LMFDB - Embedded newform 6037.2.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6037,2,Mod(1,6037)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.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:	$48.2056877002$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6037.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58711 q^{2} -3.26786 q^{3} +4.69312 q^{4} +2.66521 q^{5} +8.45431 q^{6} +2.69955 q^{7} -6.96738 q^{8} +7.67894 q^{9} +O(q^{10})$	\(q-2.58711 q^{2} -3.26786 q^{3} +4.69312 q^{4} +2.66521 q^{5} +8.45431 q^{6} +2.69955 q^{7} -6.96738 q^{8} +7.67894 q^{9} -6.89517 q^{10} +1.78104 q^{11} -15.3365 q^{12} +0.833324 q^{13} -6.98403 q^{14} -8.70953 q^{15} +8.63912 q^{16} +5.88299 q^{17} -19.8662 q^{18} +3.75980 q^{19} +12.5081 q^{20} -8.82177 q^{21} -4.60774 q^{22} +5.86102 q^{23} +22.7685 q^{24} +2.10333 q^{25} -2.15590 q^{26} -15.2901 q^{27} +12.6693 q^{28} -4.40811 q^{29} +22.5325 q^{30} -8.58372 q^{31} -8.41557 q^{32} -5.82020 q^{33} -15.2199 q^{34} +7.19486 q^{35} +36.0382 q^{36} +7.29770 q^{37} -9.72700 q^{38} -2.72319 q^{39} -18.5695 q^{40} -10.9515 q^{41} +22.8228 q^{42} +1.81334 q^{43} +8.35863 q^{44} +20.4660 q^{45} -15.1631 q^{46} -5.45378 q^{47} -28.2315 q^{48} +0.287576 q^{49} -5.44153 q^{50} -19.2248 q^{51} +3.91089 q^{52} -1.35833 q^{53} +39.5572 q^{54} +4.74684 q^{55} -18.8088 q^{56} -12.2865 q^{57} +11.4043 q^{58} +6.16715 q^{59} -40.8749 q^{60} -13.5682 q^{61} +22.2070 q^{62} +20.7297 q^{63} +4.49371 q^{64} +2.22098 q^{65} +15.0575 q^{66} +1.49479 q^{67} +27.6096 q^{68} -19.1530 q^{69} -18.6139 q^{70} +13.0574 q^{71} -53.5021 q^{72} +5.94246 q^{73} -18.8799 q^{74} -6.87339 q^{75} +17.6452 q^{76} +4.80801 q^{77} +7.04519 q^{78} +15.6967 q^{79} +23.0251 q^{80} +26.9293 q^{81} +28.3328 q^{82} +15.5119 q^{83} -41.4016 q^{84} +15.6794 q^{85} -4.69131 q^{86} +14.4051 q^{87} -12.4092 q^{88} +4.85742 q^{89} -52.9476 q^{90} +2.24960 q^{91} +27.5064 q^{92} +28.0504 q^{93} +14.1095 q^{94} +10.0206 q^{95} +27.5009 q^{96} -11.1935 q^{97} -0.743990 q^{98} +13.6765 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * 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 $

$2$	−2.58711	−1.82936	−0.914680	−	0.404178i	$-0.867557\pi$
$2$	−2.58711	−1.82936	−0.914680	+	0.404178i	$0.867557\pi$
$3$	−3.26786	−1.88670	−0.943351	−	0.331796i	$-0.892345\pi$
$3$	−3.26786	−1.88670	−0.943351	+	0.331796i	$0.892345\pi$
$4$	4.69312	2.34656
$5$	2.66521	1.19192	0.595958	−	0.803015i	$-0.296772\pi$
$5$	2.66521	1.19192	0.595958	+	0.803015i	$0.296772\pi$
$6$	8.45431	3.45146
$7$	2.69955	1.02033	0.510167	−	0.860075i	$-0.329584\pi$
$7$	2.69955	1.02033	0.510167	+	0.860075i	$0.329584\pi$
$8$	−6.96738	−2.46334
$9$	7.67894	2.55965
$10$	−6.89517	−2.18045
$11$	1.78104	0.537004	0.268502	−	0.963279i	$-0.413471\pi$
$11$	1.78104	0.537004	0.268502	+	0.963279i	$0.413471\pi$
$12$	−15.3365	−4.42726
$13$	0.833324	0.231123	0.115561	−	0.993300i	$-0.463133\pi$
$13$	0.833324	0.231123	0.115561	+	0.993300i	$0.463133\pi$
$14$	−6.98403	−1.86656
$15$	−8.70953	−2.24879
$16$	8.63912	2.15978
$17$	5.88299	1.42683	0.713417	−	0.700740i	$-0.247147\pi$
$17$	5.88299	1.42683	0.713417	+	0.700740i	$0.247147\pi$
$18$	−19.8662	−4.68252
$19$	3.75980	0.862558	0.431279	−	0.902219i	$-0.358063\pi$
$19$	3.75980	0.862558	0.431279	+	0.902219i	$0.358063\pi$
$20$	12.5081	2.79690
$21$	−8.82177	−1.92507
$22$	−4.60774	−0.982374
$23$	5.86102	1.22211	0.611053	−	0.791589i	$-0.290746\pi$
$23$	5.86102	1.22211	0.611053	+	0.791589i	$0.290746\pi$
$24$	22.7685	4.64759
$25$	2.10333	0.420665
$26$	−2.15590	−0.422807
$27$	−15.2901	−2.94259
$28$	12.6693	2.39428
$29$	−4.40811	−0.818566	−0.409283	−	0.912407i	$-0.634221\pi$
$29$	−4.40811	−0.818566	−0.409283	+	0.912407i	$0.634221\pi$
$30$	22.5325	4.11385
$31$	−8.58372	−1.54168	−0.770841	−	0.637028i	$-0.780164\pi$
$31$	−8.58372	−1.54168	−0.770841	+	0.637028i	$0.780164\pi$
$32$	−8.41557	−1.48768
$33$	−5.82020	−1.01317
$34$	−15.2199	−2.61019
$35$	7.19486	1.21615
$36$	36.0382	6.00636
$37$	7.29770	1.19973	0.599867	−	0.800099i	$-0.295220\pi$
$37$	7.29770	1.19973	0.599867	+	0.800099i	$0.295220\pi$
$38$	−9.72700	−1.57793
$39$	−2.72319	−0.436060
$40$	−18.5695	−2.93610
$41$	−10.9515	−1.71034	−0.855171	−	0.518346i	$-0.826548\pi$
$41$	−10.9515	−1.71034	−0.855171	+	0.518346i	$0.826548\pi$
$42$	22.8228	3.52164
$43$	1.81334	0.276532	0.138266	−	0.990395i	$-0.455847\pi$
$43$	1.81334	0.276532	0.138266	+	0.990395i	$0.455847\pi$
$44$	8.35863	1.26011
$45$	20.4660	3.05088
$46$	−15.1631	−2.23567
$47$	−5.45378	−0.795515	−0.397758	−	0.917491i	$-0.630211\pi$
$47$	−5.45378	−0.795515	−0.397758	+	0.917491i	$0.630211\pi$
$48$	−28.2315	−4.07486
$49$	0.287576	0.0410823
$50$	−5.44153	−0.769548
$51$	−19.2248	−2.69201
$52$	3.91089	0.542343
$53$	−1.35833	−0.186581	−0.0932905	−	0.995639i	$-0.529739\pi$
$53$	−1.35833	−0.186581	−0.0932905	+	0.995639i	$0.529739\pi$
$54$	39.5572	5.38305
$55$	4.74684	0.640064
$56$	−18.8088	−2.51343
$57$	−12.2865	−1.62739
$58$	11.4043	1.49745
$59$	6.16715	0.802895	0.401447	−	0.915882i	$-0.368507\pi$
$59$	6.16715	0.802895	0.401447	+	0.915882i	$0.368507\pi$
$60$	−40.8749	−5.27692
$61$	−13.5682	−1.73723	−0.868613	−	0.495491i	$-0.834988\pi$
$61$	−13.5682	−1.73723	−0.868613	+	0.495491i	$0.834988\pi$
$62$	22.2070	2.82029
$63$	20.7297	2.61169
$64$	4.49371	0.561714
$65$	2.22098	0.275479
$66$	15.0575	1.85345
$67$	1.49479	0.182617	0.0913087	−	0.995823i	$-0.470895\pi$
$67$	1.49479	0.182617	0.0913087	+	0.995823i	$0.470895\pi$
$68$	27.6096	3.34815
$69$	−19.1530	−2.30575
$70$	−18.6139	−2.22478
$71$	13.0574	1.54963	0.774813	−	0.632190i	$-0.217844\pi$
$71$	13.0574	1.54963	0.774813	+	0.632190i	$0.217844\pi$
$72$	−53.5021	−6.30528
$73$	5.94246	0.695513	0.347756	−	0.937585i	$-0.386944\pi$
$73$	5.94246	0.695513	0.347756	+	0.937585i	$0.386944\pi$
$74$	−18.8799	−2.19475
$75$	−6.87339	−0.793670
$76$	17.6452	2.02404
$77$	4.80801	0.547924
$78$	7.04519	0.797710
$79$	15.6967	1.76602	0.883011	−	0.469352i	$-0.155512\pi$
$79$	15.6967	1.76602	0.883011	+	0.469352i	$0.155512\pi$
$80$	23.0251	2.57428
$81$	26.9293	2.99214
$82$	28.3328	3.12883
$83$	15.5119	1.70266	0.851328	−	0.524634i	$-0.175798\pi$
$83$	15.5119	1.70266	0.851328	+	0.524634i	$0.175798\pi$
$84$	−41.4016	−4.51728
$85$	15.6794	1.70067
$86$	−4.69131	−0.505877
$87$	14.4051	1.54439
$88$	−12.4092	−1.32282
$89$	4.85742	0.514885	0.257442	−	0.966294i	$-0.417120\pi$
$89$	4.85742	0.514885	0.257442	+	0.966294i	$0.417120\pi$
$90$	−52.9476	−5.58117
$91$	2.24960	0.235822
$92$	27.5064	2.86775
$93$	28.0504	2.90869
$94$	14.1095	1.45528
$95$	10.0206	1.02810
$96$	27.5009	2.80680
$97$	−11.1935	−1.13653	−0.568263	−	0.822847i	$-0.692384\pi$
$97$	−11.1935	−1.13653	−0.568263	+	0.822847i	$0.692384\pi$
$98$	−0.743990	−0.0751544
$99$	13.6765	1.37454
$100$	9.87116	0.987116
$101$	−6.38725	−0.635555	−0.317778	−	0.948165i	$-0.602937\pi$
$101$	−6.38725	−0.635555	−0.317778	+	0.948165i	$0.602937\pi$
$102$	49.7366	4.92466
$103$	7.55629	0.744543	0.372272	−	0.928124i	$-0.378579\pi$
$103$	7.55629	0.744543	0.372272	+	0.928124i	$0.378579\pi$
$104$	−5.80609	−0.569334
$105$	−23.5118	−2.29452
$106$	3.51414	0.341324
$107$	20.2302	1.95573	0.977863	−	0.209246i	$-0.0671010\pi$
$107$	20.2302	1.95573	0.977863	+	0.209246i	$0.0671010\pi$
$108$	−71.7584	−6.90496
$109$	5.37553	0.514882	0.257441	−	0.966294i	$-0.417121\pi$
$109$	5.37553	0.514882	0.257441	+	0.966294i	$0.417121\pi$
$110$	−12.2806	−1.17091
$111$	−23.8479	−2.26354
$112$	23.3218	2.20370
$113$	−9.18266	−0.863832	−0.431916	−	0.901914i	$-0.642162\pi$
$113$	−9.18266	−0.863832	−0.431916	+	0.901914i	$0.642162\pi$
$114$	31.7865	2.97708
$115$	15.6208	1.45665
$116$	−20.6878	−1.92081
$117$	6.39905	0.591592
$118$	−15.9551	−1.46878
$119$	15.8814	1.45585
$120$	60.6827	5.53954
$121$	−7.82790	−0.711627
$122$	35.1023	3.17801
$123$	35.7881	3.22691
$124$	−40.2844	−3.61765
$125$	−7.72023	−0.690519
$126$	−53.6299	−4.77773
$127$	13.3228	1.18220	0.591102	−	0.806597i	$-0.298693\pi$
$127$	13.3228	1.18220	0.591102	+	0.806597i	$0.298693\pi$
$128$	5.20542	0.460098
$129$	−5.92576	−0.521734
$130$	−5.74592	−0.503950
$131$	−8.33750	−0.728451	−0.364226	−	0.931311i	$-0.618666\pi$
$131$	−8.33750	−0.728451	−0.364226	+	0.931311i	$0.618666\pi$
$132$	−27.3149	−2.37746
$133$	10.1498	0.880097
$134$	−3.86717	−0.334073
$135$	−40.7514	−3.50732
$136$	−40.9890	−3.51478
$137$	−0.0440816	−0.00376615	−0.00188307	−	0.999998i	$-0.500599\pi$
$137$	−0.0440816	−0.00376615	−0.00188307	+	0.999998i	$0.500599\pi$
$138$	49.5509	4.21805
$139$	−8.15248	−0.691484	−0.345742	−	0.938330i	$-0.612373\pi$
$139$	−8.15248	−0.691484	−0.345742	+	0.938330i	$0.612373\pi$
$140$	33.7663	2.85378
$141$	17.8222	1.50090
$142$	−33.7808	−2.83482
$143$	1.48418	0.124114
$144$	66.3393	5.52828
$145$	−11.7485	−0.975663
$146$	−15.3738	−1.27234
$147$	−0.939760	−0.0775101
$148$	34.2490	2.81525
$149$	13.9625	1.14385	0.571926	−	0.820305i	$-0.306197\pi$
$149$	13.9625	1.14385	0.571926	+	0.820305i	$0.306197\pi$
$150$	17.7822	1.45191
$151$	−11.1285	−0.905627	−0.452814	−	0.891605i	$-0.649580\pi$
$151$	−11.1285	−0.905627	−0.452814	+	0.891605i	$0.649580\pi$
$152$	−26.1960	−2.12477
$153$	45.1751	3.65219
$154$	−12.4388	−1.00235
$155$	−22.8774	−1.83756
$156$	−12.7803	−1.02324
$157$	9.71956	0.775705	0.387853	−	0.921721i	$-0.373217\pi$
$157$	9.71956	0.775705	0.387853	+	0.921721i	$0.373217\pi$
$158$	−40.6092	−3.23069
$159$	4.43884	0.352023
$160$	−22.4292	−1.77319
$161$	15.8221	1.24696
$162$	−69.6689	−5.47371
$163$	−14.0085	−1.09723	−0.548616	−	0.836075i	$-0.684845\pi$
$163$	−14.0085	−1.09723	−0.548616	+	0.836075i	$0.684845\pi$
$164$	−51.3968	−4.01342
$165$	−15.5120	−1.20761
$166$	−40.1310	−3.11477
$167$	−14.4959	−1.12173	−0.560864	−	0.827908i	$-0.689531\pi$
$167$	−14.4959	−1.12173	−0.560864	+	0.827908i	$0.689531\pi$
$168$	61.4646	4.74210
$169$	−12.3056	−0.946582
$170$	−40.5642	−3.11113
$171$	28.8713	2.20784
$172$	8.51024	0.648900
$173$	−8.85267	−0.673056	−0.336528	−	0.941673i	$-0.609253\pi$
$173$	−8.85267	−0.673056	−0.336528	+	0.941673i	$0.609253\pi$
$174$	−37.2676	−2.82525
$175$	5.67804	0.429219
$176$	15.3866	1.15981
$177$	−20.1534	−1.51482
$178$	−12.5666	−0.941910
$179$	15.2719	1.14148	0.570739	−	0.821131i	$-0.306657\pi$
$179$	15.2719	1.14148	0.570739	+	0.821131i	$0.306657\pi$
$180$	96.0492	7.15908
$181$	11.4202	0.848860	0.424430	−	0.905461i	$-0.360475\pi$
$181$	11.4202	0.848860	0.424430	+	0.905461i	$0.360475\pi$
$182$	−5.81996	−0.431404
$183$	44.3389	3.27763
$184$	−40.8360	−3.01047
$185$	19.4499	1.42998
$186$	−72.5694	−5.32105
$187$	10.4778	0.766215
$188$	−25.5952	−1.86672
$189$	−41.2765	−3.00242
$190$	−25.9245	−1.88076
$191$	21.7398	1.57304	0.786519	−	0.617566i	$-0.211881\pi$
$191$	21.7398	1.57304	0.786519	+	0.617566i	$0.211881\pi$
$192$	−14.6848	−1.05979
$193$	13.6555	0.982947	0.491473	−	0.870893i	$-0.336459\pi$
$193$	13.6555	0.982947	0.491473	+	0.870893i	$0.336459\pi$
$194$	28.9587	2.07911
$195$	−7.25787	−0.519747
$196$	1.34963	0.0964021
$197$	3.84837	0.274185	0.137092	−	0.990558i	$-0.456224\pi$
$197$	3.84837	0.274185	0.137092	+	0.990558i	$0.456224\pi$
$198$	−35.3826	−2.51453
$199$	6.90982	0.489824	0.244912	−	0.969545i	$-0.421241\pi$
$199$	6.90982	0.489824	0.244912	+	0.969545i	$0.421241\pi$
$200$	−14.6547	−1.03624
$201$	−4.88476	−0.344545
$202$	16.5245	1.16266
$203$	−11.8999	−0.835211
$204$	−90.2243	−6.31696
$205$	−29.1881	−2.03859
$206$	−19.5489	−1.36204
$207$	45.0064	3.12816
$208$	7.19919	0.499174
$209$	6.69636	0.463197
$210$	60.8276	4.19750
$211$	−22.2344	−1.53068	−0.765341	−	0.643625i	$-0.777430\pi$
$211$	−22.2344	−1.53068	−0.765341	+	0.643625i	$0.777430\pi$
$212$	−6.37480	−0.437823
$213$	−42.6698	−2.92368
$214$	−52.3376	−3.57773
$215$	4.83294	0.329604
$216$	106.532	7.24860
$217$	−23.1722	−1.57303
$218$	−13.9071	−0.941905
$219$	−19.4192	−1.31223
$220$	22.2775	1.50195
$221$	4.90244	0.329774
$222$	61.6971	4.14084
$223$	−2.65269	−0.177637	−0.0888185	−	0.996048i	$-0.528309\pi$
$223$	−2.65269	−0.177637	−0.0888185	+	0.996048i	$0.528309\pi$
$224$	−22.7183	−1.51793
$225$	16.1513	1.07675
$226$	23.7565	1.58026
$227$	7.90391	0.524601	0.262301	−	0.964986i	$-0.415519\pi$
$227$	7.90391	0.524601	0.262301	+	0.964986i	$0.415519\pi$
$228$	−57.6621	−3.81877
$229$	24.0296	1.58792	0.793961	−	0.607969i	$-0.208016\pi$
$229$	24.0296	1.58792	0.793961	+	0.607969i	$0.208016\pi$
$230$	−40.4127	−2.66474
$231$	−15.7119	−1.03377
$232$	30.7130	2.01641
$233$	−2.81518	−0.184429	−0.0922143	−	0.995739i	$-0.529394\pi$
$233$	−2.81518	−0.184429	−0.0922143	+	0.995739i	$0.529394\pi$
$234$	−16.5550	−1.08224
$235$	−14.5354	−0.948188
$236$	28.9432	1.88404
$237$	−51.2948	−3.33196
$238$	−41.0869	−2.66327
$239$	26.2813	1.70000	0.849999	−	0.526784i	$-0.176602\pi$
$239$	26.2813	1.70000	0.849999	+	0.526784i	$0.176602\pi$
$240$	−75.2428	−4.85690
$241$	−22.9326	−1.47722	−0.738610	−	0.674133i	$-0.764518\pi$
$241$	−22.9326	−1.47722	−0.738610	+	0.674133i	$0.764518\pi$
$242$	20.2516	1.30182
$243$	−42.1308	−2.70269
$244$	−63.6770	−4.07650
$245$	0.766450	0.0489667
$246$	−92.5877	−5.90318
$247$	3.13313	0.199357
$248$	59.8061	3.79769
$249$	−50.6909	−3.21240
$250$	19.9731	1.26321
$251$	−2.89924	−0.182998	−0.0914991	−	0.995805i	$-0.529166\pi$
$251$	−2.89924	−0.182998	−0.0914991	+	0.995805i	$0.529166\pi$
$252$	97.2869	6.12850
$253$	10.4387	0.656276
$254$	−34.4674	−2.16268
$255$	−51.2381	−3.20865
$256$	−22.4544	−1.40340
$257$	14.4049	0.898555	0.449277	−	0.893392i	$-0.351681\pi$
$257$	14.4049	0.898555	0.449277	+	0.893392i	$0.351681\pi$
$258$	15.3306	0.954440
$259$	19.7005	1.22413
$260$	10.4233	0.646428
$261$	−33.8496	−2.09524
$262$	21.5700	1.33260
$263$	29.5009	1.81910	0.909551	−	0.415592i	$-0.136425\pi$
$263$	29.5009	1.81910	0.909551	+	0.415592i	$0.136425\pi$
$264$	40.5516	2.49578
$265$	−3.62023	−0.222389
$266$	−26.2585	−1.61001
$267$	−15.8734	−0.971435
$268$	7.01521	0.428522
$269$	16.0481	0.978470	0.489235	−	0.872152i	$-0.337276\pi$
$269$	16.0481	0.978470	0.489235	+	0.872152i	$0.337276\pi$
$270$	105.428	6.41615
$271$	−12.7876	−0.776790	−0.388395	−	0.921493i	$-0.626970\pi$
$271$	−12.7876	−0.776790	−0.388395	+	0.921493i	$0.626970\pi$
$272$	50.8239	3.08165
$273$	−7.35139	−0.444927
$274$	0.114044	0.00688964
$275$	3.74611	0.225899
$276$	−89.8873	−5.41058
$277$	4.98817	0.299710	0.149855	−	0.988708i	$-0.452119\pi$
$277$	4.98817	0.299710	0.149855	+	0.988708i	$0.452119\pi$
$278$	21.0913	1.26497
$279$	−65.9138	−3.94616
$280$	−50.1294	−2.99580
$281$	−13.6316	−0.813190	−0.406595	−	0.913608i	$-0.633284\pi$
$281$	−13.6316	−0.813190	−0.406595	+	0.913608i	$0.633284\pi$
$282$	−46.1079	−2.74569
$283$	−12.9069	−0.767236	−0.383618	−	0.923492i	$-0.625322\pi$
$283$	−12.9069	−0.767236	−0.383618	+	0.923492i	$0.625322\pi$
$284$	61.2798	3.63629
$285$	−32.7461	−1.93971
$286$	−3.83974	−0.227049
$287$	−29.5642	−1.74512
$288$	−64.6226	−3.80792
$289$	17.6095	1.03586
$290$	30.3947	1.78484
$291$	36.5788	2.14428
$292$	27.8887	1.63206
$293$	−7.69534	−0.449567	−0.224783	−	0.974409i	$-0.572167\pi$
$293$	−7.69534	−0.449567	−0.224783	+	0.974409i	$0.572167\pi$
$294$	2.43126	0.141794
$295$	16.4367	0.956984
$296$	−50.8459	−2.95536
$297$	−27.2323	−1.58018
$298$	−36.1224	−2.09252
$299$	4.88413	0.282456
$300$	−32.2576	−1.86239
$301$	4.89521	0.282155
$302$	28.7907	1.65672
$303$	20.8727	1.19910
$304$	32.4814	1.86294
$305$	−36.1620	−2.07063
$306$	−116.873	−6.68117
$307$	−8.54169	−0.487500	−0.243750	−	0.969838i	$-0.578378\pi$
$307$	−8.54169	−0.487500	−0.243750	+	0.969838i	$0.578378\pi$
$308$	22.5646	1.28574
$309$	−24.6929	−1.40473
$310$	59.1862	3.36155
$311$	13.0024	0.737296	0.368648	−	0.929569i	$-0.379821\pi$
$311$	13.0024	0.737296	0.368648	+	0.929569i	$0.379821\pi$
$312$	18.9735	1.07416
$313$	−0.527559	−0.0298194	−0.0149097	−	0.999889i	$-0.504746\pi$
$313$	−0.527559	−0.0298194	−0.0149097	+	0.999889i	$0.504746\pi$
$314$	−25.1455	−1.41904
$315$	55.2489	3.11292
$316$	73.6667	4.14408
$317$	8.85398	0.497289	0.248644	−	0.968595i	$-0.420015\pi$
$317$	8.85398	0.497289	0.248644	+	0.968595i	$0.420015\pi$
$318$	−11.4837	−0.643977
$319$	−7.85103	−0.439573
$320$	11.9767	0.669516
$321$	−66.1095	−3.68987
$322$	−40.9335	−2.28113
$323$	22.1189	1.23073
$324$	126.382	7.02124
$325$	1.75275	0.0972253
$326$	36.2415	2.00723
$327$	−17.5665	−0.971430
$328$	76.3035	4.21316
$329$	−14.7228	−0.811692
$330$	40.1313	2.20915
$331$	4.38103	0.240803	0.120402	−	0.992725i	$-0.461582\pi$
$331$	4.38103	0.240803	0.120402	+	0.992725i	$0.461582\pi$
$332$	72.7993	3.99538
$333$	56.0386	3.07090
$334$	37.5025	2.05205
$335$	3.98392	0.217665
$336$	−76.2123	−4.15772
$337$	−14.5867	−0.794589	−0.397294	−	0.917691i	$-0.630051\pi$
$337$	−14.5867	−0.794589	−0.397294	+	0.917691i	$0.630051\pi$
$338$	31.8358	1.73164
$339$	30.0077	1.62979
$340$	73.5852	3.99072
$341$	−15.2880	−0.827889
$342$	−74.6931	−4.03894
$343$	−18.1205	−0.978417
$344$	−12.6343	−0.681194
$345$	−51.0467	−2.74826
$346$	22.9028	1.23126
$347$	−4.34547	−0.233277	−0.116638	−	0.993174i	$-0.537212\pi$
$347$	−4.34547	−0.233277	−0.116638	+	0.993174i	$0.537212\pi$
$348$	67.6049	3.62401
$349$	−20.7044	−1.10828	−0.554142	−	0.832422i	$-0.686953\pi$
$349$	−20.7044	−1.10828	−0.554142	+	0.832422i	$0.686953\pi$
$350$	−14.6897	−0.785197
$351$	−12.7416	−0.680099
$352$	−14.9885	−0.798888
$353$	−18.4882	−0.984030	−0.492015	−	0.870587i	$-0.663739\pi$
$353$	−18.4882	−0.984030	−0.492015	+	0.870587i	$0.663739\pi$
$354$	52.1390	2.77116
$355$	34.8006	1.84703
$356$	22.7964	1.20821
$357$	−51.8984	−2.74675
$358$	−39.5101	−2.08817
$359$	−0.00828583	−0.000437310 0	−0.000218655	−	1.00000i	$-0.500070\pi$
$359$	−0.00828583	−0.000437310 0	−0.000218655		1.00000i	$0.500070\pi$
$360$	−142.594	−7.51537
$361$	−4.86390	−0.255995
$362$	−29.5454	−1.55287
$363$	25.5805	1.34263
$364$	10.5576	0.553371
$365$	15.8379	0.828993
$366$	−114.710	−5.99596
$367$	−17.8359	−0.931029	−0.465514	−	0.885040i	$-0.654131\pi$
$367$	−17.8359	−0.931029	−0.465514	+	0.885040i	$0.654131\pi$
$368$	50.6341	2.63948
$369$	−84.0961	−4.37787
$370$	−50.3189	−2.61596
$371$	−3.66688	−0.190375
$372$	131.644	6.82542
$373$	−7.06112	−0.365611	−0.182805	−	0.983149i	$-0.558518\pi$
$373$	−7.06112	−0.365611	−0.182805	+	0.983149i	$0.558518\pi$
$374$	−27.1073	−1.40168
$375$	25.2287	1.30280
$376$	37.9986	1.95963
$377$	−3.67339	−0.189189
$378$	106.787	5.49252
$379$	−16.1473	−0.829432	−0.414716	−	0.909951i	$-0.636119\pi$
$379$	−16.1473	−0.829432	−0.414716	+	0.909951i	$0.636119\pi$
$380$	47.0281	2.41249
$381$	−43.5370	−2.23047
$382$	−56.2432	−2.87765
$383$	32.7186	1.67184	0.835922	−	0.548849i	$-0.184934\pi$
$383$	32.7186	1.67184	0.835922	+	0.548849i	$0.184934\pi$
$384$	−17.0106	−0.868069
$385$	12.8143	0.653079
$386$	−35.3283	−1.79816
$387$	13.9246	0.707825
$388$	−52.5323	−2.66692
$389$	34.3002	1.73909	0.869545	−	0.493853i	$-0.164412\pi$
$389$	34.3002	1.73909	0.869545	+	0.493853i	$0.164412\pi$
$390$	18.7769	0.950804
$391$	34.4803	1.74374
$392$	−2.00365	−0.101200
$393$	27.2458	1.37437
$394$	−9.95614	−0.501583
$395$	41.8351	2.10495
$396$	64.1854	3.22544
$397$	7.76342	0.389635	0.194817	−	0.980840i	$-0.437589\pi$
$397$	7.76342	0.389635	0.194817	+	0.980840i	$0.437589\pi$
$398$	−17.8764	−0.896064
$399$	−33.1681	−1.66048
$400$	18.1709	0.908545
$401$	−25.1007	−1.25347	−0.626735	−	0.779233i	$-0.715609\pi$
$401$	−25.1007	−1.25347	−0.626735	+	0.779233i	$0.715609\pi$
$402$	12.6374	0.630296
$403$	−7.15302	−0.356317
$404$	−29.9761	−1.49137
$405$	71.7721	3.56638
$406$	30.7864	1.52790
$407$	12.9975	0.644262
$408$	133.947	6.63135
$409$	38.2637	1.89202	0.946009	−	0.324141i	$-0.105075\pi$
$409$	38.2637	1.89202	0.946009	+	0.324141i	$0.105075\pi$
$410$	75.5127	3.72931
$411$	0.144053	0.00710560
$412$	35.4626	1.74712
$413$	16.6485	0.819221
$414$	−116.436	−5.72253
$415$	41.3425	2.02942
$416$	−7.01290	−0.343836
$417$	26.6412	1.30462
$418$	−17.3242	−0.847354
$419$	−3.99514	−0.195175	−0.0975877	−	0.995227i	$-0.531113\pi$
$419$	−3.99514	−0.195175	−0.0975877	+	0.995227i	$0.531113\pi$
$420$	−110.344	−5.38423
$421$	18.7870	0.915624	0.457812	−	0.889049i	$-0.348633\pi$
$421$	18.7870	0.915624	0.457812	+	0.889049i	$0.348633\pi$
$422$	57.5228	2.80017
$423$	−41.8792	−2.03624
$424$	9.46401	0.459613
$425$	12.3738	0.600220
$426$	110.391	5.34847
$427$	−36.6280	−1.77255
$428$	94.9427	4.58923
$429$	−4.85011	−0.234166
$430$	−12.5033	−0.602964
$431$	38.7169	1.86493	0.932463	−	0.361266i	$-0.117656\pi$
$431$	38.7169	1.86493	0.932463	+	0.361266i	$0.117656\pi$
$432$	−132.093	−6.35535
$433$	17.3288	0.832769	0.416385	−	0.909189i	$-0.363297\pi$
$433$	17.3288	0.832769	0.416385	+	0.909189i	$0.363297\pi$
$434$	59.9489	2.87764
$435$	38.3926	1.84079
$436$	25.2280	1.20820
$437$	22.0363	1.05414
$438$	50.2394	2.40053
$439$	0.353601	0.0168765	0.00843823	−	0.999964i	$-0.497314\pi$
$439$	0.353601	0.0168765	0.00843823	+	0.999964i	$0.497314\pi$
$440$	−33.0731	−1.57670
$441$	2.20828	0.105156
$442$	−12.6831	−0.603275
$443$	24.8597	1.18112	0.590561	−	0.806993i	$-0.298907\pi$
$443$	24.8597	1.18112	0.590561	+	0.806993i	$0.298907\pi$
$444$	−111.921	−5.31154
$445$	12.9460	0.613700
$446$	6.86278	0.324962
$447$	−45.6275	−2.15811
$448$	12.1310	0.573136
$449$	−29.2334	−1.37961	−0.689804	−	0.723997i	$-0.742303\pi$
$449$	−29.2334	−1.37961	−0.689804	+	0.723997i	$0.742303\pi$
$450$	−41.7852	−1.96977
$451$	−19.5051	−0.918460
$452$	−43.0953	−2.02703
$453$	36.3665	1.70865
$454$	−20.4483	−0.959685
$455$	5.99565	0.281081
$456$	85.6049	4.00882
$457$	34.5762	1.61741	0.808704	−	0.588216i	$-0.200169\pi$
$457$	34.5762	1.61741	0.808704	+	0.588216i	$0.200169\pi$
$458$	−62.1671	−2.90488
$459$	−89.9517	−4.19859
$460$	73.3104	3.41811
$461$	−18.0049	−0.838571	−0.419286	−	0.907854i	$-0.637719\pi$
$461$	−18.0049	−0.838571	−0.419286	+	0.907854i	$0.637719\pi$
$462$	40.6484	1.89114
$463$	−31.9655	−1.48556	−0.742782	−	0.669533i	$-0.766494\pi$
$463$	−31.9655	−1.48556	−0.742782	+	0.669533i	$0.766494\pi$
$464$	−38.0823	−1.76792
$465$	74.7602	3.46692
$466$	7.28317	0.337386
$467$	−37.9096	−1.75425	−0.877123	−	0.480266i	$-0.840540\pi$
$467$	−37.9096	−1.75425	−0.877123	+	0.480266i	$0.840540\pi$
$468$	30.0315	1.38821
$469$	4.03525	0.186331
$470$	37.6047	1.73458
$471$	−31.7622	−1.46352
$472$	−42.9689	−1.97780
$473$	3.22964	0.148499
$474$	132.705	6.09535
$475$	7.90809	0.362848
$476$	74.5334	3.41623
$477$	−10.4305	−0.477581
$478$	−67.9926	−3.10991
$479$	−5.03277	−0.229953	−0.114977	−	0.993368i	$-0.536679\pi$
$479$	−5.03277	−0.229953	−0.114977	+	0.993368i	$0.536679\pi$
$480$	73.2957	3.34547
$481$	6.08135	0.277286
$482$	59.3291	2.70237
$483$	−51.7045	−2.35264
$484$	−36.7372	−1.66987
$485$	−29.8329	−1.35464
$486$	108.997	4.94420
$487$	16.6581	0.754849	0.377424	−	0.926040i	$-0.376810\pi$
$487$	16.6581	0.754849	0.377424	+	0.926040i	$0.376810\pi$
$488$	94.5347	4.27938
$489$	45.7779	2.07015
$490$	−1.98289	−0.0895778
$491$	3.05886	0.138044	0.0690221	−	0.997615i	$-0.478012\pi$
$491$	3.05886	0.138044	0.0690221	+	0.997615i	$0.478012\pi$
$492$	167.958	7.57213
$493$	−25.9329	−1.16796
$494$	−8.10575	−0.364695
$495$	36.4507	1.63834
$496$	−74.1558	−3.32969
$497$	35.2491	1.58114
$498$	131.143	5.87665
$499$	−14.9054	−0.667258	−0.333629	−	0.942704i	$-0.608273\pi$
$499$	−14.9054	−0.667258	−0.333629	+	0.942704i	$0.608273\pi$
$500$	−36.2320	−1.62034
$501$	47.3707	2.11637
$502$	7.50063	0.334770
$503$	−20.2347	−0.902220	−0.451110	−	0.892468i	$-0.648972\pi$
$503$	−20.2347	−0.902220	−0.451110	+	0.892468i	$0.648972\pi$
$504$	−144.432	−6.43350
$505$	−17.0233	−0.757529
$506$	−27.0060	−1.20057
$507$	40.2129	1.78592
$508$	62.5253	2.77411
$509$	31.5475	1.39832	0.699159	−	0.714966i	$-0.253558\pi$
$509$	31.5475	1.39832	0.699159	+	0.714966i	$0.253558\pi$
$510$	132.558	5.86978
$511$	16.0420	0.709655
$512$	47.6811	2.10723
$513$	−57.4879	−2.53815
$514$	−37.2671	−1.64378
$515$	20.1391	0.887434
$516$	−27.8103	−1.22428
$517$	−9.71340	−0.427195
$518$	−50.9673	−2.23938
$519$	28.9293	1.26986
$520$	−15.4744	−0.678599
$521$	−4.88434	−0.213987	−0.106993	−	0.994260i	$-0.534122\pi$
$521$	−4.88434	−0.213987	−0.106993	+	0.994260i	$0.534122\pi$
$522$	87.5726	3.83295
$523$	18.5613	0.811630	0.405815	−	0.913955i	$-0.366988\pi$
$523$	18.5613	0.811630	0.405815	+	0.913955i	$0.366988\pi$
$524$	−39.1289	−1.70935
$525$	−18.5551	−0.809809
$526$	−76.3219	−3.32779
$527$	−50.4979	−2.19972
$528$	−50.2814	−2.18822
$529$	11.3515	0.493544
$530$	9.36592	0.406830
$531$	47.3572	2.05513
$532$	47.6341	2.06520
$533$	−9.12618	−0.395299
$534$	41.0661	1.77710
$535$	53.9176	2.33106
$536$	−10.4148	−0.449849
$537$	−49.9066	−2.15363
$538$	−41.5182	−1.78997
$539$	0.512185	0.0220614
$540$	−191.251	−8.23013
$541$	−7.28670	−0.313280	−0.156640	−	0.987656i	$-0.550066\pi$
$541$	−7.28670	−0.313280	−0.156640	+	0.987656i	$0.550066\pi$
$542$	33.0828	1.42103
$543$	−37.3198	−1.60155
$544$	−49.5087	−2.12267
$545$	14.3269	0.613697
$546$	19.0188	0.813931
$547$	7.29380	0.311860	0.155930	−	0.987768i	$-0.450163\pi$
$547$	7.29380	0.311860	0.155930	+	0.987768i	$0.450163\pi$
$548$	−0.206880	−0.00883749
$549$	−104.189	−4.44668
$550$	−9.69158	−0.413250
$551$	−16.5736	−0.706060
$552$	133.446	5.67985
$553$	42.3742	1.80193
$554$	−12.9049	−0.548278
$555$	−63.5596	−2.69795
$556$	−38.2605	−1.62261
$557$	4.00018	0.169493	0.0847465	−	0.996403i	$-0.472992\pi$
$557$	4.00018	0.169493	0.0847465	+	0.996403i	$0.472992\pi$
$558$	170.526	7.21895
$559$	1.51110	0.0639129
$560$	62.1573	2.62663
$561$	−34.2402	−1.44562
$562$	35.2663	1.48762
$563$	−14.4938	−0.610840	−0.305420	−	0.952218i	$-0.598797\pi$
$563$	−14.4938	−0.610840	−0.305420	+	0.952218i	$0.598797\pi$
$564$	83.6417	3.52195
$565$	−24.4737	−1.02962
$566$	33.3915	1.40355
$567$	72.6970	3.05299
$568$	−90.9758	−3.81726
$569$	−25.7920	−1.08125	−0.540627	−	0.841262i	$-0.681813\pi$
$569$	−25.7920	−1.08125	−0.540627	+	0.841262i	$0.681813\pi$
$570$	84.7177	3.54843
$571$	6.09385	0.255020	0.127510	−	0.991837i	$-0.459302\pi$
$571$	6.09385	0.255020	0.127510	+	0.991837i	$0.459302\pi$
$572$	6.96545	0.291240
$573$	−71.0428	−2.96785
$574$	76.4858	3.19246
$575$	12.3276	0.514098
$576$	34.5069	1.43779
$577$	2.74582	0.114310	0.0571550	−	0.998365i	$-0.481797\pi$
$577$	2.74582	0.114310	0.0571550	+	0.998365i	$0.481797\pi$
$578$	−45.5578	−1.89495
$579$	−44.6244	−1.85453
$580$	−55.1373	−2.28945
$581$	41.8753	1.73728
$582$	−94.6331	−3.92267
$583$	−2.41924	−0.100195
$584$	−41.4034	−1.71329
$585$	17.0548	0.705128
$586$	19.9087	0.822419
$587$	−6.17044	−0.254681	−0.127341	−	0.991859i	$-0.540644\pi$
$587$	−6.17044	−0.254681	−0.127341	+	0.991859i	$0.540644\pi$
$588$	−4.41041	−0.181882
$589$	−32.2731	−1.32979
$590$	−42.5236	−1.75067
$591$	−12.5759	−0.517305
$592$	63.0458	2.59116
$593$	−5.34173	−0.219359	−0.109679	−	0.993967i	$-0.534982\pi$
$593$	−5.34173	−0.219359	−0.109679	+	0.993967i	$0.534982\pi$
$594$	70.4530	2.89072
$595$	42.3273	1.73525
$596$	65.5276	2.68412
$597$	−22.5803	−0.924152
$598$	−12.6358	−0.516715
$599$	−21.3099	−0.870700	−0.435350	−	0.900261i	$-0.643375\pi$
$599$	−21.3099	−0.870700	−0.435350	+	0.900261i	$0.643375\pi$
$600$	47.8895	1.95508
$601$	−0.757251	−0.0308889	−0.0154444	−	0.999881i	$-0.504916\pi$
$601$	−0.757251	−0.0308889	−0.0154444	+	0.999881i	$0.504916\pi$
$602$	−12.6644	−0.516164
$603$	11.4784	0.467436
$604$	−52.2275	−2.12511
$605$	−20.8630	−0.848200
$606$	−53.9998	−2.19359
$607$	23.4434	0.951539	0.475770	−	0.879570i	$-0.342170\pi$
$607$	23.4434	0.951539	0.475770	+	0.879570i	$0.342170\pi$
$608$	−31.6409	−1.28321
$609$	38.8874	1.57580
$610$	93.5549	3.78793
$611$	−4.54477	−0.183862
$612$	212.012	8.57008
$613$	16.8473	0.680454	0.340227	−	0.940343i	$-0.389496\pi$
$613$	16.8473	0.680454	0.340227	+	0.940343i	$0.389496\pi$
$614$	22.0982	0.891813
$615$	95.3828	3.84620
$616$	−33.4992	−1.34972
$617$	12.3191	0.495949	0.247975	−	0.968767i	$-0.420235\pi$
$617$	12.3191	0.495949	0.247975	+	0.968767i	$0.420235\pi$
$618$	63.8832	2.56976
$619$	−37.2520	−1.49728	−0.748642	−	0.662975i	$-0.769294\pi$
$619$	−37.2520	−1.49728	−0.748642	+	0.662975i	$0.769294\pi$
$620$	−107.366	−4.31193
$621$	−89.6157	−3.59616
$622$	−33.6385	−1.34878
$623$	13.1128	0.525355
$624$	−23.5260	−0.941793
$625$	−31.0927	−1.24371
$626$	1.36485	0.0545505
$627$	−21.8828	−0.873914
$628$	45.6150	1.82024
$629$	42.9323	1.71182
$630$	−142.935	−5.69466
$631$	−3.03001	−0.120623	−0.0603114	−	0.998180i	$-0.519209\pi$
$631$	−3.03001	−0.120623	−0.0603114	+	0.998180i	$0.519209\pi$
$632$	−109.365	−4.35032
$633$	72.6591	2.88794
$634$	−22.9062	−0.909721
$635$	35.5079	1.40909
$636$	20.8320	0.826042
$637$	0.239644	0.00949505
$638$	20.3114	0.804138
$639$	100.267	3.96649
$640$	13.8735	0.548399
$641$	−19.3417	−0.763951	−0.381975	−	0.924172i	$-0.624756\pi$
$641$	−19.3417	−0.763951	−0.381975	+	0.924172i	$0.624756\pi$
$642$	171.032	6.75011
$643$	−8.14343	−0.321146	−0.160573	−	0.987024i	$-0.551334\pi$
$643$	−8.14343	−0.321146	−0.160573	+	0.987024i	$0.551334\pi$
$644$	74.2551	2.92606
$645$	−15.7934	−0.621864
$646$	−57.2239	−2.25144
$647$	3.17502	0.124823	0.0624116	−	0.998050i	$-0.480121\pi$
$647$	3.17502	0.124823	0.0624116	+	0.998050i	$0.480121\pi$
$648$	−187.627	−7.37067
$649$	10.9839	0.431158
$650$	−4.53456	−0.177860
$651$	75.7236	2.96784
$652$	−65.7436	−2.57472
$653$	18.5415	0.725586	0.362793	−	0.931870i	$-0.381823\pi$
$653$	18.5415	0.725586	0.362793	+	0.931870i	$0.381823\pi$
$654$	45.4464	1.77709
$655$	−22.2212	−0.868253
$656$	−94.6117	−3.69396
$657$	45.6318	1.78027
$658$	38.0893	1.48488
$659$	22.8098	0.888542	0.444271	−	0.895892i	$-0.353463\pi$
$659$	22.8098	0.888542	0.444271	+	0.895892i	$0.353463\pi$
$660$	−72.7998	−2.83373
$661$	10.6933	0.415922	0.207961	−	0.978137i	$-0.433317\pi$
$661$	10.6933	0.415922	0.207961	+	0.978137i	$0.433317\pi$
$662$	−11.3342	−0.440516
$663$	−16.0205	−0.622185
$664$	−108.078	−4.19422
$665$	27.0512	1.04900
$666$	−144.978	−5.61778
$667$	−25.8360	−1.00038
$668$	−68.0311	−2.63220
$669$	8.66862	0.335148
$670$	−10.3068	−0.398187
$671$	−24.1655	−0.932897
$672$	74.2402	2.86388
$673$	−28.0836	−1.08254	−0.541272	−	0.840847i	$-0.682057\pi$
$673$	−28.0836	−1.08254	−0.541272	+	0.840847i	$0.682057\pi$
$674$	37.7374	1.45359
$675$	−32.1601	−1.23784
$676$	−57.7515	−2.22121
$677$	6.95352	0.267246	0.133623	−	0.991032i	$-0.457339\pi$
$677$	6.95352	0.267246	0.133623	+	0.991032i	$0.457339\pi$
$678$	−77.6331	−2.98148
$679$	−30.2174	−1.15964
$680$	−109.244	−4.18933
$681$	−25.8289	−0.989766
$682$	39.5516	1.51451
$683$	−15.0221	−0.574803	−0.287402	−	0.957810i	$-0.592791\pi$
$683$	−15.0221	−0.574803	−0.287402	+	0.957810i	$0.592791\pi$
$684$	135.496	5.18083
$685$	−0.117487	−0.00448894
$686$	46.8797	1.78988
$687$	−78.5255	−2.99593
$688$	15.6657	0.597249
$689$	−1.13193	−0.0431231
$690$	132.063	5.02756
$691$	15.2745	0.581069	0.290534	−	0.956865i	$-0.406167\pi$
$691$	15.2745	0.581069	0.290534	+	0.956865i	$0.406167\pi$
$692$	−41.5466	−1.57937
$693$	36.9204	1.40249
$694$	11.2422	0.426748
$695$	−21.7280	−0.824191
$696$	−100.366	−3.80436
$697$	−64.4277	−2.44037
$698$	53.5646	2.02745
$699$	9.19963	0.347962
$700$	26.6477	1.00719
$701$	33.3521	1.25969	0.629845	−	0.776721i	$-0.283118\pi$
$701$	33.3521	1.25969	0.629845	+	0.776721i	$0.283118\pi$
$702$	32.9640	1.24415
$703$	27.4379	1.03484
$704$	8.00348	0.301643
$705$	47.4999	1.78895
$706$	47.8310	1.80014
$707$	−17.2427	−0.648479
$708$	−94.5824	−3.55462
$709$	0.766159	0.0287737	0.0143869	−	0.999897i	$-0.495420\pi$
$709$	0.766159	0.0287737	0.0143869	+	0.999897i	$0.495420\pi$
$710$	−90.0329	−3.37888
$711$	120.534	4.52039
$712$	−33.8435	−1.26834
$713$	−50.3093	−1.88410
$714$	134.267	5.02480
$715$	3.95566	0.147933
$716$	71.6730	2.67855
$717$	−85.8838	−3.20739
$718$	0.0214363	0.000799997 0
$719$	7.74131	0.288702	0.144351	−	0.989527i	$-0.453891\pi$
$719$	7.74131	0.288702	0.144351	+	0.989527i	$0.453891\pi$
$720$	176.808	6.58924
$721$	20.3986	0.759683
$722$	12.5834	0.468306
$723$	74.9407	2.78708
$724$	53.5965	1.99190
$725$	−9.27170	−0.344342
$726$	−66.1795	−2.45615
$727$	−15.7242	−0.583177	−0.291588	−	0.956544i	$-0.594184\pi$
$727$	−15.7242	−0.583177	−0.291588	+	0.956544i	$0.594184\pi$
$728$	−15.6738	−0.580911
$729$	56.8900	2.10704
$730$	−40.9743	−1.51653
$731$	10.6679	0.394566
$732$	208.088	7.69115
$733$	16.5868	0.612648	0.306324	−	0.951927i	$-0.400901\pi$
$733$	16.5868	0.612648	0.306324	+	0.951927i	$0.400901\pi$
$734$	46.1435	1.70319
$735$	−2.50466	−0.0923856
$736$	−49.3238	−1.81810
$737$	2.66228	0.0980662
$738$	217.566	8.00870
$739$	24.1154	0.887098	0.443549	−	0.896250i	$-0.353719\pi$
$739$	24.1154	0.887098	0.443549	+	0.896250i	$0.353719\pi$
$740$	91.2806	3.35554
$741$	−10.2387	−0.376126
$742$	9.48661	0.348264
$743$	3.34156	0.122590	0.0612950	−	0.998120i	$-0.480477\pi$
$743$	3.34156	0.122590	0.0612950	+	0.998120i	$0.480477\pi$
$744$	−195.438	−7.16511
$745$	37.2129	1.36338
$746$	18.2679	0.668834
$747$	119.115	4.35820
$748$	49.1737	1.79797
$749$	54.6124	1.99549
$750$	−65.2693	−2.38330
$751$	−9.36166	−0.341612	−0.170806	−	0.985305i	$-0.554637\pi$
$751$	−9.36166	−0.341612	−0.170806	+	0.985305i	$0.554637\pi$
$752$	−47.1159	−1.71814
$753$	9.47431	0.345263
$754$	9.50345	0.346095
$755$	−29.6598	−1.07943
$756$	−193.716	−7.04537
$757$	16.1336	0.586384	0.293192	−	0.956054i	$-0.405282\pi$
$757$	16.1336	0.586384	0.293192	+	0.956054i	$0.405282\pi$
$758$	41.7748	1.51733
$759$	−34.1123	−1.23820
$760$	−69.8177	−2.53255
$761$	1.12341	0.0407236	0.0203618	−	0.999793i	$-0.493518\pi$
$761$	1.12341	0.0407236	0.0203618	+	0.999793i	$0.493518\pi$
$762$	112.635	4.08033
$763$	14.5115	0.525352
$764$	102.028	3.69123
$765$	120.401	4.35311
$766$	−84.6466	−3.05840
$767$	5.13924	0.185567
$768$	73.3779	2.64780
$769$	−0.928771	−0.0334924	−0.0167462	−	0.999860i	$-0.505331\pi$
$769$	−0.928771	−0.0334924	−0.0167462	+	0.999860i	$0.505331\pi$
$770$	−33.1521	−1.19472
$771$	−47.0734	−1.69531
$772$	64.0870	2.30654
$773$	53.6704	1.93039	0.965194	−	0.261534i	$-0.0842283\pi$
$773$	53.6704	1.93039	0.965194	+	0.261534i	$0.0842283\pi$
$774$	−36.0243	−1.29487
$775$	−18.0544	−0.648532
$776$	77.9892	2.79965
$777$	−64.3786	−2.30957
$778$	−88.7383	−3.18142
$779$	−41.1756	−1.47527
$780$	−34.0620	−1.21962
$781$	23.2557	0.832155
$782$	−89.2042	−3.18994
$783$	67.4007	2.40870
$784$	2.48441	0.0887288
$785$	25.9046	0.924576
$786$	−70.4879	−2.51422
$787$	−2.19248	−0.0781535	−0.0390768	−	0.999236i	$-0.512442\pi$
$787$	−2.19248	−0.0781535	−0.0390768	+	0.999236i	$0.512442\pi$
$788$	18.0608	0.643391
$789$	−96.4049	−3.43211
$790$	−108.232	−3.85071
$791$	−24.7891	−0.881398
$792$	−95.2894	−3.38596
$793$	−11.3067	−0.401512
$794$	−20.0848	−0.712782
$795$	11.8304	0.419582
$796$	32.4286	1.14940
$797$	20.9898	0.743498	0.371749	−	0.928333i	$-0.378758\pi$
$797$	20.9898	0.743498	0.371749	+	0.928333i	$0.378758\pi$
$798$	85.8094	3.03762
$799$	−32.0845	−1.13507
$800$	−17.7007	−0.625814
$801$	37.2998	1.31792
$802$	64.9382	2.29305
$803$	10.5838	0.373493
$804$	−22.9248	−0.808494
$805$	42.1692	1.48627
$806$	18.5056	0.651833
$807$	−52.4430	−1.84608
$808$	44.5024	1.56559
$809$	16.9903	0.597346	0.298673	−	0.954356i	$-0.403456\pi$
$809$	16.9903	0.597346	0.298673	+	0.954356i	$0.403456\pi$
$810$	−185.682	−6.52420
$811$	41.4830	1.45666	0.728332	−	0.685224i	$-0.240296\pi$
$811$	41.4830	1.45666	0.728332	+	0.685224i	$0.240296\pi$
$812$	−55.8478	−1.95987
$813$	41.7881	1.46557
$814$	−33.6259	−1.17859
$815$	−37.3356	−1.30781
$816$	−166.086	−5.81416
$817$	6.81781	0.238525
$818$	−98.9922	−3.46118
$819$	17.2746	0.603622
$820$	−136.983	−4.78366
$821$	35.6149	1.24297	0.621485	−	0.783426i	$-0.286530\pi$
$821$	35.6149	1.24297	0.621485	+	0.783426i	$0.286530\pi$
$822$	−0.372680	−0.0129987
$823$	−53.5314	−1.86599	−0.932993	−	0.359895i	$-0.882813\pi$
$823$	−53.5314	−1.86599	−0.932993	+	0.359895i	$0.882813\pi$
$824$	−52.6476	−1.83406
$825$	−12.2418	−0.426204
$826$	−43.0716	−1.49865
$827$	−16.9070	−0.587914	−0.293957	−	0.955819i	$-0.594972\pi$
$827$	−16.9070	−0.587914	−0.293957	+	0.955819i	$0.594972\pi$
$828$	211.220	7.34041
$829$	6.72781	0.233666	0.116833	−	0.993152i	$-0.462726\pi$
$829$	6.72781	0.233666	0.116833	+	0.993152i	$0.462726\pi$
$830$	−106.957	−3.71255
$831$	−16.3007	−0.565464
$832$	3.74472	0.129825
$833$	1.69181	0.0586177
$834$	−68.9236	−2.38663
$835$	−38.6347	−1.33701
$836$	31.4268	1.08692
$837$	131.246	4.53653
$838$	10.3358	0.357046
$839$	49.9522	1.72454	0.862271	−	0.506447i	$-0.169041\pi$
$839$	49.9522	1.72454	0.862271	+	0.506447i	$0.169041\pi$
$840$	163.816	5.65219
$841$	−9.56853	−0.329949
$842$	−48.6041	−1.67501
$843$	44.5461	1.53425
$844$	−104.349	−3.59183
$845$	−32.7969	−1.12825
$846$	108.346	3.72501
$847$	−21.1318	−0.726097
$848$	−11.7348	−0.402974
$849$	42.1780	1.44755
$850$	−32.0125	−1.09802
$851$	42.7720	1.46620
$852$	−200.254	−6.86060
$853$	10.5211	0.360235	0.180118	−	0.983645i	$-0.442352\pi$
$853$	10.5211	0.360235	0.180118	+	0.983645i	$0.442352\pi$
$854$	94.7605	3.24264
$855$	76.9479	2.63156
$856$	−140.951	−4.81762
$857$	−13.9617	−0.476924	−0.238462	−	0.971152i	$-0.576643\pi$
$857$	−13.9617	−0.476924	−0.238462	+	0.971152i	$0.576643\pi$
$858$	12.5478	0.428373
$859$	−37.0411	−1.26383	−0.631913	−	0.775039i	$-0.717730\pi$
$859$	−37.0411	−1.26383	−0.631913	+	0.775039i	$0.717730\pi$
$860$	22.6815	0.773434
$861$	96.6119	3.29252
$862$	−100.165	−3.41162
$863$	45.5752	1.55140	0.775699	−	0.631103i	$-0.217398\pi$
$863$	45.5752	1.55140	0.775699	+	0.631103i	$0.217398\pi$
$864$	128.675	4.37762
$865$	−23.5942	−0.802227
$866$	−44.8315	−1.52344
$867$	−57.5456	−1.95435
$868$	−108.750	−3.69121
$869$	27.9565	0.948361
$870$	−99.3258	−3.36746
$871$	1.24564	0.0422070
$872$	−37.4534	−1.26833
$873$	−85.9540	−2.90910
$874$	−57.0101	−1.92840
$875$	−20.8412	−0.704560
$876$	−91.1364	−3.07921
$877$	−31.3022	−1.05700	−0.528500	−	0.848933i	$-0.677245\pi$
$877$	−31.3022	−1.05700	−0.528500	+	0.848933i	$0.677245\pi$
$878$	−0.914803	−0.0308731
$879$	25.1473	0.848198
$880$	41.0085	1.38240
$881$	31.0217	1.04515	0.522574	−	0.852594i	$-0.324972\pi$
$881$	31.0217	1.04515	0.522574	+	0.852594i	$0.324972\pi$
$882$	−5.71306	−0.192369
$883$	48.4340	1.62993	0.814967	−	0.579508i	$-0.196755\pi$
$883$	48.4340	1.62993	0.814967	+	0.579508i	$0.196755\pi$
$884$	23.0077	0.773833
$885$	−53.7130	−1.80554
$886$	−64.3148	−2.16070
$887$	−34.6113	−1.16213	−0.581067	−	0.813856i	$-0.697364\pi$
$887$	−34.6113	−1.16213	−0.581067	+	0.813856i	$0.697364\pi$
$888$	166.157	5.57588
$889$	35.9655	1.20624
$890$	−33.4927	−1.12268
$891$	47.9621	1.60679
$892$	−12.4494	−0.416836
$893$	−20.5051	−0.686178
$894$	118.043	3.94796
$895$	40.7029	1.36055
$896$	14.0523	0.469454
$897$	−15.9607	−0.532911
$898$	75.6298	2.52380
$899$	37.8380	1.26197
$900$	75.8000	2.52667
$901$	−7.99104	−0.266220
$902$	50.4618	1.68019
$903$	−15.9969	−0.532343
$904$	63.9791	2.12791
$905$	30.4373	1.01177
$906$	−94.0841	−3.12573
$907$	2.20511	0.0732194	0.0366097	−	0.999330i	$-0.488344\pi$
$907$	2.20511	0.0732194	0.0366097	+	0.999330i	$0.488344\pi$
$908$	37.0940	1.23101
$909$	−49.0473	−1.62680
$910$	−15.5114	−0.514198
$911$	27.6735	0.916864	0.458432	−	0.888730i	$-0.348411\pi$
$911$	27.6735	0.916864	0.458432	+	0.888730i	$0.348411\pi$
$912$	−106.145	−3.51480
$913$	27.6274	0.914333
$914$	−89.4524	−2.95882
$915$	118.172	3.90666
$916$	112.774	3.72615
$917$	−22.5075	−0.743264
$918$	232.715	7.68073
$919$	−59.5447	−1.96420	−0.982100	−	0.188362i	$-0.939682\pi$
$919$	−59.5447	−1.96420	−0.982100	+	0.188362i	$0.939682\pi$
$920$	−108.836	−3.58823
$921$	27.9131	0.919767
$922$	46.5805	1.53405
$923$	10.8810	0.358154
$924$	−73.7379	−2.42580
$925$	15.3495	0.504687
$926$	82.6983	2.71763
$927$	58.0243	1.90577
$928$	37.0968	1.21776
$929$	−22.5651	−0.740336	−0.370168	−	0.928965i	$-0.620700\pi$
$929$	−22.5651	−0.740336	−0.370168	+	0.928965i	$0.620700\pi$
$930$	−193.413	−6.34225
$931$	1.08123	0.0354359
$932$	−13.2120	−0.432773
$933$	−42.4900	−1.39106
$934$	98.0761	3.20915
$935$	27.9256	0.913265
$936$	−44.5846	−1.45729
$937$	14.5724	0.476059	0.238029	−	0.971258i	$-0.423499\pi$
$937$	14.5724	0.476059	0.238029	+	0.971258i	$0.423499\pi$
$938$	−10.4396	−0.340866
$939$	1.72399	0.0562604
$940$	−68.2166	−2.22498
$941$	−43.6673	−1.42351	−0.711756	−	0.702426i	$-0.752100\pi$
$941$	−43.6673	−1.42351	−0.711756	+	0.702426i	$0.752100\pi$
$942$	82.1722	2.67731
$943$	−64.1871	−2.09022
$944$	53.2788	1.73408
$945$	−110.010	−3.57864
$946$	−8.35542	−0.271658
$947$	−31.0708	−1.00967	−0.504833	−	0.863217i	$-0.668446\pi$
$947$	−31.0708	−1.00967	−0.504833	+	0.863217i	$0.668446\pi$
$948$	−240.733	−7.81864
$949$	4.95200	0.160749
$950$	−20.4591	−0.663780
$951$	−28.9336	−0.938236
$952$	−110.652	−3.58625
$953$	−36.1505	−1.17103	−0.585515	−	0.810661i	$-0.699108\pi$
$953$	−36.1505	−1.17103	−0.585515	+	0.810661i	$0.699108\pi$
$954$	26.9849	0.873668
$955$	57.9411	1.87493
$956$	123.341	3.98915
$957$	25.6561	0.829344
$958$	13.0203	0.420667
$959$	−0.119001	−0.00384273
$960$	−39.1381	−1.26318
$961$	42.6802	1.37678
$962$	−15.7331	−0.507256
$963$	155.346	5.00597
$964$	−107.626	−3.46639
$965$	36.3948	1.17159
$966$	133.765	4.30382
$967$	−38.6408	−1.24261	−0.621303	−	0.783571i	$-0.713396\pi$
$967$	−38.6408	−1.24261	−0.621303	+	0.783571i	$0.713396\pi$
$968$	54.5400	1.75298
$969$	−72.2814	−2.32201
$970$	77.1809	2.47813
$971$	34.0568	1.09293	0.546467	−	0.837481i	$-0.315972\pi$
$971$	34.0568	1.09293	0.546467	+	0.837481i	$0.315972\pi$
$972$	−197.725	−6.34203
$973$	−22.0080	−0.705545
$974$	−43.0962	−1.38089
$975$	−5.72776	−0.183435
$976$	−117.217	−3.75203
$977$	−35.4380	−1.13376	−0.566881	−	0.823800i	$-0.691850\pi$
$977$	−35.4380	−1.13376	−0.566881	+	0.823800i	$0.691850\pi$
$978$	−118.432	−3.78705
$979$	8.65125	0.276495
$980$	3.59704	0.114903
$981$	41.2784	1.31792
$982$	−7.91358	−0.252533
$983$	−20.1776	−0.643566	−0.321783	−	0.946814i	$-0.604282\pi$
$983$	−20.1776	−0.643566	−0.321783	+	0.946814i	$0.604282\pi$
$984$	−249.350	−7.94898
$985$	10.2567	0.326806
$986$	67.0911	2.13662
$987$	48.1120	1.53142
$988$	14.7042	0.467802
$989$	10.6280	0.337952
$990$	−94.3018	−2.99711
$991$	22.6238	0.718669	0.359334	−	0.933209i	$-0.383004\pi$
$991$	22.6238	0.718669	0.359334	+	0.933209i	$0.383004\pi$
$992$	72.2369	2.29352
$993$	−14.3166	−0.454324
$994$	−91.1931	−2.89247
$995$	18.4161	0.583829
$996$	−237.898	−7.53810
$997$	25.7781	0.816401	0.408200	−	0.912892i	$-0.366157\pi$
$997$	25.7781	0.816401	0.408200	+	0.912892i	$0.366157\pi$
$998$	38.5619	1.22066
$999$	−111.583	−3.53033

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.b.1.10	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.b.1.10	✓	259	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:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58711 q^{2} -3.26786 q^{3} +4.69312 q^{4} +2.66521 q^{5} +8.45431 q^{6} +2.69955 q^{7} -6.96738 q^{8} +7.67894 q^{9} +O(q^{10})\)	\(q-2.58711 q^{2} -3.26786 q^{3} +4.69312 q^{4} +2.66521 q^{5} +8.45431 q^{6} +2.69955 q^{7} -6.96738 q^{8} +7.67894 q^{9} -6.89517 q^{10} +1.78104 q^{11} -15.3365 q^{12} +0.833324 q^{13} -6.98403 q^{14} -8.70953 q^{15} +8.63912 q^{16} +5.88299 q^{17} -19.8662 q^{18} +3.75980 q^{19} +12.5081 q^{20} -8.82177 q^{21} -4.60774 q^{22} +5.86102 q^{23} +22.7685 q^{24} +2.10333 q^{25} -2.15590 q^{26} -15.2901 q^{27} +12.6693 q^{28} -4.40811 q^{29} +22.5325 q^{30} -8.58372 q^{31} -8.41557 q^{32} -5.82020 q^{33} -15.2199 q^{34} +7.19486 q^{35} +36.0382 q^{36} +7.29770 q^{37} -9.72700 q^{38} -2.72319 q^{39} -18.5695 q^{40} -10.9515 q^{41} +22.8228 q^{42} +1.81334 q^{43} +8.35863 q^{44} +20.4660 q^{45} -15.1631 q^{46} -5.45378 q^{47} -28.2315 q^{48} +0.287576 q^{49} -5.44153 q^{50} -19.2248 q^{51} +3.91089 q^{52} -1.35833 q^{53} +39.5572 q^{54} +4.74684 q^{55} -18.8088 q^{56} -12.2865 q^{57} +11.4043 q^{58} +6.16715 q^{59} -40.8749 q^{60} -13.5682 q^{61} +22.2070 q^{62} +20.7297 q^{63} +4.49371 q^{64} +2.22098 q^{65} +15.0575 q^{66} +1.49479 q^{67} +27.6096 q^{68} -19.1530 q^{69} -18.6139 q^{70} +13.0574 q^{71} -53.5021 q^{72} +5.94246 q^{73} -18.8799 q^{74} -6.87339 q^{75} +17.6452 q^{76} +4.80801 q^{77} +7.04519 q^{78} +15.6967 q^{79} +23.0251 q^{80} +26.9293 q^{81} +28.3328 q^{82} +15.5119 q^{83} -41.4016 q^{84} +15.6794 q^{85} -4.69131 q^{86} +14.4051 q^{87} -12.4092 q^{88} +4.85742 q^{89} -52.9476 q^{90} +2.24960 q^{91} +27.5064 q^{92} +28.0504 q^{93} +14.1095 q^{94} +10.0206 q^{95} +27.5009 q^{96} -11.1935 q^{97} -0.743990 q^{98} +13.6765 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * q^99

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