LMFDB - Embedded newform 6001.2.a.a.1.6

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:	$113$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-2.63611 q^{2} +2.68277 q^{3} +4.94905 q^{4} -3.99469 q^{5} -7.07208 q^{6} -3.60242 q^{7} -7.77401 q^{8} +4.19728 q^{9} +O(q^{10})$	\(q-2.63611 q^{2} +2.68277 q^{3} +4.94905 q^{4} -3.99469 q^{5} -7.07208 q^{6} -3.60242 q^{7} -7.77401 q^{8} +4.19728 q^{9} +10.5304 q^{10} -3.45442 q^{11} +13.2772 q^{12} -0.906083 q^{13} +9.49636 q^{14} -10.7168 q^{15} +10.5950 q^{16} -1.00000 q^{17} -11.0645 q^{18} +4.47239 q^{19} -19.7699 q^{20} -9.66448 q^{21} +9.10621 q^{22} +6.15529 q^{23} -20.8559 q^{24} +10.9575 q^{25} +2.38853 q^{26} +3.21203 q^{27} -17.8286 q^{28} -1.58186 q^{29} +28.2507 q^{30} -0.586386 q^{31} -12.3816 q^{32} -9.26743 q^{33} +2.63611 q^{34} +14.3905 q^{35} +20.7726 q^{36} +7.37035 q^{37} -11.7897 q^{38} -2.43082 q^{39} +31.0547 q^{40} +9.74515 q^{41} +25.4766 q^{42} +6.36267 q^{43} -17.0961 q^{44} -16.7668 q^{45} -16.2260 q^{46} -4.05786 q^{47} +28.4240 q^{48} +5.97743 q^{49} -28.8851 q^{50} -2.68277 q^{51} -4.48425 q^{52} -0.917521 q^{53} -8.46725 q^{54} +13.7993 q^{55} +28.0053 q^{56} +11.9984 q^{57} +4.16996 q^{58} -6.29647 q^{59} -53.0382 q^{60} -4.67072 q^{61} +1.54578 q^{62} -15.1204 q^{63} +11.4490 q^{64} +3.61952 q^{65} +24.4299 q^{66} +2.67575 q^{67} -4.94905 q^{68} +16.5133 q^{69} -37.9350 q^{70} -6.91045 q^{71} -32.6297 q^{72} -6.70031 q^{73} -19.4290 q^{74} +29.3965 q^{75} +22.1341 q^{76} +12.4443 q^{77} +6.40789 q^{78} +4.49739 q^{79} -42.3237 q^{80} -3.97468 q^{81} -25.6893 q^{82} -2.70763 q^{83} -47.8300 q^{84} +3.99469 q^{85} -16.7727 q^{86} -4.24378 q^{87} +26.8547 q^{88} -10.4892 q^{89} +44.1991 q^{90} +3.26409 q^{91} +30.4628 q^{92} -1.57314 q^{93} +10.6970 q^{94} -17.8658 q^{95} -33.2169 q^{96} +10.5208 q^{97} -15.7571 q^{98} -14.4992 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) $ 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * 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 $

$2$	−2.63611	−1.86401	−0.932004	−	0.362448i	$-0.881941\pi$
$2$	−2.63611	−1.86401	−0.932004	+	0.362448i	$0.881941\pi$
$3$	2.68277	1.54890	0.774450	−	0.632635i	$-0.218027\pi$
$3$	2.68277	1.54890	0.774450	+	0.632635i	$0.218027\pi$
$4$	4.94905	2.47453
$5$	−3.99469	−1.78648	−0.893239	−	0.449583i	$-0.851573\pi$
$5$	−3.99469	−1.78648	−0.893239	+	0.449583i	$0.851573\pi$
$6$	−7.07208	−2.88716
$7$	−3.60242	−1.36159	−0.680794	−	0.732475i	$-0.738365\pi$
$7$	−3.60242	−1.36159	−0.680794	+	0.732475i	$0.738365\pi$
$8$	−7.77401	−2.74853
$9$	4.19728	1.39909
$10$	10.5304	3.33001
$11$	−3.45442	−1.04155	−0.520773	−	0.853695i	$-0.674356\pi$
$11$	−3.45442	−1.04155	−0.520773	+	0.853695i	$0.674356\pi$
$12$	13.2772	3.83280
$13$	−0.906083	−0.251302	−0.125651	−	0.992074i	$-0.540102\pi$
$13$	−0.906083	−0.251302	−0.125651	+	0.992074i	$0.540102\pi$
$14$	9.49636	2.53801
$15$	−10.7168	−2.76708
$16$	10.5950	2.64875
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−11.0645	−2.60792
$19$	4.47239	1.02604	0.513018	−	0.858378i	$-0.328527\pi$
$19$	4.47239	1.02604	0.513018	+	0.858378i	$0.328527\pi$
$20$	−19.7699	−4.42069
$21$	−9.66448	−2.10896
$22$	9.10621	1.94145
$23$	6.15529	1.28347	0.641733	−	0.766928i	$-0.278216\pi$
$23$	6.15529	1.28347	0.641733	+	0.766928i	$0.278216\pi$
$24$	−20.8559	−4.25720
$25$	10.9575	2.19150
$26$	2.38853	0.468429
$27$	3.21203	0.618156
$28$	−17.8286	−3.36928
$29$	−1.58186	−0.293745	−0.146872	−	0.989155i	$-0.546921\pi$
$29$	−1.58186	−0.293745	−0.146872	+	0.989155i	$0.546921\pi$
$30$	28.2507	5.15785
$31$	−0.586386	−0.105318	−0.0526591	−	0.998613i	$-0.516770\pi$
$31$	−0.586386	−0.105318	−0.0526591	+	0.998613i	$0.516770\pi$
$32$	−12.3816	−2.18877
$33$	−9.26743	−1.61325
$34$	2.63611	0.452088
$35$	14.3905	2.43244
$36$	20.7726	3.46209
$37$	7.37035	1.21168	0.605839	−	0.795587i	$-0.292837\pi$
$37$	7.37035	1.21168	0.605839	+	0.795587i	$0.292837\pi$
$38$	−11.7897	−1.91254
$39$	−2.43082	−0.389242
$40$	31.0547	4.91018
$41$	9.74515	1.52194	0.760969	−	0.648789i	$-0.224724\pi$
$41$	9.74515	1.52194	0.760969	+	0.648789i	$0.224724\pi$
$42$	25.4766	3.93112
$43$	6.36267	0.970297	0.485149	−	0.874432i	$-0.338765\pi$
$43$	6.36267	0.970297	0.485149	+	0.874432i	$0.338765\pi$
$44$	−17.0961	−2.57733
$45$	−16.7668	−2.49945
$46$	−16.2260	−2.39239
$47$	−4.05786	−0.591900	−0.295950	−	0.955203i	$-0.595636\pi$
$47$	−4.05786	−0.591900	−0.295950	+	0.955203i	$0.595636\pi$
$48$	28.4240	4.10266
$49$	5.97743	0.853919
$50$	−28.8851	−4.08498
$51$	−2.68277	−0.375664
$52$	−4.48425	−0.621854
$53$	−0.917521	−0.126031	−0.0630156	−	0.998013i	$-0.520072\pi$
$53$	−0.917521	−0.126031	−0.0630156	+	0.998013i	$0.520072\pi$
$54$	−8.46725	−1.15225
$55$	13.7993	1.86070
$56$	28.0053	3.74236
$57$	11.9984	1.58923
$58$	4.16996	0.547543
$59$	−6.29647	−0.819730	−0.409865	−	0.912146i	$-0.634424\pi$
$59$	−6.29647	−0.819730	−0.409865	+	0.912146i	$0.634424\pi$
$60$	−53.0382	−6.84720
$61$	−4.67072	−0.598024	−0.299012	−	0.954249i	$-0.596657\pi$
$61$	−4.67072	−0.598024	−0.299012	+	0.954249i	$0.596657\pi$
$62$	1.54578	0.196314
$63$	−15.1204	−1.90499
$64$	11.4490	1.43113
$65$	3.61952	0.448946
$66$	24.4299	3.00712
$67$	2.67575	0.326895	0.163447	−	0.986552i	$-0.447739\pi$
$67$	2.67575	0.326895	0.163447	+	0.986552i	$0.447739\pi$
$68$	−4.94905	−0.600161
$69$	16.5133	1.98796
$70$	−37.9350	−4.53410
$71$	−6.91045	−0.820119	−0.410060	−	0.912059i	$-0.634492\pi$
$71$	−6.91045	−0.820119	−0.410060	+	0.912059i	$0.634492\pi$
$72$	−32.6297	−3.84545
$73$	−6.70031	−0.784212	−0.392106	−	0.919920i	$-0.628253\pi$
$73$	−6.70031	−0.784212	−0.392106	+	0.919920i	$0.628253\pi$
$74$	−19.4290	−2.25858
$75$	29.3965	3.39442
$76$	22.1341	2.53895
$77$	12.4443	1.41816
$78$	6.40789	0.725551
$79$	4.49739	0.505996	0.252998	−	0.967467i	$-0.418583\pi$
$79$	4.49739	0.505996	0.252998	+	0.967467i	$0.418583\pi$
$80$	−42.3237	−4.73194
$81$	−3.97468	−0.441632
$82$	−25.6893	−2.83690
$83$	−2.70763	−0.297201	−0.148601	−	0.988897i	$-0.547477\pi$
$83$	−2.70763	−0.297201	−0.148601	+	0.988897i	$0.547477\pi$
$84$	−47.8300	−5.21868
$85$	3.99469	0.433284
$86$	−16.7727	−1.80864
$87$	−4.24378	−0.454981
$88$	26.8547	2.86272
$89$	−10.4892	−1.11185	−0.555925	−	0.831233i	$-0.687636\pi$
$89$	−10.4892	−1.11185	−0.555925	+	0.831233i	$0.687636\pi$
$90$	44.1991	4.65899
$91$	3.26409	0.342170
$92$	30.4628	3.17597
$93$	−1.57314	−0.163127
$94$	10.6970	1.10331
$95$	−17.8658	−1.83299
$96$	−33.2169	−3.39019
$97$	10.5208	1.06823	0.534115	−	0.845412i	$-0.320645\pi$
$97$	10.5208	1.06823	0.534115	+	0.845412i	$0.320645\pi$
$98$	−15.7571	−1.59171
$99$	−14.4992	−1.45722
$100$	54.2293	5.42293
$101$	9.37546	0.932893	0.466447	−	0.884549i	$-0.345534\pi$
$101$	9.37546	0.932893	0.466447	+	0.884549i	$0.345534\pi$
$102$	7.07208	0.700240
$103$	−8.90162	−0.877103	−0.438551	−	0.898706i	$-0.644508\pi$
$103$	−8.90162	−0.877103	−0.438551	+	0.898706i	$0.644508\pi$
$104$	7.04390	0.690711
$105$	38.6066	3.76761
$106$	2.41868	0.234923
$107$	11.5943	1.12087	0.560434	−	0.828199i	$-0.310634\pi$
$107$	11.5943	1.12087	0.560434	+	0.828199i	$0.310634\pi$
$108$	15.8965	1.52964
$109$	4.51064	0.432041	0.216020	−	0.976389i	$-0.430692\pi$
$109$	4.51064	0.432041	0.216020	+	0.976389i	$0.430692\pi$
$110$	−36.3765	−3.46836
$111$	19.7730	1.87677
$112$	−38.1677	−3.60651
$113$	−9.45680	−0.889621	−0.444810	−	0.895625i	$-0.646729\pi$
$113$	−9.45680	−0.889621	−0.444810	+	0.895625i	$0.646729\pi$
$114$	−31.6291	−2.96233
$115$	−24.5884	−2.29288
$116$	−7.82873	−0.726879
$117$	−3.80308	−0.351595
$118$	16.5982	1.52798
$119$	3.60242	0.330233
$120$	83.3129	7.60539
$121$	0.933015	0.0848196
$122$	12.3125	1.11472
$123$	26.1441	2.35733
$124$	−2.90206	−0.260612
$125$	−23.7984	−2.12859
$126$	39.8589	3.55091
$127$	19.7292	1.75068	0.875341	−	0.483506i	$-0.160637\pi$
$127$	19.7292	1.75068	0.875341	+	0.483506i	$0.160637\pi$
$128$	−5.41779	−0.478869
$129$	17.0696	1.50289
$130$	−9.54143	−0.836839
$131$	−2.31209	−0.202008	−0.101004	−	0.994886i	$-0.532205\pi$
$131$	−2.31209	−0.202008	−0.101004	+	0.994886i	$0.532205\pi$
$132$	−45.8650	−3.99204
$133$	−16.1114	−1.39704
$134$	−7.05356	−0.609335
$135$	−12.8311	−1.10432
$136$	7.77401	0.666616
$137$	15.2545	1.30328	0.651639	−	0.758529i	$-0.274082\pi$
$137$	15.2545	1.30328	0.651639	+	0.758529i	$0.274082\pi$
$138$	−43.5307	−3.70558
$139$	8.73093	0.740548	0.370274	−	0.928923i	$-0.379264\pi$
$139$	8.73093	0.740548	0.370274	+	0.928923i	$0.379264\pi$
$140$	71.2195	6.01915
$141$	−10.8863	−0.916794
$142$	18.2167	1.52871
$143$	3.12999	0.261743
$144$	44.4702	3.70585
$145$	6.31905	0.524768
$146$	17.6627	1.46178
$147$	16.0361	1.32264
$148$	36.4763	2.99833
$149$	8.95187	0.733366	0.366683	−	0.930346i	$-0.380493\pi$
$149$	8.95187	0.733366	0.366683	+	0.930346i	$0.380493\pi$
$150$	−77.4923	−6.32722
$151$	−7.99146	−0.650336	−0.325168	−	0.945656i	$-0.605421\pi$
$151$	−7.99146	−0.650336	−0.325168	+	0.945656i	$0.605421\pi$
$152$	−34.7684	−2.82009
$153$	−4.19728	−0.339330
$154$	−32.8044	−2.64346
$155$	2.34243	0.188148
$156$	−12.0302	−0.963190
$157$	−16.9793	−1.35509	−0.677547	−	0.735480i	$-0.736957\pi$
$157$	−16.9793	−1.35509	−0.677547	+	0.735480i	$0.736957\pi$
$158$	−11.8556	−0.943180
$159$	−2.46150	−0.195210
$160$	49.4604	3.91019
$161$	−22.1739	−1.74755
$162$	10.4777	0.823205
$163$	−3.29705	−0.258245	−0.129122	−	0.991629i	$-0.541216\pi$
$163$	−3.29705	−0.258245	−0.129122	+	0.991629i	$0.541216\pi$
$164$	48.2293	3.76607
$165$	37.0205	2.88204
$166$	7.13761	0.553986
$167$	−17.6082	−1.36256	−0.681280	−	0.732023i	$-0.738577\pi$
$167$	−17.6082	−1.36256	−0.681280	+	0.732023i	$0.738577\pi$
$168$	75.1318	5.79655
$169$	−12.1790	−0.936847
$170$	−10.5304	−0.807646
$171$	18.7719	1.43552
$172$	31.4892	2.40103
$173$	−11.7982	−0.897000	−0.448500	−	0.893783i	$-0.648042\pi$
$173$	−11.7982	−0.897000	−0.448500	+	0.893783i	$0.648042\pi$
$174$	11.1871	0.848089
$175$	−39.4736	−2.98392
$176$	−36.5996	−2.75880
$177$	−16.8920	−1.26968
$178$	27.6506	2.07250
$179$	−9.84871	−0.736127	−0.368064	−	0.929801i	$-0.619979\pi$
$179$	−9.84871	−0.736127	−0.368064	+	0.929801i	$0.619979\pi$
$180$	−82.9798	−6.18495
$181$	7.09786	0.527580	0.263790	−	0.964580i	$-0.415027\pi$
$181$	7.09786	0.527580	0.263790	+	0.964580i	$0.415027\pi$
$182$	−8.60449	−0.637807
$183$	−12.5305	−0.926280
$184$	−47.8513	−3.52764
$185$	−29.4422	−2.16464
$186$	4.14697	0.304071
$187$	3.45442	0.252612
$188$	−20.0826	−1.46467
$189$	−11.5711	−0.841673
$190$	47.0961	3.41671
$191$	−3.71074	−0.268499	−0.134250	−	0.990948i	$-0.542862\pi$
$191$	−3.71074	−0.268499	−0.134250	+	0.990948i	$0.542862\pi$
$192$	30.7152	2.21668
$193$	23.0075	1.65612	0.828058	−	0.560642i	$-0.189446\pi$
$193$	23.0075	1.65612	0.828058	+	0.560642i	$0.189446\pi$
$194$	−27.7341	−1.99119
$195$	9.71035	0.695372
$196$	29.5826	2.11305
$197$	−18.5849	−1.32412	−0.662058	−	0.749453i	$-0.730317\pi$
$197$	−18.5849	−1.32412	−0.662058	+	0.749453i	$0.730317\pi$
$198$	38.2213	2.71627
$199$	−18.2846	−1.29616	−0.648082	−	0.761571i	$-0.724428\pi$
$199$	−18.2846	−1.29616	−0.648082	+	0.761571i	$0.724428\pi$
$200$	−85.1838	−6.02341
$201$	7.17843	0.506328
$202$	−24.7147	−1.73892
$203$	5.69854	0.399959
$204$	−13.2772	−0.929589
$205$	−38.9288	−2.71891
$206$	23.4656	1.63493
$207$	25.8355	1.79569
$208$	−9.59996	−0.665638
$209$	−15.4495	−1.06866
$210$	−101.771	−7.02286
$211$	16.2098	1.11593	0.557964	−	0.829865i	$-0.311583\pi$
$211$	16.2098	1.11593	0.557964	+	0.829865i	$0.311583\pi$
$212$	−4.54086	−0.311868
$213$	−18.5392	−1.27028
$214$	−30.5639	−2.08931
$215$	−25.4168	−1.73341
$216$	−24.9704	−1.69902
$217$	2.11241	0.143400
$218$	−11.8905	−0.805328
$219$	−17.9754	−1.21467
$220$	68.2936	4.60435
$221$	0.906083	0.0609498
$222$	−52.1237	−3.49831
$223$	−24.7490	−1.65731	−0.828657	−	0.559756i	$-0.810895\pi$
$223$	−24.7490	−1.65731	−0.828657	+	0.559756i	$0.810895\pi$
$224$	44.6036	2.98020
$225$	45.9917	3.06612
$226$	24.9291	1.65826
$227$	18.8449	1.25078	0.625392	−	0.780311i	$-0.284939\pi$
$227$	18.8449	1.25078	0.625392	+	0.780311i	$0.284939\pi$
$228$	59.3808	3.93259
$229$	−28.2561	−1.86721	−0.933607	−	0.358300i	$-0.883357\pi$
$229$	−28.2561	−1.86721	−0.933607	+	0.358300i	$0.883357\pi$
$230$	64.8177	4.27395
$231$	33.3852	2.19658
$232$	12.2974	0.807366
$233$	5.73163	0.375491	0.187746	−	0.982218i	$-0.439882\pi$
$233$	5.73163	0.375491	0.187746	+	0.982218i	$0.439882\pi$
$234$	10.0253	0.655376
$235$	16.2099	1.05742
$236$	−31.1616	−2.02844
$237$	12.0655	0.783737
$238$	−9.49636	−0.615558
$239$	4.30354	0.278373	0.139186	−	0.990266i	$-0.455551\pi$
$239$	4.30354	0.278373	0.139186	+	0.990266i	$0.455551\pi$
$240$	−113.545	−7.32930
$241$	8.03544	0.517608	0.258804	−	0.965930i	$-0.416672\pi$
$241$	8.03544	0.517608	0.258804	+	0.965930i	$0.416672\pi$
$242$	−2.45953	−0.158104
$243$	−20.2993	−1.30220
$244$	−23.1156	−1.47983
$245$	−23.8780	−1.52551
$246$	−68.9185	−4.39408
$247$	−4.05236	−0.257845
$248$	4.55858	0.289470
$249$	−7.26397	−0.460335
$250$	62.7350	3.96771
$251$	−24.0088	−1.51542	−0.757712	−	0.652589i	$-0.773683\pi$
$251$	−24.0088	−1.51542	−0.757712	+	0.652589i	$0.773683\pi$
$252$	−74.8315	−4.71394
$253$	−21.2630	−1.33679
$254$	−52.0082	−3.26329
$255$	10.7168	0.671115
$256$	−8.61623	−0.538514
$257$	−29.0401	−1.81147	−0.905734	−	0.423846i	$-0.860680\pi$
$257$	−29.0401	−1.81147	−0.905734	+	0.423846i	$0.860680\pi$
$258$	−44.9973	−2.80141
$259$	−26.5511	−1.64981
$260$	17.9132	1.11093
$261$	−6.63953	−0.410976
$262$	6.09490	0.376544
$263$	29.8567	1.84104	0.920522	−	0.390690i	$-0.127764\pi$
$263$	29.8567	1.84104	0.920522	+	0.390690i	$0.127764\pi$
$264$	72.0451	4.43407
$265$	3.66521	0.225152
$266$	42.4714	2.60409
$267$	−28.1401	−1.72214
$268$	13.2424	0.808910
$269$	−30.9423	−1.88658	−0.943291	−	0.331966i	$-0.892288\pi$
$269$	−30.9423	−1.88658	−0.943291	+	0.331966i	$0.892288\pi$
$270$	33.8240	2.05846
$271$	−24.2907	−1.47556	−0.737778	−	0.675044i	$-0.764125\pi$
$271$	−24.2907	−1.47556	−0.737778	+	0.675044i	$0.764125\pi$
$272$	−10.5950	−0.642417
$273$	8.75683	0.529987
$274$	−40.2124	−2.42932
$275$	−37.8518	−2.28255
$276$	81.7249	4.91926
$277$	2.37078	0.142446	0.0712231	−	0.997460i	$-0.477310\pi$
$277$	2.37078	0.142446	0.0712231	+	0.997460i	$0.477310\pi$
$278$	−23.0156	−1.38039
$279$	−2.46123	−0.147350
$280$	−111.872	−6.68564
$281$	22.1983	1.32424	0.662120	−	0.749398i	$-0.269657\pi$
$281$	22.1983	1.32424	0.662120	+	0.749398i	$0.269657\pi$
$282$	28.6975	1.70891
$283$	2.41627	0.143632	0.0718160	−	0.997418i	$-0.477121\pi$
$283$	2.41627	0.143632	0.0718160	+	0.997418i	$0.477121\pi$
$284$	−34.2002	−2.02941
$285$	−47.9299	−2.83912
$286$	−8.25099	−0.487891
$287$	−35.1061	−2.07225
$288$	−51.9688	−3.06229
$289$	1.00000	0.0588235
$290$	−16.6577	−0.978173
$291$	28.2250	1.65458
$292$	−33.1602	−1.94055
$293$	−27.7436	−1.62080	−0.810398	−	0.585879i	$-0.800749\pi$
$293$	−27.7436	−1.62080	−0.810398	+	0.585879i	$0.800749\pi$
$294$	−42.2729	−2.46540
$295$	25.1524	1.46443
$296$	−57.2972	−3.33033
$297$	−11.0957	−0.643838
$298$	−23.5981	−1.36700
$299$	−5.57720	−0.322538
$300$	145.485	8.39958
$301$	−22.9210	−1.32114
$302$	21.0663	1.21223
$303$	25.1522	1.44496
$304$	47.3850	2.71772
$305$	18.6580	1.06836
$306$	11.0645	0.632514
$307$	−26.9837	−1.54004	−0.770022	−	0.638017i	$-0.779755\pi$
$307$	−26.9837	−1.54004	−0.770022	+	0.638017i	$0.779755\pi$
$308$	61.5874	3.50927
$309$	−23.8810	−1.35855
$310$	−6.17489	−0.350710
$311$	−8.25518	−0.468108	−0.234054	−	0.972224i	$-0.575199\pi$
$311$	−8.25518	−0.468108	−0.234054	+	0.972224i	$0.575199\pi$
$312$	18.8972	1.06984
$313$	19.3212	1.09210	0.546049	−	0.837753i	$-0.316131\pi$
$313$	19.3212	1.09210	0.546049	+	0.837753i	$0.316131\pi$
$314$	44.7592	2.52591
$315$	60.4011	3.40322
$316$	22.2578	1.25210
$317$	33.8058	1.89872	0.949362	−	0.314184i	$-0.101731\pi$
$317$	33.8058	1.89872	0.949362	+	0.314184i	$0.101731\pi$
$318$	6.48878	0.363873
$319$	5.46442	0.305949
$320$	−45.7353	−2.55668
$321$	31.1050	1.73611
$322$	58.4528	3.25745
$323$	−4.47239	−0.248850
$324$	−19.6709	−1.09283
$325$	−9.92841	−0.550729
$326$	8.69136	0.481370
$327$	12.1010	0.669188
$328$	−75.7590	−4.18309
$329$	14.6181	0.805923
$330$	−97.5898	−5.37214
$331$	7.63996	0.419930	0.209965	−	0.977709i	$-0.432665\pi$
$331$	7.63996	0.419930	0.209965	+	0.977709i	$0.432665\pi$
$332$	−13.4002	−0.735433
$333$	30.9354	1.69525
$334$	46.4170	2.53982
$335$	−10.6888	−0.583990
$336$	−102.395	−5.58612
$337$	−4.80255	−0.261612	−0.130806	−	0.991408i	$-0.541756\pi$
$337$	−4.80255	−0.261612	−0.130806	+	0.991408i	$0.541756\pi$
$338$	32.1052	1.74629
$339$	−25.3705	−1.37793
$340$	19.7699	1.07217
$341$	2.02563	0.109694
$342$	−49.4846	−2.67582
$343$	3.68371	0.198902
$344$	−49.4634	−2.66689
$345$	−65.9652	−3.55145
$346$	31.1013	1.67201
$347$	15.8707	0.851984	0.425992	−	0.904727i	$-0.359925\pi$
$347$	15.8707	0.851984	0.425992	+	0.904727i	$0.359925\pi$
$348$	−21.0027	−1.12586
$349$	24.3681	1.30439	0.652197	−	0.758050i	$-0.273848\pi$
$349$	24.3681	1.30439	0.652197	+	0.758050i	$0.273848\pi$
$350$	104.056	5.56205
$351$	−2.91037	−0.155344
$352$	42.7711	2.27971
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	44.5291	2.36670
$355$	27.6051	1.46512
$356$	−51.9114	−2.75130
$357$	9.66448	0.511499
$358$	25.9622	1.37215
$359$	−32.7676	−1.72941	−0.864703	−	0.502283i	$-0.832493\pi$
$359$	−32.7676	−1.72941	−0.864703	+	0.502283i	$0.832493\pi$
$360$	130.345	6.86981
$361$	1.00226	0.0527507
$362$	−18.7107	−0.983413
$363$	2.50307	0.131377
$364$	16.1542	0.846708
$365$	26.7656	1.40098
$366$	33.0317	1.72659
$367$	24.4381	1.27566	0.637829	−	0.770178i	$-0.279833\pi$
$367$	24.4381	1.27566	0.637829	+	0.770178i	$0.279833\pi$
$368$	65.2154	3.39959
$369$	40.9031	2.12933
$370$	77.6129	4.03490
$371$	3.30530	0.171602
$372$	−7.78557	−0.403663
$373$	−16.8934	−0.874710	−0.437355	−	0.899289i	$-0.644085\pi$
$373$	−16.8934	−0.874710	−0.437355	+	0.899289i	$0.644085\pi$
$374$	−9.10621	−0.470871
$375$	−63.8457	−3.29698
$376$	31.5459	1.62685
$377$	1.43330	0.0738187
$378$	30.5026	1.56888
$379$	−15.1710	−0.779284	−0.389642	−	0.920966i	$-0.627401\pi$
$379$	−15.1710	−0.779284	−0.389642	+	0.920966i	$0.627401\pi$
$380$	−88.4187	−4.53578
$381$	52.9290	2.71163
$382$	9.78189	0.500485
$383$	29.1315	1.48855	0.744274	−	0.667874i	$-0.232796\pi$
$383$	29.1315	1.48855	0.744274	+	0.667874i	$0.232796\pi$
$384$	−14.5347	−0.741721
$385$	−49.7110	−2.53350
$386$	−60.6502	−3.08702
$387$	26.7059	1.35754
$388$	52.0682	2.64336
$389$	−34.7179	−1.76027	−0.880133	−	0.474727i	$-0.842547\pi$
$389$	−34.7179	−1.76027	−0.880133	+	0.474727i	$0.842547\pi$
$390$	−25.5975	−1.29618
$391$	−6.15529	−0.311286
$392$	−46.4687	−2.34702
$393$	−6.20280	−0.312890
$394$	48.9916	2.46816
$395$	−17.9657	−0.903950
$396$	−71.7571	−3.60593
$397$	16.5504	0.830640	0.415320	−	0.909675i	$-0.363670\pi$
$397$	16.5504	0.830640	0.415320	+	0.909675i	$0.363670\pi$
$398$	48.2002	2.41606
$399$	−43.2233	−2.16387
$400$	116.095	5.80475
$401$	7.56287	0.377671	0.188836	−	0.982009i	$-0.439529\pi$
$401$	7.56287	0.377671	0.188836	+	0.982009i	$0.439529\pi$
$402$	−18.9231	−0.943799
$403$	0.531315	0.0264667
$404$	46.3996	2.30847
$405$	15.8776	0.788965
$406$	−15.0220	−0.745527
$407$	−25.4603	−1.26202
$408$	20.8559	1.03252
$409$	−12.6780	−0.626885	−0.313442	−	0.949607i	$-0.601482\pi$
$409$	−12.6780	−0.626885	−0.313442	+	0.949607i	$0.601482\pi$
$410$	102.620	5.06806
$411$	40.9243	2.01865
$412$	−44.0546	−2.17041
$413$	22.6825	1.11613
$414$	−68.1050	−3.34718
$415$	10.8161	0.530944
$416$	11.2187	0.550043
$417$	23.4231	1.14703
$418$	40.7265	1.99200
$419$	−35.0765	−1.71360	−0.856800	−	0.515648i	$-0.827551\pi$
$419$	−35.0765	−1.71360	−0.856800	+	0.515648i	$0.827551\pi$
$420$	191.066	9.32306
$421$	12.2044	0.594805	0.297402	−	0.954752i	$-0.403880\pi$
$421$	12.2044	0.594805	0.297402	+	0.954752i	$0.403880\pi$
$422$	−42.7307	−2.08010
$423$	−17.0320	−0.828123
$424$	7.13282	0.346400
$425$	−10.9575	−0.531517
$426$	48.8712	2.36782
$427$	16.8259	0.814262
$428$	57.3810	2.77362
$429$	8.39706	0.405414
$430$	67.0015	3.23110
$431$	−26.1986	−1.26194	−0.630971	−	0.775806i	$-0.717343\pi$
$431$	−26.1986	−1.26194	−0.630971	+	0.775806i	$0.717343\pi$
$432$	34.0315	1.63734
$433$	4.06986	0.195585	0.0977925	−	0.995207i	$-0.468822\pi$
$433$	4.06986	0.195585	0.0977925	+	0.995207i	$0.468822\pi$
$434$	−5.56854	−0.267298
$435$	16.9526	0.812814
$436$	22.3234	1.06910
$437$	27.5288	1.31688
$438$	47.3851	2.26415
$439$	11.0840	0.529011	0.264506	−	0.964384i	$-0.414791\pi$
$439$	11.0840	0.529011	0.264506	+	0.964384i	$0.414791\pi$
$440$	−107.276	−5.11419
$441$	25.0890	1.19471
$442$	−2.38853	−0.113611
$443$	−10.5525	−0.501366	−0.250683	−	0.968069i	$-0.580655\pi$
$443$	−10.5525	−0.501366	−0.250683	+	0.968069i	$0.580655\pi$
$444$	97.8576	4.64412
$445$	41.9009	1.98629
$446$	65.2409	3.08925
$447$	24.0159	1.13591
$448$	−41.2443	−1.94861
$449$	23.4837	1.10826	0.554132	−	0.832429i	$-0.313050\pi$
$449$	23.4837	1.10826	0.554132	+	0.832429i	$0.313050\pi$
$450$	−121.239	−5.71526
$451$	−33.6639	−1.58517
$452$	−46.8022	−2.20139
$453$	−21.4393	−1.00731
$454$	−49.6773	−2.33147
$455$	−13.0390	−0.611279
$456$	−93.2758	−4.36804
$457$	−37.1422	−1.73744	−0.868719	−	0.495306i	$-0.835056\pi$
$457$	−37.1422	−1.73744	−0.868719	+	0.495306i	$0.835056\pi$
$458$	74.4860	3.48050
$459$	−3.21203	−0.149925
$460$	−121.689	−5.67380
$461$	35.6413	1.65998	0.829990	−	0.557778i	$-0.188346\pi$
$461$	35.6413	1.65998	0.829990	+	0.557778i	$0.188346\pi$
$462$	−88.0069	−4.09445
$463$	−13.1739	−0.612242	−0.306121	−	0.951993i	$-0.599031\pi$
$463$	−13.1739	−0.612242	−0.306121	+	0.951993i	$0.599031\pi$
$464$	−16.7599	−0.778058
$465$	6.28421	0.291423
$466$	−15.1092	−0.699919
$467$	−29.7080	−1.37472	−0.687362	−	0.726315i	$-0.741231\pi$
$467$	−29.7080	−1.37472	−0.687362	+	0.726315i	$0.741231\pi$
$468$	−18.8217	−0.870032
$469$	−9.63918	−0.445096
$470$	−42.7310	−1.97103
$471$	−45.5516	−2.09891
$472$	48.9488	2.25305
$473$	−21.9793	−1.01061
$474$	−31.8059	−1.46089
$475$	49.0062	2.24856
$476$	17.8286	0.817171
$477$	−3.85109	−0.176329
$478$	−11.3446	−0.518889
$479$	−19.2283	−0.878565	−0.439282	−	0.898349i	$-0.644767\pi$
$479$	−19.2283	−0.878565	−0.439282	+	0.898349i	$0.644767\pi$
$480$	132.691	6.05649
$481$	−6.67815	−0.304498
$482$	−21.1823	−0.964826
$483$	−59.4877	−2.70678
$484$	4.61754	0.209888
$485$	−42.0275	−1.90837
$486$	53.5110	2.42731
$487$	−6.69685	−0.303463	−0.151732	−	0.988422i	$-0.548485\pi$
$487$	−6.69685	−0.303463	−0.151732	+	0.988422i	$0.548485\pi$
$488$	36.3102	1.64369
$489$	−8.84523	−0.399995
$490$	62.9448	2.84356
$491$	16.7591	0.756326	0.378163	−	0.925739i	$-0.376556\pi$
$491$	16.7591	0.756326	0.378163	+	0.925739i	$0.376556\pi$
$492$	129.388	5.83327
$493$	1.58186	0.0712436
$494$	10.6824	0.480626
$495$	57.9196	2.60329
$496$	−6.21277	−0.278962
$497$	24.8943	1.11666
$498$	19.1486	0.858069
$499$	37.7679	1.69072	0.845362	−	0.534194i	$-0.179385\pi$
$499$	37.7679	1.69072	0.845362	+	0.534194i	$0.179385\pi$
$500$	−117.779	−5.26725
$501$	−47.2387	−2.11047
$502$	63.2898	2.82476
$503$	9.14179	0.407612	0.203806	−	0.979011i	$-0.434669\pi$
$503$	9.14179	0.407612	0.203806	+	0.979011i	$0.434669\pi$
$504$	117.546	5.23591
$505$	−37.4520	−1.66659
$506$	56.0514	2.49179
$507$	−32.6735	−1.45108
$508$	97.6408	4.33211
$509$	17.4764	0.774627	0.387313	−	0.921948i	$-0.373403\pi$
$509$	17.4764	0.774627	0.387313	+	0.921948i	$0.373403\pi$
$510$	−28.2507	−1.25096
$511$	24.1373	1.06777
$512$	33.5489	1.48266
$513$	14.3655	0.634250
$514$	76.5526	3.37659
$515$	35.5592	1.56692
$516$	84.4783	3.71895
$517$	14.0176	0.616491
$518$	69.9915	3.07525
$519$	−31.6519	−1.38936
$520$	−28.1382	−1.23394
$521$	−30.9030	−1.35388	−0.676942	−	0.736036i	$-0.736695\pi$
$521$	−30.9030	−1.35388	−0.676942	+	0.736036i	$0.736695\pi$
$522$	17.5025	0.766063
$523$	−41.4988	−1.81462	−0.907308	−	0.420466i	$-0.861867\pi$
$523$	−41.4988	−1.81462	−0.907308	+	0.420466i	$0.861867\pi$
$524$	−11.4426	−0.499874
$525$	−105.899	−4.62180
$526$	−78.7055	−3.43172
$527$	0.586386	0.0255434
$528$	−98.1886	−4.27311
$529$	14.8876	0.647286
$530$	−9.66187	−0.419685
$531$	−26.4280	−1.14688
$532$	−79.7363	−3.45701
$533$	−8.82992	−0.382466
$534$	74.1802	3.21009
$535$	−46.3158	−2.00241
$536$	−20.8013	−0.898480
$537$	−26.4219	−1.14019
$538$	81.5670	3.51660
$539$	−20.6486	−0.889397
$540$	−63.5015	−2.73267
$541$	−41.3305	−1.77694	−0.888468	−	0.458939i	$-0.848230\pi$
$541$	−41.3305	−1.77694	−0.888468	+	0.458939i	$0.848230\pi$
$542$	64.0329	2.75045
$543$	19.0420	0.817169
$544$	12.3816	0.530855
$545$	−18.0186	−0.771831
$546$	−23.0839	−0.987900
$547$	−29.7509	−1.27206	−0.636029	−	0.771665i	$-0.719424\pi$
$547$	−29.7509	−1.27206	−0.636029	+	0.771665i	$0.719424\pi$
$548$	75.4952	3.22500
$549$	−19.6043	−0.836691
$550$	99.7814	4.25469
$551$	−7.07471	−0.301393
$552$	−128.374	−5.46397
$553$	−16.2015	−0.688957
$554$	−6.24962	−0.265521
$555$	−78.9869	−3.35281
$556$	43.2098	1.83250
$557$	−3.50174	−0.148374	−0.0741868	−	0.997244i	$-0.523636\pi$
$557$	−3.50174	−0.148374	−0.0741868	+	0.997244i	$0.523636\pi$
$558$	6.48806	0.274661
$559$	−5.76510	−0.243838
$560$	152.468	6.44295
$561$	9.26743	0.391271
$562$	−58.5171	−2.46839
$563$	43.9353	1.85165	0.925826	−	0.377950i	$-0.123371\pi$
$563$	43.9353	1.85165	0.925826	+	0.377950i	$0.123371\pi$
$564$	−53.8770	−2.26863
$565$	37.7769	1.58929
$566$	−6.36953	−0.267731
$567$	14.3185	0.601320
$568$	53.7219	2.25412
$569$	14.1575	0.593512	0.296756	−	0.954953i	$-0.404095\pi$
$569$	14.1575	0.593512	0.296756	+	0.954953i	$0.404095\pi$
$570$	126.348	5.29214
$571$	−26.0351	−1.08954	−0.544768	−	0.838587i	$-0.683382\pi$
$571$	−26.0351	−1.08954	−0.544768	+	0.838587i	$0.683382\pi$
$572$	15.4905	0.647690
$573$	−9.95507	−0.415879
$574$	92.5435	3.86269
$575$	67.4466	2.81272
$576$	48.0548	2.00228
$577$	26.9288	1.12106	0.560531	−	0.828133i	$-0.310597\pi$
$577$	26.9288	1.12106	0.560531	+	0.828133i	$0.310597\pi$
$578$	−2.63611	−0.109648
$579$	61.7240	2.56516
$580$	31.2733	1.29855
$581$	9.75404	0.404666
$582$	−74.4042	−3.08415
$583$	3.16950	0.131267
$584$	52.0883	2.15543
$585$	15.1921	0.628117
$586$	73.1350	3.02118
$587$	−8.96993	−0.370229	−0.185114	−	0.982717i	$-0.559266\pi$
$587$	−8.96993	−0.370229	−0.185114	+	0.982717i	$0.559266\pi$
$588$	79.3636	3.27290
$589$	−2.62255	−0.108060
$590$	−66.3044	−2.72971
$591$	−49.8590	−2.05092
$592$	78.0890	3.20944
$593$	−26.4442	−1.08593	−0.542966	−	0.839755i	$-0.682699\pi$
$593$	−26.4442	−1.08593	−0.542966	+	0.839755i	$0.682699\pi$
$594$	29.2494	1.20012
$595$	−14.3905	−0.589954
$596$	44.3033	1.81473
$597$	−49.0536	−2.00763
$598$	14.7021	0.601213
$599$	26.8687	1.09783	0.548913	−	0.835880i	$-0.315042\pi$
$599$	26.8687	1.09783	0.548913	+	0.835880i	$0.315042\pi$
$600$	−228.529	−9.32966
$601$	−1.23231	−0.0502670	−0.0251335	−	0.999684i	$-0.508001\pi$
$601$	−1.23231	−0.0502670	−0.0251335	+	0.999684i	$0.508001\pi$
$602$	60.4222	2.46262
$603$	11.2309	0.457356
$604$	−39.5501	−1.60927
$605$	−3.72710	−0.151528
$606$	−66.3040	−2.69341
$607$	4.45687	0.180899	0.0904494	−	0.995901i	$-0.471170\pi$
$607$	4.45687	0.180899	0.0904494	+	0.995901i	$0.471170\pi$
$608$	−55.3751	−2.24576
$609$	15.2879	0.619497
$610$	−49.1846	−1.99142
$611$	3.67676	0.148746
$612$	−20.7726	−0.839681
$613$	22.7578	0.919180	0.459590	−	0.888131i	$-0.347996\pi$
$613$	22.7578	0.919180	0.459590	+	0.888131i	$0.347996\pi$
$614$	71.1320	2.87065
$615$	−104.437	−4.21132
$616$	−96.7419	−3.89784
$617$	25.9233	1.04363	0.521816	−	0.853058i	$-0.325255\pi$
$617$	25.9233	1.04363	0.521816	+	0.853058i	$0.325255\pi$
$618$	62.9529	2.53234
$619$	3.30282	0.132751	0.0663757	−	0.997795i	$-0.478856\pi$
$619$	3.30282	0.132751	0.0663757	+	0.997795i	$0.478856\pi$
$620$	11.5928	0.465578
$621$	19.7710	0.793382
$622$	21.7615	0.872558
$623$	37.7864	1.51388
$624$	−25.7545	−1.03101
$625$	40.2795	1.61118
$626$	−50.9327	−2.03568
$627$	−41.4475	−1.65526
$628$	−84.0313	−3.35321
$629$	−7.37035	−0.293875
$630$	−159.224	−6.34362
$631$	−16.5070	−0.657134	−0.328567	−	0.944481i	$-0.606566\pi$
$631$	−16.5070	−0.657134	−0.328567	+	0.944481i	$0.606566\pi$
$632$	−34.9628	−1.39074
$633$	43.4872	1.72846
$634$	−89.1157	−3.53924
$635$	−78.8119	−3.12755
$636$	−12.1821	−0.483052
$637$	−5.41605	−0.214592
$638$	−14.4048	−0.570291
$639$	−29.0051	−1.14742
$640$	21.6424	0.855489
$641$	28.6751	1.13260	0.566299	−	0.824200i	$-0.308375\pi$
$641$	28.6751	1.13260	0.566299	+	0.824200i	$0.308375\pi$
$642$	−81.9961	−3.23613
$643$	24.6705	0.972908	0.486454	−	0.873706i	$-0.338290\pi$
$643$	24.6705	0.972908	0.486454	+	0.873706i	$0.338290\pi$
$644$	−109.740	−4.32436
$645$	−68.1877	−2.68489
$646$	11.7897	0.463859
$647$	−49.4154	−1.94272	−0.971360	−	0.237611i	$-0.923636\pi$
$647$	−49.4154	−1.94272	−0.971360	+	0.237611i	$0.923636\pi$
$648$	30.8992	1.21384
$649$	21.7506	0.853787
$650$	26.1723	1.02656
$651$	5.66712	0.222112
$652$	−16.3173	−0.639033
$653$	20.6329	0.807428	0.403714	−	0.914885i	$-0.367719\pi$
$653$	20.6329	0.807428	0.403714	+	0.914885i	$0.367719\pi$
$654$	−31.8996	−1.24737
$655$	9.23605	0.360882
$656$	103.250	4.03124
$657$	−28.1231	−1.09719
$658$	−38.5349	−1.50225
$659$	17.4792	0.680891	0.340446	−	0.940264i	$-0.389422\pi$
$659$	17.4792	0.680891	0.340446	+	0.940264i	$0.389422\pi$
$660$	183.216	7.13168
$661$	3.76756	0.146541	0.0732706	−	0.997312i	$-0.476656\pi$
$661$	3.76756	0.146541	0.0732706	+	0.997312i	$0.476656\pi$
$662$	−20.1397	−0.782753
$663$	2.43082	0.0944051
$664$	21.0492	0.816867
$665$	64.3601	2.49578
$666$	−81.5491	−3.15996
$667$	−9.73683	−0.377012
$668$	−87.1437	−3.37169
$669$	−66.3960	−2.56702
$670$	28.1767	1.08856
$671$	16.1346	0.622870
$672$	119.661	4.61603
$673$	−8.69461	−0.335153	−0.167576	−	0.985859i	$-0.553594\pi$
$673$	−8.69461	−0.335153	−0.167576	+	0.985859i	$0.553594\pi$
$674$	12.6600	0.487646
$675$	35.1959	1.35469
$676$	−60.2746	−2.31825
$677$	19.5685	0.752077	0.376038	−	0.926604i	$-0.377286\pi$
$677$	19.5685	0.752077	0.376038	+	0.926604i	$0.377286\pi$
$678$	66.8792	2.56848
$679$	−37.9005	−1.45449
$680$	−31.0547	−1.19089
$681$	50.5567	1.93734
$682$	−5.33976	−0.204470
$683$	35.3653	1.35322	0.676608	−	0.736343i	$-0.263449\pi$
$683$	35.3653	1.35322	0.676608	+	0.736343i	$0.263449\pi$
$684$	92.9029	3.55223
$685$	−60.9369	−2.32828
$686$	−9.71065	−0.370754
$687$	−75.8046	−2.89213
$688$	67.4125	2.57008
$689$	0.831350	0.0316719
$690$	173.891	6.61993
$691$	−14.0838	−0.535774	−0.267887	−	0.963450i	$-0.586325\pi$
$691$	−14.0838	−0.535774	−0.267887	+	0.963450i	$0.586325\pi$
$692$	−58.3899	−2.21965
$693$	52.2321	1.98413
$694$	−41.8369	−1.58811
$695$	−34.8773	−1.32297
$696$	32.9912	1.25053
$697$	−9.74515	−0.369124
$698$	−64.2368	−2.43140
$699$	15.3767	0.581599
$700$	−195.357	−7.38379
$701$	−10.1877	−0.384785	−0.192393	−	0.981318i	$-0.561625\pi$
$701$	−10.1877	−0.384785	−0.192393	+	0.981318i	$0.561625\pi$
$702$	7.67203	0.289562
$703$	32.9631	1.24323
$704$	−39.5498	−1.49059
$705$	43.4875	1.63783
$706$	2.63611	0.0992111
$707$	−33.7744	−1.27022
$708$	−83.5994	−3.14186
$709$	−0.966195	−0.0362862	−0.0181431	−	0.999835i	$-0.505775\pi$
$709$	−0.966195	−0.0362862	−0.0181431	+	0.999835i	$0.505775\pi$
$710$	−72.7699	−2.73100
$711$	18.8768	0.707935
$712$	81.5429	3.05595
$713$	−3.60938	−0.135172
$714$	−25.4766	−0.953438
$715$	−12.5033	−0.467598
$716$	−48.7418	−1.82157
$717$	11.5454	0.431172
$718$	86.3788	3.22363
$719$	−46.0459	−1.71722	−0.858611	−	0.512627i	$-0.828672\pi$
$719$	−46.0459	−1.71722	−0.858611	+	0.512627i	$0.828672\pi$
$720$	−177.645	−6.62042
$721$	32.0674	1.19425
$722$	−2.64207	−0.0983277
$723$	21.5573	0.801724
$724$	35.1277	1.30551
$725$	−17.3333	−0.643742
$726$	−6.59835	−0.244888
$727$	10.4857	0.388894	0.194447	−	0.980913i	$-0.437709\pi$
$727$	10.4857	0.388894	0.194447	+	0.980913i	$0.437709\pi$
$728$	−25.3751	−0.940464
$729$	−42.5343	−1.57535
$730$	−70.5570	−2.61143
$731$	−6.36267	−0.235332
$732$	−62.0140	−2.29210
$733$	−25.2976	−0.934387	−0.467194	−	0.884155i	$-0.654735\pi$
$733$	−25.2976	−0.934387	−0.467194	+	0.884155i	$0.654735\pi$
$734$	−64.4213	−2.37784
$735$	−64.0592	−2.36286
$736$	−76.2120	−2.80921
$737$	−9.24316	−0.340476
$738$	−107.825	−3.96909
$739$	1.54501	0.0568341	0.0284170	−	0.999596i	$-0.490953\pi$
$739$	1.54501	0.0568341	0.0284170	+	0.999596i	$0.490953\pi$
$740$	−145.711	−5.35645
$741$	−10.8716	−0.399377
$742$	−8.71311	−0.319868
$743$	−18.4349	−0.676310	−0.338155	−	0.941090i	$-0.609803\pi$
$743$	−18.4349	−0.676310	−0.338155	+	0.941090i	$0.609803\pi$
$744$	12.2296	0.448360
$745$	−35.7599	−1.31014
$746$	44.5329	1.63047
$747$	−11.3647	−0.415812
$748$	17.0961	0.625095
$749$	−41.7677	−1.52616
$750$	168.304	6.14559
$751$	33.8817	1.23636	0.618181	−	0.786036i	$-0.287870\pi$
$751$	33.8817	1.23636	0.618181	+	0.786036i	$0.287870\pi$
$752$	−42.9931	−1.56780
$753$	−64.4103	−2.34724
$754$	−3.77833	−0.137599
$755$	31.9234	1.16181
$756$	−57.2659	−2.08274
$757$	30.4167	1.10551	0.552756	−	0.833343i	$-0.313576\pi$
$757$	30.4167	1.10551	0.552756	+	0.833343i	$0.313576\pi$
$758$	39.9925	1.45259
$759$	−57.0437	−2.07056
$760$	138.889	5.03803
$761$	0.673341	0.0244086	0.0122043	−	0.999926i	$-0.496115\pi$
$761$	0.673341	0.0244086	0.0122043	+	0.999926i	$0.496115\pi$
$762$	−139.526	−5.05451
$763$	−16.2492	−0.588261
$764$	−18.3646	−0.664409
$765$	16.7668	0.606205
$766$	−76.7936	−2.77467
$767$	5.70512	0.206000
$768$	−23.1154	−0.834105
$769$	34.9091	1.25885	0.629427	−	0.777059i	$-0.283290\pi$
$769$	34.9091	1.25885	0.629427	+	0.777059i	$0.283290\pi$
$770$	131.043	4.72247
$771$	−77.9079	−2.80579
$772$	113.865	4.09810
$773$	20.5719	0.739919	0.369960	−	0.929048i	$-0.379372\pi$
$773$	20.5719	0.739919	0.369960	+	0.929048i	$0.379372\pi$
$774$	−70.3995	−2.53046
$775$	−6.42534	−0.230805
$776$	−81.7892	−2.93606
$777$	−71.2307	−2.55539
$778$	91.5200	3.28115
$779$	43.5841	1.56156
$780$	48.0570	1.72072
$781$	23.8716	0.854193
$782$	16.2260	0.580240
$783$	−5.08100	−0.181580
$784$	63.3310	2.26182
$785$	67.8268	2.42084
$786$	16.3512	0.583230
$787$	8.65859	0.308645	0.154323	−	0.988021i	$-0.450680\pi$
$787$	8.65859	0.308645	0.154323	+	0.988021i	$0.450680\pi$
$788$	−91.9774	−3.27656
$789$	80.0989	2.85160
$790$	47.3594	1.68497
$791$	34.0674	1.21130
$792$	112.717	4.00521
$793$	4.23206	0.150285
$794$	−43.6286	−1.54832
$795$	9.83293	0.348738
$796$	−90.4916	−3.20739
$797$	−4.90938	−0.173899	−0.0869495	−	0.996213i	$-0.527712\pi$
$797$	−4.90938	−0.173899	−0.0869495	+	0.996213i	$0.527712\pi$
$798$	113.941	4.03348
$799$	4.05786	0.143557
$800$	−135.671	−4.79669
$801$	−44.0260	−1.55558
$802$	−19.9365	−0.703983
$803$	23.1457	0.816794
$804$	35.5264	1.25292
$805$	88.5779	3.12196
$806$	−1.40060	−0.0493341
$807$	−83.0111	−2.92213
$808$	−72.8850	−2.56408
$809$	−53.3202	−1.87464	−0.937319	−	0.348473i	$-0.886700\pi$
$809$	−53.3202	−1.87464	−0.937319	+	0.348473i	$0.886700\pi$
$810$	−41.8551	−1.47064
$811$	−48.0833	−1.68843	−0.844216	−	0.536003i	$-0.819934\pi$
$811$	−48.0833	−1.68843	−0.844216	+	0.536003i	$0.819934\pi$
$812$	28.2024	0.989709
$813$	−65.1665	−2.28549
$814$	67.1160	2.35242
$815$	13.1707	0.461348
$816$	−28.4240	−0.995040
$817$	28.4563	0.995560
$818$	33.4204	1.16852
$819$	13.7003	0.478728
$820$	−192.661	−6.72801
$821$	−7.05456	−0.246206	−0.123103	−	0.992394i	$-0.539285\pi$
$821$	−7.05456	−0.246206	−0.123103	+	0.992394i	$0.539285\pi$
$822$	−107.881	−3.76278
$823$	34.4316	1.20021	0.600106	−	0.799921i	$-0.295125\pi$
$823$	34.4316	1.20021	0.600106	+	0.799921i	$0.295125\pi$
$824$	69.2013	2.41074
$825$	−101.548	−3.53545
$826$	−59.7935	−2.08048
$827$	18.8297	0.654775	0.327387	−	0.944890i	$-0.393832\pi$
$827$	18.8297	0.654775	0.327387	+	0.944890i	$0.393832\pi$
$828$	127.861	4.44348
$829$	−47.7194	−1.65736	−0.828681	−	0.559721i	$-0.810908\pi$
$829$	−47.7194	−1.65736	−0.828681	+	0.559721i	$0.810908\pi$
$830$	−28.5125	−0.989683
$831$	6.36026	0.220635
$832$	−10.3738	−0.359646
$833$	−5.97743	−0.207106
$834$	−61.7458	−2.13808
$835$	70.3391	2.43418
$836$	−76.4604	−2.64444
$837$	−1.88349	−0.0651030
$838$	92.4654	3.19417
$839$	−35.3584	−1.22071	−0.610354	−	0.792129i	$-0.708973\pi$
$839$	−35.3584	−1.22071	−0.610354	+	0.792129i	$0.708973\pi$
$840$	−300.128	−10.3554
$841$	−26.4977	−0.913714
$842$	−32.1720	−1.10872
$843$	59.5530	2.05112
$844$	80.2231	2.76139
$845$	48.6513	1.67366
$846$	44.8981	1.54363
$847$	−3.36111	−0.115489
$848$	−9.72115	−0.333826
$849$	6.48230	0.222472
$850$	28.8851	0.990752
$851$	45.3667	1.55515
$852$	−91.7514	−3.14335
$853$	−15.6783	−0.536815	−0.268407	−	0.963306i	$-0.586497\pi$
$853$	−15.6783	−0.536815	−0.268407	+	0.963306i	$0.586497\pi$
$854$	−44.3548	−1.51779
$855$	−74.9877	−2.56452
$856$	−90.1346	−3.08074
$857$	23.0007	0.785687	0.392844	−	0.919605i	$-0.371491\pi$
$857$	23.0007	0.785687	0.392844	+	0.919605i	$0.371491\pi$
$858$	−22.1355	−0.755695
$859$	5.03619	0.171833	0.0859163	−	0.996302i	$-0.472618\pi$
$859$	5.03619	0.171833	0.0859163	+	0.996302i	$0.472618\pi$
$860$	−125.789	−4.28938
$861$	−94.1819	−3.20971
$862$	69.0623	2.35227
$863$	−22.2640	−0.757877	−0.378938	−	0.925422i	$-0.623711\pi$
$863$	−22.2640	−0.757877	−0.378938	+	0.925422i	$0.623711\pi$
$864$	−39.7699	−1.35300
$865$	47.1301	1.60247
$866$	−10.7286	−0.364572
$867$	2.68277	0.0911118
$868$	10.4544	0.354847
$869$	−15.5359	−0.527018
$870$	−44.6888	−1.51509
$871$	−2.42445	−0.0821494
$872$	−35.0658	−1.18748
$873$	44.1589	1.49455
$874$	−72.5689	−2.45468
$875$	85.7317	2.89826
$876$	−88.9613	−3.00572
$877$	−26.7909	−0.904666	−0.452333	−	0.891849i	$-0.649408\pi$
$877$	−26.7909	−0.904666	−0.452333	+	0.891849i	$0.649408\pi$
$878$	−29.2186	−0.986081
$879$	−74.4298	−2.51045
$880$	146.204	4.92854
$881$	54.2556	1.82792	0.913959	−	0.405807i	$-0.133009\pi$
$881$	54.2556	1.82792	0.913959	+	0.405807i	$0.133009\pi$
$882$	−66.1372	−2.22695
$883$	−28.1705	−0.948014	−0.474007	−	0.880521i	$-0.657193\pi$
$883$	−28.1705	−0.948014	−0.474007	+	0.880521i	$0.657193\pi$
$884$	4.48425	0.150822
$885$	67.4782	2.26826
$886$	27.8176	0.934549
$887$	0.749191	0.0251554	0.0125777	−	0.999921i	$-0.495996\pi$
$887$	0.749191	0.0251554	0.0125777	+	0.999921i	$0.495996\pi$
$888$	−153.716	−5.15836
$889$	−71.0728	−2.38371
$890$	−110.455	−3.70247
$891$	13.7302	0.459980
$892$	−122.484	−4.10107
$893$	−18.1483	−0.607311
$894$	−63.3083	−2.11735
$895$	39.3425	1.31507
$896$	19.5172	0.652022
$897$	−14.9624	−0.499579
$898$	−61.9055	−2.06581
$899$	0.927584	0.0309366
$900$	227.615	7.58718
$901$	0.917521	0.0305671
$902$	88.7415	2.95477
$903$	−61.4919	−2.04632
$904$	73.5173	2.44515
$905$	−28.3537	−0.942509
$906$	56.5162	1.87763
$907$	−10.6422	−0.353368	−0.176684	−	0.984268i	$-0.556537\pi$
$907$	−10.6422	−0.353368	−0.176684	+	0.984268i	$0.556537\pi$
$908$	93.2646	3.09510
$909$	39.3514	1.30520
$910$	34.3722	1.13943
$911$	−24.5321	−0.812786	−0.406393	−	0.913698i	$-0.633214\pi$
$911$	−24.5321	−0.812786	−0.406393	+	0.913698i	$0.633214\pi$
$912$	127.123	4.20947
$913$	9.35330	0.309549
$914$	97.9107	3.23860
$915$	50.0553	1.65478
$916$	−139.841	−4.62047
$917$	8.32910	0.275051
$918$	8.46725	0.279461
$919$	−13.0537	−0.430602	−0.215301	−	0.976548i	$-0.569073\pi$
$919$	−13.0537	−0.430602	−0.215301	+	0.976548i	$0.569073\pi$
$920$	191.151	6.30206
$921$	−72.3913	−2.38537
$922$	−93.9542	−3.09422
$923$	6.26144	0.206098
$924$	165.225	5.43550
$925$	80.7607	2.65540
$926$	34.7277	1.14122
$927$	−37.3626	−1.22715
$928$	19.5859	0.642940
$929$	17.7001	0.580722	0.290361	−	0.956917i	$-0.406225\pi$
$929$	17.7001	0.580722	0.290361	+	0.956917i	$0.406225\pi$
$930$	−16.5658	−0.543215
$931$	26.7334	0.876152
$932$	28.3661	0.929163
$933$	−22.1468	−0.725053
$934$	78.3135	2.56250
$935$	−13.7993	−0.451286
$936$	29.5652	0.966370
$937$	−27.5762	−0.900876	−0.450438	−	0.892808i	$-0.648732\pi$
$937$	−27.5762	−0.900876	−0.450438	+	0.892808i	$0.648732\pi$
$938$	25.4099	0.829662
$939$	51.8344	1.69155
$940$	80.2235	2.61660
$941$	−5.13521	−0.167403	−0.0837015	−	0.996491i	$-0.526674\pi$
$941$	−5.13521	−0.167403	−0.0837015	+	0.996491i	$0.526674\pi$
$942$	120.079	3.91238
$943$	59.9842	1.95336
$944$	−66.7112	−2.17126
$945$	46.2228	1.50363
$946$	57.9398	1.88379
$947$	47.4691	1.54254	0.771269	−	0.636509i	$-0.219622\pi$
$947$	47.4691	1.54254	0.771269	+	0.636509i	$0.219622\pi$
$948$	59.7127	1.93938
$949$	6.07104	0.197074
$950$	−129.186	−4.19133
$951$	90.6934	2.94094
$952$	−28.0053	−0.907656
$953$	6.86506	0.222381	0.111191	−	0.993799i	$-0.464534\pi$
$953$	6.86506	0.222381	0.111191	+	0.993799i	$0.464534\pi$
$954$	10.1519	0.328679
$955$	14.8232	0.479668
$956$	21.2985	0.688841
$957$	14.6598	0.473884
$958$	50.6879	1.63765
$959$	−54.9531	−1.77453
$960$	−122.698	−3.96005
$961$	−30.6562	−0.988908
$962$	17.6043	0.567586
$963$	48.6647	1.56820
$964$	39.7678	1.28084
$965$	−91.9078	−2.95862
$966$	156.816	5.04547
$967$	36.2549	1.16588	0.582939	−	0.812516i	$-0.301902\pi$
$967$	36.2549	1.16588	0.582939	+	0.812516i	$0.301902\pi$
$968$	−7.25327	−0.233129
$969$	−11.9984	−0.385445
$970$	110.789	3.55721
$971$	33.4421	1.07321	0.536604	−	0.843834i	$-0.319707\pi$
$971$	33.4421	1.07321	0.536604	+	0.843834i	$0.319707\pi$
$972$	−100.462	−3.22233
$973$	−31.4525	−1.00832
$974$	17.6536	0.565658
$975$	−26.6357	−0.853025
$976$	−49.4863	−1.58402
$977$	−44.7733	−1.43242	−0.716212	−	0.697883i	$-0.754126\pi$
$977$	−44.7733	−1.43242	−0.716212	+	0.697883i	$0.754126\pi$
$978$	23.3170	0.745594
$979$	36.2340	1.15804
$980$	−118.173	−3.77491
$981$	18.9324	0.604465
$982$	−44.1787	−1.40980
$983$	−35.9076	−1.14528	−0.572638	−	0.819809i	$-0.694080\pi$
$983$	−35.9076	−1.14528	−0.572638	+	0.819809i	$0.694080\pi$
$984$	−203.244	−6.47919
$985$	74.2406	2.36550
$986$	−4.16996	−0.132799
$987$	39.2171	1.24830
$988$	−20.0553	−0.638045
$989$	39.1640	1.24534
$990$	−152.682	−4.85256
$991$	43.7464	1.38965	0.694826	−	0.719178i	$-0.255481\pi$
$991$	43.7464	1.38965	0.694826	+	0.719178i	$0.255481\pi$
$992$	7.26037	0.230517
$993$	20.4963	0.650430
$994$	−65.6241	−2.08147
$995$	73.0414	2.31557
$996$	−35.9498	−1.13911
$997$	−47.8320	−1.51485	−0.757427	−	0.652920i	$-0.773544\pi$
$997$	−47.8320	−1.51485	−0.757427	+	0.652920i	$0.773544\pi$
$998$	−99.5602	−3.15152
$999$	23.6738	0.749006

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.a.1.6	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.a.1.6	✓	113	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)

\(f(q)\)	\(=\)	\(q-2.63611 q^{2} +2.68277 q^{3} +4.94905 q^{4} -3.99469 q^{5} -7.07208 q^{6} -3.60242 q^{7} -7.77401 q^{8} +4.19728 q^{9} +O(q^{10})\)	\(q-2.63611 q^{2} +2.68277 q^{3} +4.94905 q^{4} -3.99469 q^{5} -7.07208 q^{6} -3.60242 q^{7} -7.77401 q^{8} +4.19728 q^{9} +10.5304 q^{10} -3.45442 q^{11} +13.2772 q^{12} -0.906083 q^{13} +9.49636 q^{14} -10.7168 q^{15} +10.5950 q^{16} -1.00000 q^{17} -11.0645 q^{18} +4.47239 q^{19} -19.7699 q^{20} -9.66448 q^{21} +9.10621 q^{22} +6.15529 q^{23} -20.8559 q^{24} +10.9575 q^{25} +2.38853 q^{26} +3.21203 q^{27} -17.8286 q^{28} -1.58186 q^{29} +28.2507 q^{30} -0.586386 q^{31} -12.3816 q^{32} -9.26743 q^{33} +2.63611 q^{34} +14.3905 q^{35} +20.7726 q^{36} +7.37035 q^{37} -11.7897 q^{38} -2.43082 q^{39} +31.0547 q^{40} +9.74515 q^{41} +25.4766 q^{42} +6.36267 q^{43} -17.0961 q^{44} -16.7668 q^{45} -16.2260 q^{46} -4.05786 q^{47} +28.4240 q^{48} +5.97743 q^{49} -28.8851 q^{50} -2.68277 q^{51} -4.48425 q^{52} -0.917521 q^{53} -8.46725 q^{54} +13.7993 q^{55} +28.0053 q^{56} +11.9984 q^{57} +4.16996 q^{58} -6.29647 q^{59} -53.0382 q^{60} -4.67072 q^{61} +1.54578 q^{62} -15.1204 q^{63} +11.4490 q^{64} +3.61952 q^{65} +24.4299 q^{66} +2.67575 q^{67} -4.94905 q^{68} +16.5133 q^{69} -37.9350 q^{70} -6.91045 q^{71} -32.6297 q^{72} -6.70031 q^{73} -19.4290 q^{74} +29.3965 q^{75} +22.1341 q^{76} +12.4443 q^{77} +6.40789 q^{78} +4.49739 q^{79} -42.3237 q^{80} -3.97468 q^{81} -25.6893 q^{82} -2.70763 q^{83} -47.8300 q^{84} +3.99469 q^{85} -16.7727 q^{86} -4.24378 q^{87} +26.8547 q^{88} -10.4892 q^{89} +44.1991 q^{90} +3.26409 q^{91} +30.4628 q^{92} -1.57314 q^{93} +10.6970 q^{94} -17.8658 q^{95} -33.2169 q^{96} +10.5208 q^{97} -15.7571 q^{98} -14.4992 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * q^99

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