LMFDB - Embedded newform 6001.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$1$
Dimension:	$114$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69250 q^{2} +0.578947 q^{3} +5.24958 q^{4} +4.35539 q^{5} -1.55882 q^{6} -1.96736 q^{7} -8.74952 q^{8} -2.66482 q^{9} +O(q^{10})$	\(q-2.69250 q^{2} +0.578947 q^{3} +5.24958 q^{4} +4.35539 q^{5} -1.55882 q^{6} -1.96736 q^{7} -8.74952 q^{8} -2.66482 q^{9} -11.7269 q^{10} +2.40712 q^{11} +3.03923 q^{12} +3.82566 q^{13} +5.29713 q^{14} +2.52154 q^{15} +13.0590 q^{16} +1.00000 q^{17} +7.17504 q^{18} -4.69379 q^{19} +22.8640 q^{20} -1.13900 q^{21} -6.48119 q^{22} -0.242259 q^{23} -5.06550 q^{24} +13.9695 q^{25} -10.3006 q^{26} -3.27963 q^{27} -10.3278 q^{28} +2.26369 q^{29} -6.78926 q^{30} -9.72579 q^{31} -17.6623 q^{32} +1.39360 q^{33} -2.69250 q^{34} -8.56863 q^{35} -13.9892 q^{36} -7.73625 q^{37} +12.6380 q^{38} +2.21485 q^{39} -38.1076 q^{40} -1.87982 q^{41} +3.06676 q^{42} -11.1724 q^{43} +12.6364 q^{44} -11.6063 q^{45} +0.652283 q^{46} -5.16445 q^{47} +7.56044 q^{48} -3.12949 q^{49} -37.6129 q^{50} +0.578947 q^{51} +20.0831 q^{52} -2.26203 q^{53} +8.83042 q^{54} +10.4840 q^{55} +17.2135 q^{56} -2.71745 q^{57} -6.09499 q^{58} -14.1284 q^{59} +13.2370 q^{60} +1.16500 q^{61} +26.1867 q^{62} +5.24266 q^{63} +21.4378 q^{64} +16.6623 q^{65} -3.75226 q^{66} -3.92378 q^{67} +5.24958 q^{68} -0.140255 q^{69} +23.0711 q^{70} -3.51936 q^{71} +23.3159 q^{72} +16.2155 q^{73} +20.8299 q^{74} +8.08757 q^{75} -24.6404 q^{76} -4.73568 q^{77} -5.96350 q^{78} -5.97141 q^{79} +56.8769 q^{80} +6.09573 q^{81} +5.06141 q^{82} -2.20212 q^{83} -5.97926 q^{84} +4.35539 q^{85} +30.0817 q^{86} +1.31055 q^{87} -21.0612 q^{88} -6.72046 q^{89} +31.2501 q^{90} -7.52646 q^{91} -1.27176 q^{92} -5.63071 q^{93} +13.9053 q^{94} -20.4433 q^{95} -10.2255 q^{96} -18.8572 q^{97} +8.42617 q^{98} -6.41455 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) $ 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * 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 $

$2$	−2.69250	−1.90389	−0.951944	−	0.306271i	$-0.900918\pi$
$2$	−2.69250	−1.90389	−0.951944	+	0.306271i	$0.900918\pi$
$3$	0.578947	0.334255	0.167127	−	0.985935i	$-0.446551\pi$
$3$	0.578947	0.334255	0.167127	+	0.985935i	$0.446551\pi$
$4$	5.24958	2.62479
$5$	4.35539	1.94779	0.973896	−	0.226995i	$-0.0728901\pi$
$5$	4.35539	1.94779	0.973896	+	0.226995i	$0.0728901\pi$
$6$	−1.55882	−0.636384
$7$	−1.96736	−0.743593	−0.371796	−	0.928314i	$-0.621258\pi$
$7$	−1.96736	−0.743593	−0.371796	+	0.928314i	$0.621258\pi$
$8$	−8.74952	−3.09342
$9$	−2.66482	−0.888274
$10$	−11.7269	−3.70838
$11$	2.40712	0.725775	0.362887	−	0.931833i	$-0.381791\pi$
$11$	2.40712	0.725775	0.362887	+	0.931833i	$0.381791\pi$
$12$	3.03923	0.877350
$13$	3.82566	1.06105	0.530524	−	0.847670i	$-0.321995\pi$
$13$	3.82566	1.06105	0.530524	+	0.847670i	$0.321995\pi$
$14$	5.29713	1.41572
$15$	2.52154	0.651059
$16$	13.0590	3.26474
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	7.17504	1.69117
$19$	−4.69379	−1.07683	−0.538414	−	0.842680i	$-0.680976\pi$
$19$	−4.69379	−1.07683	−0.538414	+	0.842680i	$0.680976\pi$
$20$	22.8640	5.11255
$21$	−1.13900	−0.248550
$22$	−6.48119	−1.38179
$23$	−0.242259	−0.0505144	−0.0252572	−	0.999681i	$-0.508040\pi$
$23$	−0.242259	−0.0505144	−0.0252572	+	0.999681i	$0.508040\pi$
$24$	−5.06550	−1.03399
$25$	13.9695	2.79389
$26$	−10.3006	−2.02012
$27$	−3.27963	−0.631165
$28$	−10.3278	−1.95178
$29$	2.26369	0.420356	0.210178	−	0.977663i	$-0.432596\pi$
$29$	2.26369	0.420356	0.210178	+	0.977663i	$0.432596\pi$
$30$	−6.78926	−1.23954
$31$	−9.72579	−1.74680	−0.873402	−	0.487001i	$-0.838091\pi$
$31$	−9.72579	−1.74680	−0.873402	+	0.487001i	$0.838091\pi$
$32$	−17.6623	−3.12228
$33$	1.39360	0.242594
$34$	−2.69250	−0.461761
$35$	−8.56863	−1.44836
$36$	−13.9892	−2.33153
$37$	−7.73625	−1.27183	−0.635916	−	0.771758i	$-0.719378\pi$
$37$	−7.73625	−1.27183	−0.635916	+	0.771758i	$0.719378\pi$
$38$	12.6380	2.05016
$39$	2.21485	0.354660
$40$	−38.1076	−6.02534
$41$	−1.87982	−0.293578	−0.146789	−	0.989168i	$-0.546894\pi$
$41$	−1.87982	−0.293578	−0.146789	+	0.989168i	$0.546894\pi$
$42$	3.06676	0.473211
$43$	−11.1724	−1.70377	−0.851887	−	0.523726i	$-0.824542\pi$
$43$	−11.1724	−1.70377	−0.851887	+	0.523726i	$0.824542\pi$
$44$	12.6364	1.90501
$45$	−11.6063	−1.73017
$46$	0.652283	0.0961738
$47$	−5.16445	−0.753312	−0.376656	−	0.926353i	$-0.622926\pi$
$47$	−5.16445	−0.753312	−0.376656	+	0.926353i	$0.622926\pi$
$48$	7.56044	1.09125
$49$	−3.12949	−0.447070
$50$	−37.6129	−5.31926
$51$	0.578947	0.0810687
$52$	20.0831	2.78503
$53$	−2.26203	−0.310714	−0.155357	−	0.987858i	$-0.549653\pi$
$53$	−2.26203	−0.310714	−0.155357	+	0.987858i	$0.549653\pi$
$54$	8.83042	1.20167
$55$	10.4840	1.41366
$56$	17.2135	2.30025
$57$	−2.71745	−0.359935
$58$	−6.09499	−0.800311
$59$	−14.1284	−1.83935	−0.919677	−	0.392675i	$-0.871550\pi$
$59$	−14.1284	−1.83935	−0.919677	+	0.392675i	$0.871550\pi$
$60$	13.2370	1.70889
$61$	1.16500	0.149163	0.0745814	−	0.997215i	$-0.476238\pi$
$61$	1.16500	0.149163	0.0745814	+	0.997215i	$0.476238\pi$
$62$	26.1867	3.32572
$63$	5.24266	0.660514
$64$	21.4378	2.67973
$65$	16.6623	2.06670
$66$	−3.75226	−0.461871
$67$	−3.92378	−0.479365	−0.239683	−	0.970851i	$-0.577043\pi$
$67$	−3.92378	−0.479365	−0.239683	+	0.970851i	$0.577043\pi$
$68$	5.24958	0.636605
$69$	−0.140255	−0.0168847
$70$	23.0711	2.75752
$71$	−3.51936	−0.417672	−0.208836	−	0.977951i	$-0.566967\pi$
$71$	−3.51936	−0.417672	−0.208836	+	0.977951i	$0.566967\pi$
$72$	23.3159	2.74780
$73$	16.2155	1.89788	0.948939	−	0.315458i	$-0.102158\pi$
$73$	16.2155	1.89788	0.948939	+	0.315458i	$0.102158\pi$
$74$	20.8299	2.42143
$75$	8.08757	0.933873
$76$	−24.6404	−2.82645
$77$	−4.73568	−0.539681
$78$	−5.96350	−0.675234
$79$	−5.97141	−0.671836	−0.335918	−	0.941891i	$-0.609047\pi$
$79$	−5.97141	−0.671836	−0.335918	+	0.941891i	$0.609047\pi$
$80$	56.8769	6.35903
$81$	6.09573	0.677304
$82$	5.06141	0.558940
$83$	−2.20212	−0.241714	−0.120857	−	0.992670i	$-0.538564\pi$
$83$	−2.20212	−0.241714	−0.120857	+	0.992670i	$0.538564\pi$
$84$	−5.97926	−0.652391
$85$	4.35539	0.472409
$86$	30.0817	3.24379
$87$	1.31055	0.140506
$88$	−21.0612	−2.24513
$89$	−6.72046	−0.712367	−0.356184	−	0.934416i	$-0.615922\pi$
$89$	−6.72046	−0.712367	−0.356184	+	0.934416i	$0.615922\pi$
$90$	31.2501	3.29405
$91$	−7.52646	−0.788987
$92$	−1.27176	−0.132590
$93$	−5.63071	−0.583878
$94$	13.9053	1.43422
$95$	−20.4433	−2.09744
$96$	−10.2255	−1.04364
$97$	−18.8572	−1.91466	−0.957329	−	0.289002i	$-0.906677\pi$
$97$	−18.8572	−1.91466	−0.957329	+	0.289002i	$0.906677\pi$
$98$	8.42617	0.851172
$99$	−6.41455	−0.644686
$100$	73.3339	7.33339
$101$	4.88283	0.485859	0.242930	−	0.970044i	$-0.421892\pi$
$101$	4.88283	0.485859	0.242930	+	0.970044i	$0.421892\pi$
$102$	−1.55882	−0.154346
$103$	−4.63590	−0.456789	−0.228395	−	0.973569i	$-0.573348\pi$
$103$	−4.63590	−0.456789	−0.228395	+	0.973569i	$0.573348\pi$
$104$	−33.4727	−3.28227
$105$	−4.96078	−0.484123
$106$	6.09054	0.591566
$107$	−2.38370	−0.230441	−0.115221	−	0.993340i	$-0.536758\pi$
$107$	−2.38370	−0.230441	−0.115221	+	0.993340i	$0.536758\pi$
$108$	−17.2167	−1.65668
$109$	3.92893	0.376323	0.188161	−	0.982138i	$-0.439747\pi$
$109$	3.92893	0.376323	0.188161	+	0.982138i	$0.439747\pi$
$110$	−28.2281	−2.69145
$111$	−4.47888	−0.425116
$112$	−25.6917	−2.42763
$113$	−3.90331	−0.367193	−0.183596	−	0.983002i	$-0.558774\pi$
$113$	−3.90331	−0.367193	−0.183596	+	0.983002i	$0.558774\pi$
$114$	7.31675	0.685277
$115$	−1.05513	−0.0983916
$116$	11.8834	1.10335
$117$	−10.1947	−0.942501
$118$	38.0407	3.50193
$119$	−1.96736	−0.180348
$120$	−22.0623	−2.01400
$121$	−5.20576	−0.473251
$122$	−3.13676	−0.283989
$123$	−1.08831	−0.0981299
$124$	−51.0563	−4.58499
$125$	39.0656	3.49413
$126$	−14.1159	−1.25754
$127$	9.82317	0.871665	0.435832	−	0.900028i	$-0.356454\pi$
$127$	9.82317	0.871665	0.435832	+	0.900028i	$0.356454\pi$
$128$	−22.3969	−1.97962
$129$	−6.46822	−0.569495
$130$	−44.8632	−3.93477
$131$	−12.1238	−1.05926	−0.529632	−	0.848228i	$-0.677670\pi$
$131$	−12.1238	−1.05926	−0.529632	+	0.848228i	$0.677670\pi$
$132$	7.31579	0.636758
$133$	9.23438	0.800722
$134$	10.5648	0.912658
$135$	−14.2841	−1.22938
$136$	−8.74952	−0.750265
$137$	−6.37444	−0.544605	−0.272303	−	0.962212i	$-0.587785\pi$
$137$	−6.37444	−0.544605	−0.272303	+	0.962212i	$0.587785\pi$
$138$	0.377637	0.0321466
$139$	7.25620	0.615463	0.307731	−	0.951473i	$-0.400430\pi$
$139$	7.25620	0.615463	0.307731	+	0.951473i	$0.400430\pi$
$140$	−44.9818	−3.80165
$141$	−2.98994	−0.251798
$142$	9.47591	0.795200
$143$	9.20883	0.770081
$144$	−34.7998	−2.89998
$145$	9.85925	0.818767
$146$	−43.6603	−3.61335
$147$	−1.81181	−0.149435
$148$	−40.6121	−3.33829
$149$	−7.53592	−0.617366	−0.308683	−	0.951165i	$-0.599888\pi$
$149$	−7.53592	−0.617366	−0.308683	+	0.951165i	$0.599888\pi$
$150$	−21.7758	−1.77799
$151$	−7.19691	−0.585676	−0.292838	−	0.956162i	$-0.594600\pi$
$151$	−7.19691	−0.585676	−0.292838	+	0.956162i	$0.594600\pi$
$152$	41.0684	3.33109
$153$	−2.66482	−0.215438
$154$	12.7508	1.02749
$155$	−42.3597	−3.40241
$156$	11.6271	0.930910
$157$	5.65988	0.451708	0.225854	−	0.974161i	$-0.427483\pi$
$157$	5.65988	0.451708	0.225854	+	0.974161i	$0.427483\pi$
$158$	16.0780	1.27910
$159$	−1.30960	−0.103858
$160$	−76.9261	−6.08154
$161$	0.476610	0.0375621
$162$	−16.4128	−1.28951
$163$	11.7966	0.923982	0.461991	−	0.886885i	$-0.347135\pi$
$163$	11.7966	0.923982	0.461991	+	0.886885i	$0.347135\pi$
$164$	−9.86825	−0.770581
$165$	6.06966	0.472522
$166$	5.92921	0.460196
$167$	6.20708	0.480318	0.240159	−	0.970734i	$-0.422800\pi$
$167$	6.20708	0.480318	0.240159	+	0.970734i	$0.422800\pi$
$168$	9.96567	0.768868
$169$	1.63569	0.125822
$170$	−11.7269	−0.899414
$171$	12.5081	0.956519
$172$	−58.6504	−4.47205
$173$	25.6014	1.94644	0.973218	−	0.229885i	$-0.0738349\pi$
$173$	25.6014	1.94644	0.973218	+	0.229885i	$0.0738349\pi$
$174$	−3.52867	−0.267508
$175$	−27.4830	−2.07752
$176$	31.4345	2.36946
$177$	−8.17956	−0.614814
$178$	18.0949	1.35627
$179$	−10.0094	−0.748139	−0.374070	−	0.927401i	$-0.622038\pi$
$179$	−10.0094	−0.748139	−0.374070	+	0.927401i	$0.622038\pi$
$180$	−60.9285	−4.54134
$181$	2.08321	0.154844	0.0774220	−	0.996998i	$-0.475331\pi$
$181$	2.08321	0.154844	0.0774220	+	0.996998i	$0.475331\pi$
$182$	20.2650	1.50214
$183$	0.674472	0.0498584
$184$	2.11965	0.156262
$185$	−33.6944	−2.47726
$186$	15.1607	1.11164
$187$	2.40712	0.176026
$188$	−27.1112	−1.97729
$189$	6.45221	0.469330
$190$	55.0437	3.99329
$191$	5.35449	0.387437	0.193719	−	0.981057i	$-0.437945\pi$
$191$	5.35449	0.387437	0.193719	+	0.981057i	$0.437945\pi$
$192$	12.4113	0.895712
$193$	−13.8144	−0.994382	−0.497191	−	0.867641i	$-0.665635\pi$
$193$	−13.8144	−0.994382	−0.497191	+	0.867641i	$0.665635\pi$
$194$	50.7731	3.64529
$195$	9.64656	0.690805
$196$	−16.4285	−1.17347
$197$	−25.5850	−1.82286	−0.911428	−	0.411460i	$-0.865019\pi$
$197$	−25.5850	−1.82286	−0.911428	+	0.411460i	$0.865019\pi$
$198$	17.2712	1.22741
$199$	22.1085	1.56723	0.783615	−	0.621247i	$-0.213373\pi$
$199$	22.1085	1.56723	0.783615	+	0.621247i	$0.213373\pi$
$200$	−122.226	−8.64269
$201$	−2.27166	−0.160230
$202$	−13.1470	−0.925022
$203$	−4.45349	−0.312574
$204$	3.03923	0.212789
$205$	−8.18734	−0.571829
$206$	12.4822	0.869676
$207$	0.645576	0.0448706
$208$	49.9591	3.46404
$209$	−11.2985	−0.781535
$210$	13.3569	0.921716
$211$	−2.14083	−0.147381	−0.0736905	−	0.997281i	$-0.523478\pi$
$211$	−2.14083	−0.147381	−0.0736905	+	0.997281i	$0.523478\pi$
$212$	−11.8747	−0.815560
$213$	−2.03752	−0.139609
$214$	6.41814	0.438735
$215$	−48.6602	−3.31860
$216$	28.6952	1.95246
$217$	19.1341	1.29891
$218$	−10.5787	−0.716477
$219$	9.38790	0.634375
$220$	55.0364	3.71056
$221$	3.82566	0.257342
$222$	12.0594	0.809374
$223$	−10.7208	−0.717918	−0.358959	−	0.933353i	$-0.616868\pi$
$223$	−10.7208	−0.717918	−0.358959	+	0.933353i	$0.616868\pi$
$224$	34.7480	2.32170
$225$	−37.2261	−2.48174
$226$	10.5097	0.699094
$227$	20.3745	1.35231	0.676153	−	0.736762i	$-0.263646\pi$
$227$	20.3745	1.35231	0.676153	+	0.736762i	$0.263646\pi$
$228$	−14.2655	−0.944755
$229$	15.4128	1.01851	0.509254	−	0.860616i	$-0.329921\pi$
$229$	15.4128	1.01851	0.509254	+	0.860616i	$0.329921\pi$
$230$	2.84095	0.187327
$231$	−2.74170	−0.180391
$232$	−19.8062	−1.30034
$233$	29.1057	1.90678	0.953388	−	0.301749i	$-0.0975703\pi$
$233$	29.1057	1.90678	0.953388	+	0.301749i	$0.0975703\pi$
$234$	27.4493	1.79442
$235$	−22.4932	−1.46729
$236$	−74.1680	−4.82792
$237$	−3.45713	−0.224565
$238$	5.29713	0.343362
$239$	−3.61041	−0.233538	−0.116769	−	0.993159i	$-0.537254\pi$
$239$	−3.61041	−0.233538	−0.116769	+	0.993159i	$0.537254\pi$
$240$	32.9287	2.12554
$241$	11.0836	0.713956	0.356978	−	0.934113i	$-0.383807\pi$
$241$	11.0836	0.713956	0.356978	+	0.934113i	$0.383807\pi$
$242$	14.0165	0.901018
$243$	13.3680	0.857557
$244$	6.11576	0.391521
$245$	−13.6302	−0.870799
$246$	2.93029	0.186828
$247$	−17.9568	−1.14257
$248$	85.0960	5.40360
$249$	−1.27491	−0.0807940
$250$	−105.184	−6.65243
$251$	−12.0481	−0.760468	−0.380234	−	0.924890i	$-0.624157\pi$
$251$	−12.0481	−0.760468	−0.380234	+	0.924890i	$0.624157\pi$
$252$	27.5218	1.73371
$253$	−0.583146	−0.0366621
$254$	−26.4489	−1.65955
$255$	2.52154	0.157905
$256$	17.4281	1.08926
$257$	8.97975	0.560142	0.280071	−	0.959979i	$-0.409642\pi$
$257$	8.97975	0.560142	0.280071	+	0.959979i	$0.409642\pi$
$258$	17.4157	1.08425
$259$	15.2200	0.945725
$260$	87.4699	5.42466
$261$	−6.03232	−0.373391
$262$	32.6434	2.01672
$263$	15.5660	0.959840	0.479920	−	0.877312i	$-0.340666\pi$
$263$	15.5660	0.959840	0.479920	+	0.877312i	$0.340666\pi$
$264$	−12.1933	−0.750445
$265$	−9.85206	−0.605207
$266$	−24.8636	−1.52449
$267$	−3.89079	−0.238112
$268$	−20.5982	−1.25823
$269$	−23.0578	−1.40586	−0.702930	−	0.711259i	$-0.748125\pi$
$269$	−23.0578	−1.40586	−0.702930	+	0.711259i	$0.748125\pi$
$270$	38.4600	2.34060
$271$	−28.2651	−1.71698	−0.858492	−	0.512827i	$-0.828598\pi$
$271$	−28.2651	−1.71698	−0.858492	+	0.512827i	$0.828598\pi$
$272$	13.0590	0.791815
$273$	−4.35742	−0.263723
$274$	17.1632	1.03687
$275$	33.6262	2.02774
$276$	−0.736279	−0.0443188
$277$	−15.2700	−0.917488	−0.458744	−	0.888568i	$-0.651701\pi$
$277$	−15.2700	−0.917488	−0.458744	+	0.888568i	$0.651701\pi$
$278$	−19.5373	−1.17177
$279$	25.9175	1.55164
$280$	74.9714	4.48040
$281$	7.84550	0.468023	0.234012	−	0.972234i	$-0.424815\pi$
$281$	7.84550	0.468023	0.234012	+	0.972234i	$0.424815\pi$
$282$	8.05043	0.479396
$283$	0.299888	0.0178265	0.00891323	−	0.999960i	$-0.497163\pi$
$283$	0.299888	0.0178265	0.00891323	+	0.999960i	$0.497163\pi$
$284$	−18.4752	−1.09630
$285$	−11.8356	−0.701079
$286$	−24.7948	−1.46615
$287$	3.69828	0.218302
$288$	47.0667	2.77343
$289$	1.00000	0.0588235
$290$	−26.5461	−1.55884
$291$	−10.9173	−0.639984
$292$	85.1245	4.98154
$293$	−12.8401	−0.750128	−0.375064	−	0.926999i	$-0.622379\pi$
$293$	−12.8401	−0.750128	−0.375064	+	0.926999i	$0.622379\pi$
$294$	4.87830	0.284508
$295$	−61.5346	−3.58268
$296$	67.6885	3.93431
$297$	−7.89447	−0.458083
$298$	20.2905	1.17540
$299$	−0.926799	−0.0535982
$300$	42.4564	2.45122
$301$	21.9801	1.26691
$302$	19.3777	1.11506
$303$	2.82690	0.162401
$304$	−61.2959	−3.51556
$305$	5.07403	0.290538
$306$	7.17504	0.410170
$307$	25.6965	1.46658	0.733289	−	0.679917i	$-0.237984\pi$
$307$	25.6965	1.46658	0.733289	+	0.679917i	$0.237984\pi$
$308$	−24.8603	−1.41655
$309$	−2.68394	−0.152684
$310$	114.054	6.47781
$311$	−5.46339	−0.309801	−0.154900	−	0.987930i	$-0.549506\pi$
$311$	−5.46339	−0.309801	−0.154900	+	0.987930i	$0.549506\pi$
$312$	−19.3789	−1.09711
$313$	0.773421	0.0437163	0.0218582	−	0.999761i	$-0.493042\pi$
$313$	0.773421	0.0437163	0.0218582	+	0.999761i	$0.493042\pi$
$314$	−15.2393	−0.860001
$315$	22.8339	1.28654
$316$	−31.3474	−1.76343
$317$	−13.8154	−0.775951	−0.387975	−	0.921670i	$-0.626825\pi$
$317$	−13.8154	−0.775951	−0.387975	+	0.921670i	$0.626825\pi$
$318$	3.52610	0.197734
$319$	5.44897	0.305084
$320$	93.3701	5.21955
$321$	−1.38004	−0.0770262
$322$	−1.28328	−0.0715141
$323$	−4.69379	−0.261169
$324$	32.0000	1.77778
$325$	53.4424	2.96445
$326$	−31.7624	−1.75916
$327$	2.27464	0.125788
$328$	16.4475	0.908160
$329$	10.1603	0.560157
$330$	−16.3426	−0.899629
$331$	22.8517	1.25604	0.628021	−	0.778196i	$-0.283865\pi$
$331$	22.8517	1.25604	0.628021	+	0.778196i	$0.283865\pi$
$332$	−11.5602	−0.634448
$333$	20.6157	1.12974
$334$	−16.7126	−0.914473
$335$	−17.0896	−0.933704
$336$	−14.8741	−0.811449
$337$	32.1850	1.75323	0.876615	−	0.481192i	$-0.159796\pi$
$337$	32.1850	1.75323	0.876615	+	0.481192i	$0.159796\pi$
$338$	−4.40409	−0.239551
$339$	−2.25981	−0.122736
$340$	22.8640	1.23997
$341$	−23.4112	−1.26779
$342$	−33.6781	−1.82110
$343$	19.9284	1.07603
$344$	97.7530	5.27049
$345$	−0.610865	−0.0328879
$346$	−68.9318	−3.70580
$347$	−14.0641	−0.754999	−0.377499	−	0.926010i	$-0.623216\pi$
$347$	−14.0641	−0.754999	−0.377499	+	0.926010i	$0.623216\pi$
$348$	6.87986	0.368799
$349$	26.3694	1.41152	0.705761	−	0.708450i	$-0.250605\pi$
$349$	26.3694	1.41152	0.705761	+	0.708450i	$0.250605\pi$
$350$	73.9981	3.95536
$351$	−12.5468	−0.669696
$352$	−42.5152	−2.26607
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	22.0235	1.17054
$355$	−15.3282	−0.813537
$356$	−35.2796	−1.86982
$357$	−1.13900	−0.0602821
$358$	26.9504	1.42437
$359$	−8.44042	−0.445468	−0.222734	−	0.974879i	$-0.571498\pi$
$359$	−8.44042	−0.445468	−0.222734	+	0.974879i	$0.571498\pi$
$360$	101.550	5.35215
$361$	3.03165	0.159560
$362$	−5.60906	−0.294806
$363$	−3.01386	−0.158187
$364$	−39.5108	−2.07093
$365$	70.6248	3.69667
$366$	−1.81602	−0.0949248
$367$	17.2351	0.899663	0.449831	−	0.893114i	$-0.351484\pi$
$367$	17.2351	0.899663	0.449831	+	0.893114i	$0.351484\pi$
$368$	−3.16364	−0.164916
$369$	5.00937	0.260778
$370$	90.7225	4.71644
$371$	4.45024	0.231045
$372$	−29.5589	−1.53256
$373$	2.56498	0.132810	0.0664049	−	0.997793i	$-0.478847\pi$
$373$	2.56498	0.132810	0.0664049	+	0.997793i	$0.478847\pi$
$374$	−6.48119	−0.335134
$375$	22.6169	1.16793
$376$	45.1864	2.33031
$377$	8.66010	0.446018
$378$	−17.3726	−0.893551
$379$	−29.6961	−1.52538	−0.762692	−	0.646761i	$-0.776123\pi$
$379$	−29.6961	−1.52538	−0.762692	+	0.646761i	$0.776123\pi$
$380$	−107.319	−5.50534
$381$	5.68709	0.291358
$382$	−14.4170	−0.737637
$383$	−15.6091	−0.797585	−0.398793	−	0.917041i	$-0.630571\pi$
$383$	−15.6091	−0.797585	−0.398793	+	0.917041i	$0.630571\pi$
$384$	−12.9666	−0.661699
$385$	−20.6257	−1.05119
$386$	37.1953	1.89319
$387$	29.7724	1.51342
$388$	−98.9924	−5.02558
$389$	7.79792	0.395370	0.197685	−	0.980266i	$-0.436658\pi$
$389$	7.79792	0.395370	0.197685	+	0.980266i	$0.436658\pi$
$390$	−25.9734	−1.31522
$391$	−0.242259	−0.0122515
$392$	27.3815	1.38298
$393$	−7.01905	−0.354064
$394$	68.8877	3.47051
$395$	−26.0078	−1.30860
$396$	−33.6737	−1.69217
$397$	21.1464	1.06131	0.530653	−	0.847589i	$-0.321947\pi$
$397$	21.1464	1.06131	0.530653	+	0.847589i	$0.321947\pi$
$398$	−59.5273	−2.98383
$399$	5.34621	0.267645
$400$	182.427	9.12133
$401$	−12.4153	−0.619991	−0.309996	−	0.950738i	$-0.600328\pi$
$401$	−12.4153	−0.619991	−0.309996	+	0.950738i	$0.600328\pi$
$402$	6.11645	0.305061
$403$	−37.2076	−1.85344
$404$	25.6328	1.27528
$405$	26.5493	1.31925
$406$	11.9910	0.595106
$407$	−18.6221	−0.923064
$408$	−5.06550	−0.250780
$409$	−11.1828	−0.552954	−0.276477	−	0.961021i	$-0.589167\pi$
$409$	−11.1828	−0.552954	−0.276477	+	0.961021i	$0.589167\pi$
$410$	22.0445	1.08870
$411$	−3.69046	−0.182037
$412$	−24.3366	−1.19898
$413$	27.7956	1.36773
$414$	−1.73822	−0.0854287
$415$	−9.59109	−0.470808
$416$	−67.5698	−3.31288
$417$	4.20095	0.205721
$418$	30.4213	1.48796
$419$	−9.81638	−0.479562	−0.239781	−	0.970827i	$-0.577076\pi$
$419$	−9.81638	−0.479562	−0.239781	+	0.970827i	$0.577076\pi$
$420$	−26.0420	−1.27072
$421$	24.2613	1.18242	0.591212	−	0.806516i	$-0.298650\pi$
$421$	24.2613	1.18242	0.591212	+	0.806516i	$0.298650\pi$
$422$	5.76420	0.280597
$423$	13.7623	0.669147
$424$	19.7917	0.961170
$425$	13.9695	0.677619
$426$	5.48604	0.265800
$427$	−2.29197	−0.110916
$428$	−12.5135	−0.604861
$429$	5.33142	0.257404
$430$	131.018	6.31824
$431$	19.0614	0.918158	0.459079	−	0.888396i	$-0.348180\pi$
$431$	19.0614	0.918158	0.459079	+	0.888396i	$0.348180\pi$
$432$	−42.8285	−2.06059
$433$	1.34682	0.0647240	0.0323620	−	0.999476i	$-0.489697\pi$
$433$	1.34682	0.0647240	0.0323620	+	0.999476i	$0.489697\pi$
$434$	−51.5188	−2.47298
$435$	5.70798	0.273677
$436$	20.6252	0.987769
$437$	1.13711	0.0543954
$438$	−25.2770	−1.20778
$439$	12.7792	0.609918	0.304959	−	0.952365i	$-0.401357\pi$
$439$	12.7792	0.609918	0.304959	+	0.952365i	$0.401357\pi$
$440$	−91.7296	−4.37304
$441$	8.33953	0.397121
$442$	−10.3006	−0.489950
$443$	25.5572	1.21426	0.607130	−	0.794603i	$-0.292321\pi$
$443$	25.5572	1.21426	0.607130	+	0.794603i	$0.292321\pi$
$444$	−23.5122	−1.11584
$445$	−29.2703	−1.38754
$446$	28.8658	1.36684
$447$	−4.36289	−0.206358
$448$	−42.1759	−1.99262
$449$	−38.7111	−1.82689	−0.913445	−	0.406962i	$-0.866588\pi$
$449$	−38.7111	−1.82689	−0.913445	+	0.406962i	$0.866588\pi$
$450$	100.232	4.72496
$451$	−4.52495	−0.213071
$452$	−20.4908	−0.963805
$453$	−4.16662	−0.195765
$454$	−54.8585	−2.57464
$455$	−32.7807	−1.53678
$456$	23.7764	1.11343
$457$	−37.2898	−1.74434	−0.872172	−	0.489199i	$-0.837289\pi$
$457$	−37.2898	−1.74434	−0.872172	+	0.489199i	$0.837289\pi$
$458$	−41.4991	−1.93913
$459$	−3.27963	−0.153080
$460$	−5.53900	−0.258257
$461$	16.7272	0.779062	0.389531	−	0.921013i	$-0.372637\pi$
$461$	16.7272	0.779062	0.389531	+	0.921013i	$0.372637\pi$
$462$	7.38205	0.343444
$463$	42.4563	1.97311	0.986557	−	0.163418i	$-0.0522521\pi$
$463$	42.4563	1.97311	0.986557	+	0.163418i	$0.0522521\pi$
$464$	29.5614	1.37235
$465$	−24.5240	−1.13727
$466$	−78.3671	−3.63029
$467$	20.3855	0.943328	0.471664	−	0.881778i	$-0.343654\pi$
$467$	20.3855	0.943328	0.471664	+	0.881778i	$0.343654\pi$
$468$	−53.5179	−2.47387
$469$	7.71948	0.356453
$470$	60.5631	2.79357
$471$	3.27677	0.150986
$472$	123.616	5.68990
$473$	−26.8933	−1.23656
$474$	9.30833	0.427546
$475$	−65.5697	−3.00854
$476$	−10.3278	−0.473375
$477$	6.02792	0.275999
$478$	9.72106	0.444631
$479$	−27.5629	−1.25938	−0.629690	−	0.776847i	$-0.716818\pi$
$479$	−27.5629	−1.25938	−0.629690	+	0.776847i	$0.716818\pi$
$480$	−44.5361	−2.03279
$481$	−29.5963	−1.34947
$482$	−29.8426	−1.35929
$483$	0.275932	0.0125553
$484$	−27.3281	−1.24219
$485$	−82.1305	−3.72935
$486$	−35.9934	−1.63269
$487$	−4.68052	−0.212095	−0.106047	−	0.994361i	$-0.533819\pi$
$487$	−4.68052	−0.212095	−0.106047	+	0.994361i	$0.533819\pi$
$488$	−10.1932	−0.461423
$489$	6.82961	0.308846
$490$	36.6993	1.65791
$491$	7.63422	0.344527	0.172264	−	0.985051i	$-0.444892\pi$
$491$	7.63422	0.344527	0.172264	+	0.985051i	$0.444892\pi$
$492$	−5.71319	−0.257570
$493$	2.26369	0.101951
$494$	48.3489	2.17532
$495$	−27.9379	−1.25571
$496$	−127.009	−5.70285
$497$	6.92386	0.310578
$498$	3.43270	0.153823
$499$	−5.15145	−0.230611	−0.115305	−	0.993330i	$-0.536785\pi$
$499$	−5.15145	−0.230611	−0.115305	+	0.993330i	$0.536785\pi$
$500$	205.078	9.17136
$501$	3.59357	0.160549
$502$	32.4395	1.44785
$503$	−16.5271	−0.736908	−0.368454	−	0.929646i	$-0.620113\pi$
$503$	−16.5271	−0.736908	−0.368454	+	0.929646i	$0.620113\pi$
$504$	−45.8708	−2.04325
$505$	21.2666	0.946353
$506$	1.57012	0.0698005
$507$	0.946975	0.0420566
$508$	51.5675	2.28794
$509$	−38.7966	−1.71963	−0.859814	−	0.510607i	$-0.829421\pi$
$509$	−38.7966	−1.71963	−0.859814	+	0.510607i	$0.829421\pi$
$510$	−6.78926	−0.300634
$511$	−31.9017	−1.41125
$512$	−2.13152	−0.0942010
$513$	15.3939	0.679657
$514$	−24.1780	−1.06645
$515$	−20.1912	−0.889730
$516$	−33.9554	−1.49480
$517$	−12.4315	−0.546735
$518$	−40.9799	−1.80056
$519$	14.8218	0.650606
$520$	−145.787	−6.39317
$521$	−2.29483	−0.100538	−0.0502692	−	0.998736i	$-0.516008\pi$
$521$	−2.29483	−0.100538	−0.0502692	+	0.998736i	$0.516008\pi$
$522$	16.2421	0.710896
$523$	4.67119	0.204257	0.102129	−	0.994771i	$-0.467435\pi$
$523$	4.67119	0.204257	0.102129	+	0.994771i	$0.467435\pi$
$524$	−63.6450	−2.78034
$525$	−15.9112	−0.694421
$526$	−41.9115	−1.82743
$527$	−9.72579	−0.423662
$528$	18.1989	0.792005
$529$	−22.9413	−0.997448
$530$	26.5267	1.15225
$531$	37.6495	1.63385
$532$	48.4766	2.10173
$533$	−7.19154	−0.311500
$534$	10.4760	0.453339
$535$	−10.3820	−0.448852
$536$	34.3311	1.48288
$537$	−5.79492	−0.250069
$538$	62.0833	2.67660
$539$	−7.53307	−0.324472
$540$	−74.9855	−3.22686
$541$	−25.7674	−1.10783	−0.553914	−	0.832574i	$-0.686866\pi$
$541$	−25.7674	−1.10783	−0.553914	+	0.832574i	$0.686866\pi$
$542$	76.1040	3.26895
$543$	1.20607	0.0517574
$544$	−17.6623	−0.757263
$545$	17.1120	0.732999
$546$	11.7324	0.502099
$547$	33.2582	1.42202	0.711008	−	0.703183i	$-0.248239\pi$
$547$	33.2582	1.42202	0.711008	+	0.703183i	$0.248239\pi$
$548$	−33.4631	−1.42947
$549$	−3.10451	−0.132497
$550$	−90.5387	−3.86058
$551$	−10.6253	−0.452652
$552$	1.22716	0.0522315
$553$	11.7479	0.499572
$554$	41.1147	1.74680
$555$	−19.5073	−0.828038
$556$	38.0920	1.61546
$557$	10.5891	0.448673	0.224337	−	0.974512i	$-0.427979\pi$
$557$	10.5891	0.448673	0.224337	+	0.974512i	$0.427979\pi$
$558$	−69.7830	−2.95415
$559$	−42.7418	−1.80778
$560$	−111.897	−4.72853
$561$	1.39360	0.0588376
$562$	−21.1240	−0.891064
$563$	7.39860	0.311814	0.155907	−	0.987772i	$-0.450170\pi$
$563$	7.39860	0.311814	0.155907	+	0.987772i	$0.450170\pi$
$564$	−15.6959	−0.660918
$565$	−17.0005	−0.715215
$566$	−0.807449	−0.0339396
$567$	−11.9925	−0.503638
$568$	30.7927	1.29203
$569$	5.69078	0.238570	0.119285	−	0.992860i	$-0.461940\pi$
$569$	5.69078	0.238570	0.119285	+	0.992860i	$0.461940\pi$
$570$	31.8674	1.33478
$571$	9.54424	0.399414	0.199707	−	0.979856i	$-0.436001\pi$
$571$	9.54424	0.399414	0.199707	+	0.979856i	$0.436001\pi$
$572$	48.3425	2.02130
$573$	3.09996	0.129503
$574$	−9.95763	−0.415623
$575$	−3.38422	−0.141132
$576$	−57.1279	−2.38033
$577$	−35.4649	−1.47642	−0.738211	−	0.674570i	$-0.764329\pi$
$577$	−35.4649	−1.47642	−0.738211	+	0.674570i	$0.764329\pi$
$578$	−2.69250	−0.111993
$579$	−7.99780	−0.332377
$580$	51.7570	2.14909
$581$	4.33236	0.179737
$582$	29.3949	1.21846
$583$	−5.44499	−0.225509
$584$	−141.878	−5.87094
$585$	−44.4020	−1.83579
$586$	34.5721	1.42816
$587$	7.32282	0.302245	0.151123	−	0.988515i	$-0.451711\pi$
$587$	7.32282	0.302245	0.151123	+	0.988515i	$0.451711\pi$
$588$	−9.51124	−0.392237
$589$	45.6508	1.88101
$590$	165.682	6.82102
$591$	−14.8124	−0.609299
$592$	−101.027	−4.15220
$593$	−7.71402	−0.316777	−0.158388	−	0.987377i	$-0.550630\pi$
$593$	−7.71402	−0.316777	−0.158388	+	0.987377i	$0.550630\pi$
$594$	21.2559	0.872140
$595$	−8.56863	−0.351280
$596$	−39.5604	−1.62046
$597$	12.7996	0.523855
$598$	2.49541	0.102045
$599$	−11.0517	−0.451561	−0.225780	−	0.974178i	$-0.572493\pi$
$599$	−11.0517	−0.451561	−0.225780	+	0.974178i	$0.572493\pi$
$600$	−70.7624	−2.88886
$601$	34.5067	1.40756	0.703780	−	0.710418i	$-0.251494\pi$
$601$	34.5067	1.40756	0.703780	+	0.710418i	$0.251494\pi$
$602$	−59.1816	−2.41206
$603$	10.4562	0.425808
$604$	−37.7807	−1.53728
$605$	−22.6732	−0.921795
$606$	−7.61143	−0.309193
$607$	18.2206	0.739553	0.369777	−	0.929121i	$-0.379434\pi$
$607$	18.2206	0.739553	0.369777	+	0.929121i	$0.379434\pi$
$608$	82.9029	3.36216
$609$	−2.57833	−0.104479
$610$	−13.6618	−0.553152
$611$	−19.7574	−0.799300
$612$	−13.9892	−0.565480
$613$	−10.8366	−0.437685	−0.218842	−	0.975760i	$-0.570228\pi$
$613$	−10.8366	−0.437685	−0.218842	+	0.975760i	$0.570228\pi$
$614$	−69.1880	−2.79220
$615$	−4.74003	−0.191137
$616$	41.4349	1.66946
$617$	−30.8475	−1.24188	−0.620938	−	0.783860i	$-0.713248\pi$
$617$	−30.8475	−1.24188	−0.620938	+	0.783860i	$0.713248\pi$
$618$	7.22652	0.290693
$619$	42.8934	1.72403	0.862016	−	0.506881i	$-0.169201\pi$
$619$	42.8934	1.72403	0.862016	+	0.506881i	$0.169201\pi$
$620$	−222.370	−8.93061
$621$	0.794518	0.0318829
$622$	14.7102	0.589826
$623$	13.2216	0.529711
$624$	28.9237	1.15787
$625$	100.299	4.01194
$626$	−2.08244	−0.0832310
$627$	−6.54124	−0.261232
$628$	29.7120	1.18564
$629$	−7.73625	−0.308465
$630$	−61.4803	−2.44943
$631$	−10.1179	−0.402786	−0.201393	−	0.979511i	$-0.564547\pi$
$631$	−10.1179	−0.402786	−0.201393	+	0.979511i	$0.564547\pi$
$632$	52.2469	2.07827
$633$	−1.23943	−0.0492629
$634$	37.1981	1.47732
$635$	42.7838	1.69782
$636$	−6.87484	−0.272605
$637$	−11.9724	−0.474363
$638$	−14.6714	−0.580846
$639$	9.37847	0.371007
$640$	−97.5473	−3.85590
$641$	−42.4430	−1.67640	−0.838199	−	0.545364i	$-0.816391\pi$
$641$	−42.4430	−1.67640	−0.838199	+	0.545364i	$0.816391\pi$
$642$	3.71576	0.146649
$643$	6.04114	0.238239	0.119120	−	0.992880i	$-0.461993\pi$
$643$	6.04114	0.238239	0.119120	+	0.992880i	$0.461993\pi$
$644$	2.50200	0.0985928
$645$	−28.1716	−1.10926
$646$	12.6380	0.497237
$647$	−10.8239	−0.425531	−0.212765	−	0.977103i	$-0.568247\pi$
$647$	−10.8239	−0.425531	−0.212765	+	0.977103i	$0.568247\pi$
$648$	−53.3347	−2.09519
$649$	−34.0087	−1.33496
$650$	−143.894	−5.64399
$651$	11.0776	0.434167
$652$	61.9273	2.42526
$653$	37.5755	1.47044	0.735221	−	0.677827i	$-0.237078\pi$
$653$	37.5755	1.47044	0.735221	+	0.677827i	$0.237078\pi$
$654$	−6.12448	−0.239486
$655$	−52.8040	−2.06322
$656$	−24.5484	−0.958455
$657$	−43.2114	−1.68584
$658$	−27.3567	−1.06648
$659$	−43.1288	−1.68006	−0.840030	−	0.542540i	$-0.817463\pi$
$659$	−43.1288	−1.68006	−0.840030	+	0.542540i	$0.817463\pi$
$660$	31.8632	1.24027
$661$	45.3021	1.76205	0.881024	−	0.473072i	$-0.156855\pi$
$661$	45.3021	1.76205	0.881024	+	0.473072i	$0.156855\pi$
$662$	−61.5283	−2.39136
$663$	2.21485	0.0860178
$664$	19.2675	0.747722
$665$	40.2194	1.55964
$666$	−55.5080	−2.15089
$667$	−0.548398	−0.0212341
$668$	32.5846	1.26074
$669$	−6.20677	−0.239968
$670$	46.0138	1.77767
$671$	2.80429	0.108259
$672$	20.1173	0.776040
$673$	−6.43977	−0.248235	−0.124117	−	0.992268i	$-0.539610\pi$
$673$	−6.43977	−0.248235	−0.124117	+	0.992268i	$0.539610\pi$
$674$	−86.6583	−3.33795
$675$	−45.8147	−1.76341
$676$	8.58667	0.330256
$677$	−41.9931	−1.61393	−0.806963	−	0.590602i	$-0.798890\pi$
$677$	−41.9931	−1.61393	−0.806963	+	0.590602i	$0.798890\pi$
$678$	6.08455	0.233676
$679$	37.0989	1.42372
$680$	−38.1076	−1.46136
$681$	11.7958	0.452015
$682$	63.0347	2.41372
$683$	21.9314	0.839182	0.419591	−	0.907713i	$-0.362174\pi$
$683$	21.9314	0.839182	0.419591	+	0.907713i	$0.362174\pi$
$684$	65.6623	2.51066
$685$	−27.7632	−1.06078
$686$	−53.6572	−2.04864
$687$	8.92321	0.340442
$688$	−145.900	−5.56237
$689$	−8.65378	−0.329683
$690$	1.64476	0.0626148
$691$	36.8635	1.40235	0.701177	−	0.712988i	$-0.252658\pi$
$691$	36.8635	1.40235	0.701177	+	0.712988i	$0.252658\pi$
$692$	134.396	5.10899
$693$	12.6197	0.479384
$694$	37.8676	1.43743
$695$	31.6036	1.19879
$696$	−11.4667	−0.434645
$697$	−1.87982	−0.0712031
$698$	−70.9997	−2.68738
$699$	16.8506	0.637349
$700$	−144.274	−5.45305
$701$	−31.2126	−1.17888	−0.589441	−	0.807811i	$-0.700652\pi$
$701$	−31.2126	−1.17888	−0.589441	+	0.807811i	$0.700652\pi$
$702$	33.7822	1.27503
$703$	36.3123	1.36955
$704$	51.6034	1.94488
$705$	−13.0224	−0.490451
$706$	−2.69250	−0.101334
$707$	−9.60628	−0.361281
$708$	−42.9393	−1.61376
$709$	38.9362	1.46228	0.731139	−	0.682228i	$-0.238989\pi$
$709$	38.9362	1.46228	0.731139	+	0.682228i	$0.238989\pi$
$710$	41.2713	1.54888
$711$	15.9127	0.596774
$712$	58.8008	2.20365
$713$	2.35616	0.0882387
$714$	3.06676	0.114770
$715$	40.1081	1.49996
$716$	−52.5453	−1.96371
$717$	−2.09024	−0.0780614
$718$	22.7259	0.848122
$719$	−16.8161	−0.627135	−0.313567	−	0.949566i	$-0.601524\pi$
$719$	−16.8161	−0.627135	−0.313567	+	0.949566i	$0.601524\pi$
$720$	−151.567	−5.64856
$721$	9.12050	0.339665
$722$	−8.16272	−0.303785
$723$	6.41680	0.238643
$724$	10.9360	0.406433
$725$	31.6225	1.17443
$726$	8.11483	0.301170
$727$	21.2833	0.789353	0.394677	−	0.918820i	$-0.370857\pi$
$727$	21.2833	0.789353	0.394677	+	0.918820i	$0.370857\pi$
$728$	65.8529	2.44067
$729$	−10.5478	−0.390661
$730$	−190.158	−7.03805
$731$	−11.1724	−0.413226
$732$	3.54070	0.130868
$733$	−47.9327	−1.77043	−0.885217	−	0.465178i	$-0.845990\pi$
$733$	−47.9327	−1.77043	−0.885217	+	0.465178i	$0.845990\pi$
$734$	−46.4055	−1.71286
$735$	−7.89114	−0.291069
$736$	4.27883	0.157720
$737$	−9.44500	−0.347911
$738$	−13.4878	−0.496491
$739$	24.2502	0.892059	0.446030	−	0.895018i	$-0.352838\pi$
$739$	24.2502	0.892059	0.446030	+	0.895018i	$0.352838\pi$
$740$	−176.882	−6.50230
$741$	−10.3961	−0.381909
$742$	−11.9823	−0.439884
$743$	−40.0967	−1.47100	−0.735502	−	0.677522i	$-0.763054\pi$
$743$	−40.0967	−1.47100	−0.735502	+	0.677522i	$0.763054\pi$
$744$	49.2660	1.80618
$745$	−32.8219	−1.20250
$746$	−6.90623	−0.252855
$747$	5.86825	0.214708
$748$	12.6364	0.462032
$749$	4.68961	0.171355
$750$	−60.8960	−2.22361
$751$	33.2447	1.21312	0.606558	−	0.795040i	$-0.292550\pi$
$751$	33.2447	1.21312	0.606558	+	0.795040i	$0.292550\pi$
$752$	−67.4423	−2.45937
$753$	−6.97520	−0.254190
$754$	−23.3174	−0.849169
$755$	−31.3454	−1.14077
$756$	33.8714	1.23189
$757$	−16.9208	−0.614998	−0.307499	−	0.951548i	$-0.599492\pi$
$757$	−16.9208	−0.614998	−0.307499	+	0.951548i	$0.599492\pi$
$758$	79.9568	2.90416
$759$	−0.337610	−0.0122545
$760$	178.869	6.48826
$761$	38.1274	1.38212	0.691058	−	0.722799i	$-0.257145\pi$
$761$	38.1274	1.38212	0.691058	+	0.722799i	$0.257145\pi$
$762$	−15.3125	−0.554714
$763$	−7.72962	−0.279831
$764$	28.1088	1.01694
$765$	−11.6063	−0.419628
$766$	42.0275	1.51851
$767$	−54.0503	−1.95164
$768$	10.0900	0.364090
$769$	−4.79264	−0.172827	−0.0864135	−	0.996259i	$-0.527541\pi$
$769$	−4.79264	−0.172827	−0.0864135	+	0.996259i	$0.527541\pi$
$770$	55.5349	2.00134
$771$	5.19880	0.187230
$772$	−72.5198	−2.61004
$773$	42.2915	1.52112	0.760560	−	0.649268i	$-0.224925\pi$
$773$	42.2915	1.52112	0.760560	+	0.649268i	$0.224925\pi$
$774$	−80.1624	−2.88138
$775$	−135.864	−4.88038
$776$	164.991	5.92284
$777$	8.81157	0.316113
$778$	−20.9959	−0.752741
$779$	8.82346	0.316133
$780$	50.6404	1.81322
$781$	−8.47154	−0.303135
$782$	0.652283	0.0233256
$783$	−7.42406	−0.265314
$784$	−40.8679	−1.45957
$785$	24.6510	0.879833
$786$	18.8988	0.674098
$787$	17.1003	0.609560	0.304780	−	0.952423i	$-0.401417\pi$
$787$	17.1003	0.609560	0.304780	+	0.952423i	$0.401417\pi$
$788$	−134.311	−4.78462
$789$	9.01188	0.320831
$790$	70.0262	2.49142
$791$	7.67923	0.273042
$792$	56.1242	1.99429
$793$	4.45689	0.158269
$794$	−56.9367	−2.02061
$795$	−5.70381	−0.202293
$796$	116.060	4.11365
$797$	1.45387	0.0514988	0.0257494	−	0.999668i	$-0.491803\pi$
$797$	1.45387	0.0514988	0.0257494	+	0.999668i	$0.491803\pi$
$798$	−14.3947	−0.509567
$799$	−5.16445	−0.182705
$800$	−246.732	−8.72330
$801$	17.9088	0.632777
$802$	33.4283	1.18039
$803$	39.0326	1.37743
$804$	−11.9252	−0.420571
$805$	2.07583	0.0731632
$806$	100.182	3.52875
$807$	−13.3492	−0.469916
$808$	−42.7224	−1.50297
$809$	40.9266	1.43890	0.719452	−	0.694542i	$-0.244393\pi$
$809$	40.9266	1.43890	0.719452	+	0.694542i	$0.244393\pi$
$810$	−71.4842	−2.51170
$811$	−20.0773	−0.705011	−0.352505	−	0.935810i	$-0.614670\pi$
$811$	−20.0773	−0.705011	−0.352505	+	0.935810i	$0.614670\pi$
$812$	−23.3790	−0.820441
$813$	−16.3640	−0.573911
$814$	50.1401	1.75741
$815$	51.3789	1.79972
$816$	7.56044	0.264668
$817$	52.4408	1.83467
$818$	30.1097	1.05276
$819$	20.0567	0.700836
$820$	−42.9801	−1.50093
$821$	−29.2215	−1.01984	−0.509919	−	0.860223i	$-0.670324\pi$
$821$	−29.2215	−1.01984	−0.509919	+	0.860223i	$0.670324\pi$
$822$	9.93658	0.346578
$823$	−14.7251	−0.513285	−0.256643	−	0.966506i	$-0.582616\pi$
$823$	−14.7251	−0.513285	−0.256643	+	0.966506i	$0.582616\pi$
$824$	40.5619	1.41304
$825$	19.4678	0.677781
$826$	−74.8397	−2.60401
$827$	35.6780	1.24065	0.620323	−	0.784346i	$-0.287001\pi$
$827$	35.6780	1.24065	0.620323	+	0.784346i	$0.287001\pi$
$828$	3.38900	0.117776
$829$	11.0932	0.385284	0.192642	−	0.981269i	$-0.438294\pi$
$829$	11.0932	0.385284	0.192642	+	0.981269i	$0.438294\pi$
$830$	25.8241	0.896366
$831$	−8.84054	−0.306675
$832$	82.0138	2.84332
$833$	−3.12949	−0.108430
$834$	−11.3111	−0.391671
$835$	27.0343	0.935560
$836$	−59.3125	−2.05137
$837$	31.8970	1.10252
$838$	26.4307	0.913032
$839$	2.39186	0.0825763	0.0412882	−	0.999147i	$-0.486854\pi$
$839$	2.39186	0.0825763	0.0412882	+	0.999147i	$0.486854\pi$
$840$	43.4044	1.49760
$841$	−23.8757	−0.823301
$842$	−65.3237	−2.25120
$843$	4.54213	0.156439
$844$	−11.2385	−0.386844
$845$	7.12406	0.245075
$846$	−37.0551	−1.27398
$847$	10.2416	0.351906
$848$	−29.5398	−1.01440
$849$	0.173619	0.00595859
$850$	−37.6129	−1.29011
$851$	1.87417	0.0642459
$852$	−10.6962	−0.366444
$853$	35.1312	1.20287	0.601435	−	0.798922i	$-0.294596\pi$
$853$	35.1312	1.20287	0.601435	+	0.798922i	$0.294596\pi$
$854$	6.17115	0.211172
$855$	54.4777	1.86310
$856$	20.8563	0.712852
$857$	17.2762	0.590142	0.295071	−	0.955475i	$-0.404657\pi$
$857$	17.2762	0.590142	0.295071	+	0.955475i	$0.404657\pi$
$858$	−14.3549	−0.490068
$859$	−53.0012	−1.80838	−0.904188	−	0.427134i	$-0.859523\pi$
$859$	−53.0012	−1.80838	−0.904188	+	0.427134i	$0.859523\pi$
$860$	−255.446	−8.71062
$861$	2.14110	0.0729687
$862$	−51.3230	−1.74807
$863$	26.2830	0.894683	0.447341	−	0.894363i	$-0.352371\pi$
$863$	26.2830	0.894683	0.447341	+	0.894363i	$0.352371\pi$
$864$	57.9256	1.97067
$865$	111.504	3.79125
$866$	−3.62631	−0.123227
$867$	0.578947	0.0196621
$868$	100.446	3.40937
$869$	−14.3739	−0.487601
$870$	−15.3688	−0.521050
$871$	−15.0110	−0.508630
$872$	−34.3762	−1.16413
$873$	50.2510	1.70074
$874$	−3.06168	−0.103563
$875$	−76.8561	−2.59821
$876$	49.2826	1.66510
$877$	−37.4231	−1.26369	−0.631844	−	0.775096i	$-0.717702\pi$
$877$	−37.4231	−1.26369	−0.631844	+	0.775096i	$0.717702\pi$
$878$	−34.4081	−1.16122
$879$	−7.43375	−0.250734
$880$	136.910	4.61522
$881$	−36.7620	−1.23854	−0.619271	−	0.785177i	$-0.712572\pi$
$881$	−36.7620	−1.23854	−0.619271	+	0.785177i	$0.712572\pi$
$882$	−22.4542	−0.756073
$883$	−45.0552	−1.51623	−0.758115	−	0.652121i	$-0.773879\pi$
$883$	−45.0552	−1.51623	−0.758115	+	0.652121i	$0.773879\pi$
$884$	20.0831	0.675469
$885$	−35.6252	−1.19753
$886$	−68.8129	−2.31182
$887$	12.6703	0.425427	0.212713	−	0.977115i	$-0.431770\pi$
$887$	12.6703	0.425427	0.212713	+	0.977115i	$0.431770\pi$
$888$	39.1880	1.31506
$889$	−19.3257	−0.648164
$890$	78.8103	2.64173
$891$	14.6732	0.491570
$892$	−56.2797	−1.88438
$893$	24.2408	0.811188
$894$	11.7471	0.392882
$895$	−43.5950	−1.45722
$896$	44.0628	1.47203
$897$	−0.536567	−0.0179155
$898$	104.230	3.47819
$899$	−22.0162	−0.734280
$900$	−195.422	−6.51405
$901$	−2.26203	−0.0753593
$902$	12.1834	0.405664
$903$	12.7253	0.423472
$904$	34.1521	1.13588
$905$	9.07321	0.301604
$906$	11.2187	0.372715
$907$	4.73160	0.157110	0.0785551	−	0.996910i	$-0.474969\pi$
$907$	4.73160	0.157110	0.0785551	+	0.996910i	$0.474969\pi$
$908$	106.958	3.54952
$909$	−13.0119	−0.431576
$910$	88.2622	2.92586
$911$	−2.49328	−0.0826059	−0.0413030	−	0.999147i	$-0.513151\pi$
$911$	−2.49328	−0.0826059	−0.0413030	+	0.999147i	$0.513151\pi$
$912$	−35.4871	−1.17509
$913$	−5.30076	−0.175430
$914$	100.403	3.32104
$915$	2.93759	0.0971138
$916$	80.9109	2.67337
$917$	23.8519	0.787660
$918$	8.83042	0.291447
$919$	45.3839	1.49708	0.748538	−	0.663091i	$-0.230756\pi$
$919$	45.3839	1.49708	0.748538	+	0.663091i	$0.230756\pi$
$920$	9.23189	0.304367
$921$	14.8769	0.490211
$922$	−45.0380	−1.48325
$923$	−13.4639	−0.443170
$924$	−14.3928	−0.473488
$925$	−108.071	−3.55336
$926$	−114.314	−3.75659
$927$	12.3539	0.405754
$928$	−39.9818	−1.31247
$929$	−4.34099	−0.142423	−0.0712116	−	0.997461i	$-0.522687\pi$
$929$	−4.34099	−0.142423	−0.0712116	+	0.997461i	$0.522687\pi$
$930$	66.0309	2.16524
$931$	14.6892	0.481418
$932$	152.793	5.00489
$933$	−3.16301	−0.103552
$934$	−54.8880	−1.79599
$935$	10.4840	0.342862
$936$	89.1987	2.91555
$937$	−12.9542	−0.423195	−0.211597	−	0.977357i	$-0.567867\pi$
$937$	−12.9542	−0.423195	−0.211597	+	0.977357i	$0.567867\pi$
$938$	−20.7847	−0.678646
$939$	0.447769	0.0146124
$940$	−118.080	−3.85134
$941$	−2.38003	−0.0775869	−0.0387934	−	0.999247i	$-0.512351\pi$
$941$	−2.38003	−0.0775869	−0.0387934	+	0.999247i	$0.512351\pi$
$942$	−8.82272	−0.287460
$943$	0.455402	0.0148299
$944$	−184.501	−6.00501
$945$	28.1019	0.914156
$946$	72.4103	2.35426
$947$	17.4532	0.567152	0.283576	−	0.958950i	$-0.408479\pi$
$947$	17.4532	0.567152	0.283576	+	0.958950i	$0.408479\pi$
$948$	−18.1485	−0.589435
$949$	62.0349	2.01374
$950$	176.547	5.72793
$951$	−7.99839	−0.259365
$952$	17.2135	0.557891
$953$	−39.5626	−1.28156	−0.640779	−	0.767725i	$-0.721389\pi$
$953$	−39.5626	−1.28156	−0.640779	+	0.767725i	$0.721389\pi$
$954$	−16.2302	−0.525472
$955$	23.3209	0.754647
$956$	−18.9532	−0.612989
$957$	3.15466	0.101976
$958$	74.2132	2.39772
$959$	12.5408	0.404964
$960$	54.0563	1.74466
$961$	63.5910	2.05132
$962$	79.6882	2.56925
$963$	6.35215	0.204695
$964$	58.1841	1.87398
$965$	−60.1671	−1.93685
$966$	−0.742948	−0.0239040
$967$	−24.8917	−0.800464	−0.400232	−	0.916414i	$-0.631070\pi$
$967$	−24.8917	−0.800464	−0.400232	+	0.916414i	$0.631070\pi$
$968$	45.5479	1.46397
$969$	−2.71745	−0.0872972
$970$	221.137	7.10027
$971$	−6.32141	−0.202864	−0.101432	−	0.994842i	$-0.532342\pi$
$971$	−6.32141	−0.202864	−0.101432	+	0.994842i	$0.532342\pi$
$972$	70.1764	2.25091
$973$	−14.2756	−0.457653
$974$	12.6023	0.403804
$975$	30.9403	0.990883
$976$	15.2137	0.486977
$977$	−43.1950	−1.38193	−0.690965	−	0.722889i	$-0.742814\pi$
$977$	−43.1950	−1.38193	−0.690965	+	0.722889i	$0.742814\pi$
$978$	−18.3888	−0.588008
$979$	−16.1770	−0.517018
$980$	−71.5527	−2.28567
$981$	−10.4699	−0.334278
$982$	−20.5552	−0.655942
$983$	−38.4324	−1.22580	−0.612902	−	0.790159i	$-0.709998\pi$
$983$	−38.4324	−1.22580	−0.612902	+	0.790159i	$0.709998\pi$
$984$	9.52221	0.303557
$985$	−111.433	−3.55054
$986$	−6.09499	−0.194104
$987$	5.88229	0.187235
$988$	−94.2659	−2.99900
$989$	2.70661	0.0860651
$990$	75.2229	2.39074
$991$	−9.71022	−0.308455	−0.154228	−	0.988035i	$-0.549289\pi$
$991$	−9.71022	−0.308455	−0.154228	+	0.988035i	$0.549289\pi$
$992$	171.779	5.45400
$993$	13.2299	0.419838
$994$	−18.6425	−0.591305
$995$	96.2913	3.05264
$996$	−6.69274	−0.212067
$997$	−10.4351	−0.330483	−0.165241	−	0.986253i	$-0.552840\pi$
$997$	−10.4351	−0.330483	−0.165241	+	0.986253i	$0.552840\pi$
$998$	13.8703	0.439057
$999$	25.3720	0.802736

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.b.1.5	✓	114

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.b.1.5	✓	114	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69250 q^{2} +0.578947 q^{3} +5.24958 q^{4} +4.35539 q^{5} -1.55882 q^{6} -1.96736 q^{7} -8.74952 q^{8} -2.66482 q^{9} +O(q^{10})\)	\(q-2.69250 q^{2} +0.578947 q^{3} +5.24958 q^{4} +4.35539 q^{5} -1.55882 q^{6} -1.96736 q^{7} -8.74952 q^{8} -2.66482 q^{9} -11.7269 q^{10} +2.40712 q^{11} +3.03923 q^{12} +3.82566 q^{13} +5.29713 q^{14} +2.52154 q^{15} +13.0590 q^{16} +1.00000 q^{17} +7.17504 q^{18} -4.69379 q^{19} +22.8640 q^{20} -1.13900 q^{21} -6.48119 q^{22} -0.242259 q^{23} -5.06550 q^{24} +13.9695 q^{25} -10.3006 q^{26} -3.27963 q^{27} -10.3278 q^{28} +2.26369 q^{29} -6.78926 q^{30} -9.72579 q^{31} -17.6623 q^{32} +1.39360 q^{33} -2.69250 q^{34} -8.56863 q^{35} -13.9892 q^{36} -7.73625 q^{37} +12.6380 q^{38} +2.21485 q^{39} -38.1076 q^{40} -1.87982 q^{41} +3.06676 q^{42} -11.1724 q^{43} +12.6364 q^{44} -11.6063 q^{45} +0.652283 q^{46} -5.16445 q^{47} +7.56044 q^{48} -3.12949 q^{49} -37.6129 q^{50} +0.578947 q^{51} +20.0831 q^{52} -2.26203 q^{53} +8.83042 q^{54} +10.4840 q^{55} +17.2135 q^{56} -2.71745 q^{57} -6.09499 q^{58} -14.1284 q^{59} +13.2370 q^{60} +1.16500 q^{61} +26.1867 q^{62} +5.24266 q^{63} +21.4378 q^{64} +16.6623 q^{65} -3.75226 q^{66} -3.92378 q^{67} +5.24958 q^{68} -0.140255 q^{69} +23.0711 q^{70} -3.51936 q^{71} +23.3159 q^{72} +16.2155 q^{73} +20.8299 q^{74} +8.08757 q^{75} -24.6404 q^{76} -4.73568 q^{77} -5.96350 q^{78} -5.97141 q^{79} +56.8769 q^{80} +6.09573 q^{81} +5.06141 q^{82} -2.20212 q^{83} -5.97926 q^{84} +4.35539 q^{85} +30.0817 q^{86} +1.31055 q^{87} -21.0612 q^{88} -6.72046 q^{89} +31.2501 q^{90} -7.52646 q^{91} -1.27176 q^{92} -5.63071 q^{93} +13.9053 q^{94} -20.4433 q^{95} -10.2255 q^{96} -18.8572 q^{97} +8.42617 q^{98} -6.41455 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * q^99

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