LMFDB - Embedded newform 8047.2.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8047,2,Mod(1,8047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8047, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8047 = 13 \cdot 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8047.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:	$64.2556185065$
Analytic rank:	$0$
Dimension:	$156$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66092 q^{2} -2.09208 q^{3} +5.08047 q^{4} +4.25784 q^{5} +5.56685 q^{6} -2.19372 q^{7} -8.19688 q^{8} +1.37680 q^{9} +O(q^{10})$	\(q-2.66092 q^{2} -2.09208 q^{3} +5.08047 q^{4} +4.25784 q^{5} +5.56685 q^{6} -2.19372 q^{7} -8.19688 q^{8} +1.37680 q^{9} -11.3297 q^{10} -2.56177 q^{11} -10.6288 q^{12} -1.00000 q^{13} +5.83732 q^{14} -8.90774 q^{15} +11.6503 q^{16} -0.0487115 q^{17} -3.66356 q^{18} -7.89347 q^{19} +21.6318 q^{20} +4.58945 q^{21} +6.81666 q^{22} -5.85789 q^{23} +17.1485 q^{24} +13.1292 q^{25} +2.66092 q^{26} +3.39586 q^{27} -11.1452 q^{28} -3.33295 q^{29} +23.7027 q^{30} -3.07217 q^{31} -14.6066 q^{32} +5.35943 q^{33} +0.129617 q^{34} -9.34052 q^{35} +6.99481 q^{36} +0.0566053 q^{37} +21.0038 q^{38} +2.09208 q^{39} -34.9010 q^{40} +9.57989 q^{41} -12.2121 q^{42} +9.84631 q^{43} -13.0150 q^{44} +5.86220 q^{45} +15.5874 q^{46} +5.51302 q^{47} -24.3733 q^{48} -2.18757 q^{49} -34.9356 q^{50} +0.101908 q^{51} -5.08047 q^{52} -4.99157 q^{53} -9.03610 q^{54} -10.9076 q^{55} +17.9817 q^{56} +16.5138 q^{57} +8.86871 q^{58} -10.6851 q^{59} -45.2555 q^{60} -8.10502 q^{61} +8.17479 q^{62} -3.02033 q^{63} +15.5664 q^{64} -4.25784 q^{65} -14.2610 q^{66} -0.382322 q^{67} -0.247477 q^{68} +12.2552 q^{69} +24.8543 q^{70} -7.73562 q^{71} -11.2855 q^{72} -2.84179 q^{73} -0.150622 q^{74} -27.4673 q^{75} -40.1025 q^{76} +5.61982 q^{77} -5.56685 q^{78} -14.0172 q^{79} +49.6049 q^{80} -11.2348 q^{81} -25.4913 q^{82} +0.637871 q^{83} +23.3166 q^{84} -0.207406 q^{85} -26.2002 q^{86} +6.97281 q^{87} +20.9985 q^{88} -6.45214 q^{89} -15.5988 q^{90} +2.19372 q^{91} -29.7608 q^{92} +6.42723 q^{93} -14.6697 q^{94} -33.6091 q^{95} +30.5582 q^{96} +17.8441 q^{97} +5.82094 q^{98} -3.52705 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 13 q^{2} + 23 q^{3} + 161 q^{4} + 39 q^{5} + 25 q^{6} + 19 q^{7} + 42 q^{8} + 169 q^{9}+O(q^{10}) $ 156 * q + 13 * q^2 + 23 * q^3 + 161 * q^4 + 39 * q^5 + 25 * q^6 + 19 * q^7 + 42 * q^8 + 169 * q^9	\( 156 q + 13 q^{2} + 23 q^{3} + 161 q^{4} + 39 q^{5} + 25 q^{6} + 19 q^{7} + 42 q^{8} + 169 q^{9} + 11 q^{10} + 23 q^{11} + 57 q^{12} - 156 q^{13} + 18 q^{14} + 32 q^{15} + 159 q^{16} + 119 q^{17} + 36 q^{18} + 35 q^{19} + 109 q^{20} + 33 q^{21} + 11 q^{22} + 55 q^{23} + 63 q^{24} + 189 q^{25} - 13 q^{26} + 89 q^{27} + 54 q^{28} - 55 q^{29} + 47 q^{31} + 112 q^{32} + 109 q^{33} + 51 q^{34} + 25 q^{35} + 162 q^{36} + 53 q^{37} + 37 q^{38} - 23 q^{39} + 25 q^{40} + 113 q^{41} + 26 q^{42} + 31 q^{43} + 86 q^{44} + 144 q^{45} + 37 q^{46} + 115 q^{47} + 129 q^{48} + 189 q^{49} + 72 q^{50} - 4 q^{51} - 161 q^{52} + 51 q^{53} + 108 q^{54} + 22 q^{55} + 39 q^{56} + 102 q^{57} + 31 q^{58} + 75 q^{59} + 97 q^{60} + 7 q^{61} + 77 q^{62} + 94 q^{63} + 158 q^{64} - 39 q^{65} + 48 q^{66} + 37 q^{67} + 235 q^{68} + 27 q^{69} + 38 q^{70} + 70 q^{71} + 152 q^{72} + 155 q^{73} - 18 q^{74} + 80 q^{75} + 21 q^{76} + 101 q^{77} - 25 q^{78} + 10 q^{79} + 211 q^{80} + 220 q^{81} + 45 q^{82} + 132 q^{83} + 86 q^{84} + 74 q^{85} + 35 q^{86} + 53 q^{87} + 51 q^{88} + 190 q^{89} - 27 q^{90} - 19 q^{91} + 125 q^{92} + 96 q^{93} - 19 q^{94} + 72 q^{95} + 146 q^{96} + 155 q^{97} + 135 q^{98} + 89 q^{99}+O(q^{100}) \) 156 * q + 13 * q^2 + 23 * q^3 + 161 * q^4 + 39 * q^5 + 25 * q^6 + 19 * q^7 + 42 * q^8 + 169 * q^9 + 11 * q^10 + 23 * q^11 + 57 * q^12 - 156 * q^13 + 18 * q^14 + 32 * q^15 + 159 * q^16 + 119 * q^17 + 36 * q^18 + 35 * q^19 + 109 * q^20 + 33 * q^21 + 11 * q^22 + 55 * q^23 + 63 * q^24 + 189 * q^25 - 13 * q^26 + 89 * q^27 + 54 * q^28 - 55 * q^29 + 47 * q^31 + 112 * q^32 + 109 * q^33 + 51 * q^34 + 25 * q^35 + 162 * q^36 + 53 * q^37 + 37 * q^38 - 23 * q^39 + 25 * q^40 + 113 * q^41 + 26 * q^42 + 31 * q^43 + 86 * q^44 + 144 * q^45 + 37 * q^46 + 115 * q^47 + 129 * q^48 + 189 * q^49 + 72 * q^50 - 4 * q^51 - 161 * q^52 + 51 * q^53 + 108 * q^54 + 22 * q^55 + 39 * q^56 + 102 * q^57 + 31 * q^58 + 75 * q^59 + 97 * q^60 + 7 * q^61 + 77 * q^62 + 94 * q^63 + 158 * q^64 - 39 * q^65 + 48 * q^66 + 37 * q^67 + 235 * q^68 + 27 * q^69 + 38 * q^70 + 70 * q^71 + 152 * q^72 + 155 * q^73 - 18 * q^74 + 80 * q^75 + 21 * q^76 + 101 * q^77 - 25 * q^78 + 10 * q^79 + 211 * q^80 + 220 * q^81 + 45 * q^82 + 132 * q^83 + 86 * q^84 + 74 * q^85 + 35 * q^86 + 53 * q^87 + 51 * q^88 + 190 * q^89 - 27 * q^90 - 19 * q^91 + 125 * q^92 + 96 * q^93 - 19 * q^94 + 72 * q^95 + 146 * q^96 + 155 * q^97 + 135 * q^98 + 89 * 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 $

$2$	−2.66092	−1.88155	−0.940776	−	0.339029i	$-0.889901\pi$
$2$	−2.66092	−1.88155	−0.940776	+	0.339029i	$0.889901\pi$
$3$	−2.09208	−1.20786	−0.603932	−	0.797036i	$-0.706400\pi$
$3$	−2.09208	−1.20786	−0.603932	+	0.797036i	$0.706400\pi$
$4$	5.08047	2.54024
$5$	4.25784	1.90416	0.952081	−	0.305845i	$-0.0989389\pi$
$5$	4.25784	1.90416	0.952081	+	0.305845i	$0.0989389\pi$
$6$	5.56685	2.27266
$7$	−2.19372	−0.829150	−0.414575	−	0.910015i	$-0.636070\pi$
$7$	−2.19372	−0.829150	−0.414575	+	0.910015i	$0.636070\pi$
$8$	−8.19688	−2.89803
$9$	1.37680	0.458934
$10$	−11.3297	−3.58278
$11$	−2.56177	−0.772403	−0.386201	−	0.922414i	$-0.626213\pi$
$11$	−2.56177	−0.772403	−0.386201	+	0.922414i	$0.626213\pi$
$12$	−10.6288	−3.06826
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	5.83732	1.56009
$15$	−8.90774	−2.29997
$16$	11.6503	2.91256
$17$	−0.0487115	−0.0118143	−0.00590713	−	0.999983i	$-0.501880\pi$
$17$	−0.0487115	−0.0118143	−0.00590713	+	0.999983i	$0.501880\pi$
$18$	−3.66356	−0.863508
$19$	−7.89347	−1.81089	−0.905443	−	0.424469i	$-0.860461\pi$
$19$	−7.89347	−1.81089	−0.905443	+	0.424469i	$0.860461\pi$
$20$	21.6318	4.83702
$21$	4.58945	1.00150
$22$	6.81666	1.45332
$23$	−5.85789	−1.22145	−0.610727	−	0.791841i	$-0.709123\pi$
$23$	−5.85789	−1.22145	−0.610727	+	0.791841i	$0.709123\pi$
$24$	17.1485	3.50043
$25$	13.1292	2.62584
$26$	2.66092	0.521848
$27$	3.39586	0.653534
$28$	−11.1452	−2.10624
$29$	−3.33295	−0.618914	−0.309457	−	0.950913i	$-0.600147\pi$
$29$	−3.33295	−0.618914	−0.309457	+	0.950913i	$0.600147\pi$
$30$	23.7027	4.32751
$31$	−3.07217	−0.551778	−0.275889	−	0.961189i	$-0.588972\pi$
$31$	−3.07217	−0.551778	−0.275889	+	0.961189i	$0.588972\pi$
$32$	−14.6066	−2.58210
$33$	5.35943	0.932957
$34$	0.129617	0.0222292
$35$	−9.34052	−1.57884
$36$	6.99481	1.16580
$37$	0.0566053	0.00930585	0.00465292	−	0.999989i	$-0.498519\pi$
$37$	0.0566053	0.00930585	0.00465292	+	0.999989i	$0.498519\pi$
$38$	21.0038	3.40727
$39$	2.09208	0.335001
$40$	−34.9010	−5.51833
$41$	9.57989	1.49613	0.748064	−	0.663627i	$-0.230984\pi$
$41$	9.57989	1.49613	0.748064	+	0.663627i	$0.230984\pi$
$42$	−12.2121	−1.88437
$43$	9.84631	1.50155	0.750774	−	0.660559i	$-0.229681\pi$
$43$	9.84631	1.50155	0.750774	+	0.660559i	$0.229681\pi$
$44$	−13.0150	−1.96209
$45$	5.86220	0.873885
$46$	15.5874	2.29823
$47$	5.51302	0.804157	0.402079	−	0.915605i	$-0.368288\pi$
$47$	5.51302	0.804157	0.402079	+	0.915605i	$0.368288\pi$
$48$	−24.3733	−3.51798
$49$	−2.18757	−0.312510
$50$	−34.9356	−4.94064
$51$	0.101908	0.0142700
$52$	−5.08047	−0.704535
$53$	−4.99157	−0.685644	−0.342822	−	0.939400i	$-0.611383\pi$
$53$	−4.99157	−0.685644	−0.342822	+	0.939400i	$0.611383\pi$
$54$	−9.03610	−1.22966
$55$	−10.9076	−1.47078
$56$	17.9817	2.40290
$57$	16.5138	2.18730
$58$	8.86871	1.16452
$59$	−10.6851	−1.39108	−0.695538	−	0.718489i	$-0.744834\pi$
$59$	−10.6851	−1.39108	−0.695538	+	0.718489i	$0.744834\pi$
$60$	−45.2555	−5.84246
$61$	−8.10502	−1.03774	−0.518871	−	0.854853i	$-0.673647\pi$
$61$	−8.10502	−1.03774	−0.518871	+	0.854853i	$0.673647\pi$
$62$	8.17479	1.03820
$63$	−3.02033	−0.380525
$64$	15.5664	1.94580
$65$	−4.25784	−0.528120
$66$	−14.2610	−1.75541
$67$	−0.382322	−0.0467080	−0.0233540	−	0.999727i	$-0.507434\pi$
$67$	−0.382322	−0.0467080	−0.0233540	+	0.999727i	$0.507434\pi$
$68$	−0.247477	−0.0300110
$69$	12.2552	1.47535
$70$	24.8543	2.97066
$71$	−7.73562	−0.918049	−0.459025	−	0.888423i	$-0.651801\pi$
$71$	−7.73562	−0.918049	−0.459025	+	0.888423i	$0.651801\pi$
$72$	−11.2855	−1.33001
$73$	−2.84179	−0.332606	−0.166303	−	0.986075i	$-0.553183\pi$
$73$	−2.84179	−0.332606	−0.166303	+	0.986075i	$0.553183\pi$
$74$	−0.150622	−0.0175094
$75$	−27.4673	−3.17165
$76$	−40.1025	−4.60008
$77$	5.61982	0.640438
$78$	−5.56685	−0.630322
$79$	−14.0172	−1.57705	−0.788527	−	0.615000i	$-0.789156\pi$
$79$	−14.0172	−1.57705	−0.788527	+	0.615000i	$0.789156\pi$
$80$	49.6049	5.54599
$81$	−11.2348	−1.24831
$82$	−25.4913	−2.81504
$83$	0.637871	0.0700154	0.0350077	−	0.999387i	$-0.488854\pi$
$83$	0.637871	0.0700154	0.0350077	+	0.999387i	$0.488854\pi$
$84$	23.3166	2.54405
$85$	−0.207406	−0.0224963
$86$	−26.2002	−2.82524
$87$	6.97281	0.747564
$88$	20.9985	2.23845
$89$	−6.45214	−0.683926	−0.341963	−	0.939713i	$-0.611092\pi$
$89$	−6.45214	−0.683926	−0.341963	+	0.939713i	$0.611092\pi$
$90$	−15.5988	−1.64426
$91$	2.19372	0.229965
$92$	−29.7608	−3.10278
$93$	6.42723	0.666473
$94$	−14.6697	−1.51306
$95$	−33.6091	−3.44822
$96$	30.5582	3.11883
$97$	17.8441	1.81180	0.905899	−	0.423495i	$-0.139197\pi$
$97$	17.8441	1.81180	0.905899	+	0.423495i	$0.139197\pi$
$98$	5.82094	0.588004
$99$	−3.52705	−0.354482
$100$	66.7024	6.67024
$101$	−1.51832	−0.151079	−0.0755394	−	0.997143i	$-0.524068\pi$
$101$	−1.51832	−0.151079	−0.0755394	+	0.997143i	$0.524068\pi$
$102$	−0.271170	−0.0268498
$103$	11.8412	1.16674	0.583372	−	0.812205i	$-0.301733\pi$
$103$	11.8412	1.16674	0.583372	+	0.812205i	$0.301733\pi$
$104$	8.19688	0.803770
$105$	19.5411	1.90702
$106$	13.2821	1.29008
$107$	−7.61406	−0.736079	−0.368039	−	0.929810i	$-0.619971\pi$
$107$	−7.61406	−0.736079	−0.368039	+	0.929810i	$0.619971\pi$
$108$	17.2526	1.66013
$109$	−0.262369	−0.0251304	−0.0125652	−	0.999921i	$-0.504000\pi$
$109$	−0.262369	−0.0251304	−0.0125652	+	0.999921i	$0.504000\pi$
$110$	29.0242	2.76735
$111$	−0.118423	−0.0112402
$112$	−25.5575	−2.41495
$113$	−5.40954	−0.508886	−0.254443	−	0.967088i	$-0.581892\pi$
$113$	−5.40954	−0.508886	−0.254443	+	0.967088i	$0.581892\pi$
$114$	−43.9417	−4.11552
$115$	−24.9419	−2.32585
$116$	−16.9330	−1.57219
$117$	−1.37680	−0.127285
$118$	28.4321	2.61738
$119$	0.106860	0.00979580
$120$	73.0156	6.66539
$121$	−4.43733	−0.403394
$122$	21.5668	1.95256
$123$	−20.0419	−1.80712
$124$	−15.6081	−1.40165
$125$	34.6127	3.09586
$126$	8.03683	0.715978
$127$	4.70929	0.417882	0.208941	−	0.977928i	$-0.432998\pi$
$127$	4.70929	0.417882	0.208941	+	0.977928i	$0.432998\pi$
$128$	−12.2077	−1.07902
$129$	−20.5993	−1.81366
$130$	11.3297	0.993684
$131$	−0.0874575	−0.00764120	−0.00382060	−	0.999993i	$-0.501216\pi$
$131$	−0.0874575	−0.00764120	−0.00382060	+	0.999993i	$0.501216\pi$
$132$	27.2284	2.36993
$133$	17.3161	1.50150
$134$	1.01733	0.0878836
$135$	14.4590	1.24443
$136$	0.399282	0.0342382
$137$	19.9043	1.70054	0.850270	−	0.526346i	$-0.176438\pi$
$137$	19.9043	1.70054	0.850270	+	0.526346i	$0.176438\pi$
$138$	−32.6100	−2.77595
$139$	−6.83881	−0.580061	−0.290030	−	0.957017i	$-0.593665\pi$
$139$	−6.83881	−0.580061	−0.290030	+	0.957017i	$0.593665\pi$
$140$	−47.4543	−4.01062
$141$	−11.5337	−0.971312
$142$	20.5838	1.72736
$143$	2.56177	0.214226
$144$	16.0401	1.33667
$145$	−14.1912	−1.17851
$146$	7.56176	0.625816
$147$	4.57658	0.377470
$148$	0.287581	0.0236390
$149$	11.2806	0.924144	0.462072	−	0.886842i	$-0.347106\pi$
$149$	11.2806	0.924144	0.462072	+	0.886842i	$0.347106\pi$
$150$	73.0882	5.96762
$151$	9.06645	0.737817	0.368909	−	0.929466i	$-0.379732\pi$
$151$	9.06645	0.737817	0.368909	+	0.929466i	$0.379732\pi$
$152$	64.7018	5.24801
$153$	−0.0670661	−0.00542197
$154$	−14.9539	−1.20502
$155$	−13.0808	−1.05068
$156$	10.6288	0.850982
$157$	−11.9636	−0.954796	−0.477398	−	0.878687i	$-0.658420\pi$
$157$	−11.9636	−0.954796	−0.477398	+	0.878687i	$0.658420\pi$
$158$	37.2985	2.96731
$159$	10.4428	0.828165
$160$	−62.1925	−4.91675
$161$	12.8506	1.01277
$162$	29.8949	2.34877
$163$	−12.6085	−0.987575	−0.493787	−	0.869583i	$-0.664388\pi$
$163$	−12.6085	−0.987575	−0.493787	+	0.869583i	$0.664388\pi$
$164$	48.6704	3.80052
$165$	22.8196	1.77650
$166$	−1.69732	−0.131738
$167$	−5.06926	−0.392271	−0.196136	−	0.980577i	$-0.562839\pi$
$167$	−5.06926	−0.392271	−0.196136	+	0.980577i	$0.562839\pi$
$168$	−37.6192	−2.90238
$169$	1.00000	0.0769231
$170$	0.551889	0.0423279
$171$	−10.8677	−0.831077
$172$	50.0239	3.81429
$173$	−17.7761	−1.35149	−0.675745	−	0.737136i	$-0.736178\pi$
$173$	−17.7761	−1.35149	−0.675745	+	0.737136i	$0.736178\pi$
$174$	−18.5541	−1.40658
$175$	−28.8018	−2.17721
$176$	−29.8453	−2.24967
$177$	22.3540	1.68023
$178$	17.1686	1.28684
$179$	−14.7093	−1.09942	−0.549712	−	0.835354i	$-0.685262\pi$
$179$	−14.7093	−1.09942	−0.549712	+	0.835354i	$0.685262\pi$
$180$	29.7827	2.21988
$181$	26.1329	1.94244	0.971220	−	0.238184i	$-0.0765522\pi$
$181$	26.1329	1.94244	0.971220	+	0.238184i	$0.0765522\pi$
$182$	−5.83732	−0.432691
$183$	16.9564	1.25345
$184$	48.0164	3.53982
$185$	0.241016	0.0177198
$186$	−17.1023	−1.25400
$187$	0.124788	0.00912538
$188$	28.0088	2.04275
$189$	−7.44958	−0.541877
$190$	89.4310	6.48800
$191$	22.3449	1.61682	0.808411	−	0.588619i	$-0.200328\pi$
$191$	22.3449	1.61682	0.808411	+	0.588619i	$0.200328\pi$
$192$	−32.5662	−2.35026
$193$	−2.14227	−0.154204	−0.0771019	−	0.997023i	$-0.524567\pi$
$193$	−2.14227	−0.154204	−0.0771019	+	0.997023i	$0.524567\pi$
$194$	−47.4817	−3.40899
$195$	8.90774	0.637897
$196$	−11.1139	−0.793850
$197$	7.79717	0.555525	0.277763	−	0.960650i	$-0.410407\pi$
$197$	7.79717	0.555525	0.277763	+	0.960650i	$0.410407\pi$
$198$	9.38519	0.666976
$199$	1.24150	0.0880075	0.0440038	−	0.999031i	$-0.485989\pi$
$199$	1.24150	0.0880075	0.0440038	+	0.999031i	$0.485989\pi$
$200$	−107.618	−7.60976
$201$	0.799848	0.0564169
$202$	4.04013	0.284263
$203$	7.31158	0.513173
$204$	0.517743	0.0362492
$205$	40.7896	2.84887
$206$	−31.5083	−2.19529
$207$	−8.06516	−0.560567
$208$	−11.6503	−0.807800
$209$	20.2213	1.39873
$210$	−51.9973	−3.58815
$211$	−8.34576	−0.574546	−0.287273	−	0.957849i	$-0.592749\pi$
$211$	−8.34576	−0.574546	−0.287273	+	0.957849i	$0.592749\pi$
$212$	−25.3595	−1.74170
$213$	16.1835	1.10888
$214$	20.2604	1.38497
$215$	41.9240	2.85919
$216$	−27.8355	−1.89396
$217$	6.73950	0.457507
$218$	0.698143	0.0472842
$219$	5.94526	0.401743
$220$	−55.4158	−3.73613
$221$	0.0487115	0.00327669
$222$	0.315113	0.0211490
$223$	−10.3199	−0.691070	−0.345535	−	0.938406i	$-0.612303\pi$
$223$	−10.3199	−0.691070	−0.345535	+	0.938406i	$0.612303\pi$
$224$	32.0428	2.14095
$225$	18.0763	1.20509
$226$	14.3943	0.957496
$227$	7.72913	0.513000	0.256500	−	0.966544i	$-0.417431\pi$
$227$	7.72913	0.513000	0.256500	+	0.966544i	$0.417431\pi$
$228$	83.8977	5.55626
$229$	−18.9669	−1.25336	−0.626682	−	0.779275i	$-0.715588\pi$
$229$	−18.9669	−1.25336	−0.626682	+	0.779275i	$0.715588\pi$
$230$	66.3684	4.37620
$231$	−11.7571	−0.773562
$232$	27.3198	1.79363
$233$	−1.01051	−0.0662007	−0.0331004	−	0.999452i	$-0.510538\pi$
$233$	−1.01051	−0.0662007	−0.0331004	+	0.999452i	$0.510538\pi$
$234$	3.66356	0.239494
$235$	23.4736	1.53125
$236$	−54.2852	−3.53366
$237$	29.3250	1.90487
$238$	−0.284344	−0.0184313
$239$	20.4487	1.32272	0.661359	−	0.750069i	$-0.269980\pi$
$239$	20.4487	1.32272	0.661359	+	0.750069i	$0.269980\pi$
$240$	−103.777	−6.69880
$241$	−3.76017	−0.242214	−0.121107	−	0.992639i	$-0.538644\pi$
$241$	−3.76017	−0.242214	−0.121107	+	0.992639i	$0.538644\pi$
$242$	11.8074	0.759006
$243$	13.3166	0.854259
$244$	−41.1773	−2.63611
$245$	−9.31432	−0.595070
$246$	53.3298	3.40018
$247$	7.89347	0.502249
$248$	25.1822	1.59907
$249$	−1.33448	−0.0845690
$250$	−92.1015	−5.82501
$251$	24.8042	1.56563	0.782814	−	0.622256i	$-0.213784\pi$
$251$	24.8042	1.56563	0.782814	+	0.622256i	$0.213784\pi$
$252$	−15.3447	−0.966624
$253$	15.0066	0.943455
$254$	−12.5310	−0.786266
$255$	0.433909	0.0271724
$256$	1.35083	0.0844268
$257$	1.04927	0.0654518	0.0327259	−	0.999464i	$-0.489581\pi$
$257$	1.04927	0.0654518	0.0327259	+	0.999464i	$0.489581\pi$
$258$	54.8129	3.41250
$259$	−0.124176	−0.00771594
$260$	−21.6318	−1.34155
$261$	−4.58882	−0.284041
$262$	0.232717	0.0143773
$263$	−27.0288	−1.66667	−0.833333	−	0.552771i	$-0.813570\pi$
$263$	−27.0288	−1.66667	−0.833333	+	0.552771i	$0.813570\pi$
$264$	−43.9306	−2.70374
$265$	−21.2533	−1.30558
$266$	−46.0767	−2.82514
$267$	13.4984	0.826089
$268$	−1.94237	−0.118649
$269$	−28.5487	−1.74065	−0.870323	−	0.492482i	$-0.836090\pi$
$269$	−28.5487	−1.74065	−0.870323	+	0.492482i	$0.836090\pi$
$270$	−38.4742	−2.34147
$271$	10.6010	0.643964	0.321982	−	0.946746i	$-0.395651\pi$
$271$	10.6010	0.643964	0.321982	+	0.946746i	$0.395651\pi$
$272$	−0.567501	−0.0344098
$273$	−4.58945	−0.277766
$274$	−52.9637	−3.19966
$275$	−33.6339	−2.02820
$276$	62.2621	3.74774
$277$	−17.5562	−1.05485	−0.527425	−	0.849601i	$-0.676843\pi$
$277$	−17.5562	−1.05485	−0.527425	+	0.849601i	$0.676843\pi$
$278$	18.1975	1.09141
$279$	−4.22977	−0.253230
$280$	76.5631	4.57552
$281$	−12.6242	−0.753098	−0.376549	−	0.926397i	$-0.622889\pi$
$281$	−12.6242	−0.753098	−0.376549	+	0.926397i	$0.622889\pi$
$282$	30.6902	1.82757
$283$	32.3108	1.92068	0.960340	−	0.278832i	$-0.0899471\pi$
$283$	32.3108	1.92068	0.960340	+	0.278832i	$0.0899471\pi$
$284$	−39.3006	−2.33206
$285$	70.3129	4.16498
$286$	−6.81666	−0.403077
$287$	−21.0156	−1.24051
$288$	−20.1104	−1.18502
$289$	−16.9976	−0.999860
$290$	37.7615	2.21743
$291$	−37.3314	−2.18840
$292$	−14.4376	−0.844899
$293$	−1.13335	−0.0662112	−0.0331056	−	0.999452i	$-0.510540\pi$
$293$	−1.13335	−0.0662112	−0.0331056	+	0.999452i	$0.510540\pi$
$294$	−12.1779	−0.710229
$295$	−45.4953	−2.64884
$296$	−0.463986	−0.0269687
$297$	−8.69942	−0.504791
$298$	−30.0168	−1.73883
$299$	5.85789	0.338771
$300$	−139.547	−8.05674
$301$	−21.6001	−1.24501
$302$	−24.1251	−1.38824
$303$	3.17646	0.182483
$304$	−91.9609	−5.27432
$305$	−34.5099	−1.97603
$306$	0.178457	0.0102017
$307$	−15.5403	−0.886931	−0.443466	−	0.896291i	$-0.646251\pi$
$307$	−15.5403	−0.886931	−0.443466	+	0.896291i	$0.646251\pi$
$308$	28.5513	1.62686
$309$	−24.7727	−1.40927
$310$	34.8069	1.97690
$311$	−9.79658	−0.555513	−0.277757	−	0.960652i	$-0.589591\pi$
$311$	−9.79658	−0.555513	−0.277757	+	0.960652i	$0.589591\pi$
$312$	−17.1485	−0.970844
$313$	9.93644	0.561641	0.280820	−	0.959760i	$-0.409393\pi$
$313$	9.93644	0.561641	0.280820	+	0.959760i	$0.409393\pi$
$314$	31.8340	1.79650
$315$	−12.8601	−0.724582
$316$	−71.2138	−4.00609
$317$	35.0213	1.96699	0.983496	−	0.180929i	$-0.0579105\pi$
$317$	35.0213	1.96699	0.983496	+	0.180929i	$0.0579105\pi$
$318$	−27.7873	−1.55823
$319$	8.53826	0.478051
$320$	66.2792	3.70512
$321$	15.9292	0.889083
$322$	−34.1944	−1.90558
$323$	0.384502	0.0213943
$324$	−57.0782	−3.17101
$325$	−13.1292	−0.728276
$326$	33.5502	1.85817
$327$	0.548898	0.0303541
$328$	−78.5252	−4.33583
$329$	−12.0941	−0.666767
$330$	−60.7210	−3.34258
$331$	19.8516	1.09114	0.545570	−	0.838065i	$-0.316313\pi$
$331$	19.8516	1.09114	0.545570	+	0.838065i	$0.316313\pi$
$332$	3.24068	0.177856
$333$	0.0779343	0.00427077
$334$	13.4889	0.738079
$335$	−1.62786	−0.0889397
$336$	53.4683	2.91693
$337$	−3.65214	−0.198944	−0.0994722	−	0.995040i	$-0.531715\pi$
$337$	−3.65214	−0.198944	−0.0994722	+	0.995040i	$0.531715\pi$
$338$	−2.66092	−0.144735
$339$	11.3172	0.614665
$340$	−1.05372	−0.0571459
$341$	7.87020	0.426195
$342$	28.9181	1.56371
$343$	20.1550	1.08827
$344$	−80.7090	−4.35154
$345$	52.1806	2.80931
$346$	47.3006	2.54290
$347$	6.35221	0.341005	0.170502	−	0.985357i	$-0.445461\pi$
$347$	6.35221	0.341005	0.170502	+	0.985357i	$0.445461\pi$
$348$	35.4252	1.89899
$349$	−20.6778	−1.10686	−0.553428	−	0.832897i	$-0.686680\pi$
$349$	−20.6778	−1.10686	−0.553428	+	0.832897i	$0.686680\pi$
$350$	76.6392	4.09654
$351$	−3.39586	−0.181258
$352$	37.4187	1.99443
$353$	9.99774	0.532126	0.266063	−	0.963956i	$-0.414277\pi$
$353$	9.99774	0.532126	0.266063	+	0.963956i	$0.414277\pi$
$354$	−59.4822	−3.16144
$355$	−32.9370	−1.74812
$356$	−32.7799	−1.73733
$357$	−0.223559	−0.0118320
$358$	39.1402	2.06862
$359$	25.3745	1.33922	0.669608	−	0.742715i	$-0.266462\pi$
$359$	25.3745	1.33922	0.669608	+	0.742715i	$0.266462\pi$
$360$	−48.0517	−2.53255
$361$	43.3068	2.27931
$362$	−69.5373	−3.65480
$363$	9.28325	0.487244
$364$	11.1452	0.584165
$365$	−12.0999	−0.633337
$366$	−45.1194	−2.35843
$367$	14.1222	0.737174	0.368587	−	0.929593i	$-0.379842\pi$
$367$	14.1222	0.737174	0.368587	+	0.929593i	$0.379842\pi$
$368$	−68.2459	−3.55756
$369$	13.1896	0.686624
$370$	−0.641323	−0.0333408
$371$	10.9501	0.568502
$372$	32.6534	1.69300
$373$	7.88850	0.408451	0.204226	−	0.978924i	$-0.434532\pi$
$373$	7.88850	0.408451	0.204226	+	0.978924i	$0.434532\pi$
$374$	−0.332049	−0.0171699
$375$	−72.4126	−3.73937
$376$	−45.1896	−2.33047
$377$	3.33295	0.171656
$378$	19.8227	1.01957
$379$	−5.33030	−0.273799	−0.136899	−	0.990585i	$-0.543714\pi$
$379$	−5.33030	−0.273799	−0.136899	+	0.990585i	$0.543714\pi$
$380$	−170.750	−8.75929
$381$	−9.85222	−0.504744
$382$	−59.4579	−3.04213
$383$	−8.88155	−0.453826	−0.226913	−	0.973915i	$-0.572863\pi$
$383$	−8.88155	−0.453826	−0.226913	+	0.973915i	$0.572863\pi$
$384$	25.5395	1.30331
$385$	23.9283	1.21950
$386$	5.70039	0.290142
$387$	13.5564	0.689112
$388$	90.6566	4.60239
$389$	14.5176	0.736073	0.368036	−	0.929811i	$-0.380030\pi$
$389$	14.5176	0.736073	0.368036	+	0.929811i	$0.380030\pi$
$390$	−23.7027	−1.20024
$391$	0.285346	0.0144306
$392$	17.9313	0.905665
$393$	0.182968	0.00922952
$394$	−20.7476	−1.04525
$395$	−59.6828	−3.00297
$396$	−17.9191	−0.900468
$397$	−24.4665	−1.22794	−0.613970	−	0.789329i	$-0.710428\pi$
$397$	−24.4665	−1.22794	−0.613970	+	0.789329i	$0.710428\pi$
$398$	−3.30352	−0.165591
$399$	−36.2267	−1.81360
$400$	152.958	7.64791
$401$	28.4922	1.42283	0.711416	−	0.702771i	$-0.248054\pi$
$401$	28.4922	1.42283	0.711416	+	0.702771i	$0.248054\pi$
$402$	−2.12833	−0.106151
$403$	3.07217	0.153036
$404$	−7.71380	−0.383776
$405$	−47.8360	−2.37699
$406$	−19.4555	−0.965561
$407$	−0.145010	−0.00718786
$408$	−0.835330	−0.0413550
$409$	−2.31126	−0.114285	−0.0571423	−	0.998366i	$-0.518199\pi$
$409$	−2.31126	−0.114285	−0.0571423	+	0.998366i	$0.518199\pi$
$410$	−108.538	−5.36029
$411$	−41.6414	−2.05402
$412$	60.1587	2.96381
$413$	23.4401	1.15341
$414$	21.4607	1.05474
$415$	2.71595	0.133321
$416$	14.6066	0.716147
$417$	14.3073	0.700634
$418$	−53.8070	−2.63179
$419$	20.1880	0.986246	0.493123	−	0.869960i	$-0.335855\pi$
$419$	20.1880	0.986246	0.493123	+	0.869960i	$0.335855\pi$
$420$	99.2782	4.84428
$421$	31.8332	1.55145	0.775727	−	0.631069i	$-0.217383\pi$
$421$	31.8332	1.55145	0.775727	+	0.631069i	$0.217383\pi$
$422$	22.2074	1.08104
$423$	7.59035	0.369055
$424$	40.9153	1.98702
$425$	−0.639542	−0.0310223
$426$	−43.0631	−2.08641
$427$	17.7802	0.860443
$428$	−38.6830	−1.86981
$429$	−5.35943	−0.258756
$430$	−111.556	−5.37972
$431$	15.9389	0.767752	0.383876	−	0.923385i	$-0.374589\pi$
$431$	15.9389	0.767752	0.383876	+	0.923385i	$0.374589\pi$
$432$	39.5626	1.90346
$433$	21.6680	1.04130	0.520650	−	0.853770i	$-0.325690\pi$
$433$	21.6680	1.04130	0.520650	+	0.853770i	$0.325690\pi$
$434$	−17.9332	−0.860823
$435$	29.6891	1.42348
$436$	−1.33296	−0.0638372
$437$	46.2391	2.21191
$438$	−15.8198	−0.755900
$439$	−38.4248	−1.83392	−0.916958	−	0.398983i	$-0.869363\pi$
$439$	−38.4248	−1.83392	−0.916958	+	0.398983i	$0.869363\pi$
$440$	89.4083	4.26237
$441$	−3.01185	−0.143422
$442$	−0.129617	−0.00616526
$443$	6.22370	0.295697	0.147848	−	0.989010i	$-0.452765\pi$
$443$	6.22370	0.295697	0.147848	+	0.989010i	$0.452765\pi$
$444$	−0.601644	−0.0285527
$445$	−27.4722	−1.30231
$446$	27.4603	1.30028
$447$	−23.6000	−1.11624
$448$	−34.1484	−1.61336
$449$	18.7352	0.884168	0.442084	−	0.896974i	$-0.354239\pi$
$449$	18.7352	0.884168	0.442084	+	0.896974i	$0.354239\pi$
$450$	−48.0995	−2.26743
$451$	−24.5415	−1.15561
$452$	−27.4830	−1.29269
$453$	−18.9677	−0.891182
$454$	−20.5666	−0.965236
$455$	9.34052	0.437890
$456$	−135.361	−6.33888
$457$	−7.88256	−0.368731	−0.184365	−	0.982858i	$-0.559023\pi$
$457$	−7.88256	−0.368731	−0.184365	+	0.982858i	$0.559023\pi$
$458$	50.4692	2.35827
$459$	−0.165417	−0.00772102
$460$	−126.717	−5.90820
$461$	−18.6407	−0.868183	−0.434092	−	0.900869i	$-0.642931\pi$
$461$	−18.6407	−0.868183	−0.434092	+	0.900869i	$0.642931\pi$
$462$	31.2847	1.45550
$463$	6.60668	0.307039	0.153519	−	0.988146i	$-0.450939\pi$
$463$	6.60668	0.307039	0.153519	+	0.988146i	$0.450939\pi$
$464$	−38.8298	−1.80263
$465$	27.3661	1.26907
$466$	2.68888	0.124560
$467$	39.0178	1.80553	0.902765	−	0.430133i	$-0.141534\pi$
$467$	39.0178	1.80553	0.902765	+	0.430133i	$0.141534\pi$
$468$	−6.99481	−0.323335
$469$	0.838709	0.0387280
$470$	−62.4612	−2.88112
$471$	25.0287	1.15326
$472$	87.5842	4.03139
$473$	−25.2240	−1.15980
$474$	−78.0314	−3.58410
$475$	−103.635	−4.75509
$476$	0.542897	0.0248837
$477$	−6.87240	−0.314666
$478$	−54.4123	−2.48876
$479$	13.0169	0.594759	0.297380	−	0.954759i	$-0.403887\pi$
$479$	13.0169	0.594759	0.297380	+	0.954759i	$0.403887\pi$
$480$	130.112	5.93876
$481$	−0.0566053	−0.00258098
$482$	10.0055	0.455738
$483$	−26.8845	−1.22329
$484$	−22.5437	−1.02472
$485$	75.9774	3.44996
$486$	−35.4343	−1.60733
$487$	−2.03931	−0.0924101	−0.0462051	−	0.998932i	$-0.514713\pi$
$487$	−2.03931	−0.0924101	−0.0462051	+	0.998932i	$0.514713\pi$
$488$	66.4359	3.00741
$489$	26.3780	1.19286
$490$	24.7846	1.11966
$491$	26.2021	1.18249	0.591243	−	0.806493i	$-0.298637\pi$
$491$	26.2021	1.18249	0.591243	+	0.806493i	$0.298637\pi$
$492$	−101.822	−4.59050
$493$	0.162353	0.00731202
$494$	−21.0038	−0.945008
$495$	−15.0176	−0.674992
$496$	−35.7916	−1.60709
$497$	16.9698	0.761201
$498$	3.55093	0.159121
$499$	−23.2292	−1.03988	−0.519941	−	0.854202i	$-0.674046\pi$
$499$	−23.2292	−1.03988	−0.519941	+	0.854202i	$0.674046\pi$
$500$	175.849	7.86420
$501$	10.6053	0.473810
$502$	−66.0019	−2.94581
$503$	10.2239	0.455863	0.227931	−	0.973677i	$-0.426804\pi$
$503$	10.2239	0.455863	0.227931	+	0.973677i	$0.426804\pi$
$504$	24.7572	1.10278
$505$	−6.46478	−0.287679
$506$	−39.9312	−1.77516
$507$	−2.09208	−0.0929126
$508$	23.9254	1.06152
$509$	4.90604	0.217456	0.108728	−	0.994072i	$-0.465322\pi$
$509$	4.90604	0.217456	0.108728	+	0.994072i	$0.465322\pi$
$510$	−1.15460	−0.0511264
$511$	6.23411	0.275781
$512$	20.8209	0.920164
$513$	−26.8051	−1.18347
$514$	−2.79203	−0.123151
$515$	50.4178	2.22167
$516$	−104.654	−4.60714
$517$	−14.1231	−0.621133
$518$	0.330423	0.0145179
$519$	37.1890	1.63241
$520$	34.9010	1.53051
$521$	−1.52132	−0.0666500	−0.0333250	−	0.999445i	$-0.510610\pi$
$521$	−1.52132	−0.0666500	−0.0333250	+	0.999445i	$0.510610\pi$
$522$	12.2105	0.534437
$523$	−25.8525	−1.13045	−0.565226	−	0.824936i	$-0.691211\pi$
$523$	−25.8525	−1.13045	−0.565226	+	0.824936i	$0.691211\pi$
$524$	−0.444325	−0.0194104
$525$	60.2557	2.62977
$526$	71.9213	3.13592
$527$	0.149650	0.00651886
$528$	62.4387	2.71730
$529$	11.3149	0.491951
$530$	56.5532	2.45651
$531$	−14.7112	−0.638413
$532$	87.9739	3.81415
$533$	−9.57989	−0.414951
$534$	−35.9181	−1.55433
$535$	−32.4194	−1.40161
$536$	3.13384	0.135361
$537$	30.7730	1.32795
$538$	75.9657	3.27511
$539$	5.60406	0.241384
$540$	73.4587	3.16116
$541$	−23.8204	−1.02412	−0.512059	−	0.858950i	$-0.671117\pi$
$541$	−23.8204	−1.02412	−0.512059	+	0.858950i	$0.671117\pi$
$542$	−28.2083	−1.21165
$543$	−54.6721	−2.34620
$544$	0.711509	0.0305057
$545$	−1.11713	−0.0478524
$546$	12.2121	0.522631
$547$	−39.6112	−1.69365	−0.846827	−	0.531868i	$-0.821490\pi$
$547$	−39.6112	−1.69365	−0.846827	+	0.531868i	$0.821490\pi$
$548$	101.123	4.31978
$549$	−11.1590	−0.476255
$550$	89.4971	3.81617
$551$	26.3086	1.12078
$552$	−100.454	−4.27561
$553$	30.7498	1.30761
$554$	46.7156	1.98476
$555$	−0.504225	−0.0214032
$556$	−34.7444	−1.47349
$557$	−44.3056	−1.87729	−0.938645	−	0.344884i	$-0.887918\pi$
$557$	−44.3056	−1.87729	−0.938645	+	0.344884i	$0.887918\pi$
$558$	11.2551	0.476465
$559$	−9.84631	−0.416454
$560$	−108.819	−4.59846
$561$	−0.261066	−0.0110222
$562$	33.5920	1.41699
$563$	−29.5074	−1.24359	−0.621795	−	0.783180i	$-0.713596\pi$
$563$	−29.5074	−1.24359	−0.621795	+	0.783180i	$0.713596\pi$
$564$	−58.5966	−2.46736
$565$	−23.0329	−0.969003
$566$	−85.9764	−3.61386
$567$	24.6461	1.03504
$568$	63.4079	2.66054
$569$	−2.84976	−0.119468	−0.0597340	−	0.998214i	$-0.519025\pi$
$569$	−2.84976	−0.119468	−0.0597340	+	0.998214i	$0.519025\pi$
$570$	−187.097	−7.83662
$571$	7.21477	0.301929	0.150964	−	0.988539i	$-0.451762\pi$
$571$	7.21477	0.301929	0.150964	+	0.988539i	$0.451762\pi$
$572$	13.0150	0.544185
$573$	−46.7474	−1.95290
$574$	55.9208	2.33409
$575$	−76.9093	−3.20734
$576$	21.4318	0.892994
$577$	9.90077	0.412174	0.206087	−	0.978534i	$-0.433927\pi$
$577$	9.90077	0.412174	0.206087	+	0.978534i	$0.433927\pi$
$578$	45.2293	1.88129
$579$	4.48180	0.186257
$580$	−72.0979	−2.99370
$581$	−1.39931	−0.0580533
$582$	99.3356	4.11759
$583$	12.7873	0.529594
$584$	23.2938	0.963905
$585$	−5.86220	−0.242372
$586$	3.01576	0.124580
$587$	20.0961	0.829456	0.414728	−	0.909945i	$-0.363877\pi$
$587$	20.0961	0.829456	0.414728	+	0.909945i	$0.363877\pi$
$588$	23.2512	0.958862
$589$	24.2501	0.999207
$590$	121.059	4.98392
$591$	−16.3123	−0.670998
$592$	0.659466	0.0271039
$593$	−8.40611	−0.345198	−0.172599	−	0.984992i	$-0.555216\pi$
$593$	−8.40611	−0.345198	−0.172599	+	0.984992i	$0.555216\pi$
$594$	23.1484	0.949791
$595$	0.454991	0.0186528
$596$	57.3109	2.34754
$597$	−2.59732	−0.106301
$598$	−15.5874	−0.637414
$599$	−7.53129	−0.307720	−0.153860	−	0.988093i	$-0.549170\pi$
$599$	−7.53129	−0.307720	−0.153860	+	0.988093i	$0.549170\pi$
$600$	225.146	9.19155
$601$	21.6738	0.884093	0.442047	−	0.896992i	$-0.354253\pi$
$601$	21.6738	0.884093	0.442047	+	0.896992i	$0.354253\pi$
$602$	57.4760	2.34255
$603$	−0.526382	−0.0214359
$604$	46.0618	1.87423
$605$	−18.8934	−0.768127
$606$	−8.45228	−0.343351
$607$	33.6337	1.36515	0.682575	−	0.730815i	$-0.260860\pi$
$607$	33.6337	1.36515	0.682575	+	0.730815i	$0.260860\pi$
$608$	115.297	4.67590
$609$	−15.2964	−0.619842
$610$	91.8278	3.71800
$611$	−5.51302	−0.223033
$612$	−0.340727	−0.0137731
$613$	7.20338	0.290942	0.145471	−	0.989363i	$-0.453530\pi$
$613$	7.20338	0.290942	0.145471	+	0.989363i	$0.453530\pi$
$614$	41.3514	1.66881
$615$	−85.3351	−3.44105
$616$	−46.0650	−1.85601
$617$	23.6395	0.951690	0.475845	−	0.879529i	$-0.342142\pi$
$617$	23.6395	0.951690	0.475845	+	0.879529i	$0.342142\pi$
$618$	65.9180	2.65161
$619$	1.00000	0.0401934
$619$	1.00000	0.0401934
$620$	−66.4567	−2.66896
$621$	−19.8926	−0.798262
$622$	26.0679	1.04523
$623$	14.1542	0.567077
$624$	24.3733	0.975712
$625$	81.7294	3.26918
$626$	−26.4400	−1.05676
$627$	−42.3045	−1.68948
$628$	−60.7805	−2.42541
$629$	−0.00275733	−0.000109942 0
$630$	34.2195	1.36334
$631$	3.10127	0.123460	0.0617298	−	0.998093i	$-0.480338\pi$
$631$	3.10127	0.123460	0.0617298	+	0.998093i	$0.480338\pi$
$632$	114.897	4.57036
$633$	17.4600	0.693973
$634$	−93.1887	−3.70100
$635$	20.0514	0.795715
$636$	53.0542	2.10373
$637$	2.18757	0.0866747
$638$	−22.7196	−0.899478
$639$	−10.6504	−0.421324
$640$	−51.9783	−2.05462
$641$	44.3451	1.75153	0.875763	−	0.482740i	$-0.160359\pi$
$641$	44.3451	1.75153	0.875763	+	0.482740i	$0.160359\pi$
$642$	−42.3863	−1.67285
$643$	−1.77387	−0.0699544	−0.0349772	−	0.999388i	$-0.511136\pi$
$643$	−1.77387	−0.0699544	−0.0349772	+	0.999388i	$0.511136\pi$
$644$	65.2871	2.57267
$645$	−87.7084	−3.45351
$646$	−1.02313	−0.0402545
$647$	21.6865	0.852586	0.426293	−	0.904585i	$-0.359819\pi$
$647$	21.6865	0.852586	0.426293	+	0.904585i	$0.359819\pi$
$648$	92.0905	3.61765
$649$	27.3727	1.07447
$650$	34.9356	1.37029
$651$	−14.0996	−0.552606
$652$	−64.0572	−2.50867
$653$	19.6817	0.770205	0.385102	−	0.922874i	$-0.374166\pi$
$653$	19.6817	0.770205	0.385102	+	0.922874i	$0.374166\pi$
$654$	−1.46057	−0.0571129
$655$	−0.372380	−0.0145501
$656$	111.608	4.35757
$657$	−3.91258	−0.152644
$658$	32.1813	1.25456
$659$	20.0570	0.781310	0.390655	−	0.920537i	$-0.372249\pi$
$659$	20.0570	0.781310	0.390655	+	0.920537i	$0.372249\pi$
$660$	115.934	4.51274
$661$	−28.6027	−1.11252	−0.556258	−	0.831010i	$-0.687763\pi$
$661$	−28.6027	−1.11252	−0.556258	+	0.831010i	$0.687763\pi$
$662$	−52.8233	−2.05304
$663$	−0.101908	−0.00395779
$664$	−5.22855	−0.202907
$665$	73.7291	2.85909
$666$	−0.207376	−0.00803568
$667$	19.5241	0.755975
$668$	−25.7542	−0.996462
$669$	21.5900	0.834719
$670$	4.33161	0.167345
$671$	20.7632	0.801555
$672$	−67.0362	−2.58598
$673$	4.16850	0.160684	0.0803419	−	0.996767i	$-0.474399\pi$
$673$	4.16850	0.160684	0.0803419	+	0.996767i	$0.474399\pi$
$674$	9.71802	0.374324
$675$	44.5849	1.71607
$676$	5.08047	0.195403
$677$	−45.9935	−1.76768	−0.883838	−	0.467794i	$-0.845049\pi$
$677$	−45.9935	−1.76768	−0.883838	+	0.467794i	$0.845049\pi$
$678$	−30.1141	−1.15652
$679$	−39.1451	−1.50225
$680$	1.70008	0.0651950
$681$	−16.1700	−0.619634
$682$	−20.9419	−0.801908
$683$	28.2745	1.08189	0.540947	−	0.841056i	$-0.318066\pi$
$683$	28.2745	1.08189	0.540947	+	0.841056i	$0.318066\pi$
$684$	−55.2133	−2.11113
$685$	84.7494	3.23811
$686$	−53.6308	−2.04763
$687$	39.6802	1.51389
$688$	114.712	4.37335
$689$	4.99157	0.190164
$690$	−138.848	−5.28586
$691$	−11.4830	−0.436832	−0.218416	−	0.975856i	$-0.570089\pi$
$691$	−11.4830	−0.436832	−0.218416	+	0.975856i	$0.570089\pi$
$692$	−90.3108	−3.43310
$693$	7.73738	0.293919
$694$	−16.9027	−0.641618
$695$	−29.1186	−1.10453
$696$	−57.1553	−2.16646
$697$	−0.466651	−0.0176756
$698$	55.0218	2.08261
$699$	2.11407	0.0799614
$700$	−146.327	−5.53063
$701$	−23.0140	−0.869228	−0.434614	−	0.900617i	$-0.643115\pi$
$701$	−23.0140	−0.869228	−0.434614	+	0.900617i	$0.643115\pi$
$702$	9.03610	0.341046
$703$	−0.446812	−0.0168518
$704$	−39.8775	−1.50294
$705$	−49.1086	−1.84954
$706$	−26.6031	−1.00122
$707$	3.33078	0.125267
$708$	113.569	4.26818
$709$	7.52082	0.282450	0.141225	−	0.989978i	$-0.454896\pi$
$709$	7.52082	0.282450	0.141225	+	0.989978i	$0.454896\pi$
$710$	87.6426	3.28917
$711$	−19.2989	−0.723764
$712$	52.8874	1.98204
$713$	17.9964	0.673972
$714$	0.594871	0.0222625
$715$	10.9076	0.407921
$716$	−74.7301	−2.79280
$717$	−42.7804	−1.59766
$718$	−67.5195	−2.51980
$719$	21.8122	0.813456	0.406728	−	0.913549i	$-0.366670\pi$
$719$	21.8122	0.813456	0.406728	+	0.913549i	$0.366670\pi$
$720$	68.2961	2.54525
$721$	−25.9763	−0.967407
$722$	−115.236	−4.28863
$723$	7.86659	0.292562
$724$	132.767	4.93426
$725$	−43.7589	−1.62517
$726$	−24.7020	−0.916776
$727$	−1.41184	−0.0523624	−0.0261812	−	0.999657i	$-0.508335\pi$
$727$	−1.41184	−0.0523624	−0.0261812	+	0.999657i	$0.508335\pi$
$728$	−17.9817	−0.666446
$729$	5.84511	0.216486
$730$	32.1968	1.19166
$731$	−0.479628	−0.0177397
$732$	86.1463	3.18406
$733$	40.6012	1.49964	0.749821	−	0.661641i	$-0.230140\pi$
$733$	40.6012	1.49964	0.749821	+	0.661641i	$0.230140\pi$
$734$	−37.5780	−1.38703
$735$	19.4863	0.718764
$736$	85.5638	3.15392
$737$	0.979421	0.0360774
$738$	−35.0964	−1.29192
$739$	−17.3318	−0.637562	−0.318781	−	0.947828i	$-0.603273\pi$
$739$	−17.3318	−0.637562	−0.318781	+	0.947828i	$0.603273\pi$
$740$	1.22447	0.0450126
$741$	−16.5138	−0.606648
$742$	−29.1374	−1.06967
$743$	−19.4534	−0.713675	−0.356837	−	0.934167i	$-0.616145\pi$
$743$	−19.4534	−0.713675	−0.356837	+	0.934167i	$0.616145\pi$
$744$	−52.6832	−1.93146
$745$	48.0310	1.75972
$746$	−20.9906	−0.768522
$747$	0.878222	0.0321325
$748$	0.633980	0.0231806
$749$	16.7031	0.610320
$750$	192.684	7.03582
$751$	−31.6823	−1.15610	−0.578051	−	0.816001i	$-0.696187\pi$
$751$	−31.6823	−1.15610	−0.578051	+	0.816001i	$0.696187\pi$
$752$	64.2281	2.34216
$753$	−51.8924	−1.89106
$754$	−8.86871	−0.322979
$755$	38.6035	1.40492
$756$	−37.8474	−1.37650
$757$	10.3436	0.375945	0.187973	−	0.982174i	$-0.439808\pi$
$757$	10.3436	0.375945	0.187973	+	0.982174i	$0.439808\pi$
$758$	14.1835	0.515167
$759$	−31.3950	−1.13956
$760$	275.490	9.99306
$761$	−13.7473	−0.498338	−0.249169	−	0.968460i	$-0.580157\pi$
$761$	−13.7473	−0.498338	−0.249169	+	0.968460i	$0.580157\pi$
$762$	26.2159	0.949702
$763$	0.575566	0.0208369
$764$	113.523	4.10711
$765$	−0.285556	−0.0103243
$766$	23.6331	0.853897
$767$	10.6851	0.385815
$768$	−2.82604	−0.101976
$769$	46.8264	1.68860	0.844301	−	0.535869i	$-0.180016\pi$
$769$	46.8264	1.68860	0.844301	+	0.535869i	$0.180016\pi$
$770$	−63.6711	−2.29455
$771$	−2.19516	−0.0790569
$772$	−10.8837	−0.391714
$773$	40.4557	1.45509	0.727544	−	0.686061i	$-0.240662\pi$
$773$	40.4557	1.45509	0.727544	+	0.686061i	$0.240662\pi$
$774$	−36.0725	−1.29660
$775$	−40.3351	−1.44888
$776$	−146.266	−5.25065
$777$	0.259787	0.00931981
$778$	−38.6302	−1.38496
$779$	−75.6185	−2.70931
$780$	45.2555	1.62041
$781$	19.8169	0.709104
$782$	−0.759283	−0.0271519
$783$	−11.3182	−0.404481
$784$	−25.4858	−0.910206
$785$	−50.9389	−1.81809
$786$	−0.486863	−0.0173658
$787$	47.1350	1.68018	0.840090	−	0.542447i	$-0.182502\pi$
$787$	47.1350	1.68018	0.840090	+	0.542447i	$0.182502\pi$
$788$	39.6133	1.41116
$789$	56.5464	2.01310
$790$	158.811	5.65024
$791$	11.8670	0.421943
$792$	28.9108	1.02730
$793$	8.10502	0.287818
$794$	65.1034	2.31043
$795$	44.4636	1.57696
$796$	6.30740	0.223560
$797$	−50.4005	−1.78528	−0.892638	−	0.450774i	$-0.851148\pi$
$797$	−50.4005	−1.78528	−0.892638	+	0.450774i	$0.851148\pi$
$798$	96.3961	3.41239
$799$	−0.268548	−0.00950053
$800$	−191.773	−6.78018
$801$	−8.88333	−0.313877
$802$	−75.8153	−2.67713
$803$	7.28002	0.256906
$804$	4.06361	0.143312
$805$	54.7158	1.92848
$806$	−8.17479	−0.287945
$807$	59.7262	2.10246
$808$	12.4455	0.437832
$809$	49.3695	1.73574	0.867870	−	0.496792i	$-0.165489\pi$
$809$	49.3695	1.73574	0.867870	+	0.496792i	$0.165489\pi$
$810$	127.288	4.47243
$811$	−10.9313	−0.383849	−0.191924	−	0.981410i	$-0.561473\pi$
$811$	−10.9313	−0.383849	−0.191924	+	0.981410i	$0.561473\pi$
$812$	37.1463	1.30358
$813$	−22.1781	−0.777821
$814$	0.385859	0.0135243
$815$	−53.6850	−1.88050
$816$	1.18726	0.0415624
$817$	−77.7215	−2.71913
$818$	6.15008	0.215033
$819$	3.02033	0.105539
$820$	207.230	7.23680
$821$	11.4406	0.399281	0.199640	−	0.979869i	$-0.436023\pi$
$821$	11.4406	0.399281	0.199640	+	0.979869i	$0.436023\pi$
$822$	110.804	3.86475
$823$	35.7812	1.24725	0.623626	−	0.781723i	$-0.285659\pi$
$823$	35.7812	1.24725	0.623626	+	0.781723i	$0.285659\pi$
$824$	−97.0606	−3.38127
$825$	70.3649	2.44979
$826$	−62.3721	−2.17020
$827$	23.5260	0.818079	0.409039	−	0.912517i	$-0.365864\pi$
$827$	23.5260	0.818079	0.409039	+	0.912517i	$0.365864\pi$
$828$	−40.9748	−1.42397
$829$	18.2384	0.633447	0.316723	−	0.948518i	$-0.397417\pi$
$829$	18.2384	0.633447	0.316723	+	0.948518i	$0.397417\pi$
$830$	−7.22691	−0.250850
$831$	36.7290	1.27412
$832$	−15.5664	−0.539668
$833$	0.106560	0.00369208
$834$	−38.0706	−1.31828
$835$	−21.5841	−0.746948
$836$	102.734	3.55311
$837$	−10.4327	−0.360606
$838$	−53.7185	−1.85567
$839$	−25.7982	−0.890654	−0.445327	−	0.895368i	$-0.646913\pi$
$839$	−25.7982	−0.890654	−0.445327	+	0.895368i	$0.646913\pi$
$840$	−160.176	−5.52661
$841$	−17.8914	−0.616945
$842$	−84.7054	−2.91914
$843$	26.4109	0.909639
$844$	−42.4004	−1.45948
$845$	4.25784	0.146474
$846$	−20.1973	−0.694396
$847$	9.73428	0.334474
$848$	−58.1530	−1.99698
$849$	−67.5969	−2.31992
$850$	1.70177	0.0583701
$851$	−0.331587	−0.0113667
$852$	82.2201	2.81681
$853$	−2.83012	−0.0969016	−0.0484508	−	0.998826i	$-0.515428\pi$
$853$	−2.83012	−0.0969016	−0.0484508	+	0.998826i	$0.515428\pi$
$854$	−47.3116	−1.61897
$855$	−46.2731	−1.58251
$856$	62.4115	2.13318
$857$	13.8406	0.472787	0.236394	−	0.971657i	$-0.424035\pi$
$857$	13.8406	0.472787	0.236394	+	0.971657i	$0.424035\pi$
$858$	14.2610	0.486862
$859$	−28.5254	−0.973276	−0.486638	−	0.873604i	$-0.661777\pi$
$859$	−28.5254	−0.973276	−0.486638	+	0.873604i	$0.661777\pi$
$860$	212.994	7.26302
$861$	43.9664	1.49837
$862$	−42.4122	−1.44456
$863$	−53.5021	−1.82123	−0.910616	−	0.413254i	$-0.864392\pi$
$863$	−53.5021	−1.82123	−0.910616	+	0.413254i	$0.864392\pi$
$864$	−49.6019	−1.68749
$865$	−75.6876	−2.57346
$866$	−57.6568	−1.95926
$867$	35.5604	1.20769
$868$	34.2398	1.16218
$869$	35.9088	1.21812
$870$	−79.0002	−2.67836
$871$	0.382322	0.0129545
$872$	2.15061	0.0728288
$873$	24.5678	0.831496
$874$	−123.038	−4.16183
$875$	−75.9308	−2.56693
$876$	30.2047	1.02052
$877$	−20.1293	−0.679717	−0.339858	−	0.940477i	$-0.610379\pi$
$877$	−20.1293	−0.679717	−0.339858	+	0.940477i	$0.610379\pi$
$878$	102.245	3.45061
$879$	2.37107	0.0799741
$880$	−127.076	−4.28374
$881$	29.6932	1.00039	0.500194	−	0.865913i	$-0.333262\pi$
$881$	29.6932	1.00039	0.500194	+	0.865913i	$0.333262\pi$
$882$	8.01429	0.269855
$883$	−3.97795	−0.133869	−0.0669343	−	0.997757i	$-0.521322\pi$
$883$	−3.97795	−0.133869	−0.0669343	+	0.997757i	$0.521322\pi$
$884$	0.247477	0.00832356
$885$	95.1798	3.19943
$886$	−16.5607	−0.556369
$887$	37.3483	1.25403	0.627017	−	0.779006i	$-0.284276\pi$
$887$	37.3483	1.25403	0.627017	+	0.779006i	$0.284276\pi$
$888$	0.970697	0.0325745
$889$	−10.3309	−0.346487
$890$	73.1012	2.45036
$891$	28.7810	0.964201
$892$	−52.4299	−1.75548
$893$	−43.5169	−1.45624
$894$	62.7975	2.10026
$895$	−62.6297	−2.09348
$896$	26.7803	0.894667
$897$	−12.2552	−0.409189
$898$	−49.8528	−1.66361
$899$	10.2394	0.341503
$900$	91.8361	3.06120
$901$	0.243147	0.00810039
$902$	65.3028	2.17435
$903$	45.1891	1.50380
$904$	44.3413	1.47477
$905$	111.269	3.69872
$906$	50.4716	1.67681
$907$	37.6220	1.24922	0.624609	−	0.780937i	$-0.285258\pi$
$907$	37.6220	1.24922	0.624609	+	0.780937i	$0.285258\pi$
$908$	39.2676	1.30314
$909$	−2.09043	−0.0693353
$910$	−24.8543	−0.823914
$911$	−50.5532	−1.67490	−0.837451	−	0.546512i	$-0.815955\pi$
$911$	−50.5532	−1.67490	−0.837451	+	0.546512i	$0.815955\pi$
$912$	192.390	6.37066
$913$	−1.63408	−0.0540801
$914$	20.9748	0.693786
$915$	72.1974	2.38677
$916$	−96.3606	−3.18384
$917$	0.191858	0.00633570
$918$	0.440162	0.0145275
$919$	−14.4343	−0.476143	−0.238072	−	0.971248i	$-0.576515\pi$
$919$	−14.4343	−0.476143	−0.238072	+	0.971248i	$0.576515\pi$
$920$	204.446	6.74039
$921$	32.5115	1.07129
$922$	49.6013	1.63353
$923$	7.73562	0.254621
$924$	−59.7317	−1.96503
$925$	0.743180	0.0244356
$926$	−17.5798	−0.577709
$927$	16.3029	0.535459
$928$	48.6831	1.59810
$929$	27.3775	0.898227	0.449113	−	0.893475i	$-0.351740\pi$
$929$	27.3775	0.898227	0.449113	+	0.893475i	$0.351740\pi$
$930$	−72.8189	−2.38783
$931$	17.2675	0.565920
$932$	−5.13387	−0.168165
$933$	20.4952	0.670984
$934$	−103.823	−3.39720
$935$	0.531326	0.0173762
$936$	11.2855	0.368877
$937$	−41.6775	−1.36155	−0.680773	−	0.732495i	$-0.738356\pi$
$937$	−41.6775	−1.36155	−0.680773	+	0.732495i	$0.738356\pi$
$938$	−2.23173	−0.0728687
$939$	−20.7878	−0.678386
$940$	119.257	3.88973
$941$	21.4785	0.700180	0.350090	−	0.936716i	$-0.386151\pi$
$941$	21.4785	0.700180	0.350090	+	0.936716i	$0.386151\pi$
$942$	−66.5994	−2.16992
$943$	−56.1179	−1.82745
$944$	−124.484	−4.05160
$945$	−31.7191	−1.03182
$946$	67.1189	2.18222
$947$	−29.5599	−0.960569	−0.480284	−	0.877113i	$-0.659467\pi$
$947$	−29.5599	−0.960569	−0.480284	+	0.877113i	$0.659467\pi$
$948$	148.985	4.83881
$949$	2.84179	0.0922484
$950$	275.763	8.94694
$951$	−73.2674	−2.37586
$952$	−0.875915	−0.0283886
$953$	15.8945	0.514873	0.257437	−	0.966295i	$-0.417122\pi$
$953$	15.8945	0.514873	0.257437	+	0.966295i	$0.417122\pi$
$954$	18.2869	0.592060
$955$	95.1410	3.07869
$956$	103.889	3.36002
$957$	−17.8627	−0.577420
$958$	−34.6370	−1.11907
$959$	−43.6646	−1.41000
$960$	−138.661	−4.47528
$961$	−21.5618	−0.695541
$962$	0.150622	0.00485624
$963$	−10.4831	−0.337812
$964$	−19.1035	−0.615281
$965$	−9.12143	−0.293629
$966$	71.5374	2.30168
$967$	−26.5717	−0.854489	−0.427245	−	0.904136i	$-0.640516\pi$
$967$	−26.5717	−0.854489	−0.427245	+	0.904136i	$0.640516\pi$
$968$	36.3723	1.16905
$969$	−0.804410	−0.0258414
$970$	−202.169	−6.49127
$971$	44.5912	1.43100	0.715501	−	0.698612i	$-0.246199\pi$
$971$	44.5912	1.43100	0.715501	+	0.698612i	$0.246199\pi$
$972$	67.6545	2.17002
$973$	15.0025	0.480957
$974$	5.42644	0.173874
$975$	27.4673	0.879658
$976$	−94.4255	−3.02249
$977$	−28.0861	−0.898554	−0.449277	−	0.893392i	$-0.648318\pi$
$977$	−28.0861	−0.898554	−0.449277	+	0.893392i	$0.648318\pi$
$978$	−70.1897	−2.24442
$979$	16.5289	0.528266
$980$	−47.3212	−1.51162
$981$	−0.361231	−0.0115332
$982$	−69.7217	−2.22491
$983$	48.4954	1.54676	0.773381	−	0.633941i	$-0.218564\pi$
$983$	48.4954	1.54676	0.773381	+	0.633941i	$0.218564\pi$
$984$	164.281	5.23709
$985$	33.1991	1.05781
$986$	−0.432008	−0.0137579
$987$	25.3017	0.805364
$988$	40.1025	1.27583
$989$	−57.6786	−1.83407
$990$	39.9606	1.27003
$991$	−20.5805	−0.653761	−0.326880	−	0.945066i	$-0.605997\pi$
$991$	−20.5805	−0.653761	−0.326880	+	0.945066i	$0.605997\pi$
$992$	44.8739	1.42475
$993$	−41.5311	−1.31795
$994$	−45.1553	−1.43224
$995$	5.28610	0.167581
$996$	−6.77977	−0.214825
$997$	1.32641	0.0420078	0.0210039	−	0.999779i	$-0.493314\pi$
$997$	1.32641	0.0420078	0.0210039	+	0.999779i	$0.493314\pi$
$998$	61.8110	1.95659
$999$	0.192224	0.00608168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8047.2.a.d.1.4	✓	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8047.2.a.d.1.4	✓	156	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:	\( N \)	\(=\)	\( 8047 = 13 \cdot 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66092 q^{2} -2.09208 q^{3} +5.08047 q^{4} +4.25784 q^{5} +5.56685 q^{6} -2.19372 q^{7} -8.19688 q^{8} +1.37680 q^{9} +O(q^{10})\)	\(q-2.66092 q^{2} -2.09208 q^{3} +5.08047 q^{4} +4.25784 q^{5} +5.56685 q^{6} -2.19372 q^{7} -8.19688 q^{8} +1.37680 q^{9} -11.3297 q^{10} -2.56177 q^{11} -10.6288 q^{12} -1.00000 q^{13} +5.83732 q^{14} -8.90774 q^{15} +11.6503 q^{16} -0.0487115 q^{17} -3.66356 q^{18} -7.89347 q^{19} +21.6318 q^{20} +4.58945 q^{21} +6.81666 q^{22} -5.85789 q^{23} +17.1485 q^{24} +13.1292 q^{25} +2.66092 q^{26} +3.39586 q^{27} -11.1452 q^{28} -3.33295 q^{29} +23.7027 q^{30} -3.07217 q^{31} -14.6066 q^{32} +5.35943 q^{33} +0.129617 q^{34} -9.34052 q^{35} +6.99481 q^{36} +0.0566053 q^{37} +21.0038 q^{38} +2.09208 q^{39} -34.9010 q^{40} +9.57989 q^{41} -12.2121 q^{42} +9.84631 q^{43} -13.0150 q^{44} +5.86220 q^{45} +15.5874 q^{46} +5.51302 q^{47} -24.3733 q^{48} -2.18757 q^{49} -34.9356 q^{50} +0.101908 q^{51} -5.08047 q^{52} -4.99157 q^{53} -9.03610 q^{54} -10.9076 q^{55} +17.9817 q^{56} +16.5138 q^{57} +8.86871 q^{58} -10.6851 q^{59} -45.2555 q^{60} -8.10502 q^{61} +8.17479 q^{62} -3.02033 q^{63} +15.5664 q^{64} -4.25784 q^{65} -14.2610 q^{66} -0.382322 q^{67} -0.247477 q^{68} +12.2552 q^{69} +24.8543 q^{70} -7.73562 q^{71} -11.2855 q^{72} -2.84179 q^{73} -0.150622 q^{74} -27.4673 q^{75} -40.1025 q^{76} +5.61982 q^{77} -5.56685 q^{78} -14.0172 q^{79} +49.6049 q^{80} -11.2348 q^{81} -25.4913 q^{82} +0.637871 q^{83} +23.3166 q^{84} -0.207406 q^{85} -26.2002 q^{86} +6.97281 q^{87} +20.9985 q^{88} -6.45214 q^{89} -15.5988 q^{90} +2.19372 q^{91} -29.7608 q^{92} +6.42723 q^{93} -14.6697 q^{94} -33.6091 q^{95} +30.5582 q^{96} +17.8441 q^{97} +5.82094 q^{98} -3.52705 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 13 q^{2} + 23 q^{3} + 161 q^{4} + 39 q^{5} + 25 q^{6} + 19 q^{7} + 42 q^{8} + 169 q^{9}+O(q^{10}) \) 156 * q + 13 * q^2 + 23 * q^3 + 161 * q^4 + 39 * q^5 + 25 * q^6 + 19 * q^7 + 42 * q^8 + 169 * q^9	\( 156 q + 13 q^{2} + 23 q^{3} + 161 q^{4} + 39 q^{5} + 25 q^{6} + 19 q^{7} + 42 q^{8} + 169 q^{9} + 11 q^{10} + 23 q^{11} + 57 q^{12} - 156 q^{13} + 18 q^{14} + 32 q^{15} + 159 q^{16} + 119 q^{17} + 36 q^{18} + 35 q^{19} + 109 q^{20} + 33 q^{21} + 11 q^{22} + 55 q^{23} + 63 q^{24} + 189 q^{25} - 13 q^{26} + 89 q^{27} + 54 q^{28} - 55 q^{29} + 47 q^{31} + 112 q^{32} + 109 q^{33} + 51 q^{34} + 25 q^{35} + 162 q^{36} + 53 q^{37} + 37 q^{38} - 23 q^{39} + 25 q^{40} + 113 q^{41} + 26 q^{42} + 31 q^{43} + 86 q^{44} + 144 q^{45} + 37 q^{46} + 115 q^{47} + 129 q^{48} + 189 q^{49} + 72 q^{50} - 4 q^{51} - 161 q^{52} + 51 q^{53} + 108 q^{54} + 22 q^{55} + 39 q^{56} + 102 q^{57} + 31 q^{58} + 75 q^{59} + 97 q^{60} + 7 q^{61} + 77 q^{62} + 94 q^{63} + 158 q^{64} - 39 q^{65} + 48 q^{66} + 37 q^{67} + 235 q^{68} + 27 q^{69} + 38 q^{70} + 70 q^{71} + 152 q^{72} + 155 q^{73} - 18 q^{74} + 80 q^{75} + 21 q^{76} + 101 q^{77} - 25 q^{78} + 10 q^{79} + 211 q^{80} + 220 q^{81} + 45 q^{82} + 132 q^{83} + 86 q^{84} + 74 q^{85} + 35 q^{86} + 53 q^{87} + 51 q^{88} + 190 q^{89} - 27 q^{90} - 19 q^{91} + 125 q^{92} + 96 q^{93} - 19 q^{94} + 72 q^{95} + 146 q^{96} + 155 q^{97} + 135 q^{98} + 89 q^{99}+O(q^{100}) \) 156 * q + 13 * q^2 + 23 * q^3 + 161 * q^4 + 39 * q^5 + 25 * q^6 + 19 * q^7 + 42 * q^8 + 169 * q^9 + 11 * q^10 + 23 * q^11 + 57 * q^12 - 156 * q^13 + 18 * q^14 + 32 * q^15 + 159 * q^16 + 119 * q^17 + 36 * q^18 + 35 * q^19 + 109 * q^20 + 33 * q^21 + 11 * q^22 + 55 * q^23 + 63 * q^24 + 189 * q^25 - 13 * q^26 + 89 * q^27 + 54 * q^28 - 55 * q^29 + 47 * q^31 + 112 * q^32 + 109 * q^33 + 51 * q^34 + 25 * q^35 + 162 * q^36 + 53 * q^37 + 37 * q^38 - 23 * q^39 + 25 * q^40 + 113 * q^41 + 26 * q^42 + 31 * q^43 + 86 * q^44 + 144 * q^45 + 37 * q^46 + 115 * q^47 + 129 * q^48 + 189 * q^49 + 72 * q^50 - 4 * q^51 - 161 * q^52 + 51 * q^53 + 108 * q^54 + 22 * q^55 + 39 * q^56 + 102 * q^57 + 31 * q^58 + 75 * q^59 + 97 * q^60 + 7 * q^61 + 77 * q^62 + 94 * q^63 + 158 * q^64 - 39 * q^65 + 48 * q^66 + 37 * q^67 + 235 * q^68 + 27 * q^69 + 38 * q^70 + 70 * q^71 + 152 * q^72 + 155 * q^73 - 18 * q^74 + 80 * q^75 + 21 * q^76 + 101 * q^77 - 25 * q^78 + 10 * q^79 + 211 * q^80 + 220 * q^81 + 45 * q^82 + 132 * q^83 + 86 * q^84 + 74 * q^85 + 35 * q^86 + 53 * q^87 + 51 * q^88 + 190 * q^89 - 27 * q^90 - 19 * q^91 + 125 * q^92 + 96 * q^93 - 19 * q^94 + 72 * q^95 + 146 * q^96 + 155 * q^97 + 135 * q^98 + 89 * q^99

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