LMFDB - Embedded newform 4011.2.a.i.1.2

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			1.2
Root			$-2.22223$ 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)

$f(q)$	$=$	$q-2.22223 q^{2} -1.00000 q^{3} +2.93833 q^{4} +1.26699 q^{5} +2.22223 q^{6} +1.00000 q^{7} -2.08518 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.22223 q^{2} -1.00000 q^{3} +2.93833 q^{4} +1.26699 q^{5} +2.22223 q^{6} +1.00000 q^{7} -2.08518 q^{8} +1.00000 q^{9} -2.81556 q^{10} +0.583304 q^{11} -2.93833 q^{12} +0.610400 q^{13} -2.22223 q^{14} -1.26699 q^{15} -1.24289 q^{16} +4.11597 q^{17} -2.22223 q^{18} +1.55065 q^{19} +3.72284 q^{20} -1.00000 q^{21} -1.29624 q^{22} -3.40038 q^{23} +2.08518 q^{24} -3.39472 q^{25} -1.35645 q^{26} -1.00000 q^{27} +2.93833 q^{28} +0.200681 q^{29} +2.81556 q^{30} -0.624627 q^{31} +6.93236 q^{32} -0.583304 q^{33} -9.14666 q^{34} +1.26699 q^{35} +2.93833 q^{36} -0.772380 q^{37} -3.44590 q^{38} -0.610400 q^{39} -2.64191 q^{40} -6.85678 q^{41} +2.22223 q^{42} -10.1143 q^{43} +1.71394 q^{44} +1.26699 q^{45} +7.55644 q^{46} +4.38626 q^{47} +1.24289 q^{48} +1.00000 q^{49} +7.54388 q^{50} -4.11597 q^{51} +1.79355 q^{52} -8.47842 q^{53} +2.22223 q^{54} +0.739043 q^{55} -2.08518 q^{56} -1.55065 q^{57} -0.445960 q^{58} -3.18356 q^{59} -3.72284 q^{60} -0.608485 q^{61} +1.38807 q^{62} +1.00000 q^{63} -12.9195 q^{64} +0.773373 q^{65} +1.29624 q^{66} -4.84394 q^{67} +12.0941 q^{68} +3.40038 q^{69} -2.81556 q^{70} -4.65746 q^{71} -2.08518 q^{72} -13.6464 q^{73} +1.71641 q^{74} +3.39472 q^{75} +4.55630 q^{76} +0.583304 q^{77} +1.35645 q^{78} -10.2025 q^{79} -1.57473 q^{80} +1.00000 q^{81} +15.2374 q^{82} +3.58909 q^{83} -2.93833 q^{84} +5.21492 q^{85} +22.4763 q^{86} -0.200681 q^{87} -1.21630 q^{88} -1.58348 q^{89} -2.81556 q^{90} +0.610400 q^{91} -9.99143 q^{92} +0.624627 q^{93} -9.74731 q^{94} +1.96466 q^{95} -6.93236 q^{96} -17.9570 q^{97} -2.22223 q^{98} +0.583304 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.22223	−1.57136	−0.785679	−	0.618635i	$-0.787686\pi$
$2$	−2.22223	−1.57136	−0.785679	+	0.618635i	$0.787686\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.93833	1.46916
$5$	1.26699	0.566617	0.283309	−	0.959029i	$-0.408568\pi$
$5$	1.26699	0.566617	0.283309	+	0.959029i	$0.408568\pi$
$6$	2.22223	0.907223
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.08518	−0.737223
$9$	1.00000	0.333333
$10$	−2.81556	−0.890358
$11$	0.583304	0.175873	0.0879364	−	0.996126i	$-0.471973\pi$
$11$	0.583304	0.175873	0.0879364	+	0.996126i	$0.471973\pi$
$12$	−2.93833	−0.848222
$13$	0.610400	0.169294	0.0846472	−	0.996411i	$-0.473024\pi$
$13$	0.610400	0.169294	0.0846472	+	0.996411i	$0.473024\pi$
$14$	−2.22223	−0.593917
$15$	−1.26699	−0.327137
$16$	−1.24289	−0.310722
$17$	4.11597	0.998270	0.499135	−	0.866524i	$-0.333651\pi$
$17$	4.11597	0.998270	0.499135	+	0.866524i	$0.333651\pi$
$18$	−2.22223	−0.523786
$19$	1.55065	0.355743	0.177871	−	0.984054i	$-0.443079\pi$
$19$	1.55065	0.355743	0.177871	+	0.984054i	$0.443079\pi$
$20$	3.72284	0.832453
$21$	−1.00000	−0.218218
$22$	−1.29624	−0.276359
$23$	−3.40038	−0.709028	−0.354514	−	0.935051i	$-0.615354\pi$
$23$	−3.40038	−0.709028	−0.354514	+	0.935051i	$0.615354\pi$
$24$	2.08518	0.425636
$25$	−3.39472	−0.678945
$26$	−1.35645	−0.266022
$27$	−1.00000	−0.192450
$28$	2.93833	0.555292
$29$	0.200681	0.0372655	0.0186327	−	0.999826i	$-0.494069\pi$
$29$	0.200681	0.0372655	0.0186327	+	0.999826i	$0.494069\pi$
$30$	2.81556	0.514048
$31$	−0.624627	−0.112186	−0.0560932	−	0.998426i	$-0.517864\pi$
$31$	−0.624627	−0.112186	−0.0560932	+	0.998426i	$0.517864\pi$
$32$	6.93236	1.22548
$33$	−0.583304	−0.101540
$34$	−9.14666	−1.56864
$35$	1.26699	0.214161
$36$	2.93833	0.489721
$37$	−0.772380	−0.126979	−0.0634893	−	0.997983i	$-0.520223\pi$
$37$	−0.772380	−0.126979	−0.0634893	+	0.997983i	$0.520223\pi$
$38$	−3.44590	−0.558999
$39$	−0.610400	−0.0977422
$40$	−2.64191	−0.417723
$41$	−6.85678	−1.07085	−0.535425	−	0.844583i	$-0.679848\pi$
$41$	−6.85678	−1.07085	−0.535425	+	0.844583i	$0.679848\pi$
$42$	2.22223	0.342898
$43$	−10.1143	−1.54241	−0.771207	−	0.636585i	$-0.780346\pi$
$43$	−10.1143	−1.54241	−0.771207	+	0.636585i	$0.780346\pi$
$44$	1.71394	0.258386
$45$	1.26699	0.188872
$46$	7.55644	1.11414
$47$	4.38626	0.639802	0.319901	−	0.947451i	$-0.396350\pi$
$47$	4.38626	0.639802	0.319901	+	0.947451i	$0.396350\pi$
$48$	1.24289	0.179396
$49$	1.00000	0.142857
$50$	7.54388	1.06687
$51$	−4.11597	−0.576352
$52$	1.79355	0.248721
$53$	−8.47842	−1.16460	−0.582300	−	0.812974i	$-0.697847\pi$
$53$	−8.47842	−1.16460	−0.582300	+	0.812974i	$0.697847\pi$
$54$	2.22223	0.302408
$55$	0.739043	0.0996525
$56$	−2.08518	−0.278644
$57$	−1.55065	−0.205388
$58$	−0.445960	−0.0585574
$59$	−3.18356	−0.414464	−0.207232	−	0.978292i	$-0.566445\pi$
$59$	−3.18356	−0.414464	−0.207232	+	0.978292i	$0.566445\pi$
$60$	−3.72284	−0.480617
$61$	−0.608485	−0.0779085	−0.0389543	−	0.999241i	$-0.512403\pi$
$61$	−0.608485	−0.0779085	−0.0389543	+	0.999241i	$0.512403\pi$
$62$	1.38807	0.176285
$63$	1.00000	0.125988
$64$	−12.9195	−1.61494
$65$	0.773373	0.0959251
$66$	1.29624	0.159556
$67$	−4.84394	−0.591781	−0.295891	−	0.955222i	$-0.595616\pi$
$67$	−4.84394	−0.591781	−0.295891	+	0.955222i	$0.595616\pi$
$68$	12.0941	1.46662
$69$	3.40038	0.409358
$70$	−2.81556	−0.336524
$71$	−4.65746	−0.552738	−0.276369	−	0.961052i	$-0.589131\pi$
$71$	−4.65746	−0.552738	−0.276369	+	0.961052i	$0.589131\pi$
$72$	−2.08518	−0.245741
$73$	−13.6464	−1.59719	−0.798595	−	0.601869i	$-0.794423\pi$
$73$	−13.6464	−1.59719	−0.798595	+	0.601869i	$0.794423\pi$
$74$	1.71641	0.199529
$75$	3.39472	0.391989
$76$	4.55630	0.522644
$77$	0.583304	0.0664737
$78$	1.35645	0.153588
$79$	−10.2025	−1.14787	−0.573934	−	0.818902i	$-0.694583\pi$
$79$	−10.2025	−1.14787	−0.573934	+	0.818902i	$0.694583\pi$
$80$	−1.57473	−0.176061
$81$	1.00000	0.111111
$82$	15.2374	1.68269
$83$	3.58909	0.393954	0.196977	−	0.980408i	$-0.436888\pi$
$83$	3.58909	0.393954	0.196977	+	0.980408i	$0.436888\pi$
$84$	−2.93833	−0.320598
$85$	5.21492	0.565637
$86$	22.4763	2.42368
$87$	−0.200681	−0.0215152
$88$	−1.21630	−0.129657
$89$	−1.58348	−0.167849	−0.0839245	−	0.996472i	$-0.526745\pi$
$89$	−1.58348	−0.167849	−0.0839245	+	0.996472i	$0.526745\pi$
$90$	−2.81556	−0.296786
$91$	0.610400	0.0639873
$92$	−9.99143	−1.04168
$93$	0.624627	0.0647708
$94$	−9.74731	−1.00536
$95$	1.96466	0.201570
$96$	−6.93236	−0.707531
$97$	−17.9570	−1.82326	−0.911629	−	0.411014i	$-0.865175\pi$
$97$	−17.9570	−1.82326	−0.911629	+	0.411014i	$0.865175\pi$
$98$	−2.22223	−0.224480
$99$	0.583304	0.0586243
$100$	−9.97481	−0.997481
$101$	5.26532	0.523919	0.261960	−	0.965079i	$-0.415631\pi$
$101$	5.26532	0.523919	0.261960	+	0.965079i	$0.415631\pi$
$102$	9.14666	0.905654
$103$	16.1173	1.58809	0.794043	−	0.607862i	$-0.207973\pi$
$103$	16.1173	1.58809	0.794043	+	0.607862i	$0.207973\pi$
$104$	−1.27279	−0.124808
$105$	−1.26699	−0.123646
$106$	18.8410	1.83000
$107$	8.85514	0.856059	0.428029	−	0.903765i	$-0.359208\pi$
$107$	8.85514	0.856059	0.428029	+	0.903765i	$0.359208\pi$
$108$	−2.93833	−0.282741
$109$	−17.4418	−1.67062	−0.835311	−	0.549777i	$-0.814713\pi$
$109$	−17.4418	−1.67062	−0.835311	+	0.549777i	$0.814713\pi$
$110$	−1.64233	−0.156590
$111$	0.772380	0.0733111
$112$	−1.24289	−0.117442
$113$	8.82113	0.829823	0.414911	−	0.909862i	$-0.363813\pi$
$113$	8.82113	0.829823	0.414911	+	0.909862i	$0.363813\pi$
$114$	3.44590	0.322738
$115$	−4.30826	−0.401748
$116$	0.589666	0.0547491
$117$	0.610400	0.0564315
$118$	7.07461	0.651271
$119$	4.11597	0.377311
$120$	2.64191	0.241173
$121$	−10.6598	−0.969069
$122$	1.35220	0.122422
$123$	6.85678	0.618255
$124$	−1.83536	−0.164820
$125$	−10.6361	−0.951319
$126$	−2.22223	−0.197972
$127$	−3.23878	−0.287396	−0.143698	−	0.989622i	$-0.545899\pi$
$127$	−3.23878	−0.287396	−0.143698	+	0.989622i	$0.545899\pi$
$128$	14.8455	1.31217
$129$	10.1143	0.890513
$130$	−1.71862	−0.150733
$131$	7.66468	0.669666	0.334833	−	0.942278i	$-0.391320\pi$
$131$	7.66468	0.669666	0.334833	+	0.942278i	$0.391320\pi$
$132$	−1.71394	−0.149179
$133$	1.55065	0.134458
$134$	10.7644	0.929900
$135$	−1.26699	−0.109046
$136$	−8.58256	−0.735948
$137$	3.63548	0.310600	0.155300	−	0.987867i	$-0.450366\pi$
$137$	3.63548	0.310600	0.155300	+	0.987867i	$0.450366\pi$
$138$	−7.55644	−0.643247
$139$	−15.0884	−1.27978	−0.639890	−	0.768466i	$-0.721020\pi$
$139$	−15.0884	−1.27978	−0.639890	+	0.768466i	$0.721020\pi$
$140$	3.72284	0.314638
$141$	−4.38626	−0.369390
$142$	10.3500	0.868549
$143$	0.356049	0.0297743
$144$	−1.24289	−0.103574
$145$	0.254261	0.0211153
$146$	30.3255	2.50975
$147$	−1.00000	−0.0824786
$148$	−2.26951	−0.186552
$149$	−15.2768	−1.25153	−0.625763	−	0.780013i	$-0.715212\pi$
$149$	−15.2768	−1.25153	−0.625763	+	0.780013i	$0.715212\pi$
$150$	−7.54388	−0.615955
$151$	16.8093	1.36792	0.683959	−	0.729520i	$-0.260257\pi$
$151$	16.8093	1.36792	0.683959	+	0.729520i	$0.260257\pi$
$152$	−3.23338	−0.262262
$153$	4.11597	0.332757
$154$	−1.29624	−0.104454
$155$	−0.791399	−0.0635667
$156$	−1.79355	−0.143599
$157$	0.806517	0.0643671	0.0321835	−	0.999482i	$-0.489754\pi$
$157$	0.806517	0.0643671	0.0321835	+	0.999482i	$0.489754\pi$
$158$	22.6723	1.80371
$159$	8.47842	0.672382
$160$	8.78326	0.694377
$161$	−3.40038	−0.267988
$162$	−2.22223	−0.174595
$163$	8.40812	0.658575	0.329287	−	0.944230i	$-0.393191\pi$
$163$	8.40812	0.658575	0.329287	+	0.944230i	$0.393191\pi$
$164$	−20.1475	−1.57325
$165$	−0.739043	−0.0575344
$166$	−7.97581	−0.619043
$167$	17.1178	1.32462	0.662309	−	0.749231i	$-0.269577\pi$
$167$	17.1178	1.32462	0.662309	+	0.749231i	$0.269577\pi$
$168$	2.08518	0.160875
$169$	−12.6274	−0.971339
$170$	−11.5888	−0.888818
$171$	1.55065	0.118581
$172$	−29.7191	−2.26606
$173$	2.59103	0.196992	0.0984962	−	0.995137i	$-0.468597\pi$
$173$	2.59103	0.196992	0.0984962	+	0.995137i	$0.468597\pi$
$174$	0.445960	0.0338081
$175$	−3.39472	−0.256617
$176$	−0.724982	−0.0546476
$177$	3.18356	0.239291
$178$	3.51887	0.263751
$179$	20.2469	1.51333	0.756663	−	0.653805i	$-0.226828\pi$
$179$	20.2469	1.51333	0.756663	+	0.653805i	$0.226828\pi$
$180$	3.72284	0.277484
$181$	26.8109	1.99284	0.996420	−	0.0845362i	$-0.0269409\pi$
$181$	26.8109	1.99284	0.996420	+	0.0845362i	$0.0269409\pi$
$182$	−1.35645	−0.100547
$183$	0.608485	0.0449805
$184$	7.09041	0.522712
$185$	−0.978602	−0.0719482
$186$	−1.38807	−0.101778
$187$	2.40086	0.175569
$188$	12.8883	0.939974
$189$	−1.00000	−0.0727393
$190$	−4.36593	−0.316738
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	12.9195	0.932388
$193$	8.48604	0.610839	0.305419	−	0.952218i	$-0.401203\pi$
$193$	8.48604	0.610839	0.305419	+	0.952218i	$0.401203\pi$
$194$	39.9047	2.86499
$195$	−0.773373	−0.0553824
$196$	2.93833	0.209880
$197$	14.6744	1.04551	0.522755	−	0.852483i	$-0.324904\pi$
$197$	14.6744	1.04551	0.522755	+	0.852483i	$0.324904\pi$
$198$	−1.29624	−0.0921196
$199$	6.25213	0.443202	0.221601	−	0.975137i	$-0.428872\pi$
$199$	6.25213	0.443202	0.221601	+	0.975137i	$0.428872\pi$
$200$	7.07862	0.500534
$201$	4.84394	0.341665
$202$	−11.7008	−0.823264
$203$	0.200681	0.0140850
$204$	−12.0941	−0.846755
$205$	−8.68751	−0.606762
$206$	−35.8164	−2.49545
$207$	−3.40038	−0.236343
$208$	−0.758659	−0.0526036
$209$	0.904498	0.0625654
$210$	2.81556	0.194292
$211$	−20.1242	−1.38541	−0.692703	−	0.721223i	$-0.743580\pi$
$211$	−20.1242	−1.38541	−0.692703	+	0.721223i	$0.743580\pi$
$212$	−24.9124	−1.71099
$213$	4.65746	0.319124
$214$	−19.6782	−1.34517
$215$	−12.8147	−0.873958
$216$	2.08518	0.141879
$217$	−0.624627	−0.0424025
$218$	38.7598	2.62514
$219$	13.6464	0.922138
$220$	2.17155	0.146406
$221$	2.51239	0.169002
$222$	−1.71641	−0.115198
$223$	3.88890	0.260420	0.130210	−	0.991486i	$-0.458435\pi$
$223$	3.88890	0.260420	0.130210	+	0.991486i	$0.458435\pi$
$224$	6.93236	0.463188
$225$	−3.39472	−0.226315
$226$	−19.6026	−1.30395
$227$	−16.4532	−1.09204	−0.546018	−	0.837773i	$-0.683857\pi$
$227$	−16.4532	−1.09204	−0.546018	+	0.837773i	$0.683857\pi$
$228$	−4.55630	−0.301749
$229$	14.8251	0.979669	0.489835	−	0.871815i	$-0.337057\pi$
$229$	14.8251	0.979669	0.489835	+	0.871815i	$0.337057\pi$
$230$	9.57397	0.631289
$231$	−0.583304	−0.0383786
$232$	−0.418456	−0.0274730
$233$	−25.9284	−1.69862	−0.849312	−	0.527892i	$-0.822983\pi$
$233$	−25.9284	−1.69862	−0.849312	+	0.527892i	$0.822983\pi$
$234$	−1.35645	−0.0886740
$235$	5.55737	0.362523
$236$	−9.35433	−0.608915
$237$	10.2025	0.662721
$238$	−9.14666	−0.592890
$239$	−10.5162	−0.680238	−0.340119	−	0.940382i	$-0.610467\pi$
$239$	−10.5162	−0.680238	−0.340119	+	0.940382i	$0.610467\pi$
$240$	1.57473	0.101649
$241$	−8.76375	−0.564523	−0.282261	−	0.959338i	$-0.591085\pi$
$241$	−8.76375	−0.564523	−0.282261	+	0.959338i	$0.591085\pi$
$242$	23.6885	1.52275
$243$	−1.00000	−0.0641500
$244$	−1.78793	−0.114460
$245$	1.26699	0.0809453
$246$	−15.2374	−0.971500
$247$	0.946513	0.0602252
$248$	1.30246	0.0827064
$249$	−3.58909	−0.227450
$250$	23.6358	1.49486
$251$	−13.8938	−0.876967	−0.438484	−	0.898739i	$-0.644484\pi$
$251$	−13.8938	−0.876967	−0.438484	+	0.898739i	$0.644484\pi$
$252$	2.93833	0.185097
$253$	−1.98346	−0.124699
$254$	7.19734	0.451601
$255$	−5.21492	−0.326571
$256$	−7.15119	−0.446950
$257$	11.1118	0.693132	0.346566	−	0.938026i	$-0.387348\pi$
$257$	11.1118	0.693132	0.346566	+	0.938026i	$0.387348\pi$
$258$	−22.4763	−1.39931
$259$	−0.772380	−0.0479934
$260$	2.27242	0.140930
$261$	0.200681	0.0124218
$262$	−17.0327	−1.05228
$263$	−2.02775	−0.125036	−0.0625182	−	0.998044i	$-0.519913\pi$
$263$	−2.02775	−0.125036	−0.0625182	+	0.998044i	$0.519913\pi$
$264$	1.21630	0.0748578
$265$	−10.7421	−0.659882
$266$	−3.44590	−0.211282
$267$	1.58348	0.0969076
$268$	−14.2331	−0.869423
$269$	−27.4162	−1.67160	−0.835798	−	0.549038i	$-0.814994\pi$
$269$	−27.4162	−1.67160	−0.835798	+	0.549038i	$0.814994\pi$
$270$	2.81556	0.171349
$271$	2.81362	0.170915	0.0854575	−	0.996342i	$-0.472765\pi$
$271$	2.81362	0.170915	0.0854575	+	0.996342i	$0.472765\pi$
$272$	−5.11570	−0.310185
$273$	−0.610400	−0.0369431
$274$	−8.07889	−0.488064
$275$	−1.98016	−0.119408
$276$	9.99143	0.601413
$277$	−6.38611	−0.383704	−0.191852	−	0.981424i	$-0.561449\pi$
$277$	−6.38611	−0.383704	−0.191852	+	0.981424i	$0.561449\pi$
$278$	33.5300	2.01099
$279$	−0.624627	−0.0373955
$280$	−2.64191	−0.157885
$281$	19.8376	1.18341	0.591707	−	0.806153i	$-0.298454\pi$
$281$	19.8376	1.18341	0.591707	+	0.806153i	$0.298454\pi$
$282$	9.74731	0.580444
$283$	−9.08619	−0.540118	−0.270059	−	0.962844i	$-0.587043\pi$
$283$	−9.08619	−0.540118	−0.270059	+	0.962844i	$0.587043\pi$
$284$	−13.6851	−0.812063
$285$	−1.96466	−0.116376
$286$	−0.791223	−0.0467860
$287$	−6.85678	−0.404743
$288$	6.93236	0.408493
$289$	−0.0587531	−0.00345606
$290$	−0.565029	−0.0331796
$291$	17.9570	1.05266
$292$	−40.0976	−2.34653
$293$	4.64077	0.271117	0.135558	−	0.990769i	$-0.456717\pi$
$293$	4.64077	0.271117	0.135558	+	0.990769i	$0.456717\pi$
$294$	2.22223	0.129603
$295$	−4.03355	−0.234842
$296$	1.61055	0.0936115
$297$	−0.583304	−0.0338467
$298$	33.9487	1.96659
$299$	−2.07559	−0.120035
$300$	9.97481	0.575896
$301$	−10.1143	−0.582977
$302$	−37.3541	−2.14949
$303$	−5.26532	−0.302485
$304$	−1.92728	−0.110537
$305$	−0.770947	−0.0441443
$306$	−9.14666	−0.522880
$307$	6.38728	0.364541	0.182271	−	0.983248i	$-0.441655\pi$
$307$	6.38728	0.364541	0.182271	+	0.983248i	$0.441655\pi$
$308$	1.71394	0.0976607
$309$	−16.1173	−0.916881
$310$	1.75867	0.0998860
$311$	−6.18174	−0.350534	−0.175267	−	0.984521i	$-0.556079\pi$
$311$	−6.18174	−0.350534	−0.175267	+	0.984521i	$0.556079\pi$
$312$	1.27279	0.0720578
$313$	12.5496	0.709343	0.354672	−	0.934991i	$-0.384593\pi$
$313$	12.5496	0.709343	0.354672	+	0.934991i	$0.384593\pi$
$314$	−1.79227	−0.101144
$315$	1.26699	0.0713871
$316$	−29.9782	−1.68640
$317$	26.5309	1.49012	0.745062	−	0.666995i	$-0.232420\pi$
$317$	26.5309	1.49012	0.745062	+	0.666995i	$0.232420\pi$
$318$	−18.8410	−1.05655
$319$	0.117058	0.00655398
$320$	−16.3690	−0.915054
$321$	−8.85514	−0.494246
$322$	7.55644	0.421104
$323$	6.38242	0.355127
$324$	2.93833	0.163240
$325$	−2.07214	−0.114942
$326$	−18.6848	−1.03486
$327$	17.4418	0.964534
$328$	14.2976	0.789455
$329$	4.38626	0.241823
$330$	1.64233	0.0904071
$331$	−1.60791	−0.0883785	−0.0441893	−	0.999023i	$-0.514070\pi$
$331$	−1.60791	−0.0883785	−0.0441893	+	0.999023i	$0.514070\pi$
$332$	10.5459	0.578783
$333$	−0.772380	−0.0423262
$334$	−38.0399	−2.08145
$335$	−6.13724	−0.335313
$336$	1.24289	0.0678052
$337$	−1.65062	−0.0899151	−0.0449575	−	0.998989i	$-0.514315\pi$
$337$	−1.65062	−0.0899151	−0.0449575	+	0.998989i	$0.514315\pi$
$338$	28.0611	1.52632
$339$	−8.82113	−0.479098
$340$	15.3231	0.831013
$341$	−0.364348	−0.0197305
$342$	−3.44590	−0.186333
$343$	1.00000	0.0539949
$344$	21.0901	1.13710
$345$	4.30826	0.231949
$346$	−5.75788	−0.309545
$347$	8.67248	0.465563	0.232782	−	0.972529i	$-0.425217\pi$
$347$	8.67248	0.465563	0.232782	+	0.972529i	$0.425217\pi$
$348$	−0.589666	−0.0316094
$349$	−32.6376	−1.74705	−0.873526	−	0.486777i	$-0.838172\pi$
$349$	−32.6376	−1.74705	−0.873526	+	0.486777i	$0.838172\pi$
$350$	7.54388	0.403237
$351$	−0.610400	−0.0325807
$352$	4.04367	0.215528
$353$	−20.5252	−1.09244	−0.546222	−	0.837641i	$-0.683934\pi$
$353$	−20.5252	−1.09244	−0.546222	+	0.837641i	$0.683934\pi$
$354$	−7.07461	−0.376011
$355$	−5.90097	−0.313191
$356$	−4.65279	−0.246598
$357$	−4.11597	−0.217840
$358$	−44.9934	−2.37798
$359$	34.6035	1.82630	0.913152	−	0.407620i	$-0.133641\pi$
$359$	34.6035	1.82630	0.913152	+	0.407620i	$0.133641\pi$
$360$	−2.64191	−0.139241
$361$	−16.5955	−0.873447
$362$	−59.5802	−3.13146
$363$	10.6598	0.559492
$364$	1.79355	0.0940077
$365$	−17.2899	−0.904995
$366$	−1.35220	−0.0706804
$367$	−37.0761	−1.93536	−0.967679	−	0.252186i	$-0.918850\pi$
$367$	−37.0761	−1.93536	−0.967679	+	0.252186i	$0.918850\pi$
$368$	4.22630	0.220311
$369$	−6.85678	−0.356950
$370$	2.17468	0.113056
$371$	−8.47842	−0.440177
$372$	1.83536	0.0951589
$373$	−11.4946	−0.595170	−0.297585	−	0.954695i	$-0.596181\pi$
$373$	−11.4946	−0.595170	−0.297585	+	0.954695i	$0.596181\pi$
$374$	−5.33528	−0.275881
$375$	10.6361	0.549244
$376$	−9.14616	−0.471677
$377$	0.122495	0.00630884
$378$	2.22223	0.114299
$379$	−18.7493	−0.963089	−0.481544	−	0.876422i	$-0.659924\pi$
$379$	−18.7493	−0.963089	−0.481544	+	0.876422i	$0.659924\pi$
$380$	5.77281	0.296139
$381$	3.23878	0.165928
$382$	−2.22223	−0.113699
$383$	−30.7175	−1.56959	−0.784796	−	0.619754i	$-0.787232\pi$
$383$	−30.7175	−1.56959	−0.784796	+	0.619754i	$0.787232\pi$
$384$	−14.8455	−0.757583
$385$	0.739043	0.0376651
$386$	−18.8580	−0.959846
$387$	−10.1143	−0.514138
$388$	−52.7636	−2.67866
$389$	−31.9911	−1.62201	−0.811007	−	0.585036i	$-0.801080\pi$
$389$	−31.9911	−1.62201	−0.811007	+	0.585036i	$0.801080\pi$
$390$	1.71862	0.0870255
$391$	−13.9959	−0.707802
$392$	−2.08518	−0.105318
$393$	−7.66468	−0.386632
$394$	−32.6100	−1.64287
$395$	−12.9265	−0.650401
$396$	1.71394	0.0861286
$397$	13.0401	0.654462	0.327231	−	0.944944i	$-0.393884\pi$
$397$	13.0401	0.654462	0.327231	+	0.944944i	$0.393884\pi$
$398$	−13.8937	−0.696429
$399$	−1.55065	−0.0776294
$400$	4.21927	0.210963
$401$	29.7163	1.48396	0.741982	−	0.670420i	$-0.233886\pi$
$401$	29.7163	1.48396	0.741982	+	0.670420i	$0.233886\pi$
$402$	−10.7644	−0.536878
$403$	−0.381272	−0.0189925
$404$	15.4712	0.769723
$405$	1.26699	0.0629575
$406$	−0.445960	−0.0221326
$407$	−0.450533	−0.0223321
$408$	8.58256	0.424900
$409$	15.5159	0.767211	0.383606	−	0.923497i	$-0.374682\pi$
$409$	15.5159	0.767211	0.383606	+	0.923497i	$0.374682\pi$
$410$	19.3057	0.953440
$411$	−3.63548	−0.179325
$412$	47.3579	2.33316
$413$	−3.18356	−0.156653
$414$	7.55644	0.371379
$415$	4.54736	0.223221
$416$	4.23151	0.207467
$417$	15.0884	0.738882
$418$	−2.01001	−0.0983126
$419$	−12.4170	−0.606611	−0.303306	−	0.952893i	$-0.598090\pi$
$419$	−12.4170	−0.606611	−0.303306	+	0.952893i	$0.598090\pi$
$420$	−3.72284	−0.181656
$421$	−20.3974	−0.994110	−0.497055	−	0.867719i	$-0.665585\pi$
$421$	−20.3974	−0.994110	−0.497055	+	0.867719i	$0.665585\pi$
$422$	44.7207	2.17697
$423$	4.38626	0.213267
$424$	17.6790	0.858570
$425$	−13.9726	−0.677771
$426$	−10.3500	−0.501457
$427$	−0.608485	−0.0294467
$428$	26.0193	1.25769
$429$	−0.356049	−0.0171902
$430$	28.4773	1.37330
$431$	−30.4802	−1.46818	−0.734089	−	0.679053i	$-0.762391\pi$
$431$	−30.4802	−1.46818	−0.734089	+	0.679053i	$0.762391\pi$
$432$	1.24289	0.0597985
$433$	−21.6644	−1.04113	−0.520563	−	0.853823i	$-0.674278\pi$
$433$	−21.6644	−1.04113	−0.520563	+	0.853823i	$0.674278\pi$
$434$	1.38807	0.0666294
$435$	−0.254261	−0.0121909
$436$	−51.2497	−2.45442
$437$	−5.27279	−0.252232
$438$	−30.3255	−1.44901
$439$	23.1026	1.10263	0.551313	−	0.834299i	$-0.314127\pi$
$439$	23.1026	1.10263	0.551313	+	0.834299i	$0.314127\pi$
$440$	−1.54104	−0.0734662
$441$	1.00000	0.0476190
$442$	−5.58312	−0.265562
$443$	28.6142	1.35950	0.679751	−	0.733443i	$-0.262088\pi$
$443$	28.6142	1.35950	0.679751	+	0.733443i	$0.262088\pi$
$444$	2.26951	0.107706
$445$	−2.00627	−0.0951061
$446$	−8.64204	−0.409213
$447$	15.2768	0.722569
$448$	−12.9195	−0.610391
$449$	−17.4468	−0.823363	−0.411682	−	0.911328i	$-0.635058\pi$
$449$	−17.4468	−0.823363	−0.411682	+	0.911328i	$0.635058\pi$
$450$	7.54388	0.355622
$451$	−3.99959	−0.188333
$452$	25.9194	1.21914
$453$	−16.8093	−0.789768
$454$	36.5628	1.71598
$455$	0.773373	0.0362563
$456$	3.23338	0.151417
$457$	−21.1227	−0.988079	−0.494040	−	0.869439i	$-0.664480\pi$
$457$	−21.1227	−0.988079	−0.494040	+	0.869439i	$0.664480\pi$
$458$	−32.9448	−1.53941
$459$	−4.11597	−0.192117
$460$	−12.6591	−0.590233
$461$	−39.7780	−1.85264	−0.926322	−	0.376732i	$-0.877048\pi$
$461$	−39.7780	−1.85264	−0.926322	+	0.376732i	$0.877048\pi$
$462$	1.29624	0.0603065
$463$	12.9461	0.601658	0.300829	−	0.953678i	$-0.402737\pi$
$463$	12.9461	0.601658	0.300829	+	0.953678i	$0.402737\pi$
$464$	−0.249424	−0.0115792
$465$	0.791399	0.0367003
$466$	57.6189	2.66914
$467$	5.32827	0.246563	0.123281	−	0.992372i	$-0.460658\pi$
$467$	5.32827	0.246563	0.123281	+	0.992372i	$0.460658\pi$
$468$	1.79355	0.0829070
$469$	−4.84394	−0.223672
$470$	−12.3498	−0.569653
$471$	−0.806517	−0.0371624
$472$	6.63829	0.305552
$473$	−5.89970	−0.271268
$474$	−22.6723	−1.04137
$475$	−5.26402	−0.241530
$476$	12.0941	0.554331
$477$	−8.47842	−0.388200
$478$	23.3695	1.06890
$479$	−17.7638	−0.811648	−0.405824	−	0.913951i	$-0.633015\pi$
$479$	−17.7638	−0.811648	−0.405824	+	0.913951i	$0.633015\pi$
$480$	−8.78326	−0.400899
$481$	−0.471461	−0.0214968
$482$	19.4751	0.887067
$483$	3.40038	0.154723
$484$	−31.3218	−1.42372
$485$	−22.7514	−1.03309
$486$	2.22223	0.100803
$487$	23.8830	1.08224	0.541122	−	0.840944i	$-0.318000\pi$
$487$	23.8830	1.08224	0.541122	+	0.840944i	$0.318000\pi$
$488$	1.26880	0.0574360
$489$	−8.40812	−0.380228
$490$	−2.81556	−0.127194
$491$	−9.91687	−0.447542	−0.223771	−	0.974642i	$-0.571837\pi$
$491$	−9.91687	−0.447542	−0.223771	+	0.974642i	$0.571837\pi$
$492$	20.1475	0.908318
$493$	0.825997	0.0372010
$494$	−2.10337	−0.0946353
$495$	0.739043	0.0332175
$496$	0.776343	0.0348588
$497$	−4.65746	−0.208915
$498$	7.97581	0.357404
$499$	22.2869	0.997699	0.498850	−	0.866689i	$-0.333756\pi$
$499$	22.2869	0.997699	0.498850	+	0.866689i	$0.333756\pi$
$500$	−31.2523	−1.39764
$501$	−17.1178	−0.764769
$502$	30.8752	1.37803
$503$	13.6404	0.608194	0.304097	−	0.952641i	$-0.401645\pi$
$503$	13.6404	0.608194	0.304097	+	0.952641i	$0.401645\pi$
$504$	−2.08518	−0.0928814
$505$	6.67114	0.296862
$506$	4.40770	0.195946
$507$	12.6274	0.560803
$508$	−9.51660	−0.422231
$509$	39.6028	1.75536	0.877681	−	0.479246i	$-0.159090\pi$
$509$	39.6028	1.75536	0.877681	+	0.479246i	$0.159090\pi$
$510$	11.5888	0.513159
$511$	−13.6464	−0.603681
$512$	−13.7995	−0.609856
$513$	−1.55065	−0.0684627
$514$	−24.6929	−1.08916
$515$	20.4205	0.899836
$516$	29.7191	1.30831
$517$	2.55853	0.112524
$518$	1.71641	0.0754147
$519$	−2.59103	−0.113734
$520$	−1.61262	−0.0707182
$521$	12.3796	0.542361	0.271180	−	0.962529i	$-0.412586\pi$
$521$	12.3796	0.542361	0.271180	+	0.962529i	$0.412586\pi$
$522$	−0.445960	−0.0195191
$523$	−38.5936	−1.68758	−0.843790	−	0.536674i	$-0.819681\pi$
$523$	−38.5936	−1.68758	−0.843790	+	0.536674i	$0.819681\pi$
$524$	22.5213	0.983848
$525$	3.39472	0.148158
$526$	4.50613	0.196477
$527$	−2.57095	−0.111992
$528$	0.724982	0.0315508
$529$	−11.4374	−0.497279
$530$	23.8715	1.03691
$531$	−3.18356	−0.138155
$532$	4.55630	0.197541
$533$	−4.18538	−0.181289
$534$	−3.51887	−0.152277
$535$	11.2194	0.485057
$536$	10.1005	0.436275
$537$	−20.2469	−0.873719
$538$	60.9252	2.62667
$539$	0.583304	0.0251247
$540$	−3.72284	−0.160206
$541$	12.8958	0.554433	0.277216	−	0.960807i	$-0.410588\pi$
$541$	12.8958	0.554433	0.277216	+	0.960807i	$0.410588\pi$
$542$	−6.25251	−0.268568
$543$	−26.8109	−1.15057
$544$	28.5334	1.22336
$545$	−22.0987	−0.946603
$546$	1.35645	0.0580507
$547$	16.2553	0.695026	0.347513	−	0.937675i	$-0.387026\pi$
$547$	16.2553	0.695026	0.347513	+	0.937675i	$0.387026\pi$
$548$	10.6822	0.456322
$549$	−0.608485	−0.0259695
$550$	4.40037	0.187633
$551$	0.311185	0.0132569
$552$	−7.09041	−0.301788
$553$	−10.2025	−0.433853
$554$	14.1914	0.602936
$555$	0.978602	0.0415393
$556$	−44.3346	−1.88021
$557$	32.8832	1.39331	0.696654	−	0.717408i	$-0.254671\pi$
$557$	32.8832	1.39331	0.696654	+	0.717408i	$0.254671\pi$
$558$	1.38807	0.0587616
$559$	−6.17375	−0.261122
$560$	−1.57473	−0.0665447
$561$	−2.40086	−0.101365
$562$	−44.0839	−1.85957
$563$	−1.93593	−0.0815896	−0.0407948	−	0.999168i	$-0.512989\pi$
$563$	−1.93593	−0.0815896	−0.0407948	+	0.999168i	$0.512989\pi$
$564$	−12.8883	−0.542694
$565$	11.1763	0.470192
$566$	20.1916	0.848718
$567$	1.00000	0.0419961
$568$	9.71164	0.407492
$569$	−11.4255	−0.478983	−0.239491	−	0.970898i	$-0.576981\pi$
$569$	−11.4255	−0.478983	−0.239491	+	0.970898i	$0.576981\pi$
$570$	4.36593	0.182869
$571$	6.35236	0.265838	0.132919	−	0.991127i	$-0.457565\pi$
$571$	6.35236	0.265838	0.132919	+	0.991127i	$0.457565\pi$
$572$	1.04619	0.0437433
$573$	−1.00000	−0.0417756
$574$	15.2374	0.635996
$575$	11.5434	0.481391
$576$	−12.9195	−0.538314
$577$	−8.06943	−0.335935	−0.167967	−	0.985793i	$-0.553720\pi$
$577$	−8.06943	−0.335935	−0.167967	+	0.985793i	$0.553720\pi$
$578$	0.130563	0.00543071
$579$	−8.48604	−0.352668
$580$	0.747103	0.0310218
$581$	3.58909	0.148901
$582$	−39.9047	−1.65410
$583$	−4.94549	−0.204821
$584$	28.4552	1.17748
$585$	0.773373	0.0319750
$586$	−10.3129	−0.426022
$587$	9.24792	0.381703	0.190851	−	0.981619i	$-0.438875\pi$
$587$	9.24792	0.381703	0.190851	+	0.981619i	$0.438875\pi$
$588$	−2.93833	−0.121175
$589$	−0.968575	−0.0399095
$590$	8.96349	0.369021
$591$	−14.6744	−0.603625
$592$	0.959983	0.0394551
$593$	−14.5784	−0.598662	−0.299331	−	0.954149i	$-0.596763\pi$
$593$	−14.5784	−0.598662	−0.299331	+	0.954149i	$0.596763\pi$
$594$	1.29624	0.0531853
$595$	5.21492	0.213791
$596$	−44.8883	−1.83870
$597$	−6.25213	−0.255883
$598$	4.61245	0.188617
$599$	−30.0537	−1.22796	−0.613981	−	0.789321i	$-0.710433\pi$
$599$	−30.0537	−1.22796	−0.613981	+	0.789321i	$0.710433\pi$
$600$	−7.07862	−0.288983
$601$	−6.88129	−0.280694	−0.140347	−	0.990102i	$-0.544822\pi$
$601$	−6.88129	−0.280694	−0.140347	+	0.990102i	$0.544822\pi$
$602$	22.4763	0.916066
$603$	−4.84394	−0.197260
$604$	49.3911	2.00970
$605$	−13.5059	−0.549091
$606$	11.7008	0.475312
$607$	35.1584	1.42703	0.713517	−	0.700638i	$-0.247101\pi$
$607$	35.1584	1.42703	0.713517	+	0.700638i	$0.247101\pi$
$608$	10.7496	0.435955
$609$	−0.200681	−0.00813200
$610$	1.71323	0.0693665
$611$	2.67737	0.108315
$612$	12.0941	0.488874
$613$	−9.51993	−0.384507	−0.192253	−	0.981345i	$-0.561580\pi$
$613$	−9.51993	−0.384507	−0.192253	+	0.981345i	$0.561580\pi$
$614$	−14.1940	−0.572825
$615$	8.68751	0.350314
$616$	−1.21630	−0.0490059
$617$	15.1180	0.608626	0.304313	−	0.952572i	$-0.401573\pi$
$617$	15.1180	0.608626	0.304313	+	0.952572i	$0.401573\pi$
$618$	35.8164	1.44075
$619$	−12.4229	−0.499318	−0.249659	−	0.968334i	$-0.580318\pi$
$619$	−12.4229	−0.499318	−0.249659	+	0.968334i	$0.580318\pi$
$620$	−2.32539	−0.0933899
$621$	3.40038	0.136453
$622$	13.7373	0.550815
$623$	−1.58348	−0.0634409
$624$	0.758659	0.0303707
$625$	3.49778	0.139911
$626$	−27.8881	−1.11463
$627$	−0.904498	−0.0361222
$628$	2.36981	0.0945658
$629$	−3.17910	−0.126759
$630$	−2.81556	−0.112175
$631$	−16.8707	−0.671610	−0.335805	−	0.941931i	$-0.609008\pi$
$631$	−16.8707	−0.671610	−0.335805	+	0.941931i	$0.609008\pi$
$632$	21.2740	0.846234
$633$	20.1242	0.799864
$634$	−58.9579	−2.34152
$635$	−4.10352	−0.162843
$636$	24.9124	0.987839
$637$	0.610400	0.0241849
$638$	−0.260130	−0.0102986
$639$	−4.65746	−0.184246
$640$	18.8092	0.743500
$641$	−26.4455	−1.04453	−0.522267	−	0.852782i	$-0.674913\pi$
$641$	−26.4455	−1.04453	−0.522267	+	0.852782i	$0.674913\pi$
$642$	19.6782	0.776636
$643$	−18.0028	−0.709961	−0.354981	−	0.934874i	$-0.615513\pi$
$643$	−18.0028	−0.709961	−0.354981	+	0.934874i	$0.615513\pi$
$644$	−9.99143	−0.393717
$645$	12.8147	0.504580
$646$	−14.1832	−0.558032
$647$	−8.76836	−0.344720	−0.172360	−	0.985034i	$-0.555139\pi$
$647$	−8.76836	−0.344720	−0.172360	+	0.985034i	$0.555139\pi$
$648$	−2.08518	−0.0819137
$649$	−1.85698	−0.0728929
$650$	4.60478	0.180614
$651$	0.624627	0.0244811
$652$	24.7058	0.967554
$653$	9.72301	0.380491	0.190245	−	0.981737i	$-0.439072\pi$
$653$	9.72301	0.380491	0.190245	+	0.981737i	$0.439072\pi$
$654$	−38.7598	−1.51563
$655$	9.71110	0.379444
$656$	8.52222	0.332737
$657$	−13.6464	−0.532396
$658$	−9.74731	−0.379990
$659$	−28.0722	−1.09354	−0.546768	−	0.837284i	$-0.684142\pi$
$659$	−28.0722	−1.09354	−0.546768	+	0.837284i	$0.684142\pi$
$660$	−2.17155	−0.0845275
$661$	−6.05216	−0.235402	−0.117701	−	0.993049i	$-0.537552\pi$
$661$	−6.05216	−0.235402	−0.117701	+	0.993049i	$0.537552\pi$
$662$	3.57315	0.138874
$663$	−2.51239	−0.0975731
$664$	−7.48391	−0.290432
$665$	1.96466	0.0761862
$666$	1.71641	0.0665096
$667$	−0.682391	−0.0264223
$668$	50.2978	1.94608
$669$	−3.88890	−0.150353
$670$	13.6384	0.526897
$671$	−0.354932	−0.0137020
$672$	−6.93236	−0.267421
$673$	−7.57058	−0.291825	−0.145912	−	0.989298i	$-0.546612\pi$
$673$	−7.57058	−0.291825	−0.145912	+	0.989298i	$0.546612\pi$
$674$	3.66807	0.141289
$675$	3.39472	0.130663
$676$	−37.1035	−1.42706
$677$	−6.24182	−0.239893	−0.119946	−	0.992780i	$-0.538272\pi$
$677$	−6.24182	−0.239893	−0.119946	+	0.992780i	$0.538272\pi$
$678$	19.6026	0.752834
$679$	−17.9570	−0.689127
$680$	−10.8741	−0.417001
$681$	16.4532	0.630487
$682$	0.809666	0.0310037
$683$	15.8115	0.605012	0.302506	−	0.953148i	$-0.402177\pi$
$683$	15.8115	0.605012	0.302506	+	0.953148i	$0.402177\pi$
$684$	4.55630	0.174215
$685$	4.60614	0.175991
$686$	−2.22223	−0.0848453
$687$	−14.8251	−0.565612
$688$	12.5709	0.479262
$689$	−5.17522	−0.197160
$690$	−9.57397	−0.364475
$691$	−4.25613	−0.161911	−0.0809554	−	0.996718i	$-0.525797\pi$
$691$	−4.25613	−0.161911	−0.0809554	+	0.996718i	$0.525797\pi$
$692$	7.61329	0.289414
$693$	0.583304	0.0221579
$694$	−19.2723	−0.731566
$695$	−19.1169	−0.725146
$696$	0.418456	0.0158615
$697$	−28.2223	−1.06900
$698$	72.5285	2.74524
$699$	25.9284	0.980701
$700$	−9.97481	−0.377012
$701$	−45.7305	−1.72722	−0.863609	−	0.504162i	$-0.831801\pi$
$701$	−45.7305	−1.72722	−0.863609	+	0.504162i	$0.831801\pi$
$702$	1.35645	0.0511959
$703$	−1.19769	−0.0451717
$704$	−7.53602	−0.284024
$705$	−5.55737	−0.209303
$706$	45.6117	1.71662
$707$	5.26532	0.198023
$708$	9.35433	0.351557
$709$	−20.2989	−0.762341	−0.381170	−	0.924505i	$-0.624479\pi$
$709$	−20.2989	−0.762341	−0.381170	+	0.924505i	$0.624479\pi$
$710$	13.1133	0.492135
$711$	−10.2025	−0.382622
$712$	3.30185	0.123742
$713$	2.12397	0.0795433
$714$	9.14666	0.342305
$715$	0.451112	0.0168706
$716$	59.4921	2.22332
$717$	10.5162	0.392736
$718$	−76.8971	−2.86977
$719$	−34.0331	−1.26922	−0.634610	−	0.772833i	$-0.718839\pi$
$719$	−34.0331	−1.26922	−0.634610	+	0.772833i	$0.718839\pi$
$720$	−1.57473	−0.0586869
$721$	16.1173	0.600240
$722$	36.8791	1.37250
$723$	8.76375	0.325927
$724$	78.7793	2.92781
$725$	−0.681256	−0.0253012
$726$	−23.6885	−0.879162
$727$	15.3793	0.570386	0.285193	−	0.958470i	$-0.407942\pi$
$727$	15.3793	0.570386	0.285193	+	0.958470i	$0.407942\pi$
$728$	−1.27279	−0.0471729
$729$	1.00000	0.0370370
$730$	38.4222	1.42207
$731$	−41.6301	−1.53975
$732$	1.78793	0.0660837
$733$	22.2785	0.822876	0.411438	−	0.911438i	$-0.365027\pi$
$733$	22.2785	0.822876	0.411438	+	0.911438i	$0.365027\pi$
$734$	82.3918	3.04114
$735$	−1.26699	−0.0467338
$736$	−23.5727	−0.868899
$737$	−2.82549	−0.104078
$738$	15.2374	0.560896
$739$	19.1271	0.703600	0.351800	−	0.936075i	$-0.385570\pi$
$739$	19.1271	0.703600	0.351800	+	0.936075i	$0.385570\pi$
$740$	−2.87545	−0.105704
$741$	−0.946513	−0.0347710
$742$	18.8410	0.691676
$743$	47.9827	1.76032	0.880158	−	0.474682i	$-0.157437\pi$
$743$	47.9827	1.76032	0.880158	+	0.474682i	$0.157437\pi$
$744$	−1.30246	−0.0477506
$745$	−19.3557	−0.709136
$746$	25.5438	0.935224
$747$	3.58909	0.131318
$748$	7.05452	0.257939
$749$	8.85514	0.323560
$750$	−23.6358	−0.863059
$751$	29.1938	1.06530	0.532648	−	0.846337i	$-0.321197\pi$
$751$	29.1938	1.06530	0.532648	+	0.846337i	$0.321197\pi$
$752$	−5.45164	−0.198801
$753$	13.8938	0.506317
$754$	−0.272214	−0.00991344
$755$	21.2972	0.775086
$756$	−2.93833	−0.106866
$757$	7.21215	0.262130	0.131065	−	0.991374i	$-0.458160\pi$
$757$	7.21215	0.262130	0.131065	+	0.991374i	$0.458160\pi$
$758$	41.6654	1.51336
$759$	1.98346	0.0719949
$760$	−4.09667	−0.148602
$761$	−2.53989	−0.0920708	−0.0460354	−	0.998940i	$-0.514659\pi$
$761$	−2.53989	−0.0920708	−0.0460354	+	0.998940i	$0.514659\pi$
$762$	−7.19734	−0.260732
$763$	−17.4418	−0.631436
$764$	2.93833	0.106305
$765$	5.21492	0.188546
$766$	68.2615	2.46639
$767$	−1.94324	−0.0701664
$768$	7.15119	0.258047
$769$	53.1898	1.91807	0.959037	−	0.283279i	$-0.0914224\pi$
$769$	53.1898	1.91807	0.959037	+	0.283279i	$0.0914224\pi$
$770$	−1.64233	−0.0591854
$771$	−11.1118	−0.400180
$772$	24.9348	0.897422
$773$	9.09455	0.327108	0.163554	−	0.986534i	$-0.447704\pi$
$773$	9.09455	0.327108	0.163554	+	0.986534i	$0.447704\pi$
$774$	22.4763	0.807894
$775$	2.12044	0.0761684
$776$	37.4436	1.34415
$777$	0.772380	0.0277090
$778$	71.0918	2.54876
$779$	−10.6324	−0.380947
$780$	−2.27242	−0.0813658
$781$	−2.71671	−0.0972116
$782$	31.1021	1.11221
$783$	−0.200681	−0.00717175
$784$	−1.24289	−0.0443889
$785$	1.02185	0.0364715
$786$	17.0327	0.607537
$787$	32.0367	1.14198	0.570992	−	0.820956i	$-0.306559\pi$
$787$	32.0367	1.14198	0.570992	+	0.820956i	$0.306559\pi$
$788$	43.1183	1.53602
$789$	2.02775	0.0721898
$790$	28.7256	1.02201
$791$	8.82113	0.313643
$792$	−1.21630	−0.0432192
$793$	−0.371419	−0.0131895
$794$	−28.9781	−1.02839
$795$	10.7421	0.380983
$796$	18.3708	0.651136
$797$	−17.6375	−0.624752	−0.312376	−	0.949959i	$-0.601125\pi$
$797$	−17.6375	−0.624752	−0.312376	+	0.949959i	$0.601125\pi$
$798$	3.44590	0.121983
$799$	18.0538	0.638696
$800$	−23.5334	−0.832033
$801$	−1.58348	−0.0559497
$802$	−66.0367	−2.33184
$803$	−7.95999	−0.280902
$804$	14.2331	0.501962
$805$	−4.30826	−0.151846
$806$	0.847276	0.0298440
$807$	27.4162	0.965096
$808$	−10.9792	−0.386245
$809$	53.2103	1.87078	0.935388	−	0.353623i	$-0.115050\pi$
$809$	53.2103	1.87078	0.935388	+	0.353623i	$0.115050\pi$
$810$	−2.81556	−0.0989287
$811$	−28.0908	−0.986402	−0.493201	−	0.869915i	$-0.664173\pi$
$811$	−28.0908	−0.986402	−0.493201	+	0.869915i	$0.664173\pi$
$812$	0.589666	0.0206932
$813$	−2.81362	−0.0986778
$814$	1.00119	0.0350917
$815$	10.6530	0.373160
$816$	5.11570	0.179085
$817$	−15.6837	−0.548702
$818$	−34.4799	−1.20556
$819$	0.610400	0.0213291
$820$	−25.5267	−0.891432
$821$	−46.0907	−1.60858	−0.804289	−	0.594238i	$-0.797454\pi$
$821$	−46.0907	−1.60858	−0.804289	+	0.594238i	$0.797454\pi$
$822$	8.07889	0.281784
$823$	−40.0978	−1.39772	−0.698861	−	0.715258i	$-0.746309\pi$
$823$	−40.0978	−1.39772	−0.698861	+	0.715258i	$0.746309\pi$
$824$	−33.6075	−1.17077
$825$	1.98016	0.0689402
$826$	7.07461	0.246157
$827$	−26.4243	−0.918863	−0.459431	−	0.888213i	$-0.651947\pi$
$827$	−26.4243	−0.918863	−0.459431	+	0.888213i	$0.651947\pi$
$828$	−9.99143	−0.347226
$829$	−31.6402	−1.09891	−0.549455	−	0.835524i	$-0.685164\pi$
$829$	−31.6402	−1.09891	−0.549455	+	0.835524i	$0.685164\pi$
$830$	−10.1053	−0.350760
$831$	6.38611	0.221532
$832$	−7.88608	−0.273401
$833$	4.11597	0.142610
$834$	−33.5300	−1.16105
$835$	21.6882	0.750552
$836$	2.65771	0.0919188
$837$	0.624627	0.0215903
$838$	27.5935	0.953203
$839$	−2.15893	−0.0745345	−0.0372673	−	0.999305i	$-0.511865\pi$
$839$	−2.15893	−0.0745345	−0.0372673	+	0.999305i	$0.511865\pi$
$840$	2.64191	0.0911547
$841$	−28.9597	−0.998611
$842$	45.3279	1.56210
$843$	−19.8376	−0.683245
$844$	−59.1314	−2.03539
$845$	−15.9989	−0.550378
$846$	−9.74731	−0.335119
$847$	−10.6598	−0.366274
$848$	10.5377	0.361867
$849$	9.08619	0.311837
$850$	31.0504	1.06502
$851$	2.62639	0.0900314
$852$	13.6851	0.468845
$853$	5.80376	0.198717	0.0993584	−	0.995052i	$-0.468321\pi$
$853$	5.80376	0.198717	0.0993584	+	0.995052i	$0.468321\pi$
$854$	1.35220	0.0462712
$855$	1.96466	0.0671899
$856$	−18.4646	−0.631106
$857$	−3.70860	−0.126683	−0.0633416	−	0.997992i	$-0.520176\pi$
$857$	−3.70860	−0.126683	−0.0633416	+	0.997992i	$0.520176\pi$
$858$	0.791223	0.0270119
$859$	58.0811	1.98170	0.990851	−	0.134959i	$-0.0430903\pi$
$859$	58.0811	1.98170	0.990851	+	0.134959i	$0.0430903\pi$
$860$	−37.6539	−1.28399
$861$	6.85678	0.233679
$862$	67.7341	2.30703
$863$	43.0537	1.46556	0.732782	−	0.680464i	$-0.238222\pi$
$863$	43.0537	1.46556	0.732782	+	0.680464i	$0.238222\pi$
$864$	−6.93236	−0.235844
$865$	3.28282	0.111619
$866$	48.1435	1.63598
$867$	0.0587531	0.00199536
$868$	−1.83536	−0.0622961
$869$	−5.95114	−0.201879
$870$	0.565029	0.0191563
$871$	−2.95674	−0.100185
$872$	36.3694	1.23162
$873$	−17.9570	−0.607753
$874$	11.7174	0.396346
$875$	−10.6361	−0.359565
$876$	40.0976	1.35477
$877$	49.1825	1.66078	0.830388	−	0.557185i	$-0.188119\pi$
$877$	49.1825	1.66078	0.830388	+	0.557185i	$0.188119\pi$
$878$	−51.3393	−1.73262
$879$	−4.64077	−0.156529
$880$	−0.918549	−0.0309643
$881$	−11.7968	−0.397445	−0.198722	−	0.980056i	$-0.563679\pi$
$881$	−11.7968	−0.397445	−0.198722	+	0.980056i	$0.563679\pi$
$882$	−2.22223	−0.0748265
$883$	16.8670	0.567620	0.283810	−	0.958881i	$-0.408401\pi$
$883$	16.8670	0.567620	0.283810	+	0.958881i	$0.408401\pi$
$884$	7.38222	0.248291
$885$	4.03355	0.135586
$886$	−63.5875	−2.13626
$887$	−1.39508	−0.0468423	−0.0234211	−	0.999726i	$-0.507456\pi$
$887$	−1.39508	−0.0468423	−0.0234211	+	0.999726i	$0.507456\pi$
$888$	−1.61055	−0.0540466
$889$	−3.23878	−0.108625
$890$	4.45839	0.149446
$891$	0.583304	0.0195414
$892$	11.4268	0.382599
$893$	6.80154	0.227605
$894$	−33.9487	−1.13541
$895$	25.6527	0.857477
$896$	14.8455	0.495955
$897$	2.07559	0.0693020
$898$	38.7708	1.29380
$899$	−0.125351	−0.00418068
$900$	−9.97481	−0.332494
$901$	−34.8969	−1.16259
$902$	8.88803	0.295939
$903$	10.1143	0.336582
$904$	−18.3937	−0.611764
$905$	33.9693	1.12918
$906$	37.3541	1.24101
$907$	32.9681	1.09469	0.547344	−	0.836908i	$-0.315639\pi$
$907$	32.9681	1.09469	0.547344	+	0.836908i	$0.315639\pi$
$908$	−48.3448	−1.60438
$909$	5.26532	0.174640
$910$	−1.71862	−0.0569716
$911$	−25.5569	−0.846737	−0.423369	−	0.905958i	$-0.639152\pi$
$911$	−25.5569	−0.846737	−0.423369	+	0.905958i	$0.639152\pi$
$912$	1.92728	0.0638187
$913$	2.09353	0.0692858
$914$	46.9396	1.55263
$915$	0.770947	0.0254867
$916$	43.5609	1.43929
$917$	7.66468	0.253110
$918$	9.14666	0.301885
$919$	0.621070	0.0204872	0.0102436	−	0.999948i	$-0.496739\pi$
$919$	0.621070	0.0204872	0.0102436	+	0.999948i	$0.496739\pi$
$920$	8.98351	0.296178
$921$	−6.38728	−0.210468
$922$	88.3960	2.91117
$923$	−2.84291	−0.0935755
$924$	−1.71394	−0.0563844
$925$	2.62202	0.0862114
$926$	−28.7694	−0.945420
$927$	16.1173	0.529362
$928$	1.39119	0.0456681
$929$	12.1561	0.398829	0.199415	−	0.979915i	$-0.436096\pi$
$929$	12.1561	0.398829	0.199415	+	0.979915i	$0.436096\pi$
$930$	−1.75867	−0.0576692
$931$	1.55065	0.0508204
$932$	−76.1860	−2.49556
$933$	6.18174	0.202381
$934$	−11.8407	−0.387438
$935$	3.04188	0.0994802
$936$	−1.27279	−0.0416026
$937$	0.886133	0.0289487	0.0144743	−	0.999895i	$-0.495393\pi$
$937$	0.886133	0.0289487	0.0144743	+	0.999895i	$0.495393\pi$
$938$	10.7644	0.351469
$939$	−12.5496	−0.409540
$940$	16.3294	0.532605
$941$	−29.3122	−0.955551	−0.477776	−	0.878482i	$-0.658557\pi$
$941$	−29.3122	−0.955551	−0.477776	+	0.878482i	$0.658557\pi$
$942$	1.79227	0.0583953
$943$	23.3157	0.759263
$944$	3.95681	0.128783
$945$	−1.26699	−0.0412153
$946$	13.1105	0.426260
$947$	2.52386	0.0820144	0.0410072	−	0.999159i	$-0.486943\pi$
$947$	2.52386	0.0820144	0.0410072	+	0.999159i	$0.486943\pi$
$948$	29.9782	0.973646
$949$	−8.32975	−0.270395
$950$	11.6979	0.379529
$951$	−26.5309	−0.860323
$952$	−8.58256	−0.278162
$953$	49.5391	1.60473	0.802365	−	0.596833i	$-0.203575\pi$
$953$	49.5391	1.60473	0.802365	+	0.596833i	$0.203575\pi$
$954$	18.8410	0.610001
$955$	1.26699	0.0409990
$956$	−30.9001	−0.999381
$957$	−0.117058	−0.00378394
$958$	39.4753	1.27539
$959$	3.63548	0.117396
$960$	16.3690	0.528307
$961$	−30.6098	−0.987414
$962$	1.04770	0.0337791
$963$	8.85514	0.285353
$964$	−25.7508	−0.829376
$965$	10.7518	0.346112
$966$	−7.55644	−0.243125
$967$	7.26610	0.233662	0.116831	−	0.993152i	$-0.462726\pi$
$967$	7.26610	0.233662	0.116831	+	0.993152i	$0.462726\pi$
$968$	22.2275	0.714420
$969$	−6.38242	−0.205033
$970$	50.5590	1.62335
$971$	10.9681	0.351984	0.175992	−	0.984392i	$-0.443687\pi$
$971$	10.9681	0.351984	0.175992	+	0.984392i	$0.443687\pi$
$972$	−2.93833	−0.0942469
$973$	−15.0884	−0.483712
$974$	−53.0737	−1.70059
$975$	2.07214	0.0663615
$976$	0.756280	0.0242079
$977$	49.1769	1.57331	0.786654	−	0.617394i	$-0.211812\pi$
$977$	49.1769	1.57331	0.786654	+	0.617394i	$0.211812\pi$
$978$	18.6848	0.597475
$979$	−0.923652	−0.0295201
$980$	3.72284	0.118922
$981$	−17.4418	−0.556874
$982$	22.0376	0.703248
$983$	−18.7766	−0.598880	−0.299440	−	0.954115i	$-0.596800\pi$
$983$	−18.7766	−0.598880	−0.299440	+	0.954115i	$0.596800\pi$
$984$	−14.2976	−0.455792
$985$	18.5924	0.592404
$986$	−1.83556	−0.0584561
$987$	−4.38626	−0.139616
$988$	2.78117	0.0884807
$989$	34.3924	1.09361
$990$	−1.64233	−0.0521966
$991$	29.4912	0.936819	0.468410	−	0.883511i	$-0.344827\pi$
$991$	29.4912	0.936819	0.468410	+	0.883511i	$0.344827\pi$
$992$	−4.33014	−0.137482
$993$	1.60791	0.0510254
$994$	10.3500	0.328281
$995$	7.92142	0.251126
$996$	−10.5459	−0.334161
$997$	35.6776	1.12992	0.564961	−	0.825118i	$-0.308891\pi$
$997$	35.6776	1.12992	0.564961	+	0.825118i	$0.308891\pi$
$998$	−49.5268	−1.56774
$999$	0.772380	0.0244370

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.i.1.2	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.i.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-2.22223 q^{2} -1.00000 q^{3} +2.93833 q^{4} +1.26699 q^{5} +2.22223 q^{6} +1.00000 q^{7} -2.08518 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.22223 q^{2} -1.00000 q^{3} +2.93833 q^{4} +1.26699 q^{5} +2.22223 q^{6} +1.00000 q^{7} -2.08518 q^{8} +1.00000 q^{9} -2.81556 q^{10} +0.583304 q^{11} -2.93833 q^{12} +0.610400 q^{13} -2.22223 q^{14} -1.26699 q^{15} -1.24289 q^{16} +4.11597 q^{17} -2.22223 q^{18} +1.55065 q^{19} +3.72284 q^{20} -1.00000 q^{21} -1.29624 q^{22} -3.40038 q^{23} +2.08518 q^{24} -3.39472 q^{25} -1.35645 q^{26} -1.00000 q^{27} +2.93833 q^{28} +0.200681 q^{29} +2.81556 q^{30} -0.624627 q^{31} +6.93236 q^{32} -0.583304 q^{33} -9.14666 q^{34} +1.26699 q^{35} +2.93833 q^{36} -0.772380 q^{37} -3.44590 q^{38} -0.610400 q^{39} -2.64191 q^{40} -6.85678 q^{41} +2.22223 q^{42} -10.1143 q^{43} +1.71394 q^{44} +1.26699 q^{45} +7.55644 q^{46} +4.38626 q^{47} +1.24289 q^{48} +1.00000 q^{49} +7.54388 q^{50} -4.11597 q^{51} +1.79355 q^{52} -8.47842 q^{53} +2.22223 q^{54} +0.739043 q^{55} -2.08518 q^{56} -1.55065 q^{57} -0.445960 q^{58} -3.18356 q^{59} -3.72284 q^{60} -0.608485 q^{61} +1.38807 q^{62} +1.00000 q^{63} -12.9195 q^{64} +0.773373 q^{65} +1.29624 q^{66} -4.84394 q^{67} +12.0941 q^{68} +3.40038 q^{69} -2.81556 q^{70} -4.65746 q^{71} -2.08518 q^{72} -13.6464 q^{73} +1.71641 q^{74} +3.39472 q^{75} +4.55630 q^{76} +0.583304 q^{77} +1.35645 q^{78} -10.2025 q^{79} -1.57473 q^{80} +1.00000 q^{81} +15.2374 q^{82} +3.58909 q^{83} -2.93833 q^{84} +5.21492 q^{85} +22.4763 q^{86} -0.200681 q^{87} -1.21630 q^{88} -1.58348 q^{89} -2.81556 q^{90} +0.610400 q^{91} -9.99143 q^{92} +0.624627 q^{93} -9.74731 q^{94} +1.96466 q^{95} -6.93236 q^{96} -17.9570 q^{97} -2.22223 q^{98} +0.583304 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 3 q^{2} - 19 q^{3} + 11 q^{4} - 12 q^{5} - 3 q^{6} + 19 q^{7} + 6 q^{8} + 19 q^{9}+O(q^{10}) \) 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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