LMFDB - Embedded newform 1502.2.a.f.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 20x^{9} - 7x^{8} + 134x^{7} + 70x^{6} - 354x^{5} - 193x^{4} + 341x^{3} + 163x^{2} - 72x - 16 $ x^11 - 20x^9 - 7x^8 + 134x^7 + 70x^6 - 354x^5 - 193x^4 + 341x^3 + 163x^2 - 72*x - 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.21388$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.213882 q^{3} +1.00000 q^{4} -2.70660 q^{5} +0.213882 q^{6} +1.35942 q^{7} +1.00000 q^{8} -2.95425 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.213882 q^{3} +1.00000 q^{4} -2.70660 q^{5} +0.213882 q^{6} +1.35942 q^{7} +1.00000 q^{8} -2.95425 q^{9} -2.70660 q^{10} -0.885300 q^{11} +0.213882 q^{12} -1.69171 q^{13} +1.35942 q^{14} -0.578894 q^{15} +1.00000 q^{16} +3.88338 q^{17} -2.95425 q^{18} -7.31642 q^{19} -2.70660 q^{20} +0.290757 q^{21} -0.885300 q^{22} +1.41741 q^{23} +0.213882 q^{24} +2.32567 q^{25} -1.69171 q^{26} -1.27351 q^{27} +1.35942 q^{28} -10.3027 q^{29} -0.578894 q^{30} +2.96775 q^{31} +1.00000 q^{32} -0.189350 q^{33} +3.88338 q^{34} -3.67942 q^{35} -2.95425 q^{36} -3.25201 q^{37} -7.31642 q^{38} -0.361828 q^{39} -2.70660 q^{40} -2.67490 q^{41} +0.290757 q^{42} -12.8706 q^{43} -0.885300 q^{44} +7.99598 q^{45} +1.41741 q^{46} +5.26075 q^{47} +0.213882 q^{48} -5.15196 q^{49} +2.32567 q^{50} +0.830586 q^{51} -1.69171 q^{52} -1.14453 q^{53} -1.27351 q^{54} +2.39615 q^{55} +1.35942 q^{56} -1.56486 q^{57} -10.3027 q^{58} +6.68472 q^{59} -0.578894 q^{60} -8.23165 q^{61} +2.96775 q^{62} -4.01609 q^{63} +1.00000 q^{64} +4.57878 q^{65} -0.189350 q^{66} +13.7492 q^{67} +3.88338 q^{68} +0.303158 q^{69} -3.67942 q^{70} -14.6538 q^{71} -2.95425 q^{72} +0.203571 q^{73} -3.25201 q^{74} +0.497420 q^{75} -7.31642 q^{76} -1.20350 q^{77} -0.361828 q^{78} +9.68138 q^{79} -2.70660 q^{80} +8.59038 q^{81} -2.67490 q^{82} -0.507262 q^{83} +0.290757 q^{84} -10.5107 q^{85} -12.8706 q^{86} -2.20358 q^{87} -0.885300 q^{88} -1.24226 q^{89} +7.99598 q^{90} -2.29976 q^{91} +1.41741 q^{92} +0.634751 q^{93} +5.26075 q^{94} +19.8026 q^{95} +0.213882 q^{96} -1.55399 q^{97} -5.15196 q^{98} +2.61540 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 12 q^{5} - 11 q^{6} - 9 q^{7} + 11 q^{8} + 18 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 12 * q^5 - 11 * q^6 - 9 * q^7 + 11 * q^8 + 18 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 12 q^{5} - 11 q^{6} - 9 q^{7} + 11 q^{8} + 18 q^{9} - 12 q^{10} - 7 q^{11} - 11 q^{12} - 21 q^{13} - 9 q^{14} - 3 q^{15} + 11 q^{16} - 16 q^{17} + 18 q^{18} - 22 q^{19} - 12 q^{20} - q^{21} - 7 q^{22} - 2 q^{23} - 11 q^{24} + 19 q^{25} - 21 q^{26} - 44 q^{27} - 9 q^{28} + 4 q^{29} - 3 q^{30} - 28 q^{31} + 11 q^{32} - 13 q^{33} - 16 q^{34} - 11 q^{35} + 18 q^{36} - 22 q^{37} - 22 q^{38} + 9 q^{39} - 12 q^{40} - 5 q^{41} - q^{42} - 7 q^{43} - 7 q^{44} - 23 q^{45} - 2 q^{46} - 31 q^{47} - 11 q^{48} - 2 q^{49} + 19 q^{50} - 6 q^{51} - 21 q^{52} - 17 q^{53} - 44 q^{54} - 18 q^{55} - 9 q^{56} + 7 q^{57} + 4 q^{58} - 18 q^{59} - 3 q^{60} - 18 q^{61} - 28 q^{62} - 27 q^{63} + 11 q^{64} + 22 q^{65} - 13 q^{66} - 11 q^{67} - 16 q^{68} + 9 q^{69} - 11 q^{70} - 16 q^{71} + 18 q^{72} - 33 q^{73} - 22 q^{74} - 21 q^{75} - 22 q^{76} + 9 q^{78} + 9 q^{79} - 12 q^{80} + 71 q^{81} - 5 q^{82} - 18 q^{83} - q^{84} - 8 q^{85} - 7 q^{86} - 17 q^{87} - 7 q^{88} - 23 q^{90} - 22 q^{91} - 2 q^{92} + 8 q^{93} - 31 q^{94} - 23 q^{95} - 11 q^{96} - 66 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 12 * q^5 - 11 * q^6 - 9 * q^7 + 11 * q^8 + 18 * q^9 - 12 * q^10 - 7 * q^11 - 11 * q^12 - 21 * q^13 - 9 * q^14 - 3 * q^15 + 11 * q^16 - 16 * q^17 + 18 * q^18 - 22 * q^19 - 12 * q^20 - q^21 - 7 * q^22 - 2 * q^23 - 11 * q^24 + 19 * q^25 - 21 * q^26 - 44 * q^27 - 9 * q^28 + 4 * q^29 - 3 * q^30 - 28 * q^31 + 11 * q^32 - 13 * q^33 - 16 * q^34 - 11 * q^35 + 18 * q^36 - 22 * q^37 - 22 * q^38 + 9 * q^39 - 12 * q^40 - 5 * q^41 - q^42 - 7 * q^43 - 7 * q^44 - 23 * q^45 - 2 * q^46 - 31 * q^47 - 11 * q^48 - 2 * q^49 + 19 * q^50 - 6 * q^51 - 21 * q^52 - 17 * q^53 - 44 * q^54 - 18 * q^55 - 9 * q^56 + 7 * q^57 + 4 * q^58 - 18 * q^59 - 3 * q^60 - 18 * q^61 - 28 * q^62 - 27 * q^63 + 11 * q^64 + 22 * q^65 - 13 * q^66 - 11 * q^67 - 16 * q^68 + 9 * q^69 - 11 * q^70 - 16 * q^71 + 18 * q^72 - 33 * q^73 - 22 * q^74 - 21 * q^75 - 22 * q^76 + 9 * q^78 + 9 * q^79 - 12 * q^80 + 71 * q^81 - 5 * q^82 - 18 * q^83 - q^84 - 8 * q^85 - 7 * q^86 - 17 * q^87 - 7 * q^88 - 23 * q^90 - 22 * q^91 - 2 * q^92 + 8 * q^93 - 31 * q^94 - 23 * q^95 - 11 * q^96 - 66 * q^97 - 2 * 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
$3$	0.213882	0.123485	0.0617426	−	0.998092i	$-0.480334\pi$
$3$	0.213882	0.123485	0.0617426	+	0.998092i	$0.480334\pi$
$4$	1.00000	0.500000
$5$	−2.70660	−1.21043	−0.605214	−	0.796063i	$-0.706912\pi$
$5$	−2.70660	−1.21043	−0.605214	+	0.796063i	$0.706912\pi$
$6$	0.213882	0.0873172
$7$	1.35942	0.513814	0.256907	−	0.966436i	$-0.417297\pi$
$7$	1.35942	0.513814	0.256907	+	0.966436i	$0.417297\pi$
$8$	1.00000	0.353553
$9$	−2.95425	−0.984751
$10$	−2.70660	−0.855901
$11$	−0.885300	−0.266928	−0.133464	−	0.991054i	$-0.542610\pi$
$11$	−0.885300	−0.266928	−0.133464	+	0.991054i	$0.542610\pi$
$12$	0.213882	0.0617426
$13$	−1.69171	−0.469197	−0.234598	−	0.972092i	$-0.575377\pi$
$13$	−1.69171	−0.469197	−0.234598	+	0.972092i	$0.575377\pi$
$14$	1.35942	0.363322
$15$	−0.578894	−0.149470
$16$	1.00000	0.250000
$17$	3.88338	0.941857	0.470929	−	0.882171i	$-0.343919\pi$
$17$	3.88338	0.941857	0.470929	+	0.882171i	$0.343919\pi$
$18$	−2.95425	−0.696324
$19$	−7.31642	−1.67850	−0.839251	−	0.543744i	$-0.817006\pi$
$19$	−7.31642	−1.67850	−0.839251	+	0.543744i	$0.817006\pi$
$20$	−2.70660	−0.605214
$21$	0.290757	0.0634484
$22$	−0.885300	−0.188747
$23$	1.41741	0.295549	0.147775	−	0.989021i	$-0.452789\pi$
$23$	1.41741	0.295549	0.147775	+	0.989021i	$0.452789\pi$
$24$	0.213882	0.0436586
$25$	2.32567	0.465134
$26$	−1.69171	−0.331772
$27$	−1.27351	−0.245087
$28$	1.35942	0.256907
$29$	−10.3027	−1.91317	−0.956586	−	0.291449i	$-0.905863\pi$
$29$	−10.3027	−1.91317	−0.956586	+	0.291449i	$0.905863\pi$
$30$	−0.578894	−0.105691
$31$	2.96775	0.533024	0.266512	−	0.963832i	$-0.414129\pi$
$31$	2.96775	0.533024	0.266512	+	0.963832i	$0.414129\pi$
$32$	1.00000	0.176777
$33$	−0.189350	−0.0329616
$34$	3.88338	0.665994
$35$	−3.67942	−0.621935
$36$	−2.95425	−0.492376
$37$	−3.25201	−0.534628	−0.267314	−	0.963610i	$-0.586136\pi$
$37$	−3.25201	−0.534628	−0.267314	+	0.963610i	$0.586136\pi$
$38$	−7.31642	−1.18688
$39$	−0.361828	−0.0579388
$40$	−2.70660	−0.427951
$41$	−2.67490	−0.417749	−0.208875	−	0.977942i	$-0.566980\pi$
$41$	−2.67490	−0.417749	−0.208875	+	0.977942i	$0.566980\pi$
$42$	0.290757	0.0448648
$43$	−12.8706	−1.96274	−0.981372	−	0.192120i	$-0.938464\pi$
$43$	−12.8706	−1.96274	−0.981372	+	0.192120i	$0.938464\pi$
$44$	−0.885300	−0.133464
$45$	7.99598	1.19197
$46$	1.41741	0.208985
$47$	5.26075	0.767360	0.383680	−	0.923466i	$-0.374657\pi$
$47$	5.26075	0.767360	0.383680	+	0.923466i	$0.374657\pi$
$48$	0.213882	0.0308713
$49$	−5.15196	−0.735995
$50$	2.32567	0.328899
$51$	0.830586	0.116305
$52$	−1.69171	−0.234598
$53$	−1.14453	−0.157214	−0.0786068	−	0.996906i	$-0.525047\pi$
$53$	−1.14453	−0.157214	−0.0786068	+	0.996906i	$0.525047\pi$
$54$	−1.27351	−0.173303
$55$	2.39615	0.323097
$56$	1.35942	0.181661
$57$	−1.56486	−0.207270
$58$	−10.3027	−1.35282
$59$	6.68472	0.870276	0.435138	−	0.900364i	$-0.356699\pi$
$59$	6.68472	0.870276	0.435138	+	0.900364i	$0.356699\pi$
$60$	−0.578894	−0.0747349
$61$	−8.23165	−1.05395	−0.526977	−	0.849879i	$-0.676675\pi$
$61$	−8.23165	−1.05395	−0.526977	+	0.849879i	$0.676675\pi$
$62$	2.96775	0.376905
$63$	−4.01609	−0.505979
$64$	1.00000	0.125000
$65$	4.57878	0.567928
$66$	−0.189350	−0.0233074
$67$	13.7492	1.67973	0.839866	−	0.542794i	$-0.182633\pi$
$67$	13.7492	1.67973	0.839866	+	0.542794i	$0.182633\pi$
$68$	3.88338	0.470929
$69$	0.303158	0.0364960
$70$	−3.67942	−0.439774
$71$	−14.6538	−1.73908	−0.869540	−	0.493862i	$-0.835585\pi$
$71$	−14.6538	−1.73908	−0.869540	+	0.493862i	$0.835585\pi$
$72$	−2.95425	−0.348162
$73$	0.203571	0.0238262	0.0119131	−	0.999929i	$-0.496208\pi$
$73$	0.203571	0.0238262	0.0119131	+	0.999929i	$0.496208\pi$
$74$	−3.25201	−0.378039
$75$	0.497420	0.0574371
$76$	−7.31642	−0.839251
$77$	−1.20350	−0.137151
$78$	−0.361828	−0.0409689
$79$	9.68138	1.08924	0.544620	−	0.838683i	$-0.316674\pi$
$79$	9.68138	1.08924	0.544620	+	0.838683i	$0.316674\pi$
$80$	−2.70660	−0.302607
$81$	8.59038	0.954487
$82$	−2.67490	−0.295393
$83$	−0.507262	−0.0556792	−0.0278396	−	0.999612i	$-0.508863\pi$
$83$	−0.507262	−0.0556792	−0.0278396	+	0.999612i	$0.508863\pi$
$84$	0.290757	0.0317242
$85$	−10.5107	−1.14005
$86$	−12.8706	−1.38787
$87$	−2.20358	−0.236248
$88$	−0.885300	−0.0943733
$89$	−1.24226	−0.131679	−0.0658395	−	0.997830i	$-0.520973\pi$
$89$	−1.24226	−0.131679	−0.0658395	+	0.997830i	$0.520973\pi$
$90$	7.99598	0.842850
$91$	−2.29976	−0.241080
$92$	1.41741	0.147775
$93$	0.634751	0.0658206
$94$	5.26075	0.542605
$95$	19.8026	2.03171
$96$	0.213882	0.0218293
$97$	−1.55399	−0.157784	−0.0788918	−	0.996883i	$-0.525138\pi$
$97$	−1.55399	−0.157784	−0.0788918	+	0.996883i	$0.525138\pi$
$98$	−5.15196	−0.520427
$99$	2.61540	0.262858
$100$	2.32567	0.232567
$101$	−5.26219	−0.523608	−0.261804	−	0.965121i	$-0.584317\pi$
$101$	−5.26219	−0.523608	−0.261804	+	0.965121i	$0.584317\pi$
$102$	0.830586	0.0822403
$103$	1.44044	0.141930	0.0709652	−	0.997479i	$-0.477392\pi$
$103$	1.44044	0.141930	0.0709652	+	0.997479i	$0.477392\pi$
$104$	−1.69171	−0.165886
$105$	−0.786963	−0.0767997
$106$	−1.14453	−0.111167
$107$	2.35154	0.227332	0.113666	−	0.993519i	$-0.463741\pi$
$107$	2.35154	0.227332	0.113666	+	0.993519i	$0.463741\pi$
$108$	−1.27351	−0.122544
$109$	6.83127	0.654317	0.327159	−	0.944969i	$-0.393909\pi$
$109$	6.83127	0.654317	0.327159	+	0.944969i	$0.393909\pi$
$110$	2.39615	0.228464
$111$	−0.695549	−0.0660186
$112$	1.35942	0.128454
$113$	0.897127	0.0843946	0.0421973	−	0.999109i	$-0.486564\pi$
$113$	0.897127	0.0843946	0.0421973	+	0.999109i	$0.486564\pi$
$114$	−1.56486	−0.146562
$115$	−3.83634	−0.357741
$116$	−10.3027	−0.956586
$117$	4.99775	0.462042
$118$	6.68472	0.615378
$119$	5.27916	0.483940
$120$	−0.578894	−0.0528455
$121$	−10.2162	−0.928749
$122$	−8.23165	−0.745259
$123$	−0.572114	−0.0515858
$124$	2.96775	0.266512
$125$	7.23834	0.647417
$126$	−4.01609	−0.357781
$127$	17.1865	1.52506	0.762528	−	0.646955i	$-0.223958\pi$
$127$	17.1865	1.52506	0.762528	+	0.646955i	$0.223958\pi$
$128$	1.00000	0.0883883
$129$	−2.75279	−0.242370
$130$	4.57878	0.401586
$131$	−11.7424	−1.02594	−0.512970	−	0.858407i	$-0.671455\pi$
$131$	−11.7424	−1.02594	−0.512970	+	0.858407i	$0.671455\pi$
$132$	−0.189350	−0.0164808
$133$	−9.94613	−0.862439
$134$	13.7492	1.18775
$135$	3.44688	0.296660
$136$	3.88338	0.332997
$137$	17.7498	1.51647	0.758236	−	0.651980i	$-0.226062\pi$
$137$	17.7498	1.51647	0.758236	+	0.651980i	$0.226062\pi$
$138$	0.303158	0.0258065
$139$	−11.0077	−0.933660	−0.466830	−	0.884347i	$-0.654604\pi$
$139$	−11.0077	−0.933660	−0.466830	+	0.884347i	$0.654604\pi$
$140$	−3.67942	−0.310967
$141$	1.12518	0.0947575
$142$	−14.6538	−1.22972
$143$	1.49767	0.125242
$144$	−2.95425	−0.246188
$145$	27.8854	2.31576
$146$	0.203571	0.0168477
$147$	−1.10191	−0.0908844
$148$	−3.25201	−0.267314
$149$	−13.7435	−1.12591	−0.562954	−	0.826488i	$-0.690335\pi$
$149$	−13.7435	−1.12591	−0.562954	+	0.826488i	$0.690335\pi$
$150$	0.497420	0.0406142
$151$	0.813311	0.0661863	0.0330932	−	0.999452i	$-0.489464\pi$
$151$	0.813311	0.0661863	0.0330932	+	0.999452i	$0.489464\pi$
$152$	−7.31642	−0.593440
$153$	−11.4725	−0.927495
$154$	−1.20350	−0.0969807
$155$	−8.03252	−0.645187
$156$	−0.361828	−0.0289694
$157$	−20.0594	−1.60091	−0.800455	−	0.599392i	$-0.795409\pi$
$157$	−20.0594	−1.60091	−0.800455	+	0.599392i	$0.795409\pi$
$158$	9.68138	0.770209
$159$	−0.244795	−0.0194135
$160$	−2.70660	−0.213975
$161$	1.92686	0.151858
$162$	8.59038	0.674924
$163$	−3.07189	−0.240609	−0.120305	−	0.992737i	$-0.538387\pi$
$163$	−3.07189	−0.240609	−0.120305	+	0.992737i	$0.538387\pi$
$164$	−2.67490	−0.208875
$165$	0.512494	0.0398976
$166$	−0.507262	−0.0393711
$167$	16.9138	1.30883	0.654416	−	0.756135i	$-0.272915\pi$
$167$	16.9138	1.30883	0.654416	+	0.756135i	$0.272915\pi$
$168$	0.290757	0.0224324
$169$	−10.1381	−0.779855
$170$	−10.5107	−0.806137
$171$	21.6146	1.65291
$172$	−12.8706	−0.981372
$173$	22.8219	1.73512	0.867560	−	0.497332i	$-0.165687\pi$
$173$	22.8219	1.73512	0.867560	+	0.497332i	$0.165687\pi$
$174$	−2.20358	−0.167053
$175$	3.16157	0.238992
$176$	−0.885300	−0.0667320
$177$	1.42974	0.107466
$178$	−1.24226	−0.0931111
$179$	6.44607	0.481802	0.240901	−	0.970550i	$-0.422557\pi$
$179$	6.44607	0.481802	0.240901	+	0.970550i	$0.422557\pi$
$180$	7.99598	0.595985
$181$	−10.2755	−0.763775	−0.381888	−	0.924209i	$-0.624726\pi$
$181$	−10.2755	−0.763775	−0.381888	+	0.924209i	$0.624726\pi$
$182$	−2.29976	−0.170469
$183$	−1.76061	−0.130148
$184$	1.41741	0.104492
$185$	8.80189	0.647128
$186$	0.634751	0.0465422
$187$	−3.43795	−0.251408
$188$	5.26075	0.383680
$189$	−1.73124	−0.125929
$190$	19.8026	1.43663
$191$	14.5439	1.05236	0.526178	−	0.850374i	$-0.323624\pi$
$191$	14.5439	1.05236	0.526178	+	0.850374i	$0.323624\pi$
$192$	0.213882	0.0154356
$193$	12.8652	0.926059	0.463029	−	0.886343i	$-0.346762\pi$
$193$	12.8652	0.926059	0.463029	+	0.886343i	$0.346762\pi$
$194$	−1.55399	−0.111570
$195$	0.979322	0.0701307
$196$	−5.15196	−0.367997
$197$	21.8687	1.55808	0.779039	−	0.626975i	$-0.215707\pi$
$197$	21.8687	1.55808	0.779039	+	0.626975i	$0.215707\pi$
$198$	2.61540	0.185868
$199$	−18.2560	−1.29413	−0.647066	−	0.762434i	$-0.724004\pi$
$199$	−18.2560	−1.29413	−0.647066	+	0.762434i	$0.724004\pi$
$200$	2.32567	0.164450
$201$	2.94071	0.207422
$202$	−5.26219	−0.370247
$203$	−14.0058	−0.983016
$204$	0.830586	0.0581527
$205$	7.23987	0.505655
$206$	1.44044	0.100360
$207$	−4.18738	−0.291043
$208$	−1.69171	−0.117299
$209$	6.47723	0.448039
$210$	−0.786963	−0.0543056
$211$	17.1676	1.18187	0.590935	−	0.806719i	$-0.298759\pi$
$211$	17.1676	1.18187	0.590935	+	0.806719i	$0.298759\pi$
$212$	−1.14453	−0.0786068
$213$	−3.13418	−0.214751
$214$	2.35154	0.160748
$215$	34.8354	2.37576
$216$	−1.27351	−0.0866514
$217$	4.03444	0.273876
$218$	6.83127	0.462672
$219$	0.0435403	0.00294218
$220$	2.39615	0.161548
$221$	−6.56956	−0.441916
$222$	−0.695549	−0.0466822
$223$	−12.8881	−0.863050	−0.431525	−	0.902101i	$-0.642024\pi$
$223$	−12.8881	−0.863050	−0.431525	+	0.902101i	$0.642024\pi$
$224$	1.35942	0.0908304
$225$	−6.87062	−0.458041
$226$	0.897127	0.0596760
$227$	11.2680	0.747881	0.373941	−	0.927453i	$-0.378006\pi$
$227$	11.2680	0.747881	0.373941	+	0.927453i	$0.378006\pi$
$228$	−1.56486	−0.103635
$229$	−15.2104	−1.00513	−0.502565	−	0.864539i	$-0.667610\pi$
$229$	−15.2104	−1.00513	−0.502565	+	0.864539i	$0.667610\pi$
$230$	−3.83634	−0.252961
$231$	−0.257407	−0.0169362
$232$	−10.3027	−0.676409
$233$	25.4046	1.66431	0.832157	−	0.554540i	$-0.187106\pi$
$233$	25.4046	1.66431	0.832157	+	0.554540i	$0.187106\pi$
$234$	4.99775	0.326713
$235$	−14.2387	−0.928833
$236$	6.68472	0.435138
$237$	2.07068	0.134505
$238$	5.27916	0.342197
$239$	−8.43954	−0.545909	−0.272954	−	0.962027i	$-0.588001\pi$
$239$	−8.43954	−0.545909	−0.272954	+	0.962027i	$0.588001\pi$
$240$	−0.578894	−0.0373674
$241$	−9.12941	−0.588077	−0.294038	−	0.955794i	$-0.594999\pi$
$241$	−9.12941	−0.588077	−0.294038	+	0.955794i	$0.594999\pi$
$242$	−10.2162	−0.656725
$243$	5.65786	0.362952
$244$	−8.23165	−0.526977
$245$	13.9443	0.890868
$246$	−0.572114	−0.0364767
$247$	12.3773	0.787548
$248$	2.96775	0.188453
$249$	−0.108494	−0.00687555
$250$	7.23834	0.457793
$251$	−5.79206	−0.365592	−0.182796	−	0.983151i	$-0.558515\pi$
$251$	−5.79206	−0.365592	−0.182796	+	0.983151i	$0.558515\pi$
$252$	−4.01609	−0.252990
$253$	−1.25483	−0.0788904
$254$	17.1865	1.07838
$255$	−2.24806	−0.140779
$256$	1.00000	0.0625000
$257$	0.941543	0.0587319	0.0293659	−	0.999569i	$-0.490651\pi$
$257$	0.941543	0.0587319	0.0293659	+	0.999569i	$0.490651\pi$
$258$	−2.75279	−0.171381
$259$	−4.42087	−0.274699
$260$	4.57878	0.283964
$261$	30.4369	1.88400
$262$	−11.7424	−0.725449
$263$	−6.85956	−0.422979	−0.211489	−	0.977380i	$-0.567831\pi$
$263$	−6.85956	−0.422979	−0.211489	+	0.977380i	$0.567831\pi$
$264$	−0.189350	−0.0116537
$265$	3.09779	0.190296
$266$	−9.94613	−0.609836
$267$	−0.265697	−0.0162604
$268$	13.7492	0.839866
$269$	−0.998752	−0.0608950	−0.0304475	−	0.999536i	$-0.509693\pi$
$269$	−0.998752	−0.0608950	−0.0304475	+	0.999536i	$0.509693\pi$
$270$	3.44688	0.209770
$271$	−28.8944	−1.75521	−0.877606	−	0.479383i	$-0.840860\pi$
$271$	−28.8944	−1.75521	−0.877606	+	0.479383i	$0.840860\pi$
$272$	3.88338	0.235464
$273$	−0.491878	−0.0297698
$274$	17.7498	1.07231
$275$	−2.05891	−0.124157
$276$	0.303158	0.0182480
$277$	−0.887769	−0.0533409	−0.0266704	−	0.999644i	$-0.508490\pi$
$277$	−0.887769	−0.0533409	−0.0266704	+	0.999644i	$0.508490\pi$
$278$	−11.0077	−0.660198
$279$	−8.76750	−0.524897
$280$	−3.67942	−0.219887
$281$	24.2279	1.44532	0.722658	−	0.691206i	$-0.242920\pi$
$281$	24.2279	1.44532	0.722658	+	0.691206i	$0.242920\pi$
$282$	1.12518	0.0670037
$283$	9.62532	0.572166	0.286083	−	0.958205i	$-0.407647\pi$
$283$	9.62532	0.572166	0.286083	+	0.958205i	$0.407647\pi$
$284$	−14.6538	−0.869540
$285$	4.23543	0.250885
$286$	1.49767	0.0885592
$287$	−3.63632	−0.214645
$288$	−2.95425	−0.174081
$289$	−1.91939	−0.112905
$290$	27.8854	1.63749
$291$	−0.332371	−0.0194839
$292$	0.203571	0.0119131
$293$	−11.6233	−0.679038	−0.339519	−	0.940599i	$-0.610264\pi$
$293$	−11.6233	−0.679038	−0.339519	+	0.940599i	$0.610264\pi$
$294$	−1.10191	−0.0642650
$295$	−18.0928	−1.05341
$296$	−3.25201	−0.189019
$297$	1.12744	0.0654206
$298$	−13.7435	−0.796137
$299$	−2.39784	−0.138671
$300$	0.497420	0.0287185
$301$	−17.4966	−1.00849
$302$	0.813311	0.0468008
$303$	−1.12549	−0.0646578
$304$	−7.31642	−0.419626
$305$	22.2798	1.27574
$306$	−11.4725	−0.655838
$307$	−14.1224	−0.806005	−0.403003	−	0.915199i	$-0.632033\pi$
$307$	−14.1224	−0.806005	−0.403003	+	0.915199i	$0.632033\pi$
$308$	−1.20350	−0.0685757
$309$	0.308084	0.0175263
$310$	−8.03252	−0.456216
$311$	−13.4684	−0.763726	−0.381863	−	0.924219i	$-0.624717\pi$
$311$	−13.4684	−0.763726	−0.381863	+	0.924219i	$0.624717\pi$
$312$	−0.361828	−0.0204845
$313$	−20.6642	−1.16801	−0.584005	−	0.811750i	$-0.698515\pi$
$313$	−20.6642	−1.16801	−0.584005	+	0.811750i	$0.698515\pi$
$314$	−20.0594	−1.13201
$315$	10.8699	0.612451
$316$	9.68138	0.544620
$317$	3.64606	0.204783	0.102392	−	0.994744i	$-0.467350\pi$
$317$	3.64606	0.204783	0.102392	+	0.994744i	$0.467350\pi$
$318$	−0.244795	−0.0137274
$319$	9.12102	0.510679
$320$	−2.70660	−0.151303
$321$	0.502954	0.0280722
$322$	1.92686	0.107379
$323$	−28.4124	−1.58091
$324$	8.59038	0.477243
$325$	−3.93436	−0.218239
$326$	−3.07189	−0.170136
$327$	1.46109	0.0807984
$328$	−2.67490	−0.147697
$329$	7.15160	0.394280
$330$	0.512494	0.0282119
$331$	−6.74236	−0.370593	−0.185297	−	0.982683i	$-0.559325\pi$
$331$	−6.74236	−0.370593	−0.185297	+	0.982683i	$0.559325\pi$
$332$	−0.507262	−0.0278396
$333$	9.60728	0.526475
$334$	16.9138	0.925484
$335$	−37.2136	−2.03319
$336$	0.290757	0.0158621
$337$	−10.7422	−0.585167	−0.292584	−	0.956240i	$-0.594515\pi$
$337$	−10.7422	−0.585167	−0.292584	+	0.956240i	$0.594515\pi$
$338$	−10.1381	−0.551440
$339$	0.191880	0.0104215
$340$	−10.5107	−0.570025
$341$	−2.62735	−0.142279
$342$	21.6146	1.16878
$343$	−16.5197	−0.891979
$344$	−12.8706	−0.693934
$345$	−0.820527	−0.0441757
$346$	22.8219	1.22692
$347$	−2.48193	−0.133237	−0.0666185	−	0.997779i	$-0.521221\pi$
$347$	−2.48193	−0.133237	−0.0666185	+	0.997779i	$0.521221\pi$
$348$	−2.20358	−0.118124
$349$	5.30024	0.283715	0.141858	−	0.989887i	$-0.454692\pi$
$349$	5.30024	0.283715	0.141858	+	0.989887i	$0.454692\pi$
$350$	3.16157	0.168993
$351$	2.15441	0.114994
$352$	−0.885300	−0.0471866
$353$	−13.1035	−0.697427	−0.348714	−	0.937229i	$-0.613381\pi$
$353$	−13.1035	−0.697427	−0.348714	+	0.937229i	$0.613381\pi$
$354$	1.42974	0.0759901
$355$	39.6618	2.10503
$356$	−1.24226	−0.0658395
$357$	1.12912	0.0597593
$358$	6.44607	0.340685
$359$	−29.1055	−1.53613	−0.768066	−	0.640371i	$-0.778781\pi$
$359$	−29.1055	−1.53613	−0.768066	+	0.640371i	$0.778781\pi$
$360$	7.99598	0.421425
$361$	34.5301	1.81737
$362$	−10.2755	−0.540071
$363$	−2.18508	−0.114687
$364$	−2.29976	−0.120540
$365$	−0.550986	−0.0288399
$366$	−1.76061	−0.0920284
$367$	−33.6681	−1.75746	−0.878732	−	0.477316i	$-0.841610\pi$
$367$	−33.6681	−1.75746	−0.878732	+	0.477316i	$0.841610\pi$
$368$	1.41741	0.0738874
$369$	7.90233	0.411379
$370$	8.80189	0.457589
$371$	−1.55591	−0.0807786
$372$	0.634751	0.0329103
$373$	23.2011	1.20131	0.600653	−	0.799510i	$-0.294907\pi$
$373$	23.2011	1.20131	0.600653	+	0.799510i	$0.294907\pi$
$374$	−3.43795	−0.177772
$375$	1.54815	0.0799463
$376$	5.26075	0.271303
$377$	17.4293	0.897654
$378$	−1.73124	−0.0890455
$379$	27.1970	1.39701	0.698507	−	0.715603i	$-0.253848\pi$
$379$	27.1970	1.39701	0.698507	+	0.715603i	$0.253848\pi$
$380$	19.8026	1.01585
$381$	3.67589	0.188322
$382$	14.5439	0.744129
$383$	27.7896	1.41998	0.709990	−	0.704211i	$-0.248699\pi$
$383$	27.7896	1.41998	0.709990	+	0.704211i	$0.248699\pi$
$384$	0.213882	0.0109146
$385$	3.25739	0.166012
$386$	12.8652	0.654822
$387$	38.0229	1.93281
$388$	−1.55399	−0.0788918
$389$	30.5419	1.54854	0.774268	−	0.632857i	$-0.218118\pi$
$389$	30.5419	1.54854	0.774268	+	0.632857i	$0.218118\pi$
$390$	0.979322	0.0495899
$391$	5.50432	0.278365
$392$	−5.15196	−0.260213
$393$	−2.51150	−0.126688
$394$	21.8687	1.10173
$395$	−26.2036	−1.31845
$396$	2.61540	0.131429
$397$	11.4294	0.573628	0.286814	−	0.957986i	$-0.407404\pi$
$397$	11.4294	0.573628	0.286814	+	0.957986i	$0.407404\pi$
$398$	−18.2560	−0.915090
$399$	−2.12730	−0.106498
$400$	2.32567	0.116283
$401$	1.61278	0.0805383	0.0402691	−	0.999189i	$-0.487178\pi$
$401$	1.61278	0.0805383	0.0402691	+	0.999189i	$0.487178\pi$
$402$	2.94071	0.146669
$403$	−5.02059	−0.250093
$404$	−5.26219	−0.261804
$405$	−23.2507	−1.15534
$406$	−14.0058	−0.695097
$407$	2.87901	0.142707
$408$	0.830586	0.0411201
$409$	−3.20480	−0.158467	−0.0792336	−	0.996856i	$-0.525247\pi$
$409$	−3.20480	−0.158467	−0.0792336	+	0.996856i	$0.525247\pi$
$410$	7.23987	0.357552
$411$	3.79638	0.187262
$412$	1.44044	0.0709652
$413$	9.08738	0.447161
$414$	−4.18738	−0.205798
$415$	1.37295	0.0673956
$416$	−1.69171	−0.0829430
$417$	−2.35435	−0.115293
$418$	6.47723	0.316812
$419$	−15.2286	−0.743966	−0.371983	−	0.928240i	$-0.621322\pi$
$419$	−15.2286	−0.743966	−0.371983	+	0.928240i	$0.621322\pi$
$420$	−0.786963	−0.0383998
$421$	32.3567	1.57697	0.788484	−	0.615056i	$-0.210866\pi$
$421$	32.3567	1.57697	0.788484	+	0.615056i	$0.210866\pi$
$422$	17.1676	0.835708
$423$	−15.5416	−0.755658
$424$	−1.14453	−0.0555834
$425$	9.03145	0.438089
$426$	−3.13418	−0.151852
$427$	−11.1903	−0.541537
$428$	2.35154	0.113666
$429$	0.320326	0.0154655
$430$	34.8354	1.67991
$431$	−37.9195	−1.82652	−0.913258	−	0.407382i	$-0.866442\pi$
$431$	−37.9195	−1.82652	−0.913258	+	0.407382i	$0.866442\pi$
$432$	−1.27351	−0.0612718
$433$	23.4555	1.12720	0.563599	−	0.826049i	$-0.309416\pi$
$433$	23.4555	1.12720	0.563599	+	0.826049i	$0.309416\pi$
$434$	4.03444	0.193659
$435$	5.96420	0.285961
$436$	6.83127	0.327159
$437$	−10.3703	−0.496081
$438$	0.0435403	0.00208044
$439$	−24.1554	−1.15287	−0.576437	−	0.817141i	$-0.695557\pi$
$439$	−24.1554	−1.15287	−0.576437	+	0.817141i	$0.695557\pi$
$440$	2.39615	0.114232
$441$	15.2202	0.724772
$442$	−6.56956	−0.312482
$443$	−20.8170	−0.989046	−0.494523	−	0.869165i	$-0.664657\pi$
$443$	−20.8170	−0.989046	−0.494523	+	0.869165i	$0.664657\pi$
$444$	−0.695549	−0.0330093
$445$	3.36229	0.159388
$446$	−12.8881	−0.610269
$447$	−2.93949	−0.139033
$448$	1.35942	0.0642268
$449$	5.81955	0.274642	0.137321	−	0.990527i	$-0.456151\pi$
$449$	5.81955	0.274642	0.137321	+	0.990527i	$0.456151\pi$
$450$	−6.87062	−0.323884
$451$	2.36809	0.111509
$452$	0.897127	0.0421973
$453$	0.173953	0.00817302
$454$	11.2680	0.528832
$455$	6.22451	0.291810
$456$	−1.56486	−0.0732811
$457$	24.9161	1.16552	0.582762	−	0.812643i	$-0.301972\pi$
$457$	24.9161	1.16552	0.582762	+	0.812643i	$0.301972\pi$
$458$	−15.2104	−0.710734
$459$	−4.94552	−0.230837
$460$	−3.83634	−0.178871
$461$	−12.8578	−0.598846	−0.299423	−	0.954120i	$-0.596794\pi$
$461$	−12.8578	−0.598846	−0.299423	+	0.954120i	$0.596794\pi$
$462$	−0.257407	−0.0119757
$463$	−2.41369	−0.112174	−0.0560869	−	0.998426i	$-0.517862\pi$
$463$	−2.41369	−0.112174	−0.0560869	+	0.998426i	$0.517862\pi$
$464$	−10.3027	−0.478293
$465$	−1.71801	−0.0796710
$466$	25.4046	1.17685
$467$	−13.9500	−0.645530	−0.322765	−	0.946479i	$-0.604612\pi$
$467$	−13.9500	−0.645530	−0.322765	+	0.946479i	$0.604612\pi$
$468$	4.99775	0.231021
$469$	18.6910	0.863071
$470$	−14.2387	−0.656784
$471$	−4.29034	−0.197689
$472$	6.68472	0.307689
$473$	11.3943	0.523911
$474$	2.07068	0.0951093
$475$	−17.0156	−0.780728
$476$	5.27916	0.241970
$477$	3.38124	0.154816
$478$	−8.43954	−0.386016
$479$	6.62847	0.302863	0.151431	−	0.988468i	$-0.451612\pi$
$479$	6.62847	0.302863	0.151431	+	0.988468i	$0.451612\pi$
$480$	−0.578894	−0.0264228
$481$	5.50147	0.250846
$482$	−9.12941	−0.415833
$483$	0.412121	0.0187521
$484$	−10.2162	−0.464375
$485$	4.20602	0.190986
$486$	5.65786	0.256646
$487$	−18.1364	−0.821838	−0.410919	−	0.911672i	$-0.634792\pi$
$487$	−18.1364	−0.821838	−0.410919	+	0.911672i	$0.634792\pi$
$488$	−8.23165	−0.372629
$489$	−0.657024	−0.0297117
$490$	13.9443	0.629939
$491$	30.7389	1.38723	0.693615	−	0.720346i	$-0.256017\pi$
$491$	30.7389	1.38723	0.693615	+	0.720346i	$0.256017\pi$
$492$	−0.572114	−0.0257929
$493$	−40.0095	−1.80194
$494$	12.3773	0.556880
$495$	−7.07884	−0.318170
$496$	2.96775	0.133256
$497$	−19.9207	−0.893565
$498$	−0.108494	−0.00486175
$499$	−25.8213	−1.15592	−0.577960	−	0.816065i	$-0.696151\pi$
$499$	−25.8213	−1.15592	−0.577960	+	0.816065i	$0.696151\pi$
$500$	7.23834	0.323708
$501$	3.61757	0.161621
$502$	−5.79206	−0.258512
$503$	4.48751	0.200088	0.100044	−	0.994983i	$-0.468102\pi$
$503$	4.48751	0.200088	0.100044	+	0.994983i	$0.468102\pi$
$504$	−4.01609	−0.178891
$505$	14.2426	0.633789
$506$	−1.25483	−0.0557839
$507$	−2.16836	−0.0963004
$508$	17.1865	0.762528
$509$	29.6695	1.31508	0.657539	−	0.753421i	$-0.271598\pi$
$509$	29.6695	1.31508	0.657539	+	0.753421i	$0.271598\pi$
$510$	−2.24806	−0.0995459
$511$	0.276740	0.0122423
$512$	1.00000	0.0441942
$513$	9.31754	0.411380
$514$	0.941543	0.0415297
$515$	−3.89868	−0.171796
$516$	−2.75279	−0.121185
$517$	−4.65734	−0.204830
$518$	−4.42087	−0.194242
$519$	4.88121	0.214262
$520$	4.57878	0.200793
$521$	−36.9738	−1.61985	−0.809925	−	0.586534i	$-0.800492\pi$
$521$	−36.9738	−1.61985	−0.809925	+	0.586534i	$0.800492\pi$
$522$	30.4369	1.33219
$523$	−20.2507	−0.885502	−0.442751	−	0.896645i	$-0.645997\pi$
$523$	−20.2507	−0.885502	−0.442751	+	0.896645i	$0.645997\pi$
$524$	−11.7424	−0.512970
$525$	0.676205	0.0295120
$526$	−6.85956	−0.299091
$527$	11.5249	0.502033
$528$	−0.189350	−0.00824041
$529$	−20.9910	−0.912651
$530$	3.09779	0.134559
$531$	−19.7484	−0.857006
$532$	−9.94613	−0.431219
$533$	4.52516	0.196006
$534$	−0.265697	−0.0114978
$535$	−6.36468	−0.275169
$536$	13.7492	0.593875
$537$	1.37870	0.0594953
$538$	−0.998752	−0.0430593
$539$	4.56103	0.196458
$540$	3.44688	0.148330
$541$	−39.8334	−1.71257	−0.856286	−	0.516502i	$-0.827234\pi$
$541$	−39.8334	−1.71257	−0.856286	+	0.516502i	$0.827234\pi$
$542$	−28.8944	−1.24112
$543$	−2.19776	−0.0943149
$544$	3.88338	0.166498
$545$	−18.4895	−0.792003
$546$	−0.491878	−0.0210504
$547$	26.3087	1.12488	0.562440	−	0.826838i	$-0.309863\pi$
$547$	26.3087	1.12488	0.562440	+	0.826838i	$0.309863\pi$
$548$	17.7498	0.758236
$549$	24.3184	1.03788
$550$	−2.05891	−0.0877924
$551$	75.3793	3.21127
$552$	0.303158	0.0129033
$553$	13.1611	0.559667
$554$	−0.887769	−0.0377177
$555$	1.88257	0.0799107
$556$	−11.0077	−0.466830
$557$	−20.7260	−0.878189	−0.439095	−	0.898441i	$-0.644701\pi$
$557$	−20.7260	−0.878189	−0.439095	+	0.898441i	$0.644701\pi$
$558$	−8.76750	−0.371158
$559$	21.7733	0.920912
$560$	−3.67942	−0.155484
$561$	−0.735318	−0.0310451
$562$	24.2279	1.02199
$563$	41.9712	1.76887	0.884437	−	0.466660i	$-0.154543\pi$
$563$	41.9712	1.76887	0.884437	+	0.466660i	$0.154543\pi$
$564$	1.12518	0.0473787
$565$	−2.42816	−0.102153
$566$	9.62532	0.404582
$567$	11.6780	0.490429
$568$	−14.6538	−0.614858
$569$	36.6688	1.53724	0.768618	−	0.639708i	$-0.220945\pi$
$569$	36.6688	1.53724	0.768618	+	0.639708i	$0.220945\pi$
$570$	4.23543	0.177403
$571$	2.02410	0.0847060	0.0423530	−	0.999103i	$-0.486515\pi$
$571$	2.02410	0.0847060	0.0423530	+	0.999103i	$0.486515\pi$
$572$	1.49767	0.0626208
$573$	3.11068	0.129950
$574$	−3.63632	−0.151777
$575$	3.29641	0.137470
$576$	−2.95425	−0.123094
$577$	−15.0478	−0.626448	−0.313224	−	0.949679i	$-0.601409\pi$
$577$	−15.0478	−0.626448	−0.313224	+	0.949679i	$0.601409\pi$
$578$	−1.91939	−0.0798361
$579$	2.75164	0.114354
$580$	27.8854	1.15788
$581$	−0.689584	−0.0286088
$582$	−0.332371	−0.0137772
$583$	1.01325	0.0419647
$584$	0.203571	0.00842384
$585$	−13.5269	−0.559268
$586$	−11.6233	−0.480153
$587$	−6.09944	−0.251751	−0.125875	−	0.992046i	$-0.540174\pi$
$587$	−6.09944	−0.251751	−0.125875	+	0.992046i	$0.540174\pi$
$588$	−1.10191	−0.0454422
$589$	−21.7134	−0.894683
$590$	−18.0928	−0.744871
$591$	4.67733	0.192399
$592$	−3.25201	−0.133657
$593$	−22.4162	−0.920525	−0.460262	−	0.887783i	$-0.652245\pi$
$593$	−22.4162	−0.920525	−0.460262	+	0.887783i	$0.652245\pi$
$594$	1.12744	0.0462594
$595$	−14.2886	−0.585774
$596$	−13.7435	−0.562954
$597$	−3.90463	−0.159806
$598$	−2.39784	−0.0980550
$599$	−35.0649	−1.43271	−0.716357	−	0.697734i	$-0.754192\pi$
$599$	−35.0649	−1.43271	−0.716357	+	0.697734i	$0.754192\pi$
$600$	0.497420	0.0203071
$601$	7.10023	0.289624	0.144812	−	0.989459i	$-0.453742\pi$
$601$	7.10023	0.289624	0.144812	+	0.989459i	$0.453742\pi$
$602$	−17.4966	−0.713107
$603$	−40.6186	−1.65412
$604$	0.813311	0.0330932
$605$	27.6513	1.12418
$606$	−1.12549	−0.0457199
$607$	−18.8356	−0.764512	−0.382256	−	0.924056i	$-0.624853\pi$
$607$	−18.8356	−0.764512	−0.382256	+	0.924056i	$0.624853\pi$
$608$	−7.31642	−0.296720
$609$	−2.99560	−0.121388
$610$	22.2798	0.902081
$611$	−8.89968	−0.360043
$612$	−11.4725	−0.463748
$613$	−29.8991	−1.20761	−0.603807	−	0.797131i	$-0.706350\pi$
$613$	−29.8991	−1.20761	−0.603807	+	0.797131i	$0.706350\pi$
$614$	−14.1224	−0.569932
$615$	1.54848	0.0624408
$616$	−1.20350	−0.0484903
$617$	−24.9812	−1.00571	−0.502853	−	0.864372i	$-0.667716\pi$
$617$	−24.9812	−1.00571	−0.502853	+	0.864372i	$0.667716\pi$
$618$	0.308084	0.0123930
$619$	20.7976	0.835926	0.417963	−	0.908464i	$-0.362744\pi$
$619$	20.7976	0.835926	0.417963	+	0.908464i	$0.362744\pi$
$620$	−8.03252	−0.322594
$621$	−1.80508	−0.0724354
$622$	−13.4684	−0.540036
$623$	−1.68876	−0.0676586
$624$	−0.361828	−0.0144847
$625$	−31.2196	−1.24878
$626$	−20.6642	−0.825908
$627$	1.38537	0.0553262
$628$	−20.0594	−0.800455
$629$	−12.6288	−0.503543
$630$	10.8699	0.433068
$631$	−29.0331	−1.15579	−0.577894	−	0.816112i	$-0.696125\pi$
$631$	−29.0331	−1.15579	−0.577894	+	0.816112i	$0.696125\pi$
$632$	9.68138	0.385104
$633$	3.67186	0.145943
$634$	3.64606	0.144804
$635$	−46.5170	−1.84597
$636$	−0.244795	−0.00970677
$637$	8.71564	0.345326
$638$	9.12102	0.361105
$639$	43.2909	1.71256
$640$	−2.70660	−0.106988
$641$	−30.6105	−1.20904	−0.604522	−	0.796589i	$-0.706636\pi$
$641$	−30.6105	−1.20904	−0.604522	+	0.796589i	$0.706636\pi$
$642$	0.502954	0.0198500
$643$	−31.8843	−1.25740	−0.628698	−	0.777650i	$-0.716412\pi$
$643$	−31.8843	−1.25740	−0.628698	+	0.777650i	$0.716412\pi$
$644$	1.92686	0.0759288
$645$	7.45069	0.293371
$646$	−28.4124	−1.11787
$647$	−14.3594	−0.564526	−0.282263	−	0.959337i	$-0.591085\pi$
$647$	−14.3594	−0.564526	−0.282263	+	0.959337i	$0.591085\pi$
$648$	8.59038	0.337462
$649$	−5.91798	−0.232301
$650$	−3.93436	−0.154318
$651$	0.862896	0.0338196
$652$	−3.07189	−0.120305
$653$	33.4640	1.30955	0.654775	−	0.755824i	$-0.272764\pi$
$653$	33.4640	1.30955	0.654775	+	0.755824i	$0.272764\pi$
$654$	1.46109	0.0571331
$655$	31.7820	1.24183
$656$	−2.67490	−0.104437
$657$	−0.601402	−0.0234629
$658$	7.15160	0.278798
$659$	−7.94446	−0.309472	−0.154736	−	0.987956i	$-0.549453\pi$
$659$	−7.94446	−0.309472	−0.154736	+	0.987956i	$0.549453\pi$
$660$	0.512494	0.0199488
$661$	12.0478	0.468606	0.234303	−	0.972164i	$-0.424719\pi$
$661$	12.0478	0.468606	0.234303	+	0.972164i	$0.424719\pi$
$662$	−6.74236	−0.262049
$663$	−1.40511	−0.0545701
$664$	−0.507262	−0.0196856
$665$	26.9202	1.04392
$666$	9.60728	0.372274
$667$	−14.6032	−0.565437
$668$	16.9138	0.654416
$669$	−2.75654	−0.106574
$670$	−37.2136	−1.43768
$671$	7.28748	0.281330
$672$	0.290757	0.0112162
$673$	−0.865531	−0.0333638	−0.0166819	−	0.999861i	$-0.505310\pi$
$673$	−0.865531	−0.0333638	−0.0166819	+	0.999861i	$0.505310\pi$
$674$	−10.7422	−0.413776
$675$	−2.96176	−0.113998
$676$	−10.1381	−0.389927
$677$	−8.52005	−0.327452	−0.163726	−	0.986506i	$-0.552351\pi$
$677$	−8.52005	−0.327452	−0.163726	+	0.986506i	$0.552351\pi$
$678$	0.191880	0.00736909
$679$	−2.11253	−0.0810715
$680$	−10.5107	−0.403068
$681$	2.41002	0.0923522
$682$	−2.62735	−0.100607
$683$	23.7807	0.909942	0.454971	−	0.890506i	$-0.349650\pi$
$683$	23.7807	0.909942	0.454971	+	0.890506i	$0.349650\pi$
$684$	21.6146	0.826454
$685$	−48.0417	−1.83558
$686$	−16.5197	−0.630724
$687$	−3.25323	−0.124119
$688$	−12.8706	−0.490686
$689$	1.93622	0.0737641
$690$	−0.820527	−0.0312369
$691$	43.7759	1.66531	0.832657	−	0.553790i	$-0.186819\pi$
$691$	43.7759	1.66531	0.832657	+	0.553790i	$0.186819\pi$
$692$	22.8219	0.867560
$693$	3.55544	0.135060
$694$	−2.48193	−0.0942127
$695$	29.7934	1.13013
$696$	−2.20358	−0.0835264
$697$	−10.3876	−0.393460
$698$	5.30024	0.200617
$699$	5.43361	0.205518
$700$	3.16157	0.119496
$701$	−32.8162	−1.23945	−0.619726	−	0.784818i	$-0.712756\pi$
$701$	−32.8162	−1.23945	−0.619726	+	0.784818i	$0.712756\pi$
$702$	2.15441	0.0813131
$703$	23.7931	0.897374
$704$	−0.885300	−0.0333660
$705$	−3.04542	−0.114697
$706$	−13.1035	−0.493155
$707$	−7.15356	−0.269037
$708$	1.42974	0.0537331
$709$	−34.3336	−1.28942	−0.644712	−	0.764425i	$-0.723023\pi$
$709$	−34.3336	−1.28942	−0.644712	+	0.764425i	$0.723023\pi$
$710$	39.6618	1.48848
$711$	−28.6012	−1.07263
$712$	−1.24226	−0.0465556
$713$	4.20651	0.157535
$714$	1.12912	0.0422562
$715$	−4.05360	−0.151596
$716$	6.44607	0.240901
$717$	−1.80507	−0.0674116
$718$	−29.1055	−1.08621
$719$	22.7369	0.847944	0.423972	−	0.905675i	$-0.360635\pi$
$719$	22.7369	0.847944	0.423972	+	0.905675i	$0.360635\pi$
$720$	7.99598	0.297992
$721$	1.95816	0.0729258
$722$	34.5301	1.28508
$723$	−1.95262	−0.0726187
$724$	−10.2755	−0.381888
$725$	−23.9608	−0.889881
$726$	−2.18508	−0.0810958
$727$	−48.7870	−1.80941	−0.904704	−	0.426040i	$-0.859908\pi$
$727$	−48.7870	−1.80941	−0.904704	+	0.426040i	$0.859908\pi$
$728$	−2.29976	−0.0852346
$729$	−24.5610	−0.909668
$730$	−0.550986	−0.0203929
$731$	−49.9813	−1.84862
$732$	−1.76061	−0.0650739
$733$	25.1043	0.927250	0.463625	−	0.886032i	$-0.346549\pi$
$733$	25.1043	0.927250	0.463625	+	0.886032i	$0.346549\pi$
$734$	−33.6681	−1.24271
$735$	2.98244	0.110009
$736$	1.41741	0.0522462
$737$	−12.1722	−0.448367
$738$	7.90233	0.290889
$739$	4.15915	0.152997	0.0764984	−	0.997070i	$-0.475626\pi$
$739$	4.15915	0.152997	0.0764984	+	0.997070i	$0.475626\pi$
$740$	8.80189	0.323564
$741$	2.64728	0.0972504
$742$	−1.55591	−0.0571191
$743$	−49.3284	−1.80968	−0.904841	−	0.425749i	$-0.860011\pi$
$743$	−49.3284	−1.80968	−0.904841	+	0.425749i	$0.860011\pi$
$744$	0.634751	0.0232711
$745$	37.1980	1.36283
$746$	23.2011	0.849451
$747$	1.49858	0.0548302
$748$	−3.43795	−0.125704
$749$	3.19675	0.116807
$750$	1.54815	0.0565306
$751$	1.00000	0.0364905
$751$	1.00000	0.0364905
$752$	5.26075	0.191840
$753$	−1.23882	−0.0451451
$754$	17.4293	0.634737
$755$	−2.20131	−0.0801137
$756$	−1.73124	−0.0629647
$757$	−3.40412	−0.123725	−0.0618623	−	0.998085i	$-0.519704\pi$
$757$	−3.40412	−0.123725	−0.0618623	+	0.998085i	$0.519704\pi$
$758$	27.1970	0.987838
$759$	−0.268386	−0.00974179
$760$	19.8026	0.718316
$761$	−36.9480	−1.33936	−0.669682	−	0.742648i	$-0.733569\pi$
$761$	−36.9480	−1.33936	−0.669682	+	0.742648i	$0.733569\pi$
$762$	3.67589	0.133164
$763$	9.28660	0.336198
$764$	14.5439	0.526178
$765$	31.0514	1.12267
$766$	27.7896	1.00408
$767$	−11.3086	−0.408331
$768$	0.213882	0.00771782
$769$	32.7549	1.18117	0.590586	−	0.806975i	$-0.298897\pi$
$769$	32.7549	1.18117	0.590586	+	0.806975i	$0.298897\pi$
$770$	3.25739	0.117388
$771$	0.201380	0.00725251
$772$	12.8652	0.463029
$773$	−47.7981	−1.71918	−0.859589	−	0.510986i	$-0.829280\pi$
$773$	−47.7981	−1.71918	−0.859589	+	0.510986i	$0.829280\pi$
$774$	38.0229	1.36671
$775$	6.90201	0.247928
$776$	−1.55399	−0.0557850
$777$	−0.945546	−0.0339213
$778$	30.5419	1.09498
$779$	19.5707	0.701193
$780$	0.979322	0.0350653
$781$	12.9730	0.464209
$782$	5.50432	0.196834
$783$	13.1207	0.468894
$784$	−5.15196	−0.183999
$785$	54.2926	1.93779
$786$	−2.51150	−0.0895821
$787$	−19.4603	−0.693684	−0.346842	−	0.937924i	$-0.612746\pi$
$787$	−19.4603	−0.693684	−0.346842	+	0.937924i	$0.612746\pi$
$788$	21.8687	0.779039
$789$	−1.46714	−0.0522316
$790$	−26.2036	−0.932282
$791$	1.21958	0.0433631
$792$	2.61540	0.0929342
$793$	13.9256	0.494512
$794$	11.4294	0.405616
$795$	0.662562	0.0234987
$796$	−18.2560	−0.647066
$797$	28.3458	1.00406	0.502029	−	0.864851i	$-0.332587\pi$
$797$	28.3458	1.00406	0.502029	+	0.864851i	$0.332587\pi$
$798$	−2.12730	−0.0753057
$799$	20.4295	0.722743
$800$	2.32567	0.0822248
$801$	3.66994	0.129671
$802$	1.61278	0.0569492
$803$	−0.180222	−0.00635988
$804$	2.94071	0.103711
$805$	−5.21522	−0.183812
$806$	−5.02059	−0.176843
$807$	−0.213616	−0.00751962
$808$	−5.26219	−0.185123
$809$	−15.6259	−0.549376	−0.274688	−	0.961533i	$-0.588575\pi$
$809$	−15.6259	−0.549376	−0.274688	+	0.961533i	$0.588575\pi$
$810$	−23.2507	−0.816946
$811$	−27.0745	−0.950713	−0.475356	−	0.879793i	$-0.657681\pi$
$811$	−27.0745	−0.950713	−0.475356	+	0.879793i	$0.657681\pi$
$812$	−14.0058	−0.491508
$813$	−6.18001	−0.216742
$814$	2.87901	0.100909
$815$	8.31438	0.291240
$816$	0.830586	0.0290763
$817$	94.1665	3.29447
$818$	−3.20480	−0.112053
$819$	6.79406	0.237404
$820$	7.23987	0.252827
$821$	12.5652	0.438528	0.219264	−	0.975666i	$-0.429634\pi$
$821$	12.5652	0.438528	0.219264	+	0.975666i	$0.429634\pi$
$822$	3.79638	0.132414
$823$	26.5936	0.926995	0.463498	−	0.886098i	$-0.346594\pi$
$823$	26.5936	0.926995	0.463498	+	0.886098i	$0.346594\pi$
$824$	1.44044	0.0501800
$825$	−0.440366	−0.0153316
$826$	9.08738	0.316190
$827$	−16.6435	−0.578750	−0.289375	−	0.957216i	$-0.593447\pi$
$827$	−16.6435	−0.578750	−0.289375	+	0.957216i	$0.593447\pi$
$828$	−4.18738	−0.145521
$829$	−45.2062	−1.57008	−0.785038	−	0.619448i	$-0.787357\pi$
$829$	−45.2062	−1.57008	−0.785038	+	0.619448i	$0.787357\pi$
$830$	1.37295	0.0476559
$831$	−0.189878	−0.00658680
$832$	−1.69171	−0.0586496
$833$	−20.0070	−0.693202
$834$	−2.35435	−0.0815246
$835$	−45.7789	−1.58425
$836$	6.47723	0.224020
$837$	−3.77947	−0.130638
$838$	−15.2286	−0.526063
$839$	−16.1450	−0.557388	−0.278694	−	0.960380i	$-0.589902\pi$
$839$	−16.1450	−0.557388	−0.278694	+	0.960380i	$0.589902\pi$
$840$	−0.786963	−0.0271528
$841$	77.1466	2.66023
$842$	32.3567	1.11508
$843$	5.18193	0.178475
$844$	17.1676	0.590935
$845$	27.4398	0.943957
$846$	−15.5416	−0.534331
$847$	−13.8882	−0.477205
$848$	−1.14453	−0.0393034
$849$	2.05869	0.0706540
$850$	9.03145	0.309776
$851$	−4.60942	−0.158009
$852$	−3.13418	−0.107375
$853$	−9.23170	−0.316088	−0.158044	−	0.987432i	$-0.550519\pi$
$853$	−9.23170	−0.316088	−0.158044	+	0.987432i	$0.550519\pi$
$854$	−11.1903	−0.382925
$855$	−58.5020	−2.00072
$856$	2.35154	0.0803741
$857$	22.3925	0.764914	0.382457	−	0.923973i	$-0.375078\pi$
$857$	22.3925	0.764914	0.382457	+	0.923973i	$0.375078\pi$
$858$	0.320326	0.0109357
$859$	−15.6431	−0.533737	−0.266869	−	0.963733i	$-0.585989\pi$
$859$	−15.6431	−0.533737	−0.266869	+	0.963733i	$0.585989\pi$
$860$	34.8354	1.18788
$861$	−0.777746	−0.0265055
$862$	−37.9195	−1.29154
$863$	−21.8145	−0.742575	−0.371287	−	0.928518i	$-0.621084\pi$
$863$	−21.8145	−0.742575	−0.371287	+	0.928518i	$0.621084\pi$
$864$	−1.27351	−0.0433257
$865$	−61.7698	−2.10024
$866$	23.4555	0.797049
$867$	−0.410524	−0.0139421
$868$	4.03444	0.136938
$869$	−8.57092	−0.290749
$870$	5.96420	0.202205
$871$	−23.2597	−0.788125
$872$	6.83127	0.231336
$873$	4.59088	0.155378
$874$	−10.3703	−0.350782
$875$	9.83998	0.332652
$876$	0.0435403	0.00147109
$877$	8.89786	0.300460	0.150230	−	0.988651i	$-0.451999\pi$
$877$	8.89786	0.300460	0.150230	+	0.988651i	$0.451999\pi$
$878$	−24.1554	−0.815205
$879$	−2.48601	−0.0838511
$880$	2.39615	0.0807742
$881$	37.3344	1.25783	0.628914	−	0.777475i	$-0.283500\pi$
$881$	37.3344	1.25783	0.628914	+	0.777475i	$0.283500\pi$
$882$	15.2202	0.512491
$883$	8.96180	0.301589	0.150794	−	0.988565i	$-0.451817\pi$
$883$	8.96180	0.301589	0.150794	+	0.988565i	$0.451817\pi$
$884$	−6.56956	−0.220958
$885$	−3.86974	−0.130080
$886$	−20.8170	−0.699361
$887$	−2.46751	−0.0828507	−0.0414254	−	0.999142i	$-0.513190\pi$
$887$	−2.46751	−0.0828507	−0.0414254	+	0.999142i	$0.513190\pi$
$888$	−0.695549	−0.0233411
$889$	23.3638	0.783596
$890$	3.36229	0.112704
$891$	−7.60506	−0.254779
$892$	−12.8881	−0.431525
$893$	−38.4899	−1.28802
$894$	−2.93949	−0.0983111
$895$	−17.4469	−0.583186
$896$	1.35942	0.0454152
$897$	−0.512856	−0.0171238
$898$	5.81955	0.194201
$899$	−30.5760	−1.01977
$900$	−6.87062	−0.229021
$901$	−4.44465	−0.148073
$902$	2.36809	0.0788487
$903$	−3.74221	−0.124533
$904$	0.897127	0.0298380
$905$	27.8118	0.924494
$906$	0.173953	0.00577920
$907$	41.5597	1.37997	0.689984	−	0.723824i	$-0.257617\pi$
$907$	41.5597	1.37997	0.689984	+	0.723824i	$0.257617\pi$
$908$	11.2680	0.373941
$909$	15.5459	0.515624
$910$	6.22451	0.206341
$911$	1.67158	0.0553819	0.0276909	−	0.999617i	$-0.491185\pi$
$911$	1.67158	0.0553819	0.0276909	+	0.999617i	$0.491185\pi$
$912$	−1.56486	−0.0518175
$913$	0.449079	0.0148623
$914$	24.9161	0.824150
$915$	4.76525	0.157534
$916$	−15.2104	−0.502565
$917$	−15.9629	−0.527143
$918$	−4.94552	−0.163227
$919$	−30.7864	−1.01555	−0.507775	−	0.861490i	$-0.669532\pi$
$919$	−30.7864	−1.01555	−0.507775	+	0.861490i	$0.669532\pi$
$920$	−3.83634	−0.126481
$921$	−3.02052	−0.0995297
$922$	−12.8578	−0.423448
$923$	24.7899	0.815971
$924$	−0.257407	−0.00846808
$925$	−7.56311	−0.248673
$926$	−2.41369	−0.0793188
$927$	−4.25541	−0.139766
$928$	−10.3027	−0.338204
$929$	3.24694	0.106529	0.0532643	−	0.998580i	$-0.483037\pi$
$929$	3.24694	0.106529	0.0532643	+	0.998580i	$0.483037\pi$
$930$	−1.71801	−0.0563359
$931$	37.6940	1.23537
$932$	25.4046	0.832157
$933$	−2.88067	−0.0943087
$934$	−13.9500	−0.456458
$935$	9.30515	0.304311
$936$	4.99775	0.163357
$937$	61.0607	1.99477	0.997383	−	0.0722986i	$-0.0230335\pi$
$937$	61.0607	1.99477	0.997383	+	0.0722986i	$0.0230335\pi$
$938$	18.6910	0.610283
$939$	−4.41971	−0.144232
$940$	−14.2387	−0.464416
$941$	−30.5917	−0.997262	−0.498631	−	0.866814i	$-0.666164\pi$
$941$	−30.5917	−0.997262	−0.498631	+	0.866814i	$0.666164\pi$
$942$	−4.29034	−0.139787
$943$	−3.79142	−0.123465
$944$	6.68472	0.217569
$945$	4.68578	0.152428
$946$	11.3943	0.370461
$947$	−1.74903	−0.0568357	−0.0284179	−	0.999596i	$-0.509047\pi$
$947$	−1.74903	−0.0568357	−0.0284179	+	0.999596i	$0.509047\pi$
$948$	2.07068	0.0672525
$949$	−0.344384	−0.0111792
$950$	−17.0156	−0.552058
$951$	0.779829	0.0252877
$952$	5.27916	0.171099
$953$	5.39694	0.174824	0.0874120	−	0.996172i	$-0.472140\pi$
$953$	5.39694	0.174824	0.0874120	+	0.996172i	$0.472140\pi$
$954$	3.38124	0.109472
$955$	−39.3644	−1.27380
$956$	−8.43954	−0.272954
$957$	1.95083	0.0630613
$958$	6.62847	0.214156
$959$	24.1296	0.779185
$960$	−0.578894	−0.0186837
$961$	−22.1924	−0.715885
$962$	5.50147	0.177375
$963$	−6.94706	−0.223866
$964$	−9.12941	−0.294038
$965$	−34.8210	−1.12093
$966$	0.412121	0.0132598
$967$	−35.2329	−1.13301	−0.566506	−	0.824057i	$-0.691705\pi$
$967$	−35.2329	−1.13301	−0.566506	+	0.824057i	$0.691705\pi$
$968$	−10.2162	−0.328363
$969$	−6.07692	−0.195219
$970$	4.20602	0.135047
$971$	14.4708	0.464389	0.232194	−	0.972669i	$-0.425409\pi$
$971$	14.4708	0.464389	0.232194	+	0.972669i	$0.425409\pi$
$972$	5.65786	0.181476
$973$	−14.9641	−0.479728
$974$	−18.1364	−0.581127
$975$	−0.841491	−0.0269493
$976$	−8.23165	−0.263489
$977$	9.74281	0.311700	0.155850	−	0.987781i	$-0.450188\pi$
$977$	9.74281	0.311700	0.155850	+	0.987781i	$0.450188\pi$
$978$	−0.657024	−0.0210093
$979$	1.09977	0.0351488
$980$	13.9443	0.445434
$981$	−20.1813	−0.644340
$982$	30.7389	0.980919
$983$	−21.1831	−0.675636	−0.337818	−	0.941211i	$-0.609689\pi$
$983$	−21.1831	−0.675636	−0.337818	+	0.941211i	$0.609689\pi$
$984$	−0.572114	−0.0182383
$985$	−59.1897	−1.88594
$986$	−40.0095	−1.27416
$987$	1.52960	0.0486878
$988$	12.3773	0.393774
$989$	−18.2428	−0.580088
$990$	−7.07884	−0.224980
$991$	−17.8802	−0.567984	−0.283992	−	0.958827i	$-0.591659\pi$
$991$	−17.8802	−0.567984	−0.283992	+	0.958827i	$0.591659\pi$
$992$	2.96775	0.0942263
$993$	−1.44207	−0.0457628
$994$	−19.9207	−0.631846
$995$	49.4116	1.56645
$996$	−0.108494	−0.00343778
$997$	−18.2877	−0.579176	−0.289588	−	0.957151i	$-0.593518\pi$
$997$	−18.2877	−0.579176	−0.289588	+	0.957151i	$0.593518\pi$
$998$	−25.8213	−0.817359
$999$	4.14147	0.131030

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.f.1.8	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.f.1.8	✓	11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.213882 q^{3} +1.00000 q^{4} -2.70660 q^{5} +0.213882 q^{6} +1.35942 q^{7} +1.00000 q^{8} -2.95425 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.213882 q^{3} +1.00000 q^{4} -2.70660 q^{5} +0.213882 q^{6} +1.35942 q^{7} +1.00000 q^{8} -2.95425 q^{9} -2.70660 q^{10} -0.885300 q^{11} +0.213882 q^{12} -1.69171 q^{13} +1.35942 q^{14} -0.578894 q^{15} +1.00000 q^{16} +3.88338 q^{17} -2.95425 q^{18} -7.31642 q^{19} -2.70660 q^{20} +0.290757 q^{21} -0.885300 q^{22} +1.41741 q^{23} +0.213882 q^{24} +2.32567 q^{25} -1.69171 q^{26} -1.27351 q^{27} +1.35942 q^{28} -10.3027 q^{29} -0.578894 q^{30} +2.96775 q^{31} +1.00000 q^{32} -0.189350 q^{33} +3.88338 q^{34} -3.67942 q^{35} -2.95425 q^{36} -3.25201 q^{37} -7.31642 q^{38} -0.361828 q^{39} -2.70660 q^{40} -2.67490 q^{41} +0.290757 q^{42} -12.8706 q^{43} -0.885300 q^{44} +7.99598 q^{45} +1.41741 q^{46} +5.26075 q^{47} +0.213882 q^{48} -5.15196 q^{49} +2.32567 q^{50} +0.830586 q^{51} -1.69171 q^{52} -1.14453 q^{53} -1.27351 q^{54} +2.39615 q^{55} +1.35942 q^{56} -1.56486 q^{57} -10.3027 q^{58} +6.68472 q^{59} -0.578894 q^{60} -8.23165 q^{61} +2.96775 q^{62} -4.01609 q^{63} +1.00000 q^{64} +4.57878 q^{65} -0.189350 q^{66} +13.7492 q^{67} +3.88338 q^{68} +0.303158 q^{69} -3.67942 q^{70} -14.6538 q^{71} -2.95425 q^{72} +0.203571 q^{73} -3.25201 q^{74} +0.497420 q^{75} -7.31642 q^{76} -1.20350 q^{77} -0.361828 q^{78} +9.68138 q^{79} -2.70660 q^{80} +8.59038 q^{81} -2.67490 q^{82} -0.507262 q^{83} +0.290757 q^{84} -10.5107 q^{85} -12.8706 q^{86} -2.20358 q^{87} -0.885300 q^{88} -1.24226 q^{89} +7.99598 q^{90} -2.29976 q^{91} +1.41741 q^{92} +0.634751 q^{93} +5.26075 q^{94} +19.8026 q^{95} +0.213882 q^{96} -1.55399 q^{97} -5.15196 q^{98} +2.61540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 12 q^{5} - 11 q^{6} - 9 q^{7} + 11 q^{8} + 18 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 12 * q^5 - 11 * q^6 - 9 * q^7 + 11 * q^8 + 18 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 12 q^{5} - 11 q^{6} - 9 q^{7} + 11 q^{8} + 18 q^{9} - 12 q^{10} - 7 q^{11} - 11 q^{12} - 21 q^{13} - 9 q^{14} - 3 q^{15} + 11 q^{16} - 16 q^{17} + 18 q^{18} - 22 q^{19} - 12 q^{20} - q^{21} - 7 q^{22} - 2 q^{23} - 11 q^{24} + 19 q^{25} - 21 q^{26} - 44 q^{27} - 9 q^{28} + 4 q^{29} - 3 q^{30} - 28 q^{31} + 11 q^{32} - 13 q^{33} - 16 q^{34} - 11 q^{35} + 18 q^{36} - 22 q^{37} - 22 q^{38} + 9 q^{39} - 12 q^{40} - 5 q^{41} - q^{42} - 7 q^{43} - 7 q^{44} - 23 q^{45} - 2 q^{46} - 31 q^{47} - 11 q^{48} - 2 q^{49} + 19 q^{50} - 6 q^{51} - 21 q^{52} - 17 q^{53} - 44 q^{54} - 18 q^{55} - 9 q^{56} + 7 q^{57} + 4 q^{58} - 18 q^{59} - 3 q^{60} - 18 q^{61} - 28 q^{62} - 27 q^{63} + 11 q^{64} + 22 q^{65} - 13 q^{66} - 11 q^{67} - 16 q^{68} + 9 q^{69} - 11 q^{70} - 16 q^{71} + 18 q^{72} - 33 q^{73} - 22 q^{74} - 21 q^{75} - 22 q^{76} + 9 q^{78} + 9 q^{79} - 12 q^{80} + 71 q^{81} - 5 q^{82} - 18 q^{83} - q^{84} - 8 q^{85} - 7 q^{86} - 17 q^{87} - 7 q^{88} - 23 q^{90} - 22 q^{91} - 2 q^{92} + 8 q^{93} - 31 q^{94} - 23 q^{95} - 11 q^{96} - 66 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 12 * q^5 - 11 * q^6 - 9 * q^7 + 11 * q^8 + 18 * q^9 - 12 * q^10 - 7 * q^11 - 11 * q^12 - 21 * q^13 - 9 * q^14 - 3 * q^15 + 11 * q^16 - 16 * q^17 + 18 * q^18 - 22 * q^19 - 12 * q^20 - q^21 - 7 * q^22 - 2 * q^23 - 11 * q^24 + 19 * q^25 - 21 * q^26 - 44 * q^27 - 9 * q^28 + 4 * q^29 - 3 * q^30 - 28 * q^31 + 11 * q^32 - 13 * q^33 - 16 * q^34 - 11 * q^35 + 18 * q^36 - 22 * q^37 - 22 * q^38 + 9 * q^39 - 12 * q^40 - 5 * q^41 - q^42 - 7 * q^43 - 7 * q^44 - 23 * q^45 - 2 * q^46 - 31 * q^47 - 11 * q^48 - 2 * q^49 + 19 * q^50 - 6 * q^51 - 21 * q^52 - 17 * q^53 - 44 * q^54 - 18 * q^55 - 9 * q^56 + 7 * q^57 + 4 * q^58 - 18 * q^59 - 3 * q^60 - 18 * q^61 - 28 * q^62 - 27 * q^63 + 11 * q^64 + 22 * q^65 - 13 * q^66 - 11 * q^67 - 16 * q^68 + 9 * q^69 - 11 * q^70 - 16 * q^71 + 18 * q^72 - 33 * q^73 - 22 * q^74 - 21 * q^75 - 22 * q^76 + 9 * q^78 + 9 * q^79 - 12 * q^80 + 71 * q^81 - 5 * q^82 - 18 * q^83 - q^84 - 8 * q^85 - 7 * q^86 - 17 * q^87 - 7 * q^88 - 23 * q^90 - 22 * q^91 - 2 * q^92 + 8 * q^93 - 31 * q^94 - 23 * q^95 - 11 * q^96 - 66 * q^97 - 2 * q^98 - 5 * q^99

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