LMFDB - Embedded newform 6034.2.a.k.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 32 x^{18} + 106 x^{17} + 382 x^{16} - 1495 x^{15} - 1963 x^{14} + 10784 x^{13} + \cdots - 44 $ x^20 - 3x^19 - 32x^18 + 106x^17 + 382x^16 - 1495x^15 - 1963x^14 + 10784x^13 + 2170x^12 - 42069x^11 + 19553x^10 + 84697x^9 - 82713x^8 - 68589x^7 + 118845x^6 - 10051x^5 - 53572x^4 + 25598x^3 - 557x^2 - 1040*x - 44
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.937572$ of defining polynomial
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.937572 q^{3} +1.00000 q^{4} +2.71354 q^{5} +0.937572 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.12096 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.937572 q^{3} +1.00000 q^{4} +2.71354 q^{5} +0.937572 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.12096 q^{9} -2.71354 q^{10} +1.93191 q^{11} -0.937572 q^{12} -3.51810 q^{13} -1.00000 q^{14} -2.54414 q^{15} +1.00000 q^{16} -5.52882 q^{17} +2.12096 q^{18} -4.16316 q^{19} +2.71354 q^{20} -0.937572 q^{21} -1.93191 q^{22} +4.00961 q^{23} +0.937572 q^{24} +2.36332 q^{25} +3.51810 q^{26} +4.80127 q^{27} +1.00000 q^{28} -1.55674 q^{29} +2.54414 q^{30} +3.24079 q^{31} -1.00000 q^{32} -1.81130 q^{33} +5.52882 q^{34} +2.71354 q^{35} -2.12096 q^{36} +3.87327 q^{37} +4.16316 q^{38} +3.29847 q^{39} -2.71354 q^{40} +4.24933 q^{41} +0.937572 q^{42} +8.67972 q^{43} +1.93191 q^{44} -5.75532 q^{45} -4.00961 q^{46} +4.13792 q^{47} -0.937572 q^{48} +1.00000 q^{49} -2.36332 q^{50} +5.18366 q^{51} -3.51810 q^{52} -8.52441 q^{53} -4.80127 q^{54} +5.24231 q^{55} -1.00000 q^{56} +3.90326 q^{57} +1.55674 q^{58} +1.76282 q^{59} -2.54414 q^{60} -7.65899 q^{61} -3.24079 q^{62} -2.12096 q^{63} +1.00000 q^{64} -9.54652 q^{65} +1.81130 q^{66} -8.75999 q^{67} -5.52882 q^{68} -3.75929 q^{69} -2.71354 q^{70} -13.2196 q^{71} +2.12096 q^{72} +11.6292 q^{73} -3.87327 q^{74} -2.21578 q^{75} -4.16316 q^{76} +1.93191 q^{77} -3.29847 q^{78} +3.70481 q^{79} +2.71354 q^{80} +1.86135 q^{81} -4.24933 q^{82} +1.50563 q^{83} -0.937572 q^{84} -15.0027 q^{85} -8.67972 q^{86} +1.45956 q^{87} -1.93191 q^{88} -4.81379 q^{89} +5.75532 q^{90} -3.51810 q^{91} +4.00961 q^{92} -3.03847 q^{93} -4.13792 q^{94} -11.2969 q^{95} +0.937572 q^{96} -17.7786 q^{97} -1.00000 q^{98} -4.09749 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) $ 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9} + 3 q^{10} - 8 q^{11} + 3 q^{12} - 4 q^{13} - 20 q^{14} - 25 q^{15} + 20 q^{16} + 9 q^{17} - 13 q^{18} - 14 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} - 23 q^{23} - 3 q^{24} + 31 q^{25} + 4 q^{26} - 21 q^{27} + 20 q^{28} - 48 q^{29} + 25 q^{30} - q^{31} - 20 q^{32} - 29 q^{33} - 9 q^{34} - 3 q^{35} + 13 q^{36} - q^{37} + 14 q^{38} - q^{39} + 3 q^{40} - 27 q^{41} - 3 q^{42} - 3 q^{43} - 8 q^{44} - 12 q^{45} + 23 q^{46} - 26 q^{47} + 3 q^{48} + 20 q^{49} - 31 q^{50} - 17 q^{51} - 4 q^{52} - 43 q^{53} + 21 q^{54} - 16 q^{55} - 20 q^{56} - 25 q^{57} + 48 q^{58} - 19 q^{59} - 25 q^{60} + 9 q^{61} + q^{62} + 13 q^{63} + 20 q^{64} - 87 q^{65} + 29 q^{66} + 32 q^{67} + 9 q^{68} - 23 q^{69} + 3 q^{70} - 63 q^{71} - 13 q^{72} + 2 q^{73} + q^{74} - 8 q^{75} - 14 q^{76} - 8 q^{77} + q^{78} - 51 q^{79} - 3 q^{80} + 4 q^{81} + 27 q^{82} - 24 q^{83} + 3 q^{84} + 31 q^{85} + 3 q^{86} - 33 q^{87} + 8 q^{88} - 35 q^{89} + 12 q^{90} - 4 q^{91} - 23 q^{92} + 17 q^{93} + 26 q^{94} - 30 q^{95} - 3 q^{96} + 5 q^{97} - 20 q^{98} - 31 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9 + 3 * q^10 - 8 * q^11 + 3 * q^12 - 4 * q^13 - 20 * q^14 - 25 * q^15 + 20 * q^16 + 9 * q^17 - 13 * q^18 - 14 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 - 23 * q^23 - 3 * q^24 + 31 * q^25 + 4 * q^26 - 21 * q^27 + 20 * q^28 - 48 * q^29 + 25 * q^30 - q^31 - 20 * q^32 - 29 * q^33 - 9 * q^34 - 3 * q^35 + 13 * q^36 - q^37 + 14 * q^38 - q^39 + 3 * q^40 - 27 * q^41 - 3 * q^42 - 3 * q^43 - 8 * q^44 - 12 * q^45 + 23 * q^46 - 26 * q^47 + 3 * q^48 + 20 * q^49 - 31 * q^50 - 17 * q^51 - 4 * q^52 - 43 * q^53 + 21 * q^54 - 16 * q^55 - 20 * q^56 - 25 * q^57 + 48 * q^58 - 19 * q^59 - 25 * q^60 + 9 * q^61 + q^62 + 13 * q^63 + 20 * q^64 - 87 * q^65 + 29 * q^66 + 32 * q^67 + 9 * q^68 - 23 * q^69 + 3 * q^70 - 63 * q^71 - 13 * q^72 + 2 * q^73 + q^74 - 8 * q^75 - 14 * q^76 - 8 * q^77 + q^78 - 51 * q^79 - 3 * q^80 + 4 * q^81 + 27 * q^82 - 24 * q^83 + 3 * q^84 + 31 * q^85 + 3 * q^86 - 33 * q^87 + 8 * q^88 - 35 * q^89 + 12 * q^90 - 4 * q^91 - 23 * q^92 + 17 * q^93 + 26 * q^94 - 30 * q^95 - 3 * q^96 + 5 * q^97 - 20 * q^98 - 31 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.937572	−0.541307	−0.270654	−	0.962677i	$-0.587240\pi$
$3$	−0.937572	−0.541307	−0.270654	+	0.962677i	$0.587240\pi$
$4$	1.00000	0.500000
$5$	2.71354	1.21353	0.606767	−	0.794880i	$-0.292466\pi$
$5$	2.71354	1.21353	0.606767	+	0.794880i	$0.292466\pi$
$6$	0.937572	0.382762
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.12096	−0.706986
$10$	−2.71354	−0.858098
$11$	1.93191	0.582492	0.291246	−	0.956648i	$-0.405930\pi$
$11$	1.93191	0.582492	0.291246	+	0.956648i	$0.405930\pi$
$12$	−0.937572	−0.270654
$13$	−3.51810	−0.975746	−0.487873	−	0.872915i	$-0.662227\pi$
$13$	−3.51810	−0.975746	−0.487873	+	0.872915i	$0.662227\pi$
$14$	−1.00000	−0.267261
$15$	−2.54414	−0.656894
$16$	1.00000	0.250000
$17$	−5.52882	−1.34093	−0.670467	−	0.741939i	$-0.733906\pi$
$17$	−5.52882	−1.34093	−0.670467	+	0.741939i	$0.733906\pi$
$18$	2.12096	0.499915
$19$	−4.16316	−0.955095	−0.477548	−	0.878606i	$-0.658474\pi$
$19$	−4.16316	−0.955095	−0.477548	+	0.878606i	$0.658474\pi$
$20$	2.71354	0.606767
$21$	−0.937572	−0.204595
$22$	−1.93191	−0.411884
$23$	4.00961	0.836061	0.418030	−	0.908433i	$-0.362721\pi$
$23$	4.00961	0.836061	0.418030	+	0.908433i	$0.362721\pi$
$24$	0.937572	0.191381
$25$	2.36332	0.472664
$26$	3.51810	0.689957
$27$	4.80127	0.924004
$28$	1.00000	0.188982
$29$	−1.55674	−0.289080	−0.144540	−	0.989499i	$-0.546170\pi$
$29$	−1.55674	−0.289080	−0.144540	+	0.989499i	$0.546170\pi$
$30$	2.54414	0.464495
$31$	3.24079	0.582063	0.291031	−	0.956714i	$-0.406002\pi$
$31$	3.24079	0.582063	0.291031	+	0.956714i	$0.406002\pi$
$32$	−1.00000	−0.176777
$33$	−1.81130	−0.315307
$34$	5.52882	0.948184
$35$	2.71354	0.458673
$36$	−2.12096	−0.353493
$37$	3.87327	0.636762	0.318381	−	0.947963i	$-0.396861\pi$
$37$	3.87327	0.636762	0.318381	+	0.947963i	$0.396861\pi$
$38$	4.16316	0.675354
$39$	3.29847	0.528178
$40$	−2.71354	−0.429049
$41$	4.24933	0.663634	0.331817	−	0.943344i	$-0.392338\pi$
$41$	4.24933	0.663634	0.331817	+	0.943344i	$0.392338\pi$
$42$	0.937572	0.144670
$43$	8.67972	1.32365	0.661823	−	0.749660i	$-0.269783\pi$
$43$	8.67972	1.32365	0.661823	+	0.749660i	$0.269783\pi$
$44$	1.93191	0.291246
$45$	−5.75532	−0.857952
$46$	−4.00961	−0.591184
$47$	4.13792	0.603578	0.301789	−	0.953375i	$-0.402416\pi$
$47$	4.13792	0.603578	0.301789	+	0.953375i	$0.402416\pi$
$48$	−0.937572	−0.135327
$49$	1.00000	0.142857
$50$	−2.36332	−0.334224
$51$	5.18366	0.725858
$52$	−3.51810	−0.487873
$53$	−8.52441	−1.17092	−0.585459	−	0.810702i	$-0.699086\pi$
$53$	−8.52441	−1.17092	−0.585459	+	0.810702i	$0.699086\pi$
$54$	−4.80127	−0.653370
$55$	5.24231	0.706873
$56$	−1.00000	−0.133631
$57$	3.90326	0.517000
$58$	1.55674	0.204410
$59$	1.76282	0.229499	0.114750	−	0.993394i	$-0.463393\pi$
$59$	1.76282	0.229499	0.114750	+	0.993394i	$0.463393\pi$
$60$	−2.54414	−0.328447
$61$	−7.65899	−0.980633	−0.490317	−	0.871544i	$-0.663119\pi$
$61$	−7.65899	−0.980633	−0.490317	+	0.871544i	$0.663119\pi$
$62$	−3.24079	−0.411580
$63$	−2.12096	−0.267216
$64$	1.00000	0.125000
$65$	−9.54652	−1.18410
$66$	1.81130	0.222956
$67$	−8.75999	−1.07020	−0.535102	−	0.844788i	$-0.679727\pi$
$67$	−8.75999	−1.07020	−0.535102	+	0.844788i	$0.679727\pi$
$68$	−5.52882	−0.670467
$69$	−3.75929	−0.452566
$70$	−2.71354	−0.324330
$71$	−13.2196	−1.56888	−0.784442	−	0.620202i	$-0.787050\pi$
$71$	−13.2196	−1.56888	−0.784442	+	0.620202i	$0.787050\pi$
$72$	2.12096	0.249957
$73$	11.6292	1.36110	0.680549	−	0.732702i	$-0.261741\pi$
$73$	11.6292	1.36110	0.680549	+	0.732702i	$0.261741\pi$
$74$	−3.87327	−0.450259
$75$	−2.21578	−0.255856
$76$	−4.16316	−0.477548
$77$	1.93191	0.220161
$78$	−3.29847	−0.373479
$79$	3.70481	0.416824	0.208412	−	0.978041i	$-0.433171\pi$
$79$	3.70481	0.416824	0.208412	+	0.978041i	$0.433171\pi$
$80$	2.71354	0.303383
$81$	1.86135	0.206816
$82$	−4.24933	−0.469260
$83$	1.50563	0.165265	0.0826323	−	0.996580i	$-0.473667\pi$
$83$	1.50563	0.165265	0.0826323	+	0.996580i	$0.473667\pi$
$84$	−0.937572	−0.102297
$85$	−15.0027	−1.62727
$86$	−8.67972	−0.935959
$87$	1.45956	0.156481
$88$	−1.93191	−0.205942
$89$	−4.81379	−0.510261	−0.255130	−	0.966907i	$-0.582118\pi$
$89$	−4.81379	−0.510261	−0.255130	+	0.966907i	$0.582118\pi$
$90$	5.75532	0.606663
$91$	−3.51810	−0.368797
$92$	4.00961	0.418030
$93$	−3.03847	−0.315075
$94$	−4.13792	−0.426794
$95$	−11.2969	−1.15904
$96$	0.937572	0.0956905
$97$	−17.7786	−1.80514	−0.902570	−	0.430543i	$-0.858322\pi$
$97$	−17.7786	−1.80514	−0.902570	+	0.430543i	$0.858322\pi$
$98$	−1.00000	−0.101015
$99$	−4.09749	−0.411814
$100$	2.36332	0.236332
$101$	18.1915	1.81012	0.905059	−	0.425285i	$-0.139826\pi$
$101$	18.1915	1.81012	0.905059	+	0.425285i	$0.139826\pi$
$102$	−5.18366	−0.513259
$103$	−14.5968	−1.43827	−0.719133	−	0.694873i	$-0.755461\pi$
$103$	−14.5968	−1.43827	−0.719133	+	0.694873i	$0.755461\pi$
$104$	3.51810	0.344978
$105$	−2.54414	−0.248283
$106$	8.52441	0.827964
$107$	−7.73093	−0.747377	−0.373689	−	0.927554i	$-0.621907\pi$
$107$	−7.73093	−0.747377	−0.373689	+	0.927554i	$0.621907\pi$
$108$	4.80127	0.462002
$109$	−15.7711	−1.51060	−0.755298	−	0.655382i	$-0.772508\pi$
$109$	−15.7711	−1.51060	−0.755298	+	0.655382i	$0.772508\pi$
$110$	−5.24231	−0.499835
$111$	−3.63147	−0.344684
$112$	1.00000	0.0944911
$113$	12.4041	1.16688	0.583441	−	0.812156i	$-0.301706\pi$
$113$	12.4041	1.16688	0.583441	+	0.812156i	$0.301706\pi$
$114$	−3.90326	−0.365574
$115$	10.8802	1.01459
$116$	−1.55674	−0.144540
$117$	7.46175	0.689839
$118$	−1.76282	−0.162281
$119$	−5.52882	−0.506826
$120$	2.54414	0.232247
$121$	−7.26774	−0.660703
$122$	7.65899	0.693413
$123$	−3.98405	−0.359230
$124$	3.24079	0.291031
$125$	−7.15475	−0.639940
$126$	2.12096	0.188950
$127$	−8.77218	−0.778405	−0.389203	−	0.921152i	$-0.627249\pi$
$127$	−8.77218	−0.778405	−0.389203	+	0.921152i	$0.627249\pi$
$128$	−1.00000	−0.0883883
$129$	−8.13786	−0.716499
$130$	9.54652	0.837285
$131$	−7.68112	−0.671103	−0.335551	−	0.942022i	$-0.608923\pi$
$131$	−7.68112	−0.671103	−0.335551	+	0.942022i	$0.608923\pi$
$132$	−1.81130	−0.157653
$133$	−4.16316	−0.360992
$134$	8.75999	0.756748
$135$	13.0284	1.12131
$136$	5.52882	0.474092
$137$	−3.75367	−0.320698	−0.160349	−	0.987060i	$-0.551262\pi$
$137$	−3.75367	−0.320698	−0.160349	+	0.987060i	$0.551262\pi$
$138$	3.75929	0.320012
$139$	21.2693	1.80404	0.902019	−	0.431697i	$-0.142085\pi$
$139$	21.2693	1.80404	0.902019	+	0.431697i	$0.142085\pi$
$140$	2.71354	0.229336
$141$	−3.87960	−0.326721
$142$	13.2196	1.10937
$143$	−6.79664	−0.568364
$144$	−2.12096	−0.176747
$145$	−4.22429	−0.350808
$146$	−11.6292	−0.962442
$147$	−0.937572	−0.0773296
$148$	3.87327	0.318381
$149$	−9.08568	−0.744328	−0.372164	−	0.928167i	$-0.621384\pi$
$149$	−9.08568	−0.744328	−0.372164	+	0.928167i	$0.621384\pi$
$150$	2.21578	0.180918
$151$	−13.7078	−1.11553	−0.557764	−	0.829999i	$-0.688341\pi$
$151$	−13.7078	−1.11553	−0.557764	+	0.829999i	$0.688341\pi$
$152$	4.16316	0.337677
$153$	11.7264	0.948023
$154$	−1.93191	−0.155677
$155$	8.79402	0.706352
$156$	3.29847	0.264089
$157$	−11.9617	−0.954644	−0.477322	−	0.878729i	$-0.658392\pi$
$157$	−11.9617	−0.954644	−0.477322	+	0.878729i	$0.658392\pi$
$158$	−3.70481	−0.294739
$159$	7.99224	0.633826
$160$	−2.71354	−0.214524
$161$	4.00961	0.316001
$162$	−1.86135	−0.146241
$163$	6.38239	0.499907	0.249954	−	0.968258i	$-0.419585\pi$
$163$	6.38239	0.499907	0.249954	+	0.968258i	$0.419585\pi$
$164$	4.24933	0.331817
$165$	−4.91504	−0.382636
$166$	−1.50563	−0.116860
$167$	−0.890693	−0.0689239	−0.0344619	−	0.999406i	$-0.510972\pi$
$167$	−0.890693	−0.0689239	−0.0344619	+	0.999406i	$0.510972\pi$
$168$	0.937572	0.0723352
$169$	−0.622957	−0.0479198
$170$	15.0027	1.15065
$171$	8.82990	0.675239
$172$	8.67972	0.661823
$173$	0.157652	0.0119860	0.00599301	−	0.999982i	$-0.498092\pi$
$173$	0.157652	0.0119860	0.00599301	+	0.999982i	$0.498092\pi$
$174$	−1.45956	−0.110649
$175$	2.36332	0.178650
$176$	1.93191	0.145623
$177$	−1.65277	−0.124230
$178$	4.81379	0.360809
$179$	−0.844759	−0.0631402	−0.0315701	−	0.999502i	$-0.510051\pi$
$179$	−0.844759	−0.0631402	−0.0315701	+	0.999502i	$0.510051\pi$
$180$	−5.75532	−0.428976
$181$	3.97878	0.295740	0.147870	−	0.989007i	$-0.452758\pi$
$181$	3.97878	0.295740	0.147870	+	0.989007i	$0.452758\pi$
$182$	3.51810	0.260779
$183$	7.18085	0.530824
$184$	−4.00961	−0.295592
$185$	10.5103	0.772733
$186$	3.03847	0.222791
$187$	−10.6812	−0.781083
$188$	4.13792	0.301789
$189$	4.80127	0.349241
$190$	11.2969	0.819565
$191$	−12.9200	−0.934862	−0.467431	−	0.884030i	$-0.654820\pi$
$191$	−12.9200	−0.934862	−0.467431	+	0.884030i	$0.654820\pi$
$192$	−0.937572	−0.0676634
$193$	−17.8763	−1.28677	−0.643384	−	0.765544i	$-0.722470\pi$
$193$	−17.8763	−1.28677	−0.643384	+	0.765544i	$0.722470\pi$
$194$	17.7786	1.27643
$195$	8.95055	0.640962
$196$	1.00000	0.0714286
$197$	9.75917	0.695312	0.347656	−	0.937622i	$-0.386978\pi$
$197$	9.75917	0.695312	0.347656	+	0.937622i	$0.386978\pi$
$198$	4.09749	0.291196
$199$	−5.69297	−0.403564	−0.201782	−	0.979430i	$-0.564673\pi$
$199$	−5.69297	−0.403564	−0.201782	+	0.979430i	$0.564673\pi$
$200$	−2.36332	−0.167112
$201$	8.21312	0.579309
$202$	−18.1915	−1.27995
$203$	−1.55674	−0.109262
$204$	5.18366	0.362929
$205$	11.5307	0.805342
$206$	14.5968	1.01701
$207$	−8.50421	−0.591084
$208$	−3.51810	−0.243936
$209$	−8.04284	−0.556335
$210$	2.54414	0.175562
$211$	−8.54843	−0.588498	−0.294249	−	0.955729i	$-0.595070\pi$
$211$	−8.54843	−0.588498	−0.294249	+	0.955729i	$0.595070\pi$
$212$	−8.52441	−0.585459
$213$	12.3944	0.849248
$214$	7.73093	0.528475
$215$	23.5528	1.60629
$216$	−4.80127	−0.326685
$217$	3.24079	0.219999
$218$	15.7711	1.06815
$219$	−10.9032	−0.736773
$220$	5.24231	0.353437
$221$	19.4509	1.30841
$222$	3.63147	0.243728
$223$	−16.3774	−1.09671	−0.548356	−	0.836245i	$-0.684746\pi$
$223$	−16.3774	−1.09671	−0.548356	+	0.836245i	$0.684746\pi$
$224$	−1.00000	−0.0668153
$225$	−5.01250	−0.334167
$226$	−12.4041	−0.825110
$227$	−18.0928	−1.20086	−0.600432	−	0.799676i	$-0.705005\pi$
$227$	−18.0928	−1.20086	−0.600432	+	0.799676i	$0.705005\pi$
$228$	3.90326	0.258500
$229$	−6.11520	−0.404104	−0.202052	−	0.979375i	$-0.564761\pi$
$229$	−6.11520	−0.404104	−0.202052	+	0.979375i	$0.564761\pi$
$230$	−10.8802	−0.717422
$231$	−1.81130	−0.119175
$232$	1.55674	0.102205
$233$	14.1689	0.928238	0.464119	−	0.885773i	$-0.346371\pi$
$233$	14.1689	0.928238	0.464119	+	0.885773i	$0.346371\pi$
$234$	−7.46175	−0.487790
$235$	11.2284	0.732462
$236$	1.76282	0.114750
$237$	−3.47353	−0.225630
$238$	5.52882	0.358380
$239$	−22.7273	−1.47011	−0.735054	−	0.678009i	$-0.762843\pi$
$239$	−22.7273	−1.47011	−0.735054	+	0.678009i	$0.762843\pi$
$240$	−2.54414	−0.164224
$241$	8.84935	0.570037	0.285018	−	0.958522i	$-0.408000\pi$
$241$	8.84935	0.570037	0.285018	+	0.958522i	$0.408000\pi$
$242$	7.26774	0.467188
$243$	−16.1489	−1.03596
$244$	−7.65899	−0.490317
$245$	2.71354	0.173362
$246$	3.98405	0.254014
$247$	14.6464	0.931930
$248$	−3.24079	−0.205790
$249$	−1.41164	−0.0894589
$250$	7.15475	0.452506
$251$	−18.0535	−1.13952	−0.569762	−	0.821810i	$-0.692965\pi$
$251$	−18.0535	−1.13952	−0.569762	+	0.821810i	$0.692965\pi$
$252$	−2.12096	−0.133608
$253$	7.74619	0.486999
$254$	8.77218	0.550415
$255$	14.0661	0.880853
$256$	1.00000	0.0625000
$257$	15.5103	0.967505	0.483752	−	0.875205i	$-0.339273\pi$
$257$	15.5103	0.967505	0.483752	+	0.875205i	$0.339273\pi$
$258$	8.13786	0.506641
$259$	3.87327	0.240674
$260$	−9.54652	−0.592050
$261$	3.30179	0.204376
$262$	7.68112	0.474541
$263$	11.6292	0.717088	0.358544	−	0.933513i	$-0.383273\pi$
$263$	11.6292	0.717088	0.358544	+	0.933513i	$0.383273\pi$
$264$	1.81130	0.111478
$265$	−23.1313	−1.42095
$266$	4.16316	0.255260
$267$	4.51327	0.276208
$268$	−8.75999	−0.535102
$269$	29.0591	1.77177	0.885883	−	0.463909i	$-0.153553\pi$
$269$	29.0591	1.77177	0.885883	+	0.463909i	$0.153553\pi$
$270$	−13.0284	−0.792886
$271$	1.68626	0.102433	0.0512165	−	0.998688i	$-0.483690\pi$
$271$	1.68626	0.102433	0.0512165	+	0.998688i	$0.483690\pi$
$272$	−5.52882	−0.335234
$273$	3.29847	0.199633
$274$	3.75367	0.226768
$275$	4.56571	0.275323
$276$	−3.75929	−0.226283
$277$	−1.99069	−0.119609	−0.0598045	−	0.998210i	$-0.519048\pi$
$277$	−1.99069	−0.119609	−0.0598045	+	0.998210i	$0.519048\pi$
$278$	−21.2693	−1.27565
$279$	−6.87358	−0.411510
$280$	−2.71354	−0.162165
$281$	−24.2859	−1.44877	−0.724387	−	0.689393i	$-0.757877\pi$
$281$	−24.2859	−1.44877	−0.724387	+	0.689393i	$0.757877\pi$
$282$	3.87960	0.231027
$283$	3.26207	0.193910	0.0969550	−	0.995289i	$-0.469090\pi$
$283$	3.26207	0.193910	0.0969550	+	0.995289i	$0.469090\pi$
$284$	−13.2196	−0.784442
$285$	10.5917	0.627397
$286$	6.79664	0.401894
$287$	4.24933	0.250830
$288$	2.12096	0.124979
$289$	13.5678	0.798106
$290$	4.22429	0.248059
$291$	16.6687	0.977135
$292$	11.6292	0.680549
$293$	−8.00801	−0.467833	−0.233917	−	0.972257i	$-0.575154\pi$
$293$	−8.00801	−0.467833	−0.233917	+	0.972257i	$0.575154\pi$
$294$	0.937572	0.0546803
$295$	4.78348	0.278505
$296$	−3.87327	−0.225130
$297$	9.27560	0.538225
$298$	9.08568	0.526319
$299$	−14.1062	−0.815783
$300$	−2.21578	−0.127928
$301$	8.67972	0.500291
$302$	13.7078	0.788798
$303$	−17.0558	−0.979831
$304$	−4.16316	−0.238774
$305$	−20.7830	−1.19003
$306$	−11.7264	−0.670353
$307$	12.2544	0.699395	0.349698	−	0.936863i	$-0.386284\pi$
$307$	12.2544	0.699395	0.349698	+	0.936863i	$0.386284\pi$
$308$	1.93191	0.110081
$309$	13.6855	0.778543
$310$	−8.79402	−0.499467
$311$	−22.8975	−1.29840	−0.649198	−	0.760619i	$-0.724896\pi$
$311$	−22.8975	−1.29840	−0.649198	+	0.760619i	$0.724896\pi$
$312$	−3.29847	−0.186739
$313$	31.6990	1.79173	0.895866	−	0.444324i	$-0.146556\pi$
$313$	31.6990	1.79173	0.895866	+	0.444324i	$0.146556\pi$
$314$	11.9617	0.675035
$315$	−5.75532	−0.324275
$316$	3.70481	0.208412
$317$	−10.6415	−0.597688	−0.298844	−	0.954302i	$-0.596601\pi$
$317$	−10.6415	−0.597688	−0.298844	+	0.954302i	$0.596601\pi$
$318$	−7.99224	−0.448183
$319$	−3.00748	−0.168387
$320$	2.71354	0.151692
$321$	7.24830	0.404561
$322$	−4.00961	−0.223447
$323$	23.0174	1.28072
$324$	1.86135	0.103408
$325$	−8.31439	−0.461200
$326$	−6.38239	−0.353488
$327$	14.7865	0.817696
$328$	−4.24933	−0.234630
$329$	4.13792	0.228131
$330$	4.91504	0.270564
$331$	−10.4687	−0.575412	−0.287706	−	0.957719i	$-0.592893\pi$
$331$	−10.4687	−0.575412	−0.287706	+	0.957719i	$0.592893\pi$
$332$	1.50563	0.0826323
$333$	−8.21506	−0.450182
$334$	0.890693	0.0487365
$335$	−23.7706	−1.29873
$336$	−0.937572	−0.0511487
$337$	8.40000	0.457577	0.228789	−	0.973476i	$-0.426524\pi$
$337$	8.40000	0.457577	0.228789	+	0.973476i	$0.426524\pi$
$338$	0.622957	0.0338844
$339$	−11.6298	−0.631642
$340$	−15.0027	−0.813635
$341$	6.26090	0.339047
$342$	−8.82990	−0.477466
$343$	1.00000	0.0539949
$344$	−8.67972	−0.467979
$345$	−10.2010	−0.549204
$346$	−0.157652	−0.00847540
$347$	−28.1958	−1.51363	−0.756814	−	0.653630i	$-0.773245\pi$
$347$	−28.1958	−1.51363	−0.756814	+	0.653630i	$0.773245\pi$
$348$	1.45956	0.0782406
$349$	10.5560	0.565048	0.282524	−	0.959260i	$-0.408828\pi$
$349$	10.5560	0.565048	0.282524	+	0.959260i	$0.408828\pi$
$350$	−2.36332	−0.126325
$351$	−16.8913	−0.901593
$352$	−1.93191	−0.102971
$353$	2.57882	0.137257	0.0686284	−	0.997642i	$-0.478138\pi$
$353$	2.57882	0.137257	0.0686284	+	0.997642i	$0.478138\pi$
$354$	1.65277	0.0878436
$355$	−35.8721	−1.90389
$356$	−4.81379	−0.255130
$357$	5.18366	0.274348
$358$	0.844759	0.0446469
$359$	25.7069	1.35676	0.678378	−	0.734713i	$-0.262683\pi$
$359$	25.7069	1.35676	0.678378	+	0.734713i	$0.262683\pi$
$360$	5.75532	0.303332
$361$	−1.66807	−0.0877930
$362$	−3.97878	−0.209120
$363$	6.81402	0.357644
$364$	−3.51810	−0.184399
$365$	31.5564	1.65174
$366$	−7.18085	−0.375349
$367$	−17.9892	−0.939029	−0.469514	−	0.882925i	$-0.655571\pi$
$367$	−17.9892	−0.939029	−0.469514	+	0.882925i	$0.655571\pi$
$368$	4.00961	0.209015
$369$	−9.01266	−0.469180
$370$	−10.5103	−0.546404
$371$	−8.52441	−0.442565
$372$	−3.03847	−0.157537
$373$	15.5251	0.803858	0.401929	−	0.915671i	$-0.368340\pi$
$373$	15.5251	0.803858	0.401929	+	0.915671i	$0.368340\pi$
$374$	10.6812	0.552309
$375$	6.70809	0.346404
$376$	−4.13792	−0.213397
$377$	5.47678	0.282069
$378$	−4.80127	−0.246950
$379$	−10.3657	−0.532450	−0.266225	−	0.963911i	$-0.585776\pi$
$379$	−10.3657	−0.532450	−0.266225	+	0.963911i	$0.585776\pi$
$380$	−11.2969	−0.579520
$381$	8.22455	0.421356
$382$	12.9200	0.661047
$383$	12.1283	0.619730	0.309865	−	0.950781i	$-0.399716\pi$
$383$	12.1283	0.619730	0.309865	+	0.950781i	$0.399716\pi$
$384$	0.937572	0.0478453
$385$	5.24231	0.267173
$386$	17.8763	0.909882
$387$	−18.4093	−0.935799
$388$	−17.7786	−0.902570
$389$	−31.2040	−1.58211	−0.791054	−	0.611747i	$-0.790467\pi$
$389$	−31.2040	−1.58211	−0.791054	+	0.611747i	$0.790467\pi$
$390$	−8.95055	−0.453229
$391$	−22.1684	−1.12110
$392$	−1.00000	−0.0505076
$393$	7.20160	0.363273
$394$	−9.75917	−0.491660
$395$	10.0532	0.505830
$396$	−4.09749	−0.205907
$397$	−32.5096	−1.63161	−0.815806	−	0.578325i	$-0.803706\pi$
$397$	−32.5096	−1.63161	−0.815806	+	0.578325i	$0.803706\pi$
$398$	5.69297	0.285363
$399$	3.90326	0.195408
$400$	2.36332	0.118166
$401$	−18.9693	−0.947280	−0.473640	−	0.880718i	$-0.657060\pi$
$401$	−18.9693	−0.947280	−0.473640	+	0.880718i	$0.657060\pi$
$402$	−8.21312	−0.409633
$403$	−11.4014	−0.567945
$404$	18.1915	0.905059
$405$	5.05084	0.250978
$406$	1.55674	0.0772599
$407$	7.48280	0.370909
$408$	−5.18366	−0.256629
$409$	−18.4576	−0.912668	−0.456334	−	0.889809i	$-0.650838\pi$
$409$	−18.4576	−0.912668	−0.456334	+	0.889809i	$0.650838\pi$
$410$	−11.5307	−0.569463
$411$	3.51934	0.173596
$412$	−14.5968	−0.719133
$413$	1.76282	0.0867426
$414$	8.50421	0.417959
$415$	4.08560	0.200554
$416$	3.51810	0.172489
$417$	−19.9415	−0.976539
$418$	8.04284	0.393388
$419$	31.2049	1.52446	0.762229	−	0.647307i	$-0.224105\pi$
$419$	31.2049	1.52446	0.762229	+	0.647307i	$0.224105\pi$
$420$	−2.54414	−0.124141
$421$	37.4792	1.82663	0.913313	−	0.407257i	$-0.133515\pi$
$421$	37.4792	1.82663	0.913313	+	0.407257i	$0.133515\pi$
$422$	8.54843	0.416131
$423$	−8.77637	−0.426722
$424$	8.52441	0.413982
$425$	−13.0663	−0.633811
$426$	−12.3944	−0.600509
$427$	−7.65899	−0.370645
$428$	−7.73093	−0.373689
$429$	6.37234	0.307660
$430$	−23.5528	−1.13582
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	4.80127	0.231001
$433$	25.1268	1.20752	0.603758	−	0.797168i	$-0.293669\pi$
$433$	25.1268	1.20752	0.603758	+	0.797168i	$0.293669\pi$
$434$	−3.24079	−0.155563
$435$	3.96058	0.189895
$436$	−15.7711	−0.755298
$437$	−16.6927	−0.798518
$438$	10.9032	0.520977
$439$	−21.0588	−1.00508	−0.502540	−	0.864554i	$-0.667601\pi$
$439$	−21.0588	−1.00508	−0.502540	+	0.864554i	$0.667601\pi$
$440$	−5.24231	−0.249917
$441$	−2.12096	−0.100998
$442$	−19.4509	−0.925187
$443$	−22.5642	−1.07206	−0.536029	−	0.844199i	$-0.680076\pi$
$443$	−22.5642	−1.07206	−0.536029	+	0.844199i	$0.680076\pi$
$444$	−3.63147	−0.172342
$445$	−13.0624	−0.619218
$446$	16.3774	0.775492
$447$	8.51848	0.402910
$448$	1.00000	0.0472456
$449$	−13.2841	−0.626916	−0.313458	−	0.949602i	$-0.601487\pi$
$449$	−13.2841	−0.626916	−0.313458	+	0.949602i	$0.601487\pi$
$450$	5.01250	0.236292
$451$	8.20931	0.386561
$452$	12.4041	0.583441
$453$	12.8521	0.603844
$454$	18.0928	0.849139
$455$	−9.54652	−0.447548
$456$	−3.90326	−0.182787
$457$	5.82261	0.272370	0.136185	−	0.990683i	$-0.456516\pi$
$457$	5.82261	0.272370	0.136185	+	0.990683i	$0.456516\pi$
$458$	6.11520	0.285745
$459$	−26.5453	−1.23903
$460$	10.8802	0.507294
$461$	−24.0072	−1.11813	−0.559064	−	0.829125i	$-0.688839\pi$
$461$	−24.0072	−1.11813	−0.559064	+	0.829125i	$0.688839\pi$
$462$	1.81130	0.0842693
$463$	20.2702	0.942038	0.471019	−	0.882123i	$-0.343886\pi$
$463$	20.2702	0.942038	0.471019	+	0.882123i	$0.343886\pi$
$464$	−1.55674	−0.0722700
$465$	−8.24502	−0.382354
$466$	−14.1689	−0.656363
$467$	−10.7365	−0.496827	−0.248413	−	0.968654i	$-0.579909\pi$
$467$	−10.7365	−0.496827	−0.248413	+	0.968654i	$0.579909\pi$
$468$	7.46175	0.344920
$469$	−8.75999	−0.404499
$470$	−11.2284	−0.517929
$471$	11.2149	0.516756
$472$	−1.76282	−0.0811403
$473$	16.7684	0.771012
$474$	3.47353	0.159544
$475$	−9.83888	−0.451439
$476$	−5.52882	−0.253413
$477$	18.0799	0.827823
$478$	22.7273	1.03952
$479$	28.1027	1.28404	0.642022	−	0.766687i	$-0.278096\pi$
$479$	28.1027	1.28404	0.642022	+	0.766687i	$0.278096\pi$
$480$	2.54414	0.116124
$481$	−13.6266	−0.621318
$482$	−8.84935	−0.403077
$483$	−3.75929	−0.171054
$484$	−7.26774	−0.330352
$485$	−48.2429	−2.19060
$486$	16.1489	0.732531
$487$	24.3042	1.10133	0.550663	−	0.834728i	$-0.314375\pi$
$487$	24.3042	1.10133	0.550663	+	0.834728i	$0.314375\pi$
$488$	7.65899	0.346706
$489$	−5.98395	−0.270603
$490$	−2.71354	−0.122585
$491$	−24.1689	−1.09073	−0.545364	−	0.838199i	$-0.683609\pi$
$491$	−24.1689	−1.09073	−0.545364	+	0.838199i	$0.683609\pi$
$492$	−3.98405	−0.179615
$493$	8.60695	0.387638
$494$	−14.6464	−0.658974
$495$	−11.1187	−0.499750
$496$	3.24079	0.145516
$497$	−13.2196	−0.592982
$498$	1.41164	0.0632570
$499$	28.7650	1.28770	0.643850	−	0.765152i	$-0.277336\pi$
$499$	28.7650	1.28770	0.643850	+	0.765152i	$0.277336\pi$
$500$	−7.15475	−0.319970
$501$	0.835088	0.0373090
$502$	18.0535	0.805765
$503$	31.0241	1.38329	0.691647	−	0.722235i	$-0.256885\pi$
$503$	31.0241	1.38329	0.691647	+	0.722235i	$0.256885\pi$
$504$	2.12096	0.0944750
$505$	49.3633	2.19664
$506$	−7.74619	−0.344360
$507$	0.584067	0.0259393
$508$	−8.77218	−0.389203
$509$	−43.1726	−1.91359	−0.956797	−	0.290758i	$-0.906093\pi$
$509$	−43.1726	−1.91359	−0.956797	+	0.290758i	$0.906093\pi$
$510$	−14.0661	−0.622857
$511$	11.6292	0.514447
$512$	−1.00000	−0.0441942
$513$	−19.9885	−0.882512
$514$	−15.5103	−0.684129
$515$	−39.6090	−1.74538
$516$	−8.13786	−0.358249
$517$	7.99408	0.351579
$518$	−3.87327	−0.170182
$519$	−0.147810	−0.00648812
$520$	9.54652	0.418643
$521$	−17.0078	−0.745125	−0.372562	−	0.928007i	$-0.621521\pi$
$521$	−17.0078	−0.745125	−0.372562	+	0.928007i	$0.621521\pi$
$522$	−3.30179	−0.144515
$523$	23.4054	1.02345	0.511724	−	0.859150i	$-0.329007\pi$
$523$	23.4054	1.02345	0.511724	+	0.859150i	$0.329007\pi$
$524$	−7.68112	−0.335551
$525$	−2.21578	−0.0967046
$526$	−11.6292	−0.507058
$527$	−17.9177	−0.780508
$528$	−1.81130	−0.0788267
$529$	−6.92305	−0.301002
$530$	23.1313	1.00476
$531$	−3.73887	−0.162253
$532$	−4.16316	−0.180496
$533$	−14.9496	−0.647538
$534$	−4.51327	−0.195308
$535$	−20.9782	−0.906967
$536$	8.75999	0.378374
$537$	0.792022	0.0341783
$538$	−29.0591	−1.25283
$539$	1.93191	0.0832131
$540$	13.0284	0.560655
$541$	14.4163	0.619805	0.309902	−	0.950768i	$-0.399704\pi$
$541$	14.4163	0.619805	0.309902	+	0.950768i	$0.399704\pi$
$542$	−1.68626	−0.0724311
$543$	−3.73039	−0.160086
$544$	5.52882	0.237046
$545$	−42.7955	−1.83316
$546$	−3.29847	−0.141162
$547$	17.1512	0.733331	0.366665	−	0.930353i	$-0.380499\pi$
$547$	17.1512	0.733331	0.366665	+	0.930353i	$0.380499\pi$
$548$	−3.75367	−0.160349
$549$	16.2444	0.693295
$550$	−4.56571	−0.194682
$551$	6.48098	0.276099
$552$	3.75929	0.160006
$553$	3.70481	0.157545
$554$	1.99069	0.0845764
$555$	−9.85416	−0.418286
$556$	21.2693	0.902019
$557$	−18.3132	−0.775954	−0.387977	−	0.921669i	$-0.626826\pi$
$557$	−18.3132	−0.775954	−0.387977	+	0.921669i	$0.626826\pi$
$558$	6.87358	0.290982
$559$	−30.5361	−1.29154
$560$	2.71354	0.114668
$561$	10.0143	0.422806
$562$	24.2859	1.02444
$563$	12.8847	0.543023	0.271512	−	0.962435i	$-0.412476\pi$
$563$	12.8847	0.543023	0.271512	+	0.962435i	$0.412476\pi$
$564$	−3.87960	−0.163361
$565$	33.6591	1.41605
$566$	−3.26207	−0.137115
$567$	1.86135	0.0781692
$568$	13.2196	0.554684
$569$	−7.45743	−0.312632	−0.156316	−	0.987707i	$-0.549962\pi$
$569$	−7.45743	−0.312632	−0.156316	+	0.987707i	$0.549962\pi$
$570$	−10.5917	−0.443637
$571$	−21.4402	−0.897245	−0.448622	−	0.893721i	$-0.648085\pi$
$571$	−21.4402	−0.897245	−0.448622	+	0.893721i	$0.648085\pi$
$572$	−6.79664	−0.284182
$573$	12.1135	0.506048
$574$	−4.24933	−0.177364
$575$	9.47598	0.395175
$576$	−2.12096	−0.0883733
$577$	−27.2795	−1.13566	−0.567830	−	0.823146i	$-0.692217\pi$
$577$	−27.2795	−1.13566	−0.567830	+	0.823146i	$0.692217\pi$
$578$	−13.5678	−0.564346
$579$	16.7604	0.696537
$580$	−4.22429	−0.175404
$581$	1.50563	0.0624642
$582$	−16.6687	−0.690939
$583$	−16.4684	−0.682050
$584$	−11.6292	−0.481221
$585$	20.2478	0.837143
$586$	8.00801	0.330808
$587$	−27.4870	−1.13451	−0.567255	−	0.823542i	$-0.691995\pi$
$587$	−27.4870	−1.13451	−0.567255	+	0.823542i	$0.691995\pi$
$588$	−0.937572	−0.0386648
$589$	−13.4919	−0.555925
$590$	−4.78348	−0.196933
$591$	−9.14992	−0.376377
$592$	3.87327	0.159191
$593$	−22.2438	−0.913444	−0.456722	−	0.889609i	$-0.650977\pi$
$593$	−22.2438	−0.913444	−0.456722	+	0.889609i	$0.650977\pi$
$594$	−9.27560	−0.380582
$595$	−15.0027	−0.615050
$596$	−9.08568	−0.372164
$597$	5.33757	0.218452
$598$	14.1062	0.576846
$599$	−15.2994	−0.625115	−0.312558	−	0.949899i	$-0.601186\pi$
$599$	−15.2994	−0.625115	−0.312558	+	0.949899i	$0.601186\pi$
$600$	2.21578	0.0904588
$601$	44.4646	1.81375	0.906875	−	0.421400i	$-0.138461\pi$
$601$	44.4646	1.81375	0.906875	+	0.421400i	$0.138461\pi$
$602$	−8.67972	−0.353759
$603$	18.5796	0.756619
$604$	−13.7078	−0.557764
$605$	−19.7213	−0.801786
$606$	17.0558	0.692845
$607$	12.7428	0.517214	0.258607	−	0.965983i	$-0.416736\pi$
$607$	12.7428	0.517214	0.258607	+	0.965983i	$0.416736\pi$
$608$	4.16316	0.168839
$609$	1.45956	0.0591443
$610$	20.7830	0.841479
$611$	−14.5576	−0.588939
$612$	11.7264	0.474011
$613$	28.7315	1.16045	0.580226	−	0.814455i	$-0.302964\pi$
$613$	28.7315	1.16045	0.580226	+	0.814455i	$0.302964\pi$
$614$	−12.2544	−0.494547
$615$	−10.8109	−0.435937
$616$	−1.93191	−0.0778387
$617$	32.0922	1.29198	0.645992	−	0.763344i	$-0.276444\pi$
$617$	32.0922	1.29198	0.645992	+	0.763344i	$0.276444\pi$
$618$	−13.6855	−0.550513
$619$	−27.9918	−1.12508	−0.562542	−	0.826768i	$-0.690177\pi$
$619$	−27.9918	−1.12508	−0.562542	+	0.826768i	$0.690177\pi$
$620$	8.79402	0.353176
$621$	19.2512	0.772524
$622$	22.8975	0.918105
$623$	−4.81379	−0.192860
$624$	3.29847	0.132045
$625$	−31.2313	−1.24925
$626$	−31.6990	−1.26695
$627$	7.54074	0.301148
$628$	−11.9617	−0.477322
$629$	−21.4146	−0.853857
$630$	5.75532	0.229297
$631$	−32.4717	−1.29268	−0.646340	−	0.763050i	$-0.723701\pi$
$631$	−32.4717	−1.29268	−0.646340	+	0.763050i	$0.723701\pi$
$632$	−3.70481	−0.147369
$633$	8.01477	0.318558
$634$	10.6415	0.422629
$635$	−23.8037	−0.944621
$636$	7.99224	0.316913
$637$	−3.51810	−0.139392
$638$	3.00748	0.119067
$639$	28.0383	1.10918
$640$	−2.71354	−0.107262
$641$	−11.5472	−0.456085	−0.228043	−	0.973651i	$-0.573233\pi$
$641$	−11.5472	−0.456085	−0.228043	+	0.973651i	$0.573233\pi$
$642$	−7.24830	−0.286068
$643$	−13.8198	−0.545001	−0.272500	−	0.962156i	$-0.587851\pi$
$643$	−13.8198	−0.545001	−0.272500	+	0.962156i	$0.587851\pi$
$644$	4.00961	0.158001
$645$	−22.0824	−0.869495
$646$	−23.0174	−0.905606
$647$	−19.6560	−0.772756	−0.386378	−	0.922340i	$-0.626274\pi$
$647$	−19.6560	−0.772756	−0.386378	+	0.922340i	$0.626274\pi$
$648$	−1.86135	−0.0731206
$649$	3.40560	0.133681
$650$	8.31439	0.326117
$651$	−3.03847	−0.119087
$652$	6.38239	0.249954
$653$	39.3680	1.54059	0.770294	−	0.637689i	$-0.220110\pi$
$653$	39.3680	1.54059	0.770294	+	0.637689i	$0.220110\pi$
$654$	−14.7865	−0.578199
$655$	−20.8431	−0.814406
$656$	4.24933	0.165908
$657$	−24.6651	−0.962278
$658$	−4.13792	−0.161313
$659$	−11.2282	−0.437389	−0.218695	−	0.975793i	$-0.570180\pi$
$659$	−11.2282	−0.437389	−0.218695	+	0.975793i	$0.570180\pi$
$660$	−4.91504	−0.191318
$661$	−37.4092	−1.45505	−0.727525	−	0.686081i	$-0.759329\pi$
$661$	−37.4092	−1.45505	−0.727525	+	0.686081i	$0.759329\pi$
$662$	10.4687	0.406878
$663$	−18.2366	−0.708253
$664$	−1.50563	−0.0584299
$665$	−11.2969	−0.438076
$666$	8.21506	0.318327
$667$	−6.24193	−0.241689
$668$	−0.890693	−0.0344619
$669$	15.3550	0.593658
$670$	23.7706	0.918339
$671$	−14.7965	−0.571211
$672$	0.937572	0.0361676
$673$	39.7729	1.53313	0.766567	−	0.642164i	$-0.221963\pi$
$673$	39.7729	1.53313	0.766567	+	0.642164i	$0.221963\pi$
$674$	−8.40000	−0.323556
$675$	11.3469	0.436743
$676$	−0.622957	−0.0239599
$677$	34.3206	1.31905	0.659523	−	0.751684i	$-0.270758\pi$
$677$	34.3206	1.31905	0.659523	+	0.751684i	$0.270758\pi$
$678$	11.6298	0.446638
$679$	−17.7786	−0.682279
$680$	15.0027	0.575327
$681$	16.9633	0.650037
$682$	−6.26090	−0.239742
$683$	−22.5306	−0.862110	−0.431055	−	0.902326i	$-0.641858\pi$
$683$	−22.5306	−0.862110	−0.431055	+	0.902326i	$0.641858\pi$
$684$	8.82990	0.337620
$685$	−10.1858	−0.389178
$686$	−1.00000	−0.0381802
$687$	5.73344	0.218744
$688$	8.67972	0.330911
$689$	29.9897	1.14252
$690$	10.2010	0.388346
$691$	1.51103	0.0574823	0.0287412	−	0.999587i	$-0.490850\pi$
$691$	1.51103	0.0574823	0.0287412	+	0.999587i	$0.490850\pi$
$692$	0.157652	0.00599301
$693$	−4.09749	−0.155651
$694$	28.1958	1.07030
$695$	57.7151	2.18926
$696$	−1.45956	−0.0553244
$697$	−23.4938	−0.889890
$698$	−10.5560	−0.399549
$699$	−13.2844	−0.502462
$700$	2.36332	0.0893250
$701$	−10.6342	−0.401647	−0.200824	−	0.979627i	$-0.564362\pi$
$701$	−10.6342	−0.401647	−0.200824	+	0.979627i	$0.564362\pi$
$702$	16.8913	0.637523
$703$	−16.1251	−0.608169
$704$	1.93191	0.0728115
$705$	−10.5275	−0.396487
$706$	−2.57882	−0.0970552
$707$	18.1915	0.684161
$708$	−1.65277	−0.0621148
$709$	48.2857	1.81341	0.906704	−	0.421767i	$-0.138590\pi$
$709$	48.2857	1.81341	0.906704	+	0.421767i	$0.138590\pi$
$710$	35.8721	1.34626
$711$	−7.85775	−0.294689
$712$	4.81379	0.180404
$713$	12.9943	0.486640
$714$	−5.18366	−0.193994
$715$	−18.4430	−0.689729
$716$	−0.844759	−0.0315701
$717$	21.3085	0.795780
$718$	−25.7069	−0.959372
$719$	−25.5083	−0.951301	−0.475650	−	0.879634i	$-0.657787\pi$
$719$	−25.5083	−0.951301	−0.475650	+	0.879634i	$0.657787\pi$
$720$	−5.75532	−0.214488
$721$	−14.5968	−0.543613
$722$	1.66807	0.0620791
$723$	−8.29690	−0.308565
$724$	3.97878	0.147870
$725$	−3.67908	−0.136638
$726$	−6.81402	−0.252892
$727$	−6.87632	−0.255028	−0.127514	−	0.991837i	$-0.540700\pi$
$727$	−6.87632	−0.255028	−0.127514	+	0.991837i	$0.540700\pi$
$728$	3.51810	0.130390
$729$	9.55675	0.353954
$730$	−31.5564	−1.16796
$731$	−47.9886	−1.77492
$732$	7.18085	0.265412
$733$	−33.8508	−1.25031	−0.625153	−	0.780502i	$-0.714964\pi$
$733$	−33.8508	−1.25031	−0.625153	+	0.780502i	$0.714964\pi$
$734$	17.9892	0.663994
$735$	−2.54414	−0.0938421
$736$	−4.00961	−0.147796
$737$	−16.9235	−0.623384
$738$	9.01266	0.331760
$739$	−15.6549	−0.575873	−0.287937	−	0.957649i	$-0.592969\pi$
$739$	−15.6549	−0.575873	−0.287937	+	0.957649i	$0.592969\pi$
$740$	10.5103	0.386366
$741$	−13.7321	−0.504461
$742$	8.52441	0.312941
$743$	−23.1222	−0.848270	−0.424135	−	0.905599i	$-0.639422\pi$
$743$	−23.1222	−0.848270	−0.424135	+	0.905599i	$0.639422\pi$
$744$	3.03847	0.111396
$745$	−24.6544	−0.903267
$746$	−15.5251	−0.568414
$747$	−3.19338	−0.116840
$748$	−10.6812	−0.390542
$749$	−7.73093	−0.282482
$750$	−6.70809	−0.244945
$751$	11.3485	0.414113	0.207057	−	0.978329i	$-0.433612\pi$
$751$	11.3485	0.414113	0.207057	+	0.978329i	$0.433612\pi$
$752$	4.13792	0.150895
$753$	16.9264	0.616833
$754$	−5.47678	−0.199453
$755$	−37.1968	−1.35373
$756$	4.80127	0.174620
$757$	−24.8965	−0.904878	−0.452439	−	0.891795i	$-0.649446\pi$
$757$	−24.8965	−0.904878	−0.452439	+	0.891795i	$0.649446\pi$
$758$	10.3657	0.376499
$759$	−7.26260	−0.263616
$760$	11.2969	0.409783
$761$	−26.5518	−0.962501	−0.481250	−	0.876583i	$-0.659817\pi$
$761$	−26.5518	−0.962501	−0.481250	+	0.876583i	$0.659817\pi$
$762$	−8.22455	−0.297944
$763$	−15.7711	−0.570951
$764$	−12.9200	−0.467431
$765$	31.8201	1.15046
$766$	−12.1283	−0.438215
$767$	−6.20177	−0.223933
$768$	−0.937572	−0.0338317
$769$	51.6131	1.86122	0.930609	−	0.366015i	$-0.119278\pi$
$769$	51.6131	1.86122	0.930609	+	0.366015i	$0.119278\pi$
$770$	−5.24231	−0.188920
$771$	−14.5420	−0.523717
$772$	−17.8763	−0.643384
$773$	−29.8054	−1.07203	−0.536013	−	0.844210i	$-0.680070\pi$
$773$	−29.8054	−1.07203	−0.536013	+	0.844210i	$0.680070\pi$
$774$	18.4093	0.661710
$775$	7.65901	0.275120
$776$	17.7786	0.638213
$777$	−3.63147	−0.130278
$778$	31.2040	1.11872
$779$	−17.6907	−0.633834
$780$	8.95055	0.320481
$781$	−25.5391	−0.913862
$782$	22.1684	0.792740
$783$	−7.47434	−0.267111
$784$	1.00000	0.0357143
$785$	−32.4585	−1.15849
$786$	−7.20160	−0.256873
$787$	−51.0335	−1.81915	−0.909575	−	0.415540i	$-0.863593\pi$
$787$	−51.0335	−1.81915	−0.909575	+	0.415540i	$0.863593\pi$
$788$	9.75917	0.347656
$789$	−10.9032	−0.388165
$790$	−10.0532	−0.357675
$791$	12.4041	0.441040
$792$	4.09749	0.145598
$793$	26.9451	0.956849
$794$	32.5096	1.15372
$795$	21.6873	0.769169
$796$	−5.69297	−0.201782
$797$	−43.8647	−1.55377	−0.776884	−	0.629643i	$-0.783201\pi$
$797$	−43.8647	−1.55377	−0.776884	+	0.629643i	$0.783201\pi$
$798$	−3.90326	−0.138174
$799$	−22.8778	−0.809359
$800$	−2.36332	−0.0835559
$801$	10.2098	0.360747
$802$	18.9693	0.669828
$803$	22.4666	0.792829
$804$	8.21312	0.289654
$805$	10.8802	0.383478
$806$	11.4014	0.401598
$807$	−27.2450	−0.959070
$808$	−18.1915	−0.639974
$809$	41.1656	1.44730	0.723652	−	0.690165i	$-0.242462\pi$
$809$	41.1656	1.44730	0.723652	+	0.690165i	$0.242462\pi$
$810$	−5.05084	−0.177469
$811$	35.9397	1.26201	0.631007	−	0.775777i	$-0.282642\pi$
$811$	35.9397	1.26201	0.631007	+	0.775777i	$0.282642\pi$
$812$	−1.55674	−0.0546310
$813$	−1.58099	−0.0554478
$814$	−7.48280	−0.262272
$815$	17.3189	0.606654
$816$	5.18366	0.181464
$817$	−36.1351	−1.26421
$818$	18.4576	0.645354
$819$	7.46175	0.260735
$820$	11.5307	0.402671
$821$	−17.1472	−0.598442	−0.299221	−	0.954184i	$-0.596727\pi$
$821$	−17.1472	−0.598442	−0.299221	+	0.954184i	$0.596727\pi$
$822$	−3.51934	−0.122751
$823$	−9.23184	−0.321802	−0.160901	−	0.986971i	$-0.551440\pi$
$823$	−9.23184	−0.321802	−0.160901	+	0.986971i	$0.551440\pi$
$824$	14.5968	0.508504
$825$	−4.28068	−0.149034
$826$	−1.76282	−0.0613363
$827$	−47.3751	−1.64739	−0.823696	−	0.567031i	$-0.808092\pi$
$827$	−47.3751	−1.64739	−0.823696	+	0.567031i	$0.808092\pi$
$828$	−8.50421	−0.295542
$829$	20.8211	0.723147	0.361574	−	0.932344i	$-0.382240\pi$
$829$	20.8211	0.723147	0.361574	+	0.932344i	$0.382240\pi$
$830$	−4.08560	−0.141813
$831$	1.86642	0.0647453
$832$	−3.51810	−0.121968
$833$	−5.52882	−0.191562
$834$	19.9415	0.690517
$835$	−2.41693	−0.0836414
$836$	−8.04284	−0.278168
$837$	15.5599	0.537828
$838$	−31.2049	−1.07795
$839$	−26.9621	−0.930834	−0.465417	−	0.885091i	$-0.654096\pi$
$839$	−26.9621	−0.930834	−0.465417	+	0.885091i	$0.654096\pi$
$840$	2.54414	0.0877812
$841$	−26.5765	−0.916433
$842$	−37.4792	−1.29162
$843$	22.7698	0.784232
$844$	−8.54843	−0.294249
$845$	−1.69042	−0.0581523
$846$	8.77637	0.301738
$847$	−7.26774	−0.249722
$848$	−8.52441	−0.292729
$849$	−3.05843	−0.104965
$850$	13.0663	0.448172
$851$	15.5303	0.532372
$852$	12.3944	0.424624
$853$	50.2228	1.71960	0.859798	−	0.510634i	$-0.170589\pi$
$853$	50.2228	1.71960	0.859798	+	0.510634i	$0.170589\pi$
$854$	7.65899	0.262085
$855$	23.9603	0.819426
$856$	7.73093	0.264238
$857$	55.6967	1.90256	0.951282	−	0.308323i	$-0.0997679\pi$
$857$	55.6967	1.90256	0.951282	+	0.308323i	$0.0997679\pi$
$858$	−6.37234	−0.217548
$859$	24.1819	0.825075	0.412538	−	0.910941i	$-0.364642\pi$
$859$	24.1819	0.825075	0.412538	+	0.910941i	$0.364642\pi$
$860$	23.5528	0.803144
$861$	−3.98405	−0.135776
$862$	−1.00000	−0.0340601
$863$	48.3642	1.64634	0.823169	−	0.567797i	$-0.192204\pi$
$863$	48.3642	1.64634	0.823169	+	0.567797i	$0.192204\pi$
$864$	−4.80127	−0.163342
$865$	0.427794	0.0145454
$866$	−25.1268	−0.853842
$867$	−12.7208	−0.432021
$868$	3.24079	0.109999
$869$	7.15735	0.242796
$870$	−3.96058	−0.134276
$871$	30.8185	1.04425
$872$	15.7711	0.534076
$873$	37.7076	1.27621
$874$	16.6927	0.564637
$875$	−7.15475	−0.241875
$876$	−10.9032	−0.368386
$877$	27.5614	0.930683	0.465342	−	0.885131i	$-0.345931\pi$
$877$	27.5614	0.930683	0.465342	+	0.885131i	$0.345931\pi$
$878$	21.0588	0.710699
$879$	7.50809	0.253241
$880$	5.24231	0.176718
$881$	15.9289	0.536659	0.268330	−	0.963327i	$-0.413528\pi$
$881$	15.9289	0.536659	0.268330	+	0.963327i	$0.413528\pi$
$882$	2.12096	0.0714164
$883$	−24.8624	−0.836687	−0.418344	−	0.908289i	$-0.637389\pi$
$883$	−24.8624	−0.836687	−0.418344	+	0.908289i	$0.637389\pi$
$884$	19.4509	0.654206
$885$	−4.48486	−0.150757
$886$	22.5642	0.758060
$887$	−28.3189	−0.950855	−0.475427	−	0.879755i	$-0.657707\pi$
$887$	−28.3189	−0.950855	−0.475427	+	0.879755i	$0.657707\pi$
$888$	3.63147	0.121864
$889$	−8.77218	−0.294209
$890$	13.0624	0.437853
$891$	3.59595	0.120469
$892$	−16.3774	−0.548356
$893$	−17.2269	−0.576475
$894$	−8.51848	−0.284900
$895$	−2.29229	−0.0766228
$896$	−1.00000	−0.0334077
$897$	13.2256	0.441589
$898$	13.2841	0.443297
$899$	−5.04508	−0.168263
$900$	−5.01250	−0.167083
$901$	47.1299	1.57012
$902$	−8.20931	−0.273340
$903$	−8.13786	−0.270811
$904$	−12.4041	−0.412555
$905$	10.7966	0.358890
$906$	−12.8521	−0.426982
$907$	20.3361	0.675248	0.337624	−	0.941281i	$-0.390377\pi$
$907$	20.3361	0.675248	0.337624	+	0.941281i	$0.390377\pi$
$908$	−18.0928	−0.600432
$909$	−38.5834	−1.27973
$910$	9.54652	0.316464
$911$	20.6403	0.683845	0.341922	−	0.939728i	$-0.388922\pi$
$911$	20.6403	0.683845	0.341922	+	0.939728i	$0.388922\pi$
$912$	3.90326	0.129250
$913$	2.90874	0.0962653
$914$	−5.82261	−0.192595
$915$	19.4856	0.644173
$916$	−6.11520	−0.202052
$917$	−7.68112	−0.253653
$918$	26.5453	0.876126
$919$	45.9131	1.51453	0.757266	−	0.653107i	$-0.226535\pi$
$919$	45.9131	1.51453	0.757266	+	0.653107i	$0.226535\pi$
$920$	−10.8802	−0.358711
$921$	−11.4894	−0.378588
$922$	24.0072	0.790636
$923$	46.5081	1.53083
$924$	−1.81130	−0.0595874
$925$	9.15378	0.300974
$926$	−20.2702	−0.666121
$927$	30.9592	1.01683
$928$	1.55674	0.0511026
$929$	−3.93569	−0.129126	−0.0645629	−	0.997914i	$-0.520565\pi$
$929$	−3.93569	−0.129126	−0.0645629	+	0.997914i	$0.520565\pi$
$930$	8.24502	0.270365
$931$	−4.16316	−0.136442
$932$	14.1689	0.464119
$933$	21.4680	0.702832
$934$	10.7365	0.351310
$935$	−28.9838	−0.947871
$936$	−7.46175	−0.243895
$937$	36.9309	1.20648	0.603240	−	0.797559i	$-0.293876\pi$
$937$	36.9309	1.20648	0.603240	+	0.797559i	$0.293876\pi$
$938$	8.75999	0.286024
$939$	−29.7201	−0.969878
$940$	11.2284	0.366231
$941$	34.7413	1.13253	0.566266	−	0.824222i	$-0.308387\pi$
$941$	34.7413	1.13253	0.566266	+	0.824222i	$0.308387\pi$
$942$	−11.2149	−0.365401
$943$	17.0381	0.554838
$944$	1.76282	0.0573748
$945$	13.0284	0.423815
$946$	−16.7684	−0.545188
$947$	19.0456	0.618899	0.309450	−	0.950916i	$-0.399855\pi$
$947$	19.0456	0.618899	0.309450	+	0.950916i	$0.399855\pi$
$948$	−3.47353	−0.112815
$949$	−40.9128	−1.32809
$950$	9.83888	0.319215
$951$	9.97720	0.323533
$952$	5.52882	0.179190
$953$	37.7093	1.22152	0.610762	−	0.791814i	$-0.290863\pi$
$953$	37.7093	1.22152	0.610762	+	0.791814i	$0.290863\pi$
$954$	−18.0799	−0.585359
$955$	−35.0591	−1.13449
$956$	−22.7273	−0.735054
$957$	2.81973	0.0911490
$958$	−28.1027	−0.907956
$959$	−3.75367	−0.121212
$960$	−2.54414	−0.0821118
$961$	−20.4973	−0.661203
$962$	13.6266	0.439338
$963$	16.3970	0.528385
$964$	8.84935	0.285018
$965$	−48.5082	−1.56154
$966$	3.75929	0.120953
$967$	28.6647	0.921796	0.460898	−	0.887453i	$-0.347527\pi$
$967$	28.6647	0.921796	0.460898	+	0.887453i	$0.347527\pi$
$968$	7.26774	0.233594
$969$	−21.5804	−0.693263
$970$	48.2429	1.54899
$971$	4.22115	0.135463	0.0677315	−	0.997704i	$-0.478424\pi$
$971$	4.22115	0.135463	0.0677315	+	0.997704i	$0.478424\pi$
$972$	−16.1489	−0.517978
$973$	21.2693	0.681862
$974$	−24.3042	−0.778755
$975$	7.79534	0.249651
$976$	−7.65899	−0.245158
$977$	0.595491	0.0190515	0.00952573	−	0.999955i	$-0.496968\pi$
$977$	0.595491	0.0190515	0.00952573	+	0.999955i	$0.496968\pi$
$978$	5.98395	0.191346
$979$	−9.29979	−0.297223
$980$	2.71354	0.0866810
$981$	33.4498	1.06797
$982$	24.1689	0.771261
$983$	30.1974	0.963146	0.481573	−	0.876406i	$-0.340066\pi$
$983$	30.1974	0.963146	0.481573	+	0.876406i	$0.340066\pi$
$984$	3.98405	0.127007
$985$	26.4819	0.843784
$986$	−8.60695	−0.274101
$987$	−3.87960	−0.123489
$988$	14.6464	0.465965
$989$	34.8023	1.10665
$990$	11.1187	0.353376
$991$	−50.6108	−1.60770	−0.803852	−	0.594829i	$-0.797220\pi$
$991$	−50.6108	−1.60770	−0.803852	+	0.594829i	$0.797220\pi$
$992$	−3.24079	−0.102895
$993$	9.81516	0.311475
$994$	13.2196	0.419302
$995$	−15.4481	−0.489739
$996$	−1.41164	−0.0447295
$997$	50.8330	1.60990	0.804948	−	0.593345i	$-0.202193\pi$
$997$	50.8330	1.60990	0.804948	+	0.593345i	$0.202193\pi$
$998$	−28.7650	−0.910542
$999$	18.5966	0.588371

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.k.1.7	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.k.1.7	✓	20	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.937572 q^{3} +1.00000 q^{4} +2.71354 q^{5} +0.937572 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.12096 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.937572 q^{3} +1.00000 q^{4} +2.71354 q^{5} +0.937572 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.12096 q^{9} -2.71354 q^{10} +1.93191 q^{11} -0.937572 q^{12} -3.51810 q^{13} -1.00000 q^{14} -2.54414 q^{15} +1.00000 q^{16} -5.52882 q^{17} +2.12096 q^{18} -4.16316 q^{19} +2.71354 q^{20} -0.937572 q^{21} -1.93191 q^{22} +4.00961 q^{23} +0.937572 q^{24} +2.36332 q^{25} +3.51810 q^{26} +4.80127 q^{27} +1.00000 q^{28} -1.55674 q^{29} +2.54414 q^{30} +3.24079 q^{31} -1.00000 q^{32} -1.81130 q^{33} +5.52882 q^{34} +2.71354 q^{35} -2.12096 q^{36} +3.87327 q^{37} +4.16316 q^{38} +3.29847 q^{39} -2.71354 q^{40} +4.24933 q^{41} +0.937572 q^{42} +8.67972 q^{43} +1.93191 q^{44} -5.75532 q^{45} -4.00961 q^{46} +4.13792 q^{47} -0.937572 q^{48} +1.00000 q^{49} -2.36332 q^{50} +5.18366 q^{51} -3.51810 q^{52} -8.52441 q^{53} -4.80127 q^{54} +5.24231 q^{55} -1.00000 q^{56} +3.90326 q^{57} +1.55674 q^{58} +1.76282 q^{59} -2.54414 q^{60} -7.65899 q^{61} -3.24079 q^{62} -2.12096 q^{63} +1.00000 q^{64} -9.54652 q^{65} +1.81130 q^{66} -8.75999 q^{67} -5.52882 q^{68} -3.75929 q^{69} -2.71354 q^{70} -13.2196 q^{71} +2.12096 q^{72} +11.6292 q^{73} -3.87327 q^{74} -2.21578 q^{75} -4.16316 q^{76} +1.93191 q^{77} -3.29847 q^{78} +3.70481 q^{79} +2.71354 q^{80} +1.86135 q^{81} -4.24933 q^{82} +1.50563 q^{83} -0.937572 q^{84} -15.0027 q^{85} -8.67972 q^{86} +1.45956 q^{87} -1.93191 q^{88} -4.81379 q^{89} +5.75532 q^{90} -3.51810 q^{91} +4.00961 q^{92} -3.03847 q^{93} -4.13792 q^{94} -11.2969 q^{95} +0.937572 q^{96} -17.7786 q^{97} -1.00000 q^{98} -4.09749 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9} + 3 q^{10} - 8 q^{11} + 3 q^{12} - 4 q^{13} - 20 q^{14} - 25 q^{15} + 20 q^{16} + 9 q^{17} - 13 q^{18} - 14 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} - 23 q^{23} - 3 q^{24} + 31 q^{25} + 4 q^{26} - 21 q^{27} + 20 q^{28} - 48 q^{29} + 25 q^{30} - q^{31} - 20 q^{32} - 29 q^{33} - 9 q^{34} - 3 q^{35} + 13 q^{36} - q^{37} + 14 q^{38} - q^{39} + 3 q^{40} - 27 q^{41} - 3 q^{42} - 3 q^{43} - 8 q^{44} - 12 q^{45} + 23 q^{46} - 26 q^{47} + 3 q^{48} + 20 q^{49} - 31 q^{50} - 17 q^{51} - 4 q^{52} - 43 q^{53} + 21 q^{54} - 16 q^{55} - 20 q^{56} - 25 q^{57} + 48 q^{58} - 19 q^{59} - 25 q^{60} + 9 q^{61} + q^{62} + 13 q^{63} + 20 q^{64} - 87 q^{65} + 29 q^{66} + 32 q^{67} + 9 q^{68} - 23 q^{69} + 3 q^{70} - 63 q^{71} - 13 q^{72} + 2 q^{73} + q^{74} - 8 q^{75} - 14 q^{76} - 8 q^{77} + q^{78} - 51 q^{79} - 3 q^{80} + 4 q^{81} + 27 q^{82} - 24 q^{83} + 3 q^{84} + 31 q^{85} + 3 q^{86} - 33 q^{87} + 8 q^{88} - 35 q^{89} + 12 q^{90} - 4 q^{91} - 23 q^{92} + 17 q^{93} + 26 q^{94} - 30 q^{95} - 3 q^{96} + 5 q^{97} - 20 q^{98} - 31 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9 + 3 * q^10 - 8 * q^11 + 3 * q^12 - 4 * q^13 - 20 * q^14 - 25 * q^15 + 20 * q^16 + 9 * q^17 - 13 * q^18 - 14 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 - 23 * q^23 - 3 * q^24 + 31 * q^25 + 4 * q^26 - 21 * q^27 + 20 * q^28 - 48 * q^29 + 25 * q^30 - q^31 - 20 * q^32 - 29 * q^33 - 9 * q^34 - 3 * q^35 + 13 * q^36 - q^37 + 14 * q^38 - q^39 + 3 * q^40 - 27 * q^41 - 3 * q^42 - 3 * q^43 - 8 * q^44 - 12 * q^45 + 23 * q^46 - 26 * q^47 + 3 * q^48 + 20 * q^49 - 31 * q^50 - 17 * q^51 - 4 * q^52 - 43 * q^53 + 21 * q^54 - 16 * q^55 - 20 * q^56 - 25 * q^57 + 48 * q^58 - 19 * q^59 - 25 * q^60 + 9 * q^61 + q^62 + 13 * q^63 + 20 * q^64 - 87 * q^65 + 29 * q^66 + 32 * q^67 + 9 * q^68 - 23 * q^69 + 3 * q^70 - 63 * q^71 - 13 * q^72 + 2 * q^73 + q^74 - 8 * q^75 - 14 * q^76 - 8 * q^77 + q^78 - 51 * q^79 - 3 * q^80 + 4 * q^81 + 27 * q^82 - 24 * q^83 + 3 * q^84 + 31 * q^85 + 3 * q^86 - 33 * q^87 + 8 * q^88 - 35 * q^89 + 12 * q^90 - 4 * q^91 - 23 * q^92 + 17 * q^93 + 26 * q^94 - 30 * q^95 - 3 * q^96 + 5 * q^97 - 20 * q^98 - 31 * q^99

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