LMFDB - Embedded newform 6043.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6043,2,Mod(1,6043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6043, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6043 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6043.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:	$48.2535979415$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66120 q^{2} -0.520492 q^{3} +5.08201 q^{4} +3.83583 q^{5} +1.38513 q^{6} -0.144514 q^{7} -8.20186 q^{8} -2.72909 q^{9} +O(q^{10})$	\(q-2.66120 q^{2} -0.520492 q^{3} +5.08201 q^{4} +3.83583 q^{5} +1.38513 q^{6} -0.144514 q^{7} -8.20186 q^{8} -2.72909 q^{9} -10.2079 q^{10} -3.10250 q^{11} -2.64514 q^{12} -4.51024 q^{13} +0.384580 q^{14} -1.99652 q^{15} +11.6628 q^{16} +0.00372970 q^{17} +7.26266 q^{18} -5.17422 q^{19} +19.4937 q^{20} +0.0752182 q^{21} +8.25639 q^{22} -2.83489 q^{23} +4.26900 q^{24} +9.71356 q^{25} +12.0027 q^{26} +2.98194 q^{27} -0.734420 q^{28} +2.89539 q^{29} +5.31314 q^{30} -4.84141 q^{31} -14.6334 q^{32} +1.61483 q^{33} -0.00992551 q^{34} -0.554329 q^{35} -13.8693 q^{36} +9.15931 q^{37} +13.7697 q^{38} +2.34754 q^{39} -31.4609 q^{40} +4.83194 q^{41} -0.200171 q^{42} +8.24426 q^{43} -15.7669 q^{44} -10.4683 q^{45} +7.54421 q^{46} -9.24511 q^{47} -6.07039 q^{48} -6.97912 q^{49} -25.8498 q^{50} -0.00194128 q^{51} -22.9211 q^{52} -6.73966 q^{53} -7.93556 q^{54} -11.9007 q^{55} +1.18528 q^{56} +2.69314 q^{57} -7.70523 q^{58} +8.15885 q^{59} -10.1463 q^{60} +8.42396 q^{61} +12.8840 q^{62} +0.394391 q^{63} +15.6168 q^{64} -17.3005 q^{65} -4.29738 q^{66} -10.4613 q^{67} +0.0189544 q^{68} +1.47553 q^{69} +1.47518 q^{70} -3.83221 q^{71} +22.3836 q^{72} +11.2767 q^{73} -24.3748 q^{74} -5.05583 q^{75} -26.2954 q^{76} +0.448354 q^{77} -6.24729 q^{78} -11.3790 q^{79} +44.7365 q^{80} +6.63519 q^{81} -12.8588 q^{82} -0.314352 q^{83} +0.382259 q^{84} +0.0143065 q^{85} -21.9397 q^{86} -1.50703 q^{87} +25.4463 q^{88} -0.194659 q^{89} +27.8583 q^{90} +0.651791 q^{91} -14.4069 q^{92} +2.51992 q^{93} +24.6031 q^{94} -19.8474 q^{95} +7.61656 q^{96} -13.9788 q^{97} +18.5729 q^{98} +8.46700 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * 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 $

$2$	−2.66120	−1.88176	−0.940878	−	0.338746i	$-0.889997\pi$
$2$	−2.66120	−1.88176	−0.940878	+	0.338746i	$0.889997\pi$
$3$	−0.520492	−0.300506	−0.150253	−	0.988648i	$-0.548009\pi$
$3$	−0.520492	−0.300506	−0.150253	+	0.988648i	$0.548009\pi$
$4$	5.08201	2.54100
$5$	3.83583	1.71543	0.857717	−	0.514123i	$-0.171882\pi$
$5$	3.83583	1.71543	0.857717	+	0.514123i	$0.171882\pi$
$6$	1.38513	0.565479
$7$	−0.144514	−0.0546210	−0.0273105	−	0.999627i	$-0.508694\pi$
$7$	−0.144514	−0.0546210	−0.0273105	+	0.999627i	$0.508694\pi$
$8$	−8.20186	−2.89979
$9$	−2.72909	−0.909696
$10$	−10.2079	−3.22803
$11$	−3.10250	−0.935439	−0.467720	−	0.883877i	$-0.654924\pi$
$11$	−3.10250	−0.935439	−0.467720	+	0.883877i	$0.654924\pi$
$12$	−2.64514	−0.763587
$13$	−4.51024	−1.25091	−0.625457	−	0.780259i	$-0.715087\pi$
$13$	−4.51024	−1.25091	−0.625457	+	0.780259i	$0.715087\pi$
$14$	0.384580	0.102783
$15$	−1.99652	−0.515498
$16$	11.6628	2.91570
$17$	0.00372970	0.000904586 0	0.000452293	−	1.00000i	$-0.499856\pi$
$17$	0.00372970	0.000904586 0	0.000452293		1.00000i	$0.499856\pi$
$18$	7.26266	1.71183
$19$	−5.17422	−1.18705	−0.593524	−	0.804816i	$-0.702264\pi$
$19$	−5.17422	−1.18705	−0.593524	+	0.804816i	$0.702264\pi$
$20$	19.4937	4.35892
$21$	0.0752182	0.0164140
$22$	8.25639	1.76027
$23$	−2.83489	−0.591114	−0.295557	−	0.955325i	$-0.595505\pi$
$23$	−2.83489	−0.591114	−0.295557	+	0.955325i	$0.595505\pi$
$24$	4.26900	0.871406
$25$	9.71356	1.94271
$26$	12.0027	2.35392
$27$	2.98194	0.573875
$28$	−0.734420	−0.138792
$29$	2.89539	0.537661	0.268830	−	0.963188i	$-0.413363\pi$
$29$	2.89539	0.537661	0.268830	+	0.963188i	$0.413363\pi$
$30$	5.31314	0.970041
$31$	−4.84141	−0.869544	−0.434772	−	0.900541i	$-0.643171\pi$
$31$	−4.84141	−0.869544	−0.434772	+	0.900541i	$0.643171\pi$
$32$	−14.6334	−2.58684
$33$	1.61483	0.281105
$34$	−0.00992551	−0.00170221
$35$	−0.554329	−0.0936987
$36$	−13.8693	−2.31154
$37$	9.15931	1.50578	0.752890	−	0.658146i	$-0.228659\pi$
$37$	9.15931	1.50578	0.752890	+	0.658146i	$0.228659\pi$
$38$	13.7697	2.23373
$39$	2.34754	0.375907
$40$	−31.4609	−4.97440
$41$	4.83194	0.754623	0.377311	−	0.926086i	$-0.376849\pi$
$41$	4.83194	0.754623	0.377311	+	0.926086i	$0.376849\pi$
$42$	−0.200171	−0.0308870
$43$	8.24426	1.25724	0.628619	−	0.777714i	$-0.283621\pi$
$43$	8.24426	1.25724	0.628619	+	0.777714i	$0.283621\pi$
$44$	−15.7669	−2.37696
$45$	−10.4683	−1.56052
$46$	7.54421	1.11233
$47$	−9.24511	−1.34854	−0.674269	−	0.738486i	$-0.735541\pi$
$47$	−9.24511	−1.34854	−0.674269	+	0.738486i	$0.735541\pi$
$48$	−6.07039	−0.876186
$49$	−6.97912	−0.997017
$50$	−25.8498	−3.65571
$51$	−0.00194128	−0.000271834 0
$52$	−22.9211	−3.17858
$53$	−6.73966	−0.925763	−0.462881	−	0.886420i	$-0.653184\pi$
$53$	−6.73966	−0.925763	−0.462881	+	0.886420i	$0.653184\pi$
$54$	−7.93556	−1.07989
$55$	−11.9007	−1.60468
$56$	1.18528	0.158390
$57$	2.69314	0.356715
$58$	−7.70523	−1.01175
$59$	8.15885	1.06219	0.531096	−	0.847312i	$-0.321780\pi$
$59$	8.15885	1.06219	0.531096	+	0.847312i	$0.321780\pi$
$60$	−10.1463	−1.30988
$61$	8.42396	1.07858	0.539289	−	0.842121i	$-0.318693\pi$
$61$	8.42396	1.07858	0.539289	+	0.842121i	$0.318693\pi$
$62$	12.8840	1.63627
$63$	0.394391	0.0496885
$64$	15.6168	1.95210
$65$	−17.3005	−2.14586
$66$	−4.29738	−0.528971
$67$	−10.4613	−1.27805	−0.639026	−	0.769185i	$-0.720662\pi$
$67$	−10.4613	−1.27805	−0.639026	+	0.769185i	$0.720662\pi$
$68$	0.0189544	0.00229856
$69$	1.47553	0.177633
$70$	1.47518	0.176318
$71$	−3.83221	−0.454800	−0.227400	−	0.973801i	$-0.573022\pi$
$71$	−3.83221	−0.454800	−0.227400	+	0.973801i	$0.573022\pi$
$72$	22.3836	2.63793
$73$	11.2767	1.31984	0.659922	−	0.751334i	$-0.270589\pi$
$73$	11.2767	1.31984	0.659922	+	0.751334i	$0.270589\pi$
$74$	−24.3748	−2.83351
$75$	−5.05583	−0.583797
$76$	−26.2954	−3.01629
$77$	0.448354	0.0510947
$78$	−6.24729	−0.707366
$79$	−11.3790	−1.28024	−0.640118	−	0.768276i	$-0.721115\pi$
$79$	−11.3790	−1.28024	−0.640118	+	0.768276i	$0.721115\pi$
$80$	44.7365	5.00169
$81$	6.63519	0.737243
$82$	−12.8588	−1.42002
$83$	−0.314352	−0.0345046	−0.0172523	−	0.999851i	$-0.505492\pi$
$83$	−0.314352	−0.0345046	−0.0172523	+	0.999851i	$0.505492\pi$
$84$	0.382259	0.0417079
$85$	0.0143065	0.00155176
$86$	−21.9397	−2.36581
$87$	−1.50703	−0.161570
$88$	25.4463	2.71258
$89$	−0.194659	−0.0206338	−0.0103169	−	0.999947i	$-0.503284\pi$
$89$	−0.194659	−0.0206338	−0.0103169	+	0.999947i	$0.503284\pi$
$90$	27.8583	2.93652
$91$	0.651791	0.0683262
$92$	−14.4069	−1.50202
$93$	2.51992	0.261303
$94$	24.6031	2.53762
$95$	−19.8474	−2.03630
$96$	7.61656	0.777361
$97$	−13.9788	−1.41933	−0.709666	−	0.704539i	$-0.751154\pi$
$97$	−13.9788	−1.41933	−0.709666	+	0.704539i	$0.751154\pi$
$98$	18.5729	1.87614
$99$	8.46700	0.850965
$100$	49.3644	4.93644
$101$	−8.20419	−0.816347	−0.408174	−	0.912904i	$-0.633834\pi$
$101$	−8.20419	−0.816347	−0.408174	+	0.912904i	$0.633834\pi$
$102$	0.00516614	0.000511525 0
$103$	3.60120	0.354837	0.177418	−	0.984136i	$-0.443225\pi$
$103$	3.60120	0.354837	0.177418	+	0.984136i	$0.443225\pi$
$104$	36.9923	3.62739
$105$	0.288524	0.0281570
$106$	17.9356	1.74206
$107$	8.53599	0.825205	0.412603	−	0.910911i	$-0.364620\pi$
$107$	8.53599	0.825205	0.412603	+	0.910911i	$0.364620\pi$
$108$	15.1543	1.45822
$109$	18.4147	1.76381	0.881903	−	0.471431i	$-0.156262\pi$
$109$	18.4147	1.76381	0.881903	+	0.471431i	$0.156262\pi$
$110$	31.6701	3.01962
$111$	−4.76734	−0.452496
$112$	−1.68543	−0.159259
$113$	17.7873	1.67329	0.836644	−	0.547747i	$-0.184515\pi$
$113$	17.7873	1.67329	0.836644	+	0.547747i	$0.184515\pi$
$114$	−7.16699	−0.671250
$115$	−10.8741	−1.01402
$116$	14.7144	1.36620
$117$	12.3088	1.13795
$118$	−21.7124	−1.99878
$119$	−0.000538993 0	−4.94094e−5 0
$120$	16.3751	1.49484
$121$	−1.37449	−0.124953
$122$	−22.4179	−2.02962
$123$	−2.51499	−0.226769
$124$	−24.6041	−2.20951
$125$	18.0804	1.61716
$126$	−1.04955	−0.0935017
$127$	6.38106	0.566228	0.283114	−	0.959086i	$-0.408633\pi$
$127$	6.38106	0.566228	0.283114	+	0.959086i	$0.408633\pi$
$128$	−12.2928	−1.08654
$129$	−4.29107	−0.377807
$130$	46.0401	4.03798
$131$	1.96132	0.171361	0.0856805	−	0.996323i	$-0.472694\pi$
$131$	1.96132	0.171361	0.0856805	+	0.996323i	$0.472694\pi$
$132$	8.20656	0.714289
$133$	0.747746	0.0648378
$134$	27.8397	2.40498
$135$	11.4382	0.984445
$136$	−0.0305905	−0.00262311
$137$	2.10515	0.179855	0.0899273	−	0.995948i	$-0.471337\pi$
$137$	2.10515	0.179855	0.0899273	+	0.995948i	$0.471337\pi$
$138$	−3.92670	−0.334263
$139$	−5.41125	−0.458976	−0.229488	−	0.973311i	$-0.573705\pi$
$139$	−5.41125	−0.458976	−0.229488	+	0.973311i	$0.573705\pi$
$140$	−2.81711	−0.238089
$141$	4.81201	0.405244
$142$	10.1983	0.855822
$143$	13.9930	1.17015
$144$	−31.8288	−2.65240
$145$	11.1062	0.922321
$146$	−30.0097	−2.48362
$147$	3.63257	0.299610
$148$	46.5477	3.82620
$149$	−6.83234	−0.559727	−0.279863	−	0.960040i	$-0.590289\pi$
$149$	−6.83234	−0.559727	−0.279863	+	0.960040i	$0.590289\pi$
$150$	13.4546	1.09856
$151$	17.5222	1.42594	0.712969	−	0.701195i	$-0.247350\pi$
$151$	17.5222	1.42594	0.712969	+	0.701195i	$0.247350\pi$
$152$	42.4382	3.44219
$153$	−0.0101787	−0.000822899 0
$154$	−1.19316	−0.0961477
$155$	−18.5708	−1.49164
$156$	11.9302	0.955182
$157$	−5.39446	−0.430525	−0.215262	−	0.976556i	$-0.569061\pi$
$157$	−5.39446	−0.430525	−0.215262	+	0.976556i	$0.569061\pi$
$158$	30.2818	2.40909
$159$	3.50794	0.278197
$160$	−56.1311	−4.43755
$161$	0.409680	0.0322873
$162$	−17.6576	−1.38731
$163$	−6.20374	−0.485914	−0.242957	−	0.970037i	$-0.578117\pi$
$163$	−6.20374	−0.485914	−0.242957	+	0.970037i	$0.578117\pi$
$164$	24.5560	1.91750
$165$	6.19419	0.482217
$166$	0.836556	0.0649293
$167$	11.9058	0.921300	0.460650	−	0.887582i	$-0.347616\pi$
$167$	11.9058	0.921300	0.460650	+	0.887582i	$0.347616\pi$
$168$	−0.616929	−0.0475971
$169$	7.34222	0.564787
$170$	−0.0380725	−0.00292003
$171$	14.1209	1.07985
$172$	41.8974	3.19465
$173$	6.23723	0.474208	0.237104	−	0.971484i	$-0.423802\pi$
$173$	6.23723	0.474208	0.237104	+	0.971484i	$0.423802\pi$
$174$	4.01051	0.304036
$175$	−1.40374	−0.106113
$176$	−36.1838	−2.72746
$177$	−4.24661	−0.319195
$178$	0.518028	0.0388278
$179$	14.6939	1.09827	0.549137	−	0.835732i	$-0.314957\pi$
$179$	14.6939	1.09827	0.549137	+	0.835732i	$0.314957\pi$
$180$	−53.2000	−3.96530
$181$	−15.8081	−1.17501	−0.587505	−	0.809220i	$-0.699890\pi$
$181$	−15.8081	−1.17501	−0.587505	+	0.809220i	$0.699890\pi$
$182$	−1.73455	−0.128573
$183$	−4.38460	−0.324119
$184$	23.2513	1.71411
$185$	35.1335	2.58307
$186$	−6.70601	−0.491709
$187$	−0.0115714	−0.000846186 0
$188$	−46.9838	−3.42664
$189$	−0.430932	−0.0313457
$190$	52.8180	3.83182
$191$	−1.23707	−0.0895115	−0.0447557	−	0.998998i	$-0.514251\pi$
$191$	−1.23707	−0.0895115	−0.0447557	+	0.998998i	$0.514251\pi$
$192$	−8.12843	−0.586619
$193$	6.18988	0.445558	0.222779	−	0.974869i	$-0.428487\pi$
$193$	6.18988	0.445558	0.222779	+	0.974869i	$0.428487\pi$
$194$	37.2004	2.67083
$195$	9.00476	0.644844
$196$	−35.4679	−2.53342
$197$	16.5000	1.17558	0.587789	−	0.809014i	$-0.299998\pi$
$197$	16.5000	1.17558	0.587789	+	0.809014i	$0.299998\pi$
$198$	−22.5324	−1.60131
$199$	1.49201	0.105766	0.0528828	−	0.998601i	$-0.483159\pi$
$199$	1.49201	0.105766	0.0528828	+	0.998601i	$0.483159\pi$
$200$	−79.6692	−5.63346
$201$	5.44502	0.384062
$202$	21.8330	1.53617
$203$	−0.418424	−0.0293676
$204$	−0.00986561	−0.000690731 0
$205$	18.5345	1.29451
$206$	−9.58353	−0.667716
$207$	7.73665	0.537735
$208$	−52.6020	−3.64729
$209$	16.0530	1.11041
$210$	−0.767821	−0.0529847
$211$	−11.3303	−0.780007	−0.390003	−	0.920813i	$-0.627526\pi$
$211$	−11.3303	−0.780007	−0.390003	+	0.920813i	$0.627526\pi$
$212$	−34.2510	−2.35237
$213$	1.99463	0.136670
$214$	−22.7160	−1.55283
$215$	31.6235	2.15671
$216$	−24.4575	−1.66412
$217$	0.699651	0.0474954
$218$	−49.0052	−3.31905
$219$	−5.86945	−0.396621
$220$	−60.4792	−4.07751
$221$	−0.0168218	−0.00113156
$222$	12.6869	0.851487
$223$	1.49931	0.100401	0.0502006	−	0.998739i	$-0.484014\pi$
$223$	1.49931	0.100401	0.0502006	+	0.998739i	$0.484014\pi$
$224$	2.11472	0.141296
$225$	−26.5092	−1.76728
$226$	−47.3356	−3.14872
$227$	−14.6216	−0.970471	−0.485235	−	0.874384i	$-0.661266\pi$
$227$	−14.6216	−0.970471	−0.485235	+	0.874384i	$0.661266\pi$
$228$	13.6866	0.906414
$229$	−20.4565	−1.35180	−0.675900	−	0.736993i	$-0.736245\pi$
$229$	−20.4565	−1.35180	−0.675900	+	0.736993i	$0.736245\pi$
$230$	28.9383	1.90813
$231$	−0.233364	−0.0153543
$232$	−23.7476	−1.55911
$233$	5.61297	0.367718	0.183859	−	0.982953i	$-0.441141\pi$
$233$	5.61297	0.367718	0.183859	+	0.982953i	$0.441141\pi$
$234$	−32.7563	−2.14135
$235$	−35.4626	−2.31333
$236$	41.4633	2.69903
$237$	5.92267	0.384719
$238$	0.00143437	9.29765e−5 0
$239$	1.34445	0.0869651	0.0434825	−	0.999054i	$-0.486155\pi$
$239$	1.34445	0.0869651	0.0434825	+	0.999054i	$0.486155\pi$
$240$	−23.2850	−1.50304
$241$	2.53730	0.163442	0.0817208	−	0.996655i	$-0.473958\pi$
$241$	2.53730	0.163442	0.0817208	+	0.996655i	$0.473958\pi$
$242$	3.65779	0.235132
$243$	−12.3994	−0.795421
$244$	42.8107	2.74067
$245$	−26.7707	−1.71032
$246$	6.69289	0.426723
$247$	23.3370	1.48489
$248$	39.7086	2.52150
$249$	0.163618	0.0103689
$250$	−48.1156	−3.04310
$251$	8.83417	0.557608	0.278804	−	0.960348i	$-0.410062\pi$
$251$	8.83417	0.557608	0.278804	+	0.960348i	$0.410062\pi$
$252$	2.00430	0.126259
$253$	8.79523	0.552952
$254$	−16.9813	−1.06550
$255$	−0.00744641	−0.000466313 0
$256$	1.47999	0.0924997
$257$	26.6040	1.65951	0.829757	−	0.558125i	$-0.188479\pi$
$257$	26.6040	1.65951	0.829757	+	0.558125i	$0.188479\pi$
$258$	11.4194	0.710941
$259$	−1.32364	−0.0822473
$260$	−87.9212	−5.45264
$261$	−7.90178	−0.489108
$262$	−5.21946	−0.322459
$263$	26.1404	1.61189	0.805944	−	0.591992i	$-0.201658\pi$
$263$	26.1404	1.61189	0.805944	+	0.591992i	$0.201658\pi$
$264$	−13.2446	−0.815147
$265$	−25.8521	−1.58808
$266$	−1.98990	−0.122009
$267$	0.101319	0.00620059
$268$	−53.1644	−3.24754
$269$	1.78748	0.108985	0.0544924	−	0.998514i	$-0.482646\pi$
$269$	1.78748	0.108985	0.0544924	+	0.998514i	$0.482646\pi$
$270$	−30.4394	−1.85248
$271$	−1.08304	−0.0657899	−0.0328949	−	0.999459i	$-0.510473\pi$
$271$	−1.08304	−0.0657899	−0.0328949	+	0.999459i	$0.510473\pi$
$272$	0.0434988	0.00263750
$273$	−0.339252	−0.0205324
$274$	−5.60222	−0.338443
$275$	−30.1363	−1.81729
$276$	7.49868	0.451367
$277$	14.8624	0.892995	0.446498	−	0.894785i	$-0.352671\pi$
$277$	14.8624	0.892995	0.446498	+	0.894785i	$0.352671\pi$
$278$	14.4004	0.863681
$279$	13.2126	0.791021
$280$	4.54653	0.271707
$281$	8.86351	0.528753	0.264376	−	0.964420i	$-0.414834\pi$
$281$	8.86351	0.528753	0.264376	+	0.964420i	$0.414834\pi$
$282$	−12.8057	−0.762570
$283$	10.5579	0.627603	0.313801	−	0.949489i	$-0.398397\pi$
$283$	10.5579	0.627603	0.313801	+	0.949489i	$0.398397\pi$
$284$	−19.4753	−1.15565
$285$	10.3304	0.611921
$286$	−37.2383	−2.20194
$287$	−0.698282	−0.0412183
$288$	39.9358	2.35324
$289$	−17.0000	−0.999999
$290$	−29.5559	−1.73558
$291$	7.27585	0.426518
$292$	57.3085	3.35373
$293$	12.3779	0.723122	0.361561	−	0.932348i	$-0.382244\pi$
$293$	12.3779	0.723122	0.361561	+	0.932348i	$0.382244\pi$
$294$	−9.66702	−0.563792
$295$	31.2959	1.82212
$296$	−75.1233	−4.36645
$297$	−9.25148	−0.536825
$298$	18.1822	1.05327
$299$	12.7860	0.739434
$300$	−25.6938	−1.48343
$301$	−1.19141	−0.0686716
$302$	−46.6302	−2.68327
$303$	4.27021	0.245317
$304$	−60.3459	−3.46107
$305$	32.3129	1.85023
$306$	0.0270876	0.00154849
$307$	23.5758	1.34554	0.672770	−	0.739851i	$-0.265104\pi$
$307$	23.5758	1.34554	0.672770	+	0.739851i	$0.265104\pi$
$308$	2.27854	0.129832
$309$	−1.87439	−0.106631
$310$	49.4208	2.80691
$311$	5.82669	0.330401	0.165201	−	0.986260i	$-0.447173\pi$
$311$	5.82669	0.330401	0.165201	+	0.986260i	$0.447173\pi$
$312$	−19.2542	−1.09005
$313$	4.55687	0.257569	0.128785	−	0.991673i	$-0.458892\pi$
$313$	4.55687	0.257569	0.128785	+	0.991673i	$0.458892\pi$
$314$	14.3558	0.810143
$315$	1.51281	0.0852374
$316$	−57.8281	−3.25309
$317$	6.77453	0.380495	0.190248	−	0.981736i	$-0.439071\pi$
$317$	6.77453	0.380495	0.190248	+	0.981736i	$0.439071\pi$
$318$	−9.33533	−0.523500
$319$	−8.98296	−0.502949
$320$	59.9034	3.34870
$321$	−4.44291	−0.247979
$322$	−1.09024	−0.0607568
$323$	−0.0192983	−0.00107379
$324$	33.7201	1.87334
$325$	−43.8104	−2.43017
$326$	16.5094	0.914372
$327$	−9.58469	−0.530034
$328$	−39.6309	−2.18825
$329$	1.33605	0.0736586
$330$	−16.4840	−0.907415
$331$	−23.7819	−1.30717	−0.653586	−	0.756852i	$-0.726736\pi$
$331$	−23.7819	−1.30717	−0.653586	+	0.756852i	$0.726736\pi$
$332$	−1.59754	−0.0876765
$333$	−24.9966	−1.36980
$334$	−31.6838	−1.73366
$335$	−40.1277	−2.19241
$336$	0.877255	0.0478582
$337$	1.39745	0.0761237	0.0380619	−	0.999275i	$-0.487882\pi$
$337$	1.39745	0.0761237	0.0380619	+	0.999275i	$0.487882\pi$
$338$	−19.5392	−1.06279
$339$	−9.25814	−0.502833
$340$	0.0727058	0.00394302
$341$	15.0205	0.813405
$342$	−37.5786	−2.03202
$343$	2.02017	0.109079
$344$	−67.6182	−3.64573
$345$	5.65989	0.304718
$346$	−16.5985	−0.892343
$347$	−27.8967	−1.49757	−0.748787	−	0.662810i	$-0.769364\pi$
$347$	−27.8967	−1.49757	−0.748787	+	0.662810i	$0.769364\pi$
$348$	−7.65873	−0.410551
$349$	14.5106	0.776737	0.388368	−	0.921504i	$-0.373039\pi$
$349$	14.5106	0.776737	0.388368	+	0.921504i	$0.373039\pi$
$350$	3.73564	0.199679
$351$	−13.4493	−0.717869
$352$	45.4001	2.41983
$353$	6.82717	0.363373	0.181687	−	0.983356i	$-0.441844\pi$
$353$	6.82717	0.363373	0.181687	+	0.983356i	$0.441844\pi$
$354$	11.3011	0.600647
$355$	−14.6997	−0.780179
$356$	−0.989260	−0.0524307
$357$	0.000280542 0	1.48478e−5 0
$358$	−39.1035	−2.06668
$359$	11.0235	0.581796	0.290898	−	0.956754i	$-0.406046\pi$
$359$	11.0235	0.581796	0.290898	+	0.956754i	$0.406046\pi$
$360$	85.8596	4.52520
$361$	7.77256	0.409082
$362$	42.0687	2.21108
$363$	0.715410	0.0375493
$364$	3.31241	0.173617
$365$	43.2556	2.26410
$366$	11.6683	0.609913
$367$	−15.1164	−0.789068	−0.394534	−	0.918881i	$-0.629094\pi$
$367$	−15.1164	−0.789068	−0.394534	+	0.918881i	$0.629094\pi$
$368$	−33.0627	−1.72351
$369$	−13.1868	−0.686477
$370$	−93.4974	−4.86070
$371$	0.973972	0.0505661
$372$	12.8062	0.663973
$373$	−22.6255	−1.17151	−0.585753	−	0.810490i	$-0.699201\pi$
$373$	−22.6255	−1.17151	−0.585753	+	0.810490i	$0.699201\pi$
$374$	0.0307939	0.00159231
$375$	−9.41069	−0.485966
$376$	75.8271	3.91048
$377$	−13.0589	−0.672568
$378$	1.14680	0.0589849
$379$	−20.1974	−1.03747	−0.518735	−	0.854935i	$-0.673597\pi$
$379$	−20.1974	−1.03747	−0.518735	+	0.854935i	$0.673597\pi$
$380$	−100.865	−5.17425
$381$	−3.32129	−0.170155
$382$	3.29211	0.168439
$383$	24.1498	1.23400	0.616998	−	0.786965i	$-0.288349\pi$
$383$	24.1498	1.23400	0.616998	+	0.786965i	$0.288349\pi$
$384$	6.39830	0.326512
$385$	1.71981	0.0876495
$386$	−16.4725	−0.838431
$387$	−22.4993	−1.14370
$388$	−71.0403	−3.60653
$389$	15.1289	0.767065	0.383532	−	0.923527i	$-0.374707\pi$
$389$	15.1289	0.767065	0.383532	+	0.923527i	$0.374707\pi$
$390$	−23.9635	−1.21344
$391$	−0.0105733	−0.000534714 0
$392$	57.2417	2.89114
$393$	−1.02085	−0.0514950
$394$	−43.9099	−2.21215
$395$	−43.6478	−2.19616
$396$	43.0294	2.16231
$397$	9.21676	0.462576	0.231288	−	0.972885i	$-0.425706\pi$
$397$	9.21676	0.462576	0.231288	+	0.972885i	$0.425706\pi$
$398$	−3.97054	−0.199025
$399$	−0.389195	−0.0194841
$400$	113.287	5.66436
$401$	−5.36483	−0.267907	−0.133953	−	0.990988i	$-0.542767\pi$
$401$	−5.36483	−0.267907	−0.133953	+	0.990988i	$0.542767\pi$
$402$	−14.4903	−0.722711
$403$	21.8359	1.08772
$404$	−41.6938	−2.07434
$405$	25.4514	1.26469
$406$	1.11351	0.0552626
$407$	−28.4168	−1.40857
$408$	0.0159221	0.000788262 0
$409$	23.9148	1.18251	0.591254	−	0.806485i	$-0.298633\pi$
$409$	23.9148	1.18251	0.591254	+	0.806485i	$0.298633\pi$
$410$	−49.3241	−2.43594
$411$	−1.09571	−0.0540474
$412$	18.3013	0.901642
$413$	−1.17906	−0.0580180
$414$	−20.5888	−1.01189
$415$	−1.20580	−0.0591904
$416$	66.0000	3.23592
$417$	2.81651	0.137925
$418$	−42.7204	−2.08952
$419$	4.88682	0.238737	0.119368	−	0.992850i	$-0.461913\pi$
$419$	4.88682	0.238737	0.119368	+	0.992850i	$0.461913\pi$
$420$	1.46628	0.0715472
$421$	37.3482	1.82024	0.910120	−	0.414346i	$-0.135990\pi$
$421$	37.3482	1.82024	0.910120	+	0.414346i	$0.135990\pi$
$422$	30.1521	1.46778
$423$	25.2307	1.22676
$424$	55.2777	2.68452
$425$	0.0362287	0.00175735
$426$	−5.30813	−0.257180
$427$	−1.21738	−0.0589130
$428$	43.3800	2.09685
$429$	−7.28325	−0.351638
$430$	−84.1567	−4.05840
$431$	25.7940	1.24245	0.621226	−	0.783632i	$-0.286635\pi$
$431$	25.7940	1.24245	0.621226	+	0.783632i	$0.286635\pi$
$432$	34.7778	1.67325
$433$	0.113508	0.00545487	0.00272743	−	0.999996i	$-0.499132\pi$
$433$	0.113508	0.00545487	0.00272743	+	0.999996i	$0.499132\pi$
$434$	−1.86191	−0.0893747
$435$	−5.78070	−0.277163
$436$	93.5836	4.48184
$437$	14.6683	0.701681
$438$	15.6198	0.746344
$439$	−1.87195	−0.0893432	−0.0446716	−	0.999002i	$-0.514224\pi$
$439$	−1.87195	−0.0893432	−0.0446716	+	0.999002i	$0.514224\pi$
$440$	97.6075	4.65325
$441$	19.0466	0.906982
$442$	0.0447664	0.00212932
$443$	22.8042	1.08346	0.541731	−	0.840552i	$-0.317769\pi$
$443$	22.8042	1.08346	0.541731	+	0.840552i	$0.317769\pi$
$444$	−24.2277	−1.14979
$445$	−0.746679	−0.0353960
$446$	−3.98997	−0.188931
$447$	3.55617	0.168201
$448$	−2.25684	−0.106626
$449$	18.0422	0.851464	0.425732	−	0.904849i	$-0.360017\pi$
$449$	18.0422	0.851464	0.425732	+	0.904849i	$0.360017\pi$
$450$	70.5463	3.32558
$451$	−14.9911	−0.705904
$452$	90.3952	4.25183
$453$	−9.12017	−0.428503
$454$	38.9111	1.82619
$455$	2.50016	0.117209
$456$	−22.0887	−1.03440
$457$	36.1701	1.69196	0.845982	−	0.533211i	$-0.179015\pi$
$457$	36.1701	1.69196	0.845982	+	0.533211i	$0.179015\pi$
$458$	54.4388	2.54376
$459$	0.0111218	0.000519120 0
$460$	−55.2624	−2.57662
$461$	13.7500	0.640401	0.320201	−	0.947350i	$-0.396250\pi$
$461$	13.7500	0.640401	0.320201	+	0.947350i	$0.396250\pi$
$462$	0.621030	0.0288930
$463$	19.5165	0.907007	0.453504	−	0.891254i	$-0.350174\pi$
$463$	19.5165	0.907007	0.453504	+	0.891254i	$0.350174\pi$
$464$	33.7684	1.56766
$465$	9.66596	0.448248
$466$	−14.9373	−0.691955
$467$	23.2831	1.07741	0.538706	−	0.842494i	$-0.318913\pi$
$467$	23.2831	1.07741	0.538706	+	0.842494i	$0.318913\pi$
$468$	62.5536	2.89154
$469$	1.51180	0.0698085
$470$	94.3733	4.35312
$471$	2.80777	0.129375
$472$	−66.9177	−3.08014
$473$	−25.5778	−1.17607
$474$	−15.7614	−0.723947
$475$	−50.2601	−2.30609
$476$	−0.00273917	−0.000125550 0
$477$	18.3931	0.842163
$478$	−3.57785	−0.163647
$479$	33.5302	1.53203	0.766017	−	0.642820i	$-0.222236\pi$
$479$	33.5302	1.53203	0.766017	+	0.642820i	$0.222236\pi$
$480$	29.2158	1.33351
$481$	−41.3106	−1.88360
$482$	−6.75226	−0.307557
$483$	−0.213235	−0.00970252
$484$	−6.98516	−0.317507
$485$	−53.6202	−2.43477
$486$	32.9973	1.49679
$487$	−0.722001	−0.0327170	−0.0163585	−	0.999866i	$-0.505207\pi$
$487$	−0.722001	−0.0327170	−0.0163585	+	0.999866i	$0.505207\pi$
$488$	−69.0922	−3.12765
$489$	3.22899	0.146020
$490$	71.2422	3.21840
$491$	−20.8540	−0.941126	−0.470563	−	0.882366i	$-0.655949\pi$
$491$	−20.8540	−0.941126	−0.470563	+	0.882366i	$0.655949\pi$
$492$	−12.7812	−0.576220
$493$	0.0107990	0.000486361 0
$494$	−62.1044	−2.79421
$495$	32.4779	1.45977
$496$	−56.4645	−2.53533
$497$	0.553807	0.0248416
$498$	−0.435420	−0.0195117
$499$	5.31394	0.237885	0.118942	−	0.992901i	$-0.462050\pi$
$499$	5.31394	0.237885	0.118942	+	0.992901i	$0.462050\pi$
$500$	91.8847	4.10921
$501$	−6.19688	−0.276856
$502$	−23.5095	−1.04928
$503$	−21.0478	−0.938475	−0.469237	−	0.883072i	$-0.655471\pi$
$503$	−21.0478	−0.938475	−0.469237	+	0.883072i	$0.655471\pi$
$504$	−3.23474	−0.144087
$505$	−31.4698	−1.40039
$506$	−23.4059	−1.04052
$507$	−3.82157	−0.169722
$508$	32.4286	1.43879
$509$	−8.68196	−0.384821	−0.192411	−	0.981315i	$-0.561631\pi$
$509$	−8.68196	−0.384821	−0.192411	+	0.981315i	$0.561631\pi$
$510$	0.0198164	0.000877486 0
$511$	−1.62964	−0.0720912
$512$	20.6470	0.912478
$513$	−15.4292	−0.681217
$514$	−70.7988	−3.12280
$515$	13.8136	0.608699
$516$	−21.8072	−0.960010
$517$	28.6830	1.26148
$518$	3.52249	0.154769
$519$	−3.24643	−0.142502
$520$	141.896	6.22255
$521$	−1.53500	−0.0672494	−0.0336247	−	0.999435i	$-0.510705\pi$
$521$	−1.53500	−0.0672494	−0.0336247	+	0.999435i	$0.510705\pi$
$522$	21.0283	0.920382
$523$	35.7093	1.56146	0.780729	−	0.624869i	$-0.214848\pi$
$523$	35.7093	1.56146	0.780729	+	0.624869i	$0.214848\pi$
$524$	9.96743	0.435429
$525$	0.730636	0.0318876
$526$	−69.5650	−3.03318
$527$	−0.0180570	−0.000786577 0
$528$	18.8334	0.819618
$529$	−14.9634	−0.650584
$530$	68.7978	2.98839
$531$	−22.2662	−0.966271
$532$	3.80005	0.164753
$533$	−21.7932	−0.943968
$534$	−0.269629	−0.0116680
$535$	32.7426	1.41558
$536$	85.8021	3.70609
$537$	−7.64805	−0.330038
$538$	−4.75686	−0.205083
$539$	21.6527	0.932648
$540$	58.1291	2.50148
$541$	−28.0427	−1.20565	−0.602824	−	0.797874i	$-0.705958\pi$
$541$	−28.0427	−1.20565	−0.602824	+	0.797874i	$0.705958\pi$
$542$	2.88219	0.123801
$543$	8.22801	0.353098
$544$	−0.0545782	−0.00234002
$545$	70.6355	3.02569
$546$	0.902818	0.0386370
$547$	9.34564	0.399591	0.199795	−	0.979838i	$-0.435972\pi$
$547$	9.34564	0.399591	0.199795	+	0.979838i	$0.435972\pi$
$548$	10.6984	0.457012
$549$	−22.9897	−0.981178
$550$	80.1989	3.41969
$551$	−14.9814	−0.638229
$552$	−12.1021	−0.515101
$553$	1.64442	0.0699278
$554$	−39.5519	−1.68040
$555$	−18.2867	−0.776227
$556$	−27.5000	−1.16626
$557$	−6.60820	−0.279998	−0.139999	−	0.990152i	$-0.544710\pi$
$557$	−6.60820	−0.279998	−0.139999	+	0.990152i	$0.544710\pi$
$558$	−35.1616	−1.48851
$559$	−37.1835	−1.57270
$560$	−6.46503	−0.273197
$561$	0.00602282	0.000254284 0
$562$	−23.5876	−0.994984
$563$	−12.9450	−0.545566	−0.272783	−	0.962076i	$-0.587944\pi$
$563$	−12.9450	−0.545566	−0.272783	+	0.962076i	$0.587944\pi$
$564$	24.4547	1.02973
$565$	68.2289	2.87041
$566$	−28.0968	−1.18099
$567$	−0.958875	−0.0402690
$568$	31.4313	1.31883
$569$	31.8247	1.33416	0.667081	−	0.744985i	$-0.267543\pi$
$569$	31.8247	1.33416	0.667081	+	0.744985i	$0.267543\pi$
$570$	−27.4913	−1.15149
$571$	−9.61512	−0.402380	−0.201190	−	0.979552i	$-0.564481\pi$
$571$	−9.61512	−0.402380	−0.201190	+	0.979552i	$0.564481\pi$
$572$	71.1126	2.97337
$573$	0.643887	0.0268987
$574$	1.85827	0.0775627
$575$	−27.5368	−1.14836
$576$	−42.6197	−1.77582
$577$	−25.5132	−1.06213	−0.531065	−	0.847331i	$-0.678208\pi$
$577$	−25.5132	−1.06213	−0.531065	+	0.847331i	$0.678208\pi$
$578$	45.2404	1.88175
$579$	−3.22178	−0.133893
$580$	56.4419	2.34362
$581$	0.0454282	0.00188468
$582$	−19.3625	−0.802602
$583$	20.9098	0.865995
$584$	−92.4903	−3.82727
$585$	47.2145	1.95208
$586$	−32.9400	−1.36074
$587$	27.4421	1.13266	0.566328	−	0.824180i	$-0.308364\pi$
$587$	27.4421	1.13266	0.566328	+	0.824180i	$0.308364\pi$
$588$	18.4608	0.761309
$589$	25.0505	1.03219
$590$	−83.2848	−3.42878
$591$	−8.58813	−0.353268
$592$	106.823	4.39041
$593$	−25.9393	−1.06520	−0.532600	−	0.846367i	$-0.678785\pi$
$593$	−25.9393	−1.06520	−0.532600	+	0.846367i	$0.678785\pi$
$594$	24.6201	1.01017
$595$	−0.00206748	−8.47586e−5 0
$596$	−34.7220	−1.42227
$597$	−0.776578	−0.0317832
$598$	−34.0262	−1.39143
$599$	28.2886	1.15584	0.577921	−	0.816092i	$-0.303864\pi$
$599$	28.2886	1.15584	0.577921	+	0.816092i	$0.303864\pi$
$600$	41.4672	1.69289
$601$	1.44219	0.0588282	0.0294141	−	0.999567i	$-0.490636\pi$
$601$	1.44219	0.0588282	0.0294141	+	0.999567i	$0.490636\pi$
$602$	3.17058	0.129223
$603$	28.5498	1.16264
$604$	89.0481	3.62332
$605$	−5.27230	−0.214349
$606$	−11.3639	−0.461627
$607$	45.9788	1.86622	0.933111	−	0.359589i	$-0.117083\pi$
$607$	45.9788	1.86622	0.933111	+	0.359589i	$0.117083\pi$
$608$	75.7163	3.07070
$609$	0.217786	0.00882514
$610$	−85.9911	−3.48168
$611$	41.6976	1.68691
$612$	−0.0517282	−0.00209099
$613$	25.8566	1.04434	0.522170	−	0.852841i	$-0.325123\pi$
$613$	25.8566	1.04434	0.522170	+	0.852841i	$0.325123\pi$
$614$	−62.7400	−2.53198
$615$	−9.64705	−0.389007
$616$	−3.67733	−0.148164
$617$	34.9713	1.40789	0.703946	−	0.710254i	$-0.251420\pi$
$617$	34.9713	1.40789	0.703946	+	0.710254i	$0.251420\pi$
$618$	4.98815	0.200653
$619$	−3.97633	−0.159822	−0.0799110	−	0.996802i	$-0.525464\pi$
$619$	−3.97633	−0.159822	−0.0799110	+	0.996802i	$0.525464\pi$
$620$	−94.3771	−3.79028
$621$	−8.45347	−0.339226
$622$	−15.5060	−0.621734
$623$	0.0281309	0.00112704
$624$	27.3789	1.09603
$625$	20.7854	0.831416
$626$	−12.1268	−0.484683
$627$	−8.35547	−0.333685
$628$	−27.4147	−1.09397
$629$	0.0341615	0.00136211
$630$	−4.02591	−0.160396
$631$	−40.2026	−1.60044	−0.800219	−	0.599708i	$-0.795284\pi$
$631$	−40.2026	−1.60044	−0.800219	+	0.599708i	$0.795284\pi$
$632$	93.3289	3.71242
$633$	5.89730	0.234397
$634$	−18.0284	−0.715999
$635$	24.4766	0.971326
$636$	17.8274	0.706901
$637$	31.4775	1.24718
$638$	23.9055	0.946427
$639$	10.4584	0.413730
$640$	−47.1530	−1.86389
$641$	−19.8871	−0.785492	−0.392746	−	0.919647i	$-0.628475\pi$
$641$	−19.8871	−0.785492	−0.392746	+	0.919647i	$0.628475\pi$
$642$	11.8235	0.466636
$643$	−19.1628	−0.755707	−0.377854	−	0.925865i	$-0.623338\pi$
$643$	−19.1628	−0.755707	−0.377854	+	0.925865i	$0.623338\pi$
$644$	2.08200	0.0820421
$645$	−16.4598	−0.648103
$646$	0.0513568	0.00202060
$647$	−43.7161	−1.71866	−0.859328	−	0.511424i	$-0.829118\pi$
$647$	−43.7161	−1.71866	−0.859328	+	0.511424i	$0.829118\pi$
$648$	−54.4209	−2.13785
$649$	−25.3128	−0.993615
$650$	116.589	4.57298
$651$	−0.364162	−0.0142726
$652$	−31.5274	−1.23471
$653$	21.7141	0.849740	0.424870	−	0.905254i	$-0.360320\pi$
$653$	21.7141	0.849740	0.424870	+	0.905254i	$0.360320\pi$
$654$	25.5068	0.997395
$655$	7.52327	0.293958
$656$	56.3540	2.20025
$657$	−30.7752	−1.20066
$658$	−3.55549	−0.138607
$659$	−9.30127	−0.362326	−0.181163	−	0.983453i	$-0.557986\pi$
$659$	−9.30127	−0.362326	−0.181163	+	0.983453i	$0.557986\pi$
$660$	31.4789	1.22532
$661$	−40.2250	−1.56457	−0.782285	−	0.622920i	$-0.785946\pi$
$661$	−40.2250	−1.56457	−0.782285	+	0.622920i	$0.785946\pi$
$662$	63.2885	2.45978
$663$	0.00875563	0.000340041 0
$664$	2.57827	0.100056
$665$	2.86822	0.111225
$666$	66.5209	2.57763
$667$	−8.20811	−0.317819
$668$	60.5055	2.34103
$669$	−0.780378	−0.0301712
$670$	106.788	4.12558
$671$	−26.1354	−1.00894
$672$	−1.10070	−0.0424603
$673$	−35.8531	−1.38204	−0.691018	−	0.722838i	$-0.742837\pi$
$673$	−35.8531	−1.38204	−0.691018	+	0.722838i	$0.742837\pi$
$674$	−3.71889	−0.143246
$675$	28.9653	1.11487
$676$	37.3133	1.43513
$677$	−11.2993	−0.434266	−0.217133	−	0.976142i	$-0.569671\pi$
$677$	−11.2993	−0.434266	−0.217133	+	0.976142i	$0.569671\pi$
$678$	24.6378	0.946209
$679$	2.02013	0.0775253
$680$	−0.117340	−0.00449978
$681$	7.61043	0.291632
$682$	−39.9726	−1.53063
$683$	−35.5058	−1.35859	−0.679297	−	0.733864i	$-0.737715\pi$
$683$	−35.5058	−1.35859	−0.679297	+	0.733864i	$0.737715\pi$
$684$	71.7626	2.74391
$685$	8.07497	0.308529
$686$	−5.37609	−0.205260
$687$	10.6474	0.406224
$688$	96.1511	3.66573
$689$	30.3974	1.15805
$690$	−15.0621	−0.573406
$691$	31.8054	1.20994	0.604968	−	0.796250i	$-0.293186\pi$
$691$	31.8054	1.20994	0.604968	+	0.796250i	$0.293186\pi$
$692$	31.6977	1.20496
$693$	−1.22360	−0.0464806
$694$	74.2389	2.81807
$695$	−20.7566	−0.787343
$696$	12.3604	0.468521
$697$	0.0180217	0.000682621 0
$698$	−38.6158	−1.46163
$699$	−2.92150	−0.110501
$700$	−7.13383	−0.269633
$701$	−42.4999	−1.60520	−0.802599	−	0.596519i	$-0.796550\pi$
$701$	−42.4999	−1.60520	−0.802599	+	0.596519i	$0.796550\pi$
$702$	35.7912	1.35085
$703$	−47.3923	−1.78743
$704$	−48.4512	−1.82607
$705$	18.4580	0.695169
$706$	−18.1685	−0.683780
$707$	1.18562	0.0445897
$708$	−21.5813	−0.811076
$709$	−30.7754	−1.15579	−0.577897	−	0.816110i	$-0.696126\pi$
$709$	−30.7754	−1.15579	−0.577897	+	0.816110i	$0.696126\pi$
$710$	39.1189	1.46811
$711$	31.0543	1.16463
$712$	1.59657	0.0598339
$713$	13.7249	0.514000
$714$	−0.000746579 0	−2.79400e−5 0
$715$	53.6747	2.00732
$716$	74.6745	2.79072
$717$	−0.699774	−0.0261335
$718$	−29.3357	−1.09480
$719$	−42.1579	−1.57222	−0.786112	−	0.618084i	$-0.787909\pi$
$719$	−42.1579	−1.57222	−0.786112	+	0.618084i	$0.787909\pi$
$720$	−122.090	−4.55002
$721$	−0.520423	−0.0193815
$722$	−20.6844	−0.769792
$723$	−1.32064	−0.0491152
$724$	−80.3371	−2.98571
$725$	28.1246	1.04452
$726$	−1.90385	−0.0706586
$727$	19.7781	0.733528	0.366764	−	0.930314i	$-0.380466\pi$
$727$	19.7781	0.733528	0.366764	+	0.930314i	$0.380466\pi$
$728$	−5.34589	−0.198132
$729$	−13.4518	−0.498214
$730$	−115.112	−4.26049
$731$	0.0307486	0.00113728
$732$	−22.2826	−0.823589
$733$	42.9162	1.58515	0.792573	−	0.609777i	$-0.208741\pi$
$733$	42.9162	1.58515	0.792573	+	0.609777i	$0.208741\pi$
$734$	40.2278	1.48483
$735$	13.9339	0.513960
$736$	41.4840	1.52912
$737$	32.4562	1.19554
$738$	35.0928	1.29178
$739$	−18.4644	−0.679223	−0.339611	−	0.940566i	$-0.610296\pi$
$739$	−18.4644	−0.679223	−0.339611	+	0.940566i	$0.610296\pi$
$740$	178.549	6.56358
$741$	−12.1467	−0.446220
$742$	−2.59194	−0.0951531
$743$	−44.2693	−1.62408	−0.812042	−	0.583599i	$-0.801644\pi$
$743$	−44.2693	−1.62408	−0.812042	+	0.583599i	$0.801644\pi$
$744$	−20.6680	−0.757725
$745$	−26.2076	−0.960174
$746$	60.2112	2.20449
$747$	0.857895	0.0313887
$748$	−0.0588060	−0.00215016
$749$	−1.23357	−0.0450736
$750$	25.0438	0.914469
$751$	−45.9857	−1.67804	−0.839021	−	0.544098i	$-0.816872\pi$
$751$	−45.9857	−1.67804	−0.839021	+	0.544098i	$0.816872\pi$
$752$	−107.824	−3.93193
$753$	−4.59812	−0.167565
$754$	34.7524	1.26561
$755$	67.2122	2.44610
$756$	−2.19000	−0.0796495
$757$	−7.52926	−0.273656	−0.136828	−	0.990595i	$-0.543691\pi$
$757$	−7.52926	−0.273656	−0.136828	+	0.990595i	$0.543691\pi$
$758$	53.7494	1.95227
$759$	−4.57785	−0.166165
$760$	162.786	5.90485
$761$	33.0136	1.19674	0.598371	−	0.801219i	$-0.295815\pi$
$761$	33.0136	1.19674	0.598371	+	0.801219i	$0.295815\pi$
$762$	8.83863	0.320190
$763$	−2.66117	−0.0963409
$764$	−6.28682	−0.227449
$765$	−0.0390437	−0.00141163
$766$	−64.2675	−2.32208
$767$	−36.7983	−1.32871
$768$	−0.770325	−0.0277967
$769$	48.6112	1.75296	0.876482	−	0.481434i	$-0.159884\pi$
$769$	48.6112	1.75296	0.876482	+	0.481434i	$0.159884\pi$
$770$	−4.57676	−0.164935
$771$	−13.8472	−0.498694
$772$	31.4571	1.13216
$773$	33.9453	1.22093	0.610464	−	0.792044i	$-0.290983\pi$
$773$	33.9453	1.22093	0.610464	+	0.792044i	$0.290983\pi$
$774$	59.8752	2.15217
$775$	−47.0274	−1.68927
$776$	114.652	4.11577
$777$	0.688946	0.0247158
$778$	−40.2610	−1.44343
$779$	−25.0015	−0.895773
$780$	45.7623	1.63855
$781$	11.8894	0.425438
$782$	0.0281377	0.00100620
$783$	8.63390	0.308550
$784$	−81.3960	−2.90700
$785$	−20.6922	−0.738537
$786$	2.71669	0.0969010
$787$	−11.4378	−0.407712	−0.203856	−	0.979001i	$-0.565347\pi$
$787$	−11.4378	−0.407712	−0.203856	+	0.979001i	$0.565347\pi$
$788$	83.8533	2.98715
$789$	−13.6059	−0.484382
$790$	116.156	4.13264
$791$	−2.57051	−0.0913967
$792$	−69.4451	−2.46762
$793$	−37.9941	−1.34921
$794$	−24.5277	−0.870455
$795$	13.4558	0.477229
$796$	7.58240	0.268751
$797$	51.7819	1.83421	0.917104	−	0.398647i	$-0.130520\pi$
$797$	51.7819	1.83421	0.917104	+	0.398647i	$0.130520\pi$
$798$	1.03573	0.0366644
$799$	−0.0344815	−0.00121987
$800$	−142.142	−5.02549
$801$	0.531242	0.0187705
$802$	14.2769	0.504135
$803$	−34.9861	−1.23463
$804$	27.6717	0.975904
$805$	1.57146	0.0553867
$806$	−58.1098	−2.04683
$807$	−0.930370	−0.0327506
$808$	67.2896	2.36724
$809$	−30.1931	−1.06153	−0.530767	−	0.847518i	$-0.678096\pi$
$809$	−30.1931	−1.06153	−0.530767	+	0.847518i	$0.678096\pi$
$810$	−67.7314	−2.37984
$811$	−21.3638	−0.750184	−0.375092	−	0.926988i	$-0.622389\pi$
$811$	−21.3638	−0.750184	−0.375092	+	0.926988i	$0.622389\pi$
$812$	−2.12643	−0.0746232
$813$	0.563713	0.0197703
$814$	75.6228	2.65058
$815$	−23.7964	−0.833553
$816$	−0.0226408	−0.000792585 0
$817$	−42.6576	−1.49240
$818$	−63.6420	−2.22519
$819$	−1.77879	−0.0621561
$820$	94.1925	3.28934
$821$	−18.5565	−0.647628	−0.323814	−	0.946121i	$-0.604965\pi$
$821$	−18.5565	−0.647628	−0.323814	+	0.946121i	$0.604965\pi$
$822$	2.91591	0.101704
$823$	52.1757	1.81873	0.909366	−	0.415998i	$-0.136568\pi$
$823$	52.1757	1.81873	0.909366	+	0.415998i	$0.136568\pi$
$824$	−29.5365	−1.02895
$825$	15.6857	0.546106
$826$	3.13773	0.109176
$827$	7.19733	0.250276	0.125138	−	0.992139i	$-0.460063\pi$
$827$	7.19733	0.250276	0.125138	+	0.992139i	$0.460063\pi$
$828$	39.3177	1.36639
$829$	30.8159	1.07028	0.535140	−	0.844764i	$-0.320259\pi$
$829$	30.8159	1.07028	0.535140	+	0.844764i	$0.320259\pi$
$830$	3.20888	0.111382
$831$	−7.73576	−0.268350
$832$	−70.4356	−2.44191
$833$	−0.0260300	−0.000901888 0
$834$	−7.49531	−0.259541
$835$	45.6686	1.58043
$836$	81.5816	2.82156
$837$	−14.4368	−0.499010
$838$	−13.0048	−0.449245
$839$	16.6602	0.575173	0.287586	−	0.957755i	$-0.407147\pi$
$839$	16.6602	0.575173	0.287586	+	0.957755i	$0.407147\pi$
$840$	−2.36643	−0.0816496
$841$	−20.6167	−0.710921
$842$	−99.3912	−3.42525
$843$	−4.61339	−0.158893
$844$	−57.5804	−1.98200
$845$	28.1635	0.968854
$846$	−67.1441	−2.30846
$847$	0.198632	0.00682509
$848$	−78.6033	−2.69925
$849$	−5.49531	−0.188598
$850$	−0.0964120	−0.00330690
$851$	−25.9656	−0.890089
$852$	10.1368	0.347279
$853$	−37.7258	−1.29171	−0.645854	−	0.763461i	$-0.723499\pi$
$853$	−37.7258	−1.29171	−0.645854	+	0.763461i	$0.723499\pi$
$854$	3.23969	0.110860
$855$	54.1653	1.85242
$856$	−70.0110	−2.39293
$857$	11.5298	0.393852	0.196926	−	0.980418i	$-0.436904\pi$
$857$	11.5298	0.393852	0.196926	+	0.980418i	$0.436904\pi$
$858$	19.3822	0.661698
$859$	−14.1613	−0.483178	−0.241589	−	0.970379i	$-0.577669\pi$
$859$	−14.1613	−0.483178	−0.241589	+	0.970379i	$0.577669\pi$
$860$	160.711	5.48020
$861$	0.363450	0.0123863
$862$	−68.6430	−2.33799
$863$	44.9800	1.53114	0.765568	−	0.643355i	$-0.222458\pi$
$863$	44.9800	1.53114	0.765568	+	0.643355i	$0.222458\pi$
$864$	−43.6359	−1.48452
$865$	23.9249	0.813472
$866$	−0.302069	−0.0102647
$867$	8.84835	0.300506
$868$	3.55563	0.120686
$869$	35.3033	1.19758
$870$	15.3836	0.521553
$871$	47.1829	1.59873
$872$	−151.035	−5.11468
$873$	38.1494	1.29116
$874$	−39.0354	−1.32039
$875$	−2.61286	−0.0883309
$876$	−29.8286	−1.00782
$877$	−27.8766	−0.941327	−0.470663	−	0.882313i	$-0.655985\pi$
$877$	−27.8766	−0.941327	−0.470663	+	0.882313i	$0.655985\pi$
$878$	4.98163	0.168122
$879$	−6.44257	−0.217303
$880$	−138.795	−4.67878
$881$	−44.3495	−1.49417	−0.747086	−	0.664727i	$-0.768548\pi$
$881$	−44.3495	−1.49417	−0.747086	+	0.664727i	$0.768548\pi$
$882$	−50.6870	−1.70672
$883$	17.9391	0.603697	0.301849	−	0.953356i	$-0.402396\pi$
$883$	17.9391	0.603697	0.301849	+	0.953356i	$0.402396\pi$
$884$	−0.0854888	−0.00287530
$885$	−16.2893	−0.547558
$886$	−60.6868	−2.03881
$887$	41.1211	1.38071	0.690356	−	0.723470i	$-0.257454\pi$
$887$	41.1211	1.38071	0.690356	+	0.723470i	$0.257454\pi$
$888$	39.1011	1.31215
$889$	−0.922151	−0.0309279
$890$	1.98707	0.0666066
$891$	−20.5857	−0.689646
$892$	7.61951	0.255120
$893$	47.8363	1.60078
$894$	−9.46371	−0.316514
$895$	56.3632	1.88402
$896$	1.77648	0.0593479
$897$	−6.65501	−0.222204
$898$	−48.0140	−1.60225
$899$	−14.0178	−0.467520
$900$	−134.720	−4.49066
$901$	−0.0251369	−0.000837433 0
$902$	39.8944	1.32834
$903$	0.620118	0.0206362
$904$	−145.889	−4.85219
$905$	−60.6373	−2.01565
$906$	24.2706	0.806338
$907$	44.6233	1.48169	0.740846	−	0.671675i	$-0.234425\pi$
$907$	44.6233	1.48169	0.740846	+	0.671675i	$0.234425\pi$
$908$	−74.3072	−2.46597
$909$	22.3899	0.742628
$910$	−6.65342	−0.220559
$911$	46.4578	1.53922	0.769609	−	0.638516i	$-0.220451\pi$
$911$	46.4578	1.53922	0.769609	+	0.638516i	$0.220451\pi$
$912$	31.4095	1.04007
$913$	0.975278	0.0322770
$914$	−96.2560	−3.18386
$915$	−16.8186	−0.556005
$916$	−103.960	−3.43493
$917$	−0.283437	−0.00935991
$918$	−0.0295973	−0.000976856 0
$919$	−21.2863	−0.702170	−0.351085	−	0.936344i	$-0.614187\pi$
$919$	−21.2863	−0.702170	−0.351085	+	0.936344i	$0.614187\pi$
$920$	89.1880	2.94044
$921$	−12.2710	−0.404343
$922$	−36.5916	−1.20508
$923$	17.2842	0.568916
$924$	−1.18596	−0.0390152
$925$	88.9694	2.92530
$926$	−51.9373	−1.70677
$927$	−9.82799	−0.322794
$928$	−42.3694	−1.39084
$929$	21.4640	0.704212	0.352106	−	0.935960i	$-0.385466\pi$
$929$	21.4640	0.704212	0.352106	+	0.935960i	$0.385466\pi$
$930$	−25.7231	−0.843493
$931$	36.1115	1.18351
$932$	28.5252	0.934372
$933$	−3.03274	−0.0992876
$934$	−61.9610	−2.02743
$935$	−0.0443859	−0.00145157
$936$	−100.955	−3.29983
$937$	−21.4497	−0.700732	−0.350366	−	0.936613i	$-0.613943\pi$
$937$	−21.4497	−0.700732	−0.350366	+	0.936613i	$0.613943\pi$
$938$	−4.02321	−0.131363
$939$	−2.37181	−0.0774012
$940$	−180.221	−5.87818
$941$	54.5844	1.77940	0.889700	−	0.456545i	$-0.150913\pi$
$941$	54.5844	1.77940	0.889700	+	0.456545i	$0.150913\pi$
$942$	−7.47206	−0.243453
$943$	−13.6980	−0.446068
$944$	95.1550	3.09703
$945$	−1.65298	−0.0537714
$946$	68.0678	2.21307
$947$	−37.1466	−1.20710	−0.603551	−	0.797324i	$-0.706248\pi$
$947$	−37.1466	−1.20710	−0.603551	+	0.797324i	$0.706248\pi$
$948$	30.0991	0.977572
$949$	−50.8608	−1.65101
$950$	133.752	4.33950
$951$	−3.52609	−0.114341
$952$	0.00442075	0.000143277 0
$953$	−45.0458	−1.45918	−0.729588	−	0.683887i	$-0.760288\pi$
$953$	−45.0458	−1.45918	−0.729588	+	0.683887i	$0.760288\pi$
$954$	−48.9478	−1.58475
$955$	−4.74520	−0.153551
$956$	6.83250	0.220979
$957$	4.67556	0.151139
$958$	−89.2307	−2.88291
$959$	−0.304222	−0.00982385
$960$	−31.1792	−1.00631
$961$	−7.56071	−0.243894
$962$	109.936	3.54448
$963$	−23.2955	−0.750686
$964$	12.8946	0.415306
$965$	23.7433	0.764324
$966$	0.567462	0.0182578
$967$	−3.96294	−0.127440	−0.0637199	−	0.997968i	$-0.520296\pi$
$967$	−3.96294	−0.127440	−0.0637199	+	0.997968i	$0.520296\pi$
$968$	11.2734	0.362339
$969$	0.0100446	0.000322679 0
$970$	142.694	4.58164
$971$	−17.3552	−0.556955	−0.278477	−	0.960443i	$-0.589830\pi$
$971$	−17.3552	−0.556955	−0.278477	+	0.960443i	$0.589830\pi$
$972$	−63.0138	−2.02117
$973$	0.782000	0.0250698
$974$	1.92139	0.0615654
$975$	22.8030	0.730279
$976$	98.2470	3.14481
$977$	13.0702	0.418154	0.209077	−	0.977899i	$-0.432954\pi$
$977$	13.0702	0.418154	0.209077	+	0.977899i	$0.432954\pi$
$978$	−8.59301	−0.274774
$979$	0.603930	0.0193017
$980$	−136.049	−4.34592
$981$	−50.2553	−1.60453
$982$	55.4966	1.77097
$983$	10.1887	0.324970	0.162485	−	0.986711i	$-0.448049\pi$
$983$	10.1887	0.324970	0.162485	+	0.986711i	$0.448049\pi$
$984$	20.6276	0.657583
$985$	63.2912	2.01663
$986$	−0.0287382	−0.000915212 0
$987$	−0.695401	−0.0221348
$988$	118.599	3.77312
$989$	−23.3715	−0.743171
$990$	−86.4304	−2.74694
$991$	3.81858	0.121301	0.0606506	−	0.998159i	$-0.480682\pi$
$991$	3.81858	0.121301	0.0606506	+	0.998159i	$0.480682\pi$
$992$	70.8463	2.24937
$993$	12.3783	0.392813
$994$	−1.47379	−0.0467459
$995$	5.72309	0.181434
$996$	0.831507	0.0263473
$997$	−34.1054	−1.08013	−0.540064	−	0.841624i	$-0.681600\pi$
$997$	−34.1054	−1.08013	−0.540064	+	0.841624i	$0.681600\pi$
$998$	−14.1415	−0.447641
$999$	27.3125	0.864130

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.c.1.6	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.c.1.6	✓	259	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6043 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66120 q^{2} -0.520492 q^{3} +5.08201 q^{4} +3.83583 q^{5} +1.38513 q^{6} -0.144514 q^{7} -8.20186 q^{8} -2.72909 q^{9} +O(q^{10})\)	\(q-2.66120 q^{2} -0.520492 q^{3} +5.08201 q^{4} +3.83583 q^{5} +1.38513 q^{6} -0.144514 q^{7} -8.20186 q^{8} -2.72909 q^{9} -10.2079 q^{10} -3.10250 q^{11} -2.64514 q^{12} -4.51024 q^{13} +0.384580 q^{14} -1.99652 q^{15} +11.6628 q^{16} +0.00372970 q^{17} +7.26266 q^{18} -5.17422 q^{19} +19.4937 q^{20} +0.0752182 q^{21} +8.25639 q^{22} -2.83489 q^{23} +4.26900 q^{24} +9.71356 q^{25} +12.0027 q^{26} +2.98194 q^{27} -0.734420 q^{28} +2.89539 q^{29} +5.31314 q^{30} -4.84141 q^{31} -14.6334 q^{32} +1.61483 q^{33} -0.00992551 q^{34} -0.554329 q^{35} -13.8693 q^{36} +9.15931 q^{37} +13.7697 q^{38} +2.34754 q^{39} -31.4609 q^{40} +4.83194 q^{41} -0.200171 q^{42} +8.24426 q^{43} -15.7669 q^{44} -10.4683 q^{45} +7.54421 q^{46} -9.24511 q^{47} -6.07039 q^{48} -6.97912 q^{49} -25.8498 q^{50} -0.00194128 q^{51} -22.9211 q^{52} -6.73966 q^{53} -7.93556 q^{54} -11.9007 q^{55} +1.18528 q^{56} +2.69314 q^{57} -7.70523 q^{58} +8.15885 q^{59} -10.1463 q^{60} +8.42396 q^{61} +12.8840 q^{62} +0.394391 q^{63} +15.6168 q^{64} -17.3005 q^{65} -4.29738 q^{66} -10.4613 q^{67} +0.0189544 q^{68} +1.47553 q^{69} +1.47518 q^{70} -3.83221 q^{71} +22.3836 q^{72} +11.2767 q^{73} -24.3748 q^{74} -5.05583 q^{75} -26.2954 q^{76} +0.448354 q^{77} -6.24729 q^{78} -11.3790 q^{79} +44.7365 q^{80} +6.63519 q^{81} -12.8588 q^{82} -0.314352 q^{83} +0.382259 q^{84} +0.0143065 q^{85} -21.9397 q^{86} -1.50703 q^{87} +25.4463 q^{88} -0.194659 q^{89} +27.8583 q^{90} +0.651791 q^{91} -14.4069 q^{92} +2.51992 q^{93} +24.6031 q^{94} -19.8474 q^{95} +7.61656 q^{96} -13.9788 q^{97} +18.5729 q^{98} +8.46700 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * q^99

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