LMFDB - Embedded newform 574.2.a.m.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(1,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("574.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.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:	$4.58341307602$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.11348.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + x + 2 $ x^4 - x^3 - 5*x^2 + x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.64119$ of defining polynomial
Character	$\chi$	$=$	574.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.757235 q^{3} +1.00000 q^{4} +1.30651 q^{5} -0.757235 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.42659 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.757235 q^{3} +1.00000 q^{4} +1.30651 q^{5} -0.757235 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.42659 q^{9} -1.30651 q^{10} +1.45073 q^{11} +0.757235 q^{12} +3.28237 q^{13} +1.00000 q^{14} +0.989333 q^{15} +1.00000 q^{16} +7.19450 q^{17} +2.42659 q^{18} +5.28237 q^{19} +1.30651 q^{20} -0.757235 q^{21} -1.45073 q^{22} -3.28237 q^{23} -0.757235 q^{24} -3.29304 q^{25} -3.28237 q^{26} -4.10921 q^{27} -1.00000 q^{28} +6.46140 q^{29} -0.989333 q^{30} +3.01067 q^{31} -1.00000 q^{32} +1.09854 q^{33} -7.19450 q^{34} -1.30651 q^{35} -2.42659 q^{36} -3.51447 q^{37} -5.28237 q^{38} +2.48553 q^{39} -1.30651 q^{40} +1.00000 q^{41} +0.757235 q^{42} +0.525138 q^{43} +1.45073 q^{44} -3.17036 q^{45} +3.28237 q^{46} +3.15489 q^{47} +0.757235 q^{48} +1.00000 q^{49} +3.29304 q^{50} +5.44793 q^{51} +3.28237 q^{52} +11.6874 q^{53} +4.10921 q^{54} +1.89539 q^{55} +1.00000 q^{56} +4.00000 q^{57} -6.46140 q^{58} +1.68283 q^{59} +0.989333 q^{60} -0.842311 q^{61} -3.01067 q^{62} +2.42659 q^{63} +1.00000 q^{64} +4.28844 q^{65} -1.09854 q^{66} +7.88799 q^{67} +7.19450 q^{68} -2.48553 q^{69} +1.30651 q^{70} -16.4286 q^{71} +2.42659 q^{72} -13.9035 q^{73} +3.51447 q^{74} -2.49361 q^{75} +5.28237 q^{76} -1.45073 q^{77} -2.48553 q^{78} -11.4266 q^{79} +1.30651 q^{80} +4.16814 q^{81} -1.00000 q^{82} -0.168356 q^{83} -0.757235 q^{84} +9.39966 q^{85} -0.525138 q^{86} +4.89280 q^{87} -1.45073 q^{88} +11.9121 q^{89} +3.17036 q^{90} -3.28237 q^{91} -3.28237 q^{92} +2.27978 q^{93} -3.15489 q^{94} +6.90146 q^{95} -0.757235 q^{96} -3.62368 q^{97} -1.00000 q^{98} -3.52033 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - q^{3} + 4 q^{4} + 3 q^{5} + q^{6} - 4 q^{7} - 4 q^{8} + 9 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - q^3 + 4 * q^4 + 3 * q^5 + q^6 - 4 * q^7 - 4 * q^8 + 9 * q^9	\( 4 q - 4 q^{2} - q^{3} + 4 q^{4} + 3 q^{5} + q^{6} - 4 q^{7} - 4 q^{8} + 9 q^{9} - 3 q^{10} + 4 q^{11} - q^{12} - 6 q^{13} + 4 q^{14} + 11 q^{15} + 4 q^{16} - q^{17} - 9 q^{18} + 2 q^{19} + 3 q^{20} + q^{21} - 4 q^{22} + 6 q^{23} + q^{24} + 13 q^{25} + 6 q^{26} - 13 q^{27} - 4 q^{28} + 17 q^{29} - 11 q^{30} + 5 q^{31} - 4 q^{32} + 8 q^{33} + q^{34} - 3 q^{35} + 9 q^{36} - 6 q^{37} - 2 q^{38} + 18 q^{39} - 3 q^{40} + 4 q^{41} - q^{42} - 13 q^{43} + 4 q^{44} + 34 q^{45} - 6 q^{46} + 6 q^{47} - q^{48} + 4 q^{49} - 13 q^{50} - 11 q^{51} - 6 q^{52} + 29 q^{53} + 13 q^{54} - 16 q^{55} + 4 q^{56} + 16 q^{57} - 17 q^{58} + 16 q^{59} + 11 q^{60} + 21 q^{61} - 5 q^{62} - 9 q^{63} + 4 q^{64} + 18 q^{65} - 8 q^{66} + 4 q^{67} - q^{68} - 18 q^{69} + 3 q^{70} + 17 q^{71} - 9 q^{72} + 12 q^{73} + 6 q^{74} + 26 q^{75} + 2 q^{76} - 4 q^{77} - 18 q^{78} - 27 q^{79} + 3 q^{80} + 40 q^{81} - 4 q^{82} - 18 q^{83} + q^{84} - 29 q^{85} + 13 q^{86} - 41 q^{87} - 4 q^{88} + 37 q^{89} - 34 q^{90} + 6 q^{91} + 6 q^{92} - 47 q^{93} - 6 q^{94} + 24 q^{95} + q^{96} - 3 q^{97} - 4 q^{98} - 32 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - q^3 + 4 * q^4 + 3 * q^5 + q^6 - 4 * q^7 - 4 * q^8 + 9 * q^9 - 3 * q^10 + 4 * q^11 - q^12 - 6 * q^13 + 4 * q^14 + 11 * q^15 + 4 * q^16 - q^17 - 9 * q^18 + 2 * q^19 + 3 * q^20 + q^21 - 4 * q^22 + 6 * q^23 + q^24 + 13 * q^25 + 6 * q^26 - 13 * q^27 - 4 * q^28 + 17 * q^29 - 11 * q^30 + 5 * q^31 - 4 * q^32 + 8 * q^33 + q^34 - 3 * q^35 + 9 * q^36 - 6 * q^37 - 2 * q^38 + 18 * q^39 - 3 * q^40 + 4 * q^41 - q^42 - 13 * q^43 + 4 * q^44 + 34 * q^45 - 6 * q^46 + 6 * q^47 - q^48 + 4 * q^49 - 13 * q^50 - 11 * q^51 - 6 * q^52 + 29 * q^53 + 13 * q^54 - 16 * q^55 + 4 * q^56 + 16 * q^57 - 17 * q^58 + 16 * q^59 + 11 * q^60 + 21 * q^61 - 5 * q^62 - 9 * q^63 + 4 * q^64 + 18 * q^65 - 8 * q^66 + 4 * q^67 - q^68 - 18 * q^69 + 3 * q^70 + 17 * q^71 - 9 * q^72 + 12 * q^73 + 6 * q^74 + 26 * q^75 + 2 * q^76 - 4 * q^77 - 18 * q^78 - 27 * q^79 + 3 * q^80 + 40 * q^81 - 4 * q^82 - 18 * q^83 + q^84 - 29 * q^85 + 13 * q^86 - 41 * q^87 - 4 * q^88 + 37 * q^89 - 34 * q^90 + 6 * q^91 + 6 * q^92 - 47 * q^93 - 6 * q^94 + 24 * q^95 + q^96 - 3 * q^97 - 4 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.757235	0.437190	0.218595	−	0.975816i	$-0.429853\pi$
$3$	0.757235	0.437190	0.218595	+	0.975816i	$0.429853\pi$
$4$	1.00000	0.500000
$5$	1.30651	0.584288	0.292144	−	0.956374i	$-0.405631\pi$
$5$	1.30651	0.584288	0.292144	+	0.956374i	$0.405631\pi$
$6$	−0.757235	−0.309140
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.42659	−0.808865
$10$	−1.30651	−0.413154
$11$	1.45073	0.437411	0.218706	−	0.975791i	$-0.429817\pi$
$11$	1.45073	0.437411	0.218706	+	0.975791i	$0.429817\pi$
$12$	0.757235	0.218595
$13$	3.28237	0.910366	0.455183	−	0.890398i	$-0.349574\pi$
$13$	3.28237	0.910366	0.455183	+	0.890398i	$0.349574\pi$
$14$	1.00000	0.267261
$15$	0.989333	0.255445
$16$	1.00000	0.250000
$17$	7.19450	1.74492	0.872461	−	0.488684i	$-0.162523\pi$
$17$	7.19450	1.74492	0.872461	+	0.488684i	$0.162523\pi$
$18$	2.42659	0.571954
$19$	5.28237	1.21186	0.605930	−	0.795518i	$-0.292801\pi$
$19$	5.28237	1.21186	0.605930	+	0.795518i	$0.292801\pi$
$20$	1.30651	0.292144
$21$	−0.757235	−0.165242
$22$	−1.45073	−0.309296
$23$	−3.28237	−0.684422	−0.342211	−	0.939623i	$-0.611176\pi$
$23$	−3.28237	−0.684422	−0.342211	+	0.939623i	$0.611176\pi$
$24$	−0.757235	−0.154570
$25$	−3.29304	−0.658608
$26$	−3.28237	−0.643726
$27$	−4.10921	−0.790818
$28$	−1.00000	−0.188982
$29$	6.46140	1.19985	0.599925	−	0.800056i	$-0.295197\pi$
$29$	6.46140	1.19985	0.599925	+	0.800056i	$0.295197\pi$
$30$	−0.989333	−0.180627
$31$	3.01067	0.540732	0.270366	−	0.962758i	$-0.412855\pi$
$31$	3.01067	0.540732	0.270366	+	0.962758i	$0.412855\pi$
$32$	−1.00000	−0.176777
$33$	1.09854	0.191232
$34$	−7.19450	−1.23385
$35$	−1.30651	−0.220840
$36$	−2.42659	−0.404432
$37$	−3.51447	−0.577775	−0.288888	−	0.957363i	$-0.593285\pi$
$37$	−3.51447	−0.577775	−0.288888	+	0.957363i	$0.593285\pi$
$38$	−5.28237	−0.856914
$39$	2.48553	0.398003
$40$	−1.30651	−0.206577
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0.757235	0.116844
$43$	0.525138	0.0800827	0.0400414	−	0.999198i	$-0.487251\pi$
$43$	0.525138	0.0800827	0.0400414	+	0.999198i	$0.487251\pi$
$44$	1.45073	0.218706
$45$	−3.17036	−0.472610
$46$	3.28237	0.483959
$47$	3.15489	0.460188	0.230094	−	0.973168i	$-0.426097\pi$
$47$	3.15489	0.460188	0.230094	+	0.973168i	$0.426097\pi$
$48$	0.757235	0.109298
$49$	1.00000	0.142857
$50$	3.29304	0.465706
$51$	5.44793	0.762862
$52$	3.28237	0.455183
$53$	11.6874	1.60539	0.802696	−	0.596389i	$-0.203398\pi$
$53$	11.6874	1.60539	0.802696	+	0.596389i	$0.203398\pi$
$54$	4.10921	0.559193
$55$	1.89539	0.255574
$56$	1.00000	0.133631
$57$	4.00000	0.529813
$58$	−6.46140	−0.848423
$59$	1.68283	0.219085	0.109543	−	0.993982i	$-0.465061\pi$
$59$	1.68283	0.219085	0.109543	+	0.993982i	$0.465061\pi$
$60$	0.989333	0.127722
$61$	−0.842311	−0.107847	−0.0539234	−	0.998545i	$-0.517173\pi$
$61$	−0.842311	−0.107847	−0.0539234	+	0.998545i	$0.517173\pi$
$62$	−3.01067	−0.382355
$63$	2.42659	0.305722
$64$	1.00000	0.125000
$65$	4.28844	0.531916
$66$	−1.09854	−0.135221
$67$	7.88799	0.963671	0.481836	−	0.876262i	$-0.339970\pi$
$67$	7.88799	0.963671	0.481836	+	0.876262i	$0.339970\pi$
$68$	7.19450	0.872461
$69$	−2.48553	−0.299223
$70$	1.30651	0.156157
$71$	−16.4286	−1.94972	−0.974858	−	0.222826i	$-0.928472\pi$
$71$	−16.4286	−1.94972	−0.974858	+	0.222826i	$0.928472\pi$
$72$	2.42659	0.285977
$73$	−13.9035	−1.62728	−0.813639	−	0.581371i	$-0.802517\pi$
$73$	−13.9035	−1.62728	−0.813639	+	0.581371i	$0.802517\pi$
$74$	3.51447	0.408549
$75$	−2.49361	−0.287937
$76$	5.28237	0.605930
$77$	−1.45073	−0.165326
$78$	−2.48553	−0.281431
$79$	−11.4266	−1.28559	−0.642796	−	0.766037i	$-0.722226\pi$
$79$	−11.4266	−1.28559	−0.642796	+	0.766037i	$0.722226\pi$
$80$	1.30651	0.146072
$81$	4.16814	0.463127
$82$	−1.00000	−0.110432
$83$	−0.168356	−0.0184794	−0.00923971	−	0.999957i	$-0.502941\pi$
$83$	−0.168356	−0.0184794	−0.00923971	+	0.999957i	$0.502941\pi$
$84$	−0.757235	−0.0826212
$85$	9.39966	1.01954
$86$	−0.525138	−0.0566270
$87$	4.89280	0.524563
$88$	−1.45073	−0.154648
$89$	11.9121	1.26268	0.631341	−	0.775505i	$-0.282505\pi$
$89$	11.9121	1.26268	0.631341	+	0.775505i	$0.282505\pi$
$90$	3.17036	0.334186
$91$	−3.28237	−0.344086
$92$	−3.28237	−0.342211
$93$	2.27978	0.236403
$94$	−3.15489	−0.325402
$95$	6.90146	0.708075
$96$	−0.757235	−0.0772850
$97$	−3.62368	−0.367929	−0.183965	−	0.982933i	$-0.558893\pi$
$97$	−3.62368	−0.367929	−0.183965	+	0.982933i	$0.558893\pi$
$98$	−1.00000	−0.101015
$99$	−3.52033	−0.353806
$100$	−3.29304	−0.329304
$101$	4.38092	0.435917	0.217959	−	0.975958i	$-0.430060\pi$
$101$	4.38092	0.435917	0.217959	+	0.975958i	$0.430060\pi$
$102$	−5.44793	−0.539425
$103$	−10.3281	−1.01765	−0.508827	−	0.860869i	$-0.669921\pi$
$103$	−10.3281	−1.01765	−0.508827	+	0.860869i	$0.669921\pi$
$104$	−3.28237	−0.321863
$105$	−0.989333	−0.0965491
$106$	−11.6874	−1.13518
$107$	0.284962	0.0275484	0.0137742	−	0.999905i	$-0.495615\pi$
$107$	0.284962	0.0275484	0.0137742	+	0.999905i	$0.495615\pi$
$108$	−4.10921	−0.395409
$109$	2.47967	0.237509	0.118755	−	0.992924i	$-0.462110\pi$
$109$	2.47967	0.237509	0.118755	+	0.992924i	$0.462110\pi$
$110$	−1.89539	−0.180718
$111$	−2.66128	−0.252598
$112$	−1.00000	−0.0944911
$113$	−5.80751	−0.546325	−0.273162	−	0.961968i	$-0.588070\pi$
$113$	−5.80751	−0.546325	−0.273162	+	0.961968i	$0.588070\pi$
$114$	−4.00000	−0.374634
$115$	−4.28844	−0.399899
$116$	6.46140	0.599925
$117$	−7.96499	−0.736363
$118$	−1.68283	−0.154917
$119$	−7.19450	−0.659518
$120$	−0.989333	−0.0903134
$121$	−8.89539	−0.808672
$122$	0.842311	0.0762593
$123$	0.757235	0.0682776
$124$	3.01067	0.270366
$125$	−10.8349	−0.969104
$126$	−2.42659	−0.216178
$127$	−7.74657	−0.687397	−0.343698	−	0.939080i	$-0.611680\pi$
$127$	−7.74657	−0.687397	−0.343698	+	0.939080i	$0.611680\pi$
$128$	−1.00000	−0.0883883
$129$	0.397653	0.0350114
$130$	−4.28844	−0.376121
$131$	4.24757	0.371112	0.185556	−	0.982634i	$-0.440591\pi$
$131$	4.24757	0.371112	0.185556	+	0.982634i	$0.440591\pi$
$132$	1.09854	0.0956159
$133$	−5.28237	−0.458040
$134$	−7.88799	−0.681419
$135$	−5.36871	−0.462065
$136$	−7.19450	−0.616923
$137$	7.93040	0.677540	0.338770	−	0.940869i	$-0.389989\pi$
$137$	7.93040	0.677540	0.338770	+	0.940869i	$0.389989\pi$
$138$	2.48553	0.211582
$139$	−6.44466	−0.546629	−0.273314	−	0.961925i	$-0.588120\pi$
$139$	−6.44466	−0.546629	−0.273314	+	0.961925i	$0.588120\pi$
$140$	−1.30651	−0.110420
$141$	2.38899	0.201190
$142$	16.4286	1.37866
$143$	4.76183	0.398204
$144$	−2.42659	−0.202216
$145$	8.44186	0.701058
$146$	13.9035	1.15066
$147$	0.757235	0.0624557
$148$	−3.51447	−0.288888
$149$	11.2232	0.919443	0.459721	−	0.888063i	$-0.347949\pi$
$149$	11.2232	0.919443	0.459721	+	0.888063i	$0.347949\pi$
$150$	2.49361	0.203602
$151$	−19.6333	−1.59773	−0.798867	−	0.601507i	$-0.794567\pi$
$151$	−19.6333	−1.59773	−0.798867	+	0.601507i	$0.794567\pi$
$152$	−5.28237	−0.428457
$153$	−17.4581	−1.41141
$154$	1.45073	0.116903
$155$	3.93346	0.315943
$156$	2.48553	0.199002
$157$	12.3326	0.984252	0.492126	−	0.870524i	$-0.336220\pi$
$157$	12.3326	0.984252	0.492126	+	0.870524i	$0.336220\pi$
$158$	11.4266	0.909051
$159$	8.85013	0.701861
$160$	−1.30651	−0.103288
$161$	3.28237	0.258687
$162$	−4.16814	−0.327480
$163$	−13.0020	−1.01840	−0.509198	−	0.860649i	$-0.670058\pi$
$163$	−13.0020	−1.01840	−0.509198	+	0.860649i	$0.670058\pi$
$164$	1.00000	0.0780869
$165$	1.43525	0.111734
$166$	0.168356	0.0130669
$167$	−22.9324	−1.77456	−0.887281	−	0.461228i	$-0.847409\pi$
$167$	−22.9324	−1.77456	−0.887281	+	0.461228i	$0.847409\pi$
$168$	0.757235	0.0584220
$169$	−2.22603	−0.171233
$170$	−9.39966	−0.720921
$171$	−12.8182	−0.980231
$172$	0.525138	0.0400414
$173$	−23.3588	−1.77594	−0.887968	−	0.459905i	$-0.847883\pi$
$173$	−23.3588	−1.77594	−0.887968	+	0.459905i	$0.847883\pi$
$174$	−4.89280	−0.370922
$175$	3.29304	0.248930
$176$	1.45073	0.109353
$177$	1.27430	0.0957819
$178$	−11.9121	−0.892851
$179$	20.9865	1.56861	0.784304	−	0.620377i	$-0.213020\pi$
$179$	20.9865	1.56861	0.784304	+	0.620377i	$0.213020\pi$
$180$	−3.17036	−0.236305
$181$	−5.13355	−0.381574	−0.190787	−	0.981631i	$-0.561104\pi$
$181$	−5.13355	−0.381574	−0.190787	+	0.981631i	$0.561104\pi$
$182$	3.28237	0.243306
$183$	−0.637828	−0.0471496
$184$	3.28237	0.241980
$185$	−4.59168	−0.337587
$186$	−2.27978	−0.167162
$187$	10.4373	0.763248
$188$	3.15489	0.230094
$189$	4.10921	0.298901
$190$	−6.90146	−0.500684
$191$	13.1112	0.948694	0.474347	−	0.880338i	$-0.342684\pi$
$191$	13.1112	0.948694	0.474347	+	0.880338i	$0.342684\pi$
$192$	0.757235	0.0546488
$193$	−1.24736	−0.0897870	−0.0448935	−	0.998992i	$-0.514295\pi$
$193$	−1.24736	−0.0897870	−0.0448935	+	0.998992i	$0.514295\pi$
$194$	3.62368	0.260165
$195$	3.24736	0.232548
$196$	1.00000	0.0714286
$197$	−7.29045	−0.519423	−0.259712	−	0.965686i	$-0.583627\pi$
$197$	−7.29045	−0.519423	−0.259712	+	0.965686i	$0.583627\pi$
$198$	3.52033	0.250179
$199$	−2.86645	−0.203197	−0.101598	−	0.994825i	$-0.532396\pi$
$199$	−2.86645	−0.203197	−0.101598	+	0.994825i	$0.532396\pi$
$200$	3.29304	0.232853
$201$	5.97307	0.421308
$202$	−4.38092	−0.308240
$203$	−6.46140	−0.453501
$204$	5.44793	0.381431
$205$	1.30651	0.0912504
$206$	10.3281	0.719589
$207$	7.96499	0.553605
$208$	3.28237	0.227592
$209$	7.66329	0.530081
$210$	0.989333	0.0682705
$211$	−19.0871	−1.31401	−0.657004	−	0.753887i	$-0.728177\pi$
$211$	−19.0871	−1.31401	−0.657004	+	0.753887i	$0.728177\pi$
$212$	11.6874	0.802696
$213$	−12.4403	−0.852397
$214$	−0.284962	−0.0194796
$215$	0.686096	0.0467913
$216$	4.10921	0.279596
$217$	−3.01067	−0.204377
$218$	−2.47967	−0.167944
$219$	−10.5282	−0.711430
$220$	1.89539	0.127787
$221$	23.6150	1.58852
$222$	2.66128	0.178614
$223$	−23.2174	−1.55475	−0.777375	−	0.629037i	$-0.783449\pi$
$223$	−23.2174	−1.55475	−0.777375	+	0.629037i	$0.783449\pi$
$224$	1.00000	0.0668153
$225$	7.99087	0.532725
$226$	5.80751	0.386310
$227$	−18.4419	−1.22403	−0.612015	−	0.790847i	$-0.709641\pi$
$227$	−18.4419	−1.22403	−0.612015	+	0.790847i	$0.709641\pi$
$228$	4.00000	0.264906
$229$	18.0081	1.19001	0.595004	−	0.803723i	$-0.297151\pi$
$229$	18.0081	1.19001	0.595004	+	0.803723i	$0.297151\pi$
$230$	4.28844	0.282772
$231$	−1.09854	−0.0722788
$232$	−6.46140	−0.424211
$233$	4.38899	0.287533	0.143766	−	0.989612i	$-0.454079\pi$
$233$	4.38899	0.287533	0.143766	+	0.989612i	$0.454079\pi$
$234$	7.96499	0.520688
$235$	4.12188	0.268882
$236$	1.68283	0.109543
$237$	−8.65262	−0.562048
$238$	7.19450	0.466350
$239$	25.0020	1.61725	0.808623	−	0.588328i	$-0.200213\pi$
$239$	25.0020	1.61725	0.808623	+	0.588328i	$0.200213\pi$
$240$	0.989333	0.0638612
$241$	15.5145	0.999375	0.499687	−	0.866206i	$-0.333448\pi$
$241$	15.5145	0.999375	0.499687	+	0.866206i	$0.333448\pi$
$242$	8.89539	0.571817
$243$	15.4839	0.993292
$244$	−0.842311	−0.0539234
$245$	1.30651	0.0834697
$246$	−0.757235	−0.0482796
$247$	17.3387	1.10324
$248$	−3.01067	−0.191178
$249$	−0.127485	−0.00807902
$250$	10.8349	0.685260
$251$	−15.6076	−0.985144	−0.492572	−	0.870272i	$-0.663943\pi$
$251$	−15.6076	−0.985144	−0.492572	+	0.870272i	$0.663943\pi$
$252$	2.42659	0.152861
$253$	−4.76183	−0.299374
$254$	7.74657	0.486063
$255$	7.11776	0.445731
$256$	1.00000	0.0625000
$257$	−24.0706	−1.50148	−0.750740	−	0.660598i	$-0.770303\pi$
$257$	−24.0706	−1.50148	−0.750740	+	0.660598i	$0.770303\pi$
$258$	−0.397653	−0.0247568
$259$	3.51447	0.218379
$260$	4.28844	0.265958
$261$	−15.6792	−0.970517
$262$	−4.24757	−0.262416
$263$	−10.1971	−0.628779	−0.314390	−	0.949294i	$-0.601800\pi$
$263$	−10.1971	−0.628779	−0.314390	+	0.949294i	$0.601800\pi$
$264$	−1.09854	−0.0676106
$265$	15.2697	0.938010
$266$	5.28237	0.323883
$267$	9.02028	0.552032
$268$	7.88799	0.481836
$269$	20.0988	1.22544	0.612721	−	0.790299i	$-0.290075\pi$
$269$	20.0988	1.22544	0.612721	+	0.790299i	$0.290075\pi$
$270$	5.36871	0.326729
$271$	11.9035	0.723084	0.361542	−	0.932356i	$-0.382250\pi$
$271$	11.9035	0.723084	0.361542	+	0.932356i	$0.382250\pi$
$272$	7.19450	0.436230
$273$	−2.48553	−0.150431
$274$	−7.93040	−0.479093
$275$	−4.77731	−0.288082
$276$	−2.48553	−0.149611
$277$	−14.4586	−0.868733	−0.434366	−	0.900736i	$-0.643028\pi$
$277$	−14.4586	−0.868733	−0.434366	+	0.900736i	$0.643028\pi$
$278$	6.44466	0.386525
$279$	−7.30567	−0.437379
$280$	1.30651	0.0780787
$281$	7.80291	0.465483	0.232741	−	0.972539i	$-0.425230\pi$
$281$	7.80291	0.465483	0.232741	+	0.972539i	$0.425230\pi$
$282$	−2.38899	−0.142262
$283$	−15.8316	−0.941094	−0.470547	−	0.882375i	$-0.655943\pi$
$283$	−15.8316	−0.941094	−0.470547	+	0.882375i	$0.655943\pi$
$284$	−16.4286	−0.974858
$285$	5.22603	0.309563
$286$	−4.76183	−0.281573
$287$	−1.00000	−0.0590281
$288$	2.42659	0.142988
$289$	34.7608	2.04475
$290$	−8.44186	−0.495723
$291$	−2.74398	−0.160855
$292$	−13.9035	−0.813639
$293$	24.2361	1.41589	0.707944	−	0.706268i	$-0.249623\pi$
$293$	24.2361	1.41589	0.707944	+	0.706268i	$0.249623\pi$
$294$	−0.757235	−0.0441629
$295$	2.19862	0.128009
$296$	3.51447	0.204274
$297$	−5.96135	−0.345912
$298$	−11.2232	−0.650144
$299$	−10.7740	−0.623075
$300$	−2.49361	−0.143968
$301$	−0.525138	−0.0302684
$302$	19.6333	1.12977
$303$	3.31738	0.190579
$304$	5.28237	0.302965
$305$	−1.10049	−0.0630136
$306$	17.4581	0.998015
$307$	18.2689	1.04266	0.521331	−	0.853355i	$-0.325436\pi$
$307$	18.2689	1.04266	0.521331	+	0.853355i	$0.325436\pi$
$308$	−1.45073	−0.0826629
$309$	−7.82077	−0.444908
$310$	−3.93346	−0.223405
$311$	7.66175	0.434458	0.217229	−	0.976121i	$-0.430298\pi$
$311$	7.66175	0.434458	0.217229	+	0.976121i	$0.430298\pi$
$312$	−2.48553	−0.140715
$313$	−0.599758	−0.0339003	−0.0169502	−	0.999856i	$-0.505396\pi$
$313$	−0.599758	−0.0339003	−0.0169502	+	0.999856i	$0.505396\pi$
$314$	−12.3326	−0.695972
$315$	3.17036	0.178630
$316$	−11.4266	−0.642796
$317$	−18.7773	−1.05464	−0.527319	−	0.849667i	$-0.676803\pi$
$317$	−18.7773	−1.05464	−0.527319	+	0.849667i	$0.676803\pi$
$318$	−8.85013	−0.496291
$319$	9.37373	0.524828
$320$	1.30651	0.0730360
$321$	0.215784	0.0120439
$322$	−3.28237	−0.182919
$323$	38.0040	2.11460
$324$	4.16814	0.231564
$325$	−10.8090	−0.599575
$326$	13.0020	0.720115
$327$	1.87769	0.103837
$328$	−1.00000	−0.0552158
$329$	−3.15489	−0.173935
$330$	−1.43525	−0.0790081
$331$	−20.2074	−1.11070	−0.555349	−	0.831617i	$-0.687415\pi$
$331$	−20.2074	−1.11070	−0.555349	+	0.831617i	$0.687415\pi$
$332$	−0.168356	−0.00923971
$333$	8.52820	0.467342
$334$	22.9324	1.25481
$335$	10.3057	0.563061
$336$	−0.757235	−0.0413106
$337$	14.3977	0.784290	0.392145	−	0.919903i	$-0.371733\pi$
$337$	14.3977	0.784290	0.392145	+	0.919903i	$0.371733\pi$
$338$	2.22603	0.121080
$339$	−4.39765	−0.238848
$340$	9.39966	0.509768
$341$	4.36766	0.236522
$342$	12.8182	0.693128
$343$	−1.00000	−0.0539949
$344$	−0.525138	−0.0283135
$345$	−3.24736	−0.174832
$346$	23.3588	1.25578
$347$	26.2826	1.41092	0.705462	−	0.708748i	$-0.250740\pi$
$347$	26.2826	1.41092	0.705462	+	0.708748i	$0.250740\pi$
$348$	4.89280	0.262281
$349$	18.2420	0.976470	0.488235	−	0.872712i	$-0.337641\pi$
$349$	18.2420	0.976470	0.488235	+	0.872712i	$0.337641\pi$
$350$	−3.29304	−0.176020
$351$	−13.4880	−0.719934
$352$	−1.45073	−0.0773241
$353$	−16.3407	−0.869729	−0.434865	−	0.900496i	$-0.643204\pi$
$353$	−16.3407	−0.869729	−0.434865	+	0.900496i	$0.643204\pi$
$354$	−1.27430	−0.0677281
$355$	−21.4641	−1.13920
$356$	11.9121	0.631341
$357$	−5.44793	−0.288335
$358$	−20.9865	−1.10917
$359$	−1.69022	−0.0892066	−0.0446033	−	0.999005i	$-0.514202\pi$
$359$	−1.69022	−0.0892066	−0.0446033	+	0.999005i	$0.514202\pi$
$360$	3.17036	0.167093
$361$	8.90346	0.468603
$362$	5.13355	0.269814
$363$	−6.73590	−0.353543
$364$	−3.28237	−0.172043
$365$	−18.1650	−0.950798
$366$	0.637828	0.0333398
$367$	−12.9411	−0.675518	−0.337759	−	0.941233i	$-0.609669\pi$
$367$	−12.9411	−0.675518	−0.337759	+	0.941233i	$0.609669\pi$
$368$	−3.28237	−0.171106
$369$	−2.42659	−0.126323
$370$	4.59168	0.238710
$371$	−11.6874	−0.606781
$372$	2.27978	0.118201
$373$	16.6440	0.861792	0.430896	−	0.902402i	$-0.358198\pi$
$373$	16.6440	0.861792	0.430896	+	0.902402i	$0.358198\pi$
$374$	−10.4373	−0.539698
$375$	−8.20458	−0.423683
$376$	−3.15489	−0.162701
$377$	21.2087	1.09230
$378$	−4.10921	−0.211355
$379$	25.0995	1.28927	0.644637	−	0.764489i	$-0.277008\pi$
$379$	25.0995	1.28927	0.644637	+	0.764489i	$0.277008\pi$
$380$	6.90146	0.354037
$381$	−5.86598	−0.300523
$382$	−13.1112	−0.670828
$383$	−4.00000	−0.204390	−0.102195	−	0.994764i	$-0.532587\pi$
$383$	−4.00000	−0.204390	−0.102195	+	0.994764i	$0.532587\pi$
$384$	−0.757235	−0.0386425
$385$	−1.89539	−0.0965979
$386$	1.24736	0.0634890
$387$	−1.27430	−0.0647761
$388$	−3.62368	−0.183965
$389$	−1.24736	−0.0632437	−0.0316219	−	0.999500i	$-0.510067\pi$
$389$	−1.24736	−0.0632437	−0.0316219	+	0.999500i	$0.510067\pi$
$390$	−3.24736	−0.164437
$391$	−23.6150	−1.19426
$392$	−1.00000	−0.0505076
$393$	3.21641	0.162247
$394$	7.29045	0.367288
$395$	−14.9289	−0.751156
$396$	−3.52033	−0.176903
$397$	−27.3133	−1.37082	−0.685408	−	0.728159i	$-0.740376\pi$
$397$	−27.3133	−1.37082	−0.685408	+	0.728159i	$0.740376\pi$
$398$	2.86645	0.143682
$399$	−4.00000	−0.200250
$400$	−3.29304	−0.164652
$401$	13.4133	0.669830	0.334915	−	0.942248i	$-0.391292\pi$
$401$	13.4133	0.669830	0.334915	+	0.942248i	$0.391292\pi$
$402$	−5.97307	−0.297909
$403$	9.88213	0.492264
$404$	4.38092	0.217959
$405$	5.44571	0.270599
$406$	6.46140	0.320674
$407$	−5.09854	−0.252725
$408$	−5.44793	−0.269713
$409$	18.5434	0.916913	0.458456	−	0.888717i	$-0.348403\pi$
$409$	18.5434	0.916913	0.458456	+	0.888717i	$0.348403\pi$
$410$	−1.30651	−0.0645238
$411$	6.00518	0.296214
$412$	−10.3281	−0.508827
$413$	−1.68283	−0.0828065
$414$	−7.96499	−0.391458
$415$	−0.219958	−0.0107973
$416$	−3.28237	−0.160932
$417$	−4.88012	−0.238981
$418$	−7.66329	−0.374824
$419$	−25.8265	−1.26171	−0.630853	−	0.775903i	$-0.717295\pi$
$419$	−25.8265	−1.26171	−0.630853	+	0.775903i	$0.717295\pi$
$420$	−0.989333	−0.0482745
$421$	12.1460	0.591961	0.295980	−	0.955194i	$-0.404354\pi$
$421$	12.1460	0.591961	0.295980	+	0.955194i	$0.404354\pi$
$422$	19.0871	0.929145
$423$	−7.65563	−0.372230
$424$	−11.6874	−0.567591
$425$	−23.6918	−1.14922
$426$	12.4403	0.602735
$427$	0.842311	0.0407623
$428$	0.284962	0.0137742
$429$	3.60583	0.174091
$430$	−0.686096	−0.0330865
$431$	−26.8009	−1.29095	−0.645476	−	0.763781i	$-0.723341\pi$
$431$	−26.8009	−1.29095	−0.645476	+	0.763781i	$0.723341\pi$
$432$	−4.10921	−0.197704
$433$	13.6058	0.653854	0.326927	−	0.945050i	$-0.393987\pi$
$433$	13.6058	0.653854	0.326927	+	0.945050i	$0.393987\pi$
$434$	3.01067	0.144517
$435$	6.39247	0.306496
$436$	2.47967	0.118755
$437$	−17.3387	−0.829423
$438$	10.5282	0.503057
$439$	−15.4433	−0.737070	−0.368535	−	0.929614i	$-0.620141\pi$
$439$	−15.4433	−0.737070	−0.368535	+	0.929614i	$0.620141\pi$
$440$	−1.89539	−0.0903590
$441$	−2.42659	−0.115552
$442$	−23.6150	−1.12325
$443$	−20.2367	−0.961474	−0.480737	−	0.876865i	$-0.659631\pi$
$443$	−20.2367	−0.961474	−0.480737	+	0.876865i	$0.659631\pi$
$444$	−2.66128	−0.126299
$445$	15.5633	0.737770
$446$	23.2174	1.09937
$447$	8.49863	0.401971
$448$	−1.00000	−0.0472456
$449$	36.1832	1.70759	0.853797	−	0.520607i	$-0.174294\pi$
$449$	36.1832	1.70759	0.853797	+	0.520607i	$0.174294\pi$
$450$	−7.99087	−0.376693
$451$	1.45073	0.0683121
$452$	−5.80751	−0.273162
$453$	−14.8670	−0.698514
$454$	18.4419	0.865519
$455$	−4.28844	−0.201045
$456$	−4.00000	−0.187317
$457$	41.7369	1.95237	0.976185	−	0.216940i	$-0.0696075\pi$
$457$	41.7369	1.95237	0.976185	+	0.216940i	$0.0696075\pi$
$458$	−18.0081	−0.841462
$459$	−29.5637	−1.37992
$460$	−4.28844	−0.199950
$461$	−19.1038	−0.889754	−0.444877	−	0.895592i	$-0.646753\pi$
$461$	−19.1038	−0.889754	−0.444877	+	0.895592i	$0.646753\pi$
$462$	1.09854	0.0511088
$463$	−27.1874	−1.26350	−0.631752	−	0.775170i	$-0.717664\pi$
$463$	−27.1874	−1.26350	−0.631752	+	0.775170i	$0.717664\pi$
$464$	6.46140	0.299963
$465$	2.97855	0.138127
$466$	−4.38899	−0.203316
$467$	20.5787	0.952268	0.476134	−	0.879373i	$-0.342038\pi$
$467$	20.5787	0.952268	0.476134	+	0.879373i	$0.342038\pi$
$468$	−7.96499	−0.368182
$469$	−7.88799	−0.364234
$470$	−4.12188	−0.190128
$471$	9.33872	0.430305
$472$	−1.68283	−0.0774584
$473$	0.761832	0.0350291
$474$	8.65262	0.397428
$475$	−17.3951	−0.798140
$476$	−7.19450	−0.329759
$477$	−28.3606	−1.29854
$478$	−25.0020	−1.14357
$479$	−23.4525	−1.07157	−0.535787	−	0.844353i	$-0.679985\pi$
$479$	−23.4525	−1.07157	−0.535787	+	0.844353i	$0.679985\pi$
$480$	−0.989333	−0.0451567
$481$	−11.5358	−0.525987
$482$	−15.5145	−0.706665
$483$	2.48553	0.113095
$484$	−8.89539	−0.404336
$485$	−4.73436	−0.214976
$486$	−15.4839	−0.702364
$487$	23.0381	1.04396	0.521979	−	0.852958i	$-0.325194\pi$
$487$	23.0381	1.04396	0.521979	+	0.852958i	$0.325194\pi$
$488$	0.842311	0.0381296
$489$	−9.84558	−0.445233
$490$	−1.30651	−0.0590220
$491$	30.4073	1.37226	0.686130	−	0.727479i	$-0.259308\pi$
$491$	30.4073	1.37226	0.686130	+	0.727479i	$0.259308\pi$
$492$	0.757235	0.0341388
$493$	46.4865	2.09365
$494$	−17.3387	−0.780106
$495$	−4.59934	−0.206725
$496$	3.01067	0.135183
$497$	16.4286	0.736923
$498$	0.127485	0.00571273
$499$	25.0657	1.12210	0.561049	−	0.827783i	$-0.310398\pi$
$499$	25.0657	1.12210	0.561049	+	0.827783i	$0.310398\pi$
$500$	−10.8349	−0.484552
$501$	−17.3652	−0.775821
$502$	15.6076	0.696602
$503$	−25.3052	−1.12831	−0.564153	−	0.825671i	$-0.690797\pi$
$503$	−25.3052	−1.12831	−0.564153	+	0.825671i	$0.690797\pi$
$504$	−2.42659	−0.108089
$505$	5.72370	0.254701
$506$	4.76183	0.211689
$507$	−1.68563	−0.0748613
$508$	−7.74657	−0.343698
$509$	−37.2289	−1.65014	−0.825072	−	0.565028i	$-0.808865\pi$
$509$	−37.2289	−1.65014	−0.825072	+	0.565028i	$0.808865\pi$
$510$	−7.11776	−0.315180
$511$	13.9035	0.615053
$512$	−1.00000	−0.0441942
$513$	−21.7064	−0.958360
$514$	24.0706	1.06171
$515$	−13.4937	−0.594602
$516$	0.397653	0.0175057
$517$	4.57689	0.201291
$518$	−3.51447	−0.154417
$519$	−17.6881	−0.776422
$520$	−4.28844	−0.188061
$521$	43.5748	1.90905	0.954524	−	0.298134i	$-0.0963643\pi$
$521$	43.5748	1.90905	0.954524	+	0.298134i	$0.0963643\pi$
$522$	15.6792	0.686259
$523$	−15.8534	−0.693221	−0.346610	−	0.938009i	$-0.612667\pi$
$523$	−15.8534	−0.693221	−0.346610	+	0.938009i	$0.612667\pi$
$524$	4.24757	0.185556
$525$	2.49361	0.108830
$526$	10.1971	0.444614
$527$	21.6602	0.943534
$528$	1.09854	0.0478079
$529$	−12.2260	−0.531566
$530$	−15.2697	−0.663273
$531$	−4.08354	−0.177210
$532$	−5.28237	−0.229020
$533$	3.28237	0.142175
$534$	−9.02028	−0.390346
$535$	0.372305	0.0160962
$536$	−7.88799	−0.340709
$537$	15.8917	0.685779
$538$	−20.0988	−0.866519
$539$	1.45073	0.0624873
$540$	−5.36871	−0.231033
$541$	−24.7567	−1.06437	−0.532186	−	0.846628i	$-0.678629\pi$
$541$	−24.7567	−1.06437	−0.532186	+	0.846628i	$0.678629\pi$
$542$	−11.9035	−0.511298
$543$	−3.88731	−0.166820
$544$	−7.19450	−0.308461
$545$	3.23971	0.138774
$546$	2.48553	0.106371
$547$	20.6072	0.881098	0.440549	−	0.897728i	$-0.354784\pi$
$547$	20.6072	0.881098	0.440549	+	0.897728i	$0.354784\pi$
$548$	7.93040	0.338770
$549$	2.04395	0.0872336
$550$	4.77731	0.203705
$551$	34.1315	1.45405
$552$	2.48553	0.105791
$553$	11.4266	0.485908
$554$	14.4586	0.614287
$555$	−3.47698	−0.147590
$556$	−6.44466	−0.273314
$557$	−13.1388	−0.556710	−0.278355	−	0.960478i	$-0.589789\pi$
$557$	−13.1388	−0.556710	−0.278355	+	0.960478i	$0.589789\pi$
$558$	7.30567	0.309274
$559$	1.72370	0.0729046
$560$	−1.30651	−0.0552100
$561$	7.90346	0.333685
$562$	−7.80291	−0.329146
$563$	7.84712	0.330717	0.165358	−	0.986234i	$-0.447122\pi$
$563$	7.84712	0.330717	0.165358	+	0.986234i	$0.447122\pi$
$564$	2.38899	0.100595
$565$	−7.58755	−0.319211
$566$	15.8316	0.665454
$567$	−4.16814	−0.175046
$568$	16.4286	0.689329
$569$	−39.5231	−1.65689	−0.828447	−	0.560068i	$-0.810775\pi$
$569$	−39.5231	−1.65689	−0.828447	+	0.560068i	$0.810775\pi$
$570$	−5.22603	−0.218894
$571$	−18.5437	−0.776028	−0.388014	−	0.921653i	$-0.626839\pi$
$571$	−18.5437	−0.776028	−0.388014	+	0.921653i	$0.626839\pi$
$572$	4.76183	0.199102
$573$	9.92828	0.414760
$574$	1.00000	0.0417392
$575$	10.8090	0.450766
$576$	−2.42659	−0.101108
$577$	28.3905	1.18191	0.590957	−	0.806703i	$-0.298750\pi$
$577$	28.3905	1.18191	0.590957	+	0.806703i	$0.298750\pi$
$578$	−34.7608	−1.44586
$579$	−0.944546	−0.0392540
$580$	8.44186	0.350529
$581$	0.168356	0.00698456
$582$	2.74398	0.113742
$583$	16.9553	0.702216
$584$	13.9035	0.575329
$585$	−10.4063	−0.430248
$586$	−24.2361	−1.00118
$587$	13.3433	0.550738	0.275369	−	0.961339i	$-0.411200\pi$
$587$	13.3433	0.550738	0.275369	+	0.961339i	$0.411200\pi$
$588$	0.757235	0.0312279
$589$	15.9035	0.655291
$590$	−2.19862	−0.0905159
$591$	−5.52059	−0.227087
$592$	−3.51447	−0.144444
$593$	−3.51795	−0.144465	−0.0722325	−	0.997388i	$-0.523012\pi$
$593$	−3.51795	−0.144465	−0.0722325	+	0.997388i	$0.523012\pi$
$594$	5.96135	0.244597
$595$	−9.39966	−0.385348
$596$	11.2232	0.459721
$597$	−2.17057	−0.0888357
$598$	10.7740	0.440580
$599$	21.6729	0.885531	0.442765	−	0.896637i	$-0.353997\pi$
$599$	21.6729	0.885531	0.442765	+	0.896637i	$0.353997\pi$
$600$	2.49361	0.101801
$601$	19.7014	0.803635	0.401818	−	0.915720i	$-0.368379\pi$
$601$	19.7014	0.803635	0.401818	+	0.915720i	$0.368379\pi$
$602$	0.525138	0.0214030
$603$	−19.1410	−0.779480
$604$	−19.6333	−0.798867
$605$	−11.6219	−0.472497
$606$	−3.31738	−0.134760
$607$	−10.7105	−0.434726	−0.217363	−	0.976091i	$-0.569746\pi$
$607$	−10.7105	−0.434726	−0.217363	+	0.976091i	$0.569746\pi$
$608$	−5.28237	−0.214229
$609$	−4.89280	−0.198266
$610$	1.10049	0.0445573
$611$	10.3555	0.418939
$612$	−17.4581	−0.705703
$613$	−38.5744	−1.55800	−0.779002	−	0.627022i	$-0.784274\pi$
$613$	−38.5744	−1.55800	−0.779002	+	0.627022i	$0.784274\pi$
$614$	−18.2689	−0.737273
$615$	0.989333	0.0398938
$616$	1.45073	0.0584515
$617$	28.5607	1.14981	0.574905	−	0.818220i	$-0.305039\pi$
$617$	28.5607	1.14981	0.574905	+	0.818220i	$0.305039\pi$
$618$	7.82077	0.314597
$619$	10.1562	0.408213	0.204106	−	0.978949i	$-0.434571\pi$
$619$	10.1562	0.408213	0.204106	+	0.978949i	$0.434571\pi$
$620$	3.93346	0.157971
$621$	13.4880	0.541253
$622$	−7.66175	−0.307208
$623$	−11.9121	−0.477249
$624$	2.48553	0.0995008
$625$	2.30931	0.0923723
$626$	0.599758	0.0239711
$627$	5.80291	0.231746
$628$	12.3326	0.492126
$629$	−25.2848	−1.00817
$630$	−3.17036	−0.126310
$631$	14.4079	0.573567	0.286784	−	0.957995i	$-0.407414\pi$
$631$	14.4079	0.573567	0.286784	+	0.957995i	$0.407414\pi$
$632$	11.4266	0.454526
$633$	−14.4534	−0.574472
$634$	18.7773	0.745742
$635$	−10.1209	−0.401637
$636$	8.85013	0.350931
$637$	3.28237	0.130052
$638$	−9.37373	−0.371110
$639$	39.8656	1.57706
$640$	−1.30651	−0.0516442
$641$	12.8624	0.508034	0.254017	−	0.967200i	$-0.418248\pi$
$641$	12.8624	0.508034	0.254017	+	0.967200i	$0.418248\pi$
$642$	−0.215784	−0.00851630
$643$	37.9442	1.49637	0.748186	−	0.663489i	$-0.230925\pi$
$643$	37.9442	1.49637	0.748186	+	0.663489i	$0.230925\pi$
$644$	3.28237	0.129344
$645$	0.519536	0.0204567
$646$	−38.0040	−1.49525
$647$	11.4749	0.451123	0.225562	−	0.974229i	$-0.427578\pi$
$647$	11.4749	0.451123	0.225562	+	0.974229i	$0.427578\pi$
$648$	−4.16814	−0.163740
$649$	2.44132	0.0958304
$650$	10.8090	0.423963
$651$	−2.27978	−0.0893518
$652$	−13.0020	−0.509198
$653$	−41.3455	−1.61798	−0.808988	−	0.587825i	$-0.799984\pi$
$653$	−41.3455	−1.61798	−0.808988	+	0.587825i	$0.799984\pi$
$654$	−1.87769	−0.0734237
$655$	5.54948	0.216836
$656$	1.00000	0.0390434
$657$	33.7381	1.31625
$658$	3.15489	0.122990
$659$	24.2191	0.943442	0.471721	−	0.881748i	$-0.343633\pi$
$659$	24.2191	0.943442	0.471721	+	0.881748i	$0.343633\pi$
$660$	1.43525	0.0558672
$661$	9.66149	0.375789	0.187894	−	0.982189i	$-0.439834\pi$
$661$	9.66149	0.375789	0.187894	+	0.982189i	$0.439834\pi$
$662$	20.2074	0.785382
$663$	17.8821	0.694484
$664$	0.168356	0.00653346
$665$	−6.90146	−0.267627
$666$	−8.52820	−0.330461
$667$	−21.2087	−0.821204
$668$	−22.9324	−0.887281
$669$	−17.5810	−0.679721
$670$	−10.3057	−0.398144
$671$	−1.22196	−0.0471734
$672$	0.757235	0.0292110
$673$	−40.1650	−1.54825	−0.774123	−	0.633035i	$-0.781809\pi$
$673$	−40.1650	−1.54825	−0.774123	+	0.633035i	$0.781809\pi$
$674$	−14.3977	−0.554577
$675$	13.5318	0.520839
$676$	−2.22603	−0.0856165
$677$	−27.1852	−1.04481	−0.522405	−	0.852697i	$-0.674965\pi$
$677$	−27.1852	−1.04481	−0.522405	+	0.852697i	$0.674965\pi$
$678$	4.39765	0.168891
$679$	3.62368	0.139064
$680$	−9.39966	−0.360460
$681$	−13.9648	−0.535133
$682$	−4.36766	−0.167246
$683$	19.2994	0.738470	0.369235	−	0.929336i	$-0.379620\pi$
$683$	19.2994	0.738470	0.369235	+	0.929336i	$0.379620\pi$
$684$	−12.8182	−0.490115
$685$	10.3611	0.395878
$686$	1.00000	0.0381802
$687$	13.6364	0.520259
$688$	0.525138	0.0200207
$689$	38.3625	1.46149
$690$	3.24736	0.123625
$691$	21.4926	0.817615	0.408808	−	0.912621i	$-0.365945\pi$
$691$	21.4926	0.817615	0.408808	+	0.912621i	$0.365945\pi$
$692$	−23.3588	−0.887968
$693$	3.52033	0.133726
$694$	−26.2826	−0.997673
$695$	−8.41999	−0.319388
$696$	−4.89280	−0.185461
$697$	7.19450	0.272511
$698$	−18.2420	−0.690469
$699$	3.32350	0.125706
$700$	3.29304	0.124465
$701$	−37.2300	−1.40616	−0.703080	−	0.711111i	$-0.748192\pi$
$701$	−37.2300	−1.40616	−0.703080	+	0.711111i	$0.748192\pi$
$702$	13.4880	0.509070
$703$	−18.5647	−0.700183
$704$	1.45073	0.0546764
$705$	3.12124	0.117553
$706$	16.3407	0.614991
$707$	−4.38092	−0.164761
$708$	1.27430	0.0478910
$709$	−35.4003	−1.32949	−0.664744	−	0.747071i	$-0.731459\pi$
$709$	−35.4003	−1.32949	−0.664744	+	0.747071i	$0.731459\pi$
$710$	21.4641	0.805533
$711$	27.7277	1.03987
$712$	−11.9121	−0.446426
$713$	−9.88213	−0.370089
$714$	5.44793	0.203884
$715$	6.22137	0.232666
$716$	20.9865	0.784304
$717$	18.9324	0.707044
$718$	1.69022	0.0630786
$719$	−13.8821	−0.517716	−0.258858	−	0.965915i	$-0.583346\pi$
$719$	−13.8821	−0.517716	−0.258858	+	0.965915i	$0.583346\pi$
$720$	−3.17036	−0.118152
$721$	10.3281	0.384637
$722$	−8.90346	−0.331353
$723$	11.7481	0.436917
$724$	−5.13355	−0.190787
$725$	−21.2776	−0.790231
$726$	6.73590	0.249993
$727$	19.8069	0.734598	0.367299	−	0.930103i	$-0.380283\pi$
$727$	19.8069	0.734598	0.367299	+	0.930103i	$0.380283\pi$
$728$	3.28237	0.121653
$729$	−0.779478	−0.0288696
$730$	18.1650	0.672316
$731$	3.77810	0.139738
$732$	−0.637828	−0.0235748
$733$	−16.1262	−0.595636	−0.297818	−	0.954623i	$-0.596259\pi$
$733$	−16.1262	−0.595636	−0.297818	+	0.954623i	$0.596259\pi$
$734$	12.9411	0.477663
$735$	0.989333	0.0364921
$736$	3.28237	0.120990
$737$	11.4433	0.421521
$738$	2.42659	0.0893242
$739$	31.5002	1.15875	0.579377	−	0.815060i	$-0.303296\pi$
$739$	31.5002	1.15875	0.579377	+	0.815060i	$0.303296\pi$
$740$	−4.59168	−0.168794
$741$	13.1295	0.482324
$742$	11.6874	0.429059
$743$	−3.98268	−0.146110	−0.0730552	−	0.997328i	$-0.523275\pi$
$743$	−3.98268	−0.146110	−0.0730552	+	0.997328i	$0.523275\pi$
$744$	−2.27978	−0.0835809
$745$	14.6632	0.537219
$746$	−16.6440	−0.609379
$747$	0.408531	0.0149474
$748$	10.4373	0.381624
$749$	−0.284962	−0.0104123
$750$	8.20458	0.299589
$751$	32.1436	1.17294	0.586469	−	0.809972i	$-0.300518\pi$
$751$	32.1436	1.17294	0.586469	+	0.809972i	$0.300518\pi$
$752$	3.15489	0.115047
$753$	−11.8186	−0.430695
$754$	−21.2087	−0.772376
$755$	−25.6510	−0.933537
$756$	4.10921	0.149451
$757$	0.403512	0.0146659	0.00733294	−	0.999973i	$-0.497666\pi$
$757$	0.403512	0.0146659	0.00733294	+	0.999973i	$0.497666\pi$
$758$	−25.0995	−0.911655
$759$	−3.60583	−0.130883
$760$	−6.90146	−0.250342
$761$	0.997993	0.0361772	0.0180886	−	0.999836i	$-0.494242\pi$
$761$	0.997993	0.0361772	0.0180886	+	0.999836i	$0.494242\pi$
$762$	5.86598	0.212502
$763$	−2.47967	−0.0897701
$764$	13.1112	0.474347
$765$	−22.8092	−0.824667
$766$	4.00000	0.144526
$767$	5.52366	0.199448
$768$	0.757235	0.0273244
$769$	−0.595695	−0.0214813	−0.0107406	−	0.999942i	$-0.503419\pi$
$769$	−0.595695	−0.0214813	−0.0107406	+	0.999942i	$0.503419\pi$
$770$	1.89539	0.0683050
$771$	−18.2271	−0.656432
$772$	−1.24736	−0.0448935
$773$	34.2148	1.23062	0.615310	−	0.788285i	$-0.289031\pi$
$773$	34.2148	1.23062	0.615310	+	0.788285i	$0.289031\pi$
$774$	1.27430	0.0458036
$775$	−9.91424	−0.356130
$776$	3.62368	0.130083
$777$	2.66128	0.0954730
$778$	1.24736	0.0447201
$779$	5.28237	0.189261
$780$	3.24736	0.116274
$781$	−23.8334	−0.852828
$782$	23.6150	0.844471
$783$	−26.5512	−0.948863
$784$	1.00000	0.0357143
$785$	16.1127	0.575087
$786$	−3.21641	−0.114726
$787$	37.5690	1.33919	0.669595	−	0.742727i	$-0.266468\pi$
$787$	37.5690	1.33919	0.669595	+	0.742727i	$0.266468\pi$
$788$	−7.29045	−0.259712
$789$	−7.72159	−0.274896
$790$	14.9289	0.531147
$791$	5.80751	0.206491
$792$	3.52033	0.125089
$793$	−2.76478	−0.0981802
$794$	27.3133	0.969314
$795$	11.5628	0.410089
$796$	−2.86645	−0.101598
$797$	21.5101	0.761928	0.380964	−	0.924590i	$-0.375592\pi$
$797$	21.5101	0.761928	0.380964	+	0.924590i	$0.375592\pi$
$798$	4.00000	0.141598
$799$	22.6978	0.802992
$800$	3.29304	0.116427
$801$	−28.9059	−1.02134
$802$	−13.4133	−0.473641
$803$	−20.1702	−0.711789
$804$	5.97307	0.210654
$805$	4.28844	0.151148
$806$	−9.88213	−0.348083
$807$	15.2195	0.535751
$808$	−4.38092	−0.154120
$809$	−20.5982	−0.724195	−0.362097	−	0.932140i	$-0.617939\pi$
$809$	−20.5982	−0.724195	−0.362097	+	0.932140i	$0.617939\pi$
$810$	−5.44571	−0.191343
$811$	30.3481	1.06567	0.532833	−	0.846220i	$-0.321127\pi$
$811$	30.3481	1.06567	0.532833	+	0.846220i	$0.321127\pi$
$812$	−6.46140	−0.226751
$813$	9.01372	0.316125
$814$	5.09854	0.178704
$815$	−16.9872	−0.595036
$816$	5.44793	0.190716
$817$	2.77397	0.0970490
$818$	−18.5434	−0.648355
$819$	7.96499	0.278319
$820$	1.30651	0.0456252
$821$	16.5865	0.578873	0.289436	−	0.957197i	$-0.406532\pi$
$821$	16.5865	0.578873	0.289436	+	0.957197i	$0.406532\pi$
$822$	−6.00518	−0.209455
$823$	−23.9217	−0.833859	−0.416930	−	0.908939i	$-0.636894\pi$
$823$	−23.9217	−0.833859	−0.416930	+	0.908939i	$0.636894\pi$
$824$	10.3281	0.359795
$825$	−3.61755	−0.125947
$826$	1.68283	0.0585530
$827$	−29.1394	−1.01327	−0.506637	−	0.862159i	$-0.669112\pi$
$827$	−29.1394	−1.01327	−0.506637	+	0.862159i	$0.669112\pi$
$828$	7.96499	0.276802
$829$	−18.9911	−0.659589	−0.329795	−	0.944053i	$-0.606979\pi$
$829$	−18.9911	−0.659589	−0.329795	+	0.944053i	$0.606979\pi$
$830$	0.219958	0.00763484
$831$	−10.9486	−0.379801
$832$	3.28237	0.113796
$833$	7.19450	0.249275
$834$	4.88012	0.168985
$835$	−29.9613	−1.03686
$836$	7.66329	0.265040
$837$	−12.3715	−0.427620
$838$	25.8265	0.892160
$839$	42.7434	1.47567	0.737833	−	0.674983i	$-0.235849\pi$
$839$	42.7434	1.47567	0.737833	+	0.674983i	$0.235849\pi$
$840$	0.989333	0.0341352
$841$	12.7496	0.439642
$842$	−12.1460	−0.418579
$843$	5.90864	0.203504
$844$	−19.0871	−0.657004
$845$	−2.90832	−0.100049
$846$	7.65563	0.263206
$847$	8.89539	0.305649
$848$	11.6874	0.401348
$849$	−11.9883	−0.411437
$850$	23.6918	0.812621
$851$	11.5358	0.395442
$852$	−12.4403	−0.426198
$853$	−30.4304	−1.04192	−0.520958	−	0.853582i	$-0.674425\pi$
$853$	−30.4304	−1.04192	−0.520958	+	0.853582i	$0.674425\pi$
$854$	−0.842311	−0.0288233
$855$	−16.7470	−0.572737
$856$	−0.284962	−0.00973982
$857$	−39.5672	−1.35159	−0.675794	−	0.737090i	$-0.736199\pi$
$857$	−39.5672	−1.35159	−0.675794	+	0.737090i	$0.736199\pi$
$858$	−3.60583	−0.123101
$859$	−17.7286	−0.604891	−0.302445	−	0.953167i	$-0.597803\pi$
$859$	−17.7286	−0.604891	−0.302445	+	0.953167i	$0.597803\pi$
$860$	0.686096	0.0233957
$861$	−0.757235	−0.0258065
$862$	26.8009	0.912841
$863$	−6.52820	−0.222222	−0.111111	−	0.993808i	$-0.535441\pi$
$863$	−6.52820	−0.222222	−0.111111	+	0.993808i	$0.535441\pi$
$864$	4.10921	0.139798
$865$	−30.5184	−1.03766
$866$	−13.6058	−0.462345
$867$	26.3221	0.893945
$868$	−3.01067	−0.102189
$869$	−16.5769	−0.562332
$870$	−6.39247	−0.216725
$871$	25.8913	0.877294
$872$	−2.47967	−0.0839722
$873$	8.79320	0.297605
$874$	17.3387	0.586491
$875$	10.8349	0.366287
$876$	−10.5282	−0.355715
$877$	20.0065	0.675573	0.337786	−	0.941223i	$-0.390322\pi$
$877$	20.0065	0.675573	0.337786	+	0.941223i	$0.390322\pi$
$878$	15.4433	0.521187
$879$	18.3524	0.619013
$880$	1.89539	0.0638935
$881$	−4.03613	−0.135981	−0.0679903	−	0.997686i	$-0.521659\pi$
$881$	−4.03613	−0.135981	−0.0679903	+	0.997686i	$0.521659\pi$
$882$	2.42659	0.0817077
$883$	−57.2725	−1.92737	−0.963686	−	0.267039i	$-0.913955\pi$
$883$	−57.2725	−1.92737	−0.963686	+	0.267039i	$0.913955\pi$
$884$	23.6150	0.794259
$885$	1.66488	0.0559642
$886$	20.2367	0.679865
$887$	−5.83232	−0.195830	−0.0979151	−	0.995195i	$-0.531217\pi$
$887$	−5.83232	−0.195830	−0.0979151	+	0.995195i	$0.531217\pi$
$888$	2.66128	0.0893068
$889$	7.74657	0.259812
$890$	−15.5633	−0.521682
$891$	6.04685	0.202577
$892$	−23.2174	−0.777375
$893$	16.6653	0.557683
$894$	−8.49863	−0.284237
$895$	27.4191	0.916518
$896$	1.00000	0.0334077
$897$	−8.15843	−0.272402
$898$	−36.1832	−1.20745
$899$	19.4531	0.648797
$900$	7.99087	0.266362
$901$	84.0851	2.80128
$902$	−1.45073	−0.0483040
$903$	−0.397653	−0.0132331
$904$	5.80751	0.193155
$905$	−6.70703	−0.222949
$906$	14.8670	0.493924
$907$	−4.33323	−0.143883	−0.0719413	−	0.997409i	$-0.522919\pi$
$907$	−4.33323	−0.143883	−0.0719413	+	0.997409i	$0.522919\pi$
$908$	−18.4419	−0.612015
$909$	−10.6307	−0.352598
$910$	4.28844	0.142161
$911$	−25.3737	−0.840669	−0.420335	−	0.907369i	$-0.638087\pi$
$911$	−25.3737	−0.840669	−0.420335	+	0.907369i	$0.638087\pi$
$912$	4.00000	0.132453
$913$	−0.244238	−0.00808310
$914$	−41.7369	−1.38053
$915$	−0.833326	−0.0275489
$916$	18.0081	0.595004
$917$	−4.24757	−0.140267
$918$	29.5637	0.975747
$919$	23.7552	0.783611	0.391806	−	0.920048i	$-0.371851\pi$
$919$	23.7552	0.783611	0.391806	+	0.920048i	$0.371851\pi$
$920$	4.28844	0.141386
$921$	13.8339	0.455841
$922$	19.1038	0.629151
$923$	−53.9248	−1.77496
$924$	−1.09854	−0.0361394
$925$	11.5733	0.380527
$926$	27.1874	0.893433
$927$	25.0620	0.823144
$928$	−6.46140	−0.212106
$929$	−23.5906	−0.773983	−0.386991	−	0.922083i	$-0.626486\pi$
$929$	−23.5906	−0.773983	−0.386991	+	0.922083i	$0.626486\pi$
$930$	−2.97855	−0.0976706
$931$	5.28237	0.173123
$932$	4.38899	0.143766
$933$	5.80175	0.189941
$934$	−20.5787	−0.673355
$935$	13.6364	0.445956
$936$	7.96499	0.260344
$937$	−13.9954	−0.457208	−0.228604	−	0.973519i	$-0.573416\pi$
$937$	−13.9954	−0.457208	−0.228604	+	0.973519i	$0.573416\pi$
$938$	7.88799	0.257552
$939$	−0.454158	−0.0148209
$940$	4.12188	0.134441
$941$	10.1293	0.330205	0.165103	−	0.986276i	$-0.447204\pi$
$941$	10.1293	0.330205	0.165103	+	0.986276i	$0.447204\pi$
$942$	−9.33872	−0.304272
$943$	−3.28237	−0.106889
$944$	1.68283	0.0547713
$945$	5.36871	0.174644
$946$	−0.761832	−0.0247693
$947$	−48.3434	−1.57095	−0.785474	−	0.618894i	$-0.787581\pi$
$947$	−48.3434	−1.57095	−0.785474	+	0.618894i	$0.787581\pi$
$948$	−8.65262	−0.281024
$949$	−45.6364	−1.48142
$950$	17.3951	0.564370
$951$	−14.2188	−0.461078
$952$	7.19450	0.233175
$953$	36.5180	1.18293	0.591467	−	0.806329i	$-0.298549\pi$
$953$	36.5180	1.18293	0.591467	+	0.806329i	$0.298549\pi$
$954$	28.3606	0.918209
$955$	17.1299	0.554310
$956$	25.0020	0.808623
$957$	7.09812	0.229450
$958$	23.4525	0.757717
$959$	−7.93040	−0.256086
$960$	0.989333	0.0319306
$961$	−21.9359	−0.707609
$962$	11.5358	0.371929
$963$	−0.691488	−0.0222829
$964$	15.5145	0.499687
$965$	−1.62969	−0.0524614
$966$	−2.48553	−0.0799706
$967$	56.5388	1.81816	0.909082	−	0.416617i	$-0.136784\pi$
$967$	56.5388	1.81816	0.909082	+	0.416617i	$0.136784\pi$
$968$	8.89539	0.285909
$969$	28.7780	0.924482
$970$	4.73436	0.152011
$971$	7.33370	0.235350	0.117675	−	0.993052i	$-0.462456\pi$
$971$	7.33370	0.235350	0.117675	+	0.993052i	$0.462456\pi$
$972$	15.4839	0.496646
$973$	6.44466	0.206606
$974$	−23.0381	−0.738189
$975$	−8.18495	−0.262128
$976$	−0.842311	−0.0269617
$977$	−52.2738	−1.67239	−0.836193	−	0.548435i	$-0.815224\pi$
$977$	−52.2738	−1.67239	−0.836193	+	0.548435i	$0.815224\pi$
$978$	9.84558	0.314827
$979$	17.2813	0.552311
$980$	1.30651	0.0417348
$981$	−6.01715	−0.192113
$982$	−30.4073	−0.970335
$983$	22.8014	0.727253	0.363627	−	0.931545i	$-0.381538\pi$
$983$	22.8014	0.727253	0.363627	+	0.931545i	$0.381538\pi$
$984$	−0.757235	−0.0241398
$985$	−9.52502	−0.303492
$986$	−46.4865	−1.48043
$987$	−2.38899	−0.0760425
$988$	17.3387	0.551618
$989$	−1.72370	−0.0548104
$990$	4.59934	0.146176
$991$	−41.1147	−1.30605	−0.653026	−	0.757336i	$-0.726501\pi$
$991$	−41.1147	−1.30605	−0.653026	+	0.757336i	$0.726501\pi$
$992$	−3.01067	−0.0955888
$993$	−15.3017	−0.485586
$994$	−16.4286	−0.521084
$995$	−3.74503	−0.118725
$996$	−0.127485	−0.00403951
$997$	−45.2747	−1.43386	−0.716932	−	0.697144i	$-0.754454\pi$
$997$	−45.2747	−1.43386	−0.716932	+	0.697144i	$0.754454\pi$
$998$	−25.0657	−0.793442
$999$	14.4417	0.456915

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.a.m.1.3	✓	4
3.2	odd	2		5166.2.a.bx.1.3		4
4.3	odd	2		4592.2.a.ba.1.2		4
7.6	odd	2		4018.2.a.bj.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.a.m.1.3	✓	4	1.1	even	1	trivial
4018.2.a.bj.1.2		4	7.6	odd	2
4592.2.a.ba.1.2		4	4.3	odd	2
5166.2.a.bx.1.3		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.757235 q^{3} +1.00000 q^{4} +1.30651 q^{5} -0.757235 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.42659 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.757235 q^{3} +1.00000 q^{4} +1.30651 q^{5} -0.757235 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.42659 q^{9} -1.30651 q^{10} +1.45073 q^{11} +0.757235 q^{12} +3.28237 q^{13} +1.00000 q^{14} +0.989333 q^{15} +1.00000 q^{16} +7.19450 q^{17} +2.42659 q^{18} +5.28237 q^{19} +1.30651 q^{20} -0.757235 q^{21} -1.45073 q^{22} -3.28237 q^{23} -0.757235 q^{24} -3.29304 q^{25} -3.28237 q^{26} -4.10921 q^{27} -1.00000 q^{28} +6.46140 q^{29} -0.989333 q^{30} +3.01067 q^{31} -1.00000 q^{32} +1.09854 q^{33} -7.19450 q^{34} -1.30651 q^{35} -2.42659 q^{36} -3.51447 q^{37} -5.28237 q^{38} +2.48553 q^{39} -1.30651 q^{40} +1.00000 q^{41} +0.757235 q^{42} +0.525138 q^{43} +1.45073 q^{44} -3.17036 q^{45} +3.28237 q^{46} +3.15489 q^{47} +0.757235 q^{48} +1.00000 q^{49} +3.29304 q^{50} +5.44793 q^{51} +3.28237 q^{52} +11.6874 q^{53} +4.10921 q^{54} +1.89539 q^{55} +1.00000 q^{56} +4.00000 q^{57} -6.46140 q^{58} +1.68283 q^{59} +0.989333 q^{60} -0.842311 q^{61} -3.01067 q^{62} +2.42659 q^{63} +1.00000 q^{64} +4.28844 q^{65} -1.09854 q^{66} +7.88799 q^{67} +7.19450 q^{68} -2.48553 q^{69} +1.30651 q^{70} -16.4286 q^{71} +2.42659 q^{72} -13.9035 q^{73} +3.51447 q^{74} -2.49361 q^{75} +5.28237 q^{76} -1.45073 q^{77} -2.48553 q^{78} -11.4266 q^{79} +1.30651 q^{80} +4.16814 q^{81} -1.00000 q^{82} -0.168356 q^{83} -0.757235 q^{84} +9.39966 q^{85} -0.525138 q^{86} +4.89280 q^{87} -1.45073 q^{88} +11.9121 q^{89} +3.17036 q^{90} -3.28237 q^{91} -3.28237 q^{92} +2.27978 q^{93} -3.15489 q^{94} +6.90146 q^{95} -0.757235 q^{96} -3.62368 q^{97} -1.00000 q^{98} -3.52033 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - q^{3} + 4 q^{4} + 3 q^{5} + q^{6} - 4 q^{7} - 4 q^{8} + 9 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - q^3 + 4 * q^4 + 3 * q^5 + q^6 - 4 * q^7 - 4 * q^8 + 9 * q^9	\( 4 q - 4 q^{2} - q^{3} + 4 q^{4} + 3 q^{5} + q^{6} - 4 q^{7} - 4 q^{8} + 9 q^{9} - 3 q^{10} + 4 q^{11} - q^{12} - 6 q^{13} + 4 q^{14} + 11 q^{15} + 4 q^{16} - q^{17} - 9 q^{18} + 2 q^{19} + 3 q^{20} + q^{21} - 4 q^{22} + 6 q^{23} + q^{24} + 13 q^{25} + 6 q^{26} - 13 q^{27} - 4 q^{28} + 17 q^{29} - 11 q^{30} + 5 q^{31} - 4 q^{32} + 8 q^{33} + q^{34} - 3 q^{35} + 9 q^{36} - 6 q^{37} - 2 q^{38} + 18 q^{39} - 3 q^{40} + 4 q^{41} - q^{42} - 13 q^{43} + 4 q^{44} + 34 q^{45} - 6 q^{46} + 6 q^{47} - q^{48} + 4 q^{49} - 13 q^{50} - 11 q^{51} - 6 q^{52} + 29 q^{53} + 13 q^{54} - 16 q^{55} + 4 q^{56} + 16 q^{57} - 17 q^{58} + 16 q^{59} + 11 q^{60} + 21 q^{61} - 5 q^{62} - 9 q^{63} + 4 q^{64} + 18 q^{65} - 8 q^{66} + 4 q^{67} - q^{68} - 18 q^{69} + 3 q^{70} + 17 q^{71} - 9 q^{72} + 12 q^{73} + 6 q^{74} + 26 q^{75} + 2 q^{76} - 4 q^{77} - 18 q^{78} - 27 q^{79} + 3 q^{80} + 40 q^{81} - 4 q^{82} - 18 q^{83} + q^{84} - 29 q^{85} + 13 q^{86} - 41 q^{87} - 4 q^{88} + 37 q^{89} - 34 q^{90} + 6 q^{91} + 6 q^{92} - 47 q^{93} - 6 q^{94} + 24 q^{95} + q^{96} - 3 q^{97} - 4 q^{98} - 32 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - q^3 + 4 * q^4 + 3 * q^5 + q^6 - 4 * q^7 - 4 * q^8 + 9 * q^9 - 3 * q^10 + 4 * q^11 - q^12 - 6 * q^13 + 4 * q^14 + 11 * q^15 + 4 * q^16 - q^17 - 9 * q^18 + 2 * q^19 + 3 * q^20 + q^21 - 4 * q^22 + 6 * q^23 + q^24 + 13 * q^25 + 6 * q^26 - 13 * q^27 - 4 * q^28 + 17 * q^29 - 11 * q^30 + 5 * q^31 - 4 * q^32 + 8 * q^33 + q^34 - 3 * q^35 + 9 * q^36 - 6 * q^37 - 2 * q^38 + 18 * q^39 - 3 * q^40 + 4 * q^41 - q^42 - 13 * q^43 + 4 * q^44 + 34 * q^45 - 6 * q^46 + 6 * q^47 - q^48 + 4 * q^49 - 13 * q^50 - 11 * q^51 - 6 * q^52 + 29 * q^53 + 13 * q^54 - 16 * q^55 + 4 * q^56 + 16 * q^57 - 17 * q^58 + 16 * q^59 + 11 * q^60 + 21 * q^61 - 5 * q^62 - 9 * q^63 + 4 * q^64 + 18 * q^65 - 8 * q^66 + 4 * q^67 - q^68 - 18 * q^69 + 3 * q^70 + 17 * q^71 - 9 * q^72 + 12 * q^73 + 6 * q^74 + 26 * q^75 + 2 * q^76 - 4 * q^77 - 18 * q^78 - 27 * q^79 + 3 * q^80 + 40 * q^81 - 4 * q^82 - 18 * q^83 + q^84 - 29 * q^85 + 13 * q^86 - 41 * q^87 - 4 * q^88 + 37 * q^89 - 34 * q^90 + 6 * q^91 + 6 * q^92 - 47 * q^93 - 6 * q^94 + 24 * q^95 + q^96 - 3 * q^97 - 4 * q^98 - 32 * q^99

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