LMFDB - Embedded newform 4011.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$1$
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} - 3 x^{18} - 20 x^{17} + 63 x^{16} + 156 x^{15} - 531 x^{14} - 597 x^{13} + 2313 x^{12} + \cdots + 18 $ x^19 - 3x^18 - 20x^17 + 63x^16 + 156x^15 - 531x^14 - 597x^13 + 2313x^12 + 1149x^11 - 5631x^10 - 951x^9 + 7819x^8 - 87x^7 - 6025x^6 + 649x^5 + 2354x^4 - 342x^3 - 384x^2 + 45x + 18
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.38901$ of defining polynomial
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38901 q^{2} -1.00000 q^{3} +3.70736 q^{4} +2.22462 q^{5} +2.38901 q^{6} +1.00000 q^{7} -4.07890 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.38901 q^{2} -1.00000 q^{3} +3.70736 q^{4} +2.22462 q^{5} +2.38901 q^{6} +1.00000 q^{7} -4.07890 q^{8} +1.00000 q^{9} -5.31464 q^{10} -2.85836 q^{11} -3.70736 q^{12} -3.48178 q^{13} -2.38901 q^{14} -2.22462 q^{15} +2.32980 q^{16} -3.63746 q^{17} -2.38901 q^{18} +0.911520 q^{19} +8.24747 q^{20} -1.00000 q^{21} +6.82864 q^{22} +6.43483 q^{23} +4.07890 q^{24} -0.0510600 q^{25} +8.31801 q^{26} -1.00000 q^{27} +3.70736 q^{28} +6.36848 q^{29} +5.31464 q^{30} -3.53400 q^{31} +2.59189 q^{32} +2.85836 q^{33} +8.68992 q^{34} +2.22462 q^{35} +3.70736 q^{36} -6.18389 q^{37} -2.17763 q^{38} +3.48178 q^{39} -9.07400 q^{40} +0.687565 q^{41} +2.38901 q^{42} +8.33691 q^{43} -10.5970 q^{44} +2.22462 q^{45} -15.3729 q^{46} +1.74296 q^{47} -2.32980 q^{48} +1.00000 q^{49} +0.121983 q^{50} +3.63746 q^{51} -12.9082 q^{52} +10.4183 q^{53} +2.38901 q^{54} -6.35877 q^{55} -4.07890 q^{56} -0.911520 q^{57} -15.2144 q^{58} -11.9204 q^{59} -8.24747 q^{60} -9.22776 q^{61} +8.44276 q^{62} +1.00000 q^{63} -10.8516 q^{64} -7.74565 q^{65} -6.82864 q^{66} -10.3941 q^{67} -13.4854 q^{68} -6.43483 q^{69} -5.31464 q^{70} +4.04517 q^{71} -4.07890 q^{72} +12.4021 q^{73} +14.7734 q^{74} +0.0510600 q^{75} +3.37933 q^{76} -2.85836 q^{77} -8.31801 q^{78} -0.465252 q^{79} +5.18292 q^{80} +1.00000 q^{81} -1.64260 q^{82} -12.8833 q^{83} -3.70736 q^{84} -8.09197 q^{85} -19.9169 q^{86} -6.36848 q^{87} +11.6590 q^{88} +6.05486 q^{89} -5.31464 q^{90} -3.48178 q^{91} +23.8562 q^{92} +3.53400 q^{93} -4.16396 q^{94} +2.02779 q^{95} -2.59189 q^{96} -8.42169 q^{97} -2.38901 q^{98} -2.85836 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 3 q^{2} - 19 q^{3} + 11 q^{4} - 12 q^{5} - 3 q^{6} + 19 q^{7} + 6 q^{8} + 19 q^{9}+O(q^{10}) $ 19 * q + 3 * q^2 - 19 * q^3 + 11 * q^4 - 12 * q^5 - 3 * q^6 + 19 * q^7 + 6 * q^8 + 19 * q^9	\( 19 q + 3 q^{2} - 19 q^{3} + 11 q^{4} - 12 q^{5} - 3 q^{6} + 19 q^{7} + 6 q^{8} + 19 q^{9} - 12 q^{10} + q^{11} - 11 q^{12} - 25 q^{13} + 3 q^{14} + 12 q^{15} + 3 q^{16} - 9 q^{17} + 3 q^{18} - 29 q^{19} - 14 q^{20} - 19 q^{21} - 5 q^{22} + 18 q^{23} - 6 q^{24} + 3 q^{25} - 15 q^{26} - 19 q^{27} + 11 q^{28} + 2 q^{29} + 12 q^{30} - 24 q^{31} + 15 q^{32} - q^{33} - 16 q^{34} - 12 q^{35} + 11 q^{36} - 24 q^{37} - 26 q^{38} + 25 q^{39} - 44 q^{40} - 14 q^{41} - 3 q^{42} - 17 q^{43} - 6 q^{44} - 12 q^{45} - 16 q^{46} + 7 q^{47} - 3 q^{48} + 19 q^{49} + 7 q^{50} + 9 q^{51} - 64 q^{52} + 4 q^{53} - 3 q^{54} - 15 q^{55} + 6 q^{56} + 29 q^{57} - 15 q^{58} - 23 q^{59} + 14 q^{60} - 38 q^{61} - 4 q^{62} + 19 q^{63} + 33 q^{65} + 5 q^{66} - 20 q^{67} - 27 q^{68} - 18 q^{69} - 12 q^{70} + 14 q^{71} + 6 q^{72} - 19 q^{73} - 11 q^{74} - 3 q^{75} - 33 q^{76} + q^{77} + 15 q^{78} - 16 q^{79} - 10 q^{80} + 19 q^{81} - 25 q^{82} - 11 q^{83} - 11 q^{84} - 5 q^{85} + 5 q^{86} - 2 q^{87} - 25 q^{88} - 19 q^{89} - 12 q^{90} - 25 q^{91} + 22 q^{92} + 24 q^{93} - 35 q^{94} + 26 q^{95} - 15 q^{96} - 57 q^{97} + 3 q^{98} + q^{99}+O(q^{100}) \) 19 * q + 3 * q^2 - 19 * q^3 + 11 * q^4 - 12 * q^5 - 3 * q^6 + 19 * q^7 + 6 * q^8 + 19 * q^9 - 12 * q^10 + q^11 - 11 * q^12 - 25 * q^13 + 3 * q^14 + 12 * q^15 + 3 * q^16 - 9 * q^17 + 3 * q^18 - 29 * q^19 - 14 * q^20 - 19 * q^21 - 5 * q^22 + 18 * q^23 - 6 * q^24 + 3 * q^25 - 15 * q^26 - 19 * q^27 + 11 * q^28 + 2 * q^29 + 12 * q^30 - 24 * q^31 + 15 * q^32 - q^33 - 16 * q^34 - 12 * q^35 + 11 * q^36 - 24 * q^37 - 26 * q^38 + 25 * q^39 - 44 * q^40 - 14 * q^41 - 3 * q^42 - 17 * q^43 - 6 * q^44 - 12 * q^45 - 16 * q^46 + 7 * q^47 - 3 * q^48 + 19 * q^49 + 7 * q^50 + 9 * q^51 - 64 * q^52 + 4 * q^53 - 3 * q^54 - 15 * q^55 + 6 * q^56 + 29 * q^57 - 15 * q^58 - 23 * q^59 + 14 * q^60 - 38 * q^61 - 4 * q^62 + 19 * q^63 + 33 * q^65 + 5 * q^66 - 20 * q^67 - 27 * q^68 - 18 * q^69 - 12 * q^70 + 14 * q^71 + 6 * q^72 - 19 * q^73 - 11 * q^74 - 3 * q^75 - 33 * q^76 + q^77 + 15 * q^78 - 16 * q^79 - 10 * q^80 + 19 * q^81 - 25 * q^82 - 11 * q^83 - 11 * q^84 - 5 * q^85 + 5 * q^86 - 2 * q^87 - 25 * q^88 - 19 * q^89 - 12 * q^90 - 25 * q^91 + 22 * q^92 + 24 * q^93 - 35 * q^94 + 26 * q^95 - 15 * q^96 - 57 * q^97 + 3 * q^98 + 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 $

$2$	−2.38901	−1.68928	−0.844642	−	0.535332i	$-0.820187\pi$
$2$	−2.38901	−1.68928	−0.844642	+	0.535332i	$0.820187\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.70736	1.85368
$5$	2.22462	0.994881	0.497440	−	0.867498i	$-0.334273\pi$
$5$	2.22462	0.994881	0.497440	+	0.867498i	$0.334273\pi$
$6$	2.38901	0.975308
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−4.07890	−1.44211
$9$	1.00000	0.333333
$10$	−5.31464	−1.68064
$11$	−2.85836	−0.861828	−0.430914	−	0.902393i	$-0.641809\pi$
$11$	−2.85836	−0.861828	−0.430914	+	0.902393i	$0.641809\pi$
$12$	−3.70736	−1.07022
$13$	−3.48178	−0.965673	−0.482837	−	0.875710i	$-0.660394\pi$
$13$	−3.48178	−0.965673	−0.482837	+	0.875710i	$0.660394\pi$
$14$	−2.38901	−0.638489
$15$	−2.22462	−0.574395
$16$	2.32980	0.582449
$17$	−3.63746	−0.882214	−0.441107	−	0.897455i	$-0.645414\pi$
$17$	−3.63746	−0.882214	−0.441107	+	0.897455i	$0.645414\pi$
$18$	−2.38901	−0.563095
$19$	0.911520	0.209117	0.104559	−	0.994519i	$-0.466657\pi$
$19$	0.911520	0.209117	0.104559	+	0.994519i	$0.466657\pi$
$20$	8.24747	1.84419
$21$	−1.00000	−0.218218
$22$	6.82864	1.45587
$23$	6.43483	1.34175	0.670877	−	0.741568i	$-0.265918\pi$
$23$	6.43483	1.34175	0.670877	+	0.741568i	$0.265918\pi$
$24$	4.07890	0.832601
$25$	−0.0510600	−0.0102120
$26$	8.31801	1.63130
$27$	−1.00000	−0.192450
$28$	3.70736	0.700625
$29$	6.36848	1.18260	0.591299	−	0.806453i	$-0.298615\pi$
$29$	6.36848	1.18260	0.591299	+	0.806453i	$0.298615\pi$
$30$	5.31464	0.970316
$31$	−3.53400	−0.634725	−0.317363	−	0.948304i	$-0.602797\pi$
$31$	−3.53400	−0.634725	−0.317363	+	0.948304i	$0.602797\pi$
$32$	2.59189	0.458185
$33$	2.85836	0.497577
$34$	8.68992	1.49031
$35$	2.22462	0.376030
$36$	3.70736	0.617893
$37$	−6.18389	−1.01663	−0.508313	−	0.861172i	$-0.669731\pi$
$37$	−6.18389	−1.01663	−0.508313	+	0.861172i	$0.669731\pi$
$38$	−2.17763	−0.353258
$39$	3.48178	0.557532
$40$	−9.07400	−1.43473
$41$	0.687565	0.107380	0.0536898	−	0.998558i	$-0.482902\pi$
$41$	0.687565	0.107380	0.0536898	+	0.998558i	$0.482902\pi$
$42$	2.38901	0.368632
$43$	8.33691	1.27137	0.635683	−	0.771950i	$-0.280718\pi$
$43$	8.33691	1.27137	0.635683	+	0.771950i	$0.280718\pi$
$44$	−10.5970	−1.59755
$45$	2.22462	0.331627
$46$	−15.3729	−2.26660
$47$	1.74296	0.254237	0.127119	−	0.991888i	$-0.459427\pi$
$47$	1.74296	0.254237	0.127119	+	0.991888i	$0.459427\pi$
$48$	−2.32980	−0.336277
$49$	1.00000	0.142857
$50$	0.121983	0.0172510
$51$	3.63746	0.509346
$52$	−12.9082	−1.79005
$53$	10.4183	1.43106	0.715531	−	0.698581i	$-0.246185\pi$
$53$	10.4183	1.43106	0.715531	+	0.698581i	$0.246185\pi$
$54$	2.38901	0.325103
$55$	−6.35877	−0.857416
$56$	−4.07890	−0.545065
$57$	−0.911520	−0.120734
$58$	−15.2144	−1.99774
$59$	−11.9204	−1.55191	−0.775953	−	0.630791i	$-0.782730\pi$
$59$	−11.9204	−1.55191	−0.775953	+	0.630791i	$0.782730\pi$
$60$	−8.24747	−1.06474
$61$	−9.22776	−1.18149	−0.590747	−	0.806857i	$-0.701167\pi$
$61$	−9.22776	−1.18149	−0.590747	+	0.806857i	$0.701167\pi$
$62$	8.44276	1.07223
$63$	1.00000	0.125988
$64$	−10.8516	−1.35645
$65$	−7.74565	−0.960730
$66$	−6.82864	−0.840548
$67$	−10.3941	−1.26984	−0.634920	−	0.772578i	$-0.718967\pi$
$67$	−10.3941	−1.26984	−0.634920	+	0.772578i	$0.718967\pi$
$68$	−13.4854	−1.63534
$69$	−6.43483	−0.774662
$70$	−5.31464	−0.635221
$71$	4.04517	0.480074	0.240037	−	0.970764i	$-0.422840\pi$
$71$	4.04517	0.480074	0.240037	+	0.970764i	$0.422840\pi$
$72$	−4.07890	−0.480703
$73$	12.4021	1.45156	0.725780	−	0.687927i	$-0.241479\pi$
$73$	12.4021	1.45156	0.725780	+	0.687927i	$0.241479\pi$
$74$	14.7734	1.71737
$75$	0.0510600	0.00589590
$76$	3.37933	0.387636
$77$	−2.85836	−0.325740
$78$	−8.31801	−0.941829
$79$	−0.465252	−0.0523449	−0.0261724	−	0.999657i	$-0.508332\pi$
$79$	−0.465252	−0.0523449	−0.0261724	+	0.999657i	$0.508332\pi$
$80$	5.18292	0.579468
$81$	1.00000	0.111111
$82$	−1.64260	−0.181395
$83$	−12.8833	−1.41413	−0.707066	−	0.707148i	$-0.749981\pi$
$83$	−12.8833	−1.41413	−0.707066	+	0.707148i	$0.749981\pi$
$84$	−3.70736	−0.404506
$85$	−8.09197	−0.877698
$86$	−19.9169	−2.14770
$87$	−6.36848	−0.682773
$88$	11.6590	1.24285
$89$	6.05486	0.641814	0.320907	−	0.947111i	$-0.396012\pi$
$89$	6.05486	0.641814	0.320907	+	0.947111i	$0.396012\pi$
$90$	−5.31464	−0.560212
$91$	−3.48178	−0.364990
$92$	23.8562	2.48718
$93$	3.53400	0.366459
$94$	−4.16396	−0.429479
$95$	2.02779	0.208047
$96$	−2.59189	−0.264534
$97$	−8.42169	−0.855093	−0.427546	−	0.903993i	$-0.640622\pi$
$97$	−8.42169	−0.855093	−0.427546	+	0.903993i	$0.640622\pi$
$98$	−2.38901	−0.241326
$99$	−2.85836	−0.287276
$100$	−0.189298	−0.0189298
$101$	−15.8651	−1.57864	−0.789320	−	0.613982i	$-0.789567\pi$
$101$	−15.8651	−1.57864	−0.789320	+	0.613982i	$0.789567\pi$
$102$	−8.68992	−0.860431
$103$	−0.702916	−0.0692604	−0.0346302	−	0.999400i	$-0.511025\pi$
$103$	−0.702916	−0.0692604	−0.0346302	+	0.999400i	$0.511025\pi$
$104$	14.2018	1.39260
$105$	−2.22462	−0.217101
$106$	−24.8894	−2.41747
$107$	1.20892	0.116871	0.0584355	−	0.998291i	$-0.481389\pi$
$107$	1.20892	0.116871	0.0584355	+	0.998291i	$0.481389\pi$
$108$	−3.70736	−0.356741
$109$	−11.2085	−1.07358	−0.536791	−	0.843715i	$-0.680364\pi$
$109$	−11.2085	−1.07358	−0.536791	+	0.843715i	$0.680364\pi$
$110$	15.1911	1.44842
$111$	6.18389	0.586949
$112$	2.32980	0.220145
$113$	15.8727	1.49318	0.746591	−	0.665283i	$-0.231689\pi$
$113$	15.8727	1.49318	0.746591	+	0.665283i	$0.231689\pi$
$114$	2.17763	0.203954
$115$	14.3151	1.33489
$116$	23.6102	2.19216
$117$	−3.48178	−0.321891
$118$	28.4780	2.62161
$119$	−3.63746	−0.333445
$120$	9.07400	0.828339
$121$	−2.82978	−0.257253
$122$	22.0452	1.99588
$123$	−0.687565	−0.0619957
$124$	−13.1018	−1.17658
$125$	−11.2367	−1.00504
$126$	−2.38901	−0.212830
$127$	12.3692	1.09759	0.548796	−	0.835956i	$-0.315086\pi$
$127$	12.3692	1.09759	0.548796	+	0.835956i	$0.315086\pi$
$128$	20.7409	1.83325
$129$	−8.33691	−0.734024
$130$	18.5044	1.62295
$131$	4.99135	0.436096	0.218048	−	0.975938i	$-0.430031\pi$
$131$	4.99135	0.436096	0.218048	+	0.975938i	$0.430031\pi$
$132$	10.5970	0.922348
$133$	0.911520	0.0790388
$134$	24.8316	2.14512
$135$	−2.22462	−0.191465
$136$	14.8368	1.27225
$137$	−6.86289	−0.586336	−0.293168	−	0.956061i	$-0.594710\pi$
$137$	−6.86289	−0.586336	−0.293168	+	0.956061i	$0.594710\pi$
$138$	15.3729	1.30862
$139$	−4.93670	−0.418725	−0.209363	−	0.977838i	$-0.567139\pi$
$139$	−4.93670	−0.418725	−0.209363	+	0.977838i	$0.567139\pi$
$140$	8.24747	0.697039
$141$	−1.74296	−0.146784
$142$	−9.66395	−0.810981
$143$	9.95219	0.832244
$144$	2.32980	0.194150
$145$	14.1675	1.17654
$146$	−29.6288	−2.45210
$147$	−1.00000	−0.0824786
$148$	−22.9259	−1.88450
$149$	0.836914	0.0685627	0.0342813	−	0.999412i	$-0.489086\pi$
$149$	0.836914	0.0685627	0.0342813	+	0.999412i	$0.489086\pi$
$150$	−0.121983	−0.00995985
$151$	9.11066	0.741415	0.370707	−	0.928750i	$-0.379115\pi$
$151$	9.11066	0.741415	0.370707	+	0.928750i	$0.379115\pi$
$152$	−3.71800	−0.301569
$153$	−3.63746	−0.294071
$154$	6.82864	0.550268
$155$	−7.86181	−0.631476
$156$	12.9082	1.03349
$157$	−2.56363	−0.204600	−0.102300	−	0.994754i	$-0.532620\pi$
$157$	−2.56363	−0.204600	−0.102300	+	0.994754i	$0.532620\pi$
$158$	1.11149	0.0884254
$159$	−10.4183	−0.826224
$160$	5.76597	0.455840
$161$	6.43483	0.507135
$162$	−2.38901	−0.187698
$163$	−20.3027	−1.59023	−0.795114	−	0.606460i	$-0.792589\pi$
$163$	−20.3027	−1.59023	−0.795114	+	0.606460i	$0.792589\pi$
$164$	2.54905	0.199048
$165$	6.35877	0.495029
$166$	30.7784	2.38887
$167$	−6.98554	−0.540557	−0.270279	−	0.962782i	$-0.587116\pi$
$167$	−6.98554	−0.540557	−0.270279	+	0.962782i	$0.587116\pi$
$168$	4.07890	0.314694
$169$	−0.877175	−0.0674750
$170$	19.3318	1.48268
$171$	0.911520	0.0697057
$172$	30.9079	2.35671
$173$	17.0830	1.29880	0.649400	−	0.760447i	$-0.275020\pi$
$173$	17.0830	1.29880	0.649400	+	0.760447i	$0.275020\pi$
$174$	15.2144	1.15340
$175$	−0.0510600	−0.00385977
$176$	−6.65940	−0.501971
$177$	11.9204	0.895993
$178$	−14.4651	−1.08421
$179$	16.9684	1.26828	0.634139	−	0.773219i	$-0.281355\pi$
$179$	16.9684	1.26828	0.634139	+	0.773219i	$0.281355\pi$
$180$	8.24747	0.614730
$181$	−5.76598	−0.428582	−0.214291	−	0.976770i	$-0.568744\pi$
$181$	−5.76598	−0.428582	−0.214291	+	0.976770i	$0.568744\pi$
$182$	8.31801	0.616572
$183$	9.22776	0.682135
$184$	−26.2470	−1.93495
$185$	−13.7568	−1.01142
$186$	−8.44276	−0.619053
$187$	10.3972	0.760316
$188$	6.46180	0.471275
$189$	−1.00000	−0.0727393
$190$	−4.84440	−0.351450
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	10.8516	0.783149
$193$	−1.03068	−0.0741900	−0.0370950	−	0.999312i	$-0.511810\pi$
$193$	−1.03068	−0.0741900	−0.0370950	+	0.999312i	$0.511810\pi$
$194$	20.1195	1.44449
$195$	7.74565	0.554678
$196$	3.70736	0.264811
$197$	−23.5902	−1.68073	−0.840367	−	0.542018i	$-0.817660\pi$
$197$	−23.5902	−1.68073	−0.840367	+	0.542018i	$0.817660\pi$
$198$	6.82864	0.485291
$199$	−19.2030	−1.36127	−0.680633	−	0.732625i	$-0.738295\pi$
$199$	−19.2030	−1.36127	−0.680633	+	0.732625i	$0.738295\pi$
$200$	0.208269	0.0147268
$201$	10.3941	0.733143
$202$	37.9019	2.66677
$203$	6.36848	0.446980
$204$	13.4854	0.944165
$205$	1.52957	0.106830
$206$	1.67927	0.117001
$207$	6.43483	0.447251
$208$	−8.11185	−0.562456
$209$	−2.60545	−0.180223
$210$	5.31464	0.366745
$211$	−6.69065	−0.460604	−0.230302	−	0.973119i	$-0.573971\pi$
$211$	−6.69065	−0.460604	−0.230302	+	0.973119i	$0.573971\pi$
$212$	38.6243	2.65273
$213$	−4.04517	−0.277171
$214$	−2.88813	−0.197428
$215$	18.5465	1.26486
$216$	4.07890	0.277534
$217$	−3.53400	−0.239904
$218$	26.7773	1.81358
$219$	−12.4021	−0.838059
$220$	−23.5742	−1.58937
$221$	12.6649	0.851930
$222$	−14.7734	−0.991524
$223$	−5.49584	−0.368029	−0.184014	−	0.982924i	$-0.558909\pi$
$223$	−5.49584	−0.368029	−0.184014	+	0.982924i	$0.558909\pi$
$224$	2.59189	0.173178
$225$	−0.0510600	−0.00340400
$226$	−37.9201	−2.52241
$227$	−19.8022	−1.31432	−0.657158	−	0.753753i	$-0.728241\pi$
$227$	−19.8022	−1.31432	−0.657158	+	0.753753i	$0.728241\pi$
$228$	−3.37933	−0.223802
$229$	−9.03763	−0.597224	−0.298612	−	0.954375i	$-0.596524\pi$
$229$	−9.03763	−0.597224	−0.298612	+	0.954375i	$0.596524\pi$
$230$	−34.1988	−2.25500
$231$	2.85836	0.188066
$232$	−25.9764	−1.70543
$233$	24.7758	1.62312	0.811558	−	0.584272i	$-0.198620\pi$
$233$	24.7758	1.62312	0.811558	+	0.584272i	$0.198620\pi$
$234$	8.31801	0.543765
$235$	3.87744	0.252936
$236$	−44.1933	−2.87674
$237$	0.465252	0.0302213
$238$	8.68992	0.563284
$239$	−23.6880	−1.53225	−0.766125	−	0.642692i	$-0.777818\pi$
$239$	−23.6880	−1.53225	−0.766125	+	0.642692i	$0.777818\pi$
$240$	−5.18292	−0.334556
$241$	−17.8973	−1.15287	−0.576433	−	0.817144i	$-0.695556\pi$
$241$	−17.8973	−1.15287	−0.576433	+	0.817144i	$0.695556\pi$
$242$	6.76037	0.434573
$243$	−1.00000	−0.0641500
$244$	−34.2106	−2.19011
$245$	2.22462	0.142126
$246$	1.64260	0.104728
$247$	−3.17372	−0.201939
$248$	14.4148	0.915342
$249$	12.8833	0.816449
$250$	26.8446	1.69780
$251$	4.40298	0.277914	0.138957	−	0.990298i	$-0.455625\pi$
$251$	4.40298	0.277914	0.138957	+	0.990298i	$0.455625\pi$
$252$	3.70736	0.233542
$253$	−18.3931	−1.15636
$254$	−29.5502	−1.85414
$255$	8.09197	0.506739
$256$	−27.8468	−1.74043
$257$	−2.35634	−0.146985	−0.0734923	−	0.997296i	$-0.523414\pi$
$257$	−2.35634	−0.146985	−0.0734923	+	0.997296i	$0.523414\pi$
$258$	19.9169	1.23997
$259$	−6.18389	−0.384248
$260$	−28.7159	−1.78089
$261$	6.36848	0.394199
$262$	−11.9244	−0.736690
$263$	4.33941	0.267579	0.133790	−	0.991010i	$-0.457285\pi$
$263$	4.33941	0.267579	0.133790	+	0.991010i	$0.457285\pi$
$264$	−11.6590	−0.717559
$265$	23.1767	1.42374
$266$	−2.17763	−0.133519
$267$	−6.05486	−0.370552
$268$	−38.5347	−2.35388
$269$	4.94448	0.301471	0.150735	−	0.988574i	$-0.451836\pi$
$269$	4.94448	0.301471	0.150735	+	0.988574i	$0.451836\pi$
$270$	5.31464	0.323439
$271$	20.0142	1.21578	0.607888	−	0.794023i	$-0.292017\pi$
$271$	20.0142	1.21578	0.607888	+	0.794023i	$0.292017\pi$
$272$	−8.47455	−0.513845
$273$	3.48178	0.210727
$274$	16.3955	0.990488
$275$	0.145948	0.00880099
$276$	−23.8562	−1.43598
$277$	−6.82771	−0.410237	−0.205119	−	0.978737i	$-0.565758\pi$
$277$	−6.82771	−0.410237	−0.205119	+	0.978737i	$0.565758\pi$
$278$	11.7938	0.707346
$279$	−3.53400	−0.211575
$280$	−9.07400	−0.542275
$281$	−20.4985	−1.22284	−0.611420	−	0.791306i	$-0.709401\pi$
$281$	−20.4985	−1.22284	−0.611420	+	0.791306i	$0.709401\pi$
$282$	4.16396	0.247960
$283$	1.28277	0.0762525	0.0381263	−	0.999273i	$-0.487861\pi$
$283$	1.28277	0.0762525	0.0381263	+	0.999273i	$0.487861\pi$
$284$	14.9969	0.889903
$285$	−2.02779	−0.120116
$286$	−23.7759	−1.40590
$287$	0.687565	0.0405857
$288$	2.59189	0.152728
$289$	−3.76888	−0.221699
$290$	−33.8462	−1.98752
$291$	8.42169	0.493688
$292$	45.9792	2.69073
$293$	4.24236	0.247841	0.123921	−	0.992292i	$-0.460453\pi$
$293$	4.24236	0.247841	0.123921	+	0.992292i	$0.460453\pi$
$294$	2.38901	0.139330
$295$	−26.5184	−1.54396
$296$	25.2235	1.46608
$297$	2.85836	0.165859
$298$	−1.99940	−0.115822
$299$	−22.4047	−1.29570
$300$	0.189298	0.0109291
$301$	8.33691	0.480531
$302$	−21.7654	−1.25246
$303$	15.8651	0.911428
$304$	2.12366	0.121800
$305$	−20.5283	−1.17544
$306$	8.68992	0.496770
$307$	26.7393	1.52609	0.763046	−	0.646345i	$-0.223703\pi$
$307$	26.7393	1.52609	0.763046	+	0.646345i	$0.223703\pi$
$308$	−10.5970	−0.603818
$309$	0.702916	0.0399875
$310$	18.7819	1.06674
$311$	1.04200	0.0590862	0.0295431	−	0.999564i	$-0.490595\pi$
$311$	1.04200	0.0590862	0.0295431	+	0.999564i	$0.490595\pi$
$312$	−14.2018	−0.804021
$313$	−29.0620	−1.64268	−0.821339	−	0.570440i	$-0.806773\pi$
$313$	−29.0620	−1.64268	−0.821339	+	0.570440i	$0.806773\pi$
$314$	6.12452	0.345627
$315$	2.22462	0.125343
$316$	−1.72486	−0.0970307
$317$	28.6105	1.60693	0.803464	−	0.595354i	$-0.202988\pi$
$317$	28.6105	1.60693	0.803464	+	0.595354i	$0.202988\pi$
$318$	24.8894	1.39573
$319$	−18.2034	−1.01920
$320$	−24.1408	−1.34951
$321$	−1.20892	−0.0674755
$322$	−15.3729	−0.856696
$323$	−3.31562	−0.184486
$324$	3.70736	0.205964
$325$	0.177780	0.00986146
$326$	48.5033	2.68635
$327$	11.2085	0.619833
$328$	−2.80451	−0.154853
$329$	1.74296	0.0960927
$330$	−15.1911	−0.836245
$331$	−3.21203	−0.176549	−0.0882746	−	0.996096i	$-0.528135\pi$
$331$	−3.21203	−0.176549	−0.0882746	+	0.996096i	$0.528135\pi$
$332$	−47.7632	−2.62135
$333$	−6.18389	−0.338875
$334$	16.6885	0.913154
$335$	−23.1229	−1.26334
$336$	−2.32980	−0.127101
$337$	−13.8928	−0.756787	−0.378394	−	0.925645i	$-0.623523\pi$
$337$	−13.8928	−0.756787	−0.378394	+	0.925645i	$0.623523\pi$
$338$	2.09558	0.113984
$339$	−15.8727	−0.862089
$340$	−29.9999	−1.62697
$341$	10.1014	0.547024
$342$	−2.17763	−0.117753
$343$	1.00000	0.0539949
$344$	−34.0054	−1.83345
$345$	−14.3151	−0.770697
$346$	−40.8115	−2.19404
$347$	−23.1123	−1.24073	−0.620367	−	0.784312i	$-0.713016\pi$
$347$	−23.1123	−1.24073	−0.620367	+	0.784312i	$0.713016\pi$
$348$	−23.6102	−1.26564
$349$	−10.3495	−0.553997	−0.276998	−	0.960870i	$-0.589340\pi$
$349$	−10.3495	−0.553997	−0.276998	+	0.960870i	$0.589340\pi$
$350$	0.121983	0.00652025
$351$	3.48178	0.185844
$352$	−7.40855	−0.394877
$353$	−3.70323	−0.197103	−0.0985515	−	0.995132i	$-0.531421\pi$
$353$	−3.70323	−0.197103	−0.0985515	+	0.995132i	$0.531421\pi$
$354$	−28.4780	−1.51359
$355$	8.99898	0.477616
$356$	22.4476	1.18972
$357$	3.63746	0.192515
$358$	−40.5376	−2.14248
$359$	−4.69978	−0.248045	−0.124023	−	0.992279i	$-0.539580\pi$
$359$	−4.69978	−0.248045	−0.124023	+	0.992279i	$0.539580\pi$
$360$	−9.07400	−0.478242
$361$	−18.1691	−0.956270
$362$	13.7750	0.723997
$363$	2.82978	0.148525
$364$	−12.9082	−0.676575
$365$	27.5901	1.44413
$366$	−22.0452	−1.15232
$367$	29.3946	1.53439	0.767194	−	0.641415i	$-0.221652\pi$
$367$	29.3946	1.53439	0.767194	+	0.641415i	$0.221652\pi$
$368$	14.9918	0.781504
$369$	0.687565	0.0357932
$370$	32.8652	1.70858
$371$	10.4183	0.540891
$372$	13.1018	0.679297
$373$	27.2564	1.41128	0.705642	−	0.708568i	$-0.250659\pi$
$373$	27.2564	1.41128	0.705642	+	0.708568i	$0.250659\pi$
$374$	−24.8389	−1.28439
$375$	11.2367	0.580260
$376$	−7.10937	−0.366638
$377$	−22.1737	−1.14200
$378$	2.38901	0.122877
$379$	31.0559	1.59523	0.797617	−	0.603164i	$-0.206094\pi$
$379$	31.0559	1.59523	0.797617	+	0.603164i	$0.206094\pi$
$380$	7.51774	0.385652
$381$	−12.3692	−0.633695
$382$	−2.38901	−0.122232
$383$	21.5156	1.09939	0.549697	−	0.835364i	$-0.314743\pi$
$383$	21.5156	1.09939	0.549697	+	0.835364i	$0.314743\pi$
$384$	−20.7409	−1.05843
$385$	−6.35877	−0.324073
$386$	2.46230	0.125328
$387$	8.33691	0.423789
$388$	−31.2222	−1.58507
$389$	−21.3670	−1.08335	−0.541676	−	0.840588i	$-0.682210\pi$
$389$	−21.3670	−1.08335	−0.541676	+	0.840588i	$0.682210\pi$
$390$	−18.5044	−0.937008
$391$	−23.4064	−1.18371
$392$	−4.07890	−0.206015
$393$	−4.99135	−0.251780
$394$	56.3572	2.83924
$395$	−1.03501	−0.0520769
$396$	−10.5970	−0.532518
$397$	−10.7565	−0.539855	−0.269927	−	0.962881i	$-0.587000\pi$
$397$	−10.7565	−0.539855	−0.269927	+	0.962881i	$0.587000\pi$
$398$	45.8761	2.29956
$399$	−0.911520	−0.0456331
$400$	−0.118959	−0.00594797
$401$	1.45065	0.0724422	0.0362211	−	0.999344i	$-0.488468\pi$
$401$	1.45065	0.0724422	0.0362211	+	0.999344i	$0.488468\pi$
$402$	−24.8316	−1.23849
$403$	12.3046	0.612937
$404$	−58.8178	−2.92629
$405$	2.22462	0.110542
$406$	−15.2144	−0.755076
$407$	17.6758	0.876157
$408$	−14.8368	−0.734532
$409$	−37.6951	−1.86390	−0.931952	−	0.362582i	$-0.881895\pi$
$409$	−37.6951	−1.86390	−0.931952	+	0.362582i	$0.881895\pi$
$410$	−3.65416	−0.180466
$411$	6.86289	0.338521
$412$	−2.60596	−0.128387
$413$	−11.9204	−0.586565
$414$	−15.3729	−0.755535
$415$	−28.6606	−1.40689
$416$	−9.02440	−0.442458
$417$	4.93670	0.241751
$418$	6.22445	0.304448
$419$	3.55778	0.173809	0.0869046	−	0.996217i	$-0.472302\pi$
$419$	3.55778	0.173809	0.0869046	+	0.996217i	$0.472302\pi$
$420$	−8.24747	−0.402435
$421$	−22.2482	−1.08431	−0.542155	−	0.840278i	$-0.682391\pi$
$421$	−22.2482	−1.08431	−0.542155	+	0.840278i	$0.682391\pi$
$422$	15.9840	0.778090
$423$	1.74296	0.0847458
$424$	−42.4951	−2.06375
$425$	0.185729	0.00900917
$426$	9.66395	0.468220
$427$	−9.22776	−0.446562
$428$	4.48192	0.216642
$429$	−9.95219	−0.480496
$430$	−44.3077	−2.13670
$431$	28.6794	1.38144	0.690719	−	0.723123i	$-0.257294\pi$
$431$	28.6794	1.38144	0.690719	+	0.723123i	$0.257294\pi$
$432$	−2.32980	−0.112092
$433$	−11.9629	−0.574899	−0.287450	−	0.957796i	$-0.592807\pi$
$433$	−11.9629	−0.574899	−0.287450	+	0.957796i	$0.592807\pi$
$434$	8.44276	0.405265
$435$	−14.1675	−0.679278
$436$	−41.5540	−1.99008
$437$	5.86548	0.280584
$438$	29.6288	1.41572
$439$	−4.50513	−0.215018	−0.107509	−	0.994204i	$-0.534288\pi$
$439$	−4.50513	−0.215018	−0.107509	+	0.994204i	$0.534288\pi$
$440$	25.9368	1.23649
$441$	1.00000	0.0476190
$442$	−30.2564	−1.43915
$443$	−34.0230	−1.61648	−0.808242	−	0.588851i	$-0.799581\pi$
$443$	−34.0230	−1.61648	−0.808242	+	0.588851i	$0.799581\pi$
$444$	22.9259	1.08802
$445$	13.4698	0.638529
$446$	13.1296	0.621705
$447$	−0.836914	−0.0395847
$448$	−10.8516	−0.512692
$449$	−23.0655	−1.08853	−0.544265	−	0.838913i	$-0.683191\pi$
$449$	−23.0655	−1.08853	−0.544265	+	0.838913i	$0.683191\pi$
$450$	0.121983	0.00575032
$451$	−1.96531	−0.0925428
$452$	58.8460	2.76788
$453$	−9.11066	−0.428056
$454$	47.3075	2.22025
$455$	−7.74565	−0.363122
$456$	3.71800	0.174111
$457$	−6.26629	−0.293125	−0.146562	−	0.989201i	$-0.546821\pi$
$457$	−6.26629	−0.293125	−0.146562	+	0.989201i	$0.546821\pi$
$458$	21.5910	1.00888
$459$	3.63746	0.169782
$460$	53.0711	2.47445
$461$	−17.5937	−0.819422	−0.409711	−	0.912215i	$-0.634371\pi$
$461$	−17.5937	−0.819422	−0.409711	+	0.912215i	$0.634371\pi$
$462$	−6.82864	−0.317697
$463$	−11.7518	−0.546150	−0.273075	−	0.961993i	$-0.588041\pi$
$463$	−11.7518	−0.546150	−0.273075	+	0.961993i	$0.588041\pi$
$464$	14.8373	0.688803
$465$	7.86181	0.364583
$466$	−59.1895	−2.74190
$467$	15.9508	0.738113	0.369057	−	0.929407i	$-0.379681\pi$
$467$	15.9508	0.738113	0.369057	+	0.929407i	$0.379681\pi$
$468$	−12.9082	−0.596683
$469$	−10.3941	−0.479955
$470$	−9.26322	−0.427281
$471$	2.56363	0.118126
$472$	48.6221	2.23801
$473$	−23.8299	−1.09570
$474$	−1.11149	−0.0510524
$475$	−0.0465422	−0.00213550
$476$	−13.4854	−0.618101
$477$	10.4183	0.477021
$478$	56.5908	2.58840
$479$	2.44389	0.111664	0.0558321	−	0.998440i	$-0.482219\pi$
$479$	2.44389	0.111664	0.0558321	+	0.998440i	$0.482219\pi$
$480$	−5.76597	−0.263179
$481$	21.5310	0.981729
$482$	42.7568	1.94752
$483$	−6.43483	−0.292795
$484$	−10.4910	−0.476864
$485$	−18.7351	−0.850716
$486$	2.38901	0.108368
$487$	−6.66443	−0.301994	−0.150997	−	0.988534i	$-0.548248\pi$
$487$	−6.66443	−0.301994	−0.150997	+	0.988534i	$0.548248\pi$
$488$	37.6391	1.70384
$489$	20.3027	0.918119
$490$	−5.31464	−0.240091
$491$	−17.7795	−0.802379	−0.401190	−	0.915995i	$-0.631403\pi$
$491$	−17.7795	−0.802379	−0.401190	+	0.915995i	$0.631403\pi$
$492$	−2.54905	−0.114920
$493$	−23.1651	−1.04330
$494$	7.58204	0.341132
$495$	−6.35877	−0.285805
$496$	−8.23350	−0.369695
$497$	4.04517	0.181451
$498$	−30.7784	−1.37921
$499$	−10.7294	−0.480316	−0.240158	−	0.970734i	$-0.577199\pi$
$499$	−10.7294	−0.480316	−0.240158	+	0.970734i	$0.577199\pi$
$500$	−41.6585	−1.86302
$501$	6.98554	0.312091
$502$	−10.5188	−0.469475
$503$	−0.978955	−0.0436495	−0.0218247	−	0.999762i	$-0.506948\pi$
$503$	−0.978955	−0.0436495	−0.0218247	+	0.999762i	$0.506948\pi$
$504$	−4.07890	−0.181688
$505$	−35.2939	−1.57056
$506$	43.9411	1.95342
$507$	0.877175	0.0389567
$508$	45.8572	2.03458
$509$	−26.0009	−1.15247	−0.576236	−	0.817284i	$-0.695479\pi$
$509$	−26.0009	−1.15247	−0.576236	+	0.817284i	$0.695479\pi$
$510$	−19.3318	−0.856026
$511$	12.4021	0.548638
$512$	25.0446	1.10682
$513$	−0.911520	−0.0402446
$514$	5.62932	0.248299
$515$	−1.56372	−0.0689059
$516$	−30.9079	−1.36065
$517$	−4.98202	−0.219109
$518$	14.7734	0.649105
$519$	−17.0830	−0.749862
$520$	31.5937	1.38548
$521$	−17.8109	−0.780308	−0.390154	−	0.920750i	$-0.627578\pi$
$521$	−17.8109	−0.780308	−0.390154	+	0.920750i	$0.627578\pi$
$522$	−15.2144	−0.665914
$523$	6.44901	0.281995	0.140998	−	0.990010i	$-0.454969\pi$
$523$	6.44901	0.281995	0.140998	+	0.990010i	$0.454969\pi$
$524$	18.5047	0.808383
$525$	0.0510600	0.00222844
$526$	−10.3669	−0.452017
$527$	12.8548	0.559963
$528$	6.65940	0.289813
$529$	18.4070	0.800305
$530$	−55.3694	−2.40509
$531$	−11.9204	−0.517302
$532$	3.37933	0.146513
$533$	−2.39395	−0.103694
$534$	14.4651	0.625967
$535$	2.68940	0.116273
$536$	42.3964	1.83125
$537$	−16.9684	−0.732240
$538$	−11.8124	−0.509269
$539$	−2.85836	−0.123118
$540$	−8.24747	−0.354915
$541$	−18.3644	−0.789548	−0.394774	−	0.918778i	$-0.629177\pi$
$541$	−18.3644	−0.789548	−0.394774	+	0.918778i	$0.629177\pi$
$542$	−47.8141	−2.05379
$543$	5.76598	0.247442
$544$	−9.42789	−0.404218
$545$	−24.9347	−1.06809
$546$	−8.31801	−0.355978
$547$	−30.7030	−1.31277	−0.656383	−	0.754428i	$-0.727914\pi$
$547$	−30.7030	−1.31277	−0.656383	+	0.754428i	$0.727914\pi$
$548$	−25.4432	−1.08688
$549$	−9.22776	−0.393831
$550$	−0.348671	−0.0148674
$551$	5.80500	0.247301
$552$	26.2470	1.11715
$553$	−0.465252	−0.0197845
$554$	16.3114	0.693007
$555$	13.7568	0.583945
$556$	−18.3021	−0.776183
$557$	−34.9856	−1.48239	−0.741193	−	0.671292i	$-0.765740\pi$
$557$	−34.9856	−1.48239	−0.741193	+	0.671292i	$0.765740\pi$
$558$	8.44276	0.357410
$559$	−29.0273	−1.22772
$560$	5.18292	0.219018
$561$	−10.3972	−0.438969
$562$	48.9712	2.06572
$563$	38.1380	1.60733	0.803663	−	0.595085i	$-0.202881\pi$
$563$	38.1380	1.60733	0.803663	+	0.595085i	$0.202881\pi$
$564$	−6.46180	−0.272091
$565$	35.3109	1.48554
$566$	−3.06454	−0.128812
$567$	1.00000	0.0419961
$568$	−16.4998	−0.692318
$569$	23.2099	0.973008	0.486504	−	0.873678i	$-0.338272\pi$
$569$	23.2099	0.973008	0.486504	+	0.873678i	$0.338272\pi$
$570$	4.84440	0.202910
$571$	32.4897	1.35965	0.679825	−	0.733374i	$-0.262056\pi$
$571$	32.4897	1.35965	0.679825	+	0.733374i	$0.262056\pi$
$572$	36.8964	1.54271
$573$	−1.00000	−0.0417756
$574$	−1.64260	−0.0685608
$575$	−0.328562	−0.0137020
$576$	−10.8516	−0.452152
$577$	−18.8927	−0.786514	−0.393257	−	0.919429i	$-0.628652\pi$
$577$	−18.8927	−0.786514	−0.393257	+	0.919429i	$0.628652\pi$
$578$	9.00388	0.374512
$579$	1.03068	0.0428336
$580$	52.5239	2.18093
$581$	−12.8833	−0.534491
$582$	−20.1195	−0.833979
$583$	−29.7792	−1.23333
$584$	−50.5870	−2.09331
$585$	−7.74565	−0.320243
$586$	−10.1350	−0.418675
$587$	−40.1422	−1.65685	−0.828423	−	0.560102i	$-0.810762\pi$
$587$	−40.1422	−1.65685	−0.828423	+	0.560102i	$0.810762\pi$
$588$	−3.70736	−0.152889
$589$	−3.22131	−0.132732
$590$	63.3527	2.60819
$591$	23.5902	0.970372
$592$	−14.4072	−0.592133
$593$	−4.12882	−0.169550	−0.0847751	−	0.996400i	$-0.527017\pi$
$593$	−4.12882	−0.169550	−0.0847751	+	0.996400i	$0.527017\pi$
$594$	−6.82864	−0.280183
$595$	−8.09197	−0.331739
$596$	3.10274	0.127093
$597$	19.2030	0.785927
$598$	53.5250	2.18880
$599$	13.8028	0.563968	0.281984	−	0.959419i	$-0.409007\pi$
$599$	13.8028	0.563968	0.281984	+	0.959419i	$0.409007\pi$
$600$	−0.208269	−0.00850253
$601$	−8.60327	−0.350935	−0.175467	−	0.984485i	$-0.556144\pi$
$601$	−8.60327	−0.350935	−0.175467	+	0.984485i	$0.556144\pi$
$602$	−19.9169	−0.811754
$603$	−10.3941	−0.423280
$604$	33.7765	1.37435
$605$	−6.29519	−0.255936
$606$	−37.9019	−1.53966
$607$	6.61549	0.268515	0.134257	−	0.990947i	$-0.457135\pi$
$607$	6.61549	0.268515	0.134257	+	0.990947i	$0.457135\pi$
$608$	2.36256	0.0958144
$609$	−6.36848	−0.258064
$610$	49.0422	1.98566
$611$	−6.06863	−0.245510
$612$	−13.4854	−0.545114
$613$	10.6882	0.431693	0.215847	−	0.976427i	$-0.430749\pi$
$613$	10.6882	0.431693	0.215847	+	0.976427i	$0.430749\pi$
$614$	−63.8804	−2.57800
$615$	−1.52957	−0.0616783
$616$	11.6590	0.469753
$617$	−33.7444	−1.35850	−0.679249	−	0.733908i	$-0.737694\pi$
$617$	−33.7444	−1.35850	−0.679249	+	0.733908i	$0.737694\pi$
$618$	−1.67927	−0.0675503
$619$	45.5905	1.83244	0.916218	−	0.400680i	$-0.131226\pi$
$619$	45.5905	1.83244	0.916218	+	0.400680i	$0.131226\pi$
$620$	−29.1466	−1.17055
$621$	−6.43483	−0.258221
$622$	−2.48934	−0.0998134
$623$	6.05486	0.242583
$624$	8.11185	0.324734
$625$	−24.7421	−0.989684
$626$	69.4293	2.77495
$627$	2.60545	0.104052
$628$	−9.50428	−0.379262
$629$	22.4937	0.896881
$630$	−5.31464	−0.211740
$631$	28.1679	1.12135	0.560673	−	0.828037i	$-0.310542\pi$
$631$	28.1679	1.12135	0.560673	+	0.828037i	$0.310542\pi$
$632$	1.89771	0.0754870
$633$	6.69065	0.265930
$634$	−68.3508	−2.71456
$635$	27.5169	1.09197
$636$	−38.6243	−1.53156
$637$	−3.48178	−0.137953
$638$	43.4881	1.72171
$639$	4.04517	0.160025
$640$	46.1406	1.82387
$641$	−50.1122	−1.97931	−0.989657	−	0.143451i	$-0.954180\pi$
$641$	−50.1122	−1.97931	−0.989657	+	0.143451i	$0.954180\pi$
$642$	2.88813	0.113985
$643$	20.5805	0.811616	0.405808	−	0.913958i	$-0.366990\pi$
$643$	20.5805	0.811616	0.405808	+	0.913958i	$0.366990\pi$
$644$	23.8562	0.940067
$645$	−18.5465	−0.730266
$646$	7.92104	0.311649
$647$	−9.82768	−0.386366	−0.193183	−	0.981163i	$-0.561881\pi$
$647$	−9.82768	−0.386366	−0.193183	+	0.981163i	$0.561881\pi$
$648$	−4.07890	−0.160234
$649$	34.0728	1.33748
$650$	−0.424718	−0.0166588
$651$	3.53400	0.138508
$652$	−75.2693	−2.94778
$653$	−25.2431	−0.987838	−0.493919	−	0.869508i	$-0.664436\pi$
$653$	−25.2431	−0.987838	−0.493919	+	0.869508i	$0.664436\pi$
$654$	−26.7773	−1.04707
$655$	11.1039	0.433864
$656$	1.60189	0.0625432
$657$	12.4021	0.483853
$658$	−4.16396	−0.162328
$659$	−18.3772	−0.715874	−0.357937	−	0.933746i	$-0.616520\pi$
$659$	−18.3772	−0.715874	−0.357937	+	0.933746i	$0.616520\pi$
$660$	23.5742	0.917626
$661$	−11.9141	−0.463407	−0.231703	−	0.972787i	$-0.574430\pi$
$661$	−11.9141	−0.463407	−0.231703	+	0.972787i	$0.574430\pi$
$662$	7.67357	0.298242
$663$	−12.6649	−0.491862
$664$	52.5498	2.03933
$665$	2.02779	0.0786342
$666$	14.7734	0.572457
$667$	40.9801	1.58675
$668$	−25.8979	−1.00202
$669$	5.49584	0.212481
$670$	55.2409	2.13414
$671$	26.3762	1.01824
$672$	−2.59189	−0.0999843
$673$	26.9152	1.03750	0.518752	−	0.854925i	$-0.326397\pi$
$673$	26.9152	1.03750	0.518752	+	0.854925i	$0.326397\pi$
$674$	33.1899	1.27843
$675$	0.0510600	0.00196530
$676$	−3.25200	−0.125077
$677$	38.6243	1.48445	0.742226	−	0.670150i	$-0.233770\pi$
$677$	38.6243	1.48445	0.742226	+	0.670150i	$0.233770\pi$
$678$	37.9201	1.45631
$679$	−8.42169	−0.323195
$680$	33.0063	1.26573
$681$	19.8022	0.758820
$682$	−24.1324	−0.924079
$683$	49.4614	1.89259	0.946295	−	0.323305i	$-0.104794\pi$
$683$	49.4614	1.89259	0.946295	+	0.323305i	$0.104794\pi$
$684$	3.37933	0.129212
$685$	−15.2673	−0.583335
$686$	−2.38901	−0.0912128
$687$	9.03763	0.344807
$688$	19.4233	0.740507
$689$	−36.2742	−1.38194
$690$	34.1988	1.30193
$691$	11.9329	0.453948	0.226974	−	0.973901i	$-0.427117\pi$
$691$	11.9329	0.453948	0.226974	+	0.973901i	$0.427117\pi$
$692$	63.3330	2.40756
$693$	−2.85836	−0.108580
$694$	55.2155	2.09595
$695$	−10.9823	−0.416582
$696$	25.9764	0.984632
$697$	−2.50099	−0.0947318
$698$	24.7251	0.935857
$699$	−24.7758	−0.937106
$700$	−0.189298	−0.00715479
$701$	50.0952	1.89207	0.946035	−	0.324065i	$-0.105050\pi$
$701$	50.0952	1.89207	0.946035	+	0.324065i	$0.105050\pi$
$702$	−8.31801	−0.313943
$703$	−5.63674	−0.212594
$704$	31.0179	1.16903
$705$	−3.87744	−0.146033
$706$	8.84704	0.332963
$707$	−15.8651	−0.596670
$708$	44.1933	1.66088
$709$	11.9132	0.447410	0.223705	−	0.974657i	$-0.428185\pi$
$709$	11.9132	0.447410	0.223705	+	0.974657i	$0.428185\pi$
$710$	−21.4986	−0.806829
$711$	−0.465252	−0.0174483
$712$	−24.6972	−0.925565
$713$	−22.7407	−0.851645
$714$	−8.68992	−0.325212
$715$	22.1399	0.827984
$716$	62.9079	2.35098
$717$	23.6880	0.884645
$718$	11.2278	0.419019
$719$	−28.0218	−1.04504	−0.522518	−	0.852628i	$-0.675007\pi$
$719$	−28.0218	−1.04504	−0.522518	+	0.852628i	$0.675007\pi$
$720$	5.18292	0.193156
$721$	−0.702916	−0.0261780
$722$	43.4062	1.61541
$723$	17.8973	0.665608
$724$	−21.3766	−0.794454
$725$	−0.325175	−0.0120767
$726$	−6.76037	−0.250901
$727$	35.0824	1.30113	0.650566	−	0.759449i	$-0.274532\pi$
$727$	35.0824	1.30113	0.650566	+	0.759449i	$0.274532\pi$
$728$	14.2018	0.526355
$729$	1.00000	0.0370370
$730$	−65.9129	−2.43954
$731$	−30.3252	−1.12162
$732$	34.2106	1.26446
$733$	3.64732	0.134717	0.0673585	−	0.997729i	$-0.478543\pi$
$733$	3.64732	0.134717	0.0673585	+	0.997729i	$0.478543\pi$
$734$	−70.2240	−2.59202
$735$	−2.22462	−0.0820564
$736$	16.6784	0.614772
$737$	29.7101	1.09438
$738$	−1.64260	−0.0604649
$739$	−16.4541	−0.605273	−0.302636	−	0.953106i	$-0.597867\pi$
$739$	−16.4541	−0.605273	−0.302636	+	0.953106i	$0.597867\pi$
$740$	−51.0015	−1.87485
$741$	3.17372	0.116589
$742$	−24.8894	−0.913718
$743$	−40.0575	−1.46957	−0.734783	−	0.678302i	$-0.762716\pi$
$743$	−40.0575	−1.46957	−0.734783	+	0.678302i	$0.762716\pi$
$744$	−14.4148	−0.528473
$745$	1.86182	0.0682117
$746$	−65.1158	−2.38406
$747$	−12.8833	−0.471377
$748$	38.5461	1.40938
$749$	1.20892	0.0441731
$750$	−26.8446	−0.980225
$751$	11.1321	0.406217	0.203109	−	0.979156i	$-0.434896\pi$
$751$	11.1321	0.406217	0.203109	+	0.979156i	$0.434896\pi$
$752$	4.06075	0.148080
$753$	−4.40298	−0.160454
$754$	52.9731	1.92917
$755$	20.2678	0.737619
$756$	−3.70736	−0.134835
$757$	−43.1852	−1.56959	−0.784796	−	0.619754i	$-0.787232\pi$
$757$	−43.1852	−1.56959	−0.784796	+	0.619754i	$0.787232\pi$
$758$	−74.1928	−2.69480
$759$	18.3931	0.667625
$760$	−8.27113	−0.300026
$761$	28.8533	1.04593	0.522965	−	0.852354i	$-0.324826\pi$
$761$	28.8533	1.04593	0.522965	+	0.852354i	$0.324826\pi$
$762$	29.5502	1.07049
$763$	−11.2085	−0.405776
$764$	3.70736	0.134128
$765$	−8.09197	−0.292566
$766$	−51.4009	−1.85719
$767$	41.5043	1.49863
$768$	27.8468	1.00484
$769$	31.2699	1.12762	0.563811	−	0.825904i	$-0.309335\pi$
$769$	31.2699	1.12762	0.563811	+	0.825904i	$0.309335\pi$
$770$	15.1911	0.547451
$771$	2.35634	0.0848616
$772$	−3.82110	−0.137524
$773$	−14.7223	−0.529526	−0.264763	−	0.964314i	$-0.585294\pi$
$773$	−14.7223	−0.529526	−0.264763	+	0.964314i	$0.585294\pi$
$774$	−19.9169	−0.715900
$775$	0.180446	0.00648182
$776$	34.3512	1.23314
$777$	6.18389	0.221846
$778$	51.0460	1.83009
$779$	0.626730	0.0224549
$780$	28.7159	1.02819
$781$	−11.5626	−0.413741
$782$	55.9182	1.99963
$783$	−6.36848	−0.227591
$784$	2.32980	0.0832070
$785$	−5.70310	−0.203552
$786$	11.9244	0.425328
$787$	−25.7485	−0.917834	−0.458917	−	0.888479i	$-0.651762\pi$
$787$	−25.7485	−0.917834	−0.458917	+	0.888479i	$0.651762\pi$
$788$	−87.4574	−3.11554
$789$	−4.33941	−0.154487
$790$	2.47264	0.0879727
$791$	15.8727	0.564370
$792$	11.6590	0.414283
$793$	32.1291	1.14094
$794$	25.6974	0.911968
$795$	−23.1767	−0.821995
$796$	−71.1925	−2.52335
$797$	−33.0626	−1.17114	−0.585569	−	0.810623i	$-0.699129\pi$
$797$	−33.0626	−1.17114	−0.585569	+	0.810623i	$0.699129\pi$
$798$	2.17763	0.0770872
$799$	−6.33996	−0.224292
$800$	−0.132342	−0.00467899
$801$	6.05486	0.213938
$802$	−3.46562	−0.122375
$803$	−35.4498	−1.25099
$804$	38.5347	1.35901
$805$	14.3151	0.504539
$806$	−29.3959	−1.03542
$807$	−4.94448	−0.174054
$808$	64.7123	2.27657
$809$	−21.4457	−0.753991	−0.376996	−	0.926215i	$-0.623043\pi$
$809$	−21.4457	−0.753991	−0.376996	+	0.926215i	$0.623043\pi$
$810$	−5.31464	−0.186737
$811$	23.8387	0.837090	0.418545	−	0.908196i	$-0.362540\pi$
$811$	23.8387	0.837090	0.418545	+	0.908196i	$0.362540\pi$
$812$	23.6102	0.828557
$813$	−20.0142	−0.701929
$814$	−42.2276	−1.48008
$815$	−45.1658	−1.58209
$816$	8.47455	0.296668
$817$	7.59926	0.265864
$818$	90.0539	3.14866
$819$	−3.48178	−0.121663
$820$	5.67068	0.198029
$821$	21.6801	0.756639	0.378320	−	0.925675i	$-0.376502\pi$
$821$	21.6801	0.756639	0.378320	+	0.925675i	$0.376502\pi$
$822$	−16.3955	−0.571859
$823$	28.3174	0.987082	0.493541	−	0.869722i	$-0.335702\pi$
$823$	28.3174	0.987082	0.493541	+	0.869722i	$0.335702\pi$
$824$	2.86712	0.0998810
$825$	−0.145948	−0.00508125
$826$	28.4780	0.990875
$827$	10.9550	0.380944	0.190472	−	0.981693i	$-0.438998\pi$
$827$	10.9550	0.380944	0.190472	+	0.981693i	$0.438998\pi$
$828$	23.8562	0.829061
$829$	−10.3711	−0.360203	−0.180102	−	0.983648i	$-0.557643\pi$
$829$	−10.3711	−0.360203	−0.180102	+	0.983648i	$0.557643\pi$
$830$	68.4703	2.37664
$831$	6.82771	0.236851
$832$	37.7831	1.30989
$833$	−3.63746	−0.126031
$834$	−11.7938	−0.408386
$835$	−15.5402	−0.537790
$836$	−9.65935	−0.334076
$837$	3.53400	0.122153
$838$	−8.49957	−0.293613
$839$	−45.7391	−1.57909	−0.789545	−	0.613693i	$-0.789683\pi$
$839$	−45.7391	−1.57909	−0.789545	+	0.613693i	$0.789683\pi$
$840$	9.07400	0.313083
$841$	11.5575	0.398536
$842$	53.1511	1.83171
$843$	20.4985	0.706007
$844$	−24.8047	−0.853812
$845$	−1.95138	−0.0671296
$846$	−4.16396	−0.143160
$847$	−2.82978	−0.0972324
$848$	24.2725	0.833521
$849$	−1.28277	−0.0440244
$850$	−0.443708	−0.0152190
$851$	−39.7923	−1.36406
$852$	−14.9969	−0.513786
$853$	−21.0753	−0.721603	−0.360802	−	0.932643i	$-0.617497\pi$
$853$	−21.0753	−0.721603	−0.360802	+	0.932643i	$0.617497\pi$
$854$	22.0452	0.754371
$855$	2.02779	0.0693489
$856$	−4.93107	−0.168541
$857$	38.3318	1.30939	0.654695	−	0.755893i	$-0.272797\pi$
$857$	38.3318	1.30939	0.654695	+	0.755893i	$0.272797\pi$
$858$	23.7759	0.811695
$859$	18.5348	0.632400	0.316200	−	0.948693i	$-0.397593\pi$
$859$	18.5348	0.632400	0.316200	+	0.948693i	$0.397593\pi$
$860$	68.7584	2.34464
$861$	−0.687565	−0.0234322
$862$	−68.5153	−2.33364
$863$	19.0885	0.649779	0.324890	−	0.945752i	$-0.394673\pi$
$863$	19.0885	0.649779	0.324890	+	0.945752i	$0.394673\pi$
$864$	−2.59189	−0.0881778
$865$	38.0033	1.29215
$866$	28.5794	0.971168
$867$	3.76888	0.127998
$868$	−13.1018	−0.444704
$869$	1.32986	0.0451123
$870$	33.8462	1.14749
$871$	36.1900	1.22625
$872$	45.7184	1.54822
$873$	−8.42169	−0.285031
$874$	−14.0127	−0.473986
$875$	−11.2367	−0.379870
$876$	−45.9792	−1.55349
$877$	44.8950	1.51600	0.757998	−	0.652257i	$-0.226178\pi$
$877$	44.8950	1.51600	0.757998	+	0.652257i	$0.226178\pi$
$878$	10.7628	0.363227
$879$	−4.24236	−0.143091
$880$	−14.8146	−0.499401
$881$	−26.8981	−0.906220	−0.453110	−	0.891455i	$-0.649686\pi$
$881$	−26.8981	−0.906220	−0.453110	+	0.891455i	$0.649686\pi$
$882$	−2.38901	−0.0804421
$883$	36.1822	1.21763	0.608815	−	0.793313i	$-0.291645\pi$
$883$	36.1822	1.21763	0.608815	+	0.793313i	$0.291645\pi$
$884$	46.9532	1.57921
$885$	26.5184	0.891406
$886$	81.2813	2.73070
$887$	50.9642	1.71121	0.855606	−	0.517628i	$-0.173185\pi$
$887$	50.9642	1.71121	0.855606	+	0.517628i	$0.173185\pi$
$888$	−25.2235	−0.846444
$889$	12.3692	0.414851
$890$	−32.1794	−1.07866
$891$	−2.85836	−0.0957586
$892$	−20.3750	−0.682207
$893$	1.58875	0.0531654
$894$	1.99940	0.0668698
$895$	37.7483	1.26178
$896$	20.7409	0.692904
$897$	22.4047	0.748071
$898$	55.1037	1.83884
$899$	−22.5062	−0.750624
$900$	−0.189298	−0.00630993
$901$	−37.8961	−1.26250
$902$	4.69514	0.156331
$903$	−8.33691	−0.277435
$904$	−64.7433	−2.15333
$905$	−12.8271	−0.426388
$906$	21.7654	0.723108
$907$	−17.7771	−0.590280	−0.295140	−	0.955454i	$-0.595366\pi$
$907$	−17.7771	−0.590280	−0.295140	+	0.955454i	$0.595366\pi$
$908$	−73.4137	−2.43632
$909$	−15.8651	−0.526213
$910$	18.5044	0.613416
$911$	−0.827292	−0.0274094	−0.0137047	−	0.999906i	$-0.504362\pi$
$911$	−0.827292	−0.0274094	−0.0137047	+	0.999906i	$0.504362\pi$
$912$	−2.12366	−0.0703213
$913$	36.8252	1.21874
$914$	14.9702	0.495171
$915$	20.5283	0.678643
$916$	−33.5058	−1.10706
$917$	4.99135	0.164829
$918$	−8.68992	−0.286810
$919$	−13.4915	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$919$	−13.4915	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$920$	−58.3896	−1.92505
$921$	−26.7393	−0.881089
$922$	42.0316	1.38424
$923$	−14.0844	−0.463594
$924$	10.5970	0.348615
$925$	0.315750	0.0103818
$926$	28.0750	0.922603
$927$	−0.702916	−0.0230868
$928$	16.5064	0.541849
$929$	−41.2892	−1.35466	−0.677328	−	0.735681i	$-0.736862\pi$
$929$	−41.2892	−1.35466	−0.677328	+	0.735681i	$0.736862\pi$
$930$	−18.7819	−0.615884
$931$	0.911520	0.0298739
$932$	91.8527	3.00874
$933$	−1.04200	−0.0341134
$934$	−38.1065	−1.24688
$935$	23.1298	0.756424
$936$	14.2018	0.464202
$937$	−11.8451	−0.386961	−0.193481	−	0.981104i	$-0.561978\pi$
$937$	−11.8451	−0.386961	−0.193481	+	0.981104i	$0.561978\pi$
$938$	24.8316	0.810780
$939$	29.0620	0.948401
$940$	14.3750	0.468862
$941$	−39.3693	−1.28340	−0.641701	−	0.766955i	$-0.721771\pi$
$941$	−39.3693	−1.28340	−0.641701	+	0.766955i	$0.721771\pi$
$942$	−6.12452	−0.199548
$943$	4.42436	0.144077
$944$	−27.7721	−0.903906
$945$	−2.22462	−0.0723669
$946$	56.9298	1.85095
$947$	−14.6300	−0.475413	−0.237706	−	0.971337i	$-0.576396\pi$
$947$	−14.6300	−0.475413	−0.237706	+	0.971337i	$0.576396\pi$
$948$	1.72486	0.0560207
$949$	−43.1816	−1.40173
$950$	0.111190	0.00360747
$951$	−28.6105	−0.927760
$952$	14.8368	0.480864
$953$	5.52246	0.178890	0.0894449	−	0.995992i	$-0.471491\pi$
$953$	5.52246	0.178890	0.0894449	+	0.995992i	$0.471491\pi$
$954$	−24.8894	−0.805823
$955$	2.22462	0.0719871
$956$	−87.8199	−2.84030
$957$	18.2034	0.588433
$958$	−5.83848	−0.188633
$959$	−6.86289	−0.221614
$960$	24.1408	0.779140
$961$	−18.5108	−0.597124
$962$	−51.4377	−1.65842
$963$	1.20892	0.0389570
$964$	−66.3517	−2.13704
$965$	−2.29287	−0.0738102
$966$	15.3729	0.494614
$967$	30.2815	0.973786	0.486893	−	0.873462i	$-0.338130\pi$
$967$	30.2815	0.973786	0.486893	+	0.873462i	$0.338130\pi$
$968$	11.5424	0.370986
$969$	3.31562	0.106513
$970$	44.7582	1.43710
$971$	−50.9412	−1.63478	−0.817390	−	0.576085i	$-0.804580\pi$
$971$	−50.9412	−1.63478	−0.817390	+	0.576085i	$0.804580\pi$
$972$	−3.70736	−0.118914
$973$	−4.93670	−0.158263
$974$	15.9214	0.510154
$975$	−0.177780	−0.00569352
$976$	−21.4988	−0.688160
$977$	−31.9446	−1.02200	−0.510999	−	0.859581i	$-0.670725\pi$
$977$	−31.9446	−1.02200	−0.510999	+	0.859581i	$0.670725\pi$
$978$	−48.5033	−1.55096
$979$	−17.3070	−0.553133
$980$	8.24747	0.263456
$981$	−11.2085	−0.357861
$982$	42.4754	1.35545
$983$	2.49628	0.0796189	0.0398095	−	0.999207i	$-0.487325\pi$
$983$	2.49628	0.0796189	0.0398095	+	0.999207i	$0.487325\pi$
$984$	2.80451	0.0894044
$985$	−52.4793	−1.67213
$986$	55.3416	1.76244
$987$	−1.74296	−0.0554792
$988$	−11.7661	−0.374330
$989$	53.6466	1.70586
$990$	15.1911	0.482806
$991$	−28.0455	−0.890895	−0.445447	−	0.895308i	$-0.646955\pi$
$991$	−28.0455	−0.890895	−0.445447	+	0.895308i	$0.646955\pi$
$992$	−9.15974	−0.290822
$993$	3.21203	0.101931
$994$	−9.66395	−0.306522
$995$	−42.7194	−1.35430
$996$	47.7632	1.51344
$997$	−7.94500	−0.251621	−0.125810	−	0.992054i	$-0.540153\pi$
$997$	−7.94500	−0.251621	−0.125810	+	0.992054i	$0.540153\pi$
$998$	25.6327	0.811390
$999$	6.18389	0.195650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.i.1.1	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.i.1.1	✓	19	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.38901 q^{2} -1.00000 q^{3} +3.70736 q^{4} +2.22462 q^{5} +2.38901 q^{6} +1.00000 q^{7} -4.07890 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.38901 q^{2} -1.00000 q^{3} +3.70736 q^{4} +2.22462 q^{5} +2.38901 q^{6} +1.00000 q^{7} -4.07890 q^{8} +1.00000 q^{9} -5.31464 q^{10} -2.85836 q^{11} -3.70736 q^{12} -3.48178 q^{13} -2.38901 q^{14} -2.22462 q^{15} +2.32980 q^{16} -3.63746 q^{17} -2.38901 q^{18} +0.911520 q^{19} +8.24747 q^{20} -1.00000 q^{21} +6.82864 q^{22} +6.43483 q^{23} +4.07890 q^{24} -0.0510600 q^{25} +8.31801 q^{26} -1.00000 q^{27} +3.70736 q^{28} +6.36848 q^{29} +5.31464 q^{30} -3.53400 q^{31} +2.59189 q^{32} +2.85836 q^{33} +8.68992 q^{34} +2.22462 q^{35} +3.70736 q^{36} -6.18389 q^{37} -2.17763 q^{38} +3.48178 q^{39} -9.07400 q^{40} +0.687565 q^{41} +2.38901 q^{42} +8.33691 q^{43} -10.5970 q^{44} +2.22462 q^{45} -15.3729 q^{46} +1.74296 q^{47} -2.32980 q^{48} +1.00000 q^{49} +0.121983 q^{50} +3.63746 q^{51} -12.9082 q^{52} +10.4183 q^{53} +2.38901 q^{54} -6.35877 q^{55} -4.07890 q^{56} -0.911520 q^{57} -15.2144 q^{58} -11.9204 q^{59} -8.24747 q^{60} -9.22776 q^{61} +8.44276 q^{62} +1.00000 q^{63} -10.8516 q^{64} -7.74565 q^{65} -6.82864 q^{66} -10.3941 q^{67} -13.4854 q^{68} -6.43483 q^{69} -5.31464 q^{70} +4.04517 q^{71} -4.07890 q^{72} +12.4021 q^{73} +14.7734 q^{74} +0.0510600 q^{75} +3.37933 q^{76} -2.85836 q^{77} -8.31801 q^{78} -0.465252 q^{79} +5.18292 q^{80} +1.00000 q^{81} -1.64260 q^{82} -12.8833 q^{83} -3.70736 q^{84} -8.09197 q^{85} -19.9169 q^{86} -6.36848 q^{87} +11.6590 q^{88} +6.05486 q^{89} -5.31464 q^{90} -3.48178 q^{91} +23.8562 q^{92} +3.53400 q^{93} -4.16396 q^{94} +2.02779 q^{95} -2.59189 q^{96} -8.42169 q^{97} -2.38901 q^{98} -2.85836 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 3 q^{2} - 19 q^{3} + 11 q^{4} - 12 q^{5} - 3 q^{6} + 19 q^{7} + 6 q^{8} + 19 q^{9}+O(q^{10}) \) 19 * q + 3 * q^2 - 19 * q^3 + 11 * q^4 - 12 * q^5 - 3 * q^6 + 19 * q^7 + 6 * q^8 + 19 * q^9	\( 19 q + 3 q^{2} - 19 q^{3} + 11 q^{4} - 12 q^{5} - 3 q^{6} + 19 q^{7} + 6 q^{8} + 19 q^{9} - 12 q^{10} + q^{11} - 11 q^{12} - 25 q^{13} + 3 q^{14} + 12 q^{15} + 3 q^{16} - 9 q^{17} + 3 q^{18} - 29 q^{19} - 14 q^{20} - 19 q^{21} - 5 q^{22} + 18 q^{23} - 6 q^{24} + 3 q^{25} - 15 q^{26} - 19 q^{27} + 11 q^{28} + 2 q^{29} + 12 q^{30} - 24 q^{31} + 15 q^{32} - q^{33} - 16 q^{34} - 12 q^{35} + 11 q^{36} - 24 q^{37} - 26 q^{38} + 25 q^{39} - 44 q^{40} - 14 q^{41} - 3 q^{42} - 17 q^{43} - 6 q^{44} - 12 q^{45} - 16 q^{46} + 7 q^{47} - 3 q^{48} + 19 q^{49} + 7 q^{50} + 9 q^{51} - 64 q^{52} + 4 q^{53} - 3 q^{54} - 15 q^{55} + 6 q^{56} + 29 q^{57} - 15 q^{58} - 23 q^{59} + 14 q^{60} - 38 q^{61} - 4 q^{62} + 19 q^{63} + 33 q^{65} + 5 q^{66} - 20 q^{67} - 27 q^{68} - 18 q^{69} - 12 q^{70} + 14 q^{71} + 6 q^{72} - 19 q^{73} - 11 q^{74} - 3 q^{75} - 33 q^{76} + q^{77} + 15 q^{78} - 16 q^{79} - 10 q^{80} + 19 q^{81} - 25 q^{82} - 11 q^{83} - 11 q^{84} - 5 q^{85} + 5 q^{86} - 2 q^{87} - 25 q^{88} - 19 q^{89} - 12 q^{90} - 25 q^{91} + 22 q^{92} + 24 q^{93} - 35 q^{94} + 26 q^{95} - 15 q^{96} - 57 q^{97} + 3 q^{98} + q^{99}+O(q^{100}) \) 19 * q + 3 * q^2 - 19 * q^3 + 11 * q^4 - 12 * q^5 - 3 * q^6 + 19 * q^7 + 6 * q^8 + 19 * q^9 - 12 * q^10 + q^11 - 11 * q^12 - 25 * q^13 + 3 * q^14 + 12 * q^15 + 3 * q^16 - 9 * q^17 + 3 * q^18 - 29 * q^19 - 14 * q^20 - 19 * q^21 - 5 * q^22 + 18 * q^23 - 6 * q^24 + 3 * q^25 - 15 * q^26 - 19 * q^27 + 11 * q^28 + 2 * q^29 + 12 * q^30 - 24 * q^31 + 15 * q^32 - q^33 - 16 * q^34 - 12 * q^35 + 11 * q^36 - 24 * q^37 - 26 * q^38 + 25 * q^39 - 44 * q^40 - 14 * q^41 - 3 * q^42 - 17 * q^43 - 6 * q^44 - 12 * q^45 - 16 * q^46 + 7 * q^47 - 3 * q^48 + 19 * q^49 + 7 * q^50 + 9 * q^51 - 64 * q^52 + 4 * q^53 - 3 * q^54 - 15 * q^55 + 6 * q^56 + 29 * q^57 - 15 * q^58 - 23 * q^59 + 14 * q^60 - 38 * q^61 - 4 * q^62 + 19 * q^63 + 33 * q^65 + 5 * q^66 - 20 * q^67 - 27 * q^68 - 18 * q^69 - 12 * q^70 + 14 * q^71 + 6 * q^72 - 19 * q^73 - 11 * q^74 - 3 * q^75 - 33 * q^76 + q^77 + 15 * q^78 - 16 * q^79 - 10 * q^80 + 19 * q^81 - 25 * q^82 - 11 * q^83 - 11 * q^84 - 5 * q^85 + 5 * q^86 - 2 * q^87 - 25 * q^88 - 19 * q^89 - 12 * q^90 - 25 * q^91 + 22 * q^92 + 24 * q^93 - 35 * q^94 + 26 * q^95 - 15 * q^96 - 57 * q^97 + 3 * q^98 + q^99

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