LMFDB - Embedded newform 1338.2.a.h.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1338.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$10.6839837904$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.356173.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 7x^{3} + 9x^{2} + 14x - 4 $ x^5 - 2x^4 - 7x^3 + 9x^2 + 14x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.38363$ of defining polynomial
Character	$\chi$	$=$	1338.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.35484 q^{5} -1.00000 q^{6} +3.05676 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.35484 q^{5} -1.00000 q^{6} +3.05676 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.35484 q^{10} -0.734963 q^{11} +1.00000 q^{12} -2.43689 q^{13} -3.05676 q^{14} +4.35484 q^{15} +1.00000 q^{16} -0.681711 q^{17} -1.00000 q^{18} -1.87811 q^{19} +4.35484 q^{20} +3.05676 q^{21} +0.734963 q^{22} +6.91115 q^{23} -1.00000 q^{24} +13.9646 q^{25} +2.43689 q^{26} +1.00000 q^{27} +3.05676 q^{28} +0.113306 q^{29} -4.35484 q^{30} +1.56736 q^{31} -1.00000 q^{32} -0.734963 q^{33} +0.681711 q^{34} +13.3117 q^{35} +1.00000 q^{36} -3.71884 q^{37} +1.87811 q^{38} -2.43689 q^{39} -4.35484 q^{40} -11.1102 q^{41} -3.05676 q^{42} -10.9512 q^{43} -0.734963 q^{44} +4.35484 q^{45} -6.91115 q^{46} -6.22966 q^{47} +1.00000 q^{48} +2.34379 q^{49} -13.9646 q^{50} -0.681711 q^{51} -2.43689 q^{52} +6.47426 q^{53} -1.00000 q^{54} -3.20064 q^{55} -3.05676 q^{56} -1.87811 q^{57} -0.113306 q^{58} +7.94099 q^{59} +4.35484 q^{60} -4.54537 q^{61} -1.56736 q^{62} +3.05676 q^{63} +1.00000 q^{64} -10.6122 q^{65} +0.734963 q^{66} -2.23117 q^{67} -0.681711 q^{68} +6.91115 q^{69} -13.3117 q^{70} +10.5641 q^{71} -1.00000 q^{72} -3.30232 q^{73} +3.71884 q^{74} +13.9646 q^{75} -1.87811 q^{76} -2.24661 q^{77} +2.43689 q^{78} -3.98486 q^{79} +4.35484 q^{80} +1.00000 q^{81} +11.1102 q^{82} -9.77231 q^{83} +3.05676 q^{84} -2.96874 q^{85} +10.9512 q^{86} +0.113306 q^{87} +0.734963 q^{88} -3.23802 q^{89} -4.35484 q^{90} -7.44898 q^{91} +6.91115 q^{92} +1.56736 q^{93} +6.22966 q^{94} -8.17887 q^{95} -1.00000 q^{96} -11.1019 q^{97} -2.34379 q^{98} -0.734963 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9} - 5 q^{10} + 9 q^{11} + 5 q^{12} + q^{14} + 5 q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} - 4 q^{19} + 5 q^{20} - q^{21} - 9 q^{22} + 16 q^{23} - 5 q^{24} + 8 q^{25} + 5 q^{27} - q^{28} + 8 q^{29} - 5 q^{30} - q^{31} - 5 q^{32} + 9 q^{33} - 6 q^{34} + 22 q^{35} + 5 q^{36} - 2 q^{37} + 4 q^{38} - 5 q^{40} + 4 q^{41} + q^{42} + 3 q^{43} + 9 q^{44} + 5 q^{45} - 16 q^{46} + 18 q^{47} + 5 q^{48} + 2 q^{49} - 8 q^{50} + 6 q^{51} + 26 q^{53} - 5 q^{54} + q^{55} + q^{56} - 4 q^{57} - 8 q^{58} + 21 q^{59} + 5 q^{60} - 20 q^{61} + q^{62} - q^{63} + 5 q^{64} - 3 q^{65} - 9 q^{66} - 5 q^{67} + 6 q^{68} + 16 q^{69} - 22 q^{70} + 17 q^{71} - 5 q^{72} + 5 q^{73} + 2 q^{74} + 8 q^{75} - 4 q^{76} + 2 q^{77} - 21 q^{79} + 5 q^{80} + 5 q^{81} - 4 q^{82} + 11 q^{83} - q^{84} - 12 q^{85} - 3 q^{86} + 8 q^{87} - 9 q^{88} - 5 q^{89} - 5 q^{90} - 10 q^{91} + 16 q^{92} - q^{93} - 18 q^{94} + 10 q^{95} - 5 q^{96} - 11 q^{97} - 2 q^{98} + 9 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9 - 5 * q^10 + 9 * q^11 + 5 * q^12 + q^14 + 5 * q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 - 4 * q^19 + 5 * q^20 - q^21 - 9 * q^22 + 16 * q^23 - 5 * q^24 + 8 * q^25 + 5 * q^27 - q^28 + 8 * q^29 - 5 * q^30 - q^31 - 5 * q^32 + 9 * q^33 - 6 * q^34 + 22 * q^35 + 5 * q^36 - 2 * q^37 + 4 * q^38 - 5 * q^40 + 4 * q^41 + q^42 + 3 * q^43 + 9 * q^44 + 5 * q^45 - 16 * q^46 + 18 * q^47 + 5 * q^48 + 2 * q^49 - 8 * q^50 + 6 * q^51 + 26 * q^53 - 5 * q^54 + q^55 + q^56 - 4 * q^57 - 8 * q^58 + 21 * q^59 + 5 * q^60 - 20 * q^61 + q^62 - q^63 + 5 * q^64 - 3 * q^65 - 9 * q^66 - 5 * q^67 + 6 * q^68 + 16 * q^69 - 22 * q^70 + 17 * q^71 - 5 * q^72 + 5 * q^73 + 2 * q^74 + 8 * q^75 - 4 * q^76 + 2 * q^77 - 21 * q^79 + 5 * q^80 + 5 * q^81 - 4 * q^82 + 11 * q^83 - q^84 - 12 * q^85 - 3 * q^86 + 8 * q^87 - 9 * q^88 - 5 * q^89 - 5 * q^90 - 10 * q^91 + 16 * q^92 - q^93 - 18 * q^94 + 10 * q^95 - 5 * q^96 - 11 * q^97 - 2 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	4.35484	1.94754	0.973772	−	0.227528i	$-0.0730644\pi$
$5$	4.35484	1.94754	0.973772	+	0.227528i	$0.0730644\pi$
$6$	−1.00000	−0.408248
$7$	3.05676	1.15535	0.577674	−	0.816268i	$-0.303961\pi$
$7$	3.05676	1.15535	0.577674	+	0.816268i	$0.303961\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−4.35484	−1.37712
$11$	−0.734963	−0.221600	−0.110800	−	0.993843i	$-0.535341\pi$
$11$	−0.734963	−0.221600	−0.110800	+	0.993843i	$0.535341\pi$
$12$	1.00000	0.288675
$13$	−2.43689	−0.675871	−0.337935	−	0.941169i	$-0.609728\pi$
$13$	−2.43689	−0.675871	−0.337935	+	0.941169i	$0.609728\pi$
$14$	−3.05676	−0.816954
$15$	4.35484	1.12441
$16$	1.00000	0.250000
$17$	−0.681711	−0.165339	−0.0826696	−	0.996577i	$-0.526345\pi$
$17$	−0.681711	−0.165339	−0.0826696	+	0.996577i	$0.526345\pi$
$18$	−1.00000	−0.235702
$19$	−1.87811	−0.430868	−0.215434	−	0.976518i	$-0.569117\pi$
$19$	−1.87811	−0.430868	−0.215434	+	0.976518i	$0.569117\pi$
$20$	4.35484	0.973772
$21$	3.05676	0.667040
$22$	0.734963	0.156695
$23$	6.91115	1.44107	0.720537	−	0.693416i	$-0.243895\pi$
$23$	6.91115	1.44107	0.720537	+	0.693416i	$0.243895\pi$
$24$	−1.00000	−0.204124
$25$	13.9646	2.79292
$26$	2.43689	0.477913
$27$	1.00000	0.192450
$28$	3.05676	0.577674
$29$	0.113306	0.0210404	0.0105202	−	0.999945i	$-0.496651\pi$
$29$	0.113306	0.0210404	0.0105202	+	0.999945i	$0.496651\pi$
$30$	−4.35484	−0.795081
$31$	1.56736	0.281506	0.140753	−	0.990045i	$-0.455048\pi$
$31$	1.56736	0.281506	0.140753	+	0.990045i	$0.455048\pi$
$32$	−1.00000	−0.176777
$33$	−0.734963	−0.127941
$34$	0.681711	0.116912
$35$	13.3117	2.25009
$36$	1.00000	0.166667
$37$	−3.71884	−0.611374	−0.305687	−	0.952132i	$-0.598886\pi$
$37$	−3.71884	−0.611374	−0.305687	+	0.952132i	$0.598886\pi$
$38$	1.87811	0.304670
$39$	−2.43689	−0.390214
$40$	−4.35484	−0.688560
$41$	−11.1102	−1.73513	−0.867563	−	0.497327i	$-0.834315\pi$
$41$	−11.1102	−1.73513	−0.867563	+	0.497327i	$0.834315\pi$
$42$	−3.05676	−0.471669
$43$	−10.9512	−1.67004	−0.835022	−	0.550217i	$-0.814545\pi$
$43$	−10.9512	−1.67004	−0.835022	+	0.550217i	$0.814545\pi$
$44$	−0.734963	−0.110800
$45$	4.35484	0.649181
$46$	−6.91115	−1.01899
$47$	−6.22966	−0.908689	−0.454344	−	0.890826i	$-0.650126\pi$
$47$	−6.22966	−0.908689	−0.454344	+	0.890826i	$0.650126\pi$
$48$	1.00000	0.144338
$49$	2.34379	0.334827
$50$	−13.9646	−1.97490
$51$	−0.681711	−0.0954586
$52$	−2.43689	−0.337935
$53$	6.47426	0.889309	0.444654	−	0.895702i	$-0.353327\pi$
$53$	6.47426	0.889309	0.444654	+	0.895702i	$0.353327\pi$
$54$	−1.00000	−0.136083
$55$	−3.20064	−0.431575
$56$	−3.05676	−0.408477
$57$	−1.87811	−0.248762
$58$	−0.113306	−0.0148778
$59$	7.94099	1.03383	0.516915	−	0.856037i	$-0.327080\pi$
$59$	7.94099	1.03383	0.516915	+	0.856037i	$0.327080\pi$
$60$	4.35484	0.562207
$61$	−4.54537	−0.581974	−0.290987	−	0.956727i	$-0.593984\pi$
$61$	−4.54537	−0.581974	−0.290987	+	0.956727i	$0.593984\pi$
$62$	−1.56736	−0.199055
$63$	3.05676	0.385116
$64$	1.00000	0.125000
$65$	−10.6122	−1.31629
$66$	0.734963	0.0904677
$67$	−2.23117	−0.272581	−0.136290	−	0.990669i	$-0.543518\pi$
$67$	−2.23117	−0.272581	−0.136290	+	0.990669i	$0.543518\pi$
$68$	−0.681711	−0.0826696
$69$	6.91115	0.832005
$70$	−13.3117	−1.59105
$71$	10.5641	1.25372	0.626862	−	0.779130i	$-0.284339\pi$
$71$	10.5641	1.25372	0.626862	+	0.779130i	$0.284339\pi$
$72$	−1.00000	−0.117851
$73$	−3.30232	−0.386507	−0.193254	−	0.981149i	$-0.561904\pi$
$73$	−3.30232	−0.386507	−0.193254	+	0.981149i	$0.561904\pi$
$74$	3.71884	0.432307
$75$	13.9646	1.61250
$76$	−1.87811	−0.215434
$77$	−2.24661	−0.256024
$78$	2.43689	0.275923
$79$	−3.98486	−0.448332	−0.224166	−	0.974551i	$-0.571966\pi$
$79$	−3.98486	−0.448332	−0.224166	+	0.974551i	$0.571966\pi$
$80$	4.35484	0.486886
$81$	1.00000	0.111111
$82$	11.1102	1.22692
$83$	−9.77231	−1.07265	−0.536325	−	0.844011i	$-0.680188\pi$
$83$	−9.77231	−1.07265	−0.536325	+	0.844011i	$0.680188\pi$
$84$	3.05676	0.333520
$85$	−2.96874	−0.322005
$86$	10.9512	1.18090
$87$	0.113306	0.0121477
$88$	0.734963	0.0783473
$89$	−3.23802	−0.343230	−0.171615	−	0.985164i	$-0.554898\pi$
$89$	−3.23802	−0.343230	−0.171615	+	0.985164i	$0.554898\pi$
$90$	−4.35484	−0.459040
$91$	−7.44898	−0.780865
$92$	6.91115	0.720537
$93$	1.56736	0.162528
$94$	6.22966	0.642540
$95$	−8.17887	−0.839134
$96$	−1.00000	−0.102062
$97$	−11.1019	−1.12723	−0.563613	−	0.826039i	$-0.690589\pi$
$97$	−11.1019	−1.12723	−0.563613	+	0.826039i	$0.690589\pi$
$98$	−2.34379	−0.236759
$99$	−0.734963	−0.0738665
$100$	13.9646	1.39646
$101$	19.8419	1.97434	0.987171	−	0.159664i	$-0.0510410\pi$
$101$	19.8419	1.97434	0.987171	+	0.159664i	$0.0510410\pi$
$102$	0.681711	0.0674994
$103$	−4.42428	−0.435937	−0.217968	−	0.975956i	$-0.569943\pi$
$103$	−4.42428	−0.435937	−0.217968	+	0.975956i	$0.569943\pi$
$104$	2.43689	0.238956
$105$	13.3117	1.29909
$106$	−6.47426	−0.628836
$107$	11.4126	1.10330	0.551651	−	0.834075i	$-0.313998\pi$
$107$	11.4126	1.10330	0.551651	+	0.834075i	$0.313998\pi$
$108$	1.00000	0.0962250
$109$	−15.1912	−1.45506	−0.727528	−	0.686078i	$-0.759331\pi$
$109$	−15.1912	−1.45506	−0.727528	+	0.686078i	$0.759331\pi$
$110$	3.20064	0.305169
$111$	−3.71884	−0.352977
$112$	3.05676	0.288837
$113$	−0.723916	−0.0681003	−0.0340501	−	0.999420i	$-0.510841\pi$
$113$	−0.723916	−0.0681003	−0.0340501	+	0.999420i	$0.510841\pi$
$114$	1.87811	0.175901
$115$	30.0969	2.80655
$116$	0.113306	0.0105202
$117$	−2.43689	−0.225290
$118$	−7.94099	−0.731028
$119$	−2.08383	−0.191024
$120$	−4.35484	−0.397541
$121$	−10.4598	−0.950894
$122$	4.54537	0.411518
$123$	−11.1102	−1.00178
$124$	1.56736	0.140753
$125$	39.0395	3.49180
$126$	−3.05676	−0.272318
$127$	17.7134	1.57181	0.785905	−	0.618347i	$-0.212197\pi$
$127$	17.7134	1.57181	0.785905	+	0.618347i	$0.212197\pi$
$128$	−1.00000	−0.0883883
$129$	−10.9512	−0.964200
$130$	10.6122	0.930755
$131$	−4.62868	−0.404409	−0.202205	−	0.979343i	$-0.564811\pi$
$131$	−4.62868	−0.404409	−0.202205	+	0.979343i	$0.564811\pi$
$132$	−0.734963	−0.0639703
$133$	−5.74094	−0.497802
$134$	2.23117	0.192744
$135$	4.35484	0.374805
$136$	0.681711	0.0584562
$137$	−6.95121	−0.593882	−0.296941	−	0.954896i	$-0.595966\pi$
$137$	−6.95121	−0.593882	−0.296941	+	0.954896i	$0.595966\pi$
$138$	−6.91115	−0.588316
$139$	23.4964	1.99294	0.996468	−	0.0839681i	$-0.0267594\pi$
$139$	23.4964	1.99294	0.996468	+	0.0839681i	$0.0267594\pi$
$140$	13.3117	1.12504
$141$	−6.22966	−0.524632
$142$	−10.5641	−0.886517
$143$	1.79102	0.149773
$144$	1.00000	0.0833333
$145$	0.493430	0.0409772
$146$	3.30232	0.273302
$147$	2.34379	0.193313
$148$	−3.71884	−0.305687
$149$	−8.25494	−0.676271	−0.338136	−	0.941097i	$-0.609796\pi$
$149$	−8.25494	−0.676271	−0.338136	+	0.941097i	$0.609796\pi$
$150$	−13.9646	−1.14021
$151$	−15.3701	−1.25080	−0.625402	−	0.780303i	$-0.715065\pi$
$151$	−15.3701	−1.25080	−0.625402	+	0.780303i	$0.715065\pi$
$152$	1.87811	0.152335
$153$	−0.681711	−0.0551131
$154$	2.24661	0.181037
$155$	6.82559	0.548245
$156$	−2.43689	−0.195107
$157$	5.70675	0.455448	0.227724	−	0.973726i	$-0.426872\pi$
$157$	5.70675	0.455448	0.227724	+	0.973726i	$0.426872\pi$
$158$	3.98486	0.317019
$159$	6.47426	0.513443
$160$	−4.35484	−0.344280
$161$	21.1257	1.66494
$162$	−1.00000	−0.0785674
$163$	1.46144	0.114469	0.0572343	−	0.998361i	$-0.481772\pi$
$163$	1.46144	0.114469	0.0572343	+	0.998361i	$0.481772\pi$
$164$	−11.1102	−0.867563
$165$	−3.20064	−0.249170
$166$	9.77231	0.758478
$167$	−0.335943	−0.0259960	−0.0129980	−	0.999916i	$-0.504138\pi$
$167$	−0.335943	−0.0259960	−0.0129980	+	0.999916i	$0.504138\pi$
$168$	−3.05676	−0.235834
$169$	−7.06159	−0.543199
$170$	2.96874	0.227692
$171$	−1.87811	−0.143623
$172$	−10.9512	−0.835022
$173$	3.25577	0.247532	0.123766	−	0.992311i	$-0.460503\pi$
$173$	3.25577	0.247532	0.123766	+	0.992311i	$0.460503\pi$
$174$	−0.113306	−0.00858972
$175$	42.6865	3.22680
$176$	−0.734963	−0.0553999
$177$	7.94099	0.596881
$178$	3.23802	0.242700
$179$	2.01680	0.150743	0.0753715	−	0.997156i	$-0.475986\pi$
$179$	2.01680	0.150743	0.0753715	+	0.997156i	$0.475986\pi$
$180$	4.35484	0.324591
$181$	−0.718726	−0.0534225	−0.0267113	−	0.999643i	$-0.508503\pi$
$181$	−0.718726	−0.0534225	−0.0267113	+	0.999643i	$0.508503\pi$
$182$	7.44898	0.552155
$183$	−4.54537	−0.336003
$184$	−6.91115	−0.509497
$185$	−16.1950	−1.19068
$186$	−1.56736	−0.114924
$187$	0.501032	0.0366391
$188$	−6.22966	−0.454344
$189$	3.05676	0.222347
$190$	8.17887	0.593357
$191$	4.95760	0.358719	0.179360	−	0.983784i	$-0.442597\pi$
$191$	4.95760	0.358719	0.179360	+	0.983784i	$0.442597\pi$
$192$	1.00000	0.0721688
$193$	−8.59130	−0.618415	−0.309208	−	0.950995i	$-0.600064\pi$
$193$	−8.59130	−0.618415	−0.309208	+	0.950995i	$0.600064\pi$
$194$	11.1019	0.797070
$195$	−10.6122	−0.759959
$196$	2.34379	0.167414
$197$	17.0864	1.21736	0.608678	−	0.793417i	$-0.291700\pi$
$197$	17.0864	1.21736	0.608678	+	0.793417i	$0.291700\pi$
$198$	0.734963	0.0522315
$199$	−0.350646	−0.0248566	−0.0124283	−	0.999923i	$-0.503956\pi$
$199$	−0.350646	−0.0248566	−0.0124283	+	0.999923i	$0.503956\pi$
$200$	−13.9646	−0.987448
$201$	−2.23117	−0.157374
$202$	−19.8419	−1.39607
$203$	0.346350	0.0243090
$204$	−0.681711	−0.0477293
$205$	−48.3833	−3.37923
$206$	4.42428	0.308254
$207$	6.91115	0.480358
$208$	−2.43689	−0.168968
$209$	1.38034	0.0954802
$210$	−13.3117	−0.918595
$211$	−12.3103	−0.847475	−0.423738	−	0.905785i	$-0.639282\pi$
$211$	−12.3103	−0.847475	−0.423738	+	0.905785i	$0.639282\pi$
$212$	6.47426	0.444654
$213$	10.5641	0.723838
$214$	−11.4126	−0.780152
$215$	−47.6907	−3.25248
$216$	−1.00000	−0.0680414
$217$	4.79104	0.325237
$218$	15.1912	1.02888
$219$	−3.30232	−0.223150
$220$	−3.20064	−0.215787
$221$	1.66125	0.111748
$222$	3.71884	0.249592
$223$	−1.00000	−0.0669650
$223$	−1.00000	−0.0669650
$224$	−3.05676	−0.204238
$225$	13.9646	0.930975
$226$	0.723916	0.0481542
$227$	11.9814	0.795233	0.397616	−	0.917552i	$-0.369838\pi$
$227$	11.9814	0.795233	0.397616	+	0.917552i	$0.369838\pi$
$228$	−1.87811	−0.124381
$229$	−0.278694	−0.0184166	−0.00920831	−	0.999958i	$-0.502931\pi$
$229$	−0.278694	−0.0184166	−0.00920831	+	0.999958i	$0.502931\pi$
$230$	−30.0969	−1.98453
$231$	−2.24661	−0.147816
$232$	−0.113306	−0.00743892
$233$	−12.2226	−0.800732	−0.400366	−	0.916355i	$-0.631117\pi$
$233$	−12.2226	−0.800732	−0.400366	+	0.916355i	$0.631117\pi$
$234$	2.43689	0.159304
$235$	−27.1291	−1.76971
$236$	7.94099	0.516915
$237$	−3.98486	−0.258845
$238$	2.08383	0.135074
$239$	22.2407	1.43863	0.719316	−	0.694683i	$-0.244455\pi$
$239$	22.2407	1.43863	0.719316	+	0.694683i	$0.244455\pi$
$240$	4.35484	0.281104
$241$	−22.3491	−1.43963	−0.719814	−	0.694166i	$-0.755773\pi$
$241$	−22.3491	−1.43963	−0.719814	+	0.694166i	$0.755773\pi$
$242$	10.4598	0.672383
$243$	1.00000	0.0641500
$244$	−4.54537	−0.290987
$245$	10.2068	0.652091
$246$	11.1102	0.708362
$247$	4.57674	0.291211
$248$	−1.56736	−0.0995274
$249$	−9.77231	−0.619295
$250$	−39.0395	−2.46907
$251$	19.7825	1.24866	0.624331	−	0.781160i	$-0.285372\pi$
$251$	19.7825	1.24866	0.624331	+	0.781160i	$0.285372\pi$
$252$	3.05676	0.192558
$253$	−5.07944	−0.319341
$254$	−17.7134	−1.11144
$255$	−2.96874	−0.185910
$256$	1.00000	0.0625000
$257$	−11.4401	−0.713617	−0.356808	−	0.934178i	$-0.616135\pi$
$257$	−11.4401	−0.713617	−0.356808	+	0.934178i	$0.616135\pi$
$258$	10.9512	0.681793
$259$	−11.3676	−0.706349
$260$	−10.6122	−0.658143
$261$	0.113306	0.00701348
$262$	4.62868	0.285961
$263$	13.3295	0.821929	0.410965	−	0.911651i	$-0.365192\pi$
$263$	13.3295	0.821929	0.410965	+	0.911651i	$0.365192\pi$
$264$	0.734963	0.0452338
$265$	28.1944	1.73197
$266$	5.74094	0.351999
$267$	−3.23802	−0.198164
$268$	−2.23117	−0.136290
$269$	3.03055	0.184776	0.0923878	−	0.995723i	$-0.470550\pi$
$269$	3.03055	0.184776	0.0923878	+	0.995723i	$0.470550\pi$
$270$	−4.35484	−0.265027
$271$	21.4604	1.30362	0.651812	−	0.758381i	$-0.274009\pi$
$271$	21.4604	1.30362	0.651812	+	0.758381i	$0.274009\pi$
$272$	−0.681711	−0.0413348
$273$	−7.44898	−0.450833
$274$	6.95121	0.419938
$275$	−10.2635	−0.618911
$276$	6.91115	0.416002
$277$	28.2695	1.69855	0.849276	−	0.527950i	$-0.177039\pi$
$277$	28.2695	1.69855	0.849276	+	0.527950i	$0.177039\pi$
$278$	−23.4964	−1.40922
$279$	1.56736	0.0938353
$280$	−13.3117	−0.795526
$281$	−12.7637	−0.761420	−0.380710	−	0.924694i	$-0.624320\pi$
$281$	−12.7637	−0.761420	−0.380710	+	0.924694i	$0.624320\pi$
$282$	6.22966	0.370971
$283$	32.5585	1.93540	0.967702	−	0.252098i	$-0.0811205\pi$
$283$	32.5585	1.93540	0.967702	+	0.252098i	$0.0811205\pi$
$284$	10.5641	0.626862
$285$	−8.17887	−0.484474
$286$	−1.79102	−0.105905
$287$	−33.9613	−2.00467
$288$	−1.00000	−0.0589256
$289$	−16.5353	−0.972663
$290$	−0.493430	−0.0289752
$291$	−11.1019	−0.650805
$292$	−3.30232	−0.193254
$293$	28.3976	1.65901	0.829503	−	0.558503i	$-0.188624\pi$
$293$	28.3976	1.65901	0.829503	+	0.558503i	$0.188624\pi$
$294$	−2.34379	−0.136693
$295$	34.5817	2.01343
$296$	3.71884	0.216153
$297$	−0.734963	−0.0426469
$298$	8.25494	0.478196
$299$	−16.8417	−0.973980
$300$	13.9646	0.806248
$301$	−33.4752	−1.92948
$302$	15.3701	0.884452
$303$	19.8419	1.13989
$304$	−1.87811	−0.107717
$305$	−19.7943	−1.13342
$306$	0.681711	0.0389708
$307$	−27.9578	−1.59563	−0.797817	−	0.602900i	$-0.794012\pi$
$307$	−27.9578	−1.59563	−0.797817	+	0.602900i	$0.794012\pi$
$308$	−2.24661	−0.128012
$309$	−4.42428	−0.251688
$310$	−6.82559	−0.387668
$311$	−3.59459	−0.203831	−0.101915	−	0.994793i	$-0.532497\pi$
$311$	−3.59459	−0.203831	−0.101915	+	0.994793i	$0.532497\pi$
$312$	2.43689	0.137961
$313$	11.4643	0.647998	0.323999	−	0.946057i	$-0.394972\pi$
$313$	11.4643	0.647998	0.323999	+	0.946057i	$0.394972\pi$
$314$	−5.70675	−0.322050
$315$	13.3117	0.750030
$316$	−3.98486	−0.224166
$317$	−33.3632	−1.87386	−0.936931	−	0.349514i	$-0.886347\pi$
$317$	−33.3632	−1.87386	−0.936931	+	0.349514i	$0.886347\pi$
$318$	−6.47426	−0.363059
$319$	−0.0832759	−0.00466255
$320$	4.35484	0.243443
$321$	11.4126	0.636992
$322$	−21.1257	−1.17729
$323$	1.28033	0.0712394
$324$	1.00000	0.0555556
$325$	−34.0302	−1.88765
$326$	−1.46144	−0.0809415
$327$	−15.1912	−0.840077
$328$	11.1102	0.613460
$329$	−19.0426	−1.04985
$330$	3.20064	0.176190
$331$	−11.6186	−0.638615	−0.319308	−	0.947651i	$-0.603450\pi$
$331$	−11.6186	−0.638615	−0.319308	+	0.947651i	$0.603450\pi$
$332$	−9.77231	−0.536325
$333$	−3.71884	−0.203791
$334$	0.335943	0.0183820
$335$	−9.71638	−0.530862
$336$	3.05676	0.166760
$337$	−7.91263	−0.431029	−0.215514	−	0.976501i	$-0.569143\pi$
$337$	−7.91263	−0.431029	−0.215514	+	0.976501i	$0.569143\pi$
$338$	7.06159	0.384100
$339$	−0.723916	−0.0393177
$340$	−2.96874	−0.161003
$341$	−1.15195	−0.0623816
$342$	1.87811	0.101557
$343$	−14.2329	−0.768505
$344$	10.9512	0.590450
$345$	30.0969	1.62036
$346$	−3.25577	−0.175031
$347$	−21.1718	−1.13656	−0.568280	−	0.822835i	$-0.692391\pi$
$347$	−21.1718	−1.13656	−0.568280	+	0.822835i	$0.692391\pi$
$348$	0.113306	0.00607385
$349$	−11.3838	−0.609360	−0.304680	−	0.952455i	$-0.598550\pi$
$349$	−11.3838	−0.609360	−0.304680	+	0.952455i	$0.598550\pi$
$350$	−42.6865	−2.28169
$351$	−2.43689	−0.130071
$352$	0.734963	0.0391736
$353$	−20.6961	−1.10154	−0.550772	−	0.834656i	$-0.685667\pi$
$353$	−20.6961	−1.10154	−0.550772	+	0.834656i	$0.685667\pi$
$354$	−7.94099	−0.422059
$355$	46.0048	2.44168
$356$	−3.23802	−0.171615
$357$	−2.08383	−0.110288
$358$	−2.01680	−0.106591
$359$	−13.4560	−0.710183	−0.355092	−	0.934832i	$-0.615550\pi$
$359$	−13.4560	−0.710183	−0.355092	+	0.934832i	$0.615550\pi$
$360$	−4.35484	−0.229520
$361$	−15.4727	−0.814353
$362$	0.718726	0.0377754
$363$	−10.4598	−0.548999
$364$	−7.44898	−0.390433
$365$	−14.3811	−0.752740
$366$	4.54537	0.237590
$367$	8.80612	0.459675	0.229838	−	0.973229i	$-0.426180\pi$
$367$	8.80612	0.459675	0.229838	+	0.973229i	$0.426180\pi$
$368$	6.91115	0.360269
$369$	−11.1102	−0.578375
$370$	16.1950	0.841936
$371$	19.7903	1.02746
$372$	1.56736	0.0812638
$373$	5.86346	0.303598	0.151799	−	0.988411i	$-0.451493\pi$
$373$	5.86346	0.303598	0.151799	+	0.988411i	$0.451493\pi$
$374$	−0.501032	−0.0259078
$375$	39.0395	2.01599
$376$	6.22966	0.321270
$377$	−0.276114	−0.0142206
$378$	−3.05676	−0.157223
$379$	−20.7423	−1.06546	−0.532729	−	0.846286i	$-0.678833\pi$
$379$	−20.7423	−1.06546	−0.532729	+	0.846286i	$0.678833\pi$
$380$	−8.17887	−0.419567
$381$	17.7134	0.907485
$382$	−4.95760	−0.253653
$383$	25.8637	1.32158	0.660788	−	0.750573i	$-0.270222\pi$
$383$	25.8637	1.32158	0.660788	+	0.750573i	$0.270222\pi$
$384$	−1.00000	−0.0510310
$385$	−9.78361	−0.498619
$386$	8.59130	0.437286
$387$	−10.9512	−0.556681
$388$	−11.1019	−0.563613
$389$	2.44929	0.124184	0.0620920	−	0.998070i	$-0.480223\pi$
$389$	2.44929	0.124184	0.0620920	+	0.998070i	$0.480223\pi$
$390$	10.6122	0.537372
$391$	−4.71141	−0.238266
$392$	−2.34379	−0.118379
$393$	−4.62868	−0.233486
$394$	−17.0864	−0.860801
$395$	−17.3534	−0.873146
$396$	−0.734963	−0.0369333
$397$	19.7131	0.989370	0.494685	−	0.869072i	$-0.335283\pi$
$397$	19.7131	0.989370	0.494685	+	0.869072i	$0.335283\pi$
$398$	0.350646	0.0175763
$399$	−5.74094	−0.287406
$400$	13.9646	0.698231
$401$	11.7643	0.587483	0.293742	−	0.955885i	$-0.405100\pi$
$401$	11.7643	0.587483	0.293742	+	0.955885i	$0.405100\pi$
$402$	2.23117	0.111281
$403$	−3.81947	−0.190262
$404$	19.8419	0.987171
$405$	4.35484	0.216394
$406$	−0.346350	−0.0171891
$407$	2.73321	0.135480
$408$	0.681711	0.0337497
$409$	29.9196	1.47943	0.739715	−	0.672920i	$-0.234960\pi$
$409$	29.9196	1.47943	0.739715	+	0.672920i	$0.234960\pi$
$410$	48.3833	2.38948
$411$	−6.95121	−0.342878
$412$	−4.42428	−0.217968
$413$	24.2737	1.19443
$414$	−6.91115	−0.339664
$415$	−42.5568	−2.08903
$416$	2.43689	0.119478
$417$	23.4964	1.15062
$418$	−1.38034	−0.0675147
$419$	−36.6787	−1.79187	−0.895935	−	0.444185i	$-0.853493\pi$
$419$	−36.6787	−1.79187	−0.895935	+	0.444185i	$0.853493\pi$
$420$	13.3117	0.649545
$421$	30.9616	1.50898	0.754488	−	0.656313i	$-0.227885\pi$
$421$	30.9616	1.50898	0.754488	+	0.656313i	$0.227885\pi$
$422$	12.3103	0.599255
$423$	−6.22966	−0.302896
$424$	−6.47426	−0.314418
$425$	−9.51983	−0.461780
$426$	−10.5641	−0.511831
$427$	−13.8941	−0.672383
$428$	11.4126	0.551651
$429$	1.79102	0.0864713
$430$	47.6907	2.29985
$431$	−32.4852	−1.56476	−0.782378	−	0.622804i	$-0.785994\pi$
$431$	−32.4852	−1.56476	−0.782378	+	0.622804i	$0.785994\pi$
$432$	1.00000	0.0481125
$433$	−24.9126	−1.19722	−0.598612	−	0.801039i	$-0.704281\pi$
$433$	−24.9126	−1.19722	−0.598612	+	0.801039i	$0.704281\pi$
$434$	−4.79104	−0.229977
$435$	0.493430	0.0236582
$436$	−15.1912	−0.727528
$437$	−12.9799	−0.620913
$438$	3.30232	0.157791
$439$	31.8189	1.51863	0.759317	−	0.650721i	$-0.225533\pi$
$439$	31.8189	1.51863	0.759317	+	0.650721i	$0.225533\pi$
$440$	3.20064	0.152585
$441$	2.34379	0.111609
$442$	−1.66125	−0.0790177
$443$	−22.4064	−1.06456	−0.532281	−	0.846568i	$-0.678665\pi$
$443$	−22.4064	−1.06456	−0.532281	+	0.846568i	$0.678665\pi$
$444$	−3.71884	−0.176488
$445$	−14.1011	−0.668455
$446$	1.00000	0.0473514
$447$	−8.25494	−0.390445
$448$	3.05676	0.144418
$449$	27.5968	1.30237	0.651187	−	0.758917i	$-0.274271\pi$
$449$	27.5968	1.30237	0.651187	+	0.758917i	$0.274271\pi$
$450$	−13.9646	−0.658298
$451$	8.16560	0.384503
$452$	−0.723916	−0.0340501
$453$	−15.3701	−0.722152
$454$	−11.9814	−0.562314
$455$	−32.4391	−1.52077
$456$	1.87811	0.0879506
$457$	6.26270	0.292957	0.146478	−	0.989214i	$-0.453206\pi$
$457$	6.26270	0.292957	0.146478	+	0.989214i	$0.453206\pi$
$458$	0.278694	0.0130225
$459$	−0.681711	−0.0318195
$460$	30.0969	1.40328
$461$	−24.4624	−1.13933	−0.569664	−	0.821878i	$-0.692926\pi$
$461$	−24.4624	−1.13933	−0.569664	+	0.821878i	$0.692926\pi$
$462$	2.24661	0.104522
$463$	−10.5467	−0.490146	−0.245073	−	0.969505i	$-0.578812\pi$
$463$	−10.5467	−0.490146	−0.245073	+	0.969505i	$0.578812\pi$
$464$	0.113306	0.00526011
$465$	6.82559	0.316529
$466$	12.2226	0.566203
$467$	−27.0318	−1.25088	−0.625442	−	0.780271i	$-0.715081\pi$
$467$	−27.0318	−1.25088	−0.625442	+	0.780271i	$0.715081\pi$
$468$	−2.43689	−0.112645
$469$	−6.82015	−0.314925
$470$	27.1291	1.25137
$471$	5.70675	0.262953
$472$	−7.94099	−0.365514
$473$	8.04873	0.370081
$474$	3.98486	0.183031
$475$	−26.2271	−1.20338
$476$	−2.08383	−0.0955121
$477$	6.47426	0.296436
$478$	−22.2407	−1.01727
$479$	23.9419	1.09393	0.546967	−	0.837154i	$-0.315782\pi$
$479$	23.9419	1.09393	0.546967	+	0.837154i	$0.315782\pi$
$480$	−4.35484	−0.198770
$481$	9.06239	0.413210
$482$	22.3491	1.01797
$483$	21.1257	0.961254
$484$	−10.4598	−0.475447
$485$	−48.3470	−2.19532
$486$	−1.00000	−0.0453609
$487$	−2.04679	−0.0927490	−0.0463745	−	0.998924i	$-0.514767\pi$
$487$	−2.04679	−0.0927490	−0.0463745	+	0.998924i	$0.514767\pi$
$488$	4.54537	0.205759
$489$	1.46144	0.0660885
$490$	−10.2068	−0.461098
$491$	−30.6746	−1.38433	−0.692163	−	0.721741i	$-0.743342\pi$
$491$	−30.6746	−1.38433	−0.692163	+	0.721741i	$0.743342\pi$
$492$	−11.1102	−0.500888
$493$	−0.0772421	−0.00347881
$494$	−4.57674	−0.205917
$495$	−3.20064	−0.143858
$496$	1.56736	0.0703765
$497$	32.2918	1.44849
$498$	9.77231	0.437908
$499$	29.0813	1.30186	0.650929	−	0.759138i	$-0.274379\pi$
$499$	29.0813	1.30186	0.650929	+	0.759138i	$0.274379\pi$
$500$	39.0395	1.74590
$501$	−0.335943	−0.0150088
$502$	−19.7825	−0.882937
$503$	32.4064	1.44493	0.722466	−	0.691407i	$-0.243009\pi$
$503$	32.4064	1.44493	0.722466	+	0.691407i	$0.243009\pi$
$504$	−3.05676	−0.136159
$505$	86.4083	3.84512
$506$	5.07944	0.225809
$507$	−7.06159	−0.313616
$508$	17.7134	0.785905
$509$	−20.3134	−0.900376	−0.450188	−	0.892934i	$-0.648643\pi$
$509$	−20.3134	−0.900376	−0.450188	+	0.892934i	$0.648643\pi$
$510$	2.96874	0.131458
$511$	−10.0944	−0.446550
$512$	−1.00000	−0.0441942
$513$	−1.87811	−0.0829206
$514$	11.4401	0.504603
$515$	−19.2670	−0.849006
$516$	−10.9512	−0.482100
$517$	4.57856	0.201365
$518$	11.3676	0.499464
$519$	3.25577	0.142912
$520$	10.6122	0.465378
$521$	−23.8912	−1.04669	−0.523346	−	0.852120i	$-0.675317\pi$
$521$	−23.8912	−1.04669	−0.523346	+	0.852120i	$0.675317\pi$
$522$	−0.113306	−0.00495928
$523$	26.0276	1.13811	0.569054	−	0.822300i	$-0.307309\pi$
$523$	26.0276	1.13811	0.569054	+	0.822300i	$0.307309\pi$
$524$	−4.62868	−0.202205
$525$	42.6865	1.86299
$526$	−13.3295	−0.581192
$527$	−1.06849	−0.0465440
$528$	−0.734963	−0.0319851
$529$	24.7640	1.07670
$530$	−28.1944	−1.22469
$531$	7.94099	0.344610
$532$	−5.74094	−0.248901
$533$	27.0744	1.17272
$534$	3.23802	0.140123
$535$	49.7002	2.14873
$536$	2.23117	0.0963718
$537$	2.01680	0.0870315
$538$	−3.03055	−0.130656
$539$	−1.72260	−0.0741976
$540$	4.35484	0.187402
$541$	−5.46873	−0.235119	−0.117559	−	0.993066i	$-0.537507\pi$
$541$	−5.46873	−0.235119	−0.117559	+	0.993066i	$0.537507\pi$
$542$	−21.4604	−0.921801
$543$	−0.718726	−0.0308435
$544$	0.681711	0.0292281
$545$	−66.1554	−2.83378
$546$	7.44898	0.318787
$547$	0.600980	0.0256961	0.0128480	−	0.999917i	$-0.495910\pi$
$547$	0.600980	0.0256961	0.0128480	+	0.999917i	$0.495910\pi$
$548$	−6.95121	−0.296941
$549$	−4.54537	−0.193991
$550$	10.2635	0.437636
$551$	−0.212802	−0.00906565
$552$	−6.91115	−0.294158
$553$	−12.1808	−0.517979
$554$	−28.2695	−1.20106
$555$	−16.1950	−0.687438
$556$	23.4964	0.996468
$557$	−33.5046	−1.41963	−0.709817	−	0.704386i	$-0.751222\pi$
$557$	−33.5046	−1.41963	−0.709817	+	0.704386i	$0.751222\pi$
$558$	−1.56736	−0.0663516
$559$	26.6868	1.12873
$560$	13.3117	0.562522
$561$	0.501032	0.0211536
$562$	12.7637	0.538405
$563$	−0.0190630	−0.000803411 0	−0.000401705	−	1.00000i	$-0.500128\pi$
$563$	−0.0190630	−0.000803411 0	−0.000401705		1.00000i	$0.500128\pi$
$564$	−6.22966	−0.262316
$565$	−3.15254	−0.132628
$566$	−32.5585	−1.36854
$567$	3.05676	0.128372
$568$	−10.5641	−0.443258
$569$	17.4587	0.731908	0.365954	−	0.930633i	$-0.380743\pi$
$569$	17.4587	0.731908	0.365954	+	0.930633i	$0.380743\pi$
$570$	8.17887	0.342575
$571$	18.0879	0.756955	0.378477	−	0.925611i	$-0.376448\pi$
$571$	18.0879	0.756955	0.378477	+	0.925611i	$0.376448\pi$
$572$	1.79102	0.0748863
$573$	4.95760	0.207107
$574$	33.9613	1.41752
$575$	96.5116	4.02481
$576$	1.00000	0.0416667
$577$	35.8487	1.49240	0.746200	−	0.665722i	$-0.231876\pi$
$577$	35.8487	1.49240	0.746200	+	0.665722i	$0.231876\pi$
$578$	16.5353	0.687777
$579$	−8.59130	−0.357042
$580$	0.493430	0.0204886
$581$	−29.8716	−1.23928
$582$	11.1019	0.460188
$583$	−4.75834	−0.197070
$584$	3.30232	0.136651
$585$	−10.6122	−0.438762
$586$	−28.3976	−1.17309
$587$	2.69524	0.111244	0.0556222	−	0.998452i	$-0.482286\pi$
$587$	2.69524	0.111244	0.0556222	+	0.998452i	$0.482286\pi$
$588$	2.34379	0.0966563
$589$	−2.94367	−0.121292
$590$	−34.5817	−1.42371
$591$	17.0864	0.702841
$592$	−3.71884	−0.152843
$593$	−31.1847	−1.28060	−0.640302	−	0.768124i	$-0.721191\pi$
$593$	−31.1847	−1.28060	−0.640302	+	0.768124i	$0.721191\pi$
$594$	0.734963	0.0301559
$595$	−9.07473	−0.372028
$596$	−8.25494	−0.338136
$597$	−0.350646	−0.0143510
$598$	16.8417	0.688708
$599$	−5.49303	−0.224439	−0.112220	−	0.993683i	$-0.535796\pi$
$599$	−5.49303	−0.224439	−0.112220	+	0.993683i	$0.535796\pi$
$600$	−13.9646	−0.570103
$601$	−25.3653	−1.03467	−0.517335	−	0.855783i	$-0.673076\pi$
$601$	−25.3653	−1.03467	−0.517335	+	0.855783i	$0.673076\pi$
$602$	33.4752	1.36435
$603$	−2.23117	−0.0908602
$604$	−15.3701	−0.625402
$605$	−45.5509	−1.85191
$606$	−19.8419	−0.806022
$607$	−12.3964	−0.503154	−0.251577	−	0.967837i	$-0.580949\pi$
$607$	−12.3964	−0.503154	−0.251577	+	0.967837i	$0.580949\pi$
$608$	1.87811	0.0761674
$609$	0.346350	0.0140348
$610$	19.7943	0.801449
$611$	15.1810	0.614156
$612$	−0.681711	−0.0275565
$613$	11.0514	0.446363	0.223181	−	0.974777i	$-0.428356\pi$
$613$	11.0514	0.446363	0.223181	+	0.974777i	$0.428356\pi$
$614$	27.9578	1.12828
$615$	−48.3833	−1.95100
$616$	2.24661	0.0905183
$617$	24.7403	0.996006	0.498003	−	0.867175i	$-0.334067\pi$
$617$	24.7403	0.996006	0.498003	+	0.867175i	$0.334067\pi$
$618$	4.42428	0.177970
$619$	−4.37667	−0.175913	−0.0879566	−	0.996124i	$-0.528034\pi$
$619$	−4.37667	−0.175913	−0.0879566	+	0.996124i	$0.528034\pi$
$620$	6.82559	0.274122
$621$	6.91115	0.277335
$622$	3.59459	0.144130
$623$	−9.89786	−0.396550
$624$	−2.43689	−0.0975535
$625$	100.187	4.00750
$626$	−11.4643	−0.458204
$627$	1.38034	0.0551255
$628$	5.70675	0.227724
$629$	2.53518	0.101084
$630$	−13.3117	−0.530351
$631$	−39.8325	−1.58571	−0.792854	−	0.609411i	$-0.791406\pi$
$631$	−39.8325	−1.58571	−0.792854	+	0.609411i	$0.791406\pi$
$632$	3.98486	0.158509
$633$	−12.3103	−0.489290
$634$	33.3632	1.32502
$635$	77.1390	3.06117
$636$	6.47426	0.256721
$637$	−5.71155	−0.226300
$638$	0.0832759	0.00329692
$639$	10.5641	0.417908
$640$	−4.35484	−0.172140
$641$	−44.5598	−1.76000	−0.880002	−	0.474969i	$-0.842459\pi$
$641$	−44.5598	−1.76000	−0.880002	+	0.474969i	$0.842459\pi$
$642$	−11.4126	−0.450421
$643$	33.6455	1.32685	0.663425	−	0.748243i	$-0.269102\pi$
$643$	33.6455	1.32685	0.663425	+	0.748243i	$0.269102\pi$
$644$	21.1257	0.832471
$645$	−47.6907	−1.87782
$646$	−1.28033	−0.0503738
$647$	−7.69538	−0.302537	−0.151268	−	0.988493i	$-0.548336\pi$
$647$	−7.69538	−0.302537	−0.151268	+	0.988493i	$0.548336\pi$
$648$	−1.00000	−0.0392837
$649$	−5.83633	−0.229096
$650$	34.0302	1.33477
$651$	4.79104	0.187776
$652$	1.46144	0.0572343
$653$	11.4671	0.448742	0.224371	−	0.974504i	$-0.427967\pi$
$653$	11.4671	0.448742	0.224371	+	0.974504i	$0.427967\pi$
$654$	15.1912	0.594024
$655$	−20.1571	−0.787605
$656$	−11.1102	−0.433782
$657$	−3.30232	−0.128836
$658$	19.0426	0.742357
$659$	35.9351	1.39983	0.699916	−	0.714225i	$-0.253221\pi$
$659$	35.9351	1.39983	0.699916	+	0.714225i	$0.253221\pi$
$660$	−3.20064	−0.124585
$661$	−45.1850	−1.75749	−0.878747	−	0.477288i	$-0.841620\pi$
$661$	−45.1850	−1.75749	−0.878747	+	0.477288i	$0.841620\pi$
$662$	11.6186	0.451569
$663$	1.66125	0.0645177
$664$	9.77231	0.379239
$665$	−25.0009	−0.969491
$666$	3.71884	0.144102
$667$	0.783076	0.0303208
$668$	−0.335943	−0.0129980
$669$	−1.00000	−0.0386622
$670$	9.71638	0.375376
$671$	3.34067	0.128965
$672$	−3.05676	−0.117917
$673$	1.54949	0.0597284	0.0298642	−	0.999554i	$-0.490493\pi$
$673$	1.54949	0.0597284	0.0298642	+	0.999554i	$0.490493\pi$
$674$	7.91263	0.304783
$675$	13.9646	0.537498
$676$	−7.06159	−0.271600
$677$	−18.2028	−0.699590	−0.349795	−	0.936826i	$-0.613749\pi$
$677$	−18.2028	−0.699590	−0.349795	+	0.936826i	$0.613749\pi$
$678$	0.723916	0.0278018
$679$	−33.9358	−1.30234
$680$	2.96874	0.113846
$681$	11.9814	0.459128
$682$	1.15195	0.0441104
$683$	32.0454	1.22618	0.613092	−	0.790012i	$-0.289926\pi$
$683$	32.0454	1.22618	0.613092	+	0.790012i	$0.289926\pi$
$684$	−1.87811	−0.0718114
$685$	−30.2714	−1.15661
$686$	14.2329	0.543415
$687$	−0.278694	−0.0106328
$688$	−10.9512	−0.417511
$689$	−15.7770	−0.601057
$690$	−30.0969	−1.14577
$691$	8.17206	0.310880	0.155440	−	0.987845i	$-0.450321\pi$
$691$	8.17206	0.310880	0.155440	+	0.987845i	$0.450321\pi$
$692$	3.25577	0.123766
$693$	−2.24661	−0.0853415
$694$	21.1718	0.803669
$695$	102.323	3.88133
$696$	−0.113306	−0.00429486
$697$	7.57397	0.286884
$698$	11.3838	0.430883
$699$	−12.2226	−0.462303
$700$	42.6865	1.61340
$701$	−25.3718	−0.958281	−0.479140	−	0.877738i	$-0.659052\pi$
$701$	−25.3718	−0.958281	−0.479140	+	0.877738i	$0.659052\pi$
$702$	2.43689	0.0919743
$703$	6.98440	0.263422
$704$	−0.734963	−0.0276999
$705$	−27.1291	−1.02174
$706$	20.6961	0.778910
$707$	60.6520	2.28105
$708$	7.94099	0.298441
$709$	7.95024	0.298578	0.149289	−	0.988794i	$-0.452302\pi$
$709$	7.95024	0.298578	0.149289	+	0.988794i	$0.452302\pi$
$710$	−46.0048	−1.72653
$711$	−3.98486	−0.149444
$712$	3.23802	0.121350
$713$	10.8322	0.405671
$714$	2.08383	0.0779853
$715$	7.79960	0.291689
$716$	2.01680	0.0753715
$717$	22.2407	0.830595
$718$	13.4560	0.502175
$719$	−31.5123	−1.17521	−0.587606	−	0.809147i	$-0.699929\pi$
$719$	−31.5123	−1.17521	−0.587606	+	0.809147i	$0.699929\pi$
$720$	4.35484	0.162295
$721$	−13.5240	−0.503658
$722$	15.4727	0.575834
$723$	−22.3491	−0.831170
$724$	−0.718726	−0.0267113
$725$	1.58228	0.0587643
$726$	10.4598	0.388201
$727$	−41.5993	−1.54283	−0.771416	−	0.636332i	$-0.780451\pi$
$727$	−41.5993	−1.54283	−0.771416	+	0.636332i	$0.780451\pi$
$728$	7.44898	0.276078
$729$	1.00000	0.0370370
$730$	14.3811	0.532267
$731$	7.46556	0.276124
$732$	−4.54537	−0.168002
$733$	−0.280816	−0.0103722	−0.00518608	−	0.999987i	$-0.501651\pi$
$733$	−0.280816	−0.0103722	−0.00518608	+	0.999987i	$0.501651\pi$
$734$	−8.80612	−0.325040
$735$	10.2068	0.376485
$736$	−6.91115	−0.254748
$737$	1.63983	0.0604038
$738$	11.1102	0.408973
$739$	30.0973	1.10715	0.553574	−	0.832800i	$-0.313264\pi$
$739$	30.0973	1.10715	0.553574	+	0.832800i	$0.313264\pi$
$740$	−16.1950	−0.595339
$741$	4.57674	0.168131
$742$	−19.7903	−0.726524
$743$	1.49835	0.0549692	0.0274846	−	0.999622i	$-0.491250\pi$
$743$	1.49835	0.0549692	0.0274846	+	0.999622i	$0.491250\pi$
$744$	−1.56736	−0.0574621
$745$	−35.9489	−1.31707
$746$	−5.86346	−0.214676
$747$	−9.77231	−0.357550
$748$	0.501032	0.0183195
$749$	34.8857	1.27470
$750$	−39.0395	−1.42552
$751$	19.0975	0.696878	0.348439	−	0.937331i	$-0.386712\pi$
$751$	19.0975	0.696878	0.348439	+	0.937331i	$0.386712\pi$
$752$	−6.22966	−0.227172
$753$	19.7825	0.720915
$754$	0.276114	0.0100555
$755$	−66.9344	−2.43599
$756$	3.05676	0.111173
$757$	−29.6151	−1.07638	−0.538189	−	0.842824i	$-0.680891\pi$
$757$	−29.6151	−1.07638	−0.538189	+	0.842824i	$0.680891\pi$
$758$	20.7423	0.753392
$759$	−5.07944	−0.184372
$760$	8.17887	0.296679
$761$	14.8382	0.537886	0.268943	−	0.963156i	$-0.413326\pi$
$761$	14.8382	0.537886	0.268943	+	0.963156i	$0.413326\pi$
$762$	−17.7134	−0.641689
$763$	−46.4360	−1.68110
$764$	4.95760	0.179360
$765$	−2.96874	−0.107335
$766$	−25.8637	−0.934495
$767$	−19.3513	−0.698735
$768$	1.00000	0.0360844
$769$	−23.8346	−0.859498	−0.429749	−	0.902948i	$-0.641398\pi$
$769$	−23.8346	−0.859498	−0.429749	+	0.902948i	$0.641398\pi$
$770$	9.78361	0.352577
$771$	−11.4401	−0.412007
$772$	−8.59130	−0.309208
$773$	55.4521	1.99447	0.997237	−	0.0742897i	$-0.0236690\pi$
$773$	55.4521	1.99447	0.997237	+	0.0742897i	$0.0236690\pi$
$774$	10.9512	0.393633
$775$	21.8876	0.786224
$776$	11.1019	0.398535
$777$	−11.3676	−0.407811
$778$	−2.44929	−0.0878113
$779$	20.8662	0.747611
$780$	−10.6122	−0.379979
$781$	−7.76419	−0.277825
$782$	4.71141	0.168480
$783$	0.113306	0.00404923
$784$	2.34379	0.0837068
$785$	24.8520	0.887005
$786$	4.62868	0.165099
$787$	33.1602	1.18203	0.591017	−	0.806659i	$-0.298726\pi$
$787$	33.1602	1.18203	0.591017	+	0.806659i	$0.298726\pi$
$788$	17.0864	0.608678
$789$	13.3295	0.474541
$790$	17.3534	0.617407
$791$	−2.21284	−0.0786795
$792$	0.734963	0.0261158
$793$	11.0765	0.393339
$794$	−19.7131	−0.699590
$795$	28.1944	0.999951
$796$	−0.350646	−0.0124283
$797$	15.2713	0.540936	0.270468	−	0.962729i	$-0.412821\pi$
$797$	15.2713	0.540936	0.270468	+	0.962729i	$0.412821\pi$
$798$	5.74094	0.203227
$799$	4.24682	0.150242
$800$	−13.9646	−0.493724
$801$	−3.23802	−0.114410
$802$	−11.7643	−0.415413
$803$	2.42708	0.0856499
$804$	−2.23117	−0.0786872
$805$	91.9992	3.24255
$806$	3.81947	0.134535
$807$	3.03055	0.106680
$808$	−19.8419	−0.698036
$809$	39.8830	1.40221	0.701106	−	0.713057i	$-0.252690\pi$
$809$	39.8830	1.40221	0.701106	+	0.713057i	$0.252690\pi$
$810$	−4.35484	−0.153013
$811$	−21.4838	−0.754400	−0.377200	−	0.926132i	$-0.623113\pi$
$811$	−21.4838	−0.754400	−0.377200	+	0.926132i	$0.623113\pi$
$812$	0.346350	0.0121545
$813$	21.4604	0.752648
$814$	−2.73321	−0.0957990
$815$	6.36432	0.222932
$816$	−0.681711	−0.0238647
$817$	20.5676	0.719569
$818$	−29.9196	−1.04611
$819$	−7.44898	−0.260288
$820$	−48.3833	−1.68962
$821$	14.5566	0.508029	0.254014	−	0.967200i	$-0.418249\pi$
$821$	14.5566	0.508029	0.254014	+	0.967200i	$0.418249\pi$
$822$	6.95121	0.242451
$823$	3.79452	0.132269	0.0661344	−	0.997811i	$-0.478933\pi$
$823$	3.79452	0.132269	0.0661344	+	0.997811i	$0.478933\pi$
$824$	4.42428	0.154127
$825$	−10.2635	−0.357328
$826$	−24.2737	−0.844591
$827$	56.9287	1.97960	0.989802	−	0.142452i	$-0.0454986\pi$
$827$	56.9287	1.97960	0.989802	+	0.142452i	$0.0454986\pi$
$828$	6.91115	0.240179
$829$	−44.0562	−1.53013	−0.765067	−	0.643951i	$-0.777294\pi$
$829$	−44.0562	−1.53013	−0.765067	+	0.643951i	$0.777294\pi$
$830$	42.5568	1.47717
$831$	28.2695	0.980659
$832$	−2.43689	−0.0844838
$833$	−1.59779	−0.0553601
$834$	−23.4964	−0.813613
$835$	−1.46298	−0.0506284
$836$	1.38034	0.0477401
$837$	1.56736	0.0541758
$838$	36.6787	1.26704
$839$	2.03615	0.0702957	0.0351479	−	0.999382i	$-0.488810\pi$
$839$	2.03615	0.0702957	0.0351479	+	0.999382i	$0.488810\pi$
$840$	−13.3117	−0.459297
$841$	−28.9872	−0.999557
$842$	−30.9616	−1.06701
$843$	−12.7637	−0.439606
$844$	−12.3103	−0.423738
$845$	−30.7521	−1.05790
$846$	6.22966	0.214180
$847$	−31.9732	−1.09861
$848$	6.47426	0.222327
$849$	32.5585	1.11741
$850$	9.51983	0.326528
$851$	−25.7015	−0.881035
$852$	10.5641	0.361919
$853$	45.1825	1.54702	0.773510	−	0.633785i	$-0.218499\pi$
$853$	45.1825	1.54702	0.773510	+	0.633785i	$0.218499\pi$
$854$	13.8941	0.475446
$855$	−8.17887	−0.279711
$856$	−11.4126	−0.390076
$857$	−13.9020	−0.474883	−0.237442	−	0.971402i	$-0.576309\pi$
$857$	−13.9020	−0.474883	−0.237442	+	0.971402i	$0.576309\pi$
$858$	−1.79102	−0.0611444
$859$	25.9715	0.886134	0.443067	−	0.896488i	$-0.353890\pi$
$859$	25.9715	0.886134	0.443067	+	0.896488i	$0.353890\pi$
$860$	−47.6907	−1.62624
$861$	−33.9613	−1.15740
$862$	32.4852	1.10645
$863$	24.8717	0.846642	0.423321	−	0.905980i	$-0.360864\pi$
$863$	24.8717	0.846642	0.423321	+	0.905980i	$0.360864\pi$
$864$	−1.00000	−0.0340207
$865$	14.1784	0.482079
$866$	24.9126	0.846566
$867$	−16.5353	−0.561567
$868$	4.79104	0.162619
$869$	2.92872	0.0993502
$870$	−0.493430	−0.0167289
$871$	5.43710	0.184229
$872$	15.1912	0.514440
$873$	−11.1019	−0.375742
$874$	12.9799	0.439052
$875$	119.334	4.03424
$876$	−3.30232	−0.111575
$877$	−41.9092	−1.41517	−0.707586	−	0.706627i	$-0.750216\pi$
$877$	−41.9092	−1.41517	−0.707586	+	0.706627i	$0.750216\pi$
$878$	−31.8189	−1.07384
$879$	28.3976	0.957827
$880$	−3.20064	−0.107894
$881$	0.208232	0.00701552	0.00350776	−	0.999994i	$-0.498883\pi$
$881$	0.208232	0.00701552	0.00350776	+	0.999994i	$0.498883\pi$
$882$	−2.34379	−0.0789196
$883$	−4.62099	−0.155509	−0.0777544	−	0.996973i	$-0.524775\pi$
$883$	−4.62099	−0.155509	−0.0777544	+	0.996973i	$0.524775\pi$
$884$	1.66125	0.0558739
$885$	34.5817	1.16245
$886$	22.4064	0.752759
$887$	−11.1644	−0.374865	−0.187433	−	0.982277i	$-0.560017\pi$
$887$	−11.1644	−0.374865	−0.187433	+	0.982277i	$0.560017\pi$
$888$	3.71884	0.124796
$889$	54.1457	1.81599
$890$	14.1011	0.472669
$891$	−0.734963	−0.0246222
$892$	−1.00000	−0.0334825
$893$	11.7000	0.391525
$894$	8.25494	0.276087
$895$	8.78285	0.293578
$896$	−3.05676	−0.102119
$897$	−16.8417	−0.562327
$898$	−27.5968	−0.920918
$899$	0.177591	0.00592301
$900$	13.9646	0.465487
$901$	−4.41358	−0.147038
$902$	−8.16560	−0.271885
$903$	−33.4752	−1.11399
$904$	0.723916	0.0240771
$905$	−3.12994	−0.104043
$906$	15.3701	0.510638
$907$	0.749208	0.0248770	0.0124385	−	0.999923i	$-0.496041\pi$
$907$	0.749208	0.0248770	0.0124385	+	0.999923i	$0.496041\pi$
$908$	11.9814	0.397616
$909$	19.8419	0.658114
$910$	32.4391	1.07535
$911$	−45.7170	−1.51467	−0.757336	−	0.653026i	$-0.773499\pi$
$911$	−45.7170	−1.51467	−0.757336	+	0.653026i	$0.773499\pi$
$912$	−1.87811	−0.0621905
$913$	7.18228	0.237699
$914$	−6.26270	−0.207152
$915$	−19.7943	−0.654380
$916$	−0.278694	−0.00920831
$917$	−14.1488	−0.467233
$918$	0.681711	0.0224998
$919$	−4.43703	−0.146364	−0.0731821	−	0.997319i	$-0.523315\pi$
$919$	−4.43703	−0.146364	−0.0731821	+	0.997319i	$0.523315\pi$
$920$	−30.0969	−0.992267
$921$	−27.9578	−0.921240
$922$	24.4624	0.805626
$923$	−25.7434	−0.847355
$924$	−2.24661	−0.0739079
$925$	−51.9322	−1.70752
$926$	10.5467	0.346585
$927$	−4.42428	−0.145312
$928$	−0.113306	−0.00371946
$929$	0.789965	0.0259179	0.0129590	−	0.999916i	$-0.495875\pi$
$929$	0.789965	0.0259179	0.0129590	+	0.999916i	$0.495875\pi$
$930$	−6.82559	−0.223820
$931$	−4.40190	−0.144266
$932$	−12.2226	−0.400366
$933$	−3.59459	−0.117682
$934$	27.0318	0.884508
$935$	2.18191	0.0713562
$936$	2.43689	0.0796521
$937$	11.0887	0.362252	0.181126	−	0.983460i	$-0.442026\pi$
$937$	11.0887	0.362252	0.181126	+	0.983460i	$0.442026\pi$
$938$	6.82015	0.222686
$939$	11.4643	0.374122
$940$	−27.1291	−0.884855
$941$	−49.8346	−1.62456	−0.812281	−	0.583267i	$-0.801774\pi$
$941$	−49.8346	−1.62456	−0.812281	+	0.583267i	$0.801774\pi$
$942$	−5.70675	−0.185936
$943$	−76.7845	−2.50045
$944$	7.94099	0.258457
$945$	13.3117	0.433030
$946$	−8.04873	−0.261687
$947$	3.22300	0.104733	0.0523667	−	0.998628i	$-0.483324\pi$
$947$	3.22300	0.104733	0.0523667	+	0.998628i	$0.483324\pi$
$948$	−3.98486	−0.129422
$949$	8.04738	0.261229
$950$	26.2271	0.850919
$951$	−33.3632	−1.08188
$952$	2.08383	0.0675372
$953$	35.4866	1.14952	0.574762	−	0.818320i	$-0.305095\pi$
$953$	35.4866	1.14952	0.574762	+	0.818320i	$0.305095\pi$
$954$	−6.47426	−0.209612
$955$	21.5895	0.698621
$956$	22.2407	0.719316
$957$	−0.0832759	−0.00269193
$958$	−23.9419	−0.773528
$959$	−21.2482	−0.686140
$960$	4.35484	0.140552
$961$	−28.5434	−0.920754
$962$	−9.06239	−0.292183
$963$	11.4126	0.367767
$964$	−22.3491	−0.719814
$965$	−37.4137	−1.20439
$966$	−21.1257	−0.679709
$967$	−4.41806	−0.142075	−0.0710376	−	0.997474i	$-0.522631\pi$
$967$	−4.41806	−0.142075	−0.0710376	+	0.997474i	$0.522631\pi$
$968$	10.4598	0.336192
$969$	1.28033	0.0411301
$970$	48.3470	1.55233
$971$	12.8435	0.412169	0.206084	−	0.978534i	$-0.433928\pi$
$971$	12.8435	0.412169	0.206084	+	0.978534i	$0.433928\pi$
$972$	1.00000	0.0320750
$973$	71.8228	2.30253
$974$	2.04679	0.0655834
$975$	−34.0302	−1.08984
$976$	−4.54537	−0.145494
$977$	14.9739	0.479057	0.239528	−	0.970889i	$-0.423007\pi$
$977$	14.9739	0.479057	0.239528	+	0.970889i	$0.423007\pi$
$978$	−1.46144	−0.0467316
$979$	2.37983	0.0760596
$980$	10.2068	0.326045
$981$	−15.1912	−0.485019
$982$	30.6746	0.978866
$983$	−22.0615	−0.703652	−0.351826	−	0.936065i	$-0.614439\pi$
$983$	−22.0615	−0.703652	−0.351826	+	0.936065i	$0.614439\pi$
$984$	11.1102	0.354181
$985$	74.4086	2.37085
$986$	0.0772421	0.00245989
$987$	−19.0426	−0.606132
$988$	4.57674	0.145606
$989$	−75.6855	−2.40666
$990$	3.20064	0.101723
$991$	−8.96101	−0.284656	−0.142328	−	0.989820i	$-0.545459\pi$
$991$	−8.96101	−0.284656	−0.142328	+	0.989820i	$0.545459\pi$
$992$	−1.56736	−0.0497637
$993$	−11.6186	−0.368705
$994$	−32.2918	−1.02423
$995$	−1.52701	−0.0484093
$996$	−9.77231	−0.309648
$997$	51.5423	1.63236	0.816180	−	0.577798i	$-0.196088\pi$
$997$	51.5423	1.63236	0.816180	+	0.577798i	$0.196088\pi$
$998$	−29.0813	−0.920553
$999$	−3.71884	−0.117659

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1338.2.a.h.1.5	✓	5
3.2	odd	2		4014.2.a.r.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1338.2.a.h.1.5	✓	5	1.1	even	1	trivial
4014.2.a.r.1.1		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.35484 q^{5} -1.00000 q^{6} +3.05676 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.35484 q^{5} -1.00000 q^{6} +3.05676 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.35484 q^{10} -0.734963 q^{11} +1.00000 q^{12} -2.43689 q^{13} -3.05676 q^{14} +4.35484 q^{15} +1.00000 q^{16} -0.681711 q^{17} -1.00000 q^{18} -1.87811 q^{19} +4.35484 q^{20} +3.05676 q^{21} +0.734963 q^{22} +6.91115 q^{23} -1.00000 q^{24} +13.9646 q^{25} +2.43689 q^{26} +1.00000 q^{27} +3.05676 q^{28} +0.113306 q^{29} -4.35484 q^{30} +1.56736 q^{31} -1.00000 q^{32} -0.734963 q^{33} +0.681711 q^{34} +13.3117 q^{35} +1.00000 q^{36} -3.71884 q^{37} +1.87811 q^{38} -2.43689 q^{39} -4.35484 q^{40} -11.1102 q^{41} -3.05676 q^{42} -10.9512 q^{43} -0.734963 q^{44} +4.35484 q^{45} -6.91115 q^{46} -6.22966 q^{47} +1.00000 q^{48} +2.34379 q^{49} -13.9646 q^{50} -0.681711 q^{51} -2.43689 q^{52} +6.47426 q^{53} -1.00000 q^{54} -3.20064 q^{55} -3.05676 q^{56} -1.87811 q^{57} -0.113306 q^{58} +7.94099 q^{59} +4.35484 q^{60} -4.54537 q^{61} -1.56736 q^{62} +3.05676 q^{63} +1.00000 q^{64} -10.6122 q^{65} +0.734963 q^{66} -2.23117 q^{67} -0.681711 q^{68} +6.91115 q^{69} -13.3117 q^{70} +10.5641 q^{71} -1.00000 q^{72} -3.30232 q^{73} +3.71884 q^{74} +13.9646 q^{75} -1.87811 q^{76} -2.24661 q^{77} +2.43689 q^{78} -3.98486 q^{79} +4.35484 q^{80} +1.00000 q^{81} +11.1102 q^{82} -9.77231 q^{83} +3.05676 q^{84} -2.96874 q^{85} +10.9512 q^{86} +0.113306 q^{87} +0.734963 q^{88} -3.23802 q^{89} -4.35484 q^{90} -7.44898 q^{91} +6.91115 q^{92} +1.56736 q^{93} +6.22966 q^{94} -8.17887 q^{95} -1.00000 q^{96} -11.1019 q^{97} -2.34379 q^{98} -0.734963 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9} - 5 q^{10} + 9 q^{11} + 5 q^{12} + q^{14} + 5 q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} - 4 q^{19} + 5 q^{20} - q^{21} - 9 q^{22} + 16 q^{23} - 5 q^{24} + 8 q^{25} + 5 q^{27} - q^{28} + 8 q^{29} - 5 q^{30} - q^{31} - 5 q^{32} + 9 q^{33} - 6 q^{34} + 22 q^{35} + 5 q^{36} - 2 q^{37} + 4 q^{38} - 5 q^{40} + 4 q^{41} + q^{42} + 3 q^{43} + 9 q^{44} + 5 q^{45} - 16 q^{46} + 18 q^{47} + 5 q^{48} + 2 q^{49} - 8 q^{50} + 6 q^{51} + 26 q^{53} - 5 q^{54} + q^{55} + q^{56} - 4 q^{57} - 8 q^{58} + 21 q^{59} + 5 q^{60} - 20 q^{61} + q^{62} - q^{63} + 5 q^{64} - 3 q^{65} - 9 q^{66} - 5 q^{67} + 6 q^{68} + 16 q^{69} - 22 q^{70} + 17 q^{71} - 5 q^{72} + 5 q^{73} + 2 q^{74} + 8 q^{75} - 4 q^{76} + 2 q^{77} - 21 q^{79} + 5 q^{80} + 5 q^{81} - 4 q^{82} + 11 q^{83} - q^{84} - 12 q^{85} - 3 q^{86} + 8 q^{87} - 9 q^{88} - 5 q^{89} - 5 q^{90} - 10 q^{91} + 16 q^{92} - q^{93} - 18 q^{94} + 10 q^{95} - 5 q^{96} - 11 q^{97} - 2 q^{98} + 9 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9 - 5 * q^10 + 9 * q^11 + 5 * q^12 + q^14 + 5 * q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 - 4 * q^19 + 5 * q^20 - q^21 - 9 * q^22 + 16 * q^23 - 5 * q^24 + 8 * q^25 + 5 * q^27 - q^28 + 8 * q^29 - 5 * q^30 - q^31 - 5 * q^32 + 9 * q^33 - 6 * q^34 + 22 * q^35 + 5 * q^36 - 2 * q^37 + 4 * q^38 - 5 * q^40 + 4 * q^41 + q^42 + 3 * q^43 + 9 * q^44 + 5 * q^45 - 16 * q^46 + 18 * q^47 + 5 * q^48 + 2 * q^49 - 8 * q^50 + 6 * q^51 + 26 * q^53 - 5 * q^54 + q^55 + q^56 - 4 * q^57 - 8 * q^58 + 21 * q^59 + 5 * q^60 - 20 * q^61 + q^62 - q^63 + 5 * q^64 - 3 * q^65 - 9 * q^66 - 5 * q^67 + 6 * q^68 + 16 * q^69 - 22 * q^70 + 17 * q^71 - 5 * q^72 + 5 * q^73 + 2 * q^74 + 8 * q^75 - 4 * q^76 + 2 * q^77 - 21 * q^79 + 5 * q^80 + 5 * q^81 - 4 * q^82 + 11 * q^83 - q^84 - 12 * q^85 - 3 * q^86 + 8 * q^87 - 9 * q^88 - 5 * q^89 - 5 * q^90 - 10 * q^91 + 16 * q^92 - q^93 - 18 * q^94 + 10 * q^95 - 5 * q^96 - 11 * q^97 - 2 * q^98 + 9 * q^99

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