LMFDB - Embedded newform 8039.2.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8039,2,Mod(1,8039)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8039, 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("8039.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8039 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8039.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1917381849$
Analytic rank:	$1$
Dimension:	$279$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8039.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68146 q^{2} +1.09614 q^{3} +5.19020 q^{4} +0.161648 q^{5} -2.93925 q^{6} +3.85315 q^{7} -8.55439 q^{8} -1.79847 q^{9} +O(q^{10})$	\(q-2.68146 q^{2} +1.09614 q^{3} +5.19020 q^{4} +0.161648 q^{5} -2.93925 q^{6} +3.85315 q^{7} -8.55439 q^{8} -1.79847 q^{9} -0.433452 q^{10} +0.743188 q^{11} +5.68920 q^{12} -6.26789 q^{13} -10.3321 q^{14} +0.177189 q^{15} +12.5578 q^{16} +1.21365 q^{17} +4.82253 q^{18} -0.480110 q^{19} +0.838987 q^{20} +4.22360 q^{21} -1.99283 q^{22} +4.75029 q^{23} -9.37682 q^{24} -4.97387 q^{25} +16.8071 q^{26} -5.25981 q^{27} +19.9986 q^{28} +0.357335 q^{29} -0.475125 q^{30} +3.34324 q^{31} -16.5644 q^{32} +0.814639 q^{33} -3.25435 q^{34} +0.622855 q^{35} -9.33445 q^{36} +2.31848 q^{37} +1.28739 q^{38} -6.87049 q^{39} -1.38280 q^{40} -9.33898 q^{41} -11.3254 q^{42} -12.0249 q^{43} +3.85730 q^{44} -0.290720 q^{45} -12.7377 q^{46} +0.626563 q^{47} +13.7651 q^{48} +7.84678 q^{49} +13.3372 q^{50} +1.33033 q^{51} -32.5316 q^{52} +8.16777 q^{53} +14.1039 q^{54} +0.120135 q^{55} -32.9614 q^{56} -0.526268 q^{57} -0.958179 q^{58} +3.84106 q^{59} +0.919648 q^{60} +0.991493 q^{61} -8.96476 q^{62} -6.92979 q^{63} +19.3012 q^{64} -1.01319 q^{65} -2.18442 q^{66} +12.6338 q^{67} +6.29909 q^{68} +5.20698 q^{69} -1.67016 q^{70} +10.1020 q^{71} +15.3849 q^{72} -12.9432 q^{73} -6.21691 q^{74} -5.45206 q^{75} -2.49187 q^{76} +2.86362 q^{77} +18.4229 q^{78} -7.90969 q^{79} +2.02995 q^{80} -0.370066 q^{81} +25.0421 q^{82} +10.7962 q^{83} +21.9213 q^{84} +0.196184 q^{85} +32.2442 q^{86} +0.391690 q^{87} -6.35752 q^{88} +3.31801 q^{89} +0.779553 q^{90} -24.1511 q^{91} +24.6549 q^{92} +3.66467 q^{93} -1.68010 q^{94} -0.0776089 q^{95} -18.1570 q^{96} -2.95619 q^{97} -21.0408 q^{98} -1.33660 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9}+O(q^{10}) $ 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9} - 42 q^{10} - 53 q^{11} - 36 q^{12} - 75 q^{13} - 31 q^{14} - 60 q^{15} + 127 q^{16} - 55 q^{17} - 57 q^{18} - 113 q^{19} - 43 q^{20} - 103 q^{21} - 73 q^{22} - 30 q^{23} - 106 q^{24} + 75 q^{25} - 42 q^{26} - 45 q^{27} - 146 q^{28} - 92 q^{29} - 76 q^{30} - 84 q^{31} - 71 q^{32} - 117 q^{33} - 106 q^{34} - 49 q^{35} + 67 q^{36} - 123 q^{37} - 21 q^{38} - 92 q^{39} - 97 q^{40} - 116 q^{41} - 19 q^{42} - 126 q^{43} - 131 q^{44} - 85 q^{45} - 183 q^{46} - 42 q^{47} - 47 q^{48} - 22 q^{49} - 64 q^{50} - 90 q^{51} - 158 q^{52} - 60 q^{53} - 117 q^{54} - 99 q^{55} - 65 q^{56} - 182 q^{57} - 93 q^{58} - 58 q^{59} - 141 q^{60} - 217 q^{61} - 16 q^{62} - 141 q^{63} - 47 q^{64} - 197 q^{65} - 53 q^{66} - 147 q^{67} - 90 q^{68} - 103 q^{69} - 118 q^{70} - 78 q^{71} - 135 q^{72} - 282 q^{73} - 98 q^{74} - 53 q^{75} - 296 q^{76} - 53 q^{77} - 27 q^{78} - 153 q^{79} - 52 q^{80} - 89 q^{81} - 81 q^{82} - 54 q^{83} - 164 q^{84} - 303 q^{85} - 82 q^{86} - 29 q^{87} - 203 q^{88} - 185 q^{89} - 56 q^{90} - 163 q^{91} - 66 q^{92} - 156 q^{93} - 134 q^{94} - 69 q^{95} - 189 q^{96} - 212 q^{97} - 13 q^{98} - 181 q^{99}+O(q^{100}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9 - 42 * q^10 - 53 * q^11 - 36 * q^12 - 75 * q^13 - 31 * q^14 - 60 * q^15 + 127 * q^16 - 55 * q^17 - 57 * q^18 - 113 * q^19 - 43 * q^20 - 103 * q^21 - 73 * q^22 - 30 * q^23 - 106 * q^24 + 75 * q^25 - 42 * q^26 - 45 * q^27 - 146 * q^28 - 92 * q^29 - 76 * q^30 - 84 * q^31 - 71 * q^32 - 117 * q^33 - 106 * q^34 - 49 * q^35 + 67 * q^36 - 123 * q^37 - 21 * q^38 - 92 * q^39 - 97 * q^40 - 116 * q^41 - 19 * q^42 - 126 * q^43 - 131 * q^44 - 85 * q^45 - 183 * q^46 - 42 * q^47 - 47 * q^48 - 22 * q^49 - 64 * q^50 - 90 * q^51 - 158 * q^52 - 60 * q^53 - 117 * q^54 - 99 * q^55 - 65 * q^56 - 182 * q^57 - 93 * q^58 - 58 * q^59 - 141 * q^60 - 217 * q^61 - 16 * q^62 - 141 * q^63 - 47 * q^64 - 197 * q^65 - 53 * q^66 - 147 * q^67 - 90 * q^68 - 103 * q^69 - 118 * q^70 - 78 * q^71 - 135 * q^72 - 282 * q^73 - 98 * q^74 - 53 * q^75 - 296 * q^76 - 53 * q^77 - 27 * q^78 - 153 * q^79 - 52 * q^80 - 89 * q^81 - 81 * q^82 - 54 * q^83 - 164 * q^84 - 303 * q^85 - 82 * q^86 - 29 * q^87 - 203 * q^88 - 185 * q^89 - 56 * q^90 - 163 * q^91 - 66 * q^92 - 156 * q^93 - 134 * q^94 - 69 * q^95 - 189 * q^96 - 212 * q^97 - 13 * q^98 - 181 * 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 $

$2$	−2.68146	−1.89608	−0.948038	−	0.318158i	$-0.896936\pi$
$2$	−2.68146	−1.89608	−0.948038	+	0.318158i	$0.896936\pi$
$3$	1.09614	0.632857	0.316429	−	0.948616i	$-0.397516\pi$
$3$	1.09614	0.632857	0.316429	+	0.948616i	$0.397516\pi$
$4$	5.19020	2.59510
$5$	0.161648	0.0722913	0.0361456	−	0.999347i	$-0.488492\pi$
$5$	0.161648	0.0722913	0.0361456	+	0.999347i	$0.488492\pi$
$6$	−2.93925	−1.19995
$7$	3.85315	1.45635	0.728177	−	0.685389i	$-0.240368\pi$
$7$	3.85315	1.45635	0.728177	+	0.685389i	$0.240368\pi$
$8$	−8.55439	−3.02443
$9$	−1.79847	−0.599491
$10$	−0.433452	−0.137070
$11$	0.743188	0.224080	0.112040	−	0.993704i	$-0.464262\pi$
$11$	0.743188	0.224080	0.112040	+	0.993704i	$0.464262\pi$
$12$	5.68920	1.64233
$13$	−6.26789	−1.73840	−0.869200	−	0.494461i	$-0.835366\pi$
$13$	−6.26789	−1.73840	−0.869200	+	0.494461i	$0.835366\pi$
$14$	−10.3321	−2.76136
$15$	0.177189	0.0457501
$16$	12.5578	3.13945
$17$	1.21365	0.294353	0.147177	−	0.989110i	$-0.452981\pi$
$17$	1.21365	0.294353	0.147177	+	0.989110i	$0.452981\pi$
$18$	4.82253	1.13668
$19$	−0.480110	−0.110145	−0.0550724	−	0.998482i	$-0.517539\pi$
$19$	−0.480110	−0.110145	−0.0550724	+	0.998482i	$0.517539\pi$
$20$	0.838987	0.187603
$21$	4.22360	0.921665
$22$	−1.99283	−0.424872
$23$	4.75029	0.990503	0.495251	−	0.868750i	$-0.335076\pi$
$23$	4.75029	0.990503	0.495251	+	0.868750i	$0.335076\pi$
$24$	−9.37682	−1.91404
$25$	−4.97387	−0.994774
$26$	16.8071	3.29614
$27$	−5.25981	−1.01225
$28$	19.9986	3.77939
$29$	0.357335	0.0663555	0.0331778	−	0.999449i	$-0.489437\pi$
$29$	0.357335	0.0663555	0.0331778	+	0.999449i	$0.489437\pi$
$30$	−0.475125	−0.0867456
$31$	3.34324	0.600464	0.300232	−	0.953866i	$-0.402936\pi$
$31$	3.34324	0.600464	0.300232	+	0.953866i	$0.402936\pi$
$32$	−16.5644	−2.92821
$33$	0.814639	0.141810
$34$	−3.25435	−0.558116
$35$	0.622855	0.105282
$36$	−9.33445	−1.55574
$37$	2.31848	0.381156	0.190578	−	0.981672i	$-0.438964\pi$
$37$	2.31848	0.381156	0.190578	+	0.981672i	$0.438964\pi$
$38$	1.28739	0.208843
$39$	−6.87049	−1.10016
$40$	−1.38280	−0.218640
$41$	−9.33898	−1.45850	−0.729252	−	0.684245i	$-0.760132\pi$
$41$	−9.33898	−1.45850	−0.729252	+	0.684245i	$0.760132\pi$
$42$	−11.3254	−1.74755
$43$	−12.0249	−1.83378	−0.916888	−	0.399144i	$-0.869307\pi$
$43$	−12.0249	−1.83378	−0.916888	+	0.399144i	$0.869307\pi$
$44$	3.85730	0.581510
$45$	−0.290720	−0.0433380
$46$	−12.7377	−1.87807
$47$	0.626563	0.0913936	0.0456968	−	0.998955i	$-0.485449\pi$
$47$	0.626563	0.0913936	0.0456968	+	0.998955i	$0.485449\pi$
$48$	13.7651	1.98683
$49$	7.84678	1.12097
$50$	13.3372	1.88617
$51$	1.33033	0.186284
$52$	−32.5316	−4.51133
$53$	8.16777	1.12193	0.560965	−	0.827840i	$-0.310430\pi$
$53$	8.16777	1.12193	0.560965	+	0.827840i	$0.310430\pi$
$54$	14.1039	1.91930
$55$	0.120135	0.0161990
$56$	−32.9614	−4.40465
$57$	−0.526268	−0.0697059
$58$	−0.958179	−0.125815
$59$	3.84106	0.500063	0.250032	−	0.968238i	$-0.419559\pi$
$59$	3.84106	0.500063	0.250032	+	0.968238i	$0.419559\pi$
$60$	0.919648	0.118726
$61$	0.991493	0.126948	0.0634738	−	0.997984i	$-0.479782\pi$
$61$	0.991493	0.126948	0.0634738	+	0.997984i	$0.479782\pi$
$62$	−8.96476	−1.13853
$63$	−6.92979	−0.873072
$64$	19.3012	2.41265
$65$	−1.01319	−0.125671
$66$	−2.18442	−0.268883
$67$	12.6338	1.54346	0.771730	−	0.635950i	$-0.219392\pi$
$67$	12.6338	1.54346	0.771730	+	0.635950i	$0.219392\pi$
$68$	6.29909	0.763877
$69$	5.20698	0.626847
$70$	−1.67016	−0.199622
$71$	10.1020	1.19888	0.599442	−	0.800418i	$-0.295389\pi$
$71$	10.1020	1.19888	0.599442	+	0.800418i	$0.295389\pi$
$72$	15.3849	1.81312
$73$	−12.9432	−1.51488	−0.757442	−	0.652902i	$-0.773551\pi$
$73$	−12.9432	−1.51488	−0.757442	+	0.652902i	$0.773551\pi$
$74$	−6.21691	−0.722701
$75$	−5.45206	−0.629550
$76$	−2.49187	−0.285837
$77$	2.86362	0.326339
$78$	18.4229	2.08599
$79$	−7.90969	−0.889909	−0.444955	−	0.895553i	$-0.646780\pi$
$79$	−7.90969	−0.889909	−0.444955	+	0.895553i	$0.646780\pi$
$80$	2.02995	0.226955
$81$	−0.370066	−0.0411185
$82$	25.0421	2.76543
$83$	10.7962	1.18503	0.592517	−	0.805558i	$-0.298134\pi$
$83$	10.7962	1.18503	0.592517	+	0.805558i	$0.298134\pi$
$84$	21.9213	2.39181
$85$	0.196184	0.0212792
$86$	32.2442	3.47698
$87$	0.391690	0.0419936
$88$	−6.35752	−0.677714
$89$	3.31801	0.351709	0.175854	−	0.984416i	$-0.443731\pi$
$89$	3.31801	0.351709	0.175854	+	0.984416i	$0.443731\pi$
$90$	0.779553	0.0821721
$91$	−24.1511	−2.53173
$92$	24.6549	2.57046
$93$	3.66467	0.380008
$94$	−1.68010	−0.173289
$95$	−0.0776089	−0.00796250
$96$	−18.1570	−1.85314
$97$	−2.95619	−0.300156	−0.150078	−	0.988674i	$-0.547952\pi$
$97$	−2.95619	−0.300156	−0.150078	+	0.988674i	$0.547952\pi$
$98$	−21.0408	−2.12544
$99$	−1.33660	−0.134334
$100$	−25.8154	−2.58154
$101$	5.27244	0.524627	0.262314	−	0.964983i	$-0.415514\pi$
$101$	5.27244	0.524627	0.262314	+	0.964983i	$0.415514\pi$
$102$	−3.56722	−0.353208
$103$	2.52003	0.248306	0.124153	−	0.992263i	$-0.460379\pi$
$103$	2.52003	0.248306	0.124153	+	0.992263i	$0.460379\pi$
$104$	53.6180	5.25768
$105$	0.682737	0.0666283
$106$	−21.9015	−2.12726
$107$	4.58990	0.443722	0.221861	−	0.975078i	$-0.428787\pi$
$107$	4.58990	0.443722	0.221861	+	0.975078i	$0.428787\pi$
$108$	−27.2995	−2.62689
$109$	−6.40808	−0.613783	−0.306892	−	0.951744i	$-0.599289\pi$
$109$	−6.40808	−0.613783	−0.306892	+	0.951744i	$0.599289\pi$
$110$	−0.322137	−0.0307145
$111$	2.54138	0.241218
$112$	48.3871	4.57216
$113$	−1.76646	−0.166174	−0.0830872	−	0.996542i	$-0.526478\pi$
$113$	−1.76646	−0.166174	−0.0830872	+	0.996542i	$0.526478\pi$
$114$	1.41116	0.132168
$115$	0.767875	0.0716047
$116$	1.85464	0.172199
$117$	11.2726	1.04216
$118$	−10.2996	−0.948158
$119$	4.67638	0.428683
$120$	−1.51575	−0.138368
$121$	−10.4477	−0.949788
$122$	−2.65864	−0.240702
$123$	−10.2368	−0.923025
$124$	17.3521	1.55827
$125$	−1.61226	−0.144205
$126$	18.5819	1.65541
$127$	−13.8739	−1.23111	−0.615553	−	0.788096i	$-0.711067\pi$
$127$	−13.8739	−1.23111	−0.615553	+	0.788096i	$0.711067\pi$
$128$	−18.6263	−1.64635
$129$	−13.1810	−1.16052
$130$	2.71683	0.238282
$131$	15.4449	1.34943	0.674714	−	0.738079i	$-0.264267\pi$
$131$	15.4449	1.34943	0.674714	+	0.738079i	$0.264267\pi$
$132$	4.22814	0.368013
$133$	−1.84994	−0.160410
$134$	−33.8769	−2.92652
$135$	−0.850238	−0.0731768
$136$	−10.3820	−0.890252
$137$	−14.9525	−1.27748	−0.638741	−	0.769422i	$-0.720544\pi$
$137$	−14.9525	−1.27748	−0.638741	+	0.769422i	$0.720544\pi$
$138$	−13.9623	−1.18855
$139$	−12.0589	−1.02283	−0.511413	−	0.859335i	$-0.670878\pi$
$139$	−12.0589	−1.02283	−0.511413	+	0.859335i	$0.670878\pi$
$140$	3.23274	0.273217
$141$	0.686801	0.0578391
$142$	−27.0880	−2.27317
$143$	−4.65822	−0.389540
$144$	−22.5849	−1.88208
$145$	0.0577626	0.00479693
$146$	34.7066	2.87234
$147$	8.60118	0.709413
$148$	12.0334	0.989139
$149$	−18.7800	−1.53852	−0.769258	−	0.638939i	$-0.779374\pi$
$149$	−18.7800	−1.53852	−0.769258	+	0.638939i	$0.779374\pi$
$150$	14.6195	1.19367
$151$	−8.62210	−0.701657	−0.350828	−	0.936440i	$-0.614100\pi$
$151$	−8.62210	−0.701657	−0.350828	+	0.936440i	$0.614100\pi$
$152$	4.10705	0.333126
$153$	−2.18272	−0.176462
$154$	−7.67866	−0.618764
$155$	0.540429	0.0434083
$156$	−35.6593	−2.85503
$157$	11.0705	0.883521	0.441760	−	0.897133i	$-0.354354\pi$
$157$	11.0705	0.883521	0.441760	+	0.897133i	$0.354354\pi$
$158$	21.2095	1.68734
$159$	8.95303	0.710021
$160$	−2.67761	−0.211684
$161$	18.3036	1.44252
$162$	0.992316	0.0779637
$163$	4.83198	0.378470	0.189235	−	0.981932i	$-0.439399\pi$
$163$	4.83198	0.378470	0.189235	+	0.981932i	$0.439399\pi$
$164$	−48.4712	−3.78497
$165$	0.131685	0.0102517
$166$	−28.9495	−2.24691
$167$	−6.55521	−0.507258	−0.253629	−	0.967302i	$-0.581624\pi$
$167$	−6.55521	−0.507258	−0.253629	+	0.967302i	$0.581624\pi$
$168$	−36.1303	−2.78751
$169$	26.2865	2.02204
$170$	−0.526059	−0.0403469
$171$	0.863465	0.0660308
$172$	−62.4116	−4.75884
$173$	3.63345	0.276246	0.138123	−	0.990415i	$-0.455893\pi$
$173$	3.63345	0.276246	0.138123	+	0.990415i	$0.455893\pi$
$174$	−1.05030	−0.0796230
$175$	−19.1651	−1.44874
$176$	9.33282	0.703487
$177$	4.21034	0.316469
$178$	−8.89711	−0.666866
$179$	−14.4445	−1.07964	−0.539818	−	0.841782i	$-0.681507\pi$
$179$	−14.4445	−1.07964	−0.539818	+	0.841782i	$0.681507\pi$
$180$	−1.50890	−0.112467
$181$	−13.3901	−0.995280	−0.497640	−	0.867384i	$-0.665800\pi$
$181$	−13.3901	−0.995280	−0.497640	+	0.867384i	$0.665800\pi$
$182$	64.7602	4.80034
$183$	1.08682	0.0803398
$184$	−40.6358	−2.99571
$185$	0.374778	0.0275543
$186$	−9.82664	−0.720524
$187$	0.901970	0.0659586
$188$	3.25199	0.237176
$189$	−20.2668	−1.47419
$190$	0.208105	0.0150975
$191$	−14.6868	−1.06270	−0.531351	−	0.847152i	$-0.678315\pi$
$191$	−14.6868	−1.06270	−0.531351	+	0.847152i	$0.678315\pi$
$192$	21.1568	1.52686
$193$	−3.54872	−0.255442	−0.127721	−	0.991810i	$-0.540766\pi$
$193$	−3.54872	−0.255442	−0.127721	+	0.991810i	$0.540766\pi$
$194$	7.92690	0.569118
$195$	−1.11060	−0.0795319
$196$	40.7264	2.90903
$197$	−23.0761	−1.64410	−0.822052	−	0.569413i	$-0.807171\pi$
$197$	−23.0761	−1.64410	−0.822052	+	0.569413i	$0.807171\pi$
$198$	3.58405	0.254707
$199$	−13.1685	−0.933493	−0.466746	−	0.884391i	$-0.654574\pi$
$199$	−13.1685	−0.933493	−0.466746	+	0.884391i	$0.654574\pi$
$200$	42.5484	3.00863
$201$	13.8484	0.976791
$202$	−14.1378	−0.994733
$203$	1.37687	0.0966372
$204$	6.90469	0.483425
$205$	−1.50963	−0.105437
$206$	−6.75735	−0.470807
$207$	−8.54327	−0.593798
$208$	−78.7110	−5.45762
$209$	−0.356812	−0.0246812
$210$	−1.83073	−0.126332
$211$	3.55146	0.244492	0.122246	−	0.992500i	$-0.460990\pi$
$211$	3.55146	0.244492	0.122246	+	0.992500i	$0.460990\pi$
$212$	42.3924	2.91152
$213$	11.0732	0.758722
$214$	−12.3076	−0.841330
$215$	−1.94380	−0.132566
$216$	44.9944	3.06148
$217$	12.8820	0.874489
$218$	17.1830	1.16378
$219$	−14.1876	−0.958706
$220$	0.623525	0.0420381
$221$	−7.60702	−0.511704
$222$	−6.81461	−0.457367
$223$	8.68925	0.581875	0.290938	−	0.956742i	$-0.406033\pi$
$223$	8.68925	0.581875	0.290938	+	0.956742i	$0.406033\pi$
$224$	−63.8253	−4.26450
$225$	8.94538	0.596359
$226$	4.73668	0.315079
$227$	−20.6803	−1.37260	−0.686300	−	0.727318i	$-0.740766\pi$
$227$	−20.6803	−1.37260	−0.686300	+	0.727318i	$0.740766\pi$
$228$	−2.73144	−0.180894
$229$	−26.0639	−1.72235	−0.861174	−	0.508310i	$-0.830270\pi$
$229$	−26.0639	−1.72235	−0.861174	+	0.508310i	$0.830270\pi$
$230$	−2.05902	−0.135768
$231$	3.13893	0.206526
$232$	−3.05679	−0.200688
$233$	1.36501	0.0894245	0.0447122	−	0.999000i	$-0.485763\pi$
$233$	1.36501	0.0894245	0.0447122	+	0.999000i	$0.485763\pi$
$234$	−30.2271	−1.97601
$235$	0.101283	0.00660696
$236$	19.9359	1.29772
$237$	−8.67013	−0.563186
$238$	−12.5395	−0.812815
$239$	−7.38467	−0.477675	−0.238837	−	0.971060i	$-0.576766\pi$
$239$	−7.38467	−0.477675	−0.238837	+	0.971060i	$0.576766\pi$
$240$	2.22511	0.143630
$241$	4.89543	0.315342	0.157671	−	0.987492i	$-0.449601\pi$
$241$	4.89543	0.315342	0.157671	+	0.987492i	$0.449601\pi$
$242$	28.0150	1.80087
$243$	15.3738	0.986228
$244$	5.14605	0.329442
$245$	1.26842	0.0810362
$246$	27.4496	1.75013
$247$	3.00928	0.191476
$248$	−28.5994	−1.81606
$249$	11.8341	0.749958
$250$	4.32320	0.273423
$251$	3.05562	0.192869	0.0964345	−	0.995339i	$-0.469256\pi$
$251$	3.05562	0.192869	0.0964345	+	0.995339i	$0.469256\pi$
$252$	−35.9670	−2.26571
$253$	3.53036	0.221952
$254$	37.2021	2.33427
$255$	0.215046	0.0134667
$256$	11.3434	0.708963
$257$	−8.44351	−0.526692	−0.263346	−	0.964702i	$-0.584826\pi$
$257$	−8.44351	−0.526692	−0.263346	+	0.964702i	$0.584826\pi$
$258$	35.3442	2.20043
$259$	8.93346	0.555098
$260$	−5.25868	−0.326129
$261$	−0.642659	−0.0397796
$262$	−41.4149	−2.55862
$263$	−0.409133	−0.0252282	−0.0126141	−	0.999920i	$-0.504015\pi$
$263$	−0.409133	−0.0252282	−0.0126141	+	0.999920i	$0.504015\pi$
$264$	−6.96874	−0.428896
$265$	1.32031	0.0811057
$266$	4.96052	0.304149
$267$	3.63701	0.222581
$268$	65.5718	4.00544
$269$	−12.6407	−0.770718	−0.385359	−	0.922767i	$-0.625922\pi$
$269$	−12.6407	−0.770718	−0.385359	+	0.922767i	$0.625922\pi$
$270$	2.27988	0.138749
$271$	9.28927	0.564283	0.282141	−	0.959373i	$-0.408955\pi$
$271$	9.28927	0.564283	0.282141	+	0.959373i	$0.408955\pi$
$272$	15.2408	0.924108
$273$	−26.4731	−1.60222
$274$	40.0946	2.42220
$275$	−3.69652	−0.222909
$276$	27.0253	1.62673
$277$	18.4872	1.11079	0.555395	−	0.831586i	$-0.312567\pi$
$277$	18.4872	1.11079	0.555395	+	0.831586i	$0.312567\pi$
$278$	32.3355	1.93936
$279$	−6.01274	−0.359973
$280$	−5.32814	−0.318418
$281$	26.1492	1.55993	0.779964	−	0.625824i	$-0.215237\pi$
$281$	26.1492	1.55993	0.779964	+	0.625824i	$0.215237\pi$
$282$	−1.84163	−0.109667
$283$	−8.55371	−0.508465	−0.254233	−	0.967143i	$-0.581823\pi$
$283$	−8.55371	−0.508465	−0.254233	+	0.967143i	$0.581823\pi$
$284$	52.4313	3.11122
$285$	−0.0850703	−0.00503913
$286$	12.4908	0.738597
$287$	−35.9845	−2.12410
$288$	29.7907	1.75543
$289$	−15.5271	−0.913356
$290$	−0.154888	−0.00909533
$291$	−3.24040	−0.189956
$292$	−67.1778	−3.93128
$293$	3.40826	0.199112	0.0995562	−	0.995032i	$-0.468258\pi$
$293$	3.40826	0.199112	0.0995562	+	0.995032i	$0.468258\pi$
$294$	−23.0637	−1.34510
$295$	0.620900	0.0361502
$296$	−19.8332	−1.15278
$297$	−3.90902	−0.226825
$298$	50.3577	2.91714
$299$	−29.7743	−1.72189
$300$	−28.2973	−1.63375
$301$	−46.3337	−2.67063
$302$	23.1198	1.33039
$303$	5.77934	0.332014
$304$	−6.02913	−0.345794
$305$	0.160273	0.00917720
$306$	5.85286	0.334586
$307$	−26.9880	−1.54029	−0.770143	−	0.637872i	$-0.779815\pi$
$307$	−26.9880	−1.54029	−0.770143	+	0.637872i	$0.779815\pi$
$308$	14.8628	0.846884
$309$	2.76231	0.157142
$310$	−1.44914	−0.0823054
$311$	−34.6228	−1.96328	−0.981639	−	0.190750i	$-0.938908\pi$
$311$	−34.6228	−1.96328	−0.981639	+	0.190750i	$0.938908\pi$
$312$	58.7729	3.32736
$313$	−4.23745	−0.239515	−0.119757	−	0.992803i	$-0.538212\pi$
$313$	−4.23745	−0.239515	−0.119757	+	0.992803i	$0.538212\pi$
$314$	−29.6850	−1.67522
$315$	−1.12019	−0.0631155
$316$	−41.0529	−2.30941
$317$	−14.0003	−0.786334	−0.393167	−	0.919467i	$-0.628621\pi$
$317$	−14.0003	−0.786334	−0.393167	+	0.919467i	$0.628621\pi$
$318$	−24.0072	−1.34625
$319$	0.265567	0.0148689
$320$	3.12000	0.174413
$321$	5.03117	0.280813
$322$	−49.0802	−2.73513
$323$	−0.582685	−0.0324215
$324$	−1.92072	−0.106707
$325$	31.1757	1.72932
$326$	−12.9567	−0.717607
$327$	−7.02416	−0.388437
$328$	79.8893	4.41115
$329$	2.41424	0.133101
$330$	−0.353107	−0.0194379
$331$	15.8203	0.869564	0.434782	−	0.900536i	$-0.356825\pi$
$331$	15.8203	0.869564	0.434782	+	0.900536i	$0.356825\pi$
$332$	56.0343	3.07528
$333$	−4.16973	−0.228500
$334$	17.5775	0.961799
$335$	2.04223	0.111579
$336$	53.0391	2.89352
$337$	7.59703	0.413837	0.206918	−	0.978358i	$-0.433657\pi$
$337$	7.59703	0.413837	0.206918	+	0.978358i	$0.433657\pi$
$338$	−70.4860	−3.83393
$339$	−1.93629	−0.105165
$340$	1.01824	0.0552216
$341$	2.48466	0.134552
$342$	−2.31534	−0.125199
$343$	3.26276	0.176173
$344$	102.866	5.54614
$345$	0.841699	0.0453156
$346$	−9.74294	−0.523784
$347$	−30.2380	−1.62326	−0.811631	−	0.584170i	$-0.801420\pi$
$347$	−30.2380	−1.62326	−0.811631	+	0.584170i	$0.801420\pi$
$348$	2.03295	0.108978
$349$	−16.3574	−0.875591	−0.437795	−	0.899075i	$-0.644241\pi$
$349$	−16.3574	−0.875591	−0.437795	+	0.899075i	$0.644241\pi$
$350$	51.3903	2.74693
$351$	32.9679	1.75970
$352$	−12.3105	−0.656151
$353$	2.67402	0.142324	0.0711618	−	0.997465i	$-0.477329\pi$
$353$	2.67402	0.142324	0.0711618	+	0.997465i	$0.477329\pi$
$354$	−11.2898	−0.600049
$355$	1.63296	0.0866688
$356$	17.2212	0.912720
$357$	5.12597	0.271295
$358$	38.7324	2.04707
$359$	17.1072	0.902882	0.451441	−	0.892301i	$-0.350910\pi$
$359$	17.1072	0.902882	0.451441	+	0.892301i	$0.350910\pi$
$360$	2.48693	0.131073
$361$	−18.7695	−0.987868
$362$	35.9050	1.88713
$363$	−11.4521	−0.601081
$364$	−125.349	−6.57009
$365$	−2.09224	−0.109513
$366$	−2.91425	−0.152330
$367$	−4.48407	−0.234067	−0.117033	−	0.993128i	$-0.537338\pi$
$367$	−4.48407	−0.234067	−0.117033	+	0.993128i	$0.537338\pi$
$368$	59.6532	3.10964
$369$	16.7959	0.874361
$370$	−1.00495	−0.0522450
$371$	31.4717	1.63393
$372$	19.0204	0.986160
$373$	−30.5705	−1.58288	−0.791441	−	0.611246i	$-0.790669\pi$
$373$	−30.5705	−1.58288	−0.791441	+	0.611246i	$0.790669\pi$
$374$	−2.41859	−0.125062
$375$	−1.76726	−0.0912610
$376$	−5.35986	−0.276414
$377$	−2.23974	−0.115352
$378$	54.3446	2.79518
$379$	8.33259	0.428016	0.214008	−	0.976832i	$-0.431348\pi$
$379$	8.33259	0.428016	0.214008	+	0.976832i	$0.431348\pi$
$380$	−0.402806	−0.0206635
$381$	−15.2077	−0.779114
$382$	39.3821	2.01496
$383$	13.8872	0.709602	0.354801	−	0.934942i	$-0.384549\pi$
$383$	13.8872	0.709602	0.354801	+	0.934942i	$0.384549\pi$
$384$	−20.4171	−1.04191
$385$	0.462898	0.0235915
$386$	9.51573	0.484338
$387$	21.6264	1.09933
$388$	−15.3432	−0.778935
$389$	−3.85912	−0.195665	−0.0978327	−	0.995203i	$-0.531191\pi$
$389$	−3.85912	−0.195665	−0.0978327	+	0.995203i	$0.531191\pi$
$390$	2.97803	0.150799
$391$	5.76518	0.291558
$392$	−67.1244	−3.39029
$393$	16.9298	0.853996
$394$	61.8775	3.11734
$395$	−1.27859	−0.0643327
$396$	−6.93725	−0.348610
$397$	−32.6243	−1.63736	−0.818682	−	0.574246i	$-0.805295\pi$
$397$	−32.6243	−1.63736	−0.818682	+	0.574246i	$0.805295\pi$
$398$	35.3108	1.76997
$399$	−2.02779	−0.101517
$400$	−62.4609	−3.12305
$401$	37.2864	1.86199	0.930996	−	0.365028i	$-0.118941\pi$
$401$	37.2864	1.86199	0.930996	+	0.365028i	$0.118941\pi$
$402$	−37.1339	−1.85207
$403$	−20.9551	−1.04385
$404$	27.3650	1.36146
$405$	−0.0598205	−0.00297251
$406$	−3.69201	−0.183231
$407$	1.72307	0.0854093
$408$	−11.3802	−0.563403
$409$	30.0012	1.48347	0.741733	−	0.670695i	$-0.234004\pi$
$409$	30.0012	1.48347	0.741733	+	0.670695i	$0.234004\pi$
$410$	4.04800	0.199917
$411$	−16.3901	−0.808463
$412$	13.0795	0.644379
$413$	14.8002	0.728269
$414$	22.9084	1.12589
$415$	1.74518	0.0856676
$416$	103.824	5.09039
$417$	−13.2183	−0.647303
$418$	0.956775	0.0467974
$419$	−34.2463	−1.67304	−0.836520	−	0.547936i	$-0.815414\pi$
$419$	−34.2463	−1.67304	−0.836520	+	0.547936i	$0.815414\pi$
$420$	3.54354	0.172907
$421$	−1.69426	−0.0825732	−0.0412866	−	0.999147i	$-0.513146\pi$
$421$	−1.69426	−0.0825732	−0.0412866	+	0.999147i	$0.513146\pi$
$422$	−9.52308	−0.463576
$423$	−1.12686	−0.0547897
$424$	−69.8703	−3.39320
$425$	−6.03653	−0.292815
$426$	−29.6923	−1.43859
$427$	3.82037	0.184881
$428$	23.8225	1.15150
$429$	−5.10607	−0.246523
$430$	5.21221	0.251355
$431$	−29.8383	−1.43726	−0.718631	−	0.695392i	$-0.755231\pi$
$431$	−29.8383	−1.43726	−0.718631	+	0.695392i	$0.755231\pi$
$432$	−66.0516	−3.17791
$433$	30.8050	1.48039	0.740197	−	0.672390i	$-0.234732\pi$
$433$	30.8050	1.48039	0.740197	+	0.672390i	$0.234732\pi$
$434$	−34.5426	−1.65810
$435$	0.0633160	0.00303577
$436$	−33.2593	−1.59283
$437$	−2.28066	−0.109099
$438$	38.0433	1.81778
$439$	−20.5914	−0.982773	−0.491387	−	0.870942i	$-0.663510\pi$
$439$	−20.5914	−0.982773	−0.491387	+	0.870942i	$0.663510\pi$
$440$	−1.02768	−0.0489928
$441$	−14.1122	−0.672011
$442$	20.3979	0.970229
$443$	0.487114	0.0231435	0.0115717	−	0.999933i	$-0.496317\pi$
$443$	0.487114	0.0231435	0.0115717	+	0.999933i	$0.496317\pi$
$444$	13.1903	0.625984
$445$	0.536351	0.0254255
$446$	−23.2998	−1.10328
$447$	−20.5855	−0.973661
$448$	74.3703	3.51367
$449$	39.4938	1.86383	0.931915	−	0.362677i	$-0.118137\pi$
$449$	39.4938	1.86383	0.931915	+	0.362677i	$0.118137\pi$
$450$	−23.9866	−1.13074
$451$	−6.94062	−0.326821
$452$	−9.16828	−0.431240
$453$	−9.45104	−0.444049
$454$	55.4534	2.60255
$455$	−3.90399	−0.183022
$456$	4.50190	0.210821
$457$	−1.71125	−0.0800489	−0.0400244	−	0.999199i	$-0.512744\pi$
$457$	−1.71125	−0.0800489	−0.0400244	+	0.999199i	$0.512744\pi$
$458$	69.8891	3.26570
$459$	−6.38356	−0.297959
$460$	3.98543	0.185822
$461$	29.6351	1.38025	0.690123	−	0.723692i	$-0.257556\pi$
$461$	29.6351	1.38025	0.690123	+	0.723692i	$0.257556\pi$
$462$	−8.41690	−0.391589
$463$	15.3016	0.711127	0.355563	−	0.934652i	$-0.384289\pi$
$463$	15.3016	0.711127	0.355563	+	0.934652i	$0.384289\pi$
$464$	4.48735	0.208320
$465$	0.592387	0.0274713
$466$	−3.66020	−0.169556
$467$	−14.7156	−0.680958	−0.340479	−	0.940252i	$-0.610589\pi$
$467$	−14.7156	−0.680958	−0.340479	+	0.940252i	$0.610589\pi$
$468$	58.5073	2.70450
$469$	48.6798	2.24783
$470$	−0.271585	−0.0125273
$471$	12.1348	0.559143
$472$	−32.8579	−1.51241
$473$	−8.93675	−0.410912
$474$	23.2486	1.06784
$475$	2.38800	0.109569
$476$	24.2713	1.11248
$477$	−14.6895	−0.672587
$478$	19.8017	0.905707
$479$	−32.8163	−1.49941	−0.749707	−	0.661770i	$-0.769806\pi$
$479$	−32.8163	−1.49941	−0.749707	+	0.661770i	$0.769806\pi$
$480$	−2.93504	−0.133966
$481$	−14.5320	−0.662602
$482$	−13.1269	−0.597913
$483$	20.0633	0.912912
$484$	−54.2255	−2.46480
$485$	−0.477863	−0.0216986
$486$	−41.2241	−1.86996
$487$	−17.4408	−0.790318	−0.395159	−	0.918613i	$-0.629310\pi$
$487$	−17.4408	−0.790318	−0.395159	+	0.918613i	$0.629310\pi$
$488$	−8.48162	−0.383945
$489$	5.29653	0.239517
$490$	−3.40120	−0.153651
$491$	21.2371	0.958416	0.479208	−	0.877701i	$-0.340924\pi$
$491$	21.2371	0.958416	0.479208	+	0.877701i	$0.340924\pi$
$492$	−53.1313	−2.39534
$493$	0.433680	0.0195320
$494$	−8.06924	−0.363052
$495$	−0.216060	−0.00971116
$496$	41.9838	1.88513
$497$	38.9244	1.74600
$498$	−31.7327	−1.42198
$499$	2.96963	0.132939	0.0664695	−	0.997788i	$-0.478826\pi$
$499$	2.96963	0.132939	0.0664695	+	0.997788i	$0.478826\pi$
$500$	−8.36795	−0.374226
$501$	−7.18544	−0.321022
$502$	−8.19351	−0.365694
$503$	−6.87383	−0.306489	−0.153244	−	0.988188i	$-0.548972\pi$
$503$	−6.87383	−0.306489	−0.153244	+	0.988188i	$0.548972\pi$
$504$	59.2802	2.64055
$505$	0.852280	0.0379260
$506$	−9.46649	−0.420837
$507$	28.8137	1.27966
$508$	−72.0082	−3.19485
$509$	−37.0996	−1.64441	−0.822204	−	0.569192i	$-0.807256\pi$
$509$	−37.0996	−1.64441	−0.822204	+	0.569192i	$0.807256\pi$
$510$	−0.576635	−0.0255338
$511$	−49.8720	−2.20621
$512$	6.83587	0.302105
$513$	2.52528	0.111494
$514$	22.6409	0.998647
$515$	0.407358	0.0179504
$516$	−68.4119	−3.01167
$517$	0.465654	0.0204794
$518$	−23.9547	−1.05251
$519$	3.98278	0.174824
$520$	8.66725	0.380084
$521$	−17.3206	−0.758829	−0.379415	−	0.925227i	$-0.623875\pi$
$521$	−17.3206	−0.758829	−0.379415	+	0.925227i	$0.623875\pi$
$522$	1.72326	0.0754251
$523$	29.1278	1.27367	0.636834	−	0.771001i	$-0.280244\pi$
$523$	29.1278	1.27367	0.636834	+	0.771001i	$0.280244\pi$
$524$	80.1623	3.50190
$525$	−21.0076	−0.916848
$526$	1.09707	0.0478346
$527$	4.05753	0.176749
$528$	10.2301	0.445207
$529$	−0.434792	−0.0189040
$530$	−3.54034	−0.153783
$531$	−6.90805	−0.299784
$532$	−9.60155	−0.416280
$533$	58.5357	2.53546
$534$	−9.75248	−0.422031
$535$	0.741948	0.0320772
$536$	−108.074	−4.66809
$537$	−15.8333	−0.683255
$538$	33.8955	1.46134
$539$	5.83163	0.251186
$540$	−4.41291	−0.189901
$541$	21.1192	0.907986	0.453993	−	0.891005i	$-0.349999\pi$
$541$	21.1192	0.907986	0.453993	+	0.891005i	$0.349999\pi$
$542$	−24.9088	−1.06992
$543$	−14.6775	−0.629870
$544$	−20.1034	−0.861927
$545$	−1.03585	−0.0443712
$546$	70.9863	3.03793
$547$	−16.7400	−0.715750	−0.357875	−	0.933770i	$-0.616499\pi$
$547$	−16.7400	−0.715750	−0.357875	+	0.933770i	$0.616499\pi$
$548$	−77.6067	−3.31519
$549$	−1.78317	−0.0761040
$550$	9.91206	0.422652
$551$	−0.171560	−0.00730871
$552$	−44.5426	−1.89586
$553$	−30.4772	−1.29602
$554$	−49.5727	−2.10614
$555$	0.410810	0.0174379
$556$	−62.5884	−2.65434
$557$	22.2438	0.942498	0.471249	−	0.882000i	$-0.343803\pi$
$557$	22.2438	0.942498	0.471249	+	0.882000i	$0.343803\pi$
$558$	16.1229	0.682536
$559$	75.3706	3.18784
$560$	7.82169	0.330527
$561$	0.988686	0.0417424
$562$	−70.1178	−2.95774
$563$	32.1260	1.35395	0.676974	−	0.736007i	$-0.263291\pi$
$563$	32.1260	1.35395	0.676974	+	0.736007i	$0.263291\pi$
$564$	3.56464	0.150098
$565$	−0.285545	−0.0120130
$566$	22.9364	0.964089
$567$	−1.42592	−0.0598831
$568$	−86.4162	−3.62594
$569$	39.2410	1.64507	0.822534	−	0.568715i	$-0.192559\pi$
$569$	39.2410	1.64507	0.822534	+	0.568715i	$0.192559\pi$
$570$	0.228112	0.00955457
$571$	13.6261	0.570234	0.285117	−	0.958493i	$-0.407967\pi$
$571$	13.6261	0.570234	0.285117	+	0.958493i	$0.407967\pi$
$572$	−24.1771	−1.01090
$573$	−16.0988	−0.672539
$574$	96.4909	4.02745
$575$	−23.6273	−0.985327
$576$	−34.7126	−1.44636
$577$	26.4476	1.10103	0.550514	−	0.834826i	$-0.314432\pi$
$577$	26.4476	1.10103	0.550514	+	0.834826i	$0.314432\pi$
$578$	41.6351	1.73179
$579$	−3.88990	−0.161659
$580$	0.299800	0.0124485
$581$	41.5993	1.72583
$582$	8.68900	0.360171
$583$	6.07019	0.251402
$584$	110.721	4.58167
$585$	1.82220	0.0753388
$586$	−9.13909	−0.377532
$587$	−22.5884	−0.932323	−0.466161	−	0.884700i	$-0.654363\pi$
$587$	−22.5884	−0.932323	−0.466161	+	0.884700i	$0.654363\pi$
$588$	44.6419	1.84100
$589$	−1.60512	−0.0661380
$590$	−1.66492	−0.0685435
$591$	−25.2946	−1.04048
$592$	29.1151	1.19662
$593$	43.7257	1.79560	0.897800	−	0.440403i	$-0.145165\pi$
$593$	43.7257	1.79560	0.897800	+	0.440403i	$0.145165\pi$
$594$	10.4819	0.430077
$595$	0.755928	0.0309900
$596$	−97.4719	−3.99260
$597$	−14.4346	−0.590768
$598$	79.8384	3.26483
$599$	12.5107	0.511173	0.255587	−	0.966786i	$-0.417731\pi$
$599$	12.5107	0.511173	0.255587	+	0.966786i	$0.417731\pi$
$600$	46.6391	1.90403
$601$	−2.14546	−0.0875153	−0.0437576	−	0.999042i	$-0.513933\pi$
$601$	−2.14546	−0.0875153	−0.0437576	+	0.999042i	$0.513933\pi$
$602$	124.242	5.06371
$603$	−22.7215	−0.925292
$604$	−44.7505	−1.82087
$605$	−1.68885	−0.0686614
$606$	−15.4970	−0.629524
$607$	−18.7680	−0.761770	−0.380885	−	0.924622i	$-0.624381\pi$
$607$	−18.7680	−0.761770	−0.380885	+	0.924622i	$0.624381\pi$
$608$	7.95275	0.322526
$609$	1.50924	0.0611576
$610$	−0.429765	−0.0174007
$611$	−3.92723	−0.158879
$612$	−11.3288	−0.457938
$613$	−8.14353	−0.328914	−0.164457	−	0.986384i	$-0.552587\pi$
$613$	−8.14353	−0.328914	−0.164457	+	0.986384i	$0.552587\pi$
$614$	72.3671	2.92050
$615$	−1.65477	−0.0667266
$616$	−24.4965	−0.986992
$617$	13.4226	0.540372	0.270186	−	0.962808i	$-0.412915\pi$
$617$	13.4226	0.540372	0.270186	+	0.962808i	$0.412915\pi$
$618$	−7.40701	−0.297954
$619$	−6.86503	−0.275929	−0.137964	−	0.990437i	$-0.544056\pi$
$619$	−6.86503	−0.275929	−0.137964	+	0.990437i	$0.544056\pi$
$620$	2.80494	0.112649
$621$	−24.9856	−1.00264
$622$	92.8394	3.72252
$623$	12.7848	0.512213
$624$	−86.2784	−3.45390
$625$	24.6087	0.984349
$626$	11.3625	0.454138
$627$	−0.391116	−0.0156197
$628$	57.4581	2.29283
$629$	2.81383	0.112195
$630$	3.00374	0.119672
$631$	−35.7966	−1.42504	−0.712519	−	0.701653i	$-0.752446\pi$
$631$	−35.7966	−1.42504	−0.712519	+	0.701653i	$0.752446\pi$
$632$	67.6626	2.69147
$633$	3.89290	0.154729
$634$	37.5411	1.49095
$635$	−2.24268	−0.0889982
$636$	46.4680	1.84258
$637$	−49.1827	−1.94869
$638$	−0.712107	−0.0281926
$639$	−18.1681	−0.718720
$640$	−3.01092	−0.119017
$641$	12.0619	0.476415	0.238208	−	0.971214i	$-0.423440\pi$
$641$	12.0619	0.476415	0.238208	+	0.971214i	$0.423440\pi$
$642$	−13.4909	−0.532442
$643$	42.4469	1.67394	0.836971	−	0.547247i	$-0.184324\pi$
$643$	42.4469	1.67394	0.836971	+	0.547247i	$0.184324\pi$
$644$	94.9993	3.74350
$645$	−2.13068	−0.0838954
$646$	1.56244	0.0614735
$647$	−11.6974	−0.459873	−0.229937	−	0.973206i	$-0.573852\pi$
$647$	−11.6974	−0.459873	−0.229937	+	0.973206i	$0.573852\pi$
$648$	3.16569	0.124360
$649$	2.85463	0.112054
$650$	−83.5962	−3.27891
$651$	14.1205	0.553427
$652$	25.0789	0.982167
$653$	13.2794	0.519664	0.259832	−	0.965654i	$-0.416333\pi$
$653$	13.2794	0.519664	0.259832	+	0.965654i	$0.416333\pi$
$654$	18.8350	0.736506
$655$	2.49664	0.0975519
$656$	−117.277	−4.57890
$657$	23.2780	0.908161
$658$	−6.47368	−0.252370
$659$	−44.5952	−1.73718	−0.868590	−	0.495531i	$-0.834974\pi$
$659$	−44.5952	−1.73718	−0.868590	+	0.495531i	$0.834974\pi$
$660$	0.683472	0.0266041
$661$	48.4070	1.88281	0.941407	−	0.337272i	$-0.109504\pi$
$661$	48.4070	1.88281	0.941407	+	0.337272i	$0.109504\pi$
$662$	−42.4215	−1.64876
$663$	−8.33837	−0.323836
$664$	−92.3547	−3.58406
$665$	−0.299039	−0.0115962
$666$	11.1809	0.433253
$667$	1.69745	0.0657253
$668$	−34.0229	−1.31639
$669$	9.52465	0.368244
$670$	−5.47614	−0.211562
$671$	0.736866	0.0284464
$672$	−69.9615	−2.69882
$673$	0.650633	0.0250800	0.0125400	−	0.999921i	$-0.496008\pi$
$673$	0.650633	0.0250800	0.0125400	+	0.999921i	$0.496008\pi$
$674$	−20.3711	−0.784666
$675$	26.1616	1.00696
$676$	136.432	5.24739
$677$	37.4559	1.43955	0.719774	−	0.694208i	$-0.244245\pi$
$677$	37.4559	1.43955	0.719774	+	0.694208i	$0.244245\pi$
$678$	5.19207	0.199400
$679$	−11.3907	−0.437133
$680$	−1.67824	−0.0643574
$681$	−22.6685	−0.868661
$682$	−6.66250	−0.255120
$683$	−7.20145	−0.275556	−0.137778	−	0.990463i	$-0.543996\pi$
$683$	−7.20145	−0.275556	−0.137778	+	0.990463i	$0.543996\pi$
$684$	4.48156	0.171357
$685$	−2.41705	−0.0923507
$686$	−8.74895	−0.334036
$687$	−28.5697	−1.09000
$688$	−151.006	−5.75706
$689$	−51.1947	−1.95036
$690$	−2.25698	−0.0859217
$691$	−6.59685	−0.250956	−0.125478	−	0.992096i	$-0.540046\pi$
$691$	−6.59685	−0.250956	−0.125478	+	0.992096i	$0.540046\pi$
$692$	18.8584	0.716887
$693$	−5.15014	−0.195638
$694$	81.0819	3.07783
$695$	−1.94931	−0.0739414
$696$	−3.35067	−0.127007
$697$	−11.3343	−0.429315
$698$	43.8616	1.66019
$699$	1.49624	0.0565929
$700$	−99.4706	−3.75964
$701$	−15.0031	−0.566658	−0.283329	−	0.959023i	$-0.591439\pi$
$701$	−15.0031	−0.566658	−0.283329	+	0.959023i	$0.591439\pi$
$702$	−88.4019	−3.33652
$703$	−1.11313	−0.0419824
$704$	14.3444	0.540625
$705$	0.111020	0.00418126
$706$	−7.17026	−0.269856
$707$	20.3155	0.764044
$708$	21.8525	0.821269
$709$	0.972213	0.0365122	0.0182561	−	0.999833i	$-0.494189\pi$
$709$	0.972213	0.0365122	0.0182561	+	0.999833i	$0.494189\pi$
$710$	−4.37872	−0.164331
$711$	14.2254	0.533493
$712$	−28.3836	−1.06372
$713$	15.8814	0.594762
$714$	−13.7451	−0.514396
$715$	−0.752993	−0.0281603
$716$	−74.9701	−2.80176
$717$	−8.09464	−0.302300
$718$	−45.8721	−1.71193
$719$	20.4651	0.763219	0.381610	−	0.924324i	$-0.375370\pi$
$719$	20.4651	0.763219	0.381610	+	0.924324i	$0.375370\pi$
$720$	−3.65081	−0.136058
$721$	9.71006	0.361622
$722$	50.3296	1.87307
$723$	5.36608	0.199567
$724$	−69.4975	−2.58285
$725$	−1.77734	−0.0660088
$726$	30.7084	1.13969
$727$	−20.9268	−0.776131	−0.388065	−	0.921632i	$-0.626857\pi$
$727$	−20.9268	−0.776131	−0.388065	+	0.921632i	$0.626857\pi$
$728$	206.598	7.65704
$729$	17.9620	0.665260
$730$	5.61025	0.207645
$731$	−14.5940	−0.539778
$732$	5.64080	0.208490
$733$	1.41158	0.0521381	0.0260690	−	0.999660i	$-0.491701\pi$
$733$	1.41158	0.0521381	0.0260690	+	0.999660i	$0.491701\pi$
$734$	12.0238	0.443808
$735$	1.39036	0.0512844
$736$	−78.6858	−2.90040
$737$	9.38927	0.345858
$738$	−45.0375	−1.65785
$739$	−46.0592	−1.69432	−0.847158	−	0.531341i	$-0.821688\pi$
$739$	−46.0592	−1.69432	−0.847158	+	0.531341i	$0.821688\pi$
$740$	1.94518	0.0715061
$741$	3.29859	0.121177
$742$	−84.3898	−3.09805
$743$	−16.7580	−0.614791	−0.307395	−	0.951582i	$-0.599457\pi$
$743$	−16.7580	−0.614791	−0.307395	+	0.951582i	$0.599457\pi$
$744$	−31.3490	−1.14931
$745$	−3.03575	−0.111221
$746$	81.9735	3.00126
$747$	−19.4166	−0.710418
$748$	4.68141	0.171169
$749$	17.6856	0.646216
$750$	4.73884	0.173038
$751$	−13.5758	−0.495387	−0.247693	−	0.968838i	$-0.579673\pi$
$751$	−13.5758	−0.495387	−0.247693	+	0.968838i	$0.579673\pi$
$752$	7.86825	0.286926
$753$	3.34939	0.122059
$754$	6.00576	0.218717
$755$	−1.39375	−0.0507237
$756$	−105.189	−3.82569
$757$	−29.0693	−1.05654	−0.528271	−	0.849076i	$-0.677160\pi$
$757$	−29.0693	−1.05654	−0.528271	+	0.849076i	$0.677160\pi$
$758$	−22.3435	−0.811551
$759$	3.86977	0.140464
$760$	0.663897	0.0240821
$761$	−21.2531	−0.770423	−0.385212	−	0.922828i	$-0.625872\pi$
$761$	−21.2531	−0.770423	−0.385212	+	0.922828i	$0.625872\pi$
$762$	40.7788	1.47726
$763$	−24.6913	−0.893886
$764$	−76.2277	−2.75782
$765$	−0.352832	−0.0127567
$766$	−37.2379	−1.34546
$767$	−24.0753	−0.869310
$768$	12.4340	0.448672
$769$	−28.3134	−1.02101	−0.510503	−	0.859876i	$-0.670541\pi$
$769$	−28.3134	−1.02101	−0.510503	+	0.859876i	$0.670541\pi$
$770$	−1.24124	−0.0447312
$771$	−9.25528	−0.333321
$772$	−18.4186	−0.662899
$773$	−15.8629	−0.570548	−0.285274	−	0.958446i	$-0.592085\pi$
$773$	−15.8629	−0.570548	−0.285274	+	0.958446i	$0.592085\pi$
$774$	−57.9903	−2.08442
$775$	−16.6289	−0.597326
$776$	25.2884	0.907802
$777$	9.79234	0.351298
$778$	10.3481	0.370996
$779$	4.48374	0.160647
$780$	−5.76425	−0.206393
$781$	7.50766	0.268645
$782$	−15.4591	−0.552815
$783$	−1.87952	−0.0671684
$784$	98.5383	3.51923
$785$	1.78952	0.0638708
$786$	−45.3965	−1.61924
$787$	−39.1896	−1.39696	−0.698479	−	0.715630i	$-0.746140\pi$
$787$	−39.1896	−1.39696	−0.698479	+	0.715630i	$0.746140\pi$
$788$	−119.770	−4.26662
$789$	−0.448468	−0.0159659
$790$	3.42847	0.121980
$791$	−6.80643	−0.242009
$792$	11.4338	0.406284
$793$	−6.21457	−0.220686
$794$	87.4805	3.10457
$795$	1.44724	0.0513283
$796$	−68.3474	−2.42251
$797$	27.7259	0.982101	0.491050	−	0.871131i	$-0.336613\pi$
$797$	27.7259	0.982101	0.491050	+	0.871131i	$0.336613\pi$
$798$	5.43743	0.192483
$799$	0.760427	0.0269020
$800$	82.3893	2.91290
$801$	−5.96736	−0.210846
$802$	−99.9818	−3.53048
$803$	−9.61922	−0.339455
$804$	71.8760	2.53487
$805$	2.95874	0.104282
$806$	56.1901	1.97921
$807$	−13.8560	−0.487754
$808$	−45.1025	−1.58670
$809$	−0.371559	−0.0130633	−0.00653166	−	0.999979i	$-0.502079\pi$
$809$	−0.371559	−0.0130633	−0.00653166	+	0.999979i	$0.502079\pi$
$810$	0.160406	0.00563610
$811$	10.0477	0.352823	0.176412	−	0.984317i	$-0.443551\pi$
$811$	10.0477	0.352823	0.176412	+	0.984317i	$0.443551\pi$
$812$	7.14622	0.250783
$813$	10.1823	0.357111
$814$	−4.62033	−0.161943
$815$	0.781080	0.0273600
$816$	16.7060	0.584829
$817$	5.77326	0.201981
$818$	−80.4470	−2.81276
$819$	43.4352	1.51775
$820$	−7.83529	−0.273620
$821$	−7.10429	−0.247942	−0.123971	−	0.992286i	$-0.539563\pi$
$821$	−7.10429	−0.247942	−0.123971	+	0.992286i	$0.539563\pi$
$822$	43.9493	1.53291
$823$	31.2423	1.08904	0.544519	−	0.838748i	$-0.316712\pi$
$823$	31.2423	1.08904	0.544519	+	0.838748i	$0.316712\pi$
$824$	−21.5573	−0.750985
$825$	−4.05191	−0.141069
$826$	−39.6860	−1.38085
$827$	24.5115	0.852350	0.426175	−	0.904641i	$-0.359861\pi$
$827$	24.5115	0.852350	0.426175	+	0.904641i	$0.359861\pi$
$828$	−44.3413	−1.54097
$829$	−15.7315	−0.546376	−0.273188	−	0.961961i	$-0.588078\pi$
$829$	−15.7315	−0.546376	−0.273188	+	0.961961i	$0.588078\pi$
$830$	−4.67963	−0.162432
$831$	20.2646	0.702972
$832$	−120.978	−4.19414
$833$	9.52324	0.329961
$834$	35.4443	1.22734
$835$	−1.05964	−0.0366703
$836$	−1.85193	−0.0640502
$837$	−17.5848	−0.607820
$838$	91.8299	3.17221
$839$	10.2233	0.352949	0.176474	−	0.984305i	$-0.443531\pi$
$839$	10.2233	0.352949	0.176474	+	0.984305i	$0.443531\pi$
$840$	−5.84040	−0.201513
$841$	−28.8723	−0.995597
$842$	4.54309	0.156565
$843$	28.6632	0.987212
$844$	18.4328	0.634483
$845$	4.24916	0.146175
$846$	3.02162	0.103885
$847$	−40.2565	−1.38323
$848$	102.569	3.52224
$849$	−9.37607	−0.321786
$850$	16.1867	0.555199
$851$	11.0135	0.377536
$852$	57.4721	1.96896
$853$	5.07828	0.173877	0.0869385	−	0.996214i	$-0.472292\pi$
$853$	5.07828	0.173877	0.0869385	+	0.996214i	$0.472292\pi$
$854$	−10.2442	−0.350548
$855$	0.139578	0.00477345
$856$	−39.2638	−1.34201
$857$	−39.2456	−1.34060	−0.670302	−	0.742089i	$-0.733835\pi$
$857$	−39.2456	−1.34060	−0.670302	+	0.742089i	$0.733835\pi$
$858$	13.6917	0.467427
$859$	40.1653	1.37042	0.685212	−	0.728344i	$-0.259710\pi$
$859$	40.1653	1.37042	0.685212	+	0.728344i	$0.259710\pi$
$860$	−10.0887	−0.344022
$861$	−39.4441	−1.34425
$862$	80.0101	2.72516
$863$	−31.8409	−1.08388	−0.541938	−	0.840419i	$-0.682309\pi$
$863$	−31.8409	−1.08388	−0.541938	+	0.840419i	$0.682309\pi$
$864$	87.1257	2.96408
$865$	0.587341	0.0199702
$866$	−82.6022	−2.80694
$867$	−17.0198	−0.578024
$868$	66.8603	2.26939
$869$	−5.87839	−0.199411
$870$	−0.169779	−0.00575605
$871$	−79.1871	−2.68315
$872$	54.8172	1.85635
$873$	5.31664	0.179941
$874$	6.11549	0.206859
$875$	−6.21227	−0.210013
$876$	−73.6363	−2.48794
$877$	−23.2014	−0.783455	−0.391727	−	0.920081i	$-0.628122\pi$
$877$	−23.2014	−0.783455	−0.391727	+	0.920081i	$0.628122\pi$
$878$	55.2149	1.86341
$879$	3.73593	0.126010
$880$	1.50863	0.0508560
$881$	30.1988	1.01742	0.508711	−	0.860937i	$-0.330122\pi$
$881$	30.1988	1.01742	0.508711	+	0.860937i	$0.330122\pi$
$882$	37.8413	1.27418
$883$	−9.68587	−0.325955	−0.162978	−	0.986630i	$-0.552110\pi$
$883$	−9.68587	−0.325955	−0.162978	+	0.986630i	$0.552110\pi$
$884$	−39.4820	−1.32792
$885$	0.680594	0.0228779
$886$	−1.30617	−0.0438818
$887$	18.8189	0.631875	0.315938	−	0.948780i	$-0.397681\pi$
$887$	18.8189	0.631875	0.315938	+	0.948780i	$0.397681\pi$
$888$	−21.7400	−0.729546
$889$	−53.4581	−1.79293
$890$	−1.43820	−0.0482086
$891$	−0.275029	−0.00921381
$892$	45.0990	1.51003
$893$	−0.300819	−0.0100665
$894$	55.1991	1.84613
$895$	−2.33493	−0.0780482
$896$	−71.7701	−2.39767
$897$	−32.6368	−1.08971
$898$	−105.901	−3.53396
$899$	1.19466	0.0398441
$900$	46.4283	1.54761
$901$	9.91281	0.330244
$902$	18.6110	0.619677
$903$	−50.7883	−1.69013
$904$	15.1110	0.502584
$905$	−2.16449	−0.0719500
$906$	25.3426	0.841950
$907$	7.51598	0.249564	0.124782	−	0.992184i	$-0.460177\pi$
$907$	7.51598	0.249564	0.124782	+	0.992184i	$0.460177\pi$
$908$	−107.335	−3.56204
$909$	−9.48235	−0.314510
$910$	10.4684	0.347023
$911$	53.8314	1.78351	0.891756	−	0.452516i	$-0.149474\pi$
$911$	53.8314	1.78351	0.891756	+	0.452516i	$0.149474\pi$
$912$	−6.60878	−0.218838
$913$	8.02359	0.265542
$914$	4.58864	0.151779
$915$	0.175682	0.00580786
$916$	−135.277	−4.46967
$917$	59.5116	1.96525
$918$	17.1172	0.564953
$919$	−32.8766	−1.08450	−0.542249	−	0.840218i	$-0.682427\pi$
$919$	−32.8766	−1.08450	−0.542249	+	0.840218i	$0.682427\pi$
$920$	−6.56870	−0.216564
$921$	−29.5826	−0.974781
$922$	−79.4653	−2.61705
$923$	−63.3180	−2.08414
$924$	16.2917	0.535957
$925$	−11.5318	−0.379164
$926$	−41.0306	−1.34835
$927$	−4.53221	−0.148857
$928$	−5.91906	−0.194303
$929$	−33.4206	−1.09649	−0.548246	−	0.836317i	$-0.684704\pi$
$929$	−33.4206	−1.09649	−0.548246	+	0.836317i	$0.684704\pi$
$930$	−1.58846	−0.0520876
$931$	−3.76732	−0.123469
$932$	7.08465	0.232066
$933$	−37.9515	−1.24247
$934$	39.4593	1.29115
$935$	0.145802	0.00476823
$936$	−96.4306	−3.15193
$937$	34.2464	1.11878	0.559391	−	0.828904i	$-0.311035\pi$
$937$	34.2464	1.11878	0.559391	+	0.828904i	$0.311035\pi$
$938$	−130.533	−4.26205
$939$	−4.64484	−0.151579
$940$	0.525678	0.0171457
$941$	−51.3897	−1.67526	−0.837629	−	0.546240i	$-0.816059\pi$
$941$	−51.3897	−1.67526	−0.837629	+	0.546240i	$0.816059\pi$
$942$	−32.5390	−1.06018
$943$	−44.3628	−1.44465
$944$	48.2353	1.56992
$945$	−3.27610	−0.106571
$946$	23.9635	0.779120
$947$	0.610286	0.0198316	0.00991582	−	0.999951i	$-0.496844\pi$
$947$	0.610286	0.0198316	0.00991582	+	0.999951i	$0.496844\pi$
$948$	−44.9998	−1.46152
$949$	81.1264	2.63348
$950$	−6.40333	−0.207751
$951$	−15.3463	−0.497637
$952$	−40.0035	−1.29652
$953$	−10.6822	−0.346032	−0.173016	−	0.984919i	$-0.555351\pi$
$953$	−10.6822	−0.346032	−0.173016	+	0.984919i	$0.555351\pi$
$954$	39.3893	1.27528
$955$	−2.37410	−0.0768241
$956$	−38.3280	−1.23961
$957$	0.291099	0.00940991
$958$	87.9954	2.84300
$959$	−57.6144	−1.86047
$960$	3.41996	0.110379
$961$	−19.8227	−0.639443
$962$	38.9669	1.25634
$963$	−8.25481	−0.266008
$964$	25.4083	0.818345
$965$	−0.573644	−0.0184663
$966$	−53.7988	−1.73095
$967$	−0.405438	−0.0130380	−0.00651901	−	0.999979i	$-0.502075\pi$
$967$	−0.405438	−0.0130380	−0.00651901	+	0.999979i	$0.502075\pi$
$968$	89.3735	2.87257
$969$	−0.638705	−0.0205182
$970$	1.28137	0.0411423
$971$	−9.55460	−0.306622	−0.153311	−	0.988178i	$-0.548994\pi$
$971$	−9.55460	−0.306622	−0.153311	+	0.988178i	$0.548994\pi$
$972$	79.7930	2.55936
$973$	−46.4650	−1.48960
$974$	46.7667	1.49850
$975$	34.1729	1.09441
$976$	12.4510	0.398546
$977$	−11.5283	−0.368822	−0.184411	−	0.982849i	$-0.559038\pi$
$977$	−11.5283	−0.368822	−0.184411	+	0.982849i	$0.559038\pi$
$978$	−14.2024	−0.454143
$979$	2.46591	0.0788108
$980$	6.58334	0.210297
$981$	11.5248	0.367958
$982$	−56.9463	−1.81723
$983$	−16.8983	−0.538971	−0.269486	−	0.963004i	$-0.586854\pi$
$983$	−16.8983	−0.538971	−0.269486	+	0.963004i	$0.586854\pi$
$984$	87.5700	2.79163
$985$	−3.73021	−0.118854
$986$	−1.16289	−0.0370341
$987$	2.64635	0.0842342
$988$	15.6188	0.496899
$989$	−57.1216	−1.81636
$990$	0.579355	0.0184131
$991$	34.6958	1.10215	0.551075	−	0.834456i	$-0.314218\pi$
$991$	34.6958	1.10215	0.551075	+	0.834456i	$0.314218\pi$
$992$	−55.3789	−1.75828
$993$	17.3413	0.550310
$994$	−104.374	−3.31055
$995$	−2.12867	−0.0674834
$996$	61.4216	1.94622
$997$	47.8845	1.51652	0.758259	−	0.651953i	$-0.226050\pi$
$997$	47.8845	1.51652	0.758259	+	0.651953i	$0.226050\pi$
$998$	−7.96294	−0.252062
$999$	−12.1948	−0.385825

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8039.2.a.a.1.5	✓	279

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8039.2.a.a.1.5	✓	279	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:	\( N \)	\(=\)	\( 8039 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8039.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68146 q^{2} +1.09614 q^{3} +5.19020 q^{4} +0.161648 q^{5} -2.93925 q^{6} +3.85315 q^{7} -8.55439 q^{8} -1.79847 q^{9} +O(q^{10})\)	\(q-2.68146 q^{2} +1.09614 q^{3} +5.19020 q^{4} +0.161648 q^{5} -2.93925 q^{6} +3.85315 q^{7} -8.55439 q^{8} -1.79847 q^{9} -0.433452 q^{10} +0.743188 q^{11} +5.68920 q^{12} -6.26789 q^{13} -10.3321 q^{14} +0.177189 q^{15} +12.5578 q^{16} +1.21365 q^{17} +4.82253 q^{18} -0.480110 q^{19} +0.838987 q^{20} +4.22360 q^{21} -1.99283 q^{22} +4.75029 q^{23} -9.37682 q^{24} -4.97387 q^{25} +16.8071 q^{26} -5.25981 q^{27} +19.9986 q^{28} +0.357335 q^{29} -0.475125 q^{30} +3.34324 q^{31} -16.5644 q^{32} +0.814639 q^{33} -3.25435 q^{34} +0.622855 q^{35} -9.33445 q^{36} +2.31848 q^{37} +1.28739 q^{38} -6.87049 q^{39} -1.38280 q^{40} -9.33898 q^{41} -11.3254 q^{42} -12.0249 q^{43} +3.85730 q^{44} -0.290720 q^{45} -12.7377 q^{46} +0.626563 q^{47} +13.7651 q^{48} +7.84678 q^{49} +13.3372 q^{50} +1.33033 q^{51} -32.5316 q^{52} +8.16777 q^{53} +14.1039 q^{54} +0.120135 q^{55} -32.9614 q^{56} -0.526268 q^{57} -0.958179 q^{58} +3.84106 q^{59} +0.919648 q^{60} +0.991493 q^{61} -8.96476 q^{62} -6.92979 q^{63} +19.3012 q^{64} -1.01319 q^{65} -2.18442 q^{66} +12.6338 q^{67} +6.29909 q^{68} +5.20698 q^{69} -1.67016 q^{70} +10.1020 q^{71} +15.3849 q^{72} -12.9432 q^{73} -6.21691 q^{74} -5.45206 q^{75} -2.49187 q^{76} +2.86362 q^{77} +18.4229 q^{78} -7.90969 q^{79} +2.02995 q^{80} -0.370066 q^{81} +25.0421 q^{82} +10.7962 q^{83} +21.9213 q^{84} +0.196184 q^{85} +32.2442 q^{86} +0.391690 q^{87} -6.35752 q^{88} +3.31801 q^{89} +0.779553 q^{90} -24.1511 q^{91} +24.6549 q^{92} +3.66467 q^{93} -1.68010 q^{94} -0.0776089 q^{95} -18.1570 q^{96} -2.95619 q^{97} -21.0408 q^{98} -1.33660 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9}+O(q^{10}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9} - 42 q^{10} - 53 q^{11} - 36 q^{12} - 75 q^{13} - 31 q^{14} - 60 q^{15} + 127 q^{16} - 55 q^{17} - 57 q^{18} - 113 q^{19} - 43 q^{20} - 103 q^{21} - 73 q^{22} - 30 q^{23} - 106 q^{24} + 75 q^{25} - 42 q^{26} - 45 q^{27} - 146 q^{28} - 92 q^{29} - 76 q^{30} - 84 q^{31} - 71 q^{32} - 117 q^{33} - 106 q^{34} - 49 q^{35} + 67 q^{36} - 123 q^{37} - 21 q^{38} - 92 q^{39} - 97 q^{40} - 116 q^{41} - 19 q^{42} - 126 q^{43} - 131 q^{44} - 85 q^{45} - 183 q^{46} - 42 q^{47} - 47 q^{48} - 22 q^{49} - 64 q^{50} - 90 q^{51} - 158 q^{52} - 60 q^{53} - 117 q^{54} - 99 q^{55} - 65 q^{56} - 182 q^{57} - 93 q^{58} - 58 q^{59} - 141 q^{60} - 217 q^{61} - 16 q^{62} - 141 q^{63} - 47 q^{64} - 197 q^{65} - 53 q^{66} - 147 q^{67} - 90 q^{68} - 103 q^{69} - 118 q^{70} - 78 q^{71} - 135 q^{72} - 282 q^{73} - 98 q^{74} - 53 q^{75} - 296 q^{76} - 53 q^{77} - 27 q^{78} - 153 q^{79} - 52 q^{80} - 89 q^{81} - 81 q^{82} - 54 q^{83} - 164 q^{84} - 303 q^{85} - 82 q^{86} - 29 q^{87} - 203 q^{88} - 185 q^{89} - 56 q^{90} - 163 q^{91} - 66 q^{92} - 156 q^{93} - 134 q^{94} - 69 q^{95} - 189 q^{96} - 212 q^{97} - 13 q^{98} - 181 q^{99}+O(q^{100}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9 - 42 * q^10 - 53 * q^11 - 36 * q^12 - 75 * q^13 - 31 * q^14 - 60 * q^15 + 127 * q^16 - 55 * q^17 - 57 * q^18 - 113 * q^19 - 43 * q^20 - 103 * q^21 - 73 * q^22 - 30 * q^23 - 106 * q^24 + 75 * q^25 - 42 * q^26 - 45 * q^27 - 146 * q^28 - 92 * q^29 - 76 * q^30 - 84 * q^31 - 71 * q^32 - 117 * q^33 - 106 * q^34 - 49 * q^35 + 67 * q^36 - 123 * q^37 - 21 * q^38 - 92 * q^39 - 97 * q^40 - 116 * q^41 - 19 * q^42 - 126 * q^43 - 131 * q^44 - 85 * q^45 - 183 * q^46 - 42 * q^47 - 47 * q^48 - 22 * q^49 - 64 * q^50 - 90 * q^51 - 158 * q^52 - 60 * q^53 - 117 * q^54 - 99 * q^55 - 65 * q^56 - 182 * q^57 - 93 * q^58 - 58 * q^59 - 141 * q^60 - 217 * q^61 - 16 * q^62 - 141 * q^63 - 47 * q^64 - 197 * q^65 - 53 * q^66 - 147 * q^67 - 90 * q^68 - 103 * q^69 - 118 * q^70 - 78 * q^71 - 135 * q^72 - 282 * q^73 - 98 * q^74 - 53 * q^75 - 296 * q^76 - 53 * q^77 - 27 * q^78 - 153 * q^79 - 52 * q^80 - 89 * q^81 - 81 * q^82 - 54 * q^83 - 164 * q^84 - 303 * q^85 - 82 * q^86 - 29 * q^87 - 203 * q^88 - 185 * q^89 - 56 * q^90 - 163 * q^91 - 66 * q^92 - 156 * q^93 - 134 * q^94 - 69 * q^95 - 189 * q^96 - 212 * q^97 - 13 * q^98 - 181 * q^99

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