LMFDB - Embedded newform 8039.2.a.a.1.8

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			1.8
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)

$f(q)$	$=$	$q-2.65123 q^{2} +3.28882 q^{3} +5.02904 q^{4} -0.364681 q^{5} -8.71943 q^{6} -0.0824305 q^{7} -8.03069 q^{8} +7.81633 q^{9} +O(q^{10})$	\(q-2.65123 q^{2} +3.28882 q^{3} +5.02904 q^{4} -0.364681 q^{5} -8.71943 q^{6} -0.0824305 q^{7} -8.03069 q^{8} +7.81633 q^{9} +0.966855 q^{10} -5.88079 q^{11} +16.5396 q^{12} -0.739032 q^{13} +0.218542 q^{14} -1.19937 q^{15} +11.2332 q^{16} +3.72407 q^{17} -20.7229 q^{18} -3.03556 q^{19} -1.83400 q^{20} -0.271099 q^{21} +15.5913 q^{22} +1.95759 q^{23} -26.4115 q^{24} -4.86701 q^{25} +1.95935 q^{26} +15.8400 q^{27} -0.414546 q^{28} +1.02494 q^{29} +3.17981 q^{30} +0.569801 q^{31} -13.7203 q^{32} -19.3409 q^{33} -9.87339 q^{34} +0.0300608 q^{35} +39.3086 q^{36} -2.04112 q^{37} +8.04799 q^{38} -2.43054 q^{39} +2.92864 q^{40} +7.34664 q^{41} +0.718747 q^{42} -8.52769 q^{43} -29.5747 q^{44} -2.85047 q^{45} -5.19003 q^{46} -4.24307 q^{47} +36.9438 q^{48} -6.99321 q^{49} +12.9036 q^{50} +12.2478 q^{51} -3.71662 q^{52} +2.34159 q^{53} -41.9956 q^{54} +2.14461 q^{55} +0.661974 q^{56} -9.98342 q^{57} -2.71735 q^{58} +3.22721 q^{59} -6.03168 q^{60} -6.93651 q^{61} -1.51068 q^{62} -0.644304 q^{63} +13.9095 q^{64} +0.269511 q^{65} +51.2771 q^{66} -7.47838 q^{67} +18.7285 q^{68} +6.43817 q^{69} -0.0796983 q^{70} +0.0822656 q^{71} -62.7705 q^{72} -11.5244 q^{73} +5.41149 q^{74} -16.0067 q^{75} -15.2660 q^{76} +0.484756 q^{77} +6.44393 q^{78} +1.09434 q^{79} -4.09652 q^{80} +28.6460 q^{81} -19.4776 q^{82} -1.94594 q^{83} -1.36337 q^{84} -1.35810 q^{85} +22.6089 q^{86} +3.37084 q^{87} +47.2268 q^{88} -3.65501 q^{89} +7.55726 q^{90} +0.0609187 q^{91} +9.84481 q^{92} +1.87397 q^{93} +11.2494 q^{94} +1.10701 q^{95} -45.1237 q^{96} -11.4353 q^{97} +18.5406 q^{98} -45.9662 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.65123	−1.87471	−0.937353	−	0.348382i	$-0.886731\pi$
$2$	−2.65123	−1.87471	−0.937353	+	0.348382i	$0.886731\pi$
$3$	3.28882	1.89880	0.949400	−	0.314069i	$-0.101692\pi$
$3$	3.28882	1.89880	0.949400	+	0.314069i	$0.101692\pi$
$4$	5.02904	2.51452
$5$	−0.364681	−0.163090	−0.0815452	−	0.996670i	$-0.525985\pi$
$5$	−0.364681	−0.163090	−0.0815452	+	0.996670i	$0.525985\pi$
$6$	−8.71943	−3.55969
$7$	−0.0824305	−0.0311558	−0.0155779	−	0.999879i	$-0.504959\pi$
$7$	−0.0824305	−0.0311558	−0.0155779	+	0.999879i	$0.504959\pi$
$8$	−8.03069	−2.83928
$9$	7.81633	2.60544
$10$	0.966855	0.305746
$11$	−5.88079	−1.77312	−0.886562	−	0.462609i	$-0.846913\pi$
$11$	−5.88079	−1.77312	−0.886562	+	0.462609i	$0.846913\pi$
$12$	16.5396	4.77457
$13$	−0.739032	−0.204970	−0.102485	−	0.994735i	$-0.532679\pi$
$13$	−0.739032	−0.204970	−0.102485	+	0.994735i	$0.532679\pi$
$14$	0.218542	0.0584079
$15$	−1.19937	−0.309676
$16$	11.2332	2.80829
$17$	3.72407	0.903220	0.451610	−	0.892215i	$-0.350850\pi$
$17$	3.72407	0.903220	0.451610	+	0.892215i	$0.350850\pi$
$18$	−20.7229	−4.88444
$19$	−3.03556	−0.696406	−0.348203	−	0.937419i	$-0.613208\pi$
$19$	−3.03556	−0.696406	−0.348203	+	0.937419i	$0.613208\pi$
$20$	−1.83400	−0.410094
$21$	−0.271099	−0.0591586
$22$	15.5913	3.32409
$23$	1.95759	0.408186	0.204093	−	0.978951i	$-0.434575\pi$
$23$	1.95759	0.408186	0.204093	+	0.978951i	$0.434575\pi$
$24$	−26.4115	−5.39122
$25$	−4.86701	−0.973402
$26$	1.95935	0.384259
$27$	15.8400	3.04842
$28$	−0.414546	−0.0783419
$29$	1.02494	0.190326	0.0951631	−	0.995462i	$-0.469663\pi$
$29$	1.02494	0.190326	0.0951631	+	0.995462i	$0.469663\pi$
$30$	3.17981	0.580551
$31$	0.569801	0.102339	0.0511697	−	0.998690i	$-0.483705\pi$
$31$	0.569801	0.102339	0.0511697	+	0.998690i	$0.483705\pi$
$32$	−13.7203	−2.42544
$33$	−19.3409	−3.36681
$34$	−9.87339	−1.69327
$35$	0.0300608	0.00508121
$36$	39.3086	6.55144
$37$	−2.04112	−0.335558	−0.167779	−	0.985825i	$-0.553660\pi$
$37$	−2.04112	−0.335558	−0.167779	+	0.985825i	$0.553660\pi$
$38$	8.04799	1.30556
$39$	−2.43054	−0.389198
$40$	2.92864	0.463059
$41$	7.34664	1.14735	0.573676	−	0.819082i	$-0.305517\pi$
$41$	7.34664	1.14735	0.573676	+	0.819082i	$0.305517\pi$
$42$	0.718747	0.110905
$43$	−8.52769	−1.30046	−0.650231	−	0.759737i	$-0.725328\pi$
$43$	−8.52769	−1.30046	−0.650231	+	0.759737i	$0.725328\pi$
$44$	−29.5747	−4.45856
$45$	−2.85047	−0.424923
$46$	−5.19003	−0.765229
$47$	−4.24307	−0.618915	−0.309458	−	0.950913i	$-0.600148\pi$
$47$	−4.24307	−0.618915	−0.309458	+	0.950913i	$0.600148\pi$
$48$	36.9438	5.33238
$49$	−6.99321	−0.999029
$50$	12.9036	1.82484
$51$	12.2478	1.71504
$52$	−3.71662	−0.515402
$53$	2.34159	0.321642	0.160821	−	0.986984i	$-0.448586\pi$
$53$	2.34159	0.321642	0.160821	+	0.986984i	$0.448586\pi$
$54$	−41.9956	−5.71488
$55$	2.14461	0.289180
$56$	0.661974	0.0884600
$57$	−9.98342	−1.32234
$58$	−2.71735	−0.356806
$59$	3.22721	0.420147	0.210073	−	0.977686i	$-0.432630\pi$
$59$	3.22721	0.420147	0.210073	+	0.977686i	$0.432630\pi$
$60$	−6.03168	−0.778687
$61$	−6.93651	−0.888128	−0.444064	−	0.895995i	$-0.646464\pi$
$61$	−6.93651	−0.888128	−0.444064	+	0.895995i	$0.646464\pi$
$62$	−1.51068	−0.191856
$63$	−0.644304	−0.0811747
$64$	13.9095	1.73869
$65$	0.269511	0.0334287
$66$	51.2771	6.31178
$67$	−7.47838	−0.913629	−0.456815	−	0.889562i	$-0.651010\pi$
$67$	−7.47838	−0.913629	−0.456815	+	0.889562i	$0.651010\pi$
$68$	18.7285	2.27117
$69$	6.43817	0.775064
$70$	−0.0796983	−0.00952577
$71$	0.0822656	0.00976313	0.00488156	−	0.999988i	$-0.498446\pi$
$71$	0.0822656	0.00976313	0.00488156	+	0.999988i	$0.498446\pi$
$72$	−62.7705	−7.39758
$73$	−11.5244	−1.34883	−0.674413	−	0.738355i	$-0.735603\pi$
$73$	−11.5244	−1.34883	−0.674413	+	0.738355i	$0.735603\pi$
$74$	5.41149	0.629073
$75$	−16.0067	−1.84830
$76$	−15.2660	−1.75113
$77$	0.484756	0.0552431
$78$	6.44393	0.729632
$79$	1.09434	0.123123	0.0615613	−	0.998103i	$-0.480392\pi$
$79$	1.09434	0.123123	0.0615613	+	0.998103i	$0.480392\pi$
$80$	−4.09652	−0.458005
$81$	28.6460	3.18289
$82$	−19.4776	−2.15095
$83$	−1.94594	−0.213595	−0.106797	−	0.994281i	$-0.534060\pi$
$83$	−1.94594	−0.213595	−0.106797	+	0.994281i	$0.534060\pi$
$84$	−1.36337	−0.148756
$85$	−1.35810	−0.147307
$86$	22.6089	2.43798
$87$	3.37084	0.361392
$88$	47.2268	5.03439
$89$	−3.65501	−0.387430	−0.193715	−	0.981058i	$-0.562054\pi$
$89$	−3.65501	−0.387430	−0.193715	+	0.981058i	$0.562054\pi$
$90$	7.55726	0.796605
$91$	0.0609187	0.00638602
$92$	9.84481	1.02639
$93$	1.87397	0.194322
$94$	11.2494	1.16028
$95$	1.10701	0.113577
$96$	−45.1237	−4.60542
$97$	−11.4353	−1.16108	−0.580540	−	0.814232i	$-0.697159\pi$
$97$	−11.4353	−1.16108	−0.580540	+	0.814232i	$0.697159\pi$
$98$	18.5406	1.87289
$99$	−45.9662	−4.61978
$100$	−24.4764	−2.44764
$101$	−11.2333	−1.11776	−0.558878	−	0.829250i	$-0.688768\pi$
$101$	−11.2333	−1.11776	−0.558878	+	0.829250i	$0.688768\pi$
$102$	−32.4718	−3.21519
$103$	7.84306	0.772800	0.386400	−	0.922331i	$-0.373718\pi$
$103$	7.84306	0.772800	0.386400	+	0.922331i	$0.373718\pi$
$104$	5.93493	0.581968
$105$	0.0988647	0.00964820
$106$	−6.20809	−0.602983
$107$	5.46613	0.528430	0.264215	−	0.964464i	$-0.414887\pi$
$107$	5.46613	0.528430	0.264215	+	0.964464i	$0.414887\pi$
$108$	79.6601	7.66530
$109$	−18.7032	−1.79145	−0.895723	−	0.444613i	$-0.853341\pi$
$109$	−18.7032	−1.79145	−0.895723	+	0.444613i	$0.853341\pi$
$110$	−5.68587	−0.542126
$111$	−6.71288	−0.637158
$112$	−0.925955	−0.0874945
$113$	−1.97461	−0.185756	−0.0928780	−	0.995677i	$-0.529607\pi$
$113$	−1.97461	−0.185756	−0.0928780	+	0.995677i	$0.529607\pi$
$114$	26.4684	2.47899
$115$	−0.713897	−0.0665712
$116$	5.15446	0.478579
$117$	−5.77651	−0.534039
$118$	−8.55608	−0.787651
$119$	−0.306977	−0.0281405
$120$	9.63177	0.879256
$121$	23.5837	2.14397
$122$	18.3903	1.66498
$123$	24.1618	2.17859
$124$	2.86555	0.257334
$125$	3.59831	0.321843
$126$	1.70820	0.152179
$127$	−18.0852	−1.60480	−0.802401	−	0.596786i	$-0.796444\pi$
$127$	−18.0852	−1.60480	−0.802401	+	0.596786i	$0.796444\pi$
$128$	−9.43670	−0.834095
$129$	−28.0460	−2.46932
$130$	−0.714536	−0.0626690
$131$	4.82511	0.421572	0.210786	−	0.977532i	$-0.432398\pi$
$131$	4.82511	0.421572	0.210786	+	0.977532i	$0.432398\pi$
$132$	−97.2659	−8.46591
$133$	0.250223	0.0216971
$134$	19.8269	1.71279
$135$	−5.77656	−0.497167
$136$	−29.9069	−2.56449
$137$	22.3383	1.90849	0.954246	−	0.299022i	$-0.0966605\pi$
$137$	22.3383	1.90849	0.954246	+	0.299022i	$0.0966605\pi$
$138$	−17.0691	−1.45302
$139$	1.98469	0.168339	0.0841695	−	0.996451i	$-0.473176\pi$
$139$	1.98469	0.168339	0.0841695	+	0.996451i	$0.473176\pi$
$140$	0.151177	0.0127768
$141$	−13.9547	−1.17520
$142$	−0.218105	−0.0183030
$143$	4.34609	0.363438
$144$	87.8021	7.31684
$145$	−0.373776	−0.0310404
$146$	30.5538	2.52865
$147$	−22.9994	−1.89696
$148$	−10.2649	−0.843768
$149$	10.3531	0.848156	0.424078	−	0.905626i	$-0.360598\pi$
$149$	10.3531	0.848156	0.424078	+	0.905626i	$0.360598\pi$
$150$	42.4375	3.46501
$151$	−9.83547	−0.800400	−0.400200	−	0.916428i	$-0.631059\pi$
$151$	−9.83547	−0.800400	−0.400200	+	0.916428i	$0.631059\pi$
$152$	24.3777	1.97729
$153$	29.1086	2.35329
$154$	−1.28520	−0.103565
$155$	−0.207796	−0.0166906
$156$	−12.2233	−0.978646
$157$	20.9770	1.67414	0.837072	−	0.547093i	$-0.184266\pi$
$157$	20.9770	1.67414	0.837072	+	0.547093i	$0.184266\pi$
$158$	−2.90135	−0.230819
$159$	7.70106	0.610733
$160$	5.00355	0.395565
$161$	−0.161365	−0.0127174
$162$	−75.9473	−5.96698
$163$	9.91822	0.776855	0.388427	−	0.921479i	$-0.373018\pi$
$163$	9.91822	0.776855	0.388427	+	0.921479i	$0.373018\pi$
$164$	36.9465	2.88504
$165$	7.05324	0.549094
$166$	5.15914	0.400427
$167$	−18.7469	−1.45068	−0.725340	−	0.688391i	$-0.758317\pi$
$167$	−18.7469	−1.45068	−0.725340	+	0.688391i	$0.758317\pi$
$168$	2.17711	0.167968
$169$	−12.4538	−0.957987
$170$	3.60064	0.276156
$171$	−23.7270	−1.81445
$172$	−42.8861	−3.27004
$173$	−6.78346	−0.515737	−0.257869	−	0.966180i	$-0.583020\pi$
$173$	−6.78346	−0.515737	−0.257869	+	0.966180i	$0.583020\pi$
$174$	−8.93687	−0.677503
$175$	0.401190	0.0303271
$176$	−66.0598	−4.97945
$177$	10.6137	0.797775
$178$	9.69028	0.726317
$179$	18.8557	1.40934	0.704671	−	0.709534i	$-0.251095\pi$
$179$	18.8557	1.40934	0.704671	+	0.709534i	$0.251095\pi$
$180$	−14.3351	−1.06848
$181$	0.804250	0.0597795	0.0298897	−	0.999553i	$-0.490484\pi$
$181$	0.804250	0.0597795	0.0298897	+	0.999553i	$0.490484\pi$
$182$	−0.161510	−0.0119719
$183$	−22.8129	−1.68638
$184$	−15.7208	−1.15895
$185$	0.744358	0.0547263
$186$	−4.96834	−0.364297
$187$	−21.9005	−1.60152
$188$	−21.3386	−1.55628
$189$	−1.30570	−0.0949758
$190$	−2.93495	−0.212924
$191$	0.256214	0.0185390	0.00926951	−	0.999957i	$-0.497049\pi$
$191$	0.256214	0.0185390	0.00926951	+	0.999957i	$0.497049\pi$
$192$	45.7459	3.30143
$193$	20.6833	1.48882	0.744409	−	0.667724i	$-0.232732\pi$
$193$	20.6833	1.48882	0.744409	+	0.667724i	$0.232732\pi$
$194$	30.3177	2.17668
$195$	0.886372	0.0634744
$196$	−35.1691	−2.51208
$197$	−3.09668	−0.220630	−0.110315	−	0.993897i	$-0.535186\pi$
$197$	−3.09668	−0.220630	−0.110315	+	0.993897i	$0.535186\pi$
$198$	121.867	8.66072
$199$	−2.32269	−0.164651	−0.0823257	−	0.996605i	$-0.526235\pi$
$199$	−2.32269	−0.164651	−0.0823257	+	0.996605i	$0.526235\pi$
$200$	39.0854	2.76376
$201$	−24.5950	−1.73480
$202$	29.7821	2.09546
$203$	−0.0844862	−0.00592977
$204$	61.5947	4.31249
$205$	−2.67918	−0.187122
$206$	−20.7938	−1.44877
$207$	15.3012	1.06351
$208$	−8.30166	−0.575616
$209$	17.8515	1.23482
$210$	−0.262113	−0.0180875
$211$	16.2228	1.11682	0.558412	−	0.829564i	$-0.311411\pi$
$211$	16.2228	1.11682	0.558412	+	0.829564i	$0.311411\pi$
$212$	11.7759	0.808774
$213$	0.270557	0.0185382
$214$	−14.4920	−0.990651
$215$	3.10989	0.212093
$216$	−127.206	−8.65530
$217$	−0.0469690	−0.00318846
$218$	49.5867	3.35843
$219$	−37.9016	−2.56115
$220$	10.7853	0.727148
$221$	−2.75221	−0.185134
$222$	17.7974	1.19448
$223$	−4.14093	−0.277297	−0.138649	−	0.990342i	$-0.544276\pi$
$223$	−4.14093	−0.277297	−0.138649	+	0.990342i	$0.544276\pi$
$224$	1.13097	0.0755664
$225$	−38.0421	−2.53614
$226$	5.23516	0.348238
$227$	−8.60175	−0.570918	−0.285459	−	0.958391i	$-0.592146\pi$
$227$	−8.60175	−0.570918	−0.285459	+	0.958391i	$0.592146\pi$
$228$	−50.2070	−3.32504
$229$	−7.80450	−0.515736	−0.257868	−	0.966180i	$-0.583020\pi$
$229$	−7.80450	−0.515736	−0.257868	+	0.966180i	$0.583020\pi$
$230$	1.89271	0.124801
$231$	1.59428	0.104896
$232$	−8.23096	−0.540389
$233$	−23.6045	−1.54638	−0.773191	−	0.634174i	$-0.781340\pi$
$233$	−23.6045	−1.54638	−0.773191	+	0.634174i	$0.781340\pi$
$234$	15.3149	1.00117
$235$	1.54737	0.100939
$236$	16.2298	1.05647
$237$	3.59908	0.233785
$238$	0.813868	0.0527552
$239$	−22.1621	−1.43354	−0.716772	−	0.697308i	$-0.754381\pi$
$239$	−22.1621	−1.43354	−0.716772	+	0.697308i	$0.754381\pi$
$240$	−13.4727	−0.869660
$241$	−10.0878	−0.649811	−0.324906	−	0.945746i	$-0.605333\pi$
$241$	−10.0878	−0.649811	−0.324906	+	0.945746i	$0.605333\pi$
$242$	−62.5259	−4.01932
$243$	46.6914	2.99526
$244$	−34.8840	−2.23322
$245$	2.55029	0.162932
$246$	−64.0585	−4.08422
$247$	2.24338	0.142743
$248$	−4.57590	−0.290570
$249$	−6.39984	−0.405573
$250$	−9.53996	−0.603360
$251$	−18.0596	−1.13991	−0.569956	−	0.821675i	$-0.693040\pi$
$251$	−18.0596	−1.13991	−0.569956	+	0.821675i	$0.693040\pi$
$252$	−3.24023	−0.204115
$253$	−11.5122	−0.723765
$254$	47.9481	3.00853
$255$	−4.46654	−0.279706
$256$	−2.80014	−0.175009
$257$	−4.97203	−0.310147	−0.155073	−	0.987903i	$-0.549561\pi$
$257$	−4.97203	−0.310147	−0.155073	+	0.987903i	$0.549561\pi$
$258$	74.3566	4.62924
$259$	0.168251	0.0104546
$260$	1.35538	0.0840572
$261$	8.01125	0.495884
$262$	−12.7925	−0.790323
$263$	14.7305	0.908320	0.454160	−	0.890920i	$-0.349939\pi$
$263$	14.7305	0.908320	0.454160	+	0.890920i	$0.349939\pi$
$264$	155.320	9.55931
$265$	−0.853933	−0.0524567
$266$	−0.663400	−0.0406756
$267$	−12.0207	−0.735652
$268$	−37.6091	−2.29734
$269$	28.3621	1.72927	0.864634	−	0.502403i	$-0.167551\pi$
$269$	28.3621	1.72927	0.864634	+	0.502403i	$0.167551\pi$
$270$	15.3150	0.932042
$271$	5.69416	0.345896	0.172948	−	0.984931i	$-0.444671\pi$
$271$	5.69416	0.345896	0.172948	+	0.984931i	$0.444671\pi$
$272$	41.8331	2.53650
$273$	0.200351	0.0121258
$274$	−59.2241	−3.57786
$275$	28.6219	1.72596
$276$	32.3778	1.94891
$277$	−11.4341	−0.687006	−0.343503	−	0.939152i	$-0.611614\pi$
$277$	−11.4341	−0.687006	−0.343503	+	0.939152i	$0.611614\pi$
$278$	−5.26187	−0.315586
$279$	4.45376	0.266639
$280$	−0.241409	−0.0144270
$281$	−22.1251	−1.31988	−0.659938	−	0.751320i	$-0.729417\pi$
$281$	−22.1251	−1.31988	−0.659938	+	0.751320i	$0.729417\pi$
$282$	36.9971	2.20315
$283$	−8.37670	−0.497943	−0.248971	−	0.968511i	$-0.580093\pi$
$283$	−8.37670	−0.497943	−0.248971	+	0.968511i	$0.580093\pi$
$284$	0.413717	0.0245496
$285$	3.64076	0.215660
$286$	−11.5225	−0.681340
$287$	−0.605587	−0.0357467
$288$	−107.243	−6.31934
$289$	−3.13128	−0.184193
$290$	0.990967	0.0581916
$291$	−37.6087	−2.20466
$292$	−57.9565	−3.39165
$293$	−14.5433	−0.849630	−0.424815	−	0.905280i	$-0.639661\pi$
$293$	−14.5433	−0.849630	−0.424815	+	0.905280i	$0.639661\pi$
$294$	60.9767	3.55624
$295$	−1.17690	−0.0685219
$296$	16.3916	0.952743
$297$	−93.1519	−5.40522
$298$	−27.4484	−1.59004
$299$	−1.44672	−0.0836661
$300$	−80.4984	−4.64757
$301$	0.702942	0.0405169
$302$	26.0761	1.50051
$303$	−36.9443	−2.12240
$304$	−34.0990	−1.95571
$305$	2.52961	0.144845
$306$	−77.1736	−4.41172
$307$	−8.66699	−0.494651	−0.247326	−	0.968932i	$-0.579552\pi$
$307$	−8.66699	−0.494651	−0.247326	+	0.968932i	$0.579552\pi$
$308$	2.43786	0.138910
$309$	25.7944	1.46739
$310$	0.550915	0.0312899
$311$	−7.63159	−0.432748	−0.216374	−	0.976311i	$-0.569423\pi$
$311$	−7.63159	−0.432748	−0.216374	+	0.976311i	$0.569423\pi$
$312$	19.5189	1.10504
$313$	12.3991	0.700837	0.350419	−	0.936593i	$-0.386039\pi$
$313$	12.3991	0.700837	0.350419	+	0.936593i	$0.386039\pi$
$314$	−55.6148	−3.13853
$315$	0.234965	0.0132388
$316$	5.50347	0.309594
$317$	−22.7280	−1.27653	−0.638266	−	0.769816i	$-0.720348\pi$
$317$	−22.7280	−1.27653	−0.638266	+	0.769816i	$0.720348\pi$
$318$	−20.4173	−1.14495
$319$	−6.02745	−0.337472
$320$	−5.07254	−0.283564
$321$	17.9771	1.00338
$322$	0.427817	0.0238413
$323$	−11.3047	−0.629008
$324$	144.062	8.00344
$325$	3.59687	0.199519
$326$	−26.2955	−1.45637
$327$	−61.5116	−3.40160
$328$	−58.9986	−3.25765
$329$	0.349758	0.0192828
$330$	−18.6998	−1.02939
$331$	8.36864	0.459982	0.229991	−	0.973193i	$-0.426130\pi$
$331$	8.36864	0.459982	0.229991	+	0.973193i	$0.426130\pi$
$332$	−9.78620	−0.537088
$333$	−15.9541	−0.874278
$334$	49.7024	2.71960
$335$	2.72722	0.149004
$336$	−3.04530	−0.166135
$337$	−4.65990	−0.253841	−0.126921	−	0.991913i	$-0.540509\pi$
$337$	−4.65990	−0.253841	−0.126921	+	0.991913i	$0.540509\pi$
$338$	33.0180	1.79594
$339$	−6.49414	−0.352714
$340$	−6.82993	−0.370405
$341$	−3.35088	−0.181460
$342$	62.9057	3.40155
$343$	1.15347	0.0622814
$344$	68.4833	3.69237
$345$	−2.34788	−0.126405
$346$	17.9845	0.966855
$347$	−8.02063	−0.430570	−0.215285	−	0.976551i	$-0.569068\pi$
$347$	−8.02063	−0.430570	−0.215285	+	0.976551i	$0.569068\pi$
$348$	16.9521	0.908726
$349$	16.6101	0.889118	0.444559	−	0.895750i	$-0.353360\pi$
$349$	16.6101	0.889118	0.444559	+	0.895750i	$0.353360\pi$
$350$	−1.06365	−0.0568544
$351$	−11.7063	−0.624835
$352$	80.6865	4.30060
$353$	−36.4033	−1.93755	−0.968776	−	0.247939i	$-0.920247\pi$
$353$	−36.4033	−1.93755	−0.968776	+	0.247939i	$0.920247\pi$
$354$	−28.1394	−1.49559
$355$	−0.0300007	−0.00159227
$356$	−18.3812	−0.974200
$357$	−1.00959	−0.0534333
$358$	−49.9909	−2.64210
$359$	−7.50308	−0.395997	−0.197999	−	0.980202i	$-0.563444\pi$
$359$	−7.50308	−0.395997	−0.197999	+	0.980202i	$0.563444\pi$
$360$	22.8912	1.20647
$361$	−9.78535	−0.515018
$362$	−2.13226	−0.112069
$363$	77.5625	4.07097
$364$	0.306363	0.0160578
$365$	4.20272	0.219980
$366$	60.4823	3.16146
$367$	−36.5739	−1.90914	−0.954571	−	0.297984i	$-0.903686\pi$
$367$	−36.5739	−1.90914	−0.954571	+	0.297984i	$0.903686\pi$
$368$	21.9899	1.14630
$369$	57.4237	2.98936
$370$	−1.97347	−0.102596
$371$	−0.193018	−0.0100210
$372$	9.42429	0.488627
$373$	−3.14089	−0.162629	−0.0813146	−	0.996688i	$-0.525912\pi$
$373$	−3.14089	−0.162629	−0.0813146	+	0.996688i	$0.525912\pi$
$374$	58.0633	3.00238
$375$	11.8342	0.611115
$376$	34.0748	1.75727
$377$	−0.757462	−0.0390113
$378$	3.46172	0.178052
$379$	−9.85195	−0.506061	−0.253030	−	0.967458i	$-0.581427\pi$
$379$	−9.85195	−0.506061	−0.253030	+	0.967458i	$0.581427\pi$
$380$	5.56721	0.285592
$381$	−59.4789	−3.04720
$382$	−0.679284	−0.0347552
$383$	9.65220	0.493204	0.246602	−	0.969117i	$-0.420686\pi$
$383$	9.65220	0.493204	0.246602	+	0.969117i	$0.420686\pi$
$384$	−31.0356	−1.58378
$385$	−0.176782	−0.00900962
$386$	−54.8363	−2.79109
$387$	−66.6553	−3.38828
$388$	−57.5087	−2.91956
$389$	−24.8145	−1.25814	−0.629072	−	0.777347i	$-0.716565\pi$
$389$	−24.8145	−1.25814	−0.629072	+	0.777347i	$0.716565\pi$
$390$	−2.34998	−0.118996
$391$	7.29021	0.368682
$392$	56.1603	2.83652
$393$	15.8689	0.800481
$394$	8.21003	0.413616
$395$	−0.399084	−0.0200801
$396$	−231.166	−11.6165
$397$	33.7332	1.69302	0.846510	−	0.532374i	$-0.178700\pi$
$397$	33.7332	1.69302	0.846510	+	0.532374i	$0.178700\pi$
$398$	6.15800	0.308673
$399$	0.822938	0.0411984
$400$	−54.6719	−2.73359
$401$	25.8087	1.28882	0.644412	−	0.764678i	$-0.277102\pi$
$401$	25.8087	1.28882	0.644412	+	0.764678i	$0.277102\pi$
$402$	65.2072	3.25224
$403$	−0.421101	−0.0209766
$404$	−56.4928	−2.81062
$405$	−10.4467	−0.519099
$406$	0.223993	0.0111166
$407$	12.0034	0.594986
$408$	−98.3583	−4.86946
$409$	14.0107	0.692784	0.346392	−	0.938090i	$-0.387407\pi$
$409$	14.0107	0.692784	0.346392	+	0.938090i	$0.387407\pi$
$410$	7.10313	0.350799
$411$	73.4667	3.62385
$412$	39.4431	1.94322
$413$	−0.266020	−0.0130900
$414$	−40.5670	−1.99376
$415$	0.709647	0.0348352
$416$	10.1398	0.497143
$417$	6.52728	0.319642
$418$	−47.3285	−2.31491
$419$	1.08090	0.0528055	0.0264028	−	0.999651i	$-0.491595\pi$
$419$	1.08090	0.0528055	0.0264028	+	0.999651i	$0.491595\pi$
$420$	0.497194	0.0242606
$421$	−10.3513	−0.504492	−0.252246	−	0.967663i	$-0.581169\pi$
$421$	−10.3513	−0.504492	−0.252246	+	0.967663i	$0.581169\pi$
$422$	−43.0105	−2.09372
$423$	−33.1652	−1.61255
$424$	−18.8046	−0.913230
$425$	−18.1251	−0.879196
$426$	−0.717309	−0.0347537
$427$	0.571780	0.0276704
$428$	27.4894	1.32875
$429$	14.2935	0.690097
$430$	−8.24504	−0.397611
$431$	−7.07192	−0.340643	−0.170321	−	0.985389i	$-0.554481\pi$
$431$	−7.07192	−0.340643	−0.170321	+	0.985389i	$0.554481\pi$
$432$	177.934	8.56083
$433$	−11.1179	−0.534291	−0.267145	−	0.963656i	$-0.586080\pi$
$433$	−11.1179	−0.534291	−0.267145	+	0.963656i	$0.586080\pi$
$434$	0.124526	0.00597743
$435$	−1.22928	−0.0589395
$436$	−94.0594	−4.50463
$437$	−5.94240	−0.284263
$438$	100.486	4.80140
$439$	0.0168762	0.000805457 0	0.000402729	−	1.00000i	$-0.499872\pi$
$439$	0.0168762	0.000805457 0	0.000402729		1.00000i	$0.499872\pi$
$440$	−17.2227	−0.821061
$441$	−54.6612	−2.60291
$442$	7.29674	0.347071
$443$	−12.1376	−0.576673	−0.288336	−	0.957529i	$-0.593102\pi$
$443$	−12.1376	−0.576673	−0.288336	+	0.957529i	$0.593102\pi$
$444$	−33.7593	−1.60215
$445$	1.33291	0.0631861
$446$	10.9786	0.519850
$447$	34.0493	1.61048
$448$	−1.14657	−0.0541703
$449$	−26.8023	−1.26488	−0.632440	−	0.774610i	$-0.717946\pi$
$449$	−26.8023	−1.26488	−0.632440	+	0.774610i	$0.717946\pi$
$450$	100.859	4.75452
$451$	−43.2040	−2.03440
$452$	−9.93041	−0.467087
$453$	−32.3471	−1.51980
$454$	22.8053	1.07030
$455$	−0.0222159	−0.00104150
$456$	80.1738	3.75448
$457$	−13.3556	−0.624749	−0.312374	−	0.949959i	$-0.601124\pi$
$457$	−13.3556	−0.624749	−0.312374	+	0.949959i	$0.601124\pi$
$458$	20.6916	0.966853
$459$	58.9894	2.75339
$460$	−3.59022	−0.167395
$461$	26.7143	1.24421	0.622104	−	0.782934i	$-0.286278\pi$
$461$	26.7143	1.24421	0.622104	+	0.782934i	$0.286278\pi$
$462$	−4.22680	−0.196648
$463$	28.1775	1.30952	0.654760	−	0.755837i	$-0.272770\pi$
$463$	28.1775	1.30952	0.654760	+	0.755837i	$0.272770\pi$
$464$	11.5133	0.534491
$465$	−0.683403	−0.0316921
$466$	62.5810	2.89901
$467$	−20.9129	−0.967732	−0.483866	−	0.875142i	$-0.660768\pi$
$467$	−20.9129	−0.967732	−0.483866	+	0.875142i	$0.660768\pi$
$468$	−29.0503	−1.34285
$469$	0.616446	0.0284648
$470$	−4.10243	−0.189231
$471$	68.9894	3.17886
$472$	−25.9167	−1.19291
$473$	50.1496	2.30588
$474$	−9.54200	−0.438279
$475$	14.7741	0.677883
$476$	−1.54380	−0.0707600
$477$	18.3026	0.838019
$478$	58.7568	2.68747
$479$	39.3510	1.79799	0.898996	−	0.437956i	$-0.144297\pi$
$479$	39.3510	1.79799	0.898996	+	0.437956i	$0.144297\pi$
$480$	16.4558	0.751100
$481$	1.50845	0.0687795
$482$	26.7451	1.21820
$483$	−0.530701	−0.0241477
$484$	118.603	5.39106
$485$	4.17024	0.189361
$486$	−123.790	−5.61522
$487$	25.4425	1.15291	0.576455	−	0.817129i	$-0.304435\pi$
$487$	25.4425	1.15291	0.576455	+	0.817129i	$0.304435\pi$
$488$	55.7049	2.52164
$489$	32.6192	1.47509
$490$	−6.76141	−0.305450
$491$	29.0083	1.30913	0.654563	−	0.756008i	$-0.272853\pi$
$491$	29.0083	1.30913	0.654563	+	0.756008i	$0.272853\pi$
$492$	121.510	5.47811
$493$	3.81694	0.171907
$494$	−5.94772	−0.267600
$495$	16.7630	0.753441
$496$	6.40067	0.287399
$497$	−0.00678119	−0.000304178 0
$498$	16.9675	0.760330
$499$	39.3761	1.76272	0.881359	−	0.472448i	$-0.156630\pi$
$499$	39.3761	1.76272	0.881359	+	0.472448i	$0.156630\pi$
$500$	18.0961	0.809280
$501$	−61.6552	−2.75455
$502$	47.8803	2.13700
$503$	31.7662	1.41638	0.708191	−	0.706020i	$-0.249511\pi$
$503$	31.7662	1.41638	0.708191	+	0.706020i	$0.249511\pi$
$504$	5.17421	0.230477
$505$	4.09658	0.182295
$506$	30.5215	1.35685
$507$	−40.9584	−1.81903
$508$	−90.9511	−4.03530
$509$	2.14992	0.0952936	0.0476468	−	0.998864i	$-0.484828\pi$
$509$	2.14992	0.0952936	0.0476468	+	0.998864i	$0.484828\pi$
$510$	11.8418	0.524366
$511$	0.949959	0.0420237
$512$	26.2972	1.16218
$513$	−48.0834	−2.12294
$514$	13.1820	0.581433
$515$	−2.86022	−0.126036
$516$	−141.045	−6.20914
$517$	24.9526	1.09741
$518$	−0.446072	−0.0195993
$519$	−22.3096	−0.979282
$520$	−2.16436	−0.0949134
$521$	−16.5039	−0.723049	−0.361525	−	0.932363i	$-0.617744\pi$
$521$	−16.5039	−0.723049	−0.361525	+	0.932363i	$0.617744\pi$
$522$	−21.2397	−0.929637
$523$	−0.766630	−0.0335224	−0.0167612	−	0.999860i	$-0.505336\pi$
$523$	−0.766630	−0.0335224	−0.0167612	+	0.999860i	$0.505336\pi$
$524$	24.2657	1.06005
$525$	1.31944	0.0575851
$526$	−39.0539	−1.70283
$527$	2.12198	0.0924350
$528$	−217.259	−9.45498
$529$	−19.1678	−0.833384
$530$	2.26397	0.0983408
$531$	25.2249	1.09467
$532$	1.25838	0.0545578
$533$	−5.42940	−0.235173
$534$	31.8696	1.37913
$535$	−1.99339	−0.0861819
$536$	60.0565	2.59405
$537$	62.0130	2.67606
$538$	−75.1945	−3.24187
$539$	41.1256	1.77140
$540$	−29.0506	−1.25014
$541$	−8.45963	−0.363708	−0.181854	−	0.983326i	$-0.558210\pi$
$541$	−8.45963	−0.363708	−0.181854	+	0.983326i	$0.558210\pi$
$542$	−15.0966	−0.648452
$543$	2.64503	0.113509
$544$	−51.0956	−2.19070
$545$	6.82072	0.292168
$546$	−0.531176	−0.0227323
$547$	9.71151	0.415234	0.207617	−	0.978210i	$-0.433429\pi$
$547$	9.71151	0.415234	0.207617	+	0.978210i	$0.433429\pi$
$548$	112.340	4.79894
$549$	−54.2180	−2.31397
$550$	−75.8832	−3.23567
$551$	−3.11127	−0.132544
$552$	−51.7029	−2.20062
$553$	−0.0902068	−0.00383598
$554$	30.3144	1.28793
$555$	2.44806	0.103914
$556$	9.98107	0.423292
$557$	24.7590	1.04907	0.524537	−	0.851388i	$-0.324239\pi$
$557$	24.7590	1.04907	0.524537	+	0.851388i	$0.324239\pi$
$558$	−11.8079	−0.499870
$559$	6.30224	0.266556
$560$	0.337678	0.0142695
$561$	−72.0267	−3.04097
$562$	58.6589	2.47438
$563$	−29.9933	−1.26407	−0.632033	−	0.774942i	$-0.717779\pi$
$563$	−29.9933	−1.26407	−0.632033	+	0.774942i	$0.717779\pi$
$564$	−70.1787	−2.95506
$565$	0.720104	0.0302950
$566$	22.2086	0.933496
$567$	−2.36130	−0.0991655
$568$	−0.660650	−0.0277202
$569$	−39.1660	−1.64192	−0.820962	−	0.570982i	$-0.806562\pi$
$569$	−39.1660	−1.64192	−0.820962	+	0.570982i	$0.806562\pi$
$570$	−9.65252	−0.404299
$571$	−26.6349	−1.11463	−0.557317	−	0.830299i	$-0.688169\pi$
$571$	−26.6349	−1.11463	−0.557317	+	0.830299i	$0.688169\pi$
$572$	21.8567	0.913873
$573$	0.842642	0.0352019
$574$	1.60555	0.0670145
$575$	−9.52762	−0.397329
$576$	108.721	4.53006
$577$	32.7523	1.36349	0.681747	−	0.731588i	$-0.261220\pi$
$577$	32.7523	1.36349	0.681747	+	0.731588i	$0.261220\pi$
$578$	8.30176	0.345308
$579$	68.0237	2.82697
$580$	−1.87973	−0.0780516
$581$	0.160405	0.00665471
$582$	99.7094	4.13309
$583$	−13.7704	−0.570311
$584$	92.5486	3.82969
$585$	2.10659	0.0870966
$586$	38.5577	1.59281
$587$	8.05427	0.332435	0.166218	−	0.986089i	$-0.446845\pi$
$587$	8.05427	0.332435	0.166218	+	0.986089i	$0.446845\pi$
$588$	−115.665	−4.76994
$589$	−1.72967	−0.0712698
$590$	3.12024	0.128458
$591$	−10.1844	−0.418932
$592$	−22.9282	−0.942344
$593$	−34.4859	−1.41617	−0.708084	−	0.706128i	$-0.750440\pi$
$593$	−34.4859	−1.41617	−0.708084	+	0.706128i	$0.750440\pi$
$594$	246.967	10.1332
$595$	0.111949	0.00458945
$596$	52.0660	2.13270
$597$	−7.63892	−0.312640
$598$	3.83560	0.156849
$599$	−25.4487	−1.03981	−0.519903	−	0.854225i	$-0.674032\pi$
$599$	−25.4487	−1.03981	−0.519903	+	0.854225i	$0.674032\pi$
$600$	128.545	5.24782
$601$	4.47389	0.182494	0.0912468	−	0.995828i	$-0.470915\pi$
$601$	4.47389	0.182494	0.0912468	+	0.995828i	$0.470915\pi$
$602$	−1.86366	−0.0759573
$603$	−58.4535	−2.38041
$604$	−49.4630	−2.01262
$605$	−8.60053	−0.349661
$606$	97.9481	3.97887
$607$	−32.1434	−1.30466	−0.652329	−	0.757936i	$-0.726208\pi$
$607$	−32.1434	−1.30466	−0.652329	+	0.757936i	$0.726208\pi$
$608$	41.6490	1.68909
$609$	−0.277860	−0.0112594
$610$	−6.70659	−0.271542
$611$	3.13576	0.126859
$612$	146.388	5.91739
$613$	−16.1268	−0.651353	−0.325677	−	0.945481i	$-0.605592\pi$
$613$	−16.1268	−0.651353	−0.325677	+	0.945481i	$0.605592\pi$
$614$	22.9782	0.927326
$615$	−8.81134	−0.355307
$616$	−3.89293	−0.156851
$617$	−46.0015	−1.85195	−0.925976	−	0.377583i	$-0.876755\pi$
$617$	−46.0015	−1.85195	−0.925976	+	0.377583i	$0.876755\pi$
$618$	−68.3870	−2.75093
$619$	16.7869	0.674724	0.337362	−	0.941375i	$-0.390465\pi$
$619$	16.7869	0.674724	0.337362	+	0.941375i	$0.390465\pi$
$620$	−1.04501	−0.0419688
$621$	31.0083	1.24432
$622$	20.2331	0.811274
$623$	0.301284	0.0120707
$624$	−27.3027	−1.09298
$625$	23.0228	0.920912
$626$	−32.8728	−1.31386
$627$	58.7104	2.34467
$628$	105.494	4.20967
$629$	−7.60128	−0.303083
$630$	−0.622948	−0.0248189
$631$	9.33024	0.371431	0.185716	−	0.982604i	$-0.440540\pi$
$631$	9.33024	0.371431	0.185716	+	0.982604i	$0.440540\pi$
$632$	−8.78829	−0.349579
$633$	53.3539	2.12063
$634$	60.2572	2.39312
$635$	6.59533	0.261728
$636$	38.7289	1.53570
$637$	5.16820	0.204772
$638$	15.9802	0.632661
$639$	0.643015	0.0254373
$640$	3.44139	0.136033
$641$	24.0249	0.948927	0.474464	−	0.880275i	$-0.342642\pi$
$641$	24.0249	0.948927	0.474464	+	0.880275i	$0.342642\pi$
$642$	−47.6615	−1.88105
$643$	7.81599	0.308232	0.154116	−	0.988053i	$-0.450747\pi$
$643$	7.81599	0.308232	0.154116	+	0.988053i	$0.450747\pi$
$644$	−0.811512	−0.0319781
$645$	10.2279	0.402722
$646$	29.9713	1.17920
$647$	44.1087	1.73409	0.867047	−	0.498227i	$-0.166015\pi$
$647$	44.1087	1.73409	0.867047	+	0.498227i	$0.166015\pi$
$648$	−230.047	−9.03711
$649$	−18.9785	−0.744973
$650$	−9.53615	−0.374039
$651$	−0.154473	−0.00605426
$652$	49.8791	1.95342
$653$	−20.6105	−0.806549	−0.403275	−	0.915079i	$-0.632128\pi$
$653$	−20.6105	−0.806549	−0.403275	+	0.915079i	$0.632128\pi$
$654$	163.082	6.37699
$655$	−1.75963	−0.0687543
$656$	82.5259	3.22210
$657$	−90.0782	−3.51429
$658$	−0.927291	−0.0361496
$659$	35.2970	1.37497	0.687487	−	0.726197i	$-0.258714\pi$
$659$	35.2970	1.37497	0.687487	+	0.726197i	$0.258714\pi$
$660$	35.4710	1.38071
$661$	19.8819	0.773315	0.386658	−	0.922223i	$-0.373629\pi$
$661$	19.8819	0.773315	0.386658	+	0.922223i	$0.373629\pi$
$662$	−22.1872	−0.862330
$663$	−9.05151	−0.351532
$664$	15.6272	0.606454
$665$	−0.0912516	−0.00353859
$666$	42.2980	1.63901
$667$	2.00641	0.0776885
$668$	−94.2789	−3.64776
$669$	−13.6188	−0.526532
$670$	−7.23051	−0.279339
$671$	40.7921	1.57476
$672$	3.71957	0.143486
$673$	−12.7306	−0.490727	−0.245364	−	0.969431i	$-0.578907\pi$
$673$	−12.7306	−0.490727	−0.245364	+	0.969431i	$0.578907\pi$
$674$	12.3545	0.475877
$675$	−77.0936	−2.96733
$676$	−62.6308	−2.40888
$677$	5.81647	0.223545	0.111773	−	0.993734i	$-0.464347\pi$
$677$	5.81647	0.223545	0.111773	+	0.993734i	$0.464347\pi$
$678$	17.2175	0.661234
$679$	0.942619	0.0361744
$680$	10.9065	0.418244
$681$	−28.2896	−1.08406
$682$	8.88397	0.340185
$683$	−21.4999	−0.822670	−0.411335	−	0.911484i	$-0.634937\pi$
$683$	−21.4999	−0.822670	−0.411335	+	0.911484i	$0.634937\pi$
$684$	−119.324	−4.56246
$685$	−8.14637	−0.311257
$686$	−3.05811	−0.116759
$687$	−25.6676	−0.979280
$688$	−95.7929	−3.65207
$689$	−1.73051	−0.0659271
$690$	6.22477	0.236973
$691$	19.8481	0.755056	0.377528	−	0.925998i	$-0.376774\pi$
$691$	19.8481	0.755056	0.377528	+	0.925998i	$0.376774\pi$
$692$	−34.1143	−1.29683
$693$	3.78902	0.143933
$694$	21.2646	0.807191
$695$	−0.723778	−0.0274545
$696$	−27.0701	−1.02609
$697$	27.3594	1.03631
$698$	−44.0372	−1.66683
$699$	−77.6309	−2.93627
$700$	2.01760	0.0762581
$701$	−46.3893	−1.75210	−0.876050	−	0.482221i	$-0.839830\pi$
$701$	−46.3893	−1.75210	−0.876050	+	0.482221i	$0.839830\pi$
$702$	31.0361	1.17138
$703$	6.19595	0.233685
$704$	−81.7990	−3.08292
$705$	5.08901	0.191663
$706$	96.5136	3.63234
$707$	0.925968	0.0348246
$708$	53.3767	2.00602
$709$	32.4018	1.21688	0.608438	−	0.793602i	$-0.291797\pi$
$709$	32.4018	1.21688	0.608438	+	0.793602i	$0.291797\pi$
$710$	0.0795389	0.00298504
$711$	8.55371	0.320789
$712$	29.3522	1.10002
$713$	1.11544	0.0417735
$714$	2.67666	0.100172
$715$	−1.58494	−0.0592733
$716$	94.8261	3.54382
$717$	−72.8870	−2.72201
$718$	19.8924	0.742378
$719$	7.47583	0.278801	0.139401	−	0.990236i	$-0.455482\pi$
$719$	7.47583	0.278801	0.139401	+	0.990236i	$0.455482\pi$
$720$	−32.0198	−1.19331
$721$	−0.646508	−0.0240772
$722$	25.9433	0.965508
$723$	−33.1769	−1.23386
$724$	4.04461	0.150317
$725$	−4.98838	−0.185264
$726$	−205.636	−7.63188
$727$	20.4110	0.757003	0.378502	−	0.925601i	$-0.376439\pi$
$727$	20.4110	0.757003	0.378502	+	0.925601i	$0.376439\pi$
$728$	−0.489220	−0.0181317
$729$	67.6216	2.50450
$730$	−11.1424	−0.412398
$731$	−31.7578	−1.17460
$732$	−114.727	−4.24043
$733$	−14.8273	−0.547660	−0.273830	−	0.961778i	$-0.588290\pi$
$733$	−14.8273	−0.547660	−0.273830	+	0.961778i	$0.588290\pi$
$734$	96.9659	3.57908
$735$	8.38744	0.309375
$736$	−26.8588	−0.990030
$737$	43.9788	1.61998
$738$	−152.244	−5.60417
$739$	19.0781	0.701801	0.350900	−	0.936413i	$-0.385876\pi$
$739$	19.0781	0.701801	0.350900	+	0.936413i	$0.385876\pi$
$740$	3.74341	0.137610
$741$	7.37806	0.271040
$742$	0.511736	0.0187864
$743$	27.6872	1.01574	0.507872	−	0.861433i	$-0.330432\pi$
$743$	27.6872	1.01574	0.507872	+	0.861433i	$0.330432\pi$
$744$	−15.0493	−0.551734
$745$	−3.77557	−0.138326
$746$	8.32723	0.304882
$747$	−15.2101	−0.556508
$748$	−110.138	−4.02706
$749$	−0.450575	−0.0164637
$750$	−31.3752	−1.14566
$751$	32.0078	1.16798	0.583991	−	0.811760i	$-0.301490\pi$
$751$	32.0078	1.16798	0.583991	+	0.811760i	$0.301490\pi$
$752$	−47.6631	−1.73809
$753$	−59.3948	−2.16447
$754$	2.00821	0.0731346
$755$	3.58681	0.130537
$756$	−6.56643	−0.238819
$757$	−2.57691	−0.0936592	−0.0468296	−	0.998903i	$-0.514912\pi$
$757$	−2.57691	−0.0936592	−0.0468296	+	0.998903i	$0.514912\pi$
$758$	26.1198	0.948715
$759$	−37.8615	−1.37429
$760$	−8.89008	−0.322477
$761$	−13.7919	−0.499956	−0.249978	−	0.968252i	$-0.580423\pi$
$761$	−13.7919	−0.499956	−0.249978	+	0.968252i	$0.580423\pi$
$762$	157.692	5.71260
$763$	1.54172	0.0558139
$764$	1.28851	0.0466167
$765$	−10.6153	−0.383799
$766$	−25.5902	−0.924613
$767$	−2.38501	−0.0861177
$768$	−9.20916	−0.332307
$769$	11.9357	0.430413	0.215206	−	0.976569i	$-0.430958\pi$
$769$	11.9357	0.430413	0.215206	+	0.976569i	$0.430958\pi$
$770$	0.468689	0.0168904
$771$	−16.3521	−0.588906
$772$	104.017	3.74366
$773$	37.9229	1.36399	0.681996	−	0.731356i	$-0.261112\pi$
$773$	37.9229	1.36399	0.681996	+	0.731356i	$0.261112\pi$
$774$	176.719	6.35202
$775$	−2.77323	−0.0996173
$776$	91.8335	3.29663
$777$	0.553346	0.0198512
$778$	65.7890	2.35865
$779$	−22.3012	−0.799023
$780$	4.45760	0.159608
$781$	−0.483787	−0.0173112
$782$	−19.3281	−0.691170
$783$	16.2351	0.580194
$784$	−78.5558	−2.80556
$785$	−7.64990	−0.273037
$786$	−42.0722	−1.50067
$787$	−41.8666	−1.49238	−0.746191	−	0.665732i	$-0.768119\pi$
$787$	−41.8666	−1.49238	−0.746191	+	0.665732i	$0.768119\pi$
$788$	−15.5733	−0.554778
$789$	48.4459	1.72472
$790$	1.05807	0.0376443
$791$	0.162768	0.00578738
$792$	369.140	13.1168
$793$	5.12630	0.182040
$794$	−89.4345	−3.17391
$795$	−2.80843	−0.0996047
$796$	−11.6809	−0.414019
$797$	6.40054	0.226719	0.113359	−	0.993554i	$-0.463839\pi$
$797$	6.40054	0.226719	0.113359	+	0.993554i	$0.463839\pi$
$798$	−2.18180	−0.0772349
$799$	−15.8015	−0.559017
$800$	66.7770	2.36092
$801$	−28.5687	−1.00943
$802$	−68.4249	−2.41617
$803$	67.7724	2.39164
$804$	−123.689	−4.36219
$805$	0.0588469	0.00207408
$806$	1.11644	0.0393248
$807$	93.2778	3.28353
$808$	90.2113	3.17362
$809$	1.10511	0.0388536	0.0194268	−	0.999811i	$-0.493816\pi$
$809$	1.10511	0.0388536	0.0194268	+	0.999811i	$0.493816\pi$
$810$	27.6965	0.973157
$811$	31.1366	1.09335	0.546677	−	0.837343i	$-0.315892\pi$
$811$	31.1366	1.09335	0.546677	+	0.837343i	$0.315892\pi$
$812$	−0.424884	−0.0149105
$813$	18.7271	0.656787
$814$	−31.8238	−1.11542
$815$	−3.61699	−0.126698
$816$	137.581	4.81632
$817$	25.8864	0.905649
$818$	−37.1456	−1.29877
$819$	0.476161	0.0166384
$820$	−13.4737	−0.470522
$821$	−27.6939	−0.966524	−0.483262	−	0.875476i	$-0.660548\pi$
$821$	−27.6939	−0.966524	−0.483262	+	0.875476i	$0.660548\pi$
$822$	−194.777	−6.79364
$823$	9.20813	0.320975	0.160488	−	0.987038i	$-0.448693\pi$
$823$	9.20813	0.320975	0.160488	+	0.987038i	$0.448693\pi$
$824$	−62.9852	−2.19419
$825$	94.1321	3.27726
$826$	0.705282	0.0245399
$827$	47.7117	1.65910	0.829550	−	0.558433i	$-0.188597\pi$
$827$	47.7117	1.65910	0.829550	+	0.558433i	$0.188597\pi$
$828$	76.9502	2.67421
$829$	−12.5878	−0.437194	−0.218597	−	0.975815i	$-0.570148\pi$
$829$	−12.5878	−0.437194	−0.218597	+	0.975815i	$0.570148\pi$
$830$	−1.88144	−0.0653057
$831$	−37.6046	−1.30449
$832$	−10.2796	−0.356380
$833$	−26.0432	−0.902344
$834$	−17.3053	−0.599235
$835$	6.83664	0.236592
$836$	89.7760	3.10497
$837$	9.02567	0.311973
$838$	−2.86572	−0.0989948
$839$	−44.0316	−1.52014	−0.760070	−	0.649841i	$-0.774835\pi$
$839$	−44.0316	−1.52014	−0.760070	+	0.649841i	$0.774835\pi$
$840$	−0.793952	−0.0273939
$841$	−27.9495	−0.963776
$842$	27.4438	0.945774
$843$	−72.7656	−2.50618
$844$	81.5851	2.80828
$845$	4.54168	0.156238
$846$	87.9288	3.02305
$847$	−1.94402	−0.0667972
$848$	26.3034	0.903263
$849$	−27.5494	−0.945494
$850$	48.0538	1.64823
$851$	−3.99568	−0.136970
$852$	1.36064	0.0466148
$853$	−21.3432	−0.730778	−0.365389	−	0.930855i	$-0.619064\pi$
$853$	−21.3432	−0.730778	−0.365389	+	0.930855i	$0.619064\pi$
$854$	−1.51592	−0.0518738
$855$	8.65278	0.295919
$856$	−43.8968	−1.50036
$857$	18.0976	0.618202	0.309101	−	0.951029i	$-0.399972\pi$
$857$	18.0976	0.618202	0.309101	+	0.951029i	$0.399972\pi$
$858$	−37.8954	−1.29373
$859$	−27.4954	−0.938133	−0.469066	−	0.883163i	$-0.655409\pi$
$859$	−27.4954	−0.938133	−0.469066	+	0.883163i	$0.655409\pi$
$860$	15.6398	0.533311
$861$	−1.99167	−0.0678758
$862$	18.7493	0.638604
$863$	15.6664	0.533292	0.266646	−	0.963795i	$-0.414085\pi$
$863$	15.6664	0.533292	0.266646	+	0.963795i	$0.414085\pi$
$864$	−217.331	−7.39374
$865$	2.47380	0.0841117
$866$	29.4761	1.00164
$867$	−10.2982	−0.349746
$868$	−0.236209	−0.00801746
$869$	−6.43557	−0.218312
$870$	3.25911	0.110494
$871$	5.52676	0.187267
$872$	150.200	5.08641
$873$	−89.3822	−3.02513
$874$	15.7547	0.532910
$875$	−0.296611	−0.0100273
$876$	−190.608	−6.44006
$877$	−10.6926	−0.361065	−0.180533	−	0.983569i	$-0.557782\pi$
$877$	−10.6926	−0.361065	−0.180533	+	0.983569i	$0.557782\pi$
$878$	−0.0447428	−0.00151000
$879$	−47.8303	−1.61328
$880$	24.0908	0.812100
$881$	−43.8331	−1.47678	−0.738388	−	0.674376i	$-0.764413\pi$
$881$	−43.8331	−1.47678	−0.738388	+	0.674376i	$0.764413\pi$
$882$	144.920	4.87970
$883$	30.3859	1.02257	0.511283	−	0.859412i	$-0.329170\pi$
$883$	30.3859	1.02257	0.511283	+	0.859412i	$0.329170\pi$
$884$	−13.8410	−0.465522
$885$	−3.87062	−0.130109
$886$	32.1795	1.08109
$887$	−45.9703	−1.54353	−0.771766	−	0.635906i	$-0.780626\pi$
$887$	−45.9703	−1.54353	−0.771766	+	0.635906i	$0.780626\pi$
$888$	53.9090	1.80907
$889$	1.49077	0.0499989
$890$	−3.53386	−0.118455
$891$	−168.461	−5.64366
$892$	−20.8249	−0.697269
$893$	12.8801	0.431016
$894$	−90.2728	−3.01917
$895$	−6.87632	−0.229850
$896$	0.777872	0.0259869
$897$	−4.75801	−0.158865
$898$	71.0592	2.37128
$899$	0.584011	0.0194779
$900$	−191.315	−6.37718
$901$	8.72024	0.290513
$902$	114.544	3.81390
$903$	2.31185	0.0769335
$904$	15.8575	0.527413
$905$	−0.293295	−0.00974945
$906$	85.7597	2.84918
$907$	−2.58206	−0.0857358	−0.0428679	−	0.999081i	$-0.513649\pi$
$907$	−2.58206	−0.0857358	−0.0428679	+	0.999081i	$0.513649\pi$
$908$	−43.2586	−1.43559
$909$	−87.8033	−2.91225
$910$	0.0588996	0.00195250
$911$	17.6366	0.584325	0.292162	−	0.956369i	$-0.405625\pi$
$911$	17.6366	0.584325	0.292162	+	0.956369i	$0.405625\pi$
$912$	−112.145	−3.71350
$913$	11.4437	0.378730
$914$	35.4088	1.17122
$915$	8.31944	0.275032
$916$	−39.2492	−1.29683
$917$	−0.397736	−0.0131344
$918$	−156.395	−5.16180
$919$	−3.36433	−0.110979	−0.0554894	−	0.998459i	$-0.517672\pi$
$919$	−3.36433	−0.110979	−0.0554894	+	0.998459i	$0.517672\pi$
$920$	5.73309	0.189014
$921$	−28.5042	−0.939244
$922$	−70.8258	−2.33252
$923$	−0.0607969	−0.00200115
$924$	8.01768	0.263762
$925$	9.93415	0.326633
$926$	−74.7051	−2.45496
$927$	61.3040	2.01349
$928$	−14.0625	−0.461624
$929$	7.27009	0.238524	0.119262	−	0.992863i	$-0.461947\pi$
$929$	7.27009	0.238524	0.119262	+	0.992863i	$0.461947\pi$
$930$	1.81186	0.0594133
$931$	21.2283	0.695730
$932$	−118.708	−3.88841
$933$	−25.0989	−0.821701
$934$	55.4449	1.81421
$935$	7.98670	0.261193
$936$	46.3894	1.51628
$937$	−2.58967	−0.0846007	−0.0423004	−	0.999105i	$-0.513469\pi$
$937$	−2.58967	−0.0846007	−0.0423004	+	0.999105i	$0.513469\pi$
$938$	−1.63434	−0.0533632
$939$	40.7783	1.33075
$940$	7.78177	0.253813
$941$	−45.2952	−1.47658	−0.738291	−	0.674483i	$-0.764367\pi$
$941$	−45.2952	−1.47658	−0.738291	+	0.674483i	$0.764367\pi$
$942$	−182.907	−5.95943
$943$	14.3817	0.468333
$944$	36.2517	1.17989
$945$	0.476165	0.0154896
$946$	−132.958	−4.32285
$947$	−29.5627	−0.960660	−0.480330	−	0.877088i	$-0.659483\pi$
$947$	−29.5627	−0.960660	−0.480330	+	0.877088i	$0.659483\pi$
$948$	18.0999	0.587858
$949$	8.51687	0.276469
$950$	−39.1696	−1.27083
$951$	−74.7482	−2.42388
$952$	2.46524	0.0798988
$953$	7.90576	0.256093	0.128046	−	0.991768i	$-0.459129\pi$
$953$	7.90576	0.256093	0.128046	+	0.991768i	$0.459129\pi$
$954$	−48.5245	−1.57104
$955$	−0.0934365	−0.00302353
$956$	−111.454	−3.60467
$957$	−19.8232	−0.640792
$958$	−104.329	−3.37071
$959$	−1.84136	−0.0594606
$960$	−16.6827	−0.538431
$961$	−30.6753	−0.989527
$962$	−3.99926	−0.128941
$963$	42.7250	1.37680
$964$	−50.7319	−1.63396
$965$	−7.54281	−0.242812
$966$	1.40701	0.0452699
$967$	−31.2522	−1.00500	−0.502501	−	0.864577i	$-0.667587\pi$
$967$	−31.2522	−1.00500	−0.502501	+	0.864577i	$0.667587\pi$
$968$	−189.393	−6.08733
$969$	−37.1790	−1.19436
$970$	−11.0563	−0.354996
$971$	20.9548	0.672473	0.336236	−	0.941778i	$-0.390846\pi$
$971$	20.9548	0.672473	0.336236	+	0.941778i	$0.390846\pi$
$972$	234.813	7.53163
$973$	−0.163599	−0.00524474
$974$	−67.4541	−2.16137
$975$	11.8295	0.378846
$976$	−77.9189	−2.49412
$977$	−9.66555	−0.309228	−0.154614	−	0.987975i	$-0.549413\pi$
$977$	−9.66555	−0.309228	−0.154614	+	0.987975i	$0.549413\pi$
$978$	−86.4812	−2.76536
$979$	21.4943	0.686962
$980$	12.8255	0.409696
$981$	−146.191	−4.66751
$982$	−76.9077	−2.45422
$983$	44.1551	1.40833	0.704165	−	0.710036i	$-0.251321\pi$
$983$	44.1551	1.40833	0.704165	+	0.710036i	$0.251321\pi$
$984$	−194.036	−6.18563
$985$	1.12930	0.0359826
$986$	−10.1196	−0.322274
$987$	1.15029	0.0366142
$988$	11.2820	0.358929
$989$	−16.6937	−0.530830
$990$	−44.4426	−1.41248
$991$	−57.7041	−1.83303	−0.916516	−	0.399997i	$-0.869011\pi$
$991$	−57.7041	−1.83303	−0.916516	+	0.399997i	$0.869011\pi$
$992$	−7.81787	−0.248218
$993$	27.5229	0.873414
$994$	0.0179785	0.000570244 0
$995$	0.847042	0.0268530
$996$	−32.1850	−1.01982
$997$	10.3376	0.327394	0.163697	−	0.986511i	$-0.447658\pi$
$997$	10.3376	0.327394	0.163697	+	0.986511i	$0.447658\pi$
$998$	−104.395	−3.30457
$999$	−32.3314	−1.02292

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8039.2.a.a.1.8	✓	279

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8039.2.a.a.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-2.65123 q^{2} +3.28882 q^{3} +5.02904 q^{4} -0.364681 q^{5} -8.71943 q^{6} -0.0824305 q^{7} -8.03069 q^{8} +7.81633 q^{9} +O(q^{10})\)	\(q-2.65123 q^{2} +3.28882 q^{3} +5.02904 q^{4} -0.364681 q^{5} -8.71943 q^{6} -0.0824305 q^{7} -8.03069 q^{8} +7.81633 q^{9} +0.966855 q^{10} -5.88079 q^{11} +16.5396 q^{12} -0.739032 q^{13} +0.218542 q^{14} -1.19937 q^{15} +11.2332 q^{16} +3.72407 q^{17} -20.7229 q^{18} -3.03556 q^{19} -1.83400 q^{20} -0.271099 q^{21} +15.5913 q^{22} +1.95759 q^{23} -26.4115 q^{24} -4.86701 q^{25} +1.95935 q^{26} +15.8400 q^{27} -0.414546 q^{28} +1.02494 q^{29} +3.17981 q^{30} +0.569801 q^{31} -13.7203 q^{32} -19.3409 q^{33} -9.87339 q^{34} +0.0300608 q^{35} +39.3086 q^{36} -2.04112 q^{37} +8.04799 q^{38} -2.43054 q^{39} +2.92864 q^{40} +7.34664 q^{41} +0.718747 q^{42} -8.52769 q^{43} -29.5747 q^{44} -2.85047 q^{45} -5.19003 q^{46} -4.24307 q^{47} +36.9438 q^{48} -6.99321 q^{49} +12.9036 q^{50} +12.2478 q^{51} -3.71662 q^{52} +2.34159 q^{53} -41.9956 q^{54} +2.14461 q^{55} +0.661974 q^{56} -9.98342 q^{57} -2.71735 q^{58} +3.22721 q^{59} -6.03168 q^{60} -6.93651 q^{61} -1.51068 q^{62} -0.644304 q^{63} +13.9095 q^{64} +0.269511 q^{65} +51.2771 q^{66} -7.47838 q^{67} +18.7285 q^{68} +6.43817 q^{69} -0.0796983 q^{70} +0.0822656 q^{71} -62.7705 q^{72} -11.5244 q^{73} +5.41149 q^{74} -16.0067 q^{75} -15.2660 q^{76} +0.484756 q^{77} +6.44393 q^{78} +1.09434 q^{79} -4.09652 q^{80} +28.6460 q^{81} -19.4776 q^{82} -1.94594 q^{83} -1.36337 q^{84} -1.35810 q^{85} +22.6089 q^{86} +3.37084 q^{87} +47.2268 q^{88} -3.65501 q^{89} +7.55726 q^{90} +0.0609187 q^{91} +9.84481 q^{92} +1.87397 q^{93} +11.2494 q^{94} +1.10701 q^{95} -45.1237 q^{96} -11.4353 q^{97} +18.5406 q^{98} -45.9662 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9}+O(q^{10}) \) 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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