pi$
$182$	8.40741	0.623199
$183$	−1.00000	−0.0739221
$184$	8.01687	0.591012
$185$	−5.92841	−0.435865
$186$	4.38782	0.321730
$187$	6.07005	0.443886
$188$	9.02841	0.658465
$189$	−4.09482	−0.297855
$190$	13.9622	1.01292
$191$	−17.8595	−1.29227	−0.646136	−	0.763222i	$-0.723616\pi$
$191$	−17.8595	−1.29227	−0.646136	+	0.763222i	$0.723616\pi$
$192$	1.00000	0.0721688
$193$	16.6298	1.19704	0.598521	−	0.801107i	$-0.295755\pi$
$193$	16.6298	1.19704	0.598521	+	0.801107i	$0.295755\pi$
$194$	−4.94164	−0.354789
$195$	−3.34475	−0.239522
$196$	9.76758	0.697684
$197$	−6.83671	−0.487095	−0.243548	−	0.969889i	$-0.578311\pi$
$197$	−6.83671	−0.487095	−0.243548	+	0.969889i	$0.578311\pi$
$198$	1.00000	0.0710669
$199$	16.8268	1.19282	0.596409	−	0.802681i	$-0.296594\pi$
$199$	16.8268	1.19282	0.596409	+	0.802681i	$0.296594\pi$
$200$	2.34617	0.165900
$201$	−8.71870	−0.614970
$202$	−8.66695	−0.609804
$203$	−7.03129	−0.493500
$204$	−6.07005	−0.424989
$205$	−4.35072	−0.303868
$206$	−2.92477	−0.203778
$207$	−8.01687	−0.557211
$208$	2.05318	0.142362
$209$	−8.57070	−0.592848
$210$	−6.67070	−0.460322
$211$	23.2247	1.59885	0.799427	−	0.600764i	$-0.205137\pi$
$211$	23.2247	1.59885	0.799427	+	0.600764i	$0.205137\pi$
$212$	−8.44100	−0.579730
$213$	−4.87030	−0.333707
$214$	−11.9162	−0.814578
$215$	2.82477	0.192648
$216$	−1.00000	−0.0680414
$217$	17.9673	1.21970
$218$	−15.1581	−1.02664
$219$	−13.8572	−0.936384
$220$	1.62906	0.109831
$221$	−12.4629	−0.838346
$222$	−3.63917	−0.244245
$223$	11.6012	0.776871	0.388436	−	0.921476i	$-0.373016\pi$
$223$	11.6012	0.776871	0.388436	+	0.921476i	$0.373016\pi$
$224$	4.09482	0.273597
$225$	−2.34617	−0.156412
$226$	−15.9090	−1.05825
$227$	21.9215	1.45498	0.727492	−	0.686116i	$-0.240686\pi$
$227$	21.9215	1.45498	0.727492	+	0.686116i	$0.240686\pi$
$228$	8.57070	0.567608
$229$	−15.0052	−0.991573	−0.495787	−	0.868444i	$-0.665120\pi$
$229$	−15.0052	−0.991573	−0.495787	+	0.868444i	$0.665120\pi$
$230$	−13.0599	−0.861147
$231$	4.09482	0.269420
$232$	−1.71712	−0.112734
$233$	16.4547	1.07799	0.538993	−	0.842310i	$-0.318805\pi$
$233$	16.4547	1.07799	0.538993	+	0.842310i	$0.318805\pi$
$234$	−2.05318	−0.134221
$235$	−14.7078	−0.959431
$236$	6.78574	0.441714
$237$	15.9806	1.03805
$238$	−24.8558	−1.61116
$239$	28.5650	1.84772	0.923859	−	0.382734i	$-0.125017\pi$
$239$	28.5650	1.84772	0.923859	+	0.382734i	$0.125017\pi$
$240$	−1.62906	−0.105155
$241$	24.8317	1.59955	0.799775	−	0.600300i	$-0.204952\pi$
$241$	24.8317	1.59955	0.799775	+	0.600300i	$0.204952\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	−15.9119	−1.01658
$246$	−2.67070	−0.170278
$247$	17.5972	1.11968
$248$	4.38782	0.278627
$249$	−14.6824	−0.930459
$250$	−11.9673	−0.756881
$251$	−10.4083	−0.656968	−0.328484	−	0.944510i	$-0.606538\pi$
$251$	−10.4083	−0.656968	−0.328484	+	0.944510i	$0.606538\pi$
$252$	−4.09482	−0.257950
$253$	8.01687	0.504017
$254$	−12.6938	−0.796478
$255$	9.88846	0.619240
$256$	1.00000	0.0625000
$257$	−18.3426	−1.14418	−0.572089	−	0.820191i	$-0.693867\pi$
$257$	−18.3426	−1.14418	−0.572089	+	0.820191i	$0.693867\pi$
$258$	1.73399	0.107954
$259$	−14.9017	−0.925949
$260$	−3.34475	−0.207432
$261$	1.71712	0.106287
$262$	10.9774	0.678189
$263$	−9.55996	−0.589492	−0.294746	−	0.955576i	$-0.595235\pi$
$263$	−9.55996	−0.589492	−0.294746	+	0.955576i	$0.595235\pi$
$264$	1.00000	0.0615457
$265$	13.7509	0.844709
$266$	35.0955	2.15184
$267$	11.8389	0.724530
$268$	−8.71870	−0.532580
$269$	−5.13997	−0.313390	−0.156695	−	0.987647i	$-0.550084\pi$
$269$	−5.13997	−0.313390	−0.156695	+	0.987647i	$0.550084\pi$
$270$	1.62906	0.0991412
$271$	−11.4849	−0.697655	−0.348828	−	0.937187i	$-0.613420\pi$
$271$	−11.4849	−0.697655	−0.348828	+	0.937187i	$0.613420\pi$
$272$	−6.07005	−0.368051
$273$	−8.40741	−0.508840
$274$	2.77547	0.167672
$275$	2.34617	0.141480
$276$	−8.01687	−0.482559
$277$	−22.0520	−1.32498	−0.662490	−	0.749071i	$-0.730500\pi$
$277$	−22.0520	−1.32498	−0.662490	+	0.749071i	$0.730500\pi$
$278$	−17.0533	−1.02279
$279$	−4.38782	−0.262692
$280$	−6.67070	−0.398651
$281$	10.0948	0.602207	0.301103	−	0.953592i	$-0.402645\pi$
$281$	10.0948	0.602207	0.301103	+	0.953592i	$0.402645\pi$
$282$	−9.02841	−0.537634
$283$	17.7154	1.05307	0.526534	−	0.850154i	$-0.323491\pi$
$283$	17.7154	1.05307	0.526534	+	0.850154i	$0.323491\pi$
$284$	−4.87030	−0.288999
$285$	−13.9622	−0.827047
$286$	2.05318	0.121407
$287$	−10.9360	−0.645534
$288$	−1.00000	−0.0589256
$289$	19.8456	1.16739
$290$	2.79728	0.164262
$291$	4.94164	0.289684
$292$	−13.8572	−0.810933
$293$	−23.9789	−1.40086	−0.700430	−	0.713721i	$-0.747009\pi$
$293$	−23.9789	−1.40086	−0.700430	+	0.713721i	$0.747009\pi$
$294$	−9.76758	−0.569657
$295$	−11.0544	−0.643610
$296$	−3.63917	−0.211522
$297$	−1.00000	−0.0580259
$298$	0.367193	0.0212709
$299$	−16.4601	−0.951911
$300$	−2.34617	−0.135456
$301$	7.10038	0.409259
$302$	2.81051	0.161727
$303$	8.66695	0.497903
$304$	8.57070	0.491563
$305$	1.62906	0.0932795
$306$	6.07005	0.347002
$307$	−2.95252	−0.168509	−0.0842545	−	0.996444i	$-0.526851\pi$
$307$	−2.95252	−0.168509	−0.0842545	+	0.996444i	$0.526851\pi$
$308$	4.09482	0.233324
$309$	2.92477	0.166384
$310$	−7.14800	−0.405979
$311$	−18.0561	−1.02387	−0.511933	−	0.859026i	$-0.671070\pi$
$311$	−18.0561	−1.02387	−0.511933	+	0.859026i	$0.671070\pi$
$312$	−2.05318	−0.116238
$313$	29.2592	1.65383	0.826914	−	0.562329i	$-0.190094\pi$
$313$	29.2592	1.65383	0.826914	+	0.562329i	$0.190094\pi$
$314$	2.35423	0.132857
$315$	6.67070	0.375851
$316$	15.9806	0.898977
$317$	−17.1452	−0.962968	−0.481484	−	0.876455i	$-0.659902\pi$
$317$	−17.1452	−0.962968	−0.481484	+	0.876455i	$0.659902\pi$
$318$	8.44100	0.473348
$319$	−1.71712	−0.0961401
$320$	−1.62906	−0.0910670
$321$	11.9162	0.665100
$322$	−32.8277	−1.82942
$323$	−52.0246	−2.89473
$324$	1.00000	0.0555556
$325$	−4.81712	−0.267206
$326$	−23.6811	−1.31158
$327$	15.1581	0.838246
$328$	−2.67070	−0.147465
$329$	−36.9697	−2.03821
$330$	−1.62906	−0.0896766
$331$	8.59927	0.472659	0.236329	−	0.971673i	$-0.424056\pi$
$331$	8.59927	0.472659	0.236329	+	0.971673i	$0.424056\pi$
$332$	−14.6824	−0.805801
$333$	3.63917	0.199425
$334$	−1.19754	−0.0655266
$335$	14.2033	0.776007
$336$	−4.09482	−0.223391
$337$	6.29714	0.343027	0.171514	−	0.985182i	$-0.445134\pi$
$337$	6.29714	0.343027	0.171514	+	0.985182i	$0.445134\pi$
$338$	8.78445	0.477811
$339$	15.9090	0.864057
$340$	9.88846	0.536277
$341$	4.38782	0.237614
$342$	−8.57070	−0.463450
$343$	−11.3327	−0.611911
$344$	1.73399	0.0934905
$345$	13.0599	0.703124
$346$	−3.99416	−0.214727
$347$	22.5634	1.21127	0.605634	−	0.795743i	$-0.292919\pi$
$347$	22.5634	1.21127	0.605634	+	0.795743i	$0.292919\pi$
$348$	1.71712	0.0920471
$349$	−34.5368	−1.84871	−0.924355	−	0.381533i	$-0.875396\pi$
$349$	−34.5368	−1.84871	−0.924355	+	0.381533i	$0.875396\pi$
$350$	−9.60717	−0.513525
$351$	2.05318	0.109591
$352$	1.00000	0.0533002
$353$	−7.43073	−0.395498	−0.197749	−	0.980253i	$-0.563363\pi$
$353$	−7.43073	−0.395498	−0.197749	+	0.980253i	$0.563363\pi$
$354$	−6.78574	−0.360658
$355$	7.93399	0.421093
$356$	11.8389	0.627462
$357$	24.8558	1.31551
$358$	10.2150	0.539882
$359$	20.8794	1.10197	0.550987	−	0.834514i	$-0.314251\pi$
$359$	20.8794	1.10197	0.550987	+	0.834514i	$0.314251\pi$
$360$	1.62906	0.0858588
$361$	54.4569	2.86615
$362$	9.65733	0.507578
$363$	1.00000	0.0524864
$364$	−8.40741	−0.440668
$365$	22.5742	1.18159
$366$	1.00000	0.0522708
$367$	−29.7949	−1.55528	−0.777639	−	0.628711i	$-0.783583\pi$
$367$	−29.7949	−1.55528	−0.777639	+	0.628711i	$0.783583\pi$
$368$	−8.01687	−0.417908
$369$	2.67070	0.139031
$370$	5.92841	0.308203
$371$	34.5644	1.79449
$372$	−4.38782	−0.227498
$373$	33.9622	1.75849	0.879247	−	0.476366i	$-0.158046\pi$
$373$	33.9622	1.75849	0.879247	+	0.476366i	$0.158046\pi$
$374$	−6.07005	−0.313875
$375$	11.9673	0.617991
$376$	−9.02841	−0.465605
$377$	3.52555	0.181575
$378$	4.09482	0.210615
$379$	20.1239	1.03370	0.516848	−	0.856077i	$-0.327105\pi$
$379$	20.1239	1.03370	0.516848	+	0.856077i	$0.327105\pi$
$380$	−13.9622	−0.716244
$381$	12.6938	0.650322
$382$	17.8595	0.913774
$383$	−19.6855	−1.00588	−0.502942	−	0.864320i	$-0.667749\pi$
$383$	−19.6855	−1.00588	−0.502942	+	0.864320i	$0.667749\pi$
$384$	−1.00000	−0.0510310
$385$	−6.67070	−0.339970
$386$	−16.6298	−0.846437
$387$	−1.73399	−0.0881437
$388$	4.94164	0.250874
$389$	−11.7682	−0.596674	−0.298337	−	0.954461i	$-0.596432\pi$
$389$	−11.7682	−0.596674	−0.298337	+	0.954461i	$0.596432\pi$
$390$	3.34475	0.169368
$391$	48.6629	2.46099
$392$	−9.76758	−0.493337
$393$	−10.9774	−0.553739
$394$	6.83671	0.344428
$395$	−26.0333	−1.30988
$396$	−1.00000	−0.0502519
$397$	−22.3152	−1.11997	−0.559984	−	0.828503i	$-0.689193\pi$
$397$	−22.3152	−1.11997	−0.559984	+	0.828503i	$0.689193\pi$
$398$	−16.8268	−0.843449
$399$	−35.0955	−1.75697
$400$	−2.34617	−0.117309
$401$	7.01767	0.350446	0.175223	−	0.984529i	$-0.443935\pi$
$401$	7.01767	0.350446	0.175223	+	0.984529i	$0.443935\pi$
$402$	8.71870	0.434849
$403$	−9.00898	−0.448769
$404$	8.66695	0.431197
$405$	−1.62906	−0.0809485
$406$	7.03129	0.348957
$407$	−3.63917	−0.180387
$408$	6.07005	0.300512
$409$	−5.33129	−0.263615	−0.131808	−	0.991275i	$-0.542078\pi$
$409$	−5.33129	−0.263615	−0.131808	+	0.991275i	$0.542078\pi$
$410$	4.35072	0.214867
$411$	−2.77547	−0.136904
$412$	2.92477	0.144093
$413$	−27.7864	−1.36728
$414$	8.01687	0.394008
$415$	23.9185	1.17411
$416$	−2.05318	−0.100665
$417$	17.0533	0.835106
$418$	8.57070	0.419207
$419$	−10.8315	−0.529155	−0.264577	−	0.964364i	$-0.585232\pi$
$419$	−10.8315	−0.529155	−0.264577	+	0.964364i	$0.585232\pi$
$420$	6.67070	0.325497
$421$	−30.1117	−1.46756	−0.733778	−	0.679389i	$-0.762245\pi$
$421$	−30.1117	−1.46756	−0.733778	+	0.679389i	$0.762245\pi$
$422$	−23.2247	−1.13056
$423$	9.02841	0.438976
$424$	8.44100	0.409931
$425$	14.2414	0.690809
$426$	4.87030	0.235967
$427$	4.09482	0.198162
$428$	11.9162	0.575993
$429$	−2.05318	−0.0991285
$430$	−2.82477	−0.136222
$431$	−12.9374	−0.623172	−0.311586	−	0.950218i	$-0.600860\pi$
$431$	−12.9374	−0.623172	−0.311586	+	0.950218i	$0.600860\pi$
$432$	1.00000	0.0481125
$433$	25.0904	1.20577	0.602885	−	0.797828i	$-0.294018\pi$
$433$	25.0904	1.20577	0.602885	+	0.797828i	$0.294018\pi$
$434$	−17.9673	−0.862460
$435$	−2.79728	−0.134119
$436$	15.1581	0.725942
$437$	−68.7102	−3.28686
$438$	13.8572	0.662124
$439$	−9.17005	−0.437663	−0.218831	−	0.975763i	$-0.570224\pi$
$439$	−9.17005	−0.437663	−0.218831	+	0.975763i	$0.570224\pi$
$440$	−1.62906	−0.0776622
$441$	9.76758	0.465123
$442$	12.4629	0.592800
$443$	−32.2319	−1.53138	−0.765692	−	0.643207i	$-0.777603\pi$
$443$	−32.2319	−1.53138	−0.765692	+	0.643207i	$0.777603\pi$
$444$	3.63917	0.172707
$445$	−19.2863	−0.914257
$446$	−11.6012	−0.549331
$447$	−0.367193	−0.0173676
$448$	−4.09482	−0.193462
$449$	−1.29157	−0.0609528	−0.0304764	−	0.999535i	$-0.509702\pi$
$449$	−1.29157	−0.0609528	−0.0304764	+	0.999535i	$0.509702\pi$
$450$	2.34617	0.110600
$451$	−2.67070	−0.125758
$452$	15.9090	0.748295
$453$	−2.81051	−0.132049
$454$	−21.9215	−1.02883
$455$	13.6961	0.642085
$456$	−8.57070	−0.401360
$457$	−21.1257	−0.988219	−0.494110	−	0.869400i	$-0.664506\pi$
$457$	−21.1257	−0.988219	−0.494110	+	0.869400i	$0.664506\pi$
$458$	15.0052	0.701148
$459$	−6.07005	−0.283326
$460$	13.0599	0.608923
$461$	6.07148	0.282777	0.141389	−	0.989954i	$-0.454843\pi$
$461$	6.07148	0.282777	0.141389	+	0.989954i	$0.454843\pi$
$462$	−4.09482	−0.190508
$463$	−8.79221	−0.408609	−0.204304	−	0.978907i	$-0.565493\pi$
$463$	−8.79221	−0.408609	−0.204304	+	0.978907i	$0.565493\pi$
$464$	1.71712	0.0797151
$465$	7.14800	0.331481
$466$	−16.4547	−0.762251
$467$	41.2298	1.90789	0.953943	−	0.299989i	$-0.0969829\pi$
$467$	41.2298	1.90789	0.953943	+	0.299989i	$0.0969829\pi$
$468$	2.05318	0.0949083
$469$	35.7015	1.64854
$470$	14.7078	0.678420
$471$	−2.35423	−0.108477
$472$	−6.78574	−0.312339
$473$	1.73399	0.0797290
$474$	−15.9806	−0.734012
$475$	−20.1084	−0.922634
$476$	24.8558	1.13926
$477$	−8.44100	−0.386487
$478$	−28.5650	−1.30653
$479$	18.4907	0.844860	0.422430	−	0.906396i	$-0.361177\pi$
$479$	18.4907	0.844860	0.422430	+	0.906396i	$0.361177\pi$
$480$	1.62906	0.0743559
$481$	7.47187	0.340688
$482$	−24.8317	−1.13105
$483$	32.8277	1.49371
$484$	1.00000	0.0454545
$485$	−8.05022	−0.365542
$486$	−1.00000	−0.0453609
$487$	−10.4782	−0.474814	−0.237407	−	0.971410i	$-0.576297\pi$
$487$	−10.4782	−0.474814	−0.237407	+	0.971410i	$0.576297\pi$
$488$	1.00000	0.0452679
$489$	23.6811	1.07090
$490$	15.9119	0.718828
$491$	41.7373	1.88358	0.941789	−	0.336205i	$-0.109144\pi$
$491$	41.7373	1.88358	0.941789	+	0.336205i	$0.109144\pi$
$492$	2.67070	0.120404
$493$	−10.4230	−0.469428
$494$	−17.5972	−0.791735
$495$	1.62906	0.0732207
$496$	−4.38782	−0.197019
$497$	19.9430	0.894566
$498$	14.6824	0.657934
$499$	17.5898	0.787427	0.393714	−	0.919233i	$-0.371190\pi$
$499$	17.5898	0.787427	0.393714	+	0.919233i	$0.371190\pi$
$500$	11.9673	0.535195
$501$	1.19754	0.0535022
$502$	10.4083	0.464547
$503$	16.0760	0.716794	0.358397	−	0.933569i	$-0.383323\pi$
$503$	16.0760	0.716794	0.358397	+	0.933569i	$0.383323\pi$
$504$	4.09482	0.182398
$505$	−14.1190	−0.628285
$506$	−8.01687	−0.356394
$507$	−8.78445	−0.390131
$508$	12.6938	0.563195
$509$	−30.2149	−1.33925	−0.669627	−	0.742698i	$-0.733546\pi$
$509$	−30.2149	−1.33925	−0.669627	+	0.742698i	$0.733546\pi$
$510$	−9.88846	−0.437869
$511$	56.7429	2.51016
$512$	−1.00000	−0.0441942
$513$	8.57070	0.378406
$514$	18.3426	0.809057
$515$	−4.76462	−0.209954
$516$	−1.73399	−0.0763347
$517$	−9.02841	−0.397069
$518$	14.9017	0.654745
$519$	3.99416	0.175324
$520$	3.34475	0.146677
$521$	39.7338	1.74077	0.870385	−	0.492372i	$-0.163870\pi$
$521$	39.7338	1.74077	0.870385	+	0.492372i	$0.163870\pi$
$522$	−1.71712	−0.0751562
$523$	3.06186	0.133886	0.0669430	−	0.997757i	$-0.478675\pi$
$523$	3.06186	0.133886	0.0669430	+	0.997757i	$0.478675\pi$
$524$	−10.9774	−0.479552
$525$	9.60717	0.419291
$526$	9.55996	0.416834
$527$	26.6343	1.16021
$528$	−1.00000	−0.0435194
$529$	41.2703	1.79436
$530$	−13.7509	−0.597299
$531$	6.78574	0.294476
$532$	−35.0955	−1.52158
$533$	5.48343	0.237514
$534$	−11.8389	−0.512320
$535$	−19.4122	−0.839264
$536$	8.71870	0.376591
$537$	−10.2150	−0.440812
$538$	5.13997	0.221600
$539$	−9.76758	−0.420719
$540$	−1.62906	−0.0701034
$541$	−26.9818	−1.16004	−0.580018	−	0.814604i	$-0.696955\pi$
$541$	−26.9818	−1.16004	−0.580018	+	0.814604i	$0.696955\pi$
$542$	11.4849	0.493317
$543$	−9.65733	−0.414436
$544$	6.07005	0.260251
$545$	−24.6934	−1.05775
$546$	8.40741	0.359804
$547$	14.6014	0.624312	0.312156	−	0.950031i	$-0.398949\pi$
$547$	14.6014	0.624312	0.312156	+	0.950031i	$0.398949\pi$
$548$	−2.77547	−0.118562
$549$	−1.00000	−0.0426790
$550$	−2.34617	−0.100041
$551$	14.7169	0.626961
$552$	8.01687	0.341221
$553$	−65.4376	−2.78269
$554$	22.0520	0.936902
$555$	−5.92841	−0.251647
$556$	17.0533	0.723223
$557$	25.3341	1.07344	0.536721	−	0.843760i	$-0.319663\pi$
$557$	25.3341	1.07344	0.536721	+	0.843760i	$0.319663\pi$
$558$	4.38782	0.185751
$559$	−3.56019	−0.150580
$560$	6.67070	0.281889
$561$	6.07005	0.256278
$562$	−10.0948	−0.425824
$563$	−1.15888	−0.0488408	−0.0244204	−	0.999702i	$-0.507774\pi$
$563$	−1.15888	−0.0488408	−0.0244204	+	0.999702i	$0.507774\pi$
$564$	9.02841	0.380165
$565$	−25.9166	−1.09032
$566$	−17.7154	−0.744632
$567$	−4.09482	−0.171966
$568$	4.87030	0.204353
$569$	4.79768	0.201129	0.100565	−	0.994931i	$-0.467935\pi$
$569$	4.79768	0.201129	0.100565	+	0.994931i	$0.467935\pi$
$570$	13.9622	0.584810
$571$	−17.3259	−0.725065	−0.362533	−	0.931971i	$-0.618088\pi$
$571$	−17.3259	−0.725065	−0.362533	+	0.931971i	$0.618088\pi$
$572$	−2.05318	−0.0858478
$573$	−17.8595	−0.746093
$574$	10.9360	0.456462
$575$	18.8090	0.784389
$576$	1.00000	0.0416667
$577$	−14.0342	−0.584253	−0.292127	−	0.956380i	$-0.594363\pi$
$577$	−14.0342	−0.584253	−0.292127	+	0.956380i	$0.594363\pi$
$578$	−19.8456	−0.825466
$579$	16.6298	0.691113
$580$	−2.79728	−0.116151
$581$	60.1218	2.49427
$582$	−4.94164	−0.204838
$583$	8.44100	0.349590
$584$	13.8572	0.573416
$585$	−3.34475	−0.138288
$586$	23.9789	0.990558
$587$	−13.5554	−0.559490	−0.279745	−	0.960074i	$-0.590250\pi$
$587$	−13.5554	−0.559490	−0.279745	+	0.960074i	$0.590250\pi$
$588$	9.76758	0.402808
$589$	−37.6067	−1.54956
$590$	11.0544	0.455101
$591$	−6.83671	−0.281225
$592$	3.63917	0.149569
$593$	42.8640	1.76022	0.880108	−	0.474774i	$-0.157470\pi$
$593$	42.8640	1.76022	0.880108	+	0.474774i	$0.157470\pi$
$594$	1.00000	0.0410305
$595$	−40.4915	−1.65999
$596$	−0.367193	−0.0150408
$597$	16.8268	0.688673
$598$	16.4601	0.673103
$599$	−31.2808	−1.27810	−0.639050	−	0.769165i	$-0.720672\pi$
$599$	−31.2808	−1.27810	−0.639050	+	0.769165i	$0.720672\pi$
$600$	2.34617	0.0957821
$601$	−34.6508	−1.41344	−0.706718	−	0.707496i	$-0.749825\pi$
$601$	−34.6508	−1.41344	−0.706718	+	0.707496i	$0.749825\pi$
$602$	−7.10038	−0.289390
$603$	−8.71870	−0.355053
$604$	−2.81051	−0.114358
$605$	−1.62906	−0.0662306
$606$	−8.66695	−0.352071
$607$	43.1308	1.75062	0.875312	−	0.483558i	$-0.160656\pi$
$607$	43.1308	1.75062	0.875312	+	0.483558i	$0.160656\pi$
$608$	−8.57070	−0.347588
$609$	−7.03129	−0.284922
$610$	−1.62906	−0.0659586
$611$	18.5370	0.749925
$612$	−6.07005	−0.245367
$613$	6.58820	0.266095	0.133047	−	0.991110i	$-0.457524\pi$
$613$	6.58820	0.266095	0.133047	+	0.991110i	$0.457524\pi$
$614$	2.95252	0.119154
$615$	−4.35072	−0.175438
$616$	−4.09482	−0.164985
$617$	11.8746	0.478053	0.239027	−	0.971013i	$-0.423172\pi$
$617$	11.8746	0.478053	0.239027	+	0.971013i	$0.423172\pi$
$618$	−2.92477	−0.117651
$619$	−46.6701	−1.87583	−0.937915	−	0.346864i	$-0.887246\pi$
$619$	−46.6701	−1.87583	−0.937915	+	0.346864i	$0.887246\pi$
$620$	7.14800	0.287071
$621$	−8.01687	−0.321706
$622$	18.0561	0.723982
$623$	−48.4783	−1.94224
$624$	2.05318	0.0821930
$625$	−7.76460	−0.310584
$626$	−29.2592	−1.16943
$627$	−8.57070	−0.342281
$628$	−2.35423	−0.0939440
$629$	−22.0899	−0.880784
$630$	−6.67070	−0.265767
$631$	5.51443	0.219526	0.109763	−	0.993958i	$-0.464991\pi$
$631$	5.51443	0.219526	0.109763	+	0.993958i	$0.464991\pi$
$632$	−15.9806	−0.635673
$633$	23.2247	0.923098
$634$	17.1452	0.680921
$635$	−20.6789	−0.820616
$636$	−8.44100	−0.334707
$637$	20.0546	0.794592
$638$	1.71712	0.0679813
$639$	−4.87030	−0.192666
$640$	1.62906	0.0643941
$641$	6.83870	0.270112	0.135056	−	0.990838i	$-0.456879\pi$
$641$	6.83870	0.270112	0.135056	+	0.990838i	$0.456879\pi$
$642$	−11.9162	−0.470297
$643$	40.8072	1.60928	0.804639	−	0.593764i	$-0.202359\pi$
$643$	40.8072	1.60928	0.804639	+	0.593764i	$0.202359\pi$
$644$	32.8277	1.29359
$645$	2.82477	0.111225
$646$	52.0246	2.04688
$647$	23.8536	0.937782	0.468891	−	0.883256i	$-0.344654\pi$
$647$	23.8536	0.937782	0.468891	+	0.883256i	$0.344654\pi$
$648$	−1.00000	−0.0392837
$649$	−6.78574	−0.266364
$650$	4.81712	0.188943
$651$	17.9673	0.704195
$652$	23.6811	0.927424
$653$	21.7971	0.852987	0.426494	−	0.904491i	$-0.359749\pi$
$653$	21.7971	0.852987	0.426494	+	0.904491i	$0.359749\pi$
$654$	−15.1581	−0.592729
$655$	17.8829	0.698742
$656$	2.67070	0.104273
$657$	−13.8572	−0.540622
$658$	36.9697	1.44123
$659$	11.2826	0.439509	0.219755	−	0.975555i	$-0.429474\pi$
$659$	11.2826	0.439509	0.219755	+	0.975555i	$0.429474\pi$
$660$	1.62906	0.0634110
$661$	−3.85315	−0.149870	−0.0749352	−	0.997188i	$-0.523875\pi$
$661$	−3.85315	−0.149870	−0.0749352	+	0.997188i	$0.523875\pi$
$662$	−8.59927	−0.334220
$663$	−12.4629	−0.484019
$664$	14.6824	0.569788
$665$	57.1726	2.21706
$666$	−3.63917	−0.141015
$667$	−13.7659	−0.533018
$668$	1.19754	0.0463343
$669$	11.6012	0.448527
$670$	−14.2033	−0.548720
$671$	1.00000	0.0386046
$672$	4.09482	0.157961
$673$	−11.9556	−0.460856	−0.230428	−	0.973089i	$-0.574013\pi$
$673$	−11.9556	−0.460856	−0.230428	+	0.973089i	$0.574013\pi$
$674$	−6.29714	−0.242557
$675$	−2.34617	−0.0903043
$676$	−8.78445	−0.337864
$677$	36.0169	1.38424	0.692121	−	0.721782i	$-0.256677\pi$
$677$	36.0169	1.38424	0.692121	+	0.721782i	$0.256677\pi$
$678$	−15.9090	−0.610981
$679$	−20.2352	−0.776554
$680$	−9.88846	−0.379205
$681$	21.9215	0.840035
$682$	−4.38782	−0.168018
$683$	−0.0656507	−0.00251205	−0.00125603	−	0.999999i	$-0.500400\pi$
$683$	−0.0656507	−0.00251205	−0.00125603	+	0.999999i	$0.500400\pi$
$684$	8.57070	0.327709
$685$	4.52140	0.172754
$686$	11.3327	0.432686
$687$	−15.0052	−0.572485
$688$	−1.73399	−0.0661078
$689$	−17.3309	−0.660254
$690$	−13.0599	−0.497184
$691$	−11.9959	−0.456346	−0.228173	−	0.973621i	$-0.573275\pi$
$691$	−11.9959	−0.456346	−0.228173	+	0.973621i	$0.573275\pi$
$692$	3.99416	0.151835
$693$	4.09482	0.155549
$694$	−22.5634	−0.856496
$695$	−27.7809	−1.05379
$696$	−1.71712	−0.0650871
$697$	−16.2113	−0.614047
$698$	34.5368	1.30724
$699$	16.4547	0.622376
$700$	9.60717	0.363117
$701$	9.81687	0.370778	0.185389	−	0.982665i	$-0.440645\pi$
$701$	9.81687	0.370778	0.185389	+	0.982665i	$0.440645\pi$
$702$	−2.05318	−0.0774923
$703$	31.1902	1.17636
$704$	−1.00000	−0.0376889
$705$	−14.7078	−0.553928
$706$	7.43073	0.279659
$707$	−35.4896	−1.33472
$708$	6.78574	0.255024
$709$	23.1199	0.868287	0.434143	−	0.900844i	$-0.357051\pi$
$709$	23.1199	0.868287	0.434143	+	0.900844i	$0.357051\pi$
$710$	−7.93399	−0.297757
$711$	15.9806	0.599318
$712$	−11.8389	−0.443682
$713$	35.1766	1.31737
$714$	−24.8558	−0.930205
$715$	3.34475	0.125086
$716$	−10.2150	−0.381754
$717$	28.5650	1.06678
$718$	−20.8794	−0.779214
$719$	−31.3915	−1.17071	−0.585353	−	0.810779i	$-0.699044\pi$
$719$	−31.3915	−1.17071	−0.585353	+	0.810779i	$0.699044\pi$
$720$	−1.62906	−0.0607114
$721$	−11.9764	−0.446025
$722$	−54.4569	−2.02668
$723$	24.8317	0.923501
$724$	−9.65733	−0.358912
$725$	−4.02865	−0.149620
$726$	−1.00000	−0.0371135
$727$	−33.7173	−1.25050	−0.625252	−	0.780423i	$-0.715004\pi$
$727$	−33.7173	−1.25050	−0.625252	+	0.780423i	$0.715004\pi$
$728$	8.40741	0.311599
$729$	1.00000	0.0370370
$730$	−22.5742	−0.835509
$731$	10.5254	0.389297
$732$	−1.00000	−0.0369611
$733$	−7.27108	−0.268563	−0.134282	−	0.990943i	$-0.542873\pi$
$733$	−7.27108	−0.268563	−0.134282	+	0.990943i	$0.542873\pi$
$734$	29.7949	1.09975
$735$	−15.9119	−0.586921
$736$	8.01687	0.295506
$737$	8.71870	0.321158
$738$	−2.67070	−0.0983098
$739$	−46.7340	−1.71914	−0.859570	−	0.511018i	$-0.829268\pi$
$739$	−46.7340	−1.71914	−0.859570	+	0.511018i	$0.829268\pi$
$740$	−5.92841	−0.217933
$741$	17.5972	0.646449
$742$	−34.5644	−1.26890
$743$	12.7681	0.468417	0.234209	−	0.972186i	$-0.424750\pi$
$743$	12.7681	0.468417	0.234209	+	0.972186i	$0.424750\pi$
$744$	4.38782	0.160865
$745$	0.598178	0.0219155
$746$	−33.9622	−1.24344
$747$	−14.6824	−0.537201
$748$	6.07005	0.221943
$749$	−48.7949	−1.78293
$750$	−11.9673	−0.436985
$751$	−24.9789	−0.911492	−0.455746	−	0.890110i	$-0.650627\pi$
$751$	−24.9789	−0.911492	−0.455746	+	0.890110i	$0.650627\pi$
$752$	9.02841	0.329232
$753$	−10.4083	−0.379301
$754$	−3.52555	−0.128393
$755$	4.57849	0.166628
$756$	−4.09482	−0.148927
$757$	37.8111	1.37427	0.687133	−	0.726531i	$-0.258869\pi$
$757$	37.8111	1.37427	0.687133	+	0.726531i	$0.258869\pi$
$758$	−20.1239	−0.730933
$759$	8.01687	0.290994
$760$	13.9622	0.506461
$761$	−44.9661	−1.63002	−0.815009	−	0.579448i	$-0.803268\pi$
$761$	−44.9661	−1.63002	−0.815009	+	0.579448i	$0.803268\pi$
$762$	−12.6938	−0.459847
$763$	−62.0698	−2.24708
$764$	−17.8595	−0.646136
$765$	9.88846	0.357518
$766$	19.6855	0.711267
$767$	13.9324	0.503068
$768$	1.00000	0.0360844
$769$	−6.76002	−0.243772	−0.121886	−	0.992544i	$-0.538894\pi$
$769$	−6.76002	−0.243772	−0.121886	+	0.992544i	$0.538894\pi$
$770$	6.67070	0.240395
$771$	−18.3426	−0.660592
$772$	16.6298	0.598521
$773$	24.5654	0.883557	0.441778	−	0.897124i	$-0.354348\pi$
$773$	24.5654	0.883557	0.441778	+	0.897124i	$0.354348\pi$
$774$	1.73399	0.0623270
$775$	10.2946	0.369792
$776$	−4.94164	−0.177395
$777$	−14.9017	−0.534597
$778$	11.7682	0.421912
$779$	22.8898	0.820111
$780$	−3.34475	−0.119761
$781$	4.87030	0.174273
$782$	−48.6629	−1.74018
$783$	1.71712	0.0613647
$784$	9.76758	0.348842
$785$	3.83517	0.136883
$786$	10.9774	0.391552
$787$	−2.60728	−0.0929393	−0.0464697	−	0.998920i	$-0.514797\pi$
$787$	−2.60728	−0.0929393	−0.0464697	+	0.998920i	$0.514797\pi$
$788$	−6.83671	−0.243548
$789$	−9.55996	−0.340344
$790$	26.0333	0.926222
$791$	−65.1445	−2.31627
$792$	1.00000	0.0355335
$793$	−2.05318	−0.0729106
$794$	22.3152	0.791937
$795$	13.7509	0.487693
$796$	16.8268	0.596409
$797$	−28.3841	−1.00542	−0.502708	−	0.864457i	$-0.667663\pi$
$797$	−28.3841	−1.00542	−0.502708	+	0.864457i	$0.667663\pi$
$798$	35.0955	1.24237
$799$	−54.8029	−1.93879
$800$	2.34617	0.0829498
$801$	11.8389	0.418308
$802$	−7.01767	−0.247803
$803$	13.8572	0.489011
$804$	−8.71870	−0.307485
$805$	−53.4782	−1.88486
$806$	9.00898	0.317328
$807$	−5.13997	−0.180936
$808$	−8.66695	−0.304902
$809$	17.8556	0.627768	0.313884	−	0.949461i	$-0.398370\pi$
$809$	17.8556	0.627768	0.313884	+	0.949461i	$0.398370\pi$
$810$	1.62906	0.0572392
$811$	−9.73867	−0.341971	−0.170985	−	0.985274i	$-0.554695\pi$
$811$	−9.73867	−0.341971	−0.170985	+	0.985274i	$0.554695\pi$
$812$	−7.03129	−0.246750
$813$	−11.4849	−0.402791
$814$	3.63917	0.127553
$815$	−38.5779	−1.35132
$816$	−6.07005	−0.212494
$817$	−14.8615	−0.519939
$818$	5.33129	0.186404
$819$	−8.40741	−0.293779
$820$	−4.35072	−0.151934
$821$	−19.1182	−0.667228	−0.333614	−	0.942710i	$-0.608268\pi$
$821$	−19.1182	−0.667228	−0.333614	+	0.942710i	$0.608268\pi$
$822$	2.77547	0.0968058
$823$	−7.34033	−0.255868	−0.127934	−	0.991783i	$-0.540835\pi$
$823$	−7.34033	−0.255868	−0.127934	+	0.991783i	$0.540835\pi$
$824$	−2.92477	−0.101889
$825$	2.34617	0.0816833
$826$	27.7864	0.966813
$827$	6.86483	0.238713	0.119357	−	0.992851i	$-0.461917\pi$
$827$	6.86483	0.238713	0.119357	+	0.992851i	$0.461917\pi$
$828$	−8.01687	−0.278606
$829$	46.2219	1.60535	0.802676	−	0.596415i	$-0.203409\pi$
$829$	46.2219	1.60535	0.802676	+	0.596415i	$0.203409\pi$
$830$	−23.9185	−0.830222
$831$	−22.0520	−0.764977
$832$	2.05318	0.0711812
$833$	−59.2897	−2.05427
$834$	−17.0533	−0.590509
$835$	−1.95086	−0.0675125
$836$	−8.57070	−0.296424
$837$	−4.38782	−0.151665
$838$	10.8315	0.374169
$839$	19.6151	0.677189	0.338594	−	0.940932i	$-0.390049\pi$
$839$	19.6151	0.677189	0.338594	+	0.940932i	$0.390049\pi$
$840$	−6.67070	−0.230161
$841$	−26.0515	−0.898328
$842$	30.1117	1.03772
$843$	10.0948	0.347684
$844$	23.2247	0.799427
$845$	14.3104	0.492292
$846$	−9.02841	−0.310403
$847$	−4.09482	−0.140700
$848$	−8.44100	−0.289865
$849$	17.7154	0.607989
$850$	−14.2414	−0.488476
$851$	−29.1747	−1.00010
$852$	−4.87030	−0.166854
$853$	−12.0272	−0.411804	−0.205902	−	0.978573i	$-0.566013\pi$
$853$	−12.0272	−0.411804	−0.205902	+	0.978573i	$0.566013\pi$
$854$	−4.09482	−0.140122
$855$	−13.9622	−0.477496
$856$	−11.9162	−0.407289
$857$	−38.8685	−1.32772	−0.663862	−	0.747855i	$-0.731084\pi$
$857$	−38.8685	−1.32772	−0.663862	+	0.747855i	$0.731084\pi$
$858$	2.05318	0.0700944
$859$	29.4503	1.00483	0.502415	−	0.864627i	$-0.332445\pi$
$859$	29.4503	1.00483	0.502415	+	0.864627i	$0.332445\pi$
$860$	2.82477	0.0963238
$861$	−10.9360	−0.372699
$862$	12.9374	0.440649
$863$	−13.8257	−0.470633	−0.235317	−	0.971919i	$-0.575613\pi$
$863$	−13.8257	−0.470633	−0.235317	+	0.971919i	$0.575613\pi$
$864$	−1.00000	−0.0340207
$865$	−6.50671	−0.221235
$866$	−25.0904	−0.852608
$867$	19.8456	0.673990
$868$	17.9673	0.609851
$869$	−15.9806	−0.542104
$870$	2.79728	0.0948367
$871$	−17.9011	−0.606555
$872$	−15.1581	−0.513318
$873$	4.94164	0.167249
$874$	68.7102	2.32416
$875$	−49.0041	−1.65664
$876$	−13.8572	−0.468192
$877$	−40.5419	−1.36900	−0.684502	−	0.729011i	$-0.739980\pi$
$877$	−40.5419	−1.36900	−0.684502	+	0.729011i	$0.739980\pi$
$878$	9.17005	0.309474
$879$	−23.9789	−0.808787
$880$	1.62906	0.0549155
$881$	43.6711	1.47132	0.735658	−	0.677353i	$-0.236873\pi$
$881$	43.6711	1.47132	0.735658	+	0.677353i	$0.236873\pi$
$882$	−9.76758	−0.328891
$883$	26.0399	0.876314	0.438157	−	0.898899i	$-0.355631\pi$
$883$	26.0399	0.876314	0.438157	+	0.898899i	$0.355631\pi$
$884$	−12.4629	−0.419173
$885$	−11.0544	−0.371588
$886$	32.2319	1.08285
$887$	−17.2671	−0.579771	−0.289886	−	0.957061i	$-0.593617\pi$
$887$	−17.2671	−0.579771	−0.289886	+	0.957061i	$0.593617\pi$
$888$	−3.63917	−0.122122
$889$	−51.9788	−1.74331
$890$	19.2863	0.646478
$891$	−1.00000	−0.0335013
$892$	11.6012	0.388436
$893$	77.3798	2.58942
$894$	0.367193	0.0122808
$895$	16.6409	0.556244
$896$	4.09482	0.136798
$897$	−16.4601	−0.549586
$898$	1.29157	0.0431002
$899$	−7.53439	−0.251286
$900$	−2.34617	−0.0782058
$901$	51.2373	1.70696
$902$	2.67070	0.0889246
$903$	7.10038	0.236286
$904$	−15.9090	−0.529125
$905$	15.7323	0.522961
$906$	2.81051	0.0933731
$907$	−5.76021	−0.191265	−0.0956324	−	0.995417i	$-0.530487\pi$
$907$	−5.76021	−0.191265	−0.0956324	+	0.995417i	$0.530487\pi$
$908$	21.9215	0.727492
$909$	8.66695	0.287465
$910$	−13.6961	−0.454023
$911$	4.42635	0.146651	0.0733257	−	0.997308i	$-0.476639\pi$
$911$	4.42635	0.146651	0.0733257	+	0.997308i	$0.476639\pi$
$912$	8.57070	0.283804
$913$	14.6824	0.485916
$914$	21.1257	0.698777
$915$	1.62906	0.0538550
$916$	−15.0052	−0.495787
$917$	44.9507	1.48440
$918$	6.07005	0.200342
$919$	7.93867	0.261872	0.130936	−	0.991391i	$-0.458202\pi$
$919$	7.93867	0.261872	0.130936	+	0.991391i	$0.458202\pi$
$920$	−13.0599	−0.430574
$921$	−2.95252	−0.0972887
$922$	−6.07148	−0.199954
$923$	−9.99960	−0.329141
$924$	4.09482	0.134710
$925$	−8.53812	−0.280732
$926$	8.79221	0.288930
$927$	2.92477	0.0960620
$928$	−1.71712	−0.0563671
$929$	−0.954985	−0.0313320	−0.0156660	−	0.999877i	$-0.504987\pi$
$929$	−0.954985	−0.0313320	−0.0156660	+	0.999877i	$0.504987\pi$
$930$	−7.14800	−0.234392
$931$	83.7150	2.74365
$932$	16.4547	0.538993
$933$	−18.0561	−0.591129
$934$	−41.2298	−1.34908
$935$	−9.88846	−0.323387
$936$	−2.05318	−0.0671103
$937$	−52.6043	−1.71851	−0.859254	−	0.511550i	$-0.829072\pi$
$937$	−52.6043	−1.71851	−0.859254	+	0.511550i	$0.829072\pi$
$938$	−35.7015	−1.16570
$939$	29.2592	0.954838
$940$	−14.7078	−0.479715
$941$	−0.177546	−0.00578784	−0.00289392	−	0.999996i	$-0.500921\pi$
$941$	−0.177546	−0.00578784	−0.00289392	+	0.999996i	$0.500921\pi$
$942$	2.35423	0.0767049
$943$	−21.4107	−0.697227
$944$	6.78574	0.220857
$945$	6.67070	0.216998
$946$	−1.73399	−0.0563769
$947$	−35.5684	−1.15582	−0.577909	−	0.816101i	$-0.696131\pi$
$947$	−35.5684	−1.15582	−0.577909	+	0.816101i	$0.696131\pi$
$948$	15.9806	0.519025
$949$	−28.4514	−0.923571
$950$	20.1084	0.652401
$951$	−17.1452	−0.555970
$952$	−24.8558	−0.805581
$953$	−34.1171	−1.10516	−0.552580	−	0.833460i	$-0.686357\pi$
$953$	−34.1171	−1.10516	−0.552580	+	0.833460i	$0.686357\pi$
$954$	8.44100	0.273287
$955$	29.0942	0.941467
$956$	28.5650	0.923859
$957$	−1.71712	−0.0555065
$958$	−18.4907	−0.597406
$959$	11.3651	0.366997
$960$	−1.62906	−0.0525776
$961$	−11.7471	−0.378938
$962$	−7.47187	−0.240903
$963$	11.9162	0.383996
$964$	24.8317	0.799775
$965$	−27.0910	−0.872089
$966$	−32.8277	−1.05621
$967$	6.20742	0.199617	0.0998085	−	0.995007i	$-0.468177\pi$
$967$	6.20742	0.199617	0.0998085	+	0.995007i	$0.468177\pi$
$968$	−1.00000	−0.0321412
$969$	−52.0246	−1.67127
$970$	8.05022	0.258477
$971$	17.6405	0.566110	0.283055	−	0.959104i	$-0.408652\pi$
$971$	17.6405	0.566110	0.283055	+	0.959104i	$0.408652\pi$
$972$	1.00000	0.0320750
$973$	−69.8304	−2.23866
$974$	10.4782	0.335744
$975$	−4.81712	−0.154271
$976$	−1.00000	−0.0320092
$977$	29.4309	0.941578	0.470789	−	0.882246i	$-0.343969\pi$
$977$	29.4309	0.941578	0.470789	+	0.882246i	$0.343969\pi$
$978$	−23.6811	−0.757238
$979$	−11.8389	−0.378374
$980$	−15.9119	−0.508288
$981$	15.1581	0.483961
$982$	−41.7373	−1.33189
$983$	42.2313	1.34697	0.673485	−	0.739201i	$-0.264796\pi$
$983$	42.2313	1.34697	0.673485	+	0.739201i	$0.264796\pi$
$984$	−2.67070	−0.0851388
$985$	11.1374	0.354867
$986$	10.4230	0.331936
$987$	−36.9697	−1.17676
$988$	17.5972	0.559841
$989$	13.9012	0.442032
$990$	−1.62906	−0.0517748
$991$	52.3378	1.66257	0.831283	−	0.555850i	$-0.187607\pi$
$991$	52.3378	1.66257	0.831283	+	0.555850i	$0.187607\pi$
$992$	4.38782	0.139313
$993$	8.59927	0.272890
$994$	−19.9430	−0.632554
$995$	−27.4117	−0.869011
$996$	−14.6824	−0.465230
$997$	28.3257	0.897083	0.448541	−	0.893762i	$-0.351944\pi$
$997$	28.3257	0.897083	0.448541	+	0.893762i	$0.351944\pi$
$998$	−17.5898	−0.556795
$999$	3.63917	0.115138

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.u.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.u.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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.62906 q^{5} -1.00000 q^{6} -4.09482 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.62906 q^{5} -1.00000 q^{6} -4.09482 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.62906 q^{10} -1.00000 q^{11} +1.00000 q^{12} +2.05318 q^{13} +4.09482 q^{14} -1.62906 q^{15} +1.00000 q^{16} -6.07005 q^{17} -1.00000 q^{18} +8.57070 q^{19} -1.62906 q^{20} -4.09482 q^{21} +1.00000 q^{22} -8.01687 q^{23} -1.00000 q^{24} -2.34617 q^{25} -2.05318 q^{26} +1.00000 q^{27} -4.09482 q^{28} +1.71712 q^{29} +1.62906 q^{30} -4.38782 q^{31} -1.00000 q^{32} -1.00000 q^{33} +6.07005 q^{34} +6.67070 q^{35} +1.00000 q^{36} +3.63917 q^{37} -8.57070 q^{38} +2.05318 q^{39} +1.62906 q^{40} +2.67070 q^{41} +4.09482 q^{42} -1.73399 q^{43} -1.00000 q^{44} -1.62906 q^{45} +8.01687 q^{46} +9.02841 q^{47} +1.00000 q^{48} +9.76758 q^{49} +2.34617 q^{50} -6.07005 q^{51} +2.05318 q^{52} -8.44100 q^{53} -1.00000 q^{54} +1.62906 q^{55} +4.09482 q^{56} +8.57070 q^{57} -1.71712 q^{58} +6.78574 q^{59} -1.62906 q^{60} -1.00000 q^{61} +4.38782 q^{62} -4.09482 q^{63} +1.00000 q^{64} -3.34475 q^{65} +1.00000 q^{66} -8.71870 q^{67} -6.07005 q^{68} -8.01687 q^{69} -6.67070 q^{70} -4.87030 q^{71} -1.00000 q^{72} -13.8572 q^{73} -3.63917 q^{74} -2.34617 q^{75} +8.57070 q^{76} +4.09482 q^{77} -2.05318 q^{78} +15.9806 q^{79} -1.62906 q^{80} +1.00000 q^{81} -2.67070 q^{82} -14.6824 q^{83} -4.09482 q^{84} +9.88846 q^{85} +1.73399 q^{86} +1.71712 q^{87} +1.00000 q^{88} +11.8389 q^{89} +1.62906 q^{90} -8.40741 q^{91} -8.01687 q^{92} -4.38782 q^{93} -9.02841 q^{94} -13.9622 q^{95} -1.00000 q^{96} +4.94164 q^{97} -9.76758 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - 3 q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - 3 * q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - 3 q^{7} - 5 q^{8} + 5 q^{9} + q^{10} - 5 q^{11} + 5 q^{12} + 2 q^{13} + 3 q^{14} - q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} + 7 q^{19} - q^{20} - 3 q^{21} + 5 q^{22} - 12 q^{23} - 5 q^{24} - 2 q^{26} + 5 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} - q^{31} - 5 q^{32} - 5 q^{33} - 6 q^{34} + 17 q^{35} + 5 q^{36} + 3 q^{37} - 7 q^{38} + 2 q^{39} + q^{40} - 3 q^{41} + 3 q^{42} + 24 q^{43} - 5 q^{44} - q^{45} + 12 q^{46} + 18 q^{47} + 5 q^{48} + 26 q^{49} + 6 q^{51} + 2 q^{52} - 13 q^{53} - 5 q^{54} + q^{55} + 3 q^{56} + 7 q^{57} - 4 q^{58} - 16 q^{59} - q^{60} - 5 q^{61} + q^{62} - 3 q^{63} + 5 q^{64} + 4 q^{65} + 5 q^{66} + 18 q^{67} + 6 q^{68} - 12 q^{69} - 17 q^{70} - 31 q^{71} - 5 q^{72} + 8 q^{73} - 3 q^{74} + 7 q^{76} + 3 q^{77} - 2 q^{78} + 32 q^{79} - q^{80} + 5 q^{81} + 3 q^{82} + 8 q^{83} - 3 q^{84} + 29 q^{85} - 24 q^{86} + 4 q^{87} + 5 q^{88} + q^{89} + q^{90} - 3 q^{91} - 12 q^{92} - q^{93} - 18 q^{94} + 33 q^{95} - 5 q^{96} - 4 q^{97} - 26 q^{98} - 5 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - 3 * q^7 - 5 * q^8 + 5 * q^9 + q^10 - 5 * q^11 + 5 * q^12 + 2 * q^13 + 3 * q^14 - q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 + 7 * q^19 - q^20 - 3 * q^21 + 5 * q^22 - 12 * q^23 - 5 * q^24 - 2 * q^26 + 5 * q^27 - 3 * q^28 + 4 * q^29 + q^30 - q^31 - 5 * q^32 - 5 * q^33 - 6 * q^34 + 17 * q^35 + 5 * q^36 + 3 * q^37 - 7 * q^38 + 2 * q^39 + q^40 - 3 * q^41 + 3 * q^42 + 24 * q^43 - 5 * q^44 - q^45 + 12 * q^46 + 18 * q^47 + 5 * q^48 + 26 * q^49 + 6 * q^51 + 2 * q^52 - 13 * q^53 - 5 * q^54 + q^55 + 3 * q^56 + 7 * q^57 - 4 * q^58 - 16 * q^59 - q^60 - 5 * q^61 + q^62 - 3 * q^63 + 5 * q^64 + 4 * q^65 + 5 * q^66 + 18 * q^67 + 6 * q^68 - 12 * q^69 - 17 * q^70 - 31 * q^71 - 5 * q^72 + 8 * q^73 - 3 * q^74 + 7 * q^76 + 3 * q^77 - 2 * q^78 + 32 * q^79 - q^80 + 5 * q^81 + 3 * q^82 + 8 * q^83 - 3 * q^84 + 29 * q^85 - 24 * q^86 + 4 * q^87 + 5 * q^88 + q^89 + q^90 - 3 * q^91 - 12 * q^92 - q^93 - 18 * q^94 + 33 * q^95 - 5 * q^96 - 4 * q^97 - 26 * q^98 - 5 * q^99

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