LMFDB - Embedded newform 731.2.a.e.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(1,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, 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("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 2 x^{18} - 30 x^{17} + 62 x^{16} + 365 x^{15} - 786 x^{14} - 2295 x^{13} + 5233 x^{12} + \cdots + 64 $ x^19 - 2x^18 - 30x^17 + 62x^16 + 365x^15 - 786x^14 - 2295x^13 + 5233x^12 + 7816x^11 - 19517x^10 - 13527x^9 + 40173x^8 + 8942x^7 - 41911x^6 + 1140x^5 + 18520x^4 - 1520x^3 - 2640x^2 - 64x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$2.30539$ of defining polynomial
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.30539 q^{2} -0.0652591 q^{3} +3.31484 q^{4} +2.38814 q^{5} -0.150448 q^{6} +2.55322 q^{7} +3.03122 q^{8} -2.99574 q^{9} +O(q^{10})$	\(q+2.30539 q^{2} -0.0652591 q^{3} +3.31484 q^{4} +2.38814 q^{5} -0.150448 q^{6} +2.55322 q^{7} +3.03122 q^{8} -2.99574 q^{9} +5.50561 q^{10} -2.99729 q^{11} -0.216323 q^{12} +3.21874 q^{13} +5.88618 q^{14} -0.155848 q^{15} +0.358478 q^{16} +1.00000 q^{17} -6.90636 q^{18} +1.77352 q^{19} +7.91631 q^{20} -0.166621 q^{21} -6.90993 q^{22} -8.18274 q^{23} -0.197815 q^{24} +0.703234 q^{25} +7.42045 q^{26} +0.391277 q^{27} +8.46352 q^{28} -5.70862 q^{29} -0.359291 q^{30} +6.22246 q^{31} -5.23601 q^{32} +0.195600 q^{33} +2.30539 q^{34} +6.09746 q^{35} -9.93040 q^{36} +6.53907 q^{37} +4.08865 q^{38} -0.210052 q^{39} +7.23899 q^{40} -3.44030 q^{41} -0.384127 q^{42} -1.00000 q^{43} -9.93553 q^{44} -7.15426 q^{45} -18.8644 q^{46} +6.33944 q^{47} -0.0233939 q^{48} -0.481053 q^{49} +1.62123 q^{50} -0.0652591 q^{51} +10.6696 q^{52} +2.36623 q^{53} +0.902047 q^{54} -7.15796 q^{55} +7.73938 q^{56} -0.115738 q^{57} -13.1606 q^{58} -7.85816 q^{59} -0.516612 q^{60} +7.78786 q^{61} +14.3452 q^{62} -7.64879 q^{63} -12.7880 q^{64} +7.68681 q^{65} +0.450936 q^{66} -2.73358 q^{67} +3.31484 q^{68} +0.533999 q^{69} +14.0571 q^{70} -5.13666 q^{71} -9.08075 q^{72} +7.35445 q^{73} +15.0751 q^{74} -0.0458924 q^{75} +5.87892 q^{76} -7.65275 q^{77} -0.484252 q^{78} +3.37362 q^{79} +0.856096 q^{80} +8.96169 q^{81} -7.93124 q^{82} -13.1359 q^{83} -0.552322 q^{84} +2.38814 q^{85} -2.30539 q^{86} +0.372539 q^{87} -9.08544 q^{88} -6.73176 q^{89} -16.4934 q^{90} +8.21815 q^{91} -27.1245 q^{92} -0.406072 q^{93} +14.6149 q^{94} +4.23541 q^{95} +0.341697 q^{96} +16.2643 q^{97} -1.10902 q^{98} +8.97910 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) $ 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9} - 2 q^{10} + 4 q^{11} + 9 q^{12} + 14 q^{13} + 5 q^{14} - 7 q^{15} + 32 q^{16} + 19 q^{17} + 12 q^{18} + 12 q^{19} + 23 q^{20} + 16 q^{21} + 36 q^{22} - q^{23} - 13 q^{24} + 30 q^{25} - 21 q^{26} + 8 q^{27} + 5 q^{28} + 41 q^{29} - 26 q^{30} - 8 q^{31} - 20 q^{32} - 14 q^{33} + 2 q^{34} + 3 q^{35} - 5 q^{36} + 50 q^{37} - 29 q^{38} + 17 q^{39} - 15 q^{40} + 6 q^{41} - q^{42} - 19 q^{43} + 16 q^{44} + 24 q^{45} + 38 q^{46} - 21 q^{47} - 2 q^{48} + 46 q^{49} - 36 q^{50} + 5 q^{51} + 39 q^{52} - 9 q^{53} + 53 q^{54} + 10 q^{55} - 12 q^{56} - 5 q^{57} - 45 q^{58} - 4 q^{59} - 7 q^{60} + 68 q^{61} - 25 q^{62} + 61 q^{63} - 14 q^{64} + 22 q^{65} - 17 q^{66} + 26 q^{68} - 9 q^{69} - 37 q^{70} + 23 q^{71} - 4 q^{72} - q^{73} - 30 q^{74} - 25 q^{75} + 47 q^{76} - 19 q^{77} + 12 q^{78} + 16 q^{79} + 28 q^{80} - 21 q^{81} - 13 q^{82} - 32 q^{83} - 47 q^{84} + 11 q^{85} - 2 q^{86} - 8 q^{87} + 108 q^{88} + 11 q^{89} + 5 q^{90} + 52 q^{91} - 23 q^{92} - 23 q^{93} + 47 q^{94} - 25 q^{95} - 103 q^{96} + 36 q^{97} - 100 q^{98} - 11 q^{99}+O(q^{100}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9 - 2 * q^10 + 4 * q^11 + 9 * q^12 + 14 * q^13 + 5 * q^14 - 7 * q^15 + 32 * q^16 + 19 * q^17 + 12 * q^18 + 12 * q^19 + 23 * q^20 + 16 * q^21 + 36 * q^22 - q^23 - 13 * q^24 + 30 * q^25 - 21 * q^26 + 8 * q^27 + 5 * q^28 + 41 * q^29 - 26 * q^30 - 8 * q^31 - 20 * q^32 - 14 * q^33 + 2 * q^34 + 3 * q^35 - 5 * q^36 + 50 * q^37 - 29 * q^38 + 17 * q^39 - 15 * q^40 + 6 * q^41 - q^42 - 19 * q^43 + 16 * q^44 + 24 * q^45 + 38 * q^46 - 21 * q^47 - 2 * q^48 + 46 * q^49 - 36 * q^50 + 5 * q^51 + 39 * q^52 - 9 * q^53 + 53 * q^54 + 10 * q^55 - 12 * q^56 - 5 * q^57 - 45 * q^58 - 4 * q^59 - 7 * q^60 + 68 * q^61 - 25 * q^62 + 61 * q^63 - 14 * q^64 + 22 * q^65 - 17 * q^66 + 26 * q^68 - 9 * q^69 - 37 * q^70 + 23 * q^71 - 4 * q^72 - q^73 - 30 * q^74 - 25 * q^75 + 47 * q^76 - 19 * q^77 + 12 * q^78 + 16 * q^79 + 28 * q^80 - 21 * q^81 - 13 * q^82 - 32 * q^83 - 47 * q^84 + 11 * q^85 - 2 * q^86 - 8 * q^87 + 108 * q^88 + 11 * q^89 + 5 * q^90 + 52 * q^91 - 23 * q^92 - 23 * q^93 + 47 * q^94 - 25 * q^95 - 103 * q^96 + 36 * q^97 - 100 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.30539	1.63016	0.815080	−	0.579349i	$-0.196693\pi$
$2$	2.30539	1.63016	0.815080	+	0.579349i	$0.196693\pi$
$3$	−0.0652591	−0.0376774	−0.0188387	−	0.999823i	$-0.505997\pi$
$3$	−0.0652591	−0.0376774	−0.0188387	+	0.999823i	$0.505997\pi$
$4$	3.31484	1.65742
$5$	2.38814	1.06801	0.534005	−	0.845481i	$-0.320686\pi$
$5$	2.38814	1.06801	0.534005	+	0.845481i	$0.320686\pi$
$6$	−0.150448	−0.0614201
$7$	2.55322	0.965028	0.482514	−	0.875888i	$-0.339724\pi$
$7$	2.55322	0.965028	0.482514	+	0.875888i	$0.339724\pi$
$8$	3.03122	1.07170
$9$	−2.99574	−0.998580
$10$	5.50561	1.74103
$11$	−2.99729	−0.903717	−0.451858	−	0.892090i	$-0.649239\pi$
$11$	−2.99729	−0.903717	−0.451858	+	0.892090i	$0.649239\pi$
$12$	−0.216323	−0.0624472
$13$	3.21874	0.892717	0.446358	−	0.894854i	$-0.352721\pi$
$13$	3.21874	0.892717	0.446358	+	0.894854i	$0.352721\pi$
$14$	5.88618	1.57315
$15$	−0.155848	−0.0402398
$16$	0.358478	0.0896194
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−6.90636	−1.62785
$19$	1.77352	0.406873	0.203436	−	0.979088i	$-0.434789\pi$
$19$	1.77352	0.406873	0.203436	+	0.979088i	$0.434789\pi$
$20$	7.91631	1.77014
$21$	−0.166621	−0.0363597
$22$	−6.90993	−1.47320
$23$	−8.18274	−1.70622	−0.853110	−	0.521731i	$-0.825286\pi$
$23$	−8.18274	−1.70622	−0.853110	+	0.521731i	$0.825286\pi$
$24$	−0.197815	−0.0403788
$25$	0.703234	0.140647
$26$	7.42045	1.45527
$27$	0.391277	0.0753013
$28$	8.46352	1.59946
$29$	−5.70862	−1.06006	−0.530032	−	0.847978i	$-0.677820\pi$
$29$	−5.70862	−1.06006	−0.530032	+	0.847978i	$0.677820\pi$
$30$	−0.359291	−0.0655973
$31$	6.22246	1.11759	0.558793	−	0.829307i	$-0.311264\pi$
$31$	6.22246	1.11759	0.558793	+	0.829307i	$0.311264\pi$
$32$	−5.23601	−0.925604
$33$	0.195600	0.0340497
$34$	2.30539	0.395372
$35$	6.09746	1.03066
$36$	−9.93040	−1.65507
$37$	6.53907	1.07502	0.537508	−	0.843258i	$-0.319366\pi$
$37$	6.53907	1.07502	0.537508	+	0.843258i	$0.319366\pi$
$38$	4.08865	0.663267
$39$	−0.210052	−0.0336352
$40$	7.23899	1.14459
$41$	−3.44030	−0.537284	−0.268642	−	0.963240i	$-0.586575\pi$
$41$	−3.44030	−0.537284	−0.268642	+	0.963240i	$0.586575\pi$
$42$	−0.384127	−0.0592721
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−9.93553	−1.49784
$45$	−7.15426	−1.06649
$46$	−18.8644	−2.78141
$47$	6.33944	0.924702	0.462351	−	0.886697i	$-0.347006\pi$
$47$	6.33944	0.924702	0.462351	+	0.886697i	$0.347006\pi$
$48$	−0.0233939	−0.00337662
$49$	−0.481053	−0.0687219
$50$	1.62123	0.229277
$51$	−0.0652591	−0.00913810
$52$	10.6696	1.47961
$53$	2.36623	0.325026	0.162513	−	0.986706i	$-0.448040\pi$
$53$	2.36623	0.325026	0.162513	+	0.986706i	$0.448040\pi$
$54$	0.902047	0.122753
$55$	−7.15796	−0.965179
$56$	7.73938	1.03422
$57$	−0.115738	−0.0153299
$58$	−13.1606	−1.72807
$59$	−7.85816	−1.02305	−0.511523	−	0.859270i	$-0.670918\pi$
$59$	−7.85816	−1.02305	−0.511523	+	0.859270i	$0.670918\pi$
$60$	−0.516612	−0.0666943
$61$	7.78786	0.997134	0.498567	−	0.866851i	$-0.333860\pi$
$61$	7.78786	0.997134	0.498567	+	0.866851i	$0.333860\pi$
$62$	14.3452	1.82184
$63$	−7.64879	−0.963658
$64$	−12.7880	−1.59850
$65$	7.68681	0.953431
$66$	0.450936	0.0555064
$67$	−2.73358	−0.333960	−0.166980	−	0.985960i	$-0.553401\pi$
$67$	−2.73358	−0.333960	−0.166980	+	0.985960i	$0.553401\pi$
$68$	3.31484	0.401983
$69$	0.533999	0.0642859
$70$	14.0571	1.68014
$71$	−5.13666	−0.609609	−0.304805	−	0.952415i	$-0.598591\pi$
$71$	−5.13666	−0.609609	−0.304805	+	0.952415i	$0.598591\pi$
$72$	−9.08075	−1.07018
$73$	7.35445	0.860773	0.430386	−	0.902645i	$-0.358377\pi$
$73$	7.35445	0.860773	0.430386	+	0.902645i	$0.358377\pi$
$74$	15.0751	1.75245
$75$	−0.0458924	−0.00529920
$76$	5.87892	0.674358
$77$	−7.65275	−0.872112
$78$	−0.484252	−0.0548308
$79$	3.37362	0.379562	0.189781	−	0.981826i	$-0.439222\pi$
$79$	3.37362	0.379562	0.189781	+	0.981826i	$0.439222\pi$
$80$	0.856096	0.0957145
$81$	8.96169	0.995743
$82$	−7.93124	−0.875859
$83$	−13.1359	−1.44185	−0.720924	−	0.693014i	$-0.756282\pi$
$83$	−13.1359	−1.44185	−0.720924	+	0.693014i	$0.756282\pi$
$84$	−0.552322	−0.0602633
$85$	2.38814	0.259031
$86$	−2.30539	−0.248597
$87$	0.372539	0.0399404
$88$	−9.08544	−0.968512
$89$	−6.73176	−0.713565	−0.356782	−	0.934188i	$-0.616126\pi$
$89$	−6.73176	−0.713565	−0.356782	+	0.934188i	$0.616126\pi$
$90$	−16.4934	−1.73856
$91$	8.21815	0.861496
$92$	−27.1245	−2.82792
$93$	−0.406072	−0.0421077
$94$	14.6149	1.50741
$95$	4.23541	0.434544
$96$	0.341697	0.0348743
$97$	16.2643	1.65138	0.825692	−	0.564121i	$-0.190785\pi$
$97$	16.2643	1.65138	0.825692	+	0.564121i	$0.190785\pi$
$98$	−1.10902	−0.112028
$99$	8.97910	0.902434
$100$	2.33111	0.233111
$101$	4.26438	0.424321	0.212161	−	0.977235i	$-0.431950\pi$
$101$	4.26438	0.424321	0.212161	+	0.977235i	$0.431950\pi$
$102$	−0.150448	−0.0148966
$103$	−13.4340	−1.32369	−0.661844	−	0.749641i	$-0.730226\pi$
$103$	−13.4340	−1.32369	−0.661844	+	0.749641i	$0.730226\pi$
$104$	9.75670	0.956723
$105$	−0.397915	−0.0388325
$106$	5.45508	0.529845
$107$	−0.663708	−0.0641630	−0.0320815	−	0.999485i	$-0.510214\pi$
$107$	−0.663708	−0.0641630	−0.0320815	+	0.999485i	$0.510214\pi$
$108$	1.29702	0.124806
$109$	−18.8314	−1.80372	−0.901860	−	0.432029i	$-0.857798\pi$
$109$	−18.8314	−1.80372	−0.901860	+	0.432029i	$0.857798\pi$
$110$	−16.5019	−1.57340
$111$	−0.426734	−0.0405038
$112$	0.915273	0.0864852
$113$	12.0531	1.13386	0.566931	−	0.823765i	$-0.308130\pi$
$113$	12.0531	1.13386	0.566931	+	0.823765i	$0.308130\pi$
$114$	−0.266822	−0.0249902
$115$	−19.5416	−1.82226
$116$	−18.9231	−1.75697
$117$	−9.64250	−0.891450
$118$	−18.1162	−1.66773
$119$	2.55322	0.234054
$120$	−0.472410	−0.0431250
$121$	−2.01626	−0.183296
$122$	17.9541	1.62549
$123$	0.224511	0.0202435
$124$	20.6264	1.85231
$125$	−10.2613	−0.917798
$126$	−17.6335	−1.57092
$127$	12.5060	1.10973	0.554863	−	0.831942i	$-0.312771\pi$
$127$	12.5060	1.10973	0.554863	+	0.831942i	$0.312771\pi$
$128$	−19.0094	−1.68021
$129$	0.0652591	0.00574575
$130$	17.7211	1.55424
$131$	5.03821	0.440190	0.220095	−	0.975478i	$-0.429363\pi$
$131$	5.03821	0.440190	0.220095	+	0.975478i	$0.429363\pi$
$132$	0.648384	0.0564346
$133$	4.52818	0.392643
$134$	−6.30197	−0.544407
$135$	0.934425	0.0804225
$136$	3.03122	0.259925
$137$	10.1747	0.869279	0.434640	−	0.900604i	$-0.356876\pi$
$137$	10.1747	0.869279	0.434640	+	0.900604i	$0.356876\pi$
$138$	1.23108	0.104796
$139$	0.000633814 0	5.37594e−5 0	2.68797e−5	−	1.00000i	$-0.499991\pi$
$139$	0.000633814 0	5.37594e−5 0	2.68797e−5		1.00000i	$0.499991\pi$
$140$	20.2121	1.70824
$141$	−0.413706	−0.0348404
$142$	−11.8420	−0.993760
$143$	−9.64749	−0.806763
$144$	−1.07391	−0.0894922
$145$	−13.6330	−1.13216
$146$	16.9549	1.40320
$147$	0.0313931	0.00258926
$148$	21.6760	1.78175
$149$	−10.0818	−0.825937	−0.412969	−	0.910745i	$-0.635508\pi$
$149$	−10.0818	−0.825937	−0.412969	+	0.910745i	$0.635508\pi$
$150$	−0.105800	−0.00863854
$151$	−10.7544	−0.875178	−0.437589	−	0.899175i	$-0.644167\pi$
$151$	−10.7544	−0.875178	−0.437589	+	0.899175i	$0.644167\pi$
$152$	5.37592	0.436045
$153$	−2.99574	−0.242191
$154$	−17.6426	−1.42168
$155$	14.8601	1.19359
$156$	−0.696288	−0.0557477
$157$	−11.1874	−0.892851	−0.446425	−	0.894821i	$-0.647303\pi$
$157$	−11.1874	−0.892851	−0.446425	+	0.894821i	$0.647303\pi$
$158$	7.77753	0.618747
$159$	−0.154418	−0.0122461
$160$	−12.5043	−0.988555
$161$	−20.8924	−1.64655
$162$	20.6602	1.62322
$163$	18.4596	1.44587	0.722933	−	0.690918i	$-0.242793\pi$
$163$	18.4596	1.44587	0.722933	+	0.690918i	$0.242793\pi$
$164$	−11.4040	−0.890505
$165$	0.467122	0.0363654
$166$	−30.2833	−2.35044
$167$	−0.770677	−0.0596368	−0.0298184	−	0.999555i	$-0.509493\pi$
$167$	−0.770677	−0.0596368	−0.0298184	+	0.999555i	$0.509493\pi$
$168$	−0.505065	−0.0389666
$169$	−2.63974	−0.203057
$170$	5.50561	0.422261
$171$	−5.31300	−0.406295
$172$	−3.31484	−0.252754
$173$	22.2478	1.69147	0.845734	−	0.533605i	$-0.179163\pi$
$173$	22.2478	1.69147	0.845734	+	0.533605i	$0.179163\pi$
$174$	0.858850	0.0651092
$175$	1.79551	0.135728
$176$	−1.07446	−0.0809906
$177$	0.512817	0.0385457
$178$	−15.5193	−1.16322
$179$	−2.05522	−0.153614	−0.0768072	−	0.997046i	$-0.524473\pi$
$179$	−2.05522	−0.153614	−0.0768072	+	0.997046i	$0.524473\pi$
$180$	−23.7152	−1.76763
$181$	−16.1019	−1.19684	−0.598421	−	0.801182i	$-0.704205\pi$
$181$	−16.1019	−1.19684	−0.598421	+	0.801182i	$0.704205\pi$
$182$	18.9461	1.40438
$183$	−0.508229	−0.0375694
$184$	−24.8037	−1.82855
$185$	15.6162	1.14813
$186$	−0.936156	−0.0686423
$187$	−2.99729	−0.219184
$188$	21.0142	1.53262
$189$	0.999017	0.0726678
$190$	9.76429	0.708376
$191$	−10.0311	−0.725822	−0.362911	−	0.931824i	$-0.618217\pi$
$191$	−10.0311	−0.725822	−0.362911	+	0.931824i	$0.618217\pi$
$192$	0.834535	0.0602273
$193$	8.25255	0.594032	0.297016	−	0.954873i	$-0.404009\pi$
$193$	8.25255	0.594032	0.297016	+	0.954873i	$0.404009\pi$
$194$	37.4955	2.69202
$195$	−0.501634	−0.0359228
$196$	−1.59461	−0.113901
$197$	22.2027	1.58188	0.790939	−	0.611894i	$-0.209592\pi$
$197$	22.2027	1.58188	0.790939	+	0.611894i	$0.209592\pi$
$198$	20.7004	1.47111
$199$	−0.150830	−0.0106920	−0.00534601	−	0.999986i	$-0.501702\pi$
$199$	−0.150830	−0.0106920	−0.00534601	+	0.999986i	$0.501702\pi$
$200$	2.13166	0.150731
$201$	0.178391	0.0125827
$202$	9.83107	0.691711
$203$	−14.5754	−1.02299
$204$	−0.216323	−0.0151457
$205$	−8.21593	−0.573825
$206$	−30.9706	−2.15782
$207$	24.5134	1.70380
$208$	1.15385	0.0800048
$209$	−5.31574	−0.367698
$210$	−0.917351	−0.0633032
$211$	−6.05493	−0.416838	−0.208419	−	0.978040i	$-0.566832\pi$
$211$	−6.05493	−0.416838	−0.208419	+	0.978040i	$0.566832\pi$
$212$	7.84366	0.538705
$213$	0.335214	0.0229685
$214$	−1.53011	−0.104596
$215$	−2.38814	−0.162870
$216$	1.18605	0.0807002
$217$	15.8873	1.07850
$218$	−43.4137	−2.94035
$219$	−0.479945	−0.0324317
$220$	−23.7275	−1.59971
$221$	3.21874	0.216516
$222$	−0.983790	−0.0660277
$223$	4.45291	0.298189	0.149094	−	0.988823i	$-0.452364\pi$
$223$	4.45291	0.298189	0.149094	+	0.988823i	$0.452364\pi$
$224$	−13.3687	−0.893234
$225$	−2.10671	−0.140447
$226$	27.7872	1.84838
$227$	10.9982	0.729978	0.364989	−	0.931012i	$-0.381073\pi$
$227$	10.9982	0.729978	0.364989	+	0.931012i	$0.381073\pi$
$228$	−0.383653	−0.0254081
$229$	20.5912	1.36071	0.680353	−	0.732884i	$-0.261826\pi$
$229$	20.5912	1.36071	0.680353	+	0.732884i	$0.261826\pi$
$230$	−45.0510	−2.97058
$231$	0.499412	0.0328589
$232$	−17.3041	−1.13607
$233$	−3.89017	−0.254854	−0.127427	−	0.991848i	$-0.540672\pi$
$233$	−3.89017	−0.254854	−0.127427	+	0.991848i	$0.540672\pi$
$234$	−22.2298	−1.45320
$235$	15.1395	0.987592
$236$	−26.0485	−1.69562
$237$	−0.220160	−0.0143009
$238$	5.88618	0.381545
$239$	19.5695	1.26584	0.632922	−	0.774215i	$-0.281855\pi$
$239$	19.5695	1.26584	0.632922	+	0.774215i	$0.281855\pi$
$240$	−0.0558681	−0.00360627
$241$	19.8608	1.27934	0.639672	−	0.768648i	$-0.279070\pi$
$241$	19.8608	1.27934	0.639672	+	0.768648i	$0.279070\pi$
$242$	−4.64826	−0.298802
$243$	−1.75866	−0.112818
$244$	25.8155	1.65267
$245$	−1.14882	−0.0733957
$246$	0.517586	0.0330001
$247$	5.70848	0.363222
$248$	18.8616	1.19772
$249$	0.857235	0.0543251
$250$	−23.6563	−1.49616
$251$	28.1435	1.77640	0.888201	−	0.459455i	$-0.151955\pi$
$251$	28.1435	1.77640	0.888201	+	0.459455i	$0.151955\pi$
$252$	−25.3545	−1.59718
$253$	24.5261	1.54194
$254$	28.8312	1.80903
$255$	−0.155848	−0.00975959
$256$	−18.2481	−1.14051
$257$	23.4777	1.46450	0.732251	−	0.681035i	$-0.238470\pi$
$257$	23.4777	1.46450	0.732251	+	0.681035i	$0.238470\pi$
$258$	0.150448	0.00936648
$259$	16.6957	1.03742
$260$	25.4805	1.58024
$261$	17.1015	1.05856
$262$	11.6151	0.717580
$263$	−20.1971	−1.24540	−0.622702	−	0.782459i	$-0.713965\pi$
$263$	−20.1971	−1.24540	−0.622702	+	0.782459i	$0.713965\pi$
$264$	0.592908	0.0364910
$265$	5.65089	0.347131
$266$	10.4392	0.640071
$267$	0.439309	0.0268852
$268$	−9.06137	−0.553511
$269$	−2.91218	−0.177559	−0.0887794	−	0.996051i	$-0.528297\pi$
$269$	−2.91218	−0.177559	−0.0887794	+	0.996051i	$0.528297\pi$
$270$	2.15422	0.131102
$271$	−21.0146	−1.27655	−0.638273	−	0.769810i	$-0.720351\pi$
$271$	−21.0146	−1.27655	−0.638273	+	0.769810i	$0.720351\pi$
$272$	0.358478	0.0217359
$273$	−0.536309	−0.0324589
$274$	23.4566	1.41706
$275$	−2.10779	−0.127105
$276$	1.77012	0.106549
$277$	21.6645	1.30170	0.650848	−	0.759208i	$-0.274414\pi$
$277$	21.6645	1.30170	0.650848	+	0.759208i	$0.274414\pi$
$278$	0.00146119	8.76365e−5 0
$279$	−18.6409	−1.11600
$280$	18.4828	1.10456
$281$	17.3070	1.03245	0.516223	−	0.856454i	$-0.327337\pi$
$281$	17.3070	1.03245	0.516223	+	0.856454i	$0.327337\pi$
$282$	−0.953756	−0.0567953
$283$	20.0694	1.19300	0.596502	−	0.802611i	$-0.296557\pi$
$283$	20.0694	1.19300	0.596502	+	0.802611i	$0.296557\pi$
$284$	−17.0272	−1.01038
$285$	−0.276399	−0.0163725
$286$	−22.2412	−1.31515
$287$	−8.78385	−0.518494
$288$	15.6857	0.924290
$289$	1.00000	0.0588235
$290$	−31.4294	−1.84560
$291$	−1.06139	−0.0622198
$292$	24.3788	1.42666
$293$	30.5275	1.78343	0.891717	−	0.452593i	$-0.149501\pi$
$293$	30.5275	1.78343	0.891717	+	0.452593i	$0.149501\pi$
$294$	0.0723735	0.00422091
$295$	−18.7664	−1.09262
$296$	19.8214	1.15209
$297$	−1.17277	−0.0680510
$298$	−23.2426	−1.34641
$299$	−26.3381	−1.52317
$300$	−0.152126	−0.00878299
$301$	−2.55322	−0.147165
$302$	−24.7930	−1.42668
$303$	−0.278290	−0.0159873
$304$	0.635766	0.0364637
$305$	18.5985	1.06495
$306$	−6.90636	−0.394810
$307$	−8.73028	−0.498263	−0.249132	−	0.968470i	$-0.580145\pi$
$307$	−8.73028	−0.498263	−0.249132	+	0.968470i	$0.580145\pi$
$308$	−25.3676	−1.44545
$309$	0.876689	0.0498731
$310$	34.2584	1.94575
$311$	−8.44202	−0.478703	−0.239352	−	0.970933i	$-0.576935\pi$
$311$	−8.44202	−0.478703	−0.239352	+	0.970933i	$0.576935\pi$
$312$	−0.636714	−0.0360468
$313$	15.8797	0.897576	0.448788	−	0.893638i	$-0.351856\pi$
$313$	15.8797	0.897576	0.448788	+	0.893638i	$0.351856\pi$
$314$	−25.7913	−1.45549
$315$	−18.2664	−1.02920
$316$	11.1830	0.629094
$317$	−3.77307	−0.211917	−0.105958	−	0.994371i	$-0.533791\pi$
$317$	−3.77307	−0.211917	−0.105958	+	0.994371i	$0.533791\pi$
$318$	−0.355994	−0.0199631
$319$	17.1104	0.957997
$320$	−30.5396	−1.70722
$321$	0.0433130	0.00241749
$322$	−48.1651	−2.68414
$323$	1.77352	0.0986811
$324$	29.7066	1.65036
$325$	2.26352	0.125558
$326$	42.5566	2.35699
$327$	1.22892	0.0679594
$328$	−10.4283	−0.575807
$329$	16.1860	0.892363
$330$	1.07690	0.0592814
$331$	−10.1738	−0.559202	−0.279601	−	0.960116i	$-0.590202\pi$
$331$	−10.1738	−0.559202	−0.279601	+	0.960116i	$0.590202\pi$
$332$	−43.5433	−2.38975
$333$	−19.5894	−1.07349
$334$	−1.77671	−0.0972174
$335$	−6.52818	−0.356672
$336$	−0.0597299	−0.00325853
$337$	−23.0037	−1.25309	−0.626545	−	0.779385i	$-0.715531\pi$
$337$	−23.0037	−1.25309	−0.626545	+	0.779385i	$0.715531\pi$
$338$	−6.08563	−0.331015
$339$	−0.786576	−0.0427210
$340$	7.91631	0.429322
$341$	−18.6505	−1.00998
$342$	−12.2485	−0.662326
$343$	−19.1008	−1.03135
$344$	−3.03122	−0.163432
$345$	1.27527	0.0686580
$346$	51.2899	2.75736
$347$	−2.84277	−0.152608	−0.0763038	−	0.997085i	$-0.524312\pi$
$347$	−2.84277	−0.152608	−0.0763038	+	0.997085i	$0.524312\pi$
$348$	1.23491	0.0661980
$349$	−35.8871	−1.92099	−0.960496	−	0.278292i	$-0.910232\pi$
$349$	−35.8871	−1.92099	−0.960496	+	0.278292i	$0.910232\pi$
$350$	4.13936	0.221258
$351$	1.25942	0.0672227
$352$	15.6938	0.836484
$353$	19.5433	1.04018	0.520092	−	0.854110i	$-0.325898\pi$
$353$	19.5433	1.04018	0.520092	+	0.854110i	$0.325898\pi$
$354$	1.18224	0.0628356
$355$	−12.2671	−0.651069
$356$	−22.3147	−1.18268
$357$	−0.166621	−0.00881852
$358$	−4.73809	−0.250416
$359$	4.43063	0.233840	0.116920	−	0.993141i	$-0.462698\pi$
$359$	4.43063	0.233840	0.116920	+	0.993141i	$0.462698\pi$
$360$	−21.6861	−1.14296
$361$	−15.8546	−0.834455
$362$	−37.1211	−1.95104
$363$	0.131579	0.00690611
$364$	27.2418	1.42786
$365$	17.5635	0.919315
$366$	−1.17167	−0.0612441
$367$	5.48309	0.286215	0.143107	−	0.989707i	$-0.454291\pi$
$367$	5.48309	0.286215	0.143107	+	0.989707i	$0.454291\pi$
$368$	−2.93333	−0.152910
$369$	10.3062	0.536522
$370$	36.0016	1.87163
$371$	6.04150	0.313659
$372$	−1.34606	−0.0697902
$373$	−27.3949	−1.41845	−0.709227	−	0.704980i	$-0.750956\pi$
$373$	−27.3949	−1.41845	−0.709227	+	0.704980i	$0.750956\pi$
$374$	−6.90993	−0.357304
$375$	0.669643	0.0345802
$376$	19.2162	0.991002
$377$	−18.3745	−0.946336
$378$	2.30313	0.118460
$379$	18.7968	0.965525	0.482763	−	0.875751i	$-0.339633\pi$
$379$	18.7968	0.965525	0.482763	+	0.875751i	$0.339633\pi$
$380$	14.0397	0.720222
$381$	−0.816129	−0.0418116
$382$	−23.1255	−1.18321
$383$	−5.94001	−0.303520	−0.151760	−	0.988417i	$-0.548494\pi$
$383$	−5.94001	−0.303520	−0.151760	+	0.988417i	$0.548494\pi$
$384$	1.24054	0.0633058
$385$	−18.2759	−0.931424
$386$	19.0254	0.968366
$387$	2.99574	0.152282
$388$	53.9134	2.73704
$389$	9.97994	0.506003	0.253001	−	0.967466i	$-0.418582\pi$
$389$	9.97994	0.506003	0.253001	+	0.967466i	$0.418582\pi$
$390$	−1.15646	−0.0585599
$391$	−8.18274	−0.413819
$392$	−1.45818	−0.0736491
$393$	−0.328789	−0.0165852
$394$	51.1860	2.57871
$395$	8.05670	0.405377
$396$	29.7643	1.49571
$397$	2.48569	0.124753	0.0623766	−	0.998053i	$-0.480132\pi$
$397$	2.48569	0.124753	0.0623766	+	0.998053i	$0.480132\pi$
$398$	−0.347722	−0.0174297
$399$	−0.295505	−0.0147938
$400$	0.252093	0.0126047
$401$	6.02908	0.301078	0.150539	−	0.988604i	$-0.451899\pi$
$401$	6.02908	0.301078	0.150539	+	0.988604i	$0.451899\pi$
$402$	0.411261	0.0205118
$403$	20.0285	0.997689
$404$	14.1357	0.703278
$405$	21.4018	1.06346
$406$	−33.6020	−1.66764
$407$	−19.5995	−0.971511
$408$	−0.197815	−0.00979329
$409$	22.0588	1.09074	0.545368	−	0.838197i	$-0.316390\pi$
$409$	22.0588	1.09074	0.545368	+	0.838197i	$0.316390\pi$
$410$	−18.9409	−0.935427
$411$	−0.663989	−0.0327522
$412$	−44.5314	−2.19391
$413$	−20.0636	−0.987267
$414$	56.5130	2.77746
$415$	−31.3703	−1.53991
$416$	−16.8533	−0.826303
$417$	−4.13622e−5 0	−2.02551e−6 0
$418$	−12.2549	−0.599406
$419$	−22.7054	−1.10923	−0.554615	−	0.832107i	$-0.687134\pi$
$419$	−22.7054	−1.10923	−0.554615	+	0.832107i	$0.687134\pi$
$420$	−1.31902	−0.0643618
$421$	2.92092	0.142357	0.0711786	−	0.997464i	$-0.477324\pi$
$421$	2.92092	0.142357	0.0711786	+	0.997464i	$0.477324\pi$
$422$	−13.9590	−0.679513
$423$	−18.9913	−0.923390
$424$	7.17255	0.348330
$425$	0.703234	0.0341118
$426$	0.772800	0.0374423
$427$	19.8841	0.962261
$428$	−2.20008	−0.106345
$429$	0.629586	0.0303967
$430$	−5.50561	−0.265504
$431$	−33.8783	−1.63186	−0.815931	−	0.578149i	$-0.803775\pi$
$431$	−33.8783	−1.63186	−0.815931	+	0.578149i	$0.803775\pi$
$432$	0.140264	0.00674845
$433$	−32.8003	−1.57628	−0.788141	−	0.615494i	$-0.788956\pi$
$433$	−32.8003	−1.57628	−0.788141	+	0.615494i	$0.788956\pi$
$434$	36.6265	1.75813
$435$	0.889678	0.0426568
$436$	−62.4230	−2.98952
$437$	−14.5122	−0.694214
$438$	−1.10646	−0.0528688
$439$	36.0146	1.71888	0.859442	−	0.511233i	$-0.170811\pi$
$439$	36.0146	1.71888	0.859442	+	0.511233i	$0.170811\pi$
$440$	−21.6974	−1.03438
$441$	1.44111	0.0686243
$442$	7.42045	0.352955
$443$	−17.3293	−0.823341	−0.411670	−	0.911333i	$-0.635054\pi$
$443$	−17.3293	−0.823341	−0.411670	+	0.911333i	$0.635054\pi$
$444$	−1.41455	−0.0671318
$445$	−16.0764	−0.762095
$446$	10.2657	0.486095
$447$	0.657932	0.0311191
$448$	−32.6506	−1.54260
$449$	15.2847	0.721329	0.360665	−	0.932696i	$-0.382550\pi$
$449$	15.2847	0.721329	0.360665	+	0.932696i	$0.382550\pi$
$450$	−4.85679	−0.228951
$451$	10.3116	0.485553
$452$	39.9542	1.87929
$453$	0.701820	0.0329744
$454$	25.3553	1.18998
$455$	19.6261	0.920087
$456$	−0.350828	−0.0164290
$457$	36.2422	1.69534	0.847668	−	0.530526i	$-0.178006\pi$
$457$	36.2422	1.69534	0.847668	+	0.530526i	$0.178006\pi$
$458$	47.4709	2.21817
$459$	0.391277	0.0182632
$460$	−64.7772	−3.02025
$461$	−1.98244	−0.0923316	−0.0461658	−	0.998934i	$-0.514700\pi$
$461$	−1.98244	−0.0923316	−0.0461658	+	0.998934i	$0.514700\pi$
$462$	1.15134	0.0535652
$463$	−25.3252	−1.17696	−0.588480	−	0.808512i	$-0.700273\pi$
$463$	−25.3252	−1.17696	−0.588480	+	0.808512i	$0.700273\pi$
$464$	−2.04641	−0.0950023
$465$	−0.969759	−0.0449715
$466$	−8.96838	−0.415452
$467$	10.4727	0.484620	0.242310	−	0.970199i	$-0.422095\pi$
$467$	10.4727	0.484620	0.242310	+	0.970199i	$0.422095\pi$
$468$	−31.9633	−1.47751
$469$	−6.97943	−0.322280
$470$	34.9025	1.60993
$471$	0.730079	0.0336403
$472$	−23.8198	−1.09640
$473$	2.99729	0.137816
$474$	−0.507555	−0.0233128
$475$	1.24720	0.0572253
$476$	8.46352	0.387925
$477$	−7.08860	−0.324565
$478$	45.1154	2.06353
$479$	−13.2379	−0.604854	−0.302427	−	0.953173i	$-0.597797\pi$
$479$	−13.2379	−0.604854	−0.302427	+	0.953173i	$0.597797\pi$
$480$	0.816022	0.0372462
$481$	21.0475	0.959686
$482$	45.7868	2.08553
$483$	1.36342	0.0620376
$484$	−6.68356	−0.303798
$485$	38.8414	1.76370
$486$	−4.05441	−0.183912
$487$	25.7858	1.16847	0.584234	−	0.811585i	$-0.301395\pi$
$487$	25.7858	1.16847	0.584234	+	0.811585i	$0.301395\pi$
$488$	23.6067	1.06863
$489$	−1.20466	−0.0544764
$490$	−2.64849	−0.119647
$491$	−24.7571	−1.11727	−0.558636	−	0.829413i	$-0.688675\pi$
$491$	−24.7571	−1.11727	−0.558636	+	0.829413i	$0.688675\pi$
$492$	0.744217	0.0335519
$493$	−5.70862	−0.257103
$494$	13.1603	0.592110
$495$	21.4434	0.963809
$496$	2.23061	0.100157
$497$	−13.1150	−0.588290
$498$	1.97626	0.0885585
$499$	18.4233	0.824740	0.412370	−	0.911016i	$-0.364701\pi$
$499$	18.4233	0.824740	0.412370	+	0.911016i	$0.364701\pi$
$500$	−34.0145	−1.52118
$501$	0.0502937	0.00224696
$502$	64.8818	2.89582
$503$	−10.7958	−0.481360	−0.240680	−	0.970605i	$-0.577370\pi$
$503$	−10.7958	−0.481360	−0.240680	+	0.970605i	$0.577370\pi$
$504$	−23.1852	−1.03275
$505$	10.1839	0.453180
$506$	56.5422	2.51361
$507$	0.172267	0.00765064
$508$	41.4553	1.83928
$509$	18.9944	0.841913	0.420956	−	0.907081i	$-0.361695\pi$
$509$	18.9944	0.841913	0.420956	+	0.907081i	$0.361695\pi$
$510$	−0.359291	−0.0159097
$511$	18.7775	0.830670
$512$	−4.05024	−0.178997
$513$	0.693936	0.0306380
$514$	54.1254	2.38737
$515$	−32.0823	−1.41371
$516$	0.216323	0.00952311
$517$	−19.0011	−0.835669
$518$	38.4902	1.69116
$519$	−1.45187	−0.0637301
$520$	23.3004	1.02179
$521$	−26.9943	−1.18264	−0.591320	−	0.806437i	$-0.701393\pi$
$521$	−26.9943	−1.18264	−0.591320	+	0.806437i	$0.701393\pi$
$522$	39.4258	1.72562
$523$	−9.96624	−0.435793	−0.217897	−	0.975972i	$-0.569920\pi$
$523$	−9.96624	−0.435793	−0.217897	+	0.975972i	$0.569920\pi$
$524$	16.7009	0.729580
$525$	−0.117174	−0.00511387
$526$	−46.5622	−2.03021
$527$	6.22246	0.271055
$528$	0.0701184	0.00305151
$529$	43.9573	1.91119
$530$	13.0275	0.565880
$531$	23.5410	1.02159
$532$	15.0102	0.650774
$533$	−11.0734	−0.479643
$534$	1.01278	0.0438272
$535$	−1.58503	−0.0685268
$536$	−8.28607	−0.357904
$537$	0.134122	0.00578778
$538$	−6.71372	−0.289449
$539$	1.44186	0.0621051
$540$	3.09747	0.133294
$541$	−1.16261	−0.0499845	−0.0249923	−	0.999688i	$-0.507956\pi$
$541$	−1.16261	−0.0499845	−0.0249923	+	0.999688i	$0.507956\pi$
$542$	−48.4469	−2.08097
$543$	1.05079	0.0450939
$544$	−5.23601	−0.224492
$545$	−44.9721	−1.92639
$546$	−1.23640	−0.0529132
$547$	−41.3353	−1.76737	−0.883685	−	0.468081i	$-0.844945\pi$
$547$	−41.3353	−1.76737	−0.883685	+	0.468081i	$0.844945\pi$
$548$	33.7273	1.44076
$549$	−23.3304	−0.995718
$550$	−4.85930	−0.207201
$551$	−10.1243	−0.431311
$552$	1.61867	0.0688951
$553$	8.61361	0.366288
$554$	49.9453	2.12197
$555$	−1.01910	−0.0432585
$556$	0.00210099	8.91019e−5 0
$557$	18.3396	0.777074	0.388537	−	0.921433i	$-0.372981\pi$
$557$	18.3396	0.777074	0.388537	+	0.921433i	$0.372981\pi$
$558$	−42.9746	−1.81926
$559$	−3.21874	−0.136138
$560$	2.18580	0.0923671
$561$	0.195600	0.00825826
$562$	39.8994	1.68305
$563$	−9.94537	−0.419147	−0.209574	−	0.977793i	$-0.567208\pi$
$563$	−9.94537	−0.419147	−0.209574	+	0.977793i	$0.567208\pi$
$564$	−1.37137	−0.0577451
$565$	28.7846	1.21098
$566$	46.2680	1.94479
$567$	22.8812	0.960920
$568$	−15.5703	−0.653317
$569$	−10.5354	−0.441667	−0.220833	−	0.975312i	$-0.570878\pi$
$569$	−10.5354	−0.441667	−0.220833	+	0.975312i	$0.570878\pi$
$570$	−0.637209	−0.0266898
$571$	−40.1332	−1.67952	−0.839762	−	0.542955i	$-0.817305\pi$
$571$	−40.1332	−1.67952	−0.839762	+	0.542955i	$0.817305\pi$
$572$	−31.9799	−1.33714
$573$	0.654618	0.0273471
$574$	−20.2502	−0.845228
$575$	−5.75438	−0.239974
$576$	38.3096	1.59623
$577$	−1.79156	−0.0745837	−0.0372919	−	0.999304i	$-0.511873\pi$
$577$	−1.79156	−0.0745837	−0.0372919	+	0.999304i	$0.511873\pi$
$578$	2.30539	0.0958917
$579$	−0.538554	−0.0223816
$580$	−45.1912	−1.87646
$581$	−33.5388	−1.39142
$582$	−2.44692	−0.101428
$583$	−7.09227	−0.293732
$584$	22.2929	0.922489
$585$	−23.0277	−0.952078
$586$	70.3779	2.90728
$587$	5.66896	0.233983	0.116991	−	0.993133i	$-0.462675\pi$
$587$	5.66896	0.233983	0.116991	+	0.993133i	$0.462675\pi$
$588$	0.104063	0.00429149
$589$	11.0356	0.454715
$590$	−43.2640	−1.78115
$591$	−1.44893	−0.0596010
$592$	2.34411	0.0963424
$593$	−18.3941	−0.755355	−0.377677	−	0.925937i	$-0.623277\pi$
$593$	−18.3941	−0.755355	−0.377677	+	0.925937i	$0.623277\pi$
$594$	−2.70370	−0.110934
$595$	6.09746	0.249972
$596$	−33.4197	−1.36892
$597$	0.00984301	0.000402847 0
$598$	−60.7197	−2.48301
$599$	2.17089	0.0887003	0.0443501	−	0.999016i	$-0.485878\pi$
$599$	2.17089	0.0887003	0.0443501	+	0.999016i	$0.485878\pi$
$600$	−0.139110	−0.00567914
$601$	18.6539	0.760908	0.380454	−	0.924800i	$-0.375768\pi$
$601$	18.6539	0.760908	0.380454	+	0.924800i	$0.375768\pi$
$602$	−5.88618	−0.239903
$603$	8.18909	0.333485
$604$	−35.6490	−1.45054
$605$	−4.81511	−0.195762
$606$	−0.641567	−0.0260619
$607$	−42.3522	−1.71902	−0.859511	−	0.511117i	$-0.829232\pi$
$607$	−42.3522	−1.71902	−0.859511	+	0.511117i	$0.829232\pi$
$608$	−9.28615	−0.376603
$609$	0.951176	0.0385436
$610$	42.8769	1.73604
$611$	20.4050	0.825497
$612$	−9.93040	−0.401413
$613$	31.7033	1.28049	0.640243	−	0.768173i	$-0.278834\pi$
$613$	31.7033	1.28049	0.640243	+	0.768173i	$0.278834\pi$
$614$	−20.1267	−0.812249
$615$	0.536164	0.0216202
$616$	−23.1972	−0.934640
$617$	40.9319	1.64786	0.823928	−	0.566694i	$-0.191778\pi$
$617$	40.9319	1.64786	0.823928	+	0.566694i	$0.191778\pi$
$618$	2.02111	0.0813011
$619$	44.7572	1.79895	0.899473	−	0.436977i	$-0.143951\pi$
$619$	44.7572	1.79895	0.899473	+	0.436977i	$0.143951\pi$
$620$	49.2589	1.97829
$621$	−3.20172	−0.128481
$622$	−19.4622	−0.780362
$623$	−17.1877	−0.688610
$624$	−0.0752989	−0.00301437
$625$	−28.0216	−1.12087
$626$	36.6091	1.46319
$627$	0.346901	0.0138539
$628$	−37.0844	−1.47983
$629$	6.53907	0.260730
$630$	−42.1113	−1.67775
$631$	−37.1492	−1.47889	−0.739444	−	0.673218i	$-0.764912\pi$
$631$	−37.1492	−1.47889	−0.739444	+	0.673218i	$0.764912\pi$
$632$	10.2262	0.406776
$633$	0.395139	0.0157054
$634$	−8.69841	−0.345458
$635$	29.8661	1.18520
$636$	−0.511870	−0.0202970
$637$	−1.54838	−0.0613492
$638$	39.4461	1.56169
$639$	15.3881	0.608744
$640$	−45.3972	−1.79448
$641$	−29.8765	−1.18005	−0.590026	−	0.807384i	$-0.700883\pi$
$641$	−29.8765	−1.18005	−0.590026	+	0.807384i	$0.700883\pi$
$642$	0.0998534	0.00394090
$643$	−11.2773	−0.444734	−0.222367	−	0.974963i	$-0.571378\pi$
$643$	−11.2773	−0.444734	−0.222367	+	0.974963i	$0.571378\pi$
$644$	−69.2548	−2.72902
$645$	0.155848	0.00613652
$646$	4.08865	0.160866
$647$	−40.1794	−1.57962	−0.789808	−	0.613354i	$-0.789820\pi$
$647$	−40.1794	−1.57962	−0.789808	+	0.613354i	$0.789820\pi$
$648$	27.1649	1.06714
$649$	23.5532	0.924543
$650$	5.21831	0.204679
$651$	−1.03679	−0.0406351
$652$	61.1906	2.39641
$653$	5.75553	0.225231	0.112616	−	0.993639i	$-0.464077\pi$
$653$	5.75553	0.225231	0.112616	+	0.993639i	$0.464077\pi$
$654$	2.83314	0.110785
$655$	12.0320	0.470128
$656$	−1.23327	−0.0481511
$657$	−22.0320	−0.859551
$658$	37.3151	1.45469
$659$	−42.4922	−1.65526	−0.827631	−	0.561273i	$-0.810312\pi$
$659$	−42.4922	−1.65526	−0.827631	+	0.561273i	$0.810312\pi$
$660$	1.54843	0.0602727
$661$	0.623264	0.0242422	0.0121211	−	0.999927i	$-0.496142\pi$
$661$	0.623264	0.0242422	0.0121211	+	0.999927i	$0.496142\pi$
$662$	−23.4546	−0.911588
$663$	−0.210052	−0.00815774
$664$	−39.8177	−1.54523
$665$	10.8140	0.419347
$666$	−45.1612	−1.74996
$667$	46.7121	1.80870
$668$	−2.55467	−0.0988431
$669$	−0.290593	−0.0112350
$670$	−15.0500	−0.581433
$671$	−23.3425	−0.901126
$672$	0.872429	0.0336547
$673$	−38.5762	−1.48700	−0.743501	−	0.668735i	$-0.766836\pi$
$673$	−38.5762	−1.48700	−0.743501	+	0.668735i	$0.766836\pi$
$674$	−53.0325	−2.04274
$675$	0.275159	0.0105909
$676$	−8.75030	−0.336550
$677$	−6.49148	−0.249488	−0.124744	−	0.992189i	$-0.539811\pi$
$677$	−6.49148	−0.249488	−0.124744	+	0.992189i	$0.539811\pi$
$678$	−1.81337	−0.0696420
$679$	41.5263	1.59363
$680$	7.23899	0.277603
$681$	−0.717735	−0.0275037
$682$	−42.9968	−1.64643
$683$	−13.9942	−0.535475	−0.267737	−	0.963492i	$-0.586276\pi$
$683$	−13.9942	−0.535475	−0.267737	+	0.963492i	$0.586276\pi$
$684$	−17.6117	−0.673401
$685$	24.2985	0.928399
$686$	−44.0348	−1.68126
$687$	−1.34377	−0.0512679
$688$	−0.358478	−0.0136668
$689$	7.61626	0.290156
$690$	2.93999	0.111923
$691$	37.2987	1.41891	0.709455	−	0.704751i	$-0.248941\pi$
$691$	37.2987	1.41891	0.709455	+	0.704751i	$0.248941\pi$
$692$	73.7478	2.80347
$693$	22.9257	0.870874
$694$	−6.55369	−0.248775
$695$	0.00151364	5.74157e−5 0
$696$	1.12925	0.0428041
$697$	−3.44030	−0.130311
$698$	−82.7339	−3.13152
$699$	0.253869	0.00960222
$700$	5.95183	0.224958
$701$	−20.8665	−0.788115	−0.394058	−	0.919086i	$-0.628929\pi$
$701$	−20.8665	−0.788115	−0.394058	+	0.919086i	$0.628929\pi$
$702$	2.90345	0.109584
$703$	11.5972	0.437395
$704$	38.3294	1.44459
$705$	−0.987990	−0.0372099
$706$	45.0550	1.69567
$707$	10.8879	0.409482
$708$	1.69990	0.0638863
$709$	−13.1390	−0.493446	−0.246723	−	0.969086i	$-0.579354\pi$
$709$	−13.1390	−0.493446	−0.246723	+	0.969086i	$0.579354\pi$
$710$	−28.2805	−1.06135
$711$	−10.1065	−0.379024
$712$	−20.4054	−0.764726
$713$	−50.9168	−1.90685
$714$	−0.384127	−0.0143756
$715$	−23.0396	−0.861632
$716$	−6.81272	−0.254603
$717$	−1.27709	−0.0476937
$718$	10.2144	0.381196
$719$	−19.2634	−0.718404	−0.359202	−	0.933260i	$-0.616951\pi$
$719$	−19.2634	−0.718404	−0.359202	+	0.933260i	$0.616951\pi$
$720$	−2.56464	−0.0955786
$721$	−34.2999	−1.27740
$722$	−36.5512	−1.36029
$723$	−1.29610	−0.0482023
$724$	−53.3751	−1.98367
$725$	−4.01449	−0.149094
$726$	0.303342	0.0112581
$727$	−7.21673	−0.267654	−0.133827	−	0.991005i	$-0.542727\pi$
$727$	−7.21673	−0.267654	−0.133827	+	0.991005i	$0.542727\pi$
$728$	24.9110	0.923264
$729$	−26.7703	−0.991493
$730$	40.4907	1.49863
$731$	−1.00000	−0.0369863
$732$	−1.68470	−0.0622682
$733$	19.9263	0.735995	0.367998	−	0.929827i	$-0.380043\pi$
$733$	19.9263	0.735995	0.367998	+	0.929827i	$0.380043\pi$
$734$	12.6407	0.466576
$735$	0.0749713	0.00276536
$736$	42.8449	1.57928
$737$	8.19332	0.301805
$738$	23.7599	0.874616
$739$	26.5100	0.975184	0.487592	−	0.873072i	$-0.337875\pi$
$739$	26.5100	0.975184	0.487592	+	0.873072i	$0.337875\pi$
$740$	51.7653	1.90293
$741$	−0.372531	−0.0136853
$742$	13.9280	0.511315
$743$	−38.2652	−1.40382	−0.701908	−	0.712268i	$-0.747668\pi$
$743$	−38.2652	−1.40382	−0.701908	+	0.712268i	$0.747668\pi$
$744$	−1.23089	−0.0451268
$745$	−24.0769	−0.882110
$746$	−63.1560	−2.31231
$747$	39.3516	1.43980
$748$	−9.93553	−0.363279
$749$	−1.69459	−0.0619191
$750$	1.54379	0.0563713
$751$	45.0904	1.64537	0.822686	−	0.568497i	$-0.192475\pi$
$751$	45.0904	1.64537	0.822686	+	0.568497i	$0.192475\pi$
$752$	2.27255	0.0828713
$753$	−1.83662	−0.0669302
$754$	−42.3605	−1.54268
$755$	−25.6830	−0.934699
$756$	3.31158	0.120441
$757$	−6.38823	−0.232184	−0.116092	−	0.993238i	$-0.537037\pi$
$757$	−6.38823	−0.232184	−0.116092	+	0.993238i	$0.537037\pi$
$758$	43.3340	1.57396
$759$	−1.60055	−0.0580962
$760$	12.8385	0.465700
$761$	−9.56884	−0.346870	−0.173435	−	0.984845i	$-0.555487\pi$
$761$	−9.56884	−0.346870	−0.173435	+	0.984845i	$0.555487\pi$
$762$	−1.88150	−0.0681595
$763$	−48.0807	−1.74064
$764$	−33.2513	−1.20299
$765$	−7.15426	−0.258663
$766$	−13.6941	−0.494786
$767$	−25.2934	−0.913290
$768$	1.19085	0.0429712
$769$	−23.1724	−0.835619	−0.417810	−	0.908535i	$-0.637202\pi$
$769$	−23.1724	−0.835619	−0.417810	+	0.908535i	$0.637202\pi$
$770$	−42.1331	−1.51837
$771$	−1.53214	−0.0551786
$772$	27.3559	0.984560
$773$	−24.7927	−0.891731	−0.445866	−	0.895100i	$-0.647104\pi$
$773$	−24.7927	−0.891731	−0.445866	+	0.895100i	$0.647104\pi$
$774$	6.90636	0.248244
$775$	4.37584	0.157185
$776$	49.3005	1.76979
$777$	−1.08955	−0.0390873
$778$	23.0077	0.824865
$779$	−6.10143	−0.218606
$780$	−1.66284	−0.0595391
$781$	15.3961	0.550914
$782$	−18.8644	−0.674591
$783$	−2.23365	−0.0798241
$784$	−0.172447	−0.00615881
$785$	−26.7171	−0.953574
$786$	−0.757988	−0.0270365
$787$	−23.4106	−0.834499	−0.417250	−	0.908792i	$-0.637006\pi$
$787$	−23.4106	−0.834499	−0.417250	+	0.908792i	$0.637006\pi$
$788$	73.5985	2.62184
$789$	1.31804	0.0469236
$790$	18.5739	0.660828
$791$	30.7743	1.09421
$792$	27.2176	0.967137
$793$	25.0671	0.890158
$794$	5.73050	0.203368
$795$	−0.368772	−0.0130790
$796$	−0.499976	−0.0177212
$797$	35.4153	1.25448	0.627238	−	0.778828i	$-0.284185\pi$
$797$	35.4153	1.25448	0.627238	+	0.778828i	$0.284185\pi$
$798$	−0.681256	−0.0241162
$799$	6.33944	0.224273
$800$	−3.68214	−0.130183
$801$	20.1666	0.712552
$802$	13.8994	0.490805
$803$	−22.0434	−0.777895
$804$	0.591337	0.0208548
$805$	−49.8940	−1.75853
$806$	46.1735	1.62639
$807$	0.190046	0.00668995
$808$	12.9263	0.454744
$809$	−11.2091	−0.394089	−0.197045	−	0.980395i	$-0.563134\pi$
$809$	−11.2091	−0.394089	−0.197045	+	0.980395i	$0.563134\pi$
$810$	49.3396	1.73362
$811$	−12.2624	−0.430592	−0.215296	−	0.976549i	$-0.569072\pi$
$811$	−12.2624	−0.430592	−0.215296	+	0.976549i	$0.569072\pi$
$812$	−48.3150	−1.69552
$813$	1.37139	0.0480969
$814$	−45.1845	−1.58372
$815$	44.0842	1.54420
$816$	−0.0233939	−0.000818952 0
$817$	−1.77352	−0.0620475
$818$	50.8541	1.77807
$819$	−24.6195	−0.860273
$820$	−27.2345	−0.951069
$821$	15.8446	0.552982	0.276491	−	0.961017i	$-0.410828\pi$
$821$	15.8446	0.552982	0.276491	+	0.961017i	$0.410828\pi$
$822$	−1.53076	−0.0533912
$823$	28.3602	0.988575	0.494287	−	0.869299i	$-0.335429\pi$
$823$	28.3602	0.988575	0.494287	+	0.869299i	$0.335429\pi$
$824$	−40.7213	−1.41859
$825$	0.137553	0.00478897
$826$	−46.2546	−1.60940
$827$	−47.3663	−1.64709	−0.823544	−	0.567252i	$-0.808007\pi$
$827$	−47.3663	−1.64709	−0.823544	+	0.567252i	$0.808007\pi$
$828$	81.2579	2.82391
$829$	31.0699	1.07910	0.539552	−	0.841952i	$-0.318594\pi$
$829$	31.0699	1.07910	0.539552	+	0.841952i	$0.318594\pi$
$830$	−72.3210	−2.51030
$831$	−1.41381	−0.0490445
$832$	−41.1612	−1.42701
$833$	−0.481053	−0.0166675
$834$	−9.53561e−5 0	−3.30191e−6 0
$835$	−1.84049	−0.0636927
$836$	−17.6208	−0.609429
$837$	2.43470	0.0841557
$838$	−52.3448	−1.80822
$839$	15.3406	0.529617	0.264808	−	0.964301i	$-0.414691\pi$
$839$	15.3406	0.529617	0.264808	+	0.964301i	$0.414691\pi$
$840$	−1.20617	−0.0416168
$841$	3.58830	0.123734
$842$	6.73388	0.232065
$843$	−1.12944	−0.0388999
$844$	−20.0711	−0.690876
$845$	−6.30407	−0.216867
$846$	−43.7825	−1.50527
$847$	−5.14795	−0.176886
$848$	0.848239	0.0291287
$849$	−1.30971	−0.0449493
$850$	1.62123	0.0556077
$851$	−53.5076	−1.83422
$852$	1.11118	0.0380684
$853$	0.390904	0.0133843	0.00669216	−	0.999978i	$-0.497870\pi$
$853$	0.390904	0.0133843	0.00669216	+	0.999978i	$0.497870\pi$
$854$	45.8408	1.56864
$855$	−12.6882	−0.433927
$856$	−2.01184	−0.0687634
$857$	−20.5045	−0.700421	−0.350211	−	0.936671i	$-0.613890\pi$
$857$	−20.5045	−0.700421	−0.350211	+	0.936671i	$0.613890\pi$
$858$	1.45144	0.0495515
$859$	8.87496	0.302810	0.151405	−	0.988472i	$-0.451620\pi$
$859$	8.87496	0.302810	0.151405	+	0.988472i	$0.451620\pi$
$860$	−7.91631	−0.269944
$861$	0.573226	0.0195355
$862$	−78.1029	−2.66020
$863$	39.4636	1.34336	0.671679	−	0.740842i	$-0.265573\pi$
$863$	39.4636	1.34336	0.671679	+	0.740842i	$0.265573\pi$
$864$	−2.04873	−0.0696992
$865$	53.1309	1.80651
$866$	−75.6176	−2.56959
$867$	−0.0652591	−0.00221632
$868$	52.6639	1.78753
$869$	−10.1117	−0.343017
$870$	2.05106	0.0695373
$871$	−8.79866	−0.298131
$872$	−57.0821	−1.93304
$873$	−48.7235	−1.64904
$874$	−33.4564	−1.13168
$875$	−26.1994	−0.885701
$876$	−1.59094	−0.0537529
$877$	−36.0615	−1.21771	−0.608854	−	0.793282i	$-0.708371\pi$
$877$	−36.0615	−1.21771	−0.608854	+	0.793282i	$0.708371\pi$
$878$	83.0279	2.80205
$879$	−1.99220	−0.0671951
$880$	−2.56597	−0.0864988
$881$	11.3377	0.381978	0.190989	−	0.981592i	$-0.438831\pi$
$881$	11.3377	0.381978	0.190989	+	0.981592i	$0.438831\pi$
$882$	3.32233	0.111869
$883$	13.3633	0.449712	0.224856	−	0.974392i	$-0.427809\pi$
$883$	13.3633	0.449712	0.224856	+	0.974392i	$0.427809\pi$
$884$	10.6696	0.358857
$885$	1.22468	0.0411672
$886$	−39.9509	−1.34218
$887$	20.2189	0.678884	0.339442	−	0.940627i	$-0.389762\pi$
$887$	20.2189	0.678884	0.339442	+	0.940627i	$0.389762\pi$
$888$	−1.29352	−0.0434079
$889$	31.9306	1.07092
$890$	−37.0624	−1.24234
$891$	−26.8608	−0.899870
$892$	14.7607	0.494224
$893$	11.2431	0.376236
$894$	1.51679	0.0507291
$895$	−4.90816	−0.164062
$896$	−48.5352	−1.62145
$897$	1.71880	0.0573891
$898$	35.2372	1.17588
$899$	−35.5216	−1.18471
$900$	−6.98339	−0.232780
$901$	2.36623	0.0788304
$902$	23.7722	0.791529
$903$	0.166621	0.00554480
$904$	36.5357	1.21516
$905$	−38.4536	−1.27824
$906$	1.61797	0.0537535
$907$	14.8432	0.492861	0.246431	−	0.969160i	$-0.420742\pi$
$907$	14.8432	0.492861	0.246431	+	0.969160i	$0.420742\pi$
$908$	36.4574	1.20988
$909$	−12.7750	−0.423719
$910$	45.2460	1.49989
$911$	−37.3749	−1.23829	−0.619144	−	0.785278i	$-0.712520\pi$
$911$	−37.3749	−1.23829	−0.619144	+	0.785278i	$0.712520\pi$
$912$	−0.0414895	−0.00137386
$913$	39.3720	1.30302
$914$	83.5524	2.76367
$915$	−1.21372	−0.0401245
$916$	68.2566	2.25526
$917$	12.8637	0.424796
$918$	0.902047	0.0297720
$919$	−50.9570	−1.68092	−0.840458	−	0.541876i	$-0.817714\pi$
$919$	−50.9570	−1.68092	−0.840458	+	0.541876i	$0.817714\pi$
$920$	−59.2348	−1.95291
$921$	0.569730	0.0187733
$922$	−4.57031	−0.150515
$923$	−16.5336	−0.544208
$924$	1.65547	0.0544609
$925$	4.59849	0.151198
$926$	−58.3844	−1.91863
$927$	40.2447	1.32181
$928$	29.8904	0.981199
$929$	−24.2009	−0.794005	−0.397002	−	0.917818i	$-0.629949\pi$
$929$	−24.2009	−0.794005	−0.397002	+	0.917818i	$0.629949\pi$
$930$	−2.23568	−0.0733107
$931$	−0.853156	−0.0279610
$932$	−12.8953	−0.422400
$933$	0.550919	0.0180363
$934$	24.1438	0.790008
$935$	−7.15796	−0.234090
$936$	−29.2285	−0.955365
$937$	−47.4152	−1.54899	−0.774493	−	0.632582i	$-0.781995\pi$
$937$	−47.4152	−1.54899	−0.774493	+	0.632582i	$0.781995\pi$
$938$	−16.0903	−0.525368
$939$	−1.03630	−0.0338183
$940$	50.1850	1.63685
$941$	17.6566	0.575588	0.287794	−	0.957692i	$-0.407078\pi$
$941$	17.6566	0.575588	0.287794	+	0.957692i	$0.407078\pi$
$942$	1.68312	0.0548390
$943$	28.1511	0.916725
$944$	−2.81698	−0.0916847
$945$	2.38580	0.0776100
$946$	6.90993	0.224661
$947$	−37.1438	−1.20701	−0.603505	−	0.797359i	$-0.706230\pi$
$947$	−37.1438	−1.20701	−0.603505	+	0.797359i	$0.706230\pi$
$948$	−0.729794	−0.0237026
$949$	23.6720	0.768426
$950$	2.87528	0.0932863
$951$	0.246227	0.00798446
$952$	7.73938	0.250835
$953$	22.7600	0.737269	0.368634	−	0.929575i	$-0.379825\pi$
$953$	22.7600	0.737269	0.368634	+	0.929575i	$0.379825\pi$
$954$	−16.3420	−0.529092
$955$	−23.9556	−0.775186
$956$	64.8697	2.09804
$957$	−1.11661	−0.0360948
$958$	−30.5185	−0.986008
$959$	25.9782	0.838878
$960$	1.99299	0.0643234
$961$	7.71900	0.249000
$962$	48.5229	1.56444
$963$	1.98830	0.0640719
$964$	65.8352	2.12041
$965$	19.7083	0.634432
$966$	3.14321	0.101131
$967$	16.6258	0.534650	0.267325	−	0.963606i	$-0.413860\pi$
$967$	16.6258	0.534650	0.267325	+	0.963606i	$0.413860\pi$
$968$	−6.11172	−0.196438
$969$	−0.115738	−0.00371804
$970$	89.5447	2.87511
$971$	49.0979	1.57563	0.787814	−	0.615913i	$-0.211213\pi$
$971$	49.0979	1.57563	0.787814	+	0.615913i	$0.211213\pi$
$972$	−5.82968	−0.186987
$973$	0.00161827	5.18793e−5 0
$974$	59.4465	1.90479
$975$	−0.147716	−0.00473068
$976$	2.79177	0.0893625
$977$	−41.9418	−1.34184	−0.670919	−	0.741530i	$-0.734100\pi$
$977$	−41.9418	−1.34184	−0.670919	+	0.741530i	$0.734100\pi$
$978$	−2.77721	−0.0888053
$979$	20.1770	0.644860
$980$	−3.80817	−0.121647
$981$	56.4139	1.80116
$982$	−57.0749	−1.82133
$983$	18.1745	0.579676	0.289838	−	0.957076i	$-0.406399\pi$
$983$	18.1745	0.579676	0.289838	+	0.957076i	$0.406399\pi$
$984$	0.680542	0.0216949
$985$	53.0233	1.68946
$986$	−13.1606	−0.419119
$987$	−1.05628	−0.0336219
$988$	18.9227	0.602011
$989$	8.18274	0.260196
$990$	49.4355	1.57116
$991$	39.3412	1.24971	0.624857	−	0.780740i	$-0.285157\pi$
$991$	39.3412	1.24971	0.624857	+	0.780740i	$0.285157\pi$
$992$	−32.5808	−1.03444
$993$	0.663933	0.0210693
$994$	−30.2353	−0.959006
$995$	−0.360203	−0.0114192
$996$	2.84160	0.0900394
$997$	−33.0074	−1.04535	−0.522677	−	0.852530i	$-0.675067\pi$
$997$	−33.0074	−1.04535	−0.522677	+	0.852530i	$0.675067\pi$
$998$	42.4730	1.34446
$999$	2.55859	0.0809501

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.e.1.17	✓	19
3.2	odd	2		6579.2.a.t.1.3		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.e.1.17	✓	19	1.1	even	1	trivial
6579.2.a.t.1.3		19	3.2	odd	2

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.a (trivial)

\(f(q)\)	\(=\)	\(q+2.30539 q^{2} -0.0652591 q^{3} +3.31484 q^{4} +2.38814 q^{5} -0.150448 q^{6} +2.55322 q^{7} +3.03122 q^{8} -2.99574 q^{9} +O(q^{10})\)	\(q+2.30539 q^{2} -0.0652591 q^{3} +3.31484 q^{4} +2.38814 q^{5} -0.150448 q^{6} +2.55322 q^{7} +3.03122 q^{8} -2.99574 q^{9} +5.50561 q^{10} -2.99729 q^{11} -0.216323 q^{12} +3.21874 q^{13} +5.88618 q^{14} -0.155848 q^{15} +0.358478 q^{16} +1.00000 q^{17} -6.90636 q^{18} +1.77352 q^{19} +7.91631 q^{20} -0.166621 q^{21} -6.90993 q^{22} -8.18274 q^{23} -0.197815 q^{24} +0.703234 q^{25} +7.42045 q^{26} +0.391277 q^{27} +8.46352 q^{28} -5.70862 q^{29} -0.359291 q^{30} +6.22246 q^{31} -5.23601 q^{32} +0.195600 q^{33} +2.30539 q^{34} +6.09746 q^{35} -9.93040 q^{36} +6.53907 q^{37} +4.08865 q^{38} -0.210052 q^{39} +7.23899 q^{40} -3.44030 q^{41} -0.384127 q^{42} -1.00000 q^{43} -9.93553 q^{44} -7.15426 q^{45} -18.8644 q^{46} +6.33944 q^{47} -0.0233939 q^{48} -0.481053 q^{49} +1.62123 q^{50} -0.0652591 q^{51} +10.6696 q^{52} +2.36623 q^{53} +0.902047 q^{54} -7.15796 q^{55} +7.73938 q^{56} -0.115738 q^{57} -13.1606 q^{58} -7.85816 q^{59} -0.516612 q^{60} +7.78786 q^{61} +14.3452 q^{62} -7.64879 q^{63} -12.7880 q^{64} +7.68681 q^{65} +0.450936 q^{66} -2.73358 q^{67} +3.31484 q^{68} +0.533999 q^{69} +14.0571 q^{70} -5.13666 q^{71} -9.08075 q^{72} +7.35445 q^{73} +15.0751 q^{74} -0.0458924 q^{75} +5.87892 q^{76} -7.65275 q^{77} -0.484252 q^{78} +3.37362 q^{79} +0.856096 q^{80} +8.96169 q^{81} -7.93124 q^{82} -13.1359 q^{83} -0.552322 q^{84} +2.38814 q^{85} -2.30539 q^{86} +0.372539 q^{87} -9.08544 q^{88} -6.73176 q^{89} -16.4934 q^{90} +8.21815 q^{91} -27.1245 q^{92} -0.406072 q^{93} +14.6149 q^{94} +4.23541 q^{95} +0.341697 q^{96} +16.2643 q^{97} -1.10902 q^{98} +8.97910 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9} - 2 q^{10} + 4 q^{11} + 9 q^{12} + 14 q^{13} + 5 q^{14} - 7 q^{15} + 32 q^{16} + 19 q^{17} + 12 q^{18} + 12 q^{19} + 23 q^{20} + 16 q^{21} + 36 q^{22} - q^{23} - 13 q^{24} + 30 q^{25} - 21 q^{26} + 8 q^{27} + 5 q^{28} + 41 q^{29} - 26 q^{30} - 8 q^{31} - 20 q^{32} - 14 q^{33} + 2 q^{34} + 3 q^{35} - 5 q^{36} + 50 q^{37} - 29 q^{38} + 17 q^{39} - 15 q^{40} + 6 q^{41} - q^{42} - 19 q^{43} + 16 q^{44} + 24 q^{45} + 38 q^{46} - 21 q^{47} - 2 q^{48} + 46 q^{49} - 36 q^{50} + 5 q^{51} + 39 q^{52} - 9 q^{53} + 53 q^{54} + 10 q^{55} - 12 q^{56} - 5 q^{57} - 45 q^{58} - 4 q^{59} - 7 q^{60} + 68 q^{61} - 25 q^{62} + 61 q^{63} - 14 q^{64} + 22 q^{65} - 17 q^{66} + 26 q^{68} - 9 q^{69} - 37 q^{70} + 23 q^{71} - 4 q^{72} - q^{73} - 30 q^{74} - 25 q^{75} + 47 q^{76} - 19 q^{77} + 12 q^{78} + 16 q^{79} + 28 q^{80} - 21 q^{81} - 13 q^{82} - 32 q^{83} - 47 q^{84} + 11 q^{85} - 2 q^{86} - 8 q^{87} + 108 q^{88} + 11 q^{89} + 5 q^{90} + 52 q^{91} - 23 q^{92} - 23 q^{93} + 47 q^{94} - 25 q^{95} - 103 q^{96} + 36 q^{97} - 100 q^{98} - 11 q^{99}+O(q^{100}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9 - 2 * q^10 + 4 * q^11 + 9 * q^12 + 14 * q^13 + 5 * q^14 - 7 * q^15 + 32 * q^16 + 19 * q^17 + 12 * q^18 + 12 * q^19 + 23 * q^20 + 16 * q^21 + 36 * q^22 - q^23 - 13 * q^24 + 30 * q^25 - 21 * q^26 + 8 * q^27 + 5 * q^28 + 41 * q^29 - 26 * q^30 - 8 * q^31 - 20 * q^32 - 14 * q^33 + 2 * q^34 + 3 * q^35 - 5 * q^36 + 50 * q^37 - 29 * q^38 + 17 * q^39 - 15 * q^40 + 6 * q^41 - q^42 - 19 * q^43 + 16 * q^44 + 24 * q^45 + 38 * q^46 - 21 * q^47 - 2 * q^48 + 46 * q^49 - 36 * q^50 + 5 * q^51 + 39 * q^52 - 9 * q^53 + 53 * q^54 + 10 * q^55 - 12 * q^56 - 5 * q^57 - 45 * q^58 - 4 * q^59 - 7 * q^60 + 68 * q^61 - 25 * q^62 + 61 * q^63 - 14 * q^64 + 22 * q^65 - 17 * q^66 + 26 * q^68 - 9 * q^69 - 37 * q^70 + 23 * q^71 - 4 * q^72 - q^73 - 30 * q^74 - 25 * q^75 + 47 * q^76 - 19 * q^77 + 12 * q^78 + 16 * q^79 + 28 * q^80 - 21 * q^81 - 13 * q^82 - 32 * q^83 - 47 * q^84 + 11 * q^85 - 2 * q^86 - 8 * q^87 + 108 * q^88 + 11 * q^89 + 5 * q^90 + 52 * q^91 - 23 * q^92 - 23 * q^93 + 47 * q^94 - 25 * q^95 - 103 * q^96 + 36 * q^97 - 100 * q^98 - 11 * q^99

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