LMFDB - Embedded newform 8033.2.a.e.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, 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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.1438279437$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56941 q^{2} -2.98680 q^{3} +4.60185 q^{4} -2.62071 q^{5} +7.67431 q^{6} -0.147137 q^{7} -6.68522 q^{8} +5.92098 q^{9} +O(q^{10})$	\(q-2.56941 q^{2} -2.98680 q^{3} +4.60185 q^{4} -2.62071 q^{5} +7.67431 q^{6} -0.147137 q^{7} -6.68522 q^{8} +5.92098 q^{9} +6.73366 q^{10} -0.956697 q^{11} -13.7448 q^{12} +6.54586 q^{13} +0.378054 q^{14} +7.82753 q^{15} +7.97334 q^{16} -3.39513 q^{17} -15.2134 q^{18} +4.44217 q^{19} -12.0601 q^{20} +0.439468 q^{21} +2.45814 q^{22} -0.724274 q^{23} +19.9674 q^{24} +1.86811 q^{25} -16.8190 q^{26} -8.72439 q^{27} -0.677101 q^{28} -1.00000 q^{29} -20.1121 q^{30} -9.15760 q^{31} -7.11632 q^{32} +2.85746 q^{33} +8.72348 q^{34} +0.385602 q^{35} +27.2475 q^{36} +5.74579 q^{37} -11.4138 q^{38} -19.5512 q^{39} +17.5200 q^{40} +4.56254 q^{41} -1.12917 q^{42} +12.8052 q^{43} -4.40258 q^{44} -15.5172 q^{45} +1.86095 q^{46} +4.46611 q^{47} -23.8148 q^{48} -6.97835 q^{49} -4.79993 q^{50} +10.1406 q^{51} +30.1231 q^{52} +5.53185 q^{53} +22.4165 q^{54} +2.50722 q^{55} +0.983640 q^{56} -13.2679 q^{57} +2.56941 q^{58} +11.2503 q^{59} +36.0211 q^{60} +2.10401 q^{61} +23.5296 q^{62} -0.871193 q^{63} +2.33805 q^{64} -17.1548 q^{65} -7.34199 q^{66} +14.1337 q^{67} -15.6239 q^{68} +2.16326 q^{69} -0.990768 q^{70} +8.63522 q^{71} -39.5831 q^{72} +12.1743 q^{73} -14.7633 q^{74} -5.57966 q^{75} +20.4422 q^{76} +0.140765 q^{77} +50.2350 q^{78} -9.03376 q^{79} -20.8958 q^{80} +8.29508 q^{81} -11.7230 q^{82} +5.72453 q^{83} +2.02237 q^{84} +8.89765 q^{85} -32.9019 q^{86} +2.98680 q^{87} +6.39573 q^{88} -11.1348 q^{89} +39.8699 q^{90} -0.963136 q^{91} -3.33300 q^{92} +27.3519 q^{93} -11.4753 q^{94} -11.6416 q^{95} +21.2550 q^{96} +14.2571 q^{97} +17.9302 q^{98} -5.66458 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) $ 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * 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 $

$2$	−2.56941	−1.81685	−0.908423	−	0.418053i	$-0.862713\pi$
$2$	−2.56941	−1.81685	−0.908423	+	0.418053i	$0.862713\pi$
$3$	−2.98680	−1.72443	−0.862215	−	0.506542i	$-0.830924\pi$
$3$	−2.98680	−1.72443	−0.862215	+	0.506542i	$0.830924\pi$
$4$	4.60185	2.30093
$5$	−2.62071	−1.17202	−0.586008	−	0.810305i	$-0.699301\pi$
$5$	−2.62071	−1.17202	−0.586008	+	0.810305i	$0.699301\pi$
$6$	7.67431	3.13302
$7$	−0.147137	−0.0556124	−0.0278062	−	0.999613i	$-0.508852\pi$
$7$	−0.147137	−0.0556124	−0.0278062	+	0.999613i	$0.508852\pi$
$8$	−6.68522	−2.36358
$9$	5.92098	1.97366
$10$	6.73366	2.12937
$11$	−0.956697	−0.288455	−0.144227	−	0.989545i	$-0.546070\pi$
$11$	−0.956697	−0.288455	−0.144227	+	0.989545i	$0.546070\pi$
$12$	−13.7448	−3.96779
$13$	6.54586	1.81550	0.907748	−	0.419517i	$-0.137800\pi$
$13$	6.54586	1.81550	0.907748	+	0.419517i	$0.137800\pi$
$14$	0.378054	0.101039
$15$	7.82753	2.02106
$16$	7.97334	1.99334
$17$	−3.39513	−0.823441	−0.411720	−	0.911310i	$-0.635072\pi$
$17$	−3.39513	−0.823441	−0.411720	+	0.911310i	$0.635072\pi$
$18$	−15.2134	−3.58584
$19$	4.44217	1.01910	0.509552	−	0.860440i	$-0.329811\pi$
$19$	4.44217	1.01910	0.509552	+	0.860440i	$0.329811\pi$
$20$	−12.0601	−2.69672
$21$	0.439468	0.0958997
$22$	2.45814	0.524078
$23$	−0.724274	−0.151022	−0.0755108	−	0.997145i	$-0.524059\pi$
$23$	−0.724274	−0.151022	−0.0755108	+	0.997145i	$0.524059\pi$
$24$	19.9674	4.07583
$25$	1.86811	0.373621
$26$	−16.8190	−3.29847
$27$	−8.72439	−1.67901
$28$	−0.677101	−0.127960
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−20.1121	−3.67195
$31$	−9.15760	−1.64475	−0.822377	−	0.568944i	$-0.807352\pi$
$31$	−9.15760	−1.64475	−0.822377	+	0.568944i	$0.807352\pi$
$32$	−7.11632	−1.25800
$33$	2.85746	0.497421
$34$	8.72348	1.49606
$35$	0.385602	0.0651786
$36$	27.2475	4.54125
$37$	5.74579	0.944603	0.472301	−	0.881437i	$-0.343423\pi$
$37$	5.74579	0.944603	0.472301	+	0.881437i	$0.343423\pi$
$38$	−11.4138	−1.85155
$39$	−19.5512	−3.13070
$40$	17.5200	2.77015
$41$	4.56254	0.712549	0.356275	−	0.934381i	$-0.384047\pi$
$41$	4.56254	0.712549	0.356275	+	0.934381i	$0.384047\pi$
$42$	−1.12917	−0.174235
$43$	12.8052	1.95278	0.976390	−	0.216016i	$-0.0693065\pi$
$43$	12.8052	1.95278	0.976390	+	0.216016i	$0.0693065\pi$
$44$	−4.40258	−0.663714
$45$	−15.5172	−2.31316
$46$	1.86095	0.274383
$47$	4.46611	0.651449	0.325724	−	0.945465i	$-0.394392\pi$
$47$	4.46611	0.651449	0.325724	+	0.945465i	$0.394392\pi$
$48$	−23.8148	−3.43737
$49$	−6.97835	−0.996907
$50$	−4.79993	−0.678812
$51$	10.1406	1.41997
$52$	30.1231	4.17732
$53$	5.53185	0.759858	0.379929	−	0.925016i	$-0.375948\pi$
$53$	5.53185	0.759858	0.379929	+	0.925016i	$0.375948\pi$
$54$	22.4165	3.05050
$55$	2.50722	0.338074
$56$	0.983640	0.131444
$57$	−13.2679	−1.75737
$58$	2.56941	0.337380
$59$	11.2503	1.46466	0.732329	−	0.680951i	$-0.238433\pi$
$59$	11.2503	1.46466	0.732329	+	0.680951i	$0.238433\pi$
$60$	36.0211	4.65031
$61$	2.10401	0.269391	0.134696	−	0.990887i	$-0.456994\pi$
$61$	2.10401	0.269391	0.134696	+	0.990887i	$0.456994\pi$
$62$	23.5296	2.98826
$63$	−0.871193	−0.109760
$64$	2.33805	0.292256
$65$	−17.1548	−2.12779
$66$	−7.34199	−0.903736
$67$	14.1337	1.72671	0.863354	−	0.504598i	$-0.168359\pi$
$67$	14.1337	1.72671	0.863354	+	0.504598i	$0.168359\pi$
$68$	−15.6239	−1.89468
$69$	2.16326	0.260426
$70$	−0.990768	−0.118419
$71$	8.63522	1.02481	0.512406	−	0.858743i	$-0.328754\pi$
$71$	8.63522	1.02481	0.512406	+	0.858743i	$0.328754\pi$
$72$	−39.5831	−4.66491
$73$	12.1743	1.42490	0.712450	−	0.701723i	$-0.247586\pi$
$73$	12.1743	1.42490	0.712450	+	0.701723i	$0.247586\pi$
$74$	−14.7633	−1.71620
$75$	−5.57966	−0.644284
$76$	20.4422	2.34488
$77$	0.140765	0.0160417
$78$	50.2350	5.68799
$79$	−9.03376	−1.01638	−0.508188	−	0.861246i	$-0.669685\pi$
$79$	−9.03376	−1.01638	−0.508188	+	0.861246i	$0.669685\pi$
$80$	−20.8958	−2.33622
$81$	8.29508	0.921676
$82$	−11.7230	−1.29459
$83$	5.72453	0.628349	0.314174	−	0.949365i	$-0.398272\pi$
$83$	5.72453	0.628349	0.314174	+	0.949365i	$0.398272\pi$
$84$	2.02237	0.220658
$85$	8.89765	0.965086
$86$	−32.9019	−3.54790
$87$	2.98680	0.320219
$88$	6.39573	0.681787
$89$	−11.1348	−1.18028	−0.590141	−	0.807300i	$-0.700928\pi$
$89$	−11.1348	−1.18028	−0.590141	+	0.807300i	$0.700928\pi$
$90$	39.8699	4.20266
$91$	−0.963136	−0.100964
$92$	−3.33300	−0.347489
$93$	27.3519	2.83626
$94$	−11.4753	−1.18358
$95$	−11.6416	−1.19441
$96$	21.2550	2.16933
$97$	14.2571	1.44759	0.723794	−	0.690016i	$-0.242397\pi$
$97$	14.2571	1.44759	0.723794	+	0.690016i	$0.242397\pi$
$98$	17.9302	1.81123
$99$	−5.66458	−0.569312
$100$	8.59675	0.859675
$101$	0.920567	0.0915999	0.0457999	−	0.998951i	$-0.485416\pi$
$101$	0.920567	0.0915999	0.0457999	+	0.998951i	$0.485416\pi$
$102$	−26.0553	−2.57986
$103$	20.1272	1.98319	0.991597	−	0.129363i	$-0.0412933\pi$
$103$	20.1272	1.98319	0.991597	+	0.129363i	$0.0412933\pi$
$104$	−43.7605	−4.29107
$105$	−1.15172	−0.112396
$106$	−14.2136	−1.38054
$107$	−18.2687	−1.76610	−0.883050	−	0.469280i	$-0.844514\pi$
$107$	−18.2687	−1.76610	−0.883050	+	0.469280i	$0.844514\pi$
$108$	−40.1484	−3.86328
$109$	1.75626	0.168219	0.0841095	−	0.996457i	$-0.473195\pi$
$109$	1.75626	0.168219	0.0841095	+	0.996457i	$0.473195\pi$
$110$	−6.44207	−0.614228
$111$	−17.1615	−1.62890
$112$	−1.17317	−0.110854
$113$	12.2893	1.15608	0.578042	−	0.816007i	$-0.303817\pi$
$113$	12.2893	1.15608	0.578042	+	0.816007i	$0.303817\pi$
$114$	34.0906	3.19288
$115$	1.89811	0.177000
$116$	−4.60185	−0.427271
$117$	38.7579	3.58317
$118$	−28.9065	−2.66106
$119$	0.499548	0.0457935
$120$	−52.3288	−4.77694
$121$	−10.0847	−0.916794
$122$	−5.40606	−0.489442
$123$	−13.6274	−1.22874
$124$	−42.1419	−3.78446
$125$	8.20778	0.734126
$126$	2.23845	0.199417
$127$	8.42435	0.747540	0.373770	−	0.927521i	$-0.378065\pi$
$127$	8.42435	0.747540	0.373770	+	0.927521i	$0.378065\pi$
$128$	8.22525	0.727016
$129$	−38.2467	−3.36743
$130$	44.0776	3.86586
$131$	−3.98166	−0.347879	−0.173940	−	0.984756i	$-0.555650\pi$
$131$	−3.98166	−0.347879	−0.173940	+	0.984756i	$0.555650\pi$
$132$	13.1496	1.14453
$133$	−0.653606	−0.0566749
$134$	−36.3153	−3.13716
$135$	22.8641	1.96783
$136$	22.6972	1.94627
$137$	−14.1674	−1.21040	−0.605200	−	0.796073i	$-0.706907\pi$
$137$	−14.1674	−1.21040	−0.605200	+	0.796073i	$0.706907\pi$
$138$	−5.55830	−0.473154
$139$	−2.37954	−0.201830	−0.100915	−	0.994895i	$-0.532177\pi$
$139$	−2.37954	−0.201830	−0.100915	+	0.994895i	$0.532177\pi$
$140$	1.77448	0.149971
$141$	−13.3394	−1.12338
$142$	−22.1874	−1.86192
$143$	−6.26241	−0.523689
$144$	47.2100	3.93417
$145$	2.62071	0.217638
$146$	−31.2809	−2.58882
$147$	20.8429	1.71910
$148$	26.4413	2.17346
$149$	24.2081	1.98321	0.991604	−	0.129312i	$-0.0412770\pi$
$149$	24.2081	1.98321	0.991604	+	0.129312i	$0.0412770\pi$
$150$	14.3364	1.17056
$151$	17.3437	1.41141	0.705704	−	0.708507i	$-0.250631\pi$
$151$	17.3437	1.41141	0.705704	+	0.708507i	$0.250631\pi$
$152$	−29.6969	−2.40874
$153$	−20.1025	−1.62519
$154$	−0.361683	−0.0291452
$155$	23.9994	1.92768
$156$	−89.9717	−7.20350
$157$	−19.8730	−1.58604	−0.793020	−	0.609195i	$-0.791492\pi$
$157$	−19.8730	−1.58604	−0.793020	+	0.609195i	$0.791492\pi$
$158$	23.2114	1.84660
$159$	−16.5225	−1.31032
$160$	18.6498	1.47440
$161$	0.106567	0.00839867
$162$	−21.3134	−1.67454
$163$	−12.5218	−0.980785	−0.490392	−	0.871502i	$-0.663146\pi$
$163$	−12.5218	−0.980785	−0.490392	+	0.871502i	$0.663146\pi$
$164$	20.9961	1.63952
$165$	−7.48857	−0.582985
$166$	−14.7087	−1.14161
$167$	11.1766	0.864874	0.432437	−	0.901664i	$-0.357654\pi$
$167$	11.1766	0.864874	0.432437	+	0.901664i	$0.357654\pi$
$168$	−2.93794	−0.226667
$169$	29.8483	2.29602
$170$	−22.8617	−1.75341
$171$	26.3020	2.01137
$172$	58.9278	4.49320
$173$	9.21356	0.700494	0.350247	−	0.936657i	$-0.386098\pi$
$173$	9.21356	0.700494	0.350247	+	0.936657i	$0.386098\pi$
$174$	−7.67431	−0.581788
$175$	−0.274867	−0.0207780
$176$	−7.62807	−0.574987
$177$	−33.6023	−2.52570
$178$	28.6097	2.14439
$179$	19.7448	1.47580	0.737899	−	0.674911i	$-0.235818\pi$
$179$	19.7448	1.47580	0.737899	+	0.674911i	$0.235818\pi$
$180$	−71.4077	−5.32241
$181$	−14.5323	−1.08018	−0.540090	−	0.841607i	$-0.681610\pi$
$181$	−14.5323	−1.08018	−0.540090	+	0.841607i	$0.681610\pi$
$182$	2.47469	0.183436
$183$	−6.28426	−0.464546
$184$	4.84193	0.356952
$185$	−15.0580	−1.10709
$186$	−70.2782	−5.15305
$187$	3.24811	0.237526
$188$	20.5524	1.49894
$189$	1.28368	0.0933738
$190$	29.9121	2.17005
$191$	−6.65844	−0.481788	−0.240894	−	0.970551i	$-0.577441\pi$
$191$	−6.65844	−0.481788	−0.240894	+	0.970551i	$0.577441\pi$
$192$	−6.98328	−0.503975
$193$	−6.32892	−0.455566	−0.227783	−	0.973712i	$-0.573148\pi$
$193$	−6.32892	−0.455566	−0.227783	+	0.973712i	$0.573148\pi$
$194$	−36.6323	−2.63004
$195$	51.2379	3.66923
$196$	−32.1133	−2.29381
$197$	0.801722	0.0571203	0.0285601	−	0.999592i	$-0.490908\pi$
$197$	0.801722	0.0571203	0.0285601	+	0.999592i	$0.490908\pi$
$198$	14.5546	1.03435
$199$	10.9910	0.779133	0.389566	−	0.920998i	$-0.372625\pi$
$199$	10.9910	0.779133	0.389566	+	0.920998i	$0.372625\pi$
$200$	−12.4887	−0.883084
$201$	−42.2146	−2.97759
$202$	−2.36531	−0.166423
$203$	0.147137	0.0103270
$204$	46.6655	3.26724
$205$	−11.9571	−0.835119
$206$	−51.7150	−3.60316
$207$	−4.28841	−0.298065
$208$	52.1924	3.61889
$209$	−4.24981	−0.293966
$210$	2.95923	0.204206
$211$	−8.75027	−0.602393	−0.301197	−	0.953562i	$-0.597386\pi$
$211$	−8.75027	−0.602393	−0.301197	+	0.953562i	$0.597386\pi$
$212$	25.4568	1.74838
$213$	−25.7917	−1.76722
$214$	46.9397	3.20873
$215$	−33.5588	−2.28869
$216$	58.3245	3.96848
$217$	1.34742	0.0914687
$218$	−4.51254	−0.305628
$219$	−36.3624	−2.45714
$220$	11.5379	0.777883
$221$	−22.2241	−1.49495
$222$	44.0950	2.95946
$223$	−7.39763	−0.495382	−0.247691	−	0.968839i	$-0.579672\pi$
$223$	−7.39763	−0.495382	−0.247691	+	0.968839i	$0.579672\pi$
$224$	1.04707	0.0699604
$225$	11.0610	0.737402
$226$	−31.5763	−2.10043
$227$	−13.1955	−0.875815	−0.437908	−	0.899020i	$-0.644280\pi$
$227$	−13.1955	−0.875815	−0.437908	+	0.899020i	$0.644280\pi$
$228$	−61.0569	−4.04359
$229$	−27.8861	−1.84276	−0.921382	−	0.388658i	$-0.872939\pi$
$229$	−27.8861	−1.84276	−0.921382	+	0.388658i	$0.872939\pi$
$230$	−4.87702	−0.321581
$231$	−0.420437	−0.0276628
$232$	6.68522	0.438906
$233$	6.70609	0.439330	0.219665	−	0.975575i	$-0.429504\pi$
$233$	6.70609	0.439330	0.219665	+	0.975575i	$0.429504\pi$
$234$	−99.5849	−6.51007
$235$	−11.7044	−0.763509
$236$	51.7720	3.37007
$237$	26.9820	1.75267
$238$	−1.28354	−0.0831997
$239$	−12.8548	−0.831509	−0.415754	−	0.909477i	$-0.636482\pi$
$239$	−12.8548	−0.831509	−0.415754	+	0.909477i	$0.636482\pi$
$240$	62.4116	4.02865
$241$	14.2730	0.919403	0.459702	−	0.888073i	$-0.347956\pi$
$241$	14.2730	0.919403	0.459702	+	0.888073i	$0.347956\pi$
$242$	25.9118	1.66567
$243$	1.39742	0.0896443
$244$	9.68235	0.619849
$245$	18.2882	1.16839
$246$	35.0143	2.23243
$247$	29.0779	1.85018
$248$	61.2205	3.88751
$249$	−17.0980	−1.08354
$250$	−21.0891	−1.33379
$251$	22.4426	1.41657	0.708283	−	0.705929i	$-0.249470\pi$
$251$	22.4426	1.41657	0.708283	+	0.705929i	$0.249470\pi$
$252$	−4.00910	−0.252550
$253$	0.692910	0.0435629
$254$	−21.6456	−1.35816
$255$	−26.5755	−1.66422
$256$	−25.8101	−1.61313
$257$	15.3846	0.959663	0.479831	−	0.877361i	$-0.340698\pi$
$257$	15.3846	0.959663	0.479831	+	0.877361i	$0.340698\pi$
$258$	98.2713	6.11810
$259$	−0.845417	−0.0525316
$260$	−78.9438	−4.89589
$261$	−5.92098	−0.366500
$262$	10.2305	0.632043
$263$	−4.04869	−0.249653	−0.124826	−	0.992179i	$-0.539837\pi$
$263$	−4.04869	−0.249653	−0.124826	+	0.992179i	$0.539837\pi$
$264$	−19.1028	−1.17569
$265$	−14.4974	−0.890566
$266$	1.67938	0.102969
$267$	33.2573	2.03531
$268$	65.0413	3.97303
$269$	−27.5760	−1.68134	−0.840670	−	0.541548i	$-0.817838\pi$
$269$	−27.5760	−1.68134	−0.840670	+	0.541548i	$0.817838\pi$
$270$	−58.7471	−3.57524
$271$	22.6920	1.37844	0.689221	−	0.724551i	$-0.257953\pi$
$271$	22.6920	1.37844	0.689221	+	0.724551i	$0.257953\pi$
$272$	−27.0706	−1.64139
$273$	2.87670	0.174106
$274$	36.4018	2.19911
$275$	−1.78721	−0.107773
$276$	9.95501	0.599221
$277$	1.00000	0.0600842
$277$	1.00000	0.0600842
$278$	6.11401	0.366694
$279$	−54.2220	−3.24618
$280$	−2.57783	−0.154055
$281$	−0.243856	−0.0145473	−0.00727363	−	0.999974i	$-0.502315\pi$
$281$	−0.243856	−0.0145473	−0.00727363	+	0.999974i	$0.502315\pi$
$282$	34.2743	2.04100
$283$	32.2911	1.91950	0.959752	−	0.280848i	$-0.0906155\pi$
$283$	32.2911	1.91950	0.959752	+	0.280848i	$0.0906155\pi$
$284$	39.7380	2.35802
$285$	34.7713	2.05967
$286$	16.0907	0.951461
$287$	−0.671317	−0.0396266
$288$	−42.1356	−2.48286
$289$	−5.47307	−0.321945
$290$	−6.73366	−0.395414
$291$	−42.5831	−2.49626
$292$	56.0245	3.27859
$293$	−26.8941	−1.57117	−0.785585	−	0.618754i	$-0.787638\pi$
$293$	−26.8941	−1.57117	−0.785585	+	0.618754i	$0.787638\pi$
$294$	−53.5540	−3.12333
$295$	−29.4836	−1.71660
$296$	−38.4119	−2.23265
$297$	8.34660	0.484319
$298$	−62.2006	−3.60318
$299$	−4.74100	−0.274179
$300$	−25.6768	−1.48245
$301$	−1.88412	−0.108599
$302$	−44.5630	−2.56431
$303$	−2.74955	−0.157958
$304$	35.4190	2.03142
$305$	−5.51400	−0.315731
$306$	51.6516	2.95272
$307$	−1.13827	−0.0649648	−0.0324824	−	0.999472i	$-0.510341\pi$
$307$	−1.13827	−0.0649648	−0.0324824	+	0.999472i	$0.510341\pi$
$308$	0.647780	0.0369107
$309$	−60.1160	−3.41988
$310$	−61.6642	−3.50229
$311$	24.2023	1.37239	0.686193	−	0.727420i	$-0.259281\pi$
$311$	24.2023	1.37239	0.686193	+	0.727420i	$0.259281\pi$
$312$	130.704	7.39965
$313$	−13.0135	−0.735566	−0.367783	−	0.929912i	$-0.619883\pi$
$313$	−13.0135	−0.735566	−0.367783	+	0.929912i	$0.619883\pi$
$314$	51.0619	2.88159
$315$	2.28314	0.128640
$316$	−41.5720	−2.33861
$317$	−21.1443	−1.18758	−0.593792	−	0.804619i	$-0.702370\pi$
$317$	−21.1443	−1.18758	−0.593792	+	0.804619i	$0.702370\pi$
$318$	42.4531	2.38065
$319$	0.956697	0.0535647
$320$	−6.12733	−0.342528
$321$	54.5649	3.04552
$322$	−0.273814	−0.0152591
$323$	−15.0818	−0.839172
$324$	38.1727	2.12071
$325$	12.2284	0.678308
$326$	32.1737	1.78193
$327$	−5.24559	−0.290082
$328$	−30.5016	−1.68417
$329$	−0.657128	−0.0362286
$330$	19.2412	1.05919
$331$	−5.95963	−0.327571	−0.163785	−	0.986496i	$-0.552370\pi$
$331$	−5.95963	−0.327571	−0.163785	+	0.986496i	$0.552370\pi$
$332$	26.3434	1.44578
$333$	34.0207	1.86433
$334$	−28.7173	−1.57134
$335$	−37.0403	−2.02373
$336$	3.50403	0.191160
$337$	−16.6114	−0.904879	−0.452440	−	0.891795i	$-0.649446\pi$
$337$	−16.6114	−0.904879	−0.452440	+	0.891795i	$0.649446\pi$
$338$	−76.6924	−4.17152
$339$	−36.7058	−1.99359
$340$	40.9457	2.22059
$341$	8.76104	0.474437
$342$	−67.5806	−3.65434
$343$	2.05673	0.111053
$344$	−85.6058	−4.61555
$345$	−5.66928	−0.305224
$346$	−23.6734	−1.27269
$347$	−30.8421	−1.65569	−0.827846	−	0.560956i	$-0.810434\pi$
$347$	−30.8421	−1.65569	−0.827846	+	0.560956i	$0.810434\pi$
$348$	13.7448	0.736800
$349$	19.7692	1.05822	0.529110	−	0.848553i	$-0.322526\pi$
$349$	19.7692	1.05822	0.529110	+	0.848553i	$0.322526\pi$
$350$	0.706245	0.0377504
$351$	−57.1087	−3.04824
$352$	6.80816	0.362876
$353$	−3.57402	−0.190226	−0.0951129	−	0.995466i	$-0.530321\pi$
$353$	−3.57402	−0.190226	−0.0951129	+	0.995466i	$0.530321\pi$
$354$	86.3379	4.58881
$355$	−22.6304	−1.20110
$356$	−51.2405	−2.71574
$357$	−1.49205	−0.0789677
$358$	−50.7325	−2.68130
$359$	−37.5727	−1.98301	−0.991505	−	0.130067i	$-0.958481\pi$
$359$	−37.5727	−1.98301	−0.991505	+	0.130067i	$0.958481\pi$
$360$	103.736	5.46735
$361$	0.732904	0.0385739
$362$	37.3395	1.96252
$363$	30.1211	1.58095
$364$	−4.43221	−0.232311
$365$	−31.9054	−1.67000
$366$	16.1468	0.844008
$367$	−27.5715	−1.43922	−0.719611	−	0.694377i	$-0.755680\pi$
$367$	−27.5715	−1.43922	−0.719611	+	0.694377i	$0.755680\pi$
$368$	−5.77488	−0.301037
$369$	27.0147	1.40633
$370$	38.6902	2.01141
$371$	−0.813938	−0.0422575
$372$	125.870	6.52603
$373$	1.86512	0.0965723	0.0482861	−	0.998834i	$-0.484624\pi$
$373$	1.86512	0.0965723	0.0482861	+	0.998834i	$0.484624\pi$
$374$	−8.34572	−0.431547
$375$	−24.5150	−1.26595
$376$	−29.8569	−1.53975
$377$	−6.54586	−0.337129
$378$	−3.29829	−0.169646
$379$	−4.47382	−0.229804	−0.114902	−	0.993377i	$-0.536655\pi$
$379$	−4.47382	−0.229804	−0.114902	+	0.993377i	$0.536655\pi$
$380$	−53.5731	−2.74824
$381$	−25.1619	−1.28908
$382$	17.1082	0.875333
$383$	13.2608	0.677596	0.338798	−	0.940859i	$-0.389980\pi$
$383$	13.2608	0.677596	0.338798	+	0.940859i	$0.389980\pi$
$384$	−24.5672	−1.25369
$385$	−0.368904	−0.0188011
$386$	16.2616	0.827692
$387$	75.8195	3.85412
$388$	65.6090	3.33079
$389$	32.1925	1.63222	0.816112	−	0.577894i	$-0.196125\pi$
$389$	32.1925	1.63222	0.816112	+	0.577894i	$0.196125\pi$
$390$	−131.651	−6.66641
$391$	2.45901	0.124357
$392$	46.6518	2.35627
$393$	11.8924	0.599894
$394$	−2.05995	−0.103779
$395$	23.6748	1.19121
$396$	−26.0676	−1.30995
$397$	−30.9988	−1.55579	−0.777894	−	0.628396i	$-0.783712\pi$
$397$	−30.9988	−1.55579	−0.777894	+	0.628396i	$0.783712\pi$
$398$	−28.2404	−1.41556
$399$	1.95219	0.0977318
$400$	14.8950	0.744752
$401$	−0.852172	−0.0425554	−0.0212777	−	0.999774i	$-0.506773\pi$
$401$	−0.852172	−0.0425554	−0.0212777	+	0.999774i	$0.506773\pi$
$402$	108.467	5.40982
$403$	−59.9444	−2.98604
$404$	4.23632	0.210765
$405$	−21.7390	−1.08022
$406$	−0.378054	−0.0187625
$407$	−5.49698	−0.272475
$408$	−67.7920	−3.35621
$409$	13.5900	0.671980	0.335990	−	0.941866i	$-0.390929\pi$
$409$	13.5900	0.671980	0.335990	+	0.941866i	$0.390929\pi$
$410$	30.7226	1.51728
$411$	42.3151	2.08725
$412$	92.6225	4.56318
$413$	−1.65532	−0.0814532
$414$	11.0187	0.541538
$415$	−15.0023	−0.736435
$416$	−46.5825	−2.28389
$417$	7.10722	0.348042
$418$	10.9195	0.534090
$419$	−27.3725	−1.33723	−0.668617	−	0.743607i	$-0.733113\pi$
$419$	−27.3725	−1.33723	−0.668617	+	0.743607i	$0.733113\pi$
$420$	−5.30003	−0.258615
$421$	−5.18641	−0.252770	−0.126385	−	0.991981i	$-0.540337\pi$
$421$	−5.18641	−0.252770	−0.126385	+	0.991981i	$0.540337\pi$
$422$	22.4830	1.09446
$423$	26.4438	1.28574
$424$	−36.9816	−1.79599
$425$	−6.34247	−0.307655
$426$	66.2693	3.21076
$427$	−0.309577	−0.0149815
$428$	−84.0697	−4.06366
$429$	18.7046	0.903065
$430$	86.2261	4.15819
$431$	30.7539	1.48136	0.740682	−	0.671855i	$-0.234502\pi$
$431$	30.7539	1.48136	0.740682	+	0.671855i	$0.234502\pi$
$432$	−69.5626	−3.34683
$433$	−6.64905	−0.319533	−0.159766	−	0.987155i	$-0.551074\pi$
$433$	−6.64905	−0.319533	−0.159766	+	0.987155i	$0.551074\pi$
$434$	−3.46206	−0.166184
$435$	−7.82753	−0.375301
$436$	8.08204	0.387059
$437$	−3.21735	−0.153907
$438$	93.4297	4.46424
$439$	−12.8226	−0.611990	−0.305995	−	0.952033i	$-0.598989\pi$
$439$	−12.8226	−0.611990	−0.305995	+	0.952033i	$0.598989\pi$
$440$	−16.7613	−0.799065
$441$	−41.3187	−1.96756
$442$	57.1027	2.71610
$443$	26.0781	1.23901	0.619504	−	0.784994i	$-0.287334\pi$
$443$	26.0781	1.23901	0.619504	+	0.784994i	$0.287334\pi$
$444$	−78.9749	−3.74798
$445$	29.1809	1.38331
$446$	19.0075	0.900032
$447$	−72.3049	−3.41990
$448$	−0.344012	−0.0162530
$449$	−6.87002	−0.324216	−0.162108	−	0.986773i	$-0.551829\pi$
$449$	−6.87002	−0.324216	−0.162108	+	0.986773i	$0.551829\pi$
$450$	−28.4203	−1.33974
$451$	−4.36497	−0.205538
$452$	56.5537	2.66006
$453$	−51.8021	−2.43388
$454$	33.9046	1.59122
$455$	2.52410	0.118331
$456$	88.6987	4.15370
$457$	21.2017	0.991773	0.495887	−	0.868387i	$-0.334843\pi$
$457$	21.2017	0.991773	0.495887	+	0.868387i	$0.334843\pi$
$458$	71.6507	3.34802
$459$	29.6205	1.38257
$460$	8.73482	0.407263
$461$	−0.567022	−0.0264089	−0.0132044	−	0.999913i	$-0.504203\pi$
$461$	−0.567022	−0.0264089	−0.0132044	+	0.999913i	$0.504203\pi$
$462$	1.08027	0.0502589
$463$	23.2514	1.08059	0.540293	−	0.841477i	$-0.318313\pi$
$463$	23.2514	1.08059	0.540293	+	0.841477i	$0.318313\pi$
$464$	−7.97334	−0.370153
$465$	−71.6814	−3.32414
$466$	−17.2307	−0.798195
$467$	−4.57870	−0.211877	−0.105938	−	0.994373i	$-0.533785\pi$
$467$	−4.57870	−0.211877	−0.105938	+	0.994373i	$0.533785\pi$
$468$	178.358	8.24461
$469$	−2.07959	−0.0960264
$470$	30.0733	1.38718
$471$	59.3568	2.73502
$472$	−75.2104	−3.46184
$473$	−12.2507	−0.563289
$474$	−69.3278	−3.18433
$475$	8.29845	0.380759
$476$	2.29885	0.105368
$477$	32.7540	1.49970
$478$	33.0292	1.51072
$479$	−8.00728	−0.365862	−0.182931	−	0.983126i	$-0.558558\pi$
$479$	−8.00728	−0.365862	−0.182931	+	0.983126i	$0.558558\pi$
$480$	−55.7032	−2.54249
$481$	37.6112	1.71492
$482$	−36.6731	−1.67041
$483$	−0.318295	−0.0144829
$484$	−46.4084	−2.10947
$485$	−37.3636	−1.69660
$486$	−3.59053	−0.162870
$487$	−11.6135	−0.526257	−0.263128	−	0.964761i	$-0.584754\pi$
$487$	−11.6135	−0.526257	−0.263128	+	0.964761i	$0.584754\pi$
$488$	−14.0658	−0.636728
$489$	37.4002	1.69129
$490$	−46.9899	−2.12279
$491$	19.9744	0.901430	0.450715	−	0.892668i	$-0.351169\pi$
$491$	19.9744	0.901430	0.450715	+	0.892668i	$0.351169\pi$
$492$	−62.7113	−2.82724
$493$	3.39513	0.152909
$494$	−74.7128	−3.36149
$495$	14.8452	0.667243
$496$	−73.0166	−3.27854
$497$	−1.27056	−0.0569922
$498$	43.9318	1.96863
$499$	1.63772	0.0733144	0.0366572	−	0.999328i	$-0.488329\pi$
$499$	1.63772	0.0733144	0.0366572	+	0.999328i	$0.488329\pi$
$500$	37.7710	1.68917
$501$	−33.3824	−1.49142
$502$	−57.6642	−2.57368
$503$	15.3103	0.682653	0.341326	−	0.939945i	$-0.389124\pi$
$503$	15.3103	0.682653	0.341326	+	0.939945i	$0.389124\pi$
$504$	5.82412	0.259427
$505$	−2.41254	−0.107357
$506$	−1.78037	−0.0791471
$507$	−89.1510	−3.95933
$508$	38.7676	1.72003
$509$	−14.5539	−0.645088	−0.322544	−	0.946554i	$-0.604538\pi$
$509$	−14.5539	−0.645088	−0.322544	+	0.946554i	$0.604538\pi$
$510$	68.2833	3.02364
$511$	−1.79129	−0.0792421
$512$	49.8662	2.20379
$513$	−38.7553	−1.71109
$514$	−39.5292	−1.74356
$515$	−52.7476	−2.32434
$516$	−176.006	−7.74821
$517$	−4.27271	−0.187914
$518$	2.17222	0.0954418
$519$	−27.5191	−1.20795
$520$	114.683	5.02920
$521$	23.3803	1.02431	0.512154	−	0.858893i	$-0.328848\pi$
$521$	23.3803	1.02431	0.512154	+	0.858893i	$0.328848\pi$
$522$	15.2134	0.665873
$523$	3.32436	0.145364	0.0726822	−	0.997355i	$-0.476844\pi$
$523$	3.32436	0.145364	0.0726822	+	0.997355i	$0.476844\pi$
$524$	−18.3230	−0.800445
$525$	0.820973	0.0358302
$526$	10.4027	0.453581
$527$	31.0913	1.35436
$528$	22.7835	0.991526
$529$	−22.4754	−0.977192
$530$	37.2496	1.61802
$531$	66.6125	2.89074
$532$	−3.00780	−0.130405
$533$	29.8658	1.29363
$534$	−85.4515	−3.69785
$535$	47.8768	2.06990
$536$	−94.4870	−4.08122
$537$	−58.9739	−2.54491
$538$	70.8540	3.05473
$539$	6.67617	0.287563
$540$	105.217	4.52782
$541$	−5.51280	−0.237014	−0.118507	−	0.992953i	$-0.537811\pi$
$541$	−5.51280	−0.237014	−0.118507	+	0.992953i	$0.537811\pi$
$542$	−58.3051	−2.50442
$543$	43.4052	1.86269
$544$	24.1609	1.03589
$545$	−4.60264	−0.197155
$546$	−7.39140	−0.316323
$547$	−24.8999	−1.06464	−0.532322	−	0.846542i	$-0.678680\pi$
$547$	−24.8999	−1.06464	−0.532322	+	0.846542i	$0.678680\pi$
$548$	−65.1962	−2.78504
$549$	12.4578	0.531686
$550$	4.59207	0.195807
$551$	−4.44217	−0.189243
$552$	−14.4619	−0.615538
$553$	1.32920	0.0565232
$554$	−2.56941	−0.109164
$555$	44.9754	1.90910
$556$	−10.9503	−0.464396
$557$	9.28124	0.393259	0.196629	−	0.980478i	$-0.437000\pi$
$557$	9.28124	0.393259	0.196629	+	0.980478i	$0.437000\pi$
$558$	139.318	5.89781
$559$	83.8213	3.54526
$560$	3.07454	0.129923
$561$	−9.70147	−0.409596
$562$	0.626567	0.0264301
$563$	−3.34183	−0.140841	−0.0704207	−	0.997517i	$-0.522434\pi$
$563$	−3.34183	−0.140841	−0.0704207	+	0.997517i	$0.522434\pi$
$564$	−61.3859	−2.58481
$565$	−32.2068	−1.35495
$566$	−82.9689	−3.48744
$567$	−1.22051	−0.0512566
$568$	−57.7283	−2.42223
$569$	−8.77293	−0.367781	−0.183890	−	0.982947i	$-0.558869\pi$
$569$	−8.77293	−0.367781	−0.183890	+	0.982947i	$0.558869\pi$
$570$	−89.3415	−3.74210
$571$	−19.8835	−0.832100	−0.416050	−	0.909342i	$-0.636586\pi$
$571$	−19.8835	−0.832100	−0.416050	+	0.909342i	$0.636586\pi$
$572$	−28.8187	−1.20497
$573$	19.8874	0.830809
$574$	1.72489	0.0719953
$575$	−1.35302	−0.0564249
$576$	13.8435	0.576814
$577$	29.6049	1.23247	0.616234	−	0.787563i	$-0.288658\pi$
$577$	29.6049	1.23247	0.616234	+	0.787563i	$0.288658\pi$
$578$	14.0625	0.584925
$579$	18.9032	0.785591
$580$	12.0601	0.500769
$581$	−0.842288	−0.0349440
$582$	109.413	4.53533
$583$	−5.29230	−0.219185
$584$	−81.3882	−3.36787
$585$	−101.573	−4.19953
$586$	69.1019	2.85457
$587$	33.3441	1.37626	0.688129	−	0.725589i	$-0.258432\pi$
$587$	33.3441	1.37626	0.688129	+	0.725589i	$0.258432\pi$
$588$	95.9162	3.95552
$589$	−40.6796	−1.67618
$590$	75.7554	3.11880
$591$	−2.39458	−0.0985000
$592$	45.8132	1.88291
$593$	−40.9256	−1.68061	−0.840306	−	0.542112i	$-0.817625\pi$
$593$	−40.9256	−1.68061	−0.840306	+	0.542112i	$0.817625\pi$
$594$	−21.4458	−0.879932
$595$	−1.30917	−0.0536707
$596$	111.402	4.56321
$597$	−32.8280	−1.34356
$598$	12.1815	0.498141
$599$	17.1208	0.699535	0.349767	−	0.936837i	$-0.386261\pi$
$599$	17.1208	0.699535	0.349767	+	0.936837i	$0.386261\pi$
$600$	37.3013	1.52282
$601$	47.4564	1.93579	0.967894	−	0.251357i	$-0.0808768\pi$
$601$	47.4564	1.93579	0.967894	+	0.251357i	$0.0808768\pi$
$602$	4.84107	0.197307
$603$	83.6855	3.40794
$604$	79.8130	3.24755
$605$	26.4291	1.07450
$606$	7.06472	0.286985
$607$	−22.9048	−0.929677	−0.464839	−	0.885395i	$-0.653888\pi$
$607$	−22.9048	−0.929677	−0.464839	+	0.885395i	$0.653888\pi$
$608$	−31.6119	−1.28203
$609$	−0.439468	−0.0178081
$610$	14.1677	0.573634
$611$	29.2345	1.18270
$612$	−92.5088	−3.73945
$613$	−10.8586	−0.438576	−0.219288	−	0.975660i	$-0.570373\pi$
$613$	−10.8586	−0.438576	−0.219288	+	0.975660i	$0.570373\pi$
$614$	2.92469	0.118031
$615$	35.7134	1.44010
$616$	−0.941045	−0.0379158
$617$	−19.6142	−0.789639	−0.394819	−	0.918759i	$-0.629193\pi$
$617$	−19.6142	−0.789639	−0.394819	+	0.918759i	$0.629193\pi$
$618$	154.463	6.21339
$619$	−27.1665	−1.09191	−0.545956	−	0.837814i	$-0.683834\pi$
$619$	−27.1665	−1.09191	−0.545956	+	0.837814i	$0.683834\pi$
$620$	110.442	4.43544
$621$	6.31885	0.253567
$622$	−62.1855	−2.49341
$623$	1.63833	0.0656383
$624$	−155.888	−6.24053
$625$	−30.8507	−1.23403
$626$	33.4370	1.33641
$627$	12.6933	0.506923
$628$	−91.4527	−3.64936
$629$	−19.5077	−0.777824
$630$	−5.86632	−0.233720
$631$	43.7800	1.74285	0.871427	−	0.490525i	$-0.163195\pi$
$631$	43.7800	1.74285	0.871427	+	0.490525i	$0.163195\pi$
$632$	60.3926	2.40229
$633$	26.1353	1.03879
$634$	54.3284	2.15766
$635$	−22.0778	−0.876129
$636$	−76.0343	−3.01495
$637$	−45.6793	−1.80988
$638$	−2.45814	−0.0973188
$639$	51.1290	2.02263
$640$	−21.5560	−0.852075
$641$	−7.50723	−0.296518	−0.148259	−	0.988949i	$-0.547367\pi$
$641$	−7.50723	−0.296518	−0.148259	+	0.988949i	$0.547367\pi$
$642$	−140.199	−5.53323
$643$	38.7240	1.52712	0.763562	−	0.645734i	$-0.223449\pi$
$643$	38.7240	1.52712	0.763562	+	0.645734i	$0.223449\pi$
$644$	0.490406	0.0193247
$645$	100.233	3.94668
$646$	38.7512	1.52465
$647$	−21.2113	−0.833903	−0.416952	−	0.908929i	$-0.636902\pi$
$647$	−21.2113	−0.833903	−0.416952	+	0.908929i	$0.636902\pi$
$648$	−55.4544	−2.17846
$649$	−10.7631	−0.422488
$650$	−31.4196	−1.23238
$651$	−4.02447	−0.157731
$652$	−57.6236	−2.25671
$653$	14.0327	0.549143	0.274571	−	0.961567i	$-0.411464\pi$
$653$	14.0327	0.549143	0.274571	+	0.961567i	$0.411464\pi$
$654$	13.4781	0.527034
$655$	10.4348	0.407720
$656$	36.3787	1.42035
$657$	72.0841	2.81227
$658$	1.68843	0.0658218
$659$	29.9621	1.16716	0.583579	−	0.812056i	$-0.301652\pi$
$659$	29.9621	1.16716	0.583579	+	0.812056i	$0.301652\pi$
$660$	−34.4613	−1.34140
$661$	−1.32319	−0.0514660	−0.0257330	−	0.999669i	$-0.508192\pi$
$661$	−1.32319	−0.0514660	−0.0257330	+	0.999669i	$0.508192\pi$
$662$	15.3127	0.595146
$663$	66.3789	2.57794
$664$	−38.2697	−1.48515
$665$	1.71291	0.0664238
$666$	−87.4131	−3.38719
$667$	0.724274	0.0280440
$668$	51.4332	1.99001
$669$	22.0952	0.854252
$670$	95.1717	3.67680
$671$	−2.01290	−0.0777072
$672$	−3.12739	−0.120642
$673$	−33.9477	−1.30859	−0.654294	−	0.756240i	$-0.727034\pi$
$673$	−33.9477	−1.30859	−0.654294	+	0.756240i	$0.727034\pi$
$674$	42.6814	1.64403
$675$	−16.2981	−0.627314
$676$	137.358	5.28298
$677$	26.5205	1.01927	0.509633	−	0.860392i	$-0.329781\pi$
$677$	26.5205	1.01927	0.509633	+	0.860392i	$0.329781\pi$
$678$	94.3122	3.62204
$679$	−2.09774	−0.0805038
$680$	−59.4827	−2.28106
$681$	39.4123	1.51028
$682$	−22.5107	−0.861979
$683$	−14.2163	−0.543970	−0.271985	−	0.962301i	$-0.587680\pi$
$683$	−14.2163	−0.543970	−0.271985	+	0.962301i	$0.587680\pi$
$684$	121.038	4.62801
$685$	37.1285	1.41861
$686$	−5.28457	−0.201766
$687$	83.2902	3.17772
$688$	102.100	3.89254
$689$	36.2107	1.37952
$690$	14.5667	0.554544
$691$	47.6736	1.81359	0.906795	−	0.421571i	$-0.138521\pi$
$691$	47.6736	1.81359	0.906795	+	0.421571i	$0.138521\pi$
$692$	42.3994	1.61178
$693$	0.833468	0.0316608
$694$	79.2459	3.00813
$695$	6.23608	0.236548
$696$	−19.9674	−0.756863
$697$	−15.4904	−0.586742
$698$	−50.7950	−1.92262
$699$	−20.0298	−0.757595
$700$	−1.26490	−0.0478086
$701$	−15.3680	−0.580442	−0.290221	−	0.956960i	$-0.593729\pi$
$701$	−15.3680	−0.580442	−0.290221	+	0.956960i	$0.593729\pi$
$702$	146.735	5.53817
$703$	25.5238	0.962649
$704$	−2.23680	−0.0843026
$705$	34.9586	1.31662
$706$	9.18311	0.345611
$707$	−0.135449	−0.00509409
$708$	−154.633	−5.81145
$709$	−20.1715	−0.757556	−0.378778	−	0.925488i	$-0.623656\pi$
$709$	−20.1715	−0.757556	−0.378778	+	0.925488i	$0.623656\pi$
$710$	58.1466	2.18220
$711$	−53.4887	−2.00598
$712$	74.4383	2.78969
$713$	6.63261	0.248393
$714$	3.83369	0.143472
$715$	16.4119	0.613771
$716$	90.8628	3.39570
$717$	38.3948	1.43388
$718$	96.5395	3.60282
$719$	−39.2500	−1.46378	−0.731890	−	0.681423i	$-0.761361\pi$
$719$	−39.2500	−1.46378	−0.731890	+	0.681423i	$0.761361\pi$
$720$	−123.724	−4.61091
$721$	−2.96145	−0.110290
$722$	−1.88313	−0.0700828
$723$	−42.6305	−1.58545
$724$	−66.8756	−2.48541
$725$	−1.86811	−0.0693797
$726$	−77.3933	−2.87234
$727$	−6.29286	−0.233389	−0.116695	−	0.993168i	$-0.537230\pi$
$727$	−6.29286	−0.233389	−0.116695	+	0.993168i	$0.537230\pi$
$728$	6.43877	0.238637
$729$	−29.0591	−1.07626
$730$	81.9780	3.03414
$731$	−43.4755	−1.60800
$732$	−28.9193	−1.06889
$733$	−42.7706	−1.57977	−0.789883	−	0.613257i	$-0.789859\pi$
$733$	−42.7706	−1.57977	−0.789883	+	0.613257i	$0.789859\pi$
$734$	70.8425	2.61485
$735$	−54.6233	−2.01481
$736$	5.15417	0.189985
$737$	−13.5217	−0.498078
$738$	−69.4118	−2.55508
$739$	−37.9285	−1.39522	−0.697611	−	0.716477i	$-0.745753\pi$
$739$	−37.9285	−1.39522	−0.697611	+	0.716477i	$0.745753\pi$
$740$	−69.2949	−2.54733
$741$	−86.8498	−3.19051
$742$	2.09134	0.0767754
$743$	9.21674	0.338130	0.169065	−	0.985605i	$-0.445925\pi$
$743$	9.21674	0.338130	0.169065	+	0.985605i	$0.445925\pi$
$744$	−182.854	−6.70374
$745$	−63.4424	−2.32435
$746$	−4.79225	−0.175457
$747$	33.8948	1.24015
$748$	14.9473	0.546529
$749$	2.68799	0.0982170
$750$	62.9890	2.30003
$751$	22.8195	0.832697	0.416348	−	0.909205i	$-0.363310\pi$
$751$	22.8195	0.832697	0.416348	+	0.909205i	$0.363310\pi$
$752$	35.6098	1.29856
$753$	−67.0317	−2.44277
$754$	16.8190	0.612511
$755$	−45.4527	−1.65419
$756$	5.90729	0.214846
$757$	11.6912	0.424925	0.212462	−	0.977169i	$-0.431852\pi$
$757$	11.6912	0.424925	0.212462	+	0.977169i	$0.431852\pi$
$758$	11.4951	0.417519
$759$	−2.06959	−0.0751212
$760$	77.8269	2.82308
$761$	16.3564	0.592919	0.296460	−	0.955045i	$-0.404194\pi$
$761$	16.3564	0.592919	0.296460	+	0.955045i	$0.404194\pi$
$762$	64.6511	2.34206
$763$	−0.258410	−0.00935506
$764$	−30.6411	−1.10856
$765$	52.6828	1.90475
$766$	−34.0724	−1.23109
$767$	73.6426	2.65908
$768$	77.0897	2.78173
$769$	−16.3468	−0.589481	−0.294740	−	0.955577i	$-0.595233\pi$
$769$	−16.3468	−0.589481	−0.294740	+	0.955577i	$0.595233\pi$
$770$	0.947865	0.0341587
$771$	−45.9506	−1.65487
$772$	−29.1248	−1.04822
$773$	31.6403	1.13802	0.569011	−	0.822330i	$-0.307326\pi$
$773$	31.6403	1.13802	0.569011	+	0.822330i	$0.307326\pi$
$774$	−194.811	−7.00235
$775$	−17.1074	−0.614515
$776$	−95.3117	−3.42149
$777$	2.52509	0.0905872
$778$	−82.7156	−2.96550
$779$	20.2676	0.726162
$780$	235.789	8.44262
$781$	−8.26128	−0.295612
$782$	−6.31819	−0.225938
$783$	8.72439	0.311784
$784$	−55.6408	−1.98717
$785$	52.0814	1.85886
$786$	−30.5565	−1.08991
$787$	−22.9720	−0.818864	−0.409432	−	0.912341i	$-0.634273\pi$
$787$	−22.9720	−0.818864	−0.409432	+	0.912341i	$0.634273\pi$
$788$	3.68940	0.131430
$789$	12.0926	0.430509
$790$	−60.8303	−2.16424
$791$	−1.80821	−0.0642926
$792$	37.8690	1.34562
$793$	13.7726	0.489078
$794$	79.6486	2.82662
$795$	43.3007	1.53572
$796$	50.5791	1.79273
$797$	27.9453	0.989874	0.494937	−	0.868929i	$-0.335191\pi$
$797$	27.9453	0.989874	0.494937	+	0.868929i	$0.335191\pi$
$798$	−5.01598	−0.177564
$799$	−15.1630	−0.536430
$800$	−13.2940	−0.470015
$801$	−65.9287	−2.32948
$802$	2.18958	0.0773167
$803$	−11.6472	−0.411019
$804$	−194.265	−6.85121
$805$	−0.279281	−0.00984338
$806$	154.021	5.42518
$807$	82.3641	2.89935
$808$	−6.15419	−0.216504
$809$	11.3927	0.400547	0.200274	−	0.979740i	$-0.435817\pi$
$809$	11.3927	0.400547	0.200274	+	0.979740i	$0.435817\pi$
$810$	55.8563	1.96259
$811$	−17.5547	−0.616428	−0.308214	−	0.951317i	$-0.599731\pi$
$811$	−17.5547	−0.616428	−0.308214	+	0.951317i	$0.599731\pi$
$812$	0.677101	0.0237616
$813$	−67.7766	−2.37703
$814$	14.1240	0.495045
$815$	32.8160	1.14950
$816$	80.8544	2.83047
$817$	56.8831	1.99009
$818$	−34.9181	−1.22088
$819$	−5.70271	−0.199269
$820$	−55.0247	−1.92155
$821$	40.8635	1.42615	0.713073	−	0.701090i	$-0.247303\pi$
$821$	40.8635	1.42615	0.713073	+	0.701090i	$0.247303\pi$
$822$	−108.725	−3.79221
$823$	−2.96214	−0.103254	−0.0516268	−	0.998666i	$-0.516441\pi$
$823$	−2.96214	−0.103254	−0.0516268	+	0.998666i	$0.516441\pi$
$824$	−134.555	−4.68744
$825$	5.33805	0.185847
$826$	4.25320	0.147988
$827$	29.3037	1.01899	0.509495	−	0.860473i	$-0.329832\pi$
$827$	29.3037	1.01899	0.509495	+	0.860473i	$0.329832\pi$
$828$	−19.7346	−0.685826
$829$	−8.17309	−0.283863	−0.141932	−	0.989876i	$-0.545331\pi$
$829$	−8.17309	−0.283863	−0.141932	+	0.989876i	$0.545331\pi$
$830$	38.5471	1.33799
$831$	−2.98680	−0.103611
$832$	15.3045	0.530589
$833$	23.6924	0.820894
$834$	−18.2613	−0.632339
$835$	−29.2907	−1.01365
$836$	−19.5570	−0.676393
$837$	79.8945	2.76156
$838$	70.3311	2.42955
$839$	11.2595	0.388719	0.194360	−	0.980930i	$-0.437737\pi$
$839$	11.2595	0.388719	0.194360	+	0.980930i	$0.437737\pi$
$840$	7.69948	0.265657
$841$	1.00000	0.0344828
$842$	13.3260	0.459244
$843$	0.728351	0.0250857
$844$	−40.2674	−1.38606
$845$	−78.2237	−2.69098
$846$	−67.9448	−2.33599
$847$	1.48383	0.0509851
$848$	44.1073	1.51465
$849$	−96.4470	−3.31005
$850$	16.2964	0.558961
$851$	−4.16153	−0.142655
$852$	−118.689	−4.06623
$853$	−30.1170	−1.03119	−0.515593	−	0.856833i	$-0.672428\pi$
$853$	−30.1170	−1.03119	−0.515593	+	0.856833i	$0.672428\pi$
$854$	0.795429	0.0272190
$855$	−68.9299	−2.35735
$856$	122.130	4.17432
$857$	9.70981	0.331681	0.165840	−	0.986153i	$-0.446966\pi$
$857$	9.70981	0.331681	0.165840	+	0.986153i	$0.446966\pi$
$858$	−48.0596	−1.64073
$859$	36.5255	1.24623	0.623117	−	0.782128i	$-0.285866\pi$
$859$	36.5255	1.24623	0.623117	+	0.782128i	$0.285866\pi$
$860$	−154.432	−5.26610
$861$	2.00509	0.0683333
$862$	−79.0194	−2.69141
$863$	21.6837	0.738122	0.369061	−	0.929405i	$-0.379679\pi$
$863$	21.6837	0.738122	0.369061	+	0.929405i	$0.379679\pi$
$864$	62.0856	2.11219
$865$	−24.1460	−0.820990
$866$	17.0841	0.580542
$867$	16.3470	0.555172
$868$	6.20062	0.210463
$869$	8.64256	0.293179
$870$	20.1121	0.681865
$871$	92.5174	3.13483
$872$	−11.7410	−0.397599
$873$	84.4160	2.85705
$874$	8.26668	0.279625
$875$	−1.20766	−0.0408265
$876$	−167.334	−5.65370
$877$	37.4889	1.26591	0.632956	−	0.774188i	$-0.281841\pi$
$877$	37.4889	1.26591	0.632956	+	0.774188i	$0.281841\pi$
$878$	32.9465	1.11189
$879$	80.3273	2.70937
$880$	19.9909	0.673894
$881$	16.7689	0.564959	0.282479	−	0.959273i	$-0.408843\pi$
$881$	16.7689	0.564959	0.282479	+	0.959273i	$0.408843\pi$
$882$	106.165	3.57475
$883$	15.6382	0.526266	0.263133	−	0.964760i	$-0.415244\pi$
$883$	15.6382	0.526266	0.263133	+	0.964760i	$0.415244\pi$
$884$	−102.272	−3.43978
$885$	88.0617	2.96016
$886$	−67.0052	−2.25109
$887$	−5.73067	−0.192417	−0.0962086	−	0.995361i	$-0.530672\pi$
$887$	−5.73067	−0.192417	−0.0962086	+	0.995361i	$0.530672\pi$
$888$	114.729	3.85004
$889$	−1.23953	−0.0415725
$890$	−74.9777	−2.51326
$891$	−7.93588	−0.265862
$892$	−34.0428	−1.13984
$893$	19.8392	0.663895
$894$	185.781	6.21344
$895$	−51.7454	−1.72966
$896$	−1.21024	−0.0404311
$897$	14.1604	0.472802
$898$	17.6519	0.589050
$899$	9.15760	0.305423
$900$	50.9012	1.69671
$901$	−18.7814	−0.625698
$902$	11.2154	0.373431
$903$	5.62749	0.187271
$904$	−82.1569	−2.73250
$905$	38.0850	1.26599
$906$	133.101	4.42197
$907$	3.50277	0.116307	0.0581537	−	0.998308i	$-0.481479\pi$
$907$	3.50277	0.116307	0.0581537	+	0.998308i	$0.481479\pi$
$908$	−60.7237	−2.01519
$909$	5.45066	0.180787
$910$	−6.48543	−0.214990
$911$	−26.4058	−0.874864	−0.437432	−	0.899251i	$-0.644112\pi$
$911$	−26.4058	−0.874864	−0.437432	+	0.899251i	$0.644112\pi$
$912$	−105.789	−3.50304
$913$	−5.47664	−0.181250
$914$	−54.4758	−1.80190
$915$	16.4692	0.544455
$916$	−128.328	−4.24006
$917$	0.585848	0.0193464
$918$	−76.1071	−2.51191
$919$	6.85308	0.226062	0.113031	−	0.993591i	$-0.463944\pi$
$919$	6.85308	0.226062	0.113031	+	0.993591i	$0.463944\pi$
$920$	−12.6893	−0.418353
$921$	3.39980	0.112027
$922$	1.45691	0.0479808
$923$	56.5249	1.86054
$924$	−1.93479	−0.0636500
$925$	10.7338	0.352924
$926$	−59.7424	−1.96326
$927$	119.173	3.91415
$928$	7.11632	0.233605
$929$	−42.3234	−1.38859	−0.694293	−	0.719692i	$-0.744283\pi$
$929$	−42.3234	−1.38859	−0.694293	+	0.719692i	$0.744283\pi$
$930$	184.179	6.03946
$931$	−30.9990	−1.01595
$932$	30.8604	1.01087
$933$	−72.2874	−2.36658
$934$	11.7645	0.384948
$935$	−8.51235	−0.278384
$936$	−259.105	−8.46912
$937$	32.7766	1.07077	0.535383	−	0.844610i	$-0.320167\pi$
$937$	32.7766	1.07077	0.535383	+	0.844610i	$0.320167\pi$
$938$	5.34331	0.174465
$939$	38.8687	1.26843
$940$	−53.8618	−1.75678
$941$	4.71363	0.153660	0.0768299	−	0.997044i	$-0.475520\pi$
$941$	4.71363	0.153660	0.0768299	+	0.997044i	$0.475520\pi$
$942$	−152.512	−4.96910
$943$	−3.30453	−0.107610
$944$	89.7021	2.91955
$945$	−3.36414	−0.109436
$946$	31.4771	1.02341
$947$	27.8665	0.905540	0.452770	−	0.891627i	$-0.350436\pi$
$947$	27.8665	0.905540	0.452770	+	0.891627i	$0.350436\pi$
$948$	124.167	4.03277
$949$	79.6916	2.58690
$950$	−21.3221	−0.691780
$951$	63.1539	2.04791
$952$	−3.33959	−0.108237
$953$	−15.5945	−0.505154	−0.252577	−	0.967577i	$-0.581278\pi$
$953$	−15.5945	−0.505154	−0.252577	+	0.967577i	$0.581278\pi$
$954$	−84.1583	−2.72473
$955$	17.4498	0.564663
$956$	−59.1560	−1.91324
$957$	−2.85746	−0.0923687
$958$	20.5740	0.664714
$959$	2.08454	0.0673133
$960$	18.3011	0.590666
$961$	52.8616	1.70521
$962$	−96.6384	−3.11575
$963$	−108.168	−3.48568
$964$	65.6821	2.11548
$965$	16.5863	0.533930
$966$	0.817829	0.0263132
$967$	−28.0360	−0.901577	−0.450789	−	0.892631i	$-0.648857\pi$
$967$	−28.0360	−0.901577	−0.450789	+	0.892631i	$0.648857\pi$
$968$	67.4186	2.16692
$969$	45.0462	1.44709
$970$	96.0024	3.08245
$971$	−14.8304	−0.475932	−0.237966	−	0.971274i	$-0.576481\pi$
$971$	−14.8304	−0.475932	−0.237966	+	0.971274i	$0.576481\pi$
$972$	6.43071	0.206265
$973$	0.350118	0.0112243
$974$	29.8398	0.956127
$975$	−36.5237	−1.16969
$976$	16.7760	0.536987
$977$	−36.2276	−1.15902	−0.579512	−	0.814964i	$-0.696757\pi$
$977$	−36.2276	−1.15902	−0.579512	+	0.814964i	$0.696757\pi$
$978$	−96.0963	−3.07282
$979$	10.6526	0.340458
$980$	84.1597	2.68838
$981$	10.3988	0.332007
$982$	−51.3223	−1.63776
$983$	40.4111	1.28891	0.644456	−	0.764641i	$-0.277084\pi$
$983$	40.4111	1.28891	0.644456	+	0.764641i	$0.277084\pi$
$984$	91.1021	2.90423
$985$	−2.10108	−0.0669459
$986$	−8.72348	−0.277812
$987$	1.96271	0.0624738
$988$	133.812	4.25713
$989$	−9.27449	−0.294912
$990$	−38.1434	−1.21228
$991$	39.6706	1.26018	0.630089	−	0.776523i	$-0.283018\pi$
$991$	39.6706	1.26018	0.630089	+	0.776523i	$0.283018\pi$
$992$	65.1684	2.06910
$993$	17.8002	0.564873
$994$	3.26458	0.103546
$995$	−28.8043	−0.913156
$996$	−78.6826	−2.49316
$997$	−5.61798	−0.177923	−0.0889617	−	0.996035i	$-0.528355\pi$
$997$	−5.61798	−0.177923	−0.0889617	+	0.996035i	$0.528355\pi$
$998$	−4.20797	−0.133201
$999$	−50.1286	−1.58600

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.e.1.12	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.e.1.12	✓	169	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.56941 q^{2} -2.98680 q^{3} +4.60185 q^{4} -2.62071 q^{5} +7.67431 q^{6} -0.147137 q^{7} -6.68522 q^{8} +5.92098 q^{9} +O(q^{10})\)	\(q-2.56941 q^{2} -2.98680 q^{3} +4.60185 q^{4} -2.62071 q^{5} +7.67431 q^{6} -0.147137 q^{7} -6.68522 q^{8} +5.92098 q^{9} +6.73366 q^{10} -0.956697 q^{11} -13.7448 q^{12} +6.54586 q^{13} +0.378054 q^{14} +7.82753 q^{15} +7.97334 q^{16} -3.39513 q^{17} -15.2134 q^{18} +4.44217 q^{19} -12.0601 q^{20} +0.439468 q^{21} +2.45814 q^{22} -0.724274 q^{23} +19.9674 q^{24} +1.86811 q^{25} -16.8190 q^{26} -8.72439 q^{27} -0.677101 q^{28} -1.00000 q^{29} -20.1121 q^{30} -9.15760 q^{31} -7.11632 q^{32} +2.85746 q^{33} +8.72348 q^{34} +0.385602 q^{35} +27.2475 q^{36} +5.74579 q^{37} -11.4138 q^{38} -19.5512 q^{39} +17.5200 q^{40} +4.56254 q^{41} -1.12917 q^{42} +12.8052 q^{43} -4.40258 q^{44} -15.5172 q^{45} +1.86095 q^{46} +4.46611 q^{47} -23.8148 q^{48} -6.97835 q^{49} -4.79993 q^{50} +10.1406 q^{51} +30.1231 q^{52} +5.53185 q^{53} +22.4165 q^{54} +2.50722 q^{55} +0.983640 q^{56} -13.2679 q^{57} +2.56941 q^{58} +11.2503 q^{59} +36.0211 q^{60} +2.10401 q^{61} +23.5296 q^{62} -0.871193 q^{63} +2.33805 q^{64} -17.1548 q^{65} -7.34199 q^{66} +14.1337 q^{67} -15.6239 q^{68} +2.16326 q^{69} -0.990768 q^{70} +8.63522 q^{71} -39.5831 q^{72} +12.1743 q^{73} -14.7633 q^{74} -5.57966 q^{75} +20.4422 q^{76} +0.140765 q^{77} +50.2350 q^{78} -9.03376 q^{79} -20.8958 q^{80} +8.29508 q^{81} -11.7230 q^{82} +5.72453 q^{83} +2.02237 q^{84} +8.89765 q^{85} -32.9019 q^{86} +2.98680 q^{87} +6.39573 q^{88} -11.1348 q^{89} +39.8699 q^{90} -0.963136 q^{91} -3.33300 q^{92} +27.3519 q^{93} -11.4753 q^{94} -11.6416 q^{95} +21.2550 q^{96} +14.2571 q^{97} +17.9302 q^{98} -5.66458 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * q^99

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