LMFDB - Embedded newform 1334.2.a.g.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, 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("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.978400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 7x^{3} + 6x^{2} + 14x + 2 $ x^5 - 2x^4 - 7x^3 + 6x^2 + 14x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.154912$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.66618 q^{3} +1.00000 q^{4} +1.70044 q^{5} -2.66618 q^{6} -0.855351 q^{7} -1.00000 q^{8} +4.10851 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.66618 q^{3} +1.00000 q^{4} +1.70044 q^{5} -2.66618 q^{6} -0.855351 q^{7} -1.00000 q^{8} +4.10851 q^{9} -1.70044 q^{10} +5.83135 q^{11} +2.66618 q^{12} +3.52153 q^{13} +0.855351 q^{14} +4.53367 q^{15} +1.00000 q^{16} -5.68859 q^{17} -4.10851 q^{18} +3.55767 q^{19} +1.70044 q^{20} -2.28052 q^{21} -5.83135 q^{22} +1.00000 q^{23} -2.66618 q^{24} -2.10851 q^{25} -3.52153 q^{26} +2.95548 q^{27} -0.855351 q^{28} -1.00000 q^{29} -4.53367 q^{30} -3.83135 q^{31} -1.00000 q^{32} +15.5474 q^{33} +5.68859 q^{34} -1.45447 q^{35} +4.10851 q^{36} -9.92270 q^{37} -3.55767 q^{38} +9.38903 q^{39} -1.70044 q^{40} -6.21200 q^{41} +2.28052 q^{42} +4.94670 q^{43} +5.83135 q^{44} +6.98627 q^{45} -1.00000 q^{46} +6.34758 q^{47} +2.66618 q^{48} -6.26837 q^{49} +2.10851 q^{50} -15.1668 q^{51} +3.52153 q^{52} +4.81578 q^{53} -2.95548 q^{54} +9.91586 q^{55} +0.855351 q^{56} +9.48539 q^{57} +1.00000 q^{58} +4.24130 q^{59} +4.53367 q^{60} +14.2805 q^{61} +3.83135 q^{62} -3.51422 q^{63} +1.00000 q^{64} +5.98815 q^{65} -15.5474 q^{66} +0.621238 q^{67} -5.68859 q^{68} +2.66618 q^{69} +1.45447 q^{70} -6.73323 q^{71} -4.10851 q^{72} +3.71948 q^{73} +9.92270 q^{74} -5.62165 q^{75} +3.55767 q^{76} -4.98786 q^{77} -9.38903 q^{78} +7.65244 q^{79} +1.70044 q^{80} -4.44569 q^{81} +6.21200 q^{82} -15.4097 q^{83} -2.28052 q^{84} -9.67309 q^{85} -4.94670 q^{86} -2.66618 q^{87} -5.83135 q^{88} -8.61831 q^{89} -6.98627 q^{90} -3.01214 q^{91} +1.00000 q^{92} -10.2151 q^{93} -6.34758 q^{94} +6.04960 q^{95} -2.66618 q^{96} -16.7420 q^{97} +6.26837 q^{98} +23.9582 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + q^{3} + 5 q^{4} + 3 q^{5} - q^{6} + 4 q^{7} - 5 q^{8} + 12 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 + q^3 + 5 * q^4 + 3 * q^5 - q^6 + 4 * q^7 - 5 * q^8 + 12 * q^9	\( 5 q - 5 q^{2} + q^{3} + 5 q^{4} + 3 q^{5} - q^{6} + 4 q^{7} - 5 q^{8} + 12 q^{9} - 3 q^{10} + 3 q^{11} + q^{12} - 3 q^{13} - 4 q^{14} + q^{15} + 5 q^{16} - 4 q^{17} - 12 q^{18} + 14 q^{19} + 3 q^{20} + 10 q^{21} - 3 q^{22} + 5 q^{23} - q^{24} - 2 q^{25} + 3 q^{26} + 19 q^{27} + 4 q^{28} - 5 q^{29} - q^{30} + 7 q^{31} - 5 q^{32} - q^{33} + 4 q^{34} - 10 q^{35} + 12 q^{36} + 2 q^{37} - 14 q^{38} + 17 q^{39} - 3 q^{40} + 4 q^{41} - 10 q^{42} - 9 q^{43} + 3 q^{44} + 6 q^{45} - 5 q^{46} - 13 q^{47} + q^{48} - 11 q^{49} + 2 q^{50} - 6 q^{51} - 3 q^{52} + 11 q^{53} - 19 q^{54} - 3 q^{55} - 4 q^{56} + 10 q^{57} + 5 q^{58} + 2 q^{59} + q^{60} + 50 q^{61} - 7 q^{62} + 4 q^{63} + 5 q^{64} + 11 q^{65} + q^{66} + 22 q^{67} - 4 q^{68} + q^{69} + 10 q^{70} + 2 q^{71} - 12 q^{72} + 40 q^{73} - 2 q^{74} - 20 q^{75} + 14 q^{76} - 26 q^{77} - 17 q^{78} - 3 q^{79} + 3 q^{80} + 13 q^{81} - 4 q^{82} - 18 q^{83} + 10 q^{84} + 22 q^{85} + 9 q^{86} - q^{87} - 3 q^{88} + 12 q^{89} - 6 q^{90} - 14 q^{91} + 5 q^{92} + 3 q^{93} + 13 q^{94} + 10 q^{95} - q^{96} + 11 q^{98} + 46 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + q^3 + 5 * q^4 + 3 * q^5 - q^6 + 4 * q^7 - 5 * q^8 + 12 * q^9 - 3 * q^10 + 3 * q^11 + q^12 - 3 * q^13 - 4 * q^14 + q^15 + 5 * q^16 - 4 * q^17 - 12 * q^18 + 14 * q^19 + 3 * q^20 + 10 * q^21 - 3 * q^22 + 5 * q^23 - q^24 - 2 * q^25 + 3 * q^26 + 19 * q^27 + 4 * q^28 - 5 * q^29 - q^30 + 7 * q^31 - 5 * q^32 - q^33 + 4 * q^34 - 10 * q^35 + 12 * q^36 + 2 * q^37 - 14 * q^38 + 17 * q^39 - 3 * q^40 + 4 * q^41 - 10 * q^42 - 9 * q^43 + 3 * q^44 + 6 * q^45 - 5 * q^46 - 13 * q^47 + q^48 - 11 * q^49 + 2 * q^50 - 6 * q^51 - 3 * q^52 + 11 * q^53 - 19 * q^54 - 3 * q^55 - 4 * q^56 + 10 * q^57 + 5 * q^58 + 2 * q^59 + q^60 + 50 * q^61 - 7 * q^62 + 4 * q^63 + 5 * q^64 + 11 * q^65 + q^66 + 22 * q^67 - 4 * q^68 + q^69 + 10 * q^70 + 2 * q^71 - 12 * q^72 + 40 * q^73 - 2 * q^74 - 20 * q^75 + 14 * q^76 - 26 * q^77 - 17 * q^78 - 3 * q^79 + 3 * q^80 + 13 * q^81 - 4 * q^82 - 18 * q^83 + 10 * q^84 + 22 * q^85 + 9 * q^86 - q^87 - 3 * q^88 + 12 * q^89 - 6 * q^90 - 14 * q^91 + 5 * q^92 + 3 * q^93 + 13 * q^94 + 10 * q^95 - q^96 + 11 * q^98 + 46 * 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
$3$	2.66618	1.53932	0.769659	−	0.638455i	$-0.220426\pi$
$3$	2.66618	1.53932	0.769659	+	0.638455i	$0.220426\pi$
$4$	1.00000	0.500000
$5$	1.70044	0.760460	0.380230	−	0.924892i	$-0.375845\pi$
$5$	1.70044	0.760460	0.380230	+	0.924892i	$0.375845\pi$
$6$	−2.66618	−1.08846
$7$	−0.855351	−0.323292	−0.161646	−	0.986849i	$-0.551680\pi$
$7$	−0.855351	−0.323292	−0.161646	+	0.986849i	$0.551680\pi$
$8$	−1.00000	−0.353553
$9$	4.10851	1.36950
$10$	−1.70044	−0.537726
$11$	5.83135	1.75822	0.879110	−	0.476620i	$-0.158138\pi$
$11$	5.83135	1.75822	0.879110	+	0.476620i	$0.158138\pi$
$12$	2.66618	0.769659
$13$	3.52153	0.976697	0.488348	−	0.872649i	$-0.337600\pi$
$13$	3.52153	0.976697	0.488348	+	0.872649i	$0.337600\pi$
$14$	0.855351	0.228602
$15$	4.53367	1.17059
$16$	1.00000	0.250000
$17$	−5.68859	−1.37968	−0.689842	−	0.723960i	$-0.742320\pi$
$17$	−5.68859	−1.37968	−0.689842	+	0.723960i	$0.742320\pi$
$18$	−4.10851	−0.968384
$19$	3.55767	0.816186	0.408093	−	0.912940i	$-0.366194\pi$
$19$	3.55767	0.816186	0.408093	+	0.912940i	$0.366194\pi$
$20$	1.70044	0.380230
$21$	−2.28052	−0.497650
$22$	−5.83135	−1.24325
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.66618	−0.544231
$25$	−2.10851	−0.421701
$26$	−3.52153	−0.690629
$27$	2.95548	0.568782
$28$	−0.855351	−0.161646
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−4.53367	−0.827732
$31$	−3.83135	−0.688131	−0.344066	−	0.938946i	$-0.611804\pi$
$31$	−3.83135	−0.688131	−0.344066	+	0.938946i	$0.611804\pi$
$32$	−1.00000	−0.176777
$33$	15.5474	2.70646
$34$	5.68859	0.975584
$35$	−1.45447	−0.245851
$36$	4.10851	0.684751
$37$	−9.92270	−1.63128	−0.815641	−	0.578559i	$-0.803615\pi$
$37$	−9.92270	−1.63128	−0.815641	+	0.578559i	$0.803615\pi$
$38$	−3.55767	−0.577131
$39$	9.38903	1.50345
$40$	−1.70044	−0.268863
$41$	−6.21200	−0.970151	−0.485075	−	0.874472i	$-0.661208\pi$
$41$	−6.21200	−0.970151	−0.485075	+	0.874472i	$0.661208\pi$
$42$	2.28052	0.351892
$43$	4.94670	0.754364	0.377182	−	0.926139i	$-0.376893\pi$
$43$	4.94670	0.754364	0.377182	+	0.926139i	$0.376893\pi$
$44$	5.83135	0.879110
$45$	6.98627	1.04145
$46$	−1.00000	−0.147442
$47$	6.34758	0.925889	0.462945	−	0.886387i	$-0.346793\pi$
$47$	6.34758	0.925889	0.462945	+	0.886387i	$0.346793\pi$
$48$	2.66618	0.384830
$49$	−6.26837	−0.895482
$50$	2.10851	0.298188
$51$	−15.1668	−2.12377
$52$	3.52153	0.488348
$53$	4.81578	0.661499	0.330749	−	0.943719i	$-0.392699\pi$
$53$	4.81578	0.661499	0.330749	+	0.943719i	$0.392699\pi$
$54$	−2.95548	−0.402189
$55$	9.91586	1.33705
$56$	0.855351	0.114301
$57$	9.48539	1.25637
$58$	1.00000	0.131306
$59$	4.24130	0.552170	0.276085	−	0.961133i	$-0.410963\pi$
$59$	4.24130	0.552170	0.276085	+	0.961133i	$0.410963\pi$
$60$	4.53367	0.585295
$61$	14.2805	1.82843	0.914217	−	0.405226i	$-0.132807\pi$
$61$	14.2805	1.82843	0.914217	+	0.405226i	$0.132807\pi$
$62$	3.83135	0.486582
$63$	−3.51422	−0.442750
$64$	1.00000	0.125000
$65$	5.98815	0.742738
$66$	−15.5474	−1.91376
$67$	0.621238	0.0758963	0.0379481	−	0.999280i	$-0.487918\pi$
$67$	0.621238	0.0758963	0.0379481	+	0.999280i	$0.487918\pi$
$68$	−5.68859	−0.689842
$69$	2.66618	0.320970
$70$	1.45447	0.173843
$71$	−6.73323	−0.799088	−0.399544	−	0.916714i	$-0.630832\pi$
$71$	−6.73323	−0.799088	−0.399544	+	0.916714i	$0.630832\pi$
$72$	−4.10851	−0.484192
$73$	3.71948	0.435332	0.217666	−	0.976023i	$-0.430156\pi$
$73$	3.71948	0.435332	0.217666	+	0.976023i	$0.430156\pi$
$74$	9.92270	1.15349
$75$	−5.62165	−0.649133
$76$	3.55767	0.408093
$77$	−4.98786	−0.568419
$78$	−9.38903	−1.06310
$79$	7.65244	0.860967	0.430484	−	0.902598i	$-0.358343\pi$
$79$	7.65244	0.860967	0.430484	+	0.902598i	$0.358343\pi$
$80$	1.70044	0.190115
$81$	−4.44569	−0.493966
$82$	6.21200	0.686000
$83$	−15.4097	−1.69143	−0.845716	−	0.533633i	$-0.820826\pi$
$83$	−15.4097	−1.69143	−0.845716	+	0.533633i	$0.820826\pi$
$84$	−2.28052	−0.248825
$85$	−9.67309	−1.04919
$86$	−4.94670	−0.533416
$87$	−2.66618	−0.285844
$88$	−5.83135	−0.621624
$89$	−8.61831	−0.913539	−0.456769	−	0.889585i	$-0.650994\pi$
$89$	−8.61831	−0.913539	−0.456769	+	0.889585i	$0.650994\pi$
$90$	−6.98627	−0.736417
$91$	−3.01214	−0.315759
$92$	1.00000	0.104257
$93$	−10.2151	−1.05925
$94$	−6.34758	−0.654702
$95$	6.04960	0.620676
$96$	−2.66618	−0.272116
$97$	−16.7420	−1.69990	−0.849948	−	0.526867i	$-0.823367\pi$
$97$	−16.7420	−1.69990	−0.849948	+	0.526867i	$0.823367\pi$
$98$	6.26837	0.633201
$99$	23.9582	2.40789
$100$	−2.10851	−0.210851
$101$	16.4335	1.63520	0.817600	−	0.575787i	$-0.195304\pi$
$101$	16.4335	1.63520	0.817600	+	0.575787i	$0.195304\pi$
$102$	15.1668	1.50174
$103$	−9.55928	−0.941904	−0.470952	−	0.882159i	$-0.656089\pi$
$103$	−9.55928	−0.941904	−0.470952	+	0.882159i	$0.656089\pi$
$104$	−3.52153	−0.345314
$105$	−3.87788	−0.378443
$106$	−4.81578	−0.467750
$107$	−10.6764	−1.03213	−0.516065	−	0.856549i	$-0.672604\pi$
$107$	−10.6764	−1.03213	−0.516065	+	0.856549i	$0.672604\pi$
$108$	2.95548	0.284391
$109$	19.4128	1.85940	0.929702	−	0.368312i	$-0.120064\pi$
$109$	19.4128	1.85940	0.929702	+	0.368312i	$0.120064\pi$
$110$	−9.91586	−0.945440
$111$	−26.4557	−2.51106
$112$	−0.855351	−0.0808231
$113$	1.83602	0.172718	0.0863590	−	0.996264i	$-0.472477\pi$
$113$	1.83602	0.172718	0.0863590	+	0.996264i	$0.472477\pi$
$114$	−9.48539	−0.888388
$115$	1.70044	0.158567
$116$	−1.00000	−0.0928477
$117$	14.4682	1.33759
$118$	−4.24130	−0.390444
$119$	4.86574	0.446042
$120$	−4.53367	−0.413866
$121$	23.0047	2.09133
$122$	−14.2805	−1.29290
$123$	−16.5623	−1.49337
$124$	−3.83135	−0.344066
$125$	−12.0876	−1.08115
$126$	3.51422	0.313071
$127$	−1.91710	−0.170115	−0.0850576	−	0.996376i	$-0.527107\pi$
$127$	−1.91710	−0.170115	−0.0850576	+	0.996376i	$0.527107\pi$
$128$	−1.00000	−0.0883883
$129$	13.1888	1.16121
$130$	−5.98815	−0.525195
$131$	−0.359429	−0.0314034	−0.0157017	−	0.999877i	$-0.504998\pi$
$131$	−0.359429	−0.0314034	−0.0157017	+	0.999877i	$0.504998\pi$
$132$	15.5474	1.35323
$133$	−3.04306	−0.263867
$134$	−0.621238	−0.0536668
$135$	5.02561	0.432535
$136$	5.68859	0.487792
$137$	16.4666	1.40684	0.703420	−	0.710775i	$-0.251655\pi$
$137$	16.4666	1.40684	0.703420	+	0.710775i	$0.251655\pi$
$138$	−2.66618	−0.226960
$139$	9.77421	0.829038	0.414519	−	0.910041i	$-0.363950\pi$
$139$	9.77421	0.829038	0.414519	+	0.910041i	$0.363950\pi$
$140$	−1.45447	−0.122925
$141$	16.9238	1.42524
$142$	6.73323	0.565041
$143$	20.5353	1.71725
$144$	4.10851	0.342376
$145$	−1.70044	−0.141214
$146$	−3.71948	−0.307826
$147$	−16.7126	−1.37843
$148$	−9.92270	−0.815641
$149$	−14.1687	−1.16074	−0.580371	−	0.814352i	$-0.697093\pi$
$149$	−14.1687	−1.16074	−0.580371	+	0.814352i	$0.697093\pi$
$150$	5.62165	0.459006
$151$	15.2844	1.24382	0.621912	−	0.783087i	$-0.286356\pi$
$151$	15.2844	1.24382	0.621912	+	0.783087i	$0.286356\pi$
$152$	−3.55767	−0.288565
$153$	−23.3716	−1.88948
$154$	4.98786	0.401933
$155$	−6.51498	−0.523296
$156$	9.38903	0.751724
$157$	−22.8829	−1.82625	−0.913125	−	0.407679i	$-0.866338\pi$
$157$	−22.8829	−1.82625	−0.913125	+	0.407679i	$0.866338\pi$
$158$	−7.65244	−0.608796
$159$	12.8397	1.01826
$160$	−1.70044	−0.134432
$161$	−0.855351	−0.0674111
$162$	4.44569	0.349287
$163$	0.931187	0.0729362	0.0364681	−	0.999335i	$-0.488389\pi$
$163$	0.931187	0.0729362	0.0364681	+	0.999335i	$0.488389\pi$
$164$	−6.21200	−0.485075
$165$	26.4375	2.05815
$166$	15.4097	1.19602
$167$	7.28436	0.563681	0.281840	−	0.959461i	$-0.409055\pi$
$167$	7.28436	0.563681	0.281840	+	0.959461i	$0.409055\pi$
$168$	2.28052	0.175946
$169$	−0.598830	−0.0460639
$170$	9.67309	0.741893
$171$	14.6167	1.11777
$172$	4.94670	0.377182
$173$	19.9725	1.51848	0.759242	−	0.650809i	$-0.225570\pi$
$173$	19.9725	1.51848	0.759242	+	0.650809i	$0.225570\pi$
$174$	2.66618	0.202122
$175$	1.80351	0.136333
$176$	5.83135	0.439555
$177$	11.3081	0.849966
$178$	8.61831	0.645969
$179$	−16.7730	−1.25368	−0.626838	−	0.779150i	$-0.715651\pi$
$179$	−16.7730	−1.25368	−0.626838	+	0.779150i	$0.715651\pi$
$180$	6.98627	0.520725
$181$	−4.47713	−0.332782	−0.166391	−	0.986060i	$-0.553211\pi$
$181$	−4.47713	−0.332782	−0.166391	+	0.986060i	$0.553211\pi$
$182$	3.01214	0.223275
$183$	38.0744	2.81454
$184$	−1.00000	−0.0737210
$185$	−16.8729	−1.24052
$186$	10.2151	0.749005
$187$	−33.1722	−2.42579
$188$	6.34758	0.462945
$189$	−2.52797	−0.183883
$190$	−6.04960	−0.438884
$191$	−21.7201	−1.57161	−0.785805	−	0.618474i	$-0.787751\pi$
$191$	−21.7201	−1.57161	−0.785805	+	0.618474i	$0.787751\pi$
$192$	2.66618	0.192415
$193$	10.3549	0.745361	0.372681	−	0.927960i	$-0.378439\pi$
$193$	10.3549	0.745361	0.372681	+	0.927960i	$0.378439\pi$
$194$	16.7420	1.20201
$195$	15.9655	1.14331
$196$	−6.26837	−0.447741
$197$	−8.55113	−0.609243	−0.304621	−	0.952474i	$-0.598530\pi$
$197$	−8.55113	−0.609243	−0.304621	+	0.952474i	$0.598530\pi$
$198$	−23.9582	−1.70263
$199$	11.1801	0.792536	0.396268	−	0.918135i	$-0.370305\pi$
$199$	11.1801	0.792536	0.396268	+	0.918135i	$0.370305\pi$
$200$	2.10851	0.149094
$201$	1.65633	0.116829
$202$	−16.4335	−1.15626
$203$	0.855351	0.0600339
$204$	−15.1668	−1.06189
$205$	−10.5631	−0.737761
$206$	9.55928	0.666027
$207$	4.10851	0.285561
$208$	3.52153	0.244174
$209$	20.7460	1.43503
$210$	3.87788	0.267599
$211$	−4.68294	−0.322387	−0.161194	−	0.986923i	$-0.551534\pi$
$211$	−4.68294	−0.322387	−0.161194	+	0.986923i	$0.551534\pi$
$212$	4.81578	0.330749
$213$	−17.9520	−1.23005
$214$	10.6764	0.729827
$215$	8.41156	0.573663
$216$	−2.95548	−0.201095
$217$	3.27715	0.222468
$218$	−19.4128	−1.31480
$219$	9.91680	0.670115
$220$	9.91586	0.668527
$221$	−20.0325	−1.34753
$222$	26.4557	1.77559
$223$	15.8006	1.05809	0.529043	−	0.848595i	$-0.322551\pi$
$223$	15.8006	1.05809	0.529043	+	0.848595i	$0.322551\pi$
$224$	0.855351	0.0571506
$225$	−8.66281	−0.577521
$226$	−1.83602	−0.122130
$227$	−25.1513	−1.66935	−0.834675	−	0.550743i	$-0.814345\pi$
$227$	−25.1513	−1.66935	−0.834675	+	0.550743i	$0.814345\pi$
$228$	9.48539	0.628185
$229$	−0.762291	−0.0503736	−0.0251868	−	0.999683i	$-0.508018\pi$
$229$	−0.762291	−0.0503736	−0.0251868	+	0.999683i	$0.508018\pi$
$230$	−1.70044	−0.112124
$231$	−13.2985	−0.874978
$232$	1.00000	0.0656532
$233$	−0.137732	−0.00902313	−0.00451157	−	0.999990i	$-0.501436\pi$
$233$	−0.137732	−0.00902313	−0.00451157	+	0.999990i	$0.501436\pi$
$234$	−14.4682	−0.945818
$235$	10.7937	0.704101
$236$	4.24130	0.276085
$237$	20.4028	1.32530
$238$	−4.86574	−0.315399
$239$	−7.59313	−0.491158	−0.245579	−	0.969377i	$-0.578978\pi$
$239$	−7.59313	−0.491158	−0.245579	+	0.969377i	$0.578978\pi$
$240$	4.53367	0.292647
$241$	22.2852	1.43552	0.717758	−	0.696293i	$-0.245168\pi$
$241$	22.2852	1.43552	0.717758	+	0.696293i	$0.245168\pi$
$242$	−23.0047	−1.47880
$243$	−20.7194	−1.32915
$244$	14.2805	0.914217
$245$	−10.6590	−0.680978
$246$	16.5623	1.05597
$247$	12.5284	0.797166
$248$	3.83135	0.243291
$249$	−41.0849	−2.60365
$250$	12.0876	0.764486
$251$	−18.2510	−1.15199	−0.575997	−	0.817452i	$-0.695386\pi$
$251$	−18.2510	−1.15199	−0.575997	+	0.817452i	$0.695386\pi$
$252$	−3.51422	−0.221375
$253$	5.83135	0.366614
$254$	1.91710	0.120290
$255$	−25.7902	−1.61504
$256$	1.00000	0.0625000
$257$	0.607568	0.0378990	0.0189495	−	0.999820i	$-0.493968\pi$
$257$	0.607568	0.0378990	0.0189495	+	0.999820i	$0.493968\pi$
$258$	−13.1888	−0.821097
$259$	8.48739	0.527381
$260$	5.98815	0.371369
$261$	−4.10851	−0.254310
$262$	0.359429	0.0222056
$263$	−11.9175	−0.734862	−0.367431	−	0.930051i	$-0.619763\pi$
$263$	−11.9175	−0.734862	−0.367431	+	0.930051i	$0.619763\pi$
$264$	−15.5474	−0.956878
$265$	8.18895	0.503043
$266$	3.04306	0.186582
$267$	−22.9779	−1.40623
$268$	0.621238	0.0379481
$269$	2.13434	0.130133	0.0650665	−	0.997881i	$-0.479274\pi$
$269$	2.13434	0.130133	0.0650665	+	0.997881i	$0.479274\pi$
$270$	−5.02561	−0.305849
$271$	−11.9244	−0.724357	−0.362178	−	0.932109i	$-0.617967\pi$
$271$	−11.9244	−0.724357	−0.362178	+	0.932109i	$0.617967\pi$
$272$	−5.68859	−0.344921
$273$	−8.03091	−0.486053
$274$	−16.4666	−0.994786
$275$	−12.2954	−0.741443
$276$	2.66618	0.160485
$277$	−7.68861	−0.461964	−0.230982	−	0.972958i	$-0.574194\pi$
$277$	−7.68861	−0.461964	−0.230982	+	0.972958i	$0.574194\pi$
$278$	−9.77421	−0.586218
$279$	−15.7411	−0.942397
$280$	1.45447	0.0869214
$281$	−16.8021	−1.00233	−0.501165	−	0.865351i	$-0.667095\pi$
$281$	−16.8021	−1.00233	−0.501165	+	0.865351i	$0.667095\pi$
$282$	−16.9238	−1.00780
$283$	16.8892	1.00396	0.501980	−	0.864879i	$-0.332605\pi$
$283$	16.8892	1.00396	0.501980	+	0.864879i	$0.332605\pi$
$284$	−6.73323	−0.399544
$285$	16.1293	0.955419
$286$	−20.5353	−1.21428
$287$	5.31344	0.313642
$288$	−4.10851	−0.242096
$289$	15.3600	0.903530
$290$	1.70044	0.0998532
$291$	−44.6372	−2.61668
$292$	3.71948	0.217666
$293$	−0.421325	−0.0246141	−0.0123070	−	0.999924i	$-0.503918\pi$
$293$	−0.421325	−0.0246141	−0.0123070	+	0.999924i	$0.503918\pi$
$294$	16.7126	0.974699
$295$	7.21208	0.419903
$296$	9.92270	0.576745
$297$	17.2344	1.00004
$298$	14.1687	0.820769
$299$	3.52153	0.203655
$300$	−5.62165	−0.324566
$301$	−4.23116	−0.243880
$302$	−15.2844	−0.879516
$303$	43.8148	2.51709
$304$	3.55767	0.204046
$305$	24.2832	1.39045
$306$	23.3716	1.33607
$307$	30.0457	1.71480	0.857400	−	0.514650i	$-0.172078\pi$
$307$	30.0457	1.71480	0.857400	+	0.514650i	$0.172078\pi$
$308$	−4.98786	−0.284209
$309$	−25.4867	−1.44989
$310$	6.51498	0.370026
$311$	4.44745	0.252192	0.126096	−	0.992018i	$-0.459755\pi$
$311$	4.44745	0.252192	0.126096	+	0.992018i	$0.459755\pi$
$312$	−9.38903	−0.531549
$313$	−20.3620	−1.15093	−0.575463	−	0.817828i	$-0.695178\pi$
$313$	−20.3620	−1.15093	−0.575463	+	0.817828i	$0.695178\pi$
$314$	22.8829	1.29135
$315$	−5.97571	−0.336693
$316$	7.65244	0.430484
$317$	16.8713	0.947589	0.473794	−	0.880636i	$-0.342884\pi$
$317$	16.8713	0.947589	0.473794	+	0.880636i	$0.342884\pi$
$318$	−12.8397	−0.720017
$319$	−5.83135	−0.326493
$320$	1.70044	0.0950574
$321$	−28.4653	−1.58878
$322$	0.855351	0.0476669
$323$	−20.2381	−1.12608
$324$	−4.44569	−0.246983
$325$	−7.42517	−0.411874
$326$	−0.931187	−0.0515737
$327$	51.7579	2.86222
$328$	6.21200	0.343000
$329$	−5.42941	−0.299333
$330$	−26.4375	−1.45533
$331$	10.5710	0.581033	0.290516	−	0.956870i	$-0.406173\pi$
$331$	10.5710	0.581033	0.290516	+	0.956870i	$0.406173\pi$
$332$	−15.4097	−0.845716
$333$	−40.7675	−2.23404
$334$	−7.28436	−0.398583
$335$	1.05638	0.0577161
$336$	−2.28052	−0.124413
$337$	−19.8437	−1.08096	−0.540478	−	0.841358i	$-0.681756\pi$
$337$	−19.8437	−1.08096	−0.540478	+	0.841358i	$0.681756\pi$
$338$	0.598830	0.0325721
$339$	4.89515	0.265868
$340$	−9.67309	−0.524597
$341$	−22.3420	−1.20989
$342$	−14.6167	−0.790382
$343$	11.3491	0.612795
$344$	−4.94670	−0.266708
$345$	4.53367	0.244085
$346$	−19.9725	−1.07373
$347$	−18.6615	−1.00180	−0.500902	−	0.865504i	$-0.666998\pi$
$347$	−18.6615	−1.00180	−0.500902	+	0.865504i	$0.666998\pi$
$348$	−2.66618	−0.142922
$349$	−24.8689	−1.33120	−0.665601	−	0.746307i	$-0.731825\pi$
$349$	−24.8689	−1.33120	−0.665601	+	0.746307i	$0.731825\pi$
$350$	−1.80351	−0.0964019
$351$	10.4078	0.555527
$352$	−5.83135	−0.310812
$353$	−36.7896	−1.95811	−0.979056	−	0.203593i	$-0.934738\pi$
$353$	−36.7896	−1.95811	−0.979056	+	0.203593i	$0.934738\pi$
$354$	−11.3081	−0.601017
$355$	−11.4495	−0.607674
$356$	−8.61831	−0.456769
$357$	12.9729	0.686600
$358$	16.7730	0.886482
$359$	−21.0450	−1.11071	−0.555357	−	0.831612i	$-0.687418\pi$
$359$	−21.0450	−1.11071	−0.555357	+	0.831612i	$0.687418\pi$
$360$	−6.98627	−0.368209
$361$	−6.34297	−0.333841
$362$	4.47713	0.235313
$363$	61.3346	3.21923
$364$	−3.01214	−0.157879
$365$	6.32475	0.331053
$366$	−38.0744	−1.99018
$367$	9.65552	0.504014	0.252007	−	0.967725i	$-0.418909\pi$
$367$	9.65552	0.504014	0.252007	+	0.967725i	$0.418909\pi$
$368$	1.00000	0.0521286
$369$	−25.5220	−1.32862
$370$	16.8729	0.877183
$371$	−4.11919	−0.213857
$372$	−10.2151	−0.529627
$373$	−3.19789	−0.165581	−0.0827903	−	0.996567i	$-0.526383\pi$
$373$	−3.19789	−0.165581	−0.0827903	+	0.996567i	$0.526383\pi$
$374$	33.1722	1.71529
$375$	−32.2277	−1.66423
$376$	−6.34758	−0.327351
$377$	−3.52153	−0.181368
$378$	2.52797	0.130025
$379$	20.3440	1.04500	0.522501	−	0.852639i	$-0.324999\pi$
$379$	20.3440	1.04500	0.522501	+	0.852639i	$0.324999\pi$
$380$	6.04960	0.310338
$381$	−5.11133	−0.261861
$382$	21.7201	1.11130
$383$	−15.0076	−0.766853	−0.383426	−	0.923571i	$-0.625256\pi$
$383$	−15.0076	−0.766853	−0.383426	+	0.923571i	$0.625256\pi$
$384$	−2.66618	−0.136058
$385$	−8.48154	−0.432260
$386$	−10.3549	−0.527050
$387$	20.3235	1.03310
$388$	−16.7420	−0.849948
$389$	−14.8574	−0.753302	−0.376651	−	0.926355i	$-0.622924\pi$
$389$	−14.8574	−0.753302	−0.376651	+	0.926355i	$0.622924\pi$
$390$	−15.9655	−0.808443
$391$	−5.68859	−0.287684
$392$	6.26837	0.316601
$393$	−0.958301	−0.0483399
$394$	8.55113	0.430800
$395$	13.0125	0.654731
$396$	23.9582	1.20394
$397$	5.85052	0.293629	0.146815	−	0.989164i	$-0.453098\pi$
$397$	5.85052	0.293629	0.146815	+	0.989164i	$0.453098\pi$
$398$	−11.1801	−0.560408
$399$	−8.11334	−0.406175
$400$	−2.10851	−0.105425
$401$	5.32050	0.265693	0.132847	−	0.991137i	$-0.457588\pi$
$401$	5.32050	0.265693	0.132847	+	0.991137i	$0.457588\pi$
$402$	−1.65633	−0.0826103
$403$	−13.4922	−0.672096
$404$	16.4335	0.817600
$405$	−7.55963	−0.375641
$406$	−0.855351	−0.0424504
$407$	−57.8628	−2.86815
$408$	15.1668	0.750868
$409$	−2.27676	−0.112578	−0.0562892	−	0.998415i	$-0.517927\pi$
$409$	−2.27676	−0.112578	−0.0562892	+	0.998415i	$0.517927\pi$
$410$	10.5631	0.521675
$411$	43.9030	2.16557
$412$	−9.55928	−0.470952
$413$	−3.62780	−0.178513
$414$	−4.10851	−0.201922
$415$	−26.2032	−1.28627
$416$	−3.52153	−0.172657
$417$	26.0598	1.27615
$418$	−20.7460	−1.01472
$419$	32.6799	1.59652	0.798258	−	0.602315i	$-0.205755\pi$
$419$	32.6799	1.59652	0.798258	+	0.602315i	$0.205755\pi$
$420$	−3.87788	−0.189221
$421$	22.6645	1.10460	0.552299	−	0.833646i	$-0.313751\pi$
$421$	22.6645	1.10460	0.552299	+	0.833646i	$0.313751\pi$
$422$	4.68294	0.227962
$423$	26.0791	1.26801
$424$	−4.81578	−0.233875
$425$	11.9944	0.581815
$426$	17.9520	0.869777
$427$	−12.2149	−0.591118
$428$	−10.6764	−0.516065
$429$	54.7507	2.64339
$430$	−8.41156	−0.405641
$431$	−8.70338	−0.419227	−0.209614	−	0.977784i	$-0.567221\pi$
$431$	−8.70338	−0.419227	−0.209614	+	0.977784i	$0.567221\pi$
$432$	2.95548	0.142195
$433$	38.4043	1.84559	0.922796	−	0.385290i	$-0.125899\pi$
$433$	38.4043	1.84559	0.922796	+	0.385290i	$0.125899\pi$
$434$	−3.27715	−0.157308
$435$	−4.53367	−0.217373
$436$	19.4128	0.929702
$437$	3.55767	0.170187
$438$	−9.91680	−0.473843
$439$	4.34450	0.207352	0.103676	−	0.994611i	$-0.466940\pi$
$439$	4.34450	0.207352	0.103676	+	0.994611i	$0.466940\pi$
$440$	−9.91586	−0.472720
$441$	−25.7537	−1.22636
$442$	20.0325	0.952850
$443$	−36.8543	−1.75100	−0.875501	−	0.483216i	$-0.839468\pi$
$443$	−36.8543	−1.75100	−0.875501	+	0.483216i	$0.839468\pi$
$444$	−26.4557	−1.25553
$445$	−14.6549	−0.694709
$446$	−15.8006	−0.748179
$447$	−37.7762	−1.78675
$448$	−0.855351	−0.0404115
$449$	22.7892	1.07549	0.537745	−	0.843108i	$-0.319276\pi$
$449$	22.7892	1.07549	0.537745	+	0.843108i	$0.319276\pi$
$450$	8.66281	0.408369
$451$	−36.2243	−1.70574
$452$	1.83602	0.0863590
$453$	40.7508	1.91464
$454$	25.1513	1.18041
$455$	−5.12197	−0.240122
$456$	−9.48539	−0.444194
$457$	12.5719	0.588089	0.294044	−	0.955792i	$-0.404999\pi$
$457$	12.5719	0.588089	0.294044	+	0.955792i	$0.404999\pi$
$458$	0.762291	0.0356195
$459$	−16.8125	−0.784739
$460$	1.70044	0.0792834
$461$	−13.4971	−0.628624	−0.314312	−	0.949320i	$-0.601774\pi$
$461$	−13.4971	−0.628624	−0.314312	+	0.949320i	$0.601774\pi$
$462$	13.2985	0.618703
$463$	19.1228	0.888711	0.444355	−	0.895851i	$-0.353433\pi$
$463$	19.1228	0.888711	0.444355	+	0.895851i	$0.353433\pi$
$464$	−1.00000	−0.0464238
$465$	−17.3701	−0.805519
$466$	0.137732	0.00638032
$467$	−0.400694	−0.0185419	−0.00927094	−	0.999957i	$-0.502951\pi$
$467$	−0.400694	−0.0185419	−0.00927094	+	0.999957i	$0.502951\pi$
$468$	14.4682	0.668794
$469$	−0.531377	−0.0245367
$470$	−10.7937	−0.497875
$471$	−61.0098	−2.81118
$472$	−4.24130	−0.195222
$473$	28.8459	1.32634
$474$	−20.4028	−0.937131
$475$	−7.50137	−0.344187
$476$	4.86574	0.223021
$477$	19.7857	0.905924
$478$	7.59313	0.347301
$479$	2.95436	0.134988	0.0674941	−	0.997720i	$-0.478500\pi$
$479$	2.95436	0.134988	0.0674941	+	0.997720i	$0.478500\pi$
$480$	−4.53367	−0.206933
$481$	−34.9431	−1.59327
$482$	−22.2852	−1.01506
$483$	−2.28052	−0.103767
$484$	23.0047	1.04567
$485$	−28.4688	−1.29270
$486$	20.7194	0.939853
$487$	39.8315	1.80494	0.902469	−	0.430755i	$-0.141753\pi$
$487$	39.8315	1.80494	0.902469	+	0.430755i	$0.141753\pi$
$488$	−14.2805	−0.646449
$489$	2.48271	0.112272
$490$	10.6590	0.481524
$491$	−12.5185	−0.564953	−0.282476	−	0.959274i	$-0.591156\pi$
$491$	−12.5185	−0.564953	−0.282476	+	0.959274i	$0.591156\pi$
$492$	−16.5623	−0.746686
$493$	5.68859	0.256201
$494$	−12.5284	−0.563681
$495$	40.7394	1.83110
$496$	−3.83135	−0.172033
$497$	5.75928	0.258339
$498$	41.0849	1.84106
$499$	−28.3237	−1.26794	−0.633971	−	0.773357i	$-0.718576\pi$
$499$	−28.3237	−1.26794	−0.633971	+	0.773357i	$0.718576\pi$
$500$	−12.0876	−0.540573
$501$	19.4214	0.867684
$502$	18.2510	0.814582
$503$	−14.1559	−0.631180	−0.315590	−	0.948896i	$-0.602202\pi$
$503$	−14.1559	−0.631180	−0.315590	+	0.948896i	$0.602202\pi$
$504$	3.51422	0.156536
$505$	27.9443	1.24350
$506$	−5.83135	−0.259235
$507$	−1.59659	−0.0709070
$508$	−1.91710	−0.0850576
$509$	40.3757	1.78962	0.894810	−	0.446447i	$-0.147311\pi$
$509$	40.3757	1.78962	0.894810	+	0.446447i	$0.147311\pi$
$510$	25.7902	1.14201
$511$	−3.18146	−0.140740
$512$	−1.00000	−0.0441942
$513$	10.5146	0.464231
$514$	−0.607568	−0.0267987
$515$	−16.2550	−0.716280
$516$	13.1888	0.580603
$517$	37.0150	1.62792
$518$	−8.48739	−0.372915
$519$	53.2503	2.33743
$520$	−5.98815	−0.262598
$521$	0.967224	0.0423748	0.0211874	−	0.999776i	$-0.493255\pi$
$521$	0.967224	0.0423748	0.0211874	+	0.999776i	$0.493255\pi$
$522$	4.10851	0.179824
$523$	−6.38476	−0.279186	−0.139593	−	0.990209i	$-0.544579\pi$
$523$	−6.38476	−0.279186	−0.139593	+	0.990209i	$0.544579\pi$
$524$	−0.359429	−0.0157017
$525$	4.80849	0.209860
$526$	11.9175	0.519626
$527$	21.7950	0.949404
$528$	15.5474	0.676615
$529$	1.00000	0.0434783
$530$	−8.18895	−0.355705
$531$	17.4254	0.756199
$532$	−3.04306	−0.131933
$533$	−21.8757	−0.947543
$534$	22.9779	0.994353
$535$	−18.1546	−0.784894
$536$	−0.621238	−0.0268334
$537$	−44.7199	−1.92981
$538$	−2.13434	−0.0920179
$539$	−36.5531	−1.57445
$540$	5.02561	0.216268
$541$	12.3003	0.528830	0.264415	−	0.964409i	$-0.414821\pi$
$541$	12.3003	0.528830	0.264415	+	0.964409i	$0.414821\pi$
$542$	11.9244	0.512197
$543$	−11.9368	−0.512258
$544$	5.68859	0.243896
$545$	33.0102	1.41400
$546$	8.03091	0.343691
$547$	−19.9534	−0.853145	−0.426573	−	0.904453i	$-0.640279\pi$
$547$	−19.9534	−0.853145	−0.426573	+	0.904453i	$0.640279\pi$
$548$	16.4666	0.703420
$549$	58.6716	2.50404
$550$	12.2954	0.524280
$551$	−3.55767	−0.151562
$552$	−2.66618	−0.113480
$553$	−6.54553	−0.278344
$554$	7.68861	0.326658
$555$	−44.9863	−1.90956
$556$	9.77421	0.414519
$557$	4.95719	0.210043	0.105021	−	0.994470i	$-0.466509\pi$
$557$	4.95719	0.210043	0.105021	+	0.994470i	$0.466509\pi$
$558$	15.7411	0.666376
$559$	17.4199	0.736785
$560$	−1.45447	−0.0614627
$561$	−88.4429	−3.73406
$562$	16.8021	0.708755
$563$	−20.8402	−0.878310	−0.439155	−	0.898411i	$-0.644722\pi$
$563$	−20.8402	−0.878310	−0.439155	+	0.898411i	$0.644722\pi$
$564$	16.9238	0.712619
$565$	3.12204	0.131345
$566$	−16.8892	−0.709907
$567$	3.80263	0.159695
$568$	6.73323	0.282520
$569$	35.6966	1.49648	0.748240	−	0.663428i	$-0.230899\pi$
$569$	35.6966	1.49648	0.748240	+	0.663428i	$0.230899\pi$
$570$	−16.1293	−0.675583
$571$	−27.2489	−1.14033	−0.570166	−	0.821529i	$-0.693121\pi$
$571$	−27.2489	−1.14033	−0.570166	+	0.821529i	$0.693121\pi$
$572$	20.5353	0.858623
$573$	−57.9096	−2.41921
$574$	−5.31344	−0.221779
$575$	−2.10851	−0.0879308
$576$	4.10851	0.171188
$577$	−5.69519	−0.237094	−0.118547	−	0.992948i	$-0.537824\pi$
$577$	−5.69519	−0.237094	−0.118547	+	0.992948i	$0.537824\pi$
$578$	−15.3600	−0.638892
$579$	27.6080	1.14735
$580$	−1.70044	−0.0706069
$581$	13.1807	0.546827
$582$	44.6372	1.85027
$583$	28.0825	1.16306
$584$	−3.71948	−0.153913
$585$	24.6023	1.01718
$586$	0.421325	0.0174048
$587$	13.9718	0.576679	0.288340	−	0.957528i	$-0.406897\pi$
$587$	13.9718	0.576679	0.288340	+	0.957528i	$0.406897\pi$
$588$	−16.7126	−0.689216
$589$	−13.6307	−0.561643
$590$	−7.21208	−0.296916
$591$	−22.7988	−0.937818
$592$	−9.92270	−0.407820
$593$	5.84013	0.239825	0.119913	−	0.992784i	$-0.461739\pi$
$593$	5.84013	0.239825	0.119913	+	0.992784i	$0.461739\pi$
$594$	−17.2344	−0.707137
$595$	8.27389	0.339197
$596$	−14.1687	−0.580371
$597$	29.8081	1.21997
$598$	−3.52153	−0.144006
$599$	23.3189	0.952786	0.476393	−	0.879233i	$-0.341944\pi$
$599$	23.3189	0.952786	0.476393	+	0.879233i	$0.341944\pi$
$600$	5.62165	0.229503
$601$	37.7353	1.53925	0.769627	−	0.638494i	$-0.220442\pi$
$601$	37.7353	1.53925	0.769627	+	0.638494i	$0.220442\pi$
$602$	4.23116	0.172449
$603$	2.55236	0.103940
$604$	15.2844	0.621912
$605$	39.1181	1.59038
$606$	−43.8148	−1.77985
$607$	−35.2763	−1.43182	−0.715911	−	0.698192i	$-0.753988\pi$
$607$	−35.2763	−1.43182	−0.715911	+	0.698192i	$0.753988\pi$
$608$	−3.55767	−0.144283
$609$	2.28052	0.0924113
$610$	−24.2832	−0.983196
$611$	22.3532	0.904313
$612$	−23.3716	−0.944741
$613$	−34.1983	−1.38126	−0.690629	−	0.723210i	$-0.742666\pi$
$613$	−34.1983	−1.38126	−0.690629	+	0.723210i	$0.742666\pi$
$614$	−30.0457	−1.21255
$615$	−28.1632	−1.13565
$616$	4.98786	0.200966
$617$	−7.38230	−0.297200	−0.148600	−	0.988897i	$-0.547477\pi$
$617$	−7.38230	−0.297200	−0.148600	+	0.988897i	$0.547477\pi$
$618$	25.4867	1.02523
$619$	−45.2476	−1.81865	−0.909326	−	0.416084i	$-0.863402\pi$
$619$	−45.2476	−1.81865	−0.909326	+	0.416084i	$0.863402\pi$
$620$	−6.51498	−0.261648
$621$	2.95548	0.118599
$622$	−4.44745	−0.178327
$623$	7.37168	0.295340
$624$	9.38903	0.375862
$625$	−10.0117	−0.400467
$626$	20.3620	0.813827
$627$	55.3126	2.20897
$628$	−22.8829	−0.913125
$629$	56.4461	2.25065
$630$	5.97571	0.238078
$631$	5.27078	0.209826	0.104913	−	0.994481i	$-0.466544\pi$
$631$	5.27078	0.209826	0.104913	+	0.994481i	$0.466544\pi$
$632$	−7.65244	−0.304398
$633$	−12.4856	−0.496256
$634$	−16.8713	−0.670046
$635$	−3.25991	−0.129366
$636$	12.8397	0.509129
$637$	−22.0743	−0.874614
$638$	5.83135	0.230865
$639$	−27.6635	−1.09435
$640$	−1.70044	−0.0672158
$641$	24.3500	0.961768	0.480884	−	0.876784i	$-0.340316\pi$
$641$	24.3500	0.961768	0.480884	+	0.876784i	$0.340316\pi$
$642$	28.4653	1.12344
$643$	−21.6256	−0.852832	−0.426416	−	0.904527i	$-0.640224\pi$
$643$	−21.6256	−0.852832	−0.426416	+	0.904527i	$0.640224\pi$
$644$	−0.855351	−0.0337056
$645$	22.4267	0.883051
$646$	20.2381	0.796258
$647$	−26.1922	−1.02972	−0.514862	−	0.857273i	$-0.672157\pi$
$647$	−26.1922	−1.02972	−0.514862	+	0.857273i	$0.672157\pi$
$648$	4.44569	0.174643
$649$	24.7325	0.970837
$650$	7.42517	0.291239
$651$	8.73747	0.342449
$652$	0.931187	0.0364681
$653$	21.3985	0.837389	0.418695	−	0.908127i	$-0.362488\pi$
$653$	21.3985	0.837389	0.418695	+	0.908127i	$0.362488\pi$
$654$	−51.7579	−2.02389
$655$	−0.611187	−0.0238810
$656$	−6.21200	−0.242538
$657$	15.2815	0.596189
$658$	5.42941	0.211660
$659$	−32.0676	−1.24918	−0.624588	−	0.780955i	$-0.714733\pi$
$659$	−32.0676	−1.24918	−0.624588	+	0.780955i	$0.714733\pi$
$660$	26.4375	1.02908
$661$	11.8565	0.461166	0.230583	−	0.973053i	$-0.425937\pi$
$661$	11.8565	0.461166	0.230583	+	0.973053i	$0.425937\pi$
$662$	−10.5710	−0.410852
$663$	−53.4103	−2.07428
$664$	15.4097	0.598011
$665$	−5.17454	−0.200660
$666$	40.7675	1.57971
$667$	−1.00000	−0.0387202
$668$	7.28436	0.281840
$669$	42.1272	1.62873
$670$	−1.05638	−0.0408114
$671$	83.2748	3.21479
$672$	2.28052	0.0879729
$673$	−0.182214	−0.00702384	−0.00351192	−	0.999994i	$-0.501118\pi$
$673$	−0.182214	−0.00702384	−0.00351192	+	0.999994i	$0.501118\pi$
$674$	19.8437	0.764351
$675$	−6.23164	−0.239856
$676$	−0.598830	−0.0230319
$677$	30.5773	1.17518	0.587590	−	0.809159i	$-0.300077\pi$
$677$	30.5773	1.17518	0.587590	+	0.809159i	$0.300077\pi$
$678$	−4.89515	−0.187997
$679$	14.3203	0.549563
$680$	9.67309	0.370946
$681$	−67.0578	−2.56966
$682$	22.3420	0.855519
$683$	−3.92478	−0.150178	−0.0750889	−	0.997177i	$-0.523924\pi$
$683$	−3.92478	−0.150178	−0.0750889	+	0.997177i	$0.523924\pi$
$684$	14.6167	0.558884
$685$	28.0005	1.06984
$686$	−11.3491	−0.433311
$687$	−2.03240	−0.0775410
$688$	4.94670	0.188591
$689$	16.9589	0.646083
$690$	−4.53367	−0.172594
$691$	21.0485	0.800724	0.400362	−	0.916357i	$-0.368884\pi$
$691$	21.0485	0.800724	0.400362	+	0.916357i	$0.368884\pi$
$692$	19.9725	0.759242
$693$	−20.4926	−0.778451
$694$	18.6615	0.708382
$695$	16.6204	0.630450
$696$	2.66618	0.101061
$697$	35.3375	1.33850
$698$	24.8689	0.941303
$699$	−0.367218	−0.0138895
$700$	1.80351	0.0681664
$701$	−6.32855	−0.239026	−0.119513	−	0.992833i	$-0.538133\pi$
$701$	−6.32855	−0.239026	−0.119513	+	0.992833i	$0.538133\pi$
$702$	−10.4078	−0.392817
$703$	−35.3017	−1.33143
$704$	5.83135	0.219777
$705$	28.7778	1.08384
$706$	36.7896	1.38459
$707$	−14.0565	−0.528647
$708$	11.3081	0.424983
$709$	−17.8754	−0.671323	−0.335662	−	0.941983i	$-0.608960\pi$
$709$	−17.8754	−0.671323	−0.335662	+	0.941983i	$0.608960\pi$
$710$	11.4495	0.429690
$711$	31.4401	1.17910
$712$	8.61831	0.322985
$713$	−3.83135	−0.143485
$714$	−12.9729	−0.485500
$715$	34.9190	1.30590
$716$	−16.7730	−0.626838
$717$	−20.2446	−0.756049
$718$	21.0450	0.785393
$719$	29.6529	1.10587	0.552934	−	0.833225i	$-0.313508\pi$
$719$	29.6529	1.10587	0.552934	+	0.833225i	$0.313508\pi$
$720$	6.98627	0.260363
$721$	8.17654	0.304510
$722$	6.34297	0.236061
$723$	59.4163	2.20972
$724$	−4.47713	−0.166391
$725$	2.10851	0.0783080
$726$	−61.3346	−2.27634
$727$	10.7183	0.397519	0.198759	−	0.980048i	$-0.436309\pi$
$727$	10.7183	0.397519	0.198759	+	0.980048i	$0.436309\pi$
$728$	3.01214	0.111638
$729$	−41.9046	−1.55202
$730$	−6.32475	−0.234090
$731$	−28.1397	−1.04078
$732$	38.0744	1.40727
$733$	15.0377	0.555430	0.277715	−	0.960663i	$-0.410423\pi$
$733$	15.0377	0.555430	0.277715	+	0.960663i	$0.410423\pi$
$734$	−9.65552	−0.356392
$735$	−28.4188	−1.04824
$736$	−1.00000	−0.0368605
$737$	3.62266	0.133442
$738$	25.5220	0.939479
$739$	−12.6539	−0.465480	−0.232740	−	0.972539i	$-0.574769\pi$
$739$	−12.6539	−0.465480	−0.232740	+	0.972539i	$0.574769\pi$
$740$	−16.8729	−0.620262
$741$	33.4031	1.22709
$742$	4.11919	0.151220
$743$	−13.6380	−0.500328	−0.250164	−	0.968203i	$-0.580485\pi$
$743$	−13.6380	−0.500328	−0.250164	+	0.968203i	$0.580485\pi$
$744$	10.2151	0.374503
$745$	−24.0930	−0.882698
$746$	3.19789	0.117083
$747$	−63.3108	−2.31642
$748$	−33.1722	−1.21289
$749$	9.13211	0.333680
$750$	32.2277	1.17679
$751$	28.7725	1.04992	0.524961	−	0.851126i	$-0.324080\pi$
$751$	28.7725	1.04992	0.524961	+	0.851126i	$0.324080\pi$
$752$	6.34758	0.231472
$753$	−48.6604	−1.77328
$754$	3.52153	0.128247
$755$	25.9901	0.945878
$756$	−2.52797	−0.0919414
$757$	44.9191	1.63261	0.816307	−	0.577618i	$-0.196018\pi$
$757$	44.9191	1.63261	0.816307	+	0.577618i	$0.196018\pi$
$758$	−20.3440	−0.738928
$759$	15.5474	0.564336
$760$	−6.04960	−0.219442
$761$	2.74546	0.0995228	0.0497614	−	0.998761i	$-0.484154\pi$
$761$	2.74546	0.0995228	0.0497614	+	0.998761i	$0.484154\pi$
$762$	5.11133	0.185164
$763$	−16.6047	−0.601131
$764$	−21.7201	−0.785805
$765$	−39.7420	−1.43687
$766$	15.0076	0.542247
$767$	14.9359	0.539303
$768$	2.66618	0.0962074
$769$	31.1169	1.12210	0.561051	−	0.827781i	$-0.310397\pi$
$769$	31.1169	1.12210	0.561051	+	0.827781i	$0.310397\pi$
$770$	8.48154	0.305654
$771$	1.61988	0.0583387
$772$	10.3549	0.372681
$773$	51.5614	1.85453	0.927267	−	0.374400i	$-0.122151\pi$
$773$	51.5614	1.85453	0.927267	+	0.374400i	$0.122151\pi$
$774$	−20.3235	−0.730514
$775$	8.07843	0.290186
$776$	16.7420	0.601004
$777$	22.6289	0.811807
$778$	14.8574	0.532665
$779$	−22.1002	−0.791823
$780$	15.9655	0.571655
$781$	−39.2639	−1.40497
$782$	5.68859	0.203423
$783$	−2.95548	−0.105620
$784$	−6.26837	−0.223871
$785$	−38.9109	−1.38879
$786$	0.958301	0.0341815
$787$	−36.3326	−1.29512	−0.647558	−	0.762016i	$-0.724210\pi$
$787$	−36.3326	−1.29512	−0.647558	+	0.762016i	$0.724210\pi$
$788$	−8.55113	−0.304621
$789$	−31.7741	−1.13119
$790$	−13.0125	−0.462965
$791$	−1.57044	−0.0558384
$792$	−23.9582	−0.851316
$793$	50.2893	1.78582
$794$	−5.85052	−0.207627
$795$	21.8332	0.774343
$796$	11.1801	0.396268
$797$	−3.32566	−0.117801	−0.0589005	−	0.998264i	$-0.518759\pi$
$797$	−3.32566	−0.117801	−0.0589005	+	0.998264i	$0.518759\pi$
$798$	8.11334	0.287209
$799$	−36.1087	−1.27744
$800$	2.10851	0.0745470
$801$	−35.4084	−1.25109
$802$	−5.32050	−0.187874
$803$	21.6896	0.765410
$804$	1.65633	0.0584143
$805$	−1.45447	−0.0512634
$806$	13.4922	0.475243
$807$	5.69053	0.200316
$808$	−16.4335	−0.578130
$809$	−7.08203	−0.248991	−0.124495	−	0.992220i	$-0.539731\pi$
$809$	−7.08203	−0.248991	−0.124495	+	0.992220i	$0.539731\pi$
$810$	7.55963	0.265618
$811$	5.69088	0.199834	0.0999169	−	0.994996i	$-0.468142\pi$
$811$	5.69088	0.199834	0.0999169	+	0.994996i	$0.468142\pi$
$812$	0.855351	0.0300169
$813$	−31.7926	−1.11502
$814$	57.8628	2.02809
$815$	1.58343	0.0554650
$816$	−15.1668	−0.530944
$817$	17.5987	0.615701
$818$	2.27676	0.0796049
$819$	−12.3754	−0.432432
$820$	−10.5631	−0.368880
$821$	37.9023	1.32280	0.661400	−	0.750033i	$-0.269963\pi$
$821$	37.9023	1.32280	0.661400	+	0.750033i	$0.269963\pi$
$822$	−43.9030	−1.53129
$823$	7.88827	0.274968	0.137484	−	0.990504i	$-0.456098\pi$
$823$	7.88827	0.274968	0.137484	+	0.990504i	$0.456098\pi$
$824$	9.55928	0.333013
$825$	−32.7819	−1.14132
$826$	3.62780	0.126227
$827$	−16.5985	−0.577185	−0.288593	−	0.957452i	$-0.593187\pi$
$827$	−16.5985	−0.577185	−0.288593	+	0.957452i	$0.593187\pi$
$828$	4.10851	0.142780
$829$	−21.8176	−0.757756	−0.378878	−	0.925447i	$-0.623690\pi$
$829$	−21.8176	−0.757756	−0.378878	+	0.925447i	$0.623690\pi$
$830$	26.2032	0.909527
$831$	−20.4992	−0.711109
$832$	3.52153	0.122087
$833$	35.6582	1.23548
$834$	−26.0598	−0.902376
$835$	12.3866	0.428656
$836$	20.7460	0.717517
$837$	−11.3235	−0.391396
$838$	−32.6799	−1.12891
$839$	34.2556	1.18264	0.591318	−	0.806439i	$-0.298608\pi$
$839$	34.2556	1.18264	0.591318	+	0.806439i	$0.298608\pi$
$840$	3.87788	0.133800
$841$	1.00000	0.0344828
$842$	−22.6645	−0.781069
$843$	−44.7975	−1.54291
$844$	−4.68294	−0.161194
$845$	−1.01827	−0.0350297
$846$	−26.0791	−0.896616
$847$	−19.6771	−0.676113
$848$	4.81578	0.165375
$849$	45.0297	1.54541
$850$	−11.9944	−0.411405
$851$	−9.92270	−0.340146
$852$	−17.9520	−0.615026
$853$	38.5831	1.32106	0.660530	−	0.750800i	$-0.270332\pi$
$853$	38.5831	1.32106	0.660530	+	0.750800i	$0.270332\pi$
$854$	12.2149	0.417984
$855$	24.8548	0.850018
$856$	10.6764	0.364913
$857$	14.3892	0.491526	0.245763	−	0.969330i	$-0.420962\pi$
$857$	14.3892	0.491526	0.245763	+	0.969330i	$0.420962\pi$
$858$	−54.7507	−1.86916
$859$	2.56173	0.0874050	0.0437025	−	0.999045i	$-0.486085\pi$
$859$	2.56173	0.0874050	0.0437025	+	0.999045i	$0.486085\pi$
$860$	8.41156	0.286832
$861$	14.1666	0.482796
$862$	8.70338	0.296438
$863$	16.9392	0.576616	0.288308	−	0.957538i	$-0.406907\pi$
$863$	16.9392	0.576616	0.288308	+	0.957538i	$0.406907\pi$
$864$	−2.95548	−0.100547
$865$	33.9621	1.15475
$866$	−38.4043	−1.30503
$867$	40.9525	1.39082
$868$	3.27715	0.111234
$869$	44.6241	1.51377
$870$	4.53367	0.153706
$871$	2.18771	0.0741276
$872$	−19.4128	−0.657399
$873$	−68.7848	−2.32801
$874$	−3.55767	−0.120340
$875$	10.3391	0.349526
$876$	9.91680	0.335058
$877$	−41.9655	−1.41707	−0.708537	−	0.705674i	$-0.750644\pi$
$877$	−41.9655	−1.41707	−0.708537	+	0.705674i	$0.750644\pi$
$878$	−4.34450	−0.146620
$879$	−1.12333	−0.0378889
$880$	9.91586	0.334264
$881$	−51.7200	−1.74249	−0.871246	−	0.490847i	$-0.836687\pi$
$881$	−51.7200	−1.74249	−0.871246	+	0.490847i	$0.836687\pi$
$882$	25.7537	0.867171
$883$	19.4048	0.653024	0.326512	−	0.945193i	$-0.394127\pi$
$883$	19.4048	0.653024	0.326512	+	0.945193i	$0.394127\pi$
$884$	−20.0325	−0.673767
$885$	19.2287	0.646365
$886$	36.8543	1.23815
$887$	27.7780	0.932693	0.466347	−	0.884602i	$-0.345570\pi$
$887$	27.7780	0.932693	0.466347	+	0.884602i	$0.345570\pi$
$888$	26.4557	0.887795
$889$	1.63979	0.0549969
$890$	14.6549	0.491234
$891$	−25.9244	−0.868501
$892$	15.8006	0.529043
$893$	22.5826	0.755698
$894$	37.7762	1.26342
$895$	−28.5215	−0.953369
$896$	0.855351	0.0285753
$897$	9.38903	0.313490
$898$	−22.7892	−0.760486
$899$	3.83135	0.127783
$900$	−8.66281	−0.288760
$901$	−27.3950	−0.912660
$902$	36.2243	1.20614
$903$	−11.2810	−0.375409
$904$	−1.83602	−0.0610650
$905$	−7.61309	−0.253068
$906$	−40.7508	−1.35386
$907$	−5.19013	−0.172336	−0.0861678	−	0.996281i	$-0.527462\pi$
$907$	−5.19013	−0.172336	−0.0861678	+	0.996281i	$0.527462\pi$
$908$	−25.1513	−0.834675
$909$	67.5173	2.23941
$910$	5.12197	0.169792
$911$	3.78632	0.125447	0.0627233	−	0.998031i	$-0.480021\pi$
$911$	3.78632	0.125447	0.0627233	+	0.998031i	$0.480021\pi$
$912$	9.48539	0.314093
$913$	−89.8593	−2.97391
$914$	−12.5719	−0.415842
$915$	64.7432	2.14034
$916$	−0.762291	−0.0251868
$917$	0.307438	0.0101525
$918$	16.8125	0.554894
$919$	−45.8918	−1.51383	−0.756915	−	0.653514i	$-0.773294\pi$
$919$	−45.8918	−1.51383	−0.756915	+	0.653514i	$0.773294\pi$
$920$	−1.70044	−0.0560618
$921$	80.1073	2.63962
$922$	13.4971	0.444504
$923$	−23.7113	−0.780466
$924$	−13.2985	−0.437489
$925$	20.9221	0.687914
$926$	−19.1228	−0.628413
$927$	−39.2744	−1.28994
$928$	1.00000	0.0328266
$929$	−48.9309	−1.60537	−0.802685	−	0.596403i	$-0.796596\pi$
$929$	−48.9309	−1.60537	−0.802685	+	0.596403i	$0.796596\pi$
$930$	17.3701	0.569588
$931$	−22.3008	−0.730880
$932$	−0.137732	−0.00451157
$933$	11.8577	0.388204
$934$	0.400694	0.0131111
$935$	−56.4072	−1.84471
$936$	−14.4682	−0.472909
$937$	53.9467	1.76236	0.881181	−	0.472778i	$-0.156749\pi$
$937$	53.9467	1.76236	0.881181	+	0.472778i	$0.156749\pi$
$938$	0.531377	0.0173501
$939$	−54.2886	−1.77164
$940$	10.7937	0.352051
$941$	−41.5313	−1.35388	−0.676940	−	0.736038i	$-0.736694\pi$
$941$	−41.5313	−1.35388	−0.676940	+	0.736038i	$0.736694\pi$
$942$	61.0098	1.98781
$943$	−6.21200	−0.202290
$944$	4.24130	0.138043
$945$	−4.29866	−0.139835
$946$	−28.8459	−0.937862
$947$	55.6668	1.80893	0.904464	−	0.426551i	$-0.140272\pi$
$947$	55.6668	1.80893	0.904464	+	0.426551i	$0.140272\pi$
$948$	20.4028	0.662651
$949$	13.0983	0.425188
$950$	7.50137	0.243377
$951$	44.9820	1.45864
$952$	−4.86574	−0.157700
$953$	−21.9874	−0.712240	−0.356120	−	0.934440i	$-0.615901\pi$
$953$	−21.9874	−0.712240	−0.356120	+	0.934440i	$0.615901\pi$
$954$	−19.7857	−0.640585
$955$	−36.9337	−1.19515
$956$	−7.59313	−0.245579
$957$	−15.5474	−0.502577
$958$	−2.95436	−0.0954511
$959$	−14.0848	−0.454821
$960$	4.53367	0.146324
$961$	−16.3207	−0.526475
$962$	34.9431	1.12661
$963$	−43.8642	−1.41351
$964$	22.2852	0.717758
$965$	17.6079	0.566817
$966$	2.28052	0.0733745
$967$	39.1360	1.25853	0.629265	−	0.777191i	$-0.283356\pi$
$967$	39.1360	1.25853	0.629265	+	0.777191i	$0.283356\pi$
$968$	−23.0047	−0.739399
$969$	−53.9584	−1.73339
$970$	28.4688	0.914078
$971$	−6.74691	−0.216519	−0.108259	−	0.994123i	$-0.534528\pi$
$971$	−6.74691	−0.216519	−0.108259	+	0.994123i	$0.534528\pi$
$972$	−20.7194	−0.664576
$973$	−8.36038	−0.268022
$974$	−39.8315	−1.27628
$975$	−19.7968	−0.634006
$976$	14.2805	0.457108
$977$	9.54652	0.305420	0.152710	−	0.988271i	$-0.451200\pi$
$977$	9.54652	0.305420	0.152710	+	0.988271i	$0.451200\pi$
$978$	−2.48271	−0.0793883
$979$	−50.2564	−1.60620
$980$	−10.6590	−0.340489
$981$	79.7574	2.54646
$982$	12.5185	0.399482
$983$	−45.9130	−1.46440	−0.732199	−	0.681090i	$-0.761506\pi$
$983$	−45.9130	−1.46440	−0.732199	+	0.681090i	$0.761506\pi$
$984$	16.5623	0.527987
$985$	−14.5407	−0.463304
$986$	−5.68859	−0.181161
$987$	−14.4758	−0.460769
$988$	12.5284	0.398583
$989$	4.94670	0.157296
$990$	−40.7394	−1.29478
$991$	−41.4321	−1.31613	−0.658067	−	0.752960i	$-0.728626\pi$
$991$	−41.4321	−1.31613	−0.658067	+	0.752960i	$0.728626\pi$
$992$	3.83135	0.121646
$993$	28.1841	0.894395
$994$	−5.75928	−0.182673
$995$	19.0111	0.602692
$996$	−41.0849	−1.30183
$997$	−21.7210	−0.687910	−0.343955	−	0.938986i	$-0.611767\pi$
$997$	−21.7210	−0.687910	−0.343955	+	0.938986i	$0.611767\pi$
$998$	28.3237	0.896570
$999$	−29.3263	−0.927843

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.g.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.g.1.4	✓	5	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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.66618 q^{3} +1.00000 q^{4} +1.70044 q^{5} -2.66618 q^{6} -0.855351 q^{7} -1.00000 q^{8} +4.10851 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.66618 q^{3} +1.00000 q^{4} +1.70044 q^{5} -2.66618 q^{6} -0.855351 q^{7} -1.00000 q^{8} +4.10851 q^{9} -1.70044 q^{10} +5.83135 q^{11} +2.66618 q^{12} +3.52153 q^{13} +0.855351 q^{14} +4.53367 q^{15} +1.00000 q^{16} -5.68859 q^{17} -4.10851 q^{18} +3.55767 q^{19} +1.70044 q^{20} -2.28052 q^{21} -5.83135 q^{22} +1.00000 q^{23} -2.66618 q^{24} -2.10851 q^{25} -3.52153 q^{26} +2.95548 q^{27} -0.855351 q^{28} -1.00000 q^{29} -4.53367 q^{30} -3.83135 q^{31} -1.00000 q^{32} +15.5474 q^{33} +5.68859 q^{34} -1.45447 q^{35} +4.10851 q^{36} -9.92270 q^{37} -3.55767 q^{38} +9.38903 q^{39} -1.70044 q^{40} -6.21200 q^{41} +2.28052 q^{42} +4.94670 q^{43} +5.83135 q^{44} +6.98627 q^{45} -1.00000 q^{46} +6.34758 q^{47} +2.66618 q^{48} -6.26837 q^{49} +2.10851 q^{50} -15.1668 q^{51} +3.52153 q^{52} +4.81578 q^{53} -2.95548 q^{54} +9.91586 q^{55} +0.855351 q^{56} +9.48539 q^{57} +1.00000 q^{58} +4.24130 q^{59} +4.53367 q^{60} +14.2805 q^{61} +3.83135 q^{62} -3.51422 q^{63} +1.00000 q^{64} +5.98815 q^{65} -15.5474 q^{66} +0.621238 q^{67} -5.68859 q^{68} +2.66618 q^{69} +1.45447 q^{70} -6.73323 q^{71} -4.10851 q^{72} +3.71948 q^{73} +9.92270 q^{74} -5.62165 q^{75} +3.55767 q^{76} -4.98786 q^{77} -9.38903 q^{78} +7.65244 q^{79} +1.70044 q^{80} -4.44569 q^{81} +6.21200 q^{82} -15.4097 q^{83} -2.28052 q^{84} -9.67309 q^{85} -4.94670 q^{86} -2.66618 q^{87} -5.83135 q^{88} -8.61831 q^{89} -6.98627 q^{90} -3.01214 q^{91} +1.00000 q^{92} -10.2151 q^{93} -6.34758 q^{94} +6.04960 q^{95} -2.66618 q^{96} -16.7420 q^{97} +6.26837 q^{98} +23.9582 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + q^{3} + 5 q^{4} + 3 q^{5} - q^{6} + 4 q^{7} - 5 q^{8} + 12 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 + q^3 + 5 * q^4 + 3 * q^5 - q^6 + 4 * q^7 - 5 * q^8 + 12 * q^9	\( 5 q - 5 q^{2} + q^{3} + 5 q^{4} + 3 q^{5} - q^{6} + 4 q^{7} - 5 q^{8} + 12 q^{9} - 3 q^{10} + 3 q^{11} + q^{12} - 3 q^{13} - 4 q^{14} + q^{15} + 5 q^{16} - 4 q^{17} - 12 q^{18} + 14 q^{19} + 3 q^{20} + 10 q^{21} - 3 q^{22} + 5 q^{23} - q^{24} - 2 q^{25} + 3 q^{26} + 19 q^{27} + 4 q^{28} - 5 q^{29} - q^{30} + 7 q^{31} - 5 q^{32} - q^{33} + 4 q^{34} - 10 q^{35} + 12 q^{36} + 2 q^{37} - 14 q^{38} + 17 q^{39} - 3 q^{40} + 4 q^{41} - 10 q^{42} - 9 q^{43} + 3 q^{44} + 6 q^{45} - 5 q^{46} - 13 q^{47} + q^{48} - 11 q^{49} + 2 q^{50} - 6 q^{51} - 3 q^{52} + 11 q^{53} - 19 q^{54} - 3 q^{55} - 4 q^{56} + 10 q^{57} + 5 q^{58} + 2 q^{59} + q^{60} + 50 q^{61} - 7 q^{62} + 4 q^{63} + 5 q^{64} + 11 q^{65} + q^{66} + 22 q^{67} - 4 q^{68} + q^{69} + 10 q^{70} + 2 q^{71} - 12 q^{72} + 40 q^{73} - 2 q^{74} - 20 q^{75} + 14 q^{76} - 26 q^{77} - 17 q^{78} - 3 q^{79} + 3 q^{80} + 13 q^{81} - 4 q^{82} - 18 q^{83} + 10 q^{84} + 22 q^{85} + 9 q^{86} - q^{87} - 3 q^{88} + 12 q^{89} - 6 q^{90} - 14 q^{91} + 5 q^{92} + 3 q^{93} + 13 q^{94} + 10 q^{95} - q^{96} + 11 q^{98} + 46 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + q^3 + 5 * q^4 + 3 * q^5 - q^6 + 4 * q^7 - 5 * q^8 + 12 * q^9 - 3 * q^10 + 3 * q^11 + q^12 - 3 * q^13 - 4 * q^14 + q^15 + 5 * q^16 - 4 * q^17 - 12 * q^18 + 14 * q^19 + 3 * q^20 + 10 * q^21 - 3 * q^22 + 5 * q^23 - q^24 - 2 * q^25 + 3 * q^26 + 19 * q^27 + 4 * q^28 - 5 * q^29 - q^30 + 7 * q^31 - 5 * q^32 - q^33 + 4 * q^34 - 10 * q^35 + 12 * q^36 + 2 * q^37 - 14 * q^38 + 17 * q^39 - 3 * q^40 + 4 * q^41 - 10 * q^42 - 9 * q^43 + 3 * q^44 + 6 * q^45 - 5 * q^46 - 13 * q^47 + q^48 - 11 * q^49 + 2 * q^50 - 6 * q^51 - 3 * q^52 + 11 * q^53 - 19 * q^54 - 3 * q^55 - 4 * q^56 + 10 * q^57 + 5 * q^58 + 2 * q^59 + q^60 + 50 * q^61 - 7 * q^62 + 4 * q^63 + 5 * q^64 + 11 * q^65 + q^66 + 22 * q^67 - 4 * q^68 + q^69 + 10 * q^70 + 2 * q^71 - 12 * q^72 + 40 * q^73 - 2 * q^74 - 20 * q^75 + 14 * q^76 - 26 * q^77 - 17 * q^78 - 3 * q^79 + 3 * q^80 + 13 * q^81 - 4 * q^82 - 18 * q^83 + 10 * q^84 + 22 * q^85 + 9 * q^86 - q^87 - 3 * q^88 + 12 * q^89 - 6 * q^90 - 14 * q^91 + 5 * q^92 + 3 * q^93 + 13 * q^94 + 10 * q^95 - q^96 + 11 * q^98 + 46 * q^99

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