LMFDB - Embedded newform 381.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [381,2,Mod(1,381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(381, 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("381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 381 = 3 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	381.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:	$3.04230031701$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.81509.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 5x^{3} + 3x^{2} + 5x - 2 $ x^5 - x^4 - 5x^3 + 3x^2 + 5*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.370865$ of defining polynomial
Character	$\chi$	$=$	381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.370865 q^{2} -1.00000 q^{3} -1.86246 q^{4} -0.926151 q^{5} +0.370865 q^{6} +4.31895 q^{7} +1.43245 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.370865 q^{2} -1.00000 q^{3} -1.86246 q^{4} -0.926151 q^{5} +0.370865 q^{6} +4.31895 q^{7} +1.43245 q^{8} +1.00000 q^{9} +0.343477 q^{10} -2.82826 q^{11} +1.86246 q^{12} -3.82281 q^{13} -1.60175 q^{14} +0.926151 q^{15} +3.19367 q^{16} -5.22106 q^{17} -0.370865 q^{18} -6.42455 q^{19} +1.72492 q^{20} -4.31895 q^{21} +1.04890 q^{22} -1.47210 q^{23} -1.43245 q^{24} -4.14224 q^{25} +1.41775 q^{26} -1.00000 q^{27} -8.04387 q^{28} -8.13453 q^{29} -0.343477 q^{30} +7.07562 q^{31} -4.04932 q^{32} +2.82826 q^{33} +1.93631 q^{34} -4.00000 q^{35} -1.86246 q^{36} +0.319436 q^{37} +2.38264 q^{38} +3.82281 q^{39} -1.32667 q^{40} +12.0511 q^{41} +1.60175 q^{42} +2.98319 q^{43} +5.26752 q^{44} -0.926151 q^{45} +0.545951 q^{46} -10.9651 q^{47} -3.19367 q^{48} +11.6533 q^{49} +1.53621 q^{50} +5.22106 q^{51} +7.11982 q^{52} -3.38792 q^{53} +0.370865 q^{54} +2.61940 q^{55} +6.18668 q^{56} +6.42455 q^{57} +3.01681 q^{58} -8.40051 q^{59} -1.72492 q^{60} +8.61386 q^{61} -2.62410 q^{62} +4.31895 q^{63} -4.88559 q^{64} +3.54050 q^{65} -1.04890 q^{66} -3.82778 q^{67} +9.72401 q^{68} +1.47210 q^{69} +1.48346 q^{70} -13.8042 q^{71} +1.43245 q^{72} -9.06144 q^{73} -0.118468 q^{74} +4.14224 q^{75} +11.9655 q^{76} -12.2151 q^{77} -1.41775 q^{78} -9.26550 q^{79} -2.95782 q^{80} +1.00000 q^{81} -4.46933 q^{82} +4.71458 q^{83} +8.04387 q^{84} +4.83549 q^{85} -1.10636 q^{86} +8.13453 q^{87} -4.05134 q^{88} +5.47029 q^{89} +0.343477 q^{90} -16.5105 q^{91} +2.74173 q^{92} -7.07562 q^{93} +4.06655 q^{94} +5.95011 q^{95} +4.04932 q^{96} +16.9635 q^{97} -4.32181 q^{98} -2.82826 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} - 5 q^{3} + q^{4} - 5 q^{5} + q^{6} - 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - q^2 - 5 * q^3 + q^4 - 5 * q^5 + q^6 - 3 * q^8 + 5 * q^9	\( 5 q - q^{2} - 5 q^{3} + q^{4} - 5 q^{5} + q^{6} - 3 q^{8} + 5 q^{9} - 2 q^{10} - 16 q^{11} - q^{12} + 3 q^{13} - 6 q^{14} + 5 q^{15} - 7 q^{16} - 6 q^{17} - q^{18} - 8 q^{19} - 12 q^{20} - 8 q^{22} - 9 q^{23} + 3 q^{24} + 4 q^{25} - 2 q^{26} - 5 q^{27} + 2 q^{28} - 17 q^{29} + 2 q^{30} - 9 q^{31} - 2 q^{32} + 16 q^{33} - q^{34} - 20 q^{35} + q^{36} - q^{37} + q^{38} - 3 q^{39} + 16 q^{40} - 2 q^{41} + 6 q^{42} - 4 q^{43} + 3 q^{44} - 5 q^{45} + 4 q^{46} - 8 q^{47} + 7 q^{48} + 13 q^{49} + 15 q^{50} + 6 q^{51} + 13 q^{52} - 15 q^{53} + q^{54} + 20 q^{55} + 8 q^{56} + 8 q^{57} + 34 q^{58} - 19 q^{59} + 12 q^{60} + q^{61} + 15 q^{62} + q^{64} - 5 q^{65} + 8 q^{66} - 2 q^{67} + 14 q^{68} + 9 q^{69} + 4 q^{70} - 3 q^{72} + 13 q^{73} - 17 q^{74} - 4 q^{75} + 8 q^{76} + 2 q^{77} + 2 q^{78} - 28 q^{79} + 12 q^{80} + 5 q^{81} + 30 q^{82} - q^{83} - 2 q^{84} + 6 q^{85} + 32 q^{86} + 17 q^{87} + 3 q^{88} + q^{89} - 2 q^{90} - 18 q^{91} + 12 q^{92} + 9 q^{93} + 16 q^{94} + 4 q^{95} + 2 q^{96} + 28 q^{97} + 15 q^{98} - 16 q^{99}+O(q^{100}) \) 5 * q - q^2 - 5 * q^3 + q^4 - 5 * q^5 + q^6 - 3 * q^8 + 5 * q^9 - 2 * q^10 - 16 * q^11 - q^12 + 3 * q^13 - 6 * q^14 + 5 * q^15 - 7 * q^16 - 6 * q^17 - q^18 - 8 * q^19 - 12 * q^20 - 8 * q^22 - 9 * q^23 + 3 * q^24 + 4 * q^25 - 2 * q^26 - 5 * q^27 + 2 * q^28 - 17 * q^29 + 2 * q^30 - 9 * q^31 - 2 * q^32 + 16 * q^33 - q^34 - 20 * q^35 + q^36 - q^37 + q^38 - 3 * q^39 + 16 * q^40 - 2 * q^41 + 6 * q^42 - 4 * q^43 + 3 * q^44 - 5 * q^45 + 4 * q^46 - 8 * q^47 + 7 * q^48 + 13 * q^49 + 15 * q^50 + 6 * q^51 + 13 * q^52 - 15 * q^53 + q^54 + 20 * q^55 + 8 * q^56 + 8 * q^57 + 34 * q^58 - 19 * q^59 + 12 * q^60 + q^61 + 15 * q^62 + q^64 - 5 * q^65 + 8 * q^66 - 2 * q^67 + 14 * q^68 + 9 * q^69 + 4 * q^70 - 3 * q^72 + 13 * q^73 - 17 * q^74 - 4 * q^75 + 8 * q^76 + 2 * q^77 + 2 * q^78 - 28 * q^79 + 12 * q^80 + 5 * q^81 + 30 * q^82 - q^83 - 2 * q^84 + 6 * q^85 + 32 * q^86 + 17 * q^87 + 3 * q^88 + q^89 - 2 * q^90 - 18 * q^91 + 12 * q^92 + 9 * q^93 + 16 * q^94 + 4 * q^95 + 2 * q^96 + 28 * q^97 + 15 * q^98 - 16 * 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 $

$2$	−0.370865	−0.262241	−0.131121	−	0.991366i	$-0.541857\pi$
$2$	−0.370865	−0.262241	−0.131121	+	0.991366i	$0.541857\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.86246	−0.931230
$5$	−0.926151	−0.414187	−0.207094	−	0.978321i	$-0.566400\pi$
$5$	−0.926151	−0.414187	−0.207094	+	0.978321i	$0.566400\pi$
$6$	0.370865	0.151405
$7$	4.31895	1.63241	0.816205	−	0.577763i	$-0.196074\pi$
$7$	4.31895	1.63241	0.816205	+	0.577763i	$0.196074\pi$
$8$	1.43245	0.506448
$9$	1.00000	0.333333
$10$	0.343477	0.108617
$11$	−2.82826	−0.852753	−0.426376	−	0.904546i	$-0.640210\pi$
$11$	−2.82826	−0.852753	−0.426376	+	0.904546i	$0.640210\pi$
$12$	1.86246	0.537646
$13$	−3.82281	−1.06026	−0.530128	−	0.847918i	$-0.677856\pi$
$13$	−3.82281	−1.06026	−0.530128	+	0.847918i	$0.677856\pi$
$14$	−1.60175	−0.428085
$15$	0.926151	0.239131
$16$	3.19367	0.798418
$17$	−5.22106	−1.26629	−0.633147	−	0.774032i	$-0.718237\pi$
$17$	−5.22106	−1.26629	−0.633147	+	0.774032i	$0.718237\pi$
$18$	−0.370865	−0.0874137
$19$	−6.42455	−1.47389	−0.736947	−	0.675951i	$-0.763733\pi$
$19$	−6.42455	−1.47389	−0.736947	+	0.675951i	$0.763733\pi$
$20$	1.72492	0.385703
$21$	−4.31895	−0.942472
$22$	1.04890	0.223627
$23$	−1.47210	−0.306954	−0.153477	−	0.988152i	$-0.549047\pi$
$23$	−1.47210	−0.306954	−0.153477	+	0.988152i	$0.549047\pi$
$24$	−1.43245	−0.292398
$25$	−4.14224	−0.828449
$26$	1.41775	0.278043
$27$	−1.00000	−0.192450
$28$	−8.04387	−1.52015
$29$	−8.13453	−1.51054	−0.755272	−	0.655411i	$-0.772495\pi$
$29$	−8.13453	−1.51054	−0.755272	+	0.655411i	$0.772495\pi$
$30$	−0.343477	−0.0627100
$31$	7.07562	1.27082	0.635410	−	0.772175i	$-0.280831\pi$
$31$	7.07562	1.27082	0.635410	+	0.772175i	$0.280831\pi$
$32$	−4.04932	−0.715826
$33$	2.82826	0.492337
$34$	1.93631	0.332074
$35$	−4.00000	−0.676123
$36$	−1.86246	−0.310410
$37$	0.319436	0.0525150	0.0262575	−	0.999655i	$-0.491641\pi$
$37$	0.319436	0.0525150	0.0262575	+	0.999655i	$0.491641\pi$
$38$	2.38264	0.386516
$39$	3.82281	0.612139
$40$	−1.32667	−0.209764
$41$	12.0511	1.88207	0.941033	−	0.338316i	$-0.109857\pi$
$41$	12.0511	1.88207	0.941033	+	0.338316i	$0.109857\pi$
$42$	1.60175	0.247155
$43$	2.98319	0.454932	0.227466	−	0.973786i	$-0.426956\pi$
$43$	2.98319	0.454932	0.227466	+	0.973786i	$0.426956\pi$
$44$	5.26752	0.794109
$45$	−0.926151	−0.138062
$46$	0.545951	0.0804961
$47$	−10.9651	−1.59942	−0.799709	−	0.600388i	$-0.795013\pi$
$47$	−10.9651	−1.59942	−0.799709	+	0.600388i	$0.795013\pi$
$48$	−3.19367	−0.460967
$49$	11.6533	1.66476
$50$	1.53621	0.217253
$51$	5.22106	0.731095
$52$	7.11982	0.987342
$53$	−3.38792	−0.465366	−0.232683	−	0.972553i	$-0.574750\pi$
$53$	−3.38792	−0.465366	−0.232683	+	0.972553i	$0.574750\pi$
$54$	0.370865	0.0504683
$55$	2.61940	0.353199
$56$	6.18668	0.826730
$57$	6.42455	0.850953
$58$	3.01681	0.396127
$59$	−8.40051	−1.09365	−0.546827	−	0.837246i	$-0.684164\pi$
$59$	−8.40051	−1.09365	−0.546827	+	0.837246i	$0.684164\pi$
$60$	−1.72492	−0.222686
$61$	8.61386	1.10289	0.551446	−	0.834211i	$-0.314076\pi$
$61$	8.61386	1.10289	0.551446	+	0.834211i	$0.314076\pi$
$62$	−2.62410	−0.333261
$63$	4.31895	0.544137
$64$	−4.88559	−0.610699
$65$	3.54050	0.439145
$66$	−1.04890	−0.129111
$67$	−3.82778	−0.467637	−0.233819	−	0.972280i	$-0.575122\pi$
$67$	−3.82778	−0.467637	−0.233819	+	0.972280i	$0.575122\pi$
$68$	9.72401	1.17921
$69$	1.47210	0.177220
$70$	1.48346	0.177307
$71$	−13.8042	−1.63826	−0.819128	−	0.573611i	$-0.805542\pi$
$71$	−13.8042	−1.63826	−0.819128	+	0.573611i	$0.805542\pi$
$72$	1.43245	0.168816
$73$	−9.06144	−1.06056	−0.530280	−	0.847822i	$-0.677913\pi$
$73$	−9.06144	−1.06056	−0.530280	+	0.847822i	$0.677913\pi$
$74$	−0.118468	−0.0137716
$75$	4.14224	0.478305
$76$	11.9655	1.37253
$77$	−12.2151	−1.39204
$78$	−1.41775	−0.160528
$79$	−9.26550	−1.04245	−0.521225	−	0.853419i	$-0.674525\pi$
$79$	−9.26550	−1.04245	−0.521225	+	0.853419i	$0.674525\pi$
$80$	−2.95782	−0.330695
$81$	1.00000	0.111111
$82$	−4.46933	−0.493555
$83$	4.71458	0.517492	0.258746	−	0.965945i	$-0.416691\pi$
$83$	4.71458	0.517492	0.258746	+	0.965945i	$0.416691\pi$
$84$	8.04387	0.877658
$85$	4.83549	0.524483
$86$	−1.10636	−0.119302
$87$	8.13453	0.872113
$88$	−4.05134	−0.431875
$89$	5.47029	0.579850	0.289925	−	0.957049i	$-0.406370\pi$
$89$	5.47029	0.579850	0.289925	+	0.957049i	$0.406370\pi$
$90$	0.343477	0.0362056
$91$	−16.5105	−1.73077
$92$	2.74173	0.285845
$93$	−7.07562	−0.733708
$94$	4.06655	0.419433
$95$	5.95011	0.610468
$96$	4.04932	0.413282
$97$	16.9635	1.72239	0.861194	−	0.508277i	$-0.169717\pi$
$97$	16.9635	1.72239	0.861194	+	0.508277i	$0.169717\pi$
$98$	−4.32181	−0.436569
$99$	−2.82826	−0.284251
$100$	7.71476	0.771476
$101$	−13.5844	−1.35169	−0.675847	−	0.737042i	$-0.736222\pi$
$101$	−13.5844	−1.35169	−0.675847	+	0.737042i	$0.736222\pi$
$102$	−1.93631	−0.191723
$103$	14.8857	1.46674	0.733368	−	0.679832i	$-0.237947\pi$
$103$	14.8857	1.46674	0.733368	+	0.679832i	$0.237947\pi$
$104$	−5.47598	−0.536964
$105$	4.00000	0.390360
$106$	1.25646	0.122038
$107$	8.70031	0.841091	0.420545	−	0.907272i	$-0.361839\pi$
$107$	8.70031	0.841091	0.420545	+	0.907272i	$0.361839\pi$
$108$	1.86246	0.179215
$109$	1.77300	0.169823	0.0849113	−	0.996389i	$-0.472939\pi$
$109$	1.77300	0.169823	0.0849113	+	0.996389i	$0.472939\pi$
$110$	−0.971443	−0.0926234
$111$	−0.319436	−0.0303196
$112$	13.7933	1.30335
$113$	3.17662	0.298831	0.149416	−	0.988774i	$-0.452261\pi$
$113$	3.17662	0.298831	0.149416	+	0.988774i	$0.452261\pi$
$114$	−2.38264	−0.223155
$115$	1.36339	0.127137
$116$	15.1502	1.40666
$117$	−3.82281	−0.353419
$118$	3.11546	0.286801
$119$	−22.5495	−2.06711
$120$	1.32667	0.121107
$121$	−3.00094	−0.272812
$122$	−3.19458	−0.289224
$123$	−12.0511	−1.08661
$124$	−13.1781	−1.18342
$125$	8.46710	0.757320
$126$	−1.60175	−0.142695
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	9.91054	0.875976
$129$	−2.98319	−0.262655
$130$	−1.31305	−0.115162
$131$	15.2912	1.33600	0.668001	−	0.744161i	$-0.267150\pi$
$131$	15.2912	1.33600	0.668001	+	0.744161i	$0.267150\pi$
$132$	−5.26752	−0.458479
$133$	−27.7473	−2.40600
$134$	1.41959	0.122634
$135$	0.926151	0.0797104
$136$	−7.47891	−0.641311
$137$	11.1658	0.953959	0.476979	−	0.878915i	$-0.341732\pi$
$137$	11.1658	0.953959	0.476979	+	0.878915i	$0.341732\pi$
$138$	−0.545951	−0.0464744
$139$	−1.64983	−0.139937	−0.0699683	−	0.997549i	$-0.522290\pi$
$139$	−1.64983	−0.139937	−0.0699683	+	0.997549i	$0.522290\pi$
$140$	7.44984	0.629626
$141$	10.9651	0.923424
$142$	5.11949	0.429618
$143$	10.8119	0.904137
$144$	3.19367	0.266139
$145$	7.53380	0.625648
$146$	3.36057	0.278123
$147$	−11.6533	−0.961151
$148$	−0.594937	−0.0489036
$149$	15.8734	1.30040	0.650201	−	0.759763i	$-0.274685\pi$
$149$	15.8734	1.30040	0.650201	+	0.759763i	$0.274685\pi$
$150$	−1.53621	−0.125431
$151$	−17.8120	−1.44952	−0.724759	−	0.689002i	$-0.758049\pi$
$151$	−17.8120	−1.44952	−0.724759	+	0.689002i	$0.758049\pi$
$152$	−9.20286	−0.746450
$153$	−5.22106	−0.422098
$154$	4.53016	0.365051
$155$	−6.55310	−0.526357
$156$	−7.11982	−0.570042
$157$	−2.66966	−0.213062	−0.106531	−	0.994309i	$-0.533974\pi$
$157$	−2.66966	−0.213062	−0.106531	+	0.994309i	$0.533974\pi$
$158$	3.43625	0.273373
$159$	3.38792	0.268679
$160$	3.75028	0.296486
$161$	−6.35793	−0.501075
$162$	−0.370865	−0.0291379
$163$	−9.68150	−0.758314	−0.379157	−	0.925332i	$-0.623786\pi$
$163$	−9.68150	−0.758314	−0.379157	+	0.925332i	$0.623786\pi$
$164$	−22.4447	−1.75263
$165$	−2.61940	−0.203920
$166$	−1.74847	−0.135708
$167$	4.91479	0.380318	0.190159	−	0.981753i	$-0.439100\pi$
$167$	4.91479	0.380318	0.190159	+	0.981753i	$0.439100\pi$
$168$	−6.18668	−0.477313
$169$	1.61386	0.124143
$170$	−1.79331	−0.137541
$171$	−6.42455	−0.491298
$172$	−5.55607	−0.423646
$173$	10.6201	0.807429	0.403714	−	0.914885i	$-0.367719\pi$
$173$	10.6201	0.807429	0.403714	+	0.914885i	$0.367719\pi$
$174$	−3.01681	−0.228704
$175$	−17.8901	−1.35237
$176$	−9.03254	−0.680853
$177$	8.40051	0.631421
$178$	−2.02874	−0.152060
$179$	−10.9959	−0.821870	−0.410935	−	0.911665i	$-0.634798\pi$
$179$	−10.9959	−0.821870	−0.410935	+	0.911665i	$0.634798\pi$
$180$	1.72492	0.128568
$181$	3.00102	0.223064	0.111532	−	0.993761i	$-0.464424\pi$
$181$	3.00102	0.223064	0.111532	+	0.993761i	$0.464424\pi$
$182$	6.12317	0.453880
$183$	−8.61386	−0.636755
$184$	−2.10871	−0.155456
$185$	−0.295846	−0.0217511
$186$	2.62410	0.192408
$187$	14.7665	1.07984
$188$	20.4220	1.48942
$189$	−4.31895	−0.314157
$190$	−2.20669	−0.160090
$191$	9.96638	0.721142	0.360571	−	0.932732i	$-0.382582\pi$
$191$	9.96638	0.721142	0.360571	+	0.932732i	$0.382582\pi$
$192$	4.88559	0.352587
$193$	−5.11998	−0.368544	−0.184272	−	0.982875i	$-0.558993\pi$
$193$	−5.11998	−0.368544	−0.184272	+	0.982875i	$0.558993\pi$
$194$	−6.29118	−0.451681
$195$	−3.54050	−0.253540
$196$	−21.7039	−1.55028
$197$	8.49171	0.605009	0.302505	−	0.953148i	$-0.402177\pi$
$197$	8.49171	0.605009	0.302505	+	0.953148i	$0.402177\pi$
$198$	1.04890	0.0745423
$199$	11.7172	0.830608	0.415304	−	0.909683i	$-0.363675\pi$
$199$	11.7172	0.830608	0.415304	+	0.909683i	$0.363675\pi$
$200$	−5.93356	−0.419566
$201$	3.82778	0.269990
$202$	5.03796	0.354470
$203$	−35.1326	−2.46583
$204$	−9.72401	−0.680817
$205$	−11.1611	−0.779528
$206$	−5.52060	−0.384639
$207$	−1.47210	−0.102318
$208$	−12.2088	−0.846528
$209$	18.1703	1.25687
$210$	−1.48346	−0.102368
$211$	0.234680	0.0161560	0.00807802	−	0.999967i	$-0.497429\pi$
$211$	0.234680	0.0161560	0.00807802	+	0.999967i	$0.497429\pi$
$212$	6.30985	0.433363
$213$	13.8042	0.945847
$214$	−3.22664	−0.220569
$215$	−2.76288	−0.188427
$216$	−1.43245	−0.0974659
$217$	30.5593	2.07450
$218$	−0.657543	−0.0445344
$219$	9.06144	0.612315
$220$	−4.87852	−0.328910
$221$	19.9591	1.34260
$222$	0.118468	0.00795104
$223$	−24.1017	−1.61397	−0.806985	−	0.590572i	$-0.798902\pi$
$223$	−24.1017	−1.61397	−0.806985	+	0.590572i	$0.798902\pi$
$224$	−17.4888	−1.16852
$225$	−4.14224	−0.276150
$226$	−1.17810	−0.0783659
$227$	20.8842	1.38614	0.693068	−	0.720872i	$-0.256259\pi$
$227$	20.8842	1.38614	0.693068	+	0.720872i	$0.256259\pi$
$228$	−11.9655	−0.792433
$229$	−7.83718	−0.517896	−0.258948	−	0.965891i	$-0.583376\pi$
$229$	−7.83718	−0.517896	−0.258948	+	0.965891i	$0.583376\pi$
$230$	−0.505633	−0.0333405
$231$	12.2151	0.803696
$232$	−11.6523	−0.765012
$233$	−7.70363	−0.504681	−0.252341	−	0.967638i	$-0.581200\pi$
$233$	−7.70363	−0.504681	−0.252341	+	0.967638i	$0.581200\pi$
$234$	1.41775	0.0926809
$235$	10.1553	0.662458
$236$	15.6456	1.01844
$237$	9.26550	0.601859
$238$	8.36282	0.542081
$239$	−19.7995	−1.28072	−0.640361	−	0.768074i	$-0.721215\pi$
$239$	−19.7995	−1.28072	−0.640361	+	0.768074i	$0.721215\pi$
$240$	2.95782	0.190927
$241$	−4.24453	−0.273414	−0.136707	−	0.990612i	$-0.543652\pi$
$241$	−4.24453	−0.273414	−0.136707	+	0.990612i	$0.543652\pi$
$242$	1.11294	0.0715426
$243$	−1.00000	−0.0641500
$244$	−16.0430	−1.02705
$245$	−10.7927	−0.689523
$246$	4.46933	0.284954
$247$	24.5598	1.56271
$248$	10.1355	0.643604
$249$	−4.71458	−0.298774
$250$	−3.14015	−0.198601
$251$	−29.4697	−1.86011	−0.930056	−	0.367418i	$-0.880242\pi$
$251$	−29.4697	−1.86011	−0.930056	+	0.367418i	$0.880242\pi$
$252$	−8.04387	−0.506716
$253$	4.16349	0.261756
$254$	0.370865	0.0232701
$255$	−4.83549	−0.302810
$256$	6.09572	0.380982
$257$	−23.0196	−1.43592	−0.717962	−	0.696082i	$-0.754925\pi$
$257$	−23.0196	−1.43592	−0.717962	+	0.696082i	$0.754925\pi$
$258$	1.10636	0.0688790
$259$	1.37963	0.0857261
$260$	−6.59403	−0.408944
$261$	−8.13453	−0.503515
$262$	−5.67098	−0.350354
$263$	−13.4607	−0.830023	−0.415011	−	0.909816i	$-0.636222\pi$
$263$	−13.4607	−0.830023	−0.415011	+	0.909816i	$0.636222\pi$
$264$	4.05134	0.249343
$265$	3.13772	0.192749
$266$	10.2905	0.630952
$267$	−5.47029	−0.334776
$268$	7.12908	0.435478
$269$	10.8413	0.661006	0.330503	−	0.943805i	$-0.392782\pi$
$269$	10.8413	0.661006	0.330503	+	0.943805i	$0.392782\pi$
$270$	−0.343477	−0.0209033
$271$	−0.439860	−0.0267196	−0.0133598	−	0.999911i	$-0.504253\pi$
$271$	−0.439860	−0.0267196	−0.0133598	+	0.999911i	$0.504253\pi$
$272$	−16.6744	−1.01103
$273$	16.5105	0.999262
$274$	−4.14100	−0.250167
$275$	11.7154	0.706462
$276$	−2.74173	−0.165033
$277$	12.8943	0.774744	0.387372	−	0.921923i	$-0.373383\pi$
$277$	12.8943	0.774744	0.387372	+	0.921923i	$0.373383\pi$
$278$	0.611863	0.0366971
$279$	7.07562	0.423607
$280$	−5.72980	−0.342421
$281$	1.31486	0.0784378	0.0392189	−	0.999231i	$-0.487513\pi$
$281$	1.31486	0.0784378	0.0392189	+	0.999231i	$0.487513\pi$
$282$	−4.06655	−0.242160
$283$	−25.5939	−1.52140	−0.760700	−	0.649104i	$-0.775144\pi$
$283$	−25.5939	−1.52140	−0.760700	+	0.649104i	$0.775144\pi$
$284$	25.7097	1.52559
$285$	−5.95011	−0.352454
$286$	−4.00975	−0.237102
$287$	52.0481	3.07230
$288$	−4.04932	−0.238609
$289$	10.2595	0.603499
$290$	−2.79402	−0.164071
$291$	−16.9635	−0.994421
$292$	16.8766	0.987626
$293$	4.89612	0.286035	0.143017	−	0.989720i	$-0.454320\pi$
$293$	4.89612	0.286035	0.143017	+	0.989720i	$0.454320\pi$
$294$	4.32181	0.252053
$295$	7.78014	0.452978
$296$	0.457577	0.0265961
$297$	2.82826	0.164112
$298$	−5.88689	−0.341019
$299$	5.62756	0.325450
$300$	−7.71476	−0.445412
$301$	12.8842	0.742635
$302$	6.60584	0.380123
$303$	13.5844	0.780401
$304$	−20.5179	−1.17678
$305$	−7.97773	−0.456804
$306$	1.93631	0.110691
$307$	−30.3388	−1.73153	−0.865763	−	0.500455i	$-0.833166\pi$
$307$	−30.3388	−1.73153	−0.865763	+	0.500455i	$0.833166\pi$
$308$	22.7502	1.29631
$309$	−14.8857	−0.846821
$310$	2.43031	0.138033
$311$	−27.8232	−1.57771	−0.788854	−	0.614581i	$-0.789325\pi$
$311$	−27.8232	−1.57771	−0.788854	+	0.614581i	$0.789325\pi$
$312$	5.47598	0.310017
$313$	33.7179	1.90585	0.952925	−	0.303207i	$-0.0980572\pi$
$313$	33.7179	1.90585	0.952925	+	0.303207i	$0.0980572\pi$
$314$	0.990082	0.0558735
$315$	−4.00000	−0.225374
$316$	17.2566	0.970760
$317$	11.2137	0.629826	0.314913	−	0.949120i	$-0.398025\pi$
$317$	11.2137	0.629826	0.314913	+	0.949120i	$0.398025\pi$
$318$	−1.25646	−0.0704587
$319$	23.0066	1.28812
$320$	4.52480	0.252944
$321$	−8.70031	−0.485604
$322$	2.35793	0.131403
$323$	33.5430	1.86638
$324$	−1.86246	−0.103470
$325$	15.8350	0.878368
$326$	3.59053	0.198861
$327$	−1.77300	−0.0980471
$328$	17.2626	0.953168
$329$	−47.3575	−2.61090
$330$	0.971443	0.0534762
$331$	−28.4207	−1.56214	−0.781071	−	0.624443i	$-0.785326\pi$
$331$	−28.4207	−1.56214	−0.781071	+	0.624443i	$0.785326\pi$
$332$	−8.78071	−0.481904
$333$	0.319436	0.0175050
$334$	−1.82272	−0.0997350
$335$	3.54510	0.193689
$336$	−13.7933	−0.752487
$337$	−5.56715	−0.303262	−0.151631	−	0.988437i	$-0.548453\pi$
$337$	−5.56715	−0.303262	−0.151631	+	0.988437i	$0.548453\pi$
$338$	−0.598524	−0.0325554
$339$	−3.17662	−0.172530
$340$	−9.00590	−0.488414
$341$	−20.0117	−1.08370
$342$	2.38264	0.128839
$343$	20.0975	1.08516
$344$	4.27327	0.230399
$345$	−1.36339	−0.0734024
$346$	−3.93861	−0.211741
$347$	20.8605	1.11985	0.559924	−	0.828544i	$-0.310830\pi$
$347$	20.8605	1.11985	0.559924	+	0.828544i	$0.310830\pi$
$348$	−15.1502	−0.812138
$349$	−15.3948	−0.824063	−0.412031	−	0.911170i	$-0.635181\pi$
$349$	−15.3948	−0.824063	−0.412031	+	0.911170i	$0.635181\pi$
$350$	6.63483	0.354646
$351$	3.82281	0.204046
$352$	11.4525	0.610423
$353$	15.9322	0.847988	0.423994	−	0.905665i	$-0.360628\pi$
$353$	15.9322	0.847988	0.423994	+	0.905665i	$0.360628\pi$
$354$	−3.11546	−0.165585
$355$	12.7848	0.678545
$356$	−10.1882	−0.539973
$357$	22.5495	1.19345
$358$	4.07798	0.215528
$359$	11.2968	0.596221	0.298111	−	0.954531i	$-0.403644\pi$
$359$	11.2968	0.596221	0.298111	+	0.954531i	$0.403644\pi$
$360$	−1.32667	−0.0699214
$361$	22.2749	1.17236
$362$	−1.11297	−0.0584966
$363$	3.00094	0.157508
$364$	30.7502	1.61175
$365$	8.39226	0.439271
$366$	3.19458	0.166983
$367$	2.39709	0.125127	0.0625637	−	0.998041i	$-0.480072\pi$
$367$	2.39709	0.125127	0.0625637	+	0.998041i	$0.480072\pi$
$368$	−4.70141	−0.245078
$369$	12.0511	0.627355
$370$	0.109719	0.00570402
$371$	−14.6322	−0.759668
$372$	13.1781	0.683251
$373$	7.54293	0.390558	0.195279	−	0.980748i	$-0.437439\pi$
$373$	7.54293	0.390558	0.195279	+	0.980748i	$0.437439\pi$
$374$	−5.47639	−0.283177
$375$	−8.46710	−0.437239
$376$	−15.7069	−0.810021
$377$	31.0967	1.60156
$378$	1.60175	0.0823850
$379$	−22.9487	−1.17880	−0.589398	−	0.807842i	$-0.700635\pi$
$379$	−22.9487	−1.17880	−0.589398	+	0.807842i	$0.700635\pi$
$380$	−11.0818	−0.568486
$381$	1.00000	0.0512316
$382$	−3.69618	−0.189113
$383$	5.08213	0.259685	0.129842	−	0.991535i	$-0.458553\pi$
$383$	5.08213	0.259685	0.129842	+	0.991535i	$0.458553\pi$
$384$	−9.91054	−0.505745
$385$	11.3130	0.576566
$386$	1.89882	0.0966474
$387$	2.98319	0.151644
$388$	−31.5939	−1.60394
$389$	2.00675	0.101746	0.0508732	−	0.998705i	$-0.483800\pi$
$389$	2.00675	0.101746	0.0508732	+	0.998705i	$0.483800\pi$
$390$	1.31305	0.0664887
$391$	7.68593	0.388694
$392$	16.6928	0.843115
$393$	−15.2912	−0.771341
$394$	−3.14928	−0.158658
$395$	8.58125	0.431770
$396$	5.26752	0.264703
$397$	−2.92469	−0.146786	−0.0733929	−	0.997303i	$-0.523383\pi$
$397$	−2.92469	−0.146786	−0.0733929	+	0.997303i	$0.523383\pi$
$398$	−4.34549	−0.217820
$399$	27.7473	1.38910
$400$	−13.2290	−0.661449
$401$	−15.2297	−0.760533	−0.380267	−	0.924877i	$-0.624168\pi$
$401$	−15.2297	−0.760533	−0.380267	+	0.924877i	$0.624168\pi$
$402$	−1.41959	−0.0708026
$403$	−27.0488	−1.34739
$404$	25.3003	1.25874
$405$	−0.926151	−0.0460208
$406$	13.0295	0.646641
$407$	−0.903450	−0.0447823
$408$	7.47891	0.370261
$409$	−0.527147	−0.0260657	−0.0130329	−	0.999915i	$-0.504149\pi$
$409$	−0.527147	−0.0260657	−0.0130329	+	0.999915i	$0.504149\pi$
$410$	4.13927	0.204424
$411$	−11.1658	−0.550768
$412$	−27.7241	−1.36587
$413$	−36.2814	−1.78529
$414$	0.545951	0.0268320
$415$	−4.36641	−0.214339
$416$	15.4798	0.758959
$417$	1.64983	0.0807924
$418$	−6.73873	−0.329602
$419$	12.0124	0.586843	0.293422	−	0.955983i	$-0.405206\pi$
$419$	12.0124	0.586843	0.293422	+	0.955983i	$0.405206\pi$
$420$	−7.44984	−0.363515
$421$	1.43276	0.0698285	0.0349143	−	0.999390i	$-0.488884\pi$
$421$	1.43276	0.0698285	0.0349143	+	0.999390i	$0.488884\pi$
$422$	−0.0870346	−0.00423678
$423$	−10.9651	−0.533139
$424$	−4.85302	−0.235684
$425$	21.6269	1.04906
$426$	−5.11949	−0.248040
$427$	37.2028	1.80037
$428$	−16.2040	−0.783248
$429$	−10.8119	−0.522003
$430$	1.02466	0.0494133
$431$	3.58849	0.172852	0.0864259	−	0.996258i	$-0.472455\pi$
$431$	3.58849	0.172852	0.0864259	+	0.996258i	$0.472455\pi$
$432$	−3.19367	−0.153656
$433$	37.8258	1.81779	0.908896	−	0.417022i	$-0.136926\pi$
$433$	37.8258	1.81779	0.908896	+	0.417022i	$0.136926\pi$
$434$	−11.3334	−0.544019
$435$	−7.53380	−0.361218
$436$	−3.30214	−0.158144
$437$	9.45760	0.452418
$438$	−3.36057	−0.160574
$439$	−1.51840	−0.0724692	−0.0362346	−	0.999343i	$-0.511536\pi$
$439$	−1.51840	−0.0724692	−0.0362346	+	0.999343i	$0.511536\pi$
$440$	3.75216	0.178877
$441$	11.6533	0.554921
$442$	−7.40213	−0.352084
$443$	9.57478	0.454912	0.227456	−	0.973788i	$-0.426959\pi$
$443$	9.57478	0.454912	0.227456	+	0.973788i	$0.426959\pi$
$444$	0.594937	0.0282345
$445$	−5.06632	−0.240166
$446$	8.93848	0.423249
$447$	−15.8734	−0.750787
$448$	−21.1006	−0.996911
$449$	−0.782582	−0.0369323	−0.0184662	−	0.999829i	$-0.505878\pi$
$449$	−0.782582	−0.0369323	−0.0184662	+	0.999829i	$0.505878\pi$
$450$	1.53621	0.0724178
$451$	−34.0837	−1.60494
$452$	−5.91633	−0.278281
$453$	17.8120	0.836880
$454$	−7.74523	−0.363502
$455$	15.2912	0.716864
$456$	9.20286	0.430963
$457$	−26.7324	−1.25049	−0.625245	−	0.780429i	$-0.715001\pi$
$457$	−26.7324	−1.25049	−0.625245	+	0.780429i	$0.715001\pi$
$458$	2.90654	0.135814
$459$	5.22106	0.243698
$460$	−2.53926	−0.118393
$461$	−4.69220	−0.218537	−0.109269	−	0.994012i	$-0.534851\pi$
$461$	−4.69220	−0.218537	−0.109269	+	0.994012i	$0.534851\pi$
$462$	−4.53016	−0.210762
$463$	4.17498	0.194028	0.0970138	−	0.995283i	$-0.469071\pi$
$463$	4.17498	0.194028	0.0970138	+	0.995283i	$0.469071\pi$
$464$	−25.9790	−1.20605
$465$	6.55310	0.303893
$466$	2.85700	0.132348
$467$	2.53097	0.117119	0.0585597	−	0.998284i	$-0.481349\pi$
$467$	2.53097	0.117119	0.0585597	+	0.998284i	$0.481349\pi$
$468$	7.11982	0.329114
$469$	−16.5320	−0.763375
$470$	−3.76624	−0.173724
$471$	2.66966	0.123011
$472$	−12.0333	−0.553879
$473$	−8.43724	−0.387945
$474$	−3.43625	−0.157832
$475$	26.6121	1.22105
$476$	41.9975	1.92495
$477$	−3.38792	−0.155122
$478$	7.34293	0.335858
$479$	−15.6537	−0.715235	−0.357618	−	0.933868i	$-0.616411\pi$
$479$	−15.6537	−0.715235	−0.357618	+	0.933868i	$0.616411\pi$
$480$	−3.75028	−0.171176
$481$	−1.22114	−0.0556794
$482$	1.57415	0.0717005
$483$	6.35793	0.289296
$484$	5.58912	0.254051
$485$	−15.7108	−0.713391
$486$	0.370865	0.0168228
$487$	−22.6967	−1.02849	−0.514243	−	0.857644i	$-0.671927\pi$
$487$	−22.6967	−1.02849	−0.514243	+	0.857644i	$0.671927\pi$
$488$	12.3389	0.558557
$489$	9.68150	0.437813
$490$	4.00265	0.180821
$491$	7.91649	0.357266	0.178633	−	0.983916i	$-0.442833\pi$
$491$	7.91649	0.357266	0.178633	+	0.983916i	$0.442833\pi$
$492$	22.4447	1.01188
$493$	42.4709	1.91279
$494$	−9.10838	−0.409806
$495$	2.61940	0.117733
$496$	22.5972	1.01465
$497$	−59.6196	−2.67430
$498$	1.74847	0.0783509
$499$	36.2920	1.62465	0.812325	−	0.583204i	$-0.198201\pi$
$499$	36.2920	1.62465	0.812325	+	0.583204i	$0.198201\pi$
$500$	−15.7696	−0.705239
$501$	−4.91479	−0.219577
$502$	10.9293	0.487798
$503$	12.5447	0.559339	0.279670	−	0.960096i	$-0.409775\pi$
$503$	12.5447	0.559339	0.279670	+	0.960096i	$0.409775\pi$
$504$	6.18668	0.275577
$505$	12.5812	0.559855
$506$	−1.54409	−0.0686433
$507$	−1.61386	−0.0716740
$508$	1.86246	0.0826333
$509$	3.22417	0.142909	0.0714544	−	0.997444i	$-0.477236\pi$
$509$	3.22417	0.142909	0.0714544	+	0.997444i	$0.477236\pi$
$510$	1.79331	0.0794093
$511$	−39.1359	−1.73127
$512$	−22.0818	−0.975885
$513$	6.42455	0.283651
$514$	8.53717	0.376558
$515$	−13.7865	−0.607504
$516$	5.55607	0.244592
$517$	31.0120	1.36391
$518$	−0.511656	−0.0224809
$519$	−10.6201	−0.466169
$520$	5.07159	0.222404
$521$	−29.0153	−1.27119	−0.635593	−	0.772025i	$-0.719244\pi$
$521$	−29.0153	−1.27119	−0.635593	+	0.772025i	$0.719244\pi$
$522$	3.01681	0.132042
$523$	−5.27602	−0.230704	−0.115352	−	0.993325i	$-0.536800\pi$
$523$	−5.27602	−0.230704	−0.115352	+	0.993325i	$0.536800\pi$
$524$	−28.4793	−1.24412
$525$	17.8901	0.780790
$526$	4.99210	0.217666
$527$	−36.9423	−1.60923
$528$	9.03254	0.393091
$529$	−20.8329	−0.905779
$530$	−1.16367	−0.0505466
$531$	−8.40051	−0.364551
$532$	51.6783	2.24054
$533$	−46.0690	−1.99547
$534$	2.02874	0.0877921
$535$	−8.05780	−0.348369
$536$	−5.48310	−0.236834
$537$	10.9959	0.474507
$538$	−4.02066	−0.173343
$539$	−32.9587	−1.41963
$540$	−1.72492	−0.0742287
$541$	3.98457	0.171310	0.0856550	−	0.996325i	$-0.472702\pi$
$541$	3.98457	0.171310	0.0856550	+	0.996325i	$0.472702\pi$
$542$	0.163129	0.00700697
$543$	−3.00102	−0.128786
$544$	21.1418	0.906445
$545$	−1.64207	−0.0703383
$546$	−6.12317	−0.262048
$547$	−16.5087	−0.705861	−0.352931	−	0.935649i	$-0.614815\pi$
$547$	−16.5087	−0.705861	−0.352931	+	0.935649i	$0.614815\pi$
$548$	−20.7958	−0.888354
$549$	8.61386	0.367631
$550$	−4.34481	−0.185263
$551$	52.2607	2.22638
$552$	2.10871	0.0897528
$553$	−40.0172	−1.70171
$554$	−4.78205	−0.203170
$555$	0.295846	0.0125580
$556$	3.07274	0.130313
$557$	−27.9137	−1.18274	−0.591371	−	0.806400i	$-0.701413\pi$
$557$	−27.9137	−1.18274	−0.591371	+	0.806400i	$0.701413\pi$
$558$	−2.62410	−0.111087
$559$	−11.4042	−0.482344
$560$	−12.7747	−0.539829
$561$	−14.7665	−0.623443
$562$	−0.487634	−0.0205696
$563$	44.0042	1.85455	0.927277	−	0.374376i	$-0.122143\pi$
$563$	44.0042	1.85455	0.927277	+	0.374376i	$0.122143\pi$
$564$	−20.4220	−0.859920
$565$	−2.94203	−0.123772
$566$	9.49188	0.398974
$567$	4.31895	0.181379
$568$	−19.7738	−0.829691
$569$	−46.1052	−1.93283	−0.966416	−	0.256985i	$-0.917271\pi$
$569$	−46.1052	−1.93283	−0.966416	+	0.256985i	$0.917271\pi$
$570$	2.20669	0.0924279
$571$	−6.62994	−0.277455	−0.138727	−	0.990331i	$-0.544301\pi$
$571$	−6.62994	−0.277455	−0.138727	+	0.990331i	$0.544301\pi$
$572$	−20.1367	−0.841959
$573$	−9.96638	−0.416351
$574$	−19.3028	−0.805684
$575$	6.09781	0.254296
$576$	−4.88559	−0.203566
$577$	−17.1150	−0.712506	−0.356253	−	0.934390i	$-0.615946\pi$
$577$	−17.1150	−0.712506	−0.356253	+	0.934390i	$0.615946\pi$
$578$	−3.80488	−0.158262
$579$	5.11998	0.212779
$580$	−14.0314	−0.582622
$581$	20.3620	0.844760
$582$	6.29118	0.260778
$583$	9.58191	0.396842
$584$	−12.9801	−0.537119
$585$	3.54050	0.146382
$586$	−1.81580	−0.0750100
$587$	12.3136	0.508235	0.254117	−	0.967173i	$-0.418215\pi$
$587$	12.3136	0.508235	0.254117	+	0.967173i	$0.418215\pi$
$588$	21.7039	0.895052
$589$	−45.4577	−1.87305
$590$	−2.88538	−0.118789
$591$	−8.49171	−0.349302
$592$	1.02018	0.0419290
$593$	−28.4142	−1.16683	−0.583416	−	0.812174i	$-0.698284\pi$
$593$	−28.4142	−1.16683	−0.583416	+	0.812174i	$0.698284\pi$
$594$	−1.04890	−0.0430370
$595$	20.8842	0.856170
$596$	−29.5636	−1.21097
$597$	−11.7172	−0.479552
$598$	−2.08707	−0.0853465
$599$	35.5303	1.45173	0.725864	−	0.687839i	$-0.241440\pi$
$599$	35.5303	1.45173	0.725864	+	0.687839i	$0.241440\pi$
$600$	5.93356	0.242237
$601$	8.76445	0.357509	0.178755	−	0.983894i	$-0.442793\pi$
$601$	8.76445	0.357509	0.178755	+	0.983894i	$0.442793\pi$
$602$	−4.77831	−0.194750
$603$	−3.82778	−0.155879
$604$	33.1741	1.34983
$605$	2.77932	0.112995
$606$	−5.03796	−0.204653
$607$	9.37928	0.380693	0.190347	−	0.981717i	$-0.439039\pi$
$607$	9.37928	0.380693	0.190347	+	0.981717i	$0.439039\pi$
$608$	26.0151	1.05505
$609$	35.1326	1.42365
$610$	2.95866	0.119793
$611$	41.9173	1.69579
$612$	9.72401	0.393070
$613$	30.5658	1.23454	0.617270	−	0.786751i	$-0.288239\pi$
$613$	30.5658	1.23454	0.617270	+	0.786751i	$0.288239\pi$
$614$	11.2516	0.454077
$615$	11.1611	0.450060
$616$	−17.4976	−0.704997
$617$	0.488780	0.0196775	0.00983876	−	0.999952i	$-0.496868\pi$
$617$	0.488780	0.0196775	0.00983876	+	0.999952i	$0.496868\pi$
$618$	5.52060	0.222071
$619$	−15.9895	−0.642670	−0.321335	−	0.946966i	$-0.604132\pi$
$619$	−15.9895	−0.642670	−0.321335	+	0.946966i	$0.604132\pi$
$620$	12.2049	0.490160
$621$	1.47210	0.0590734
$622$	10.3186	0.413740
$623$	23.6259	0.946552
$624$	12.2088	0.488743
$625$	12.8694	0.514776
$626$	−12.5048	−0.499792
$627$	−18.1703	−0.725653
$628$	4.97213	0.198409
$629$	−1.66780	−0.0664994
$630$	1.48346	0.0591024
$631$	−40.7147	−1.62083	−0.810414	−	0.585858i	$-0.800758\pi$
$631$	−40.7147	−1.62083	−0.810414	+	0.585858i	$0.800758\pi$
$632$	−13.2724	−0.527947
$633$	−0.234680	−0.00932770
$634$	−4.15878	−0.165166
$635$	0.926151	0.0367532
$636$	−6.30985	−0.250202
$637$	−44.5484	−1.76507
$638$	−8.53233	−0.337798
$639$	−13.8042	−0.546085
$640$	−9.17866	−0.362818
$641$	−22.9823	−0.907748	−0.453874	−	0.891066i	$-0.649958\pi$
$641$	−22.9823	−0.907748	−0.453874	+	0.891066i	$0.649958\pi$
$642$	3.22664	0.127345
$643$	3.69068	0.145546	0.0727731	−	0.997349i	$-0.476815\pi$
$643$	3.69068	0.145546	0.0727731	+	0.997349i	$0.476815\pi$
$644$	11.8414	0.466616
$645$	2.76288	0.108788
$646$	−12.4399	−0.489442
$647$	27.1882	1.06888	0.534440	−	0.845206i	$-0.320523\pi$
$647$	27.1882	1.06888	0.534440	+	0.845206i	$0.320523\pi$
$648$	1.43245	0.0562720
$649$	23.7589	0.932617
$650$	−5.87265	−0.230344
$651$	−30.5593	−1.19771
$652$	18.0314	0.706164
$653$	−22.2117	−0.869213	−0.434606	−	0.900621i	$-0.643112\pi$
$653$	−22.2117	−0.869213	−0.434606	+	0.900621i	$0.643112\pi$
$654$	0.657543	0.0257120
$655$	−14.1620	−0.553355
$656$	38.4873	1.50268
$657$	−9.06144	−0.353520
$658$	17.5632	0.684686
$659$	−6.61926	−0.257850	−0.128925	−	0.991654i	$-0.541153\pi$
$659$	−6.61926	−0.257850	−0.128925	+	0.991654i	$0.541153\pi$
$660$	4.87852	0.189896
$661$	2.91568	0.113407	0.0567034	−	0.998391i	$-0.481941\pi$
$661$	2.91568	0.113407	0.0567034	+	0.998391i	$0.481941\pi$
$662$	10.5402	0.409658
$663$	−19.9591	−0.775148
$664$	6.75340	0.262083
$665$	25.6982	0.996534
$666$	−0.118468	−0.00459053
$667$	11.9749	0.463668
$668$	−9.15360	−0.354163
$669$	24.1017	0.931826
$670$	−1.31475	−0.0507933
$671$	−24.3622	−0.940494
$672$	17.4888	0.674646
$673$	−16.8985	−0.651390	−0.325695	−	0.945475i	$-0.605598\pi$
$673$	−16.8985	−0.651390	−0.325695	+	0.945475i	$0.605598\pi$
$674$	2.06466	0.0795278
$675$	4.14224	0.159435
$676$	−3.00575	−0.115606
$677$	−18.1631	−0.698066	−0.349033	−	0.937110i	$-0.613490\pi$
$677$	−18.1631	−0.698066	−0.349033	+	0.937110i	$0.613490\pi$
$678$	1.17810	0.0452446
$679$	73.2647	2.81164
$680$	6.92660	0.265623
$681$	−20.8842	−0.800286
$682$	7.42164	0.284189
$683$	−21.3781	−0.818009	−0.409005	−	0.912532i	$-0.634124\pi$
$683$	−21.3781	−0.818009	−0.409005	+	0.912532i	$0.634124\pi$
$684$	11.9655	0.457511
$685$	−10.3412	−0.395118
$686$	−7.45346	−0.284574
$687$	7.83718	0.299007
$688$	9.52733	0.363226
$689$	12.9513	0.493407
$690$	0.505633	0.0192491
$691$	24.6246	0.936764	0.468382	−	0.883526i	$-0.344837\pi$
$691$	24.6246	0.936764	0.468382	+	0.883526i	$0.344837\pi$
$692$	−19.7794	−0.751902
$693$	−12.2151	−0.464014
$694$	−7.73642	−0.293670
$695$	1.52799	0.0579600
$696$	11.6523	0.441680
$697$	−62.9195	−2.38325
$698$	5.70938	0.216103
$699$	7.70363	0.291378
$700$	33.3197	1.25937
$701$	30.6650	1.15820	0.579100	−	0.815256i	$-0.303404\pi$
$701$	30.6650	1.15820	0.579100	+	0.815256i	$0.303404\pi$
$702$	−1.41775	−0.0535093
$703$	−2.05224	−0.0774016
$704$	13.8177	0.520776
$705$	−10.1553	−0.382470
$706$	−5.90871	−0.222377
$707$	−58.6702	−2.20652
$708$	−15.6456	−0.587998
$709$	16.3232	0.613029	0.306515	−	0.951866i	$-0.400837\pi$
$709$	16.3232	0.613029	0.306515	+	0.951866i	$0.400837\pi$
$710$	−4.74142	−0.177942
$711$	−9.26550	−0.347483
$712$	7.83592	0.293664
$713$	−10.4160	−0.390084
$714$	−8.36282	−0.312971
$715$	−10.0135	−0.374482
$716$	20.4794	0.765350
$717$	19.7995	0.739425
$718$	−4.18958	−0.156354
$719$	−45.3109	−1.68981	−0.844906	−	0.534915i	$-0.820344\pi$
$719$	−45.3109	−1.68981	−0.844906	+	0.534915i	$0.820344\pi$
$720$	−2.95782	−0.110232
$721$	64.2908	2.39431
$722$	−8.26098	−0.307442
$723$	4.24453	0.157856
$724$	−5.58928	−0.207724
$725$	33.6952	1.25141
$726$	−1.11294	−0.0413052
$727$	28.7594	1.06663	0.533313	−	0.845918i	$-0.320947\pi$
$727$	28.7594	1.06663	0.533313	+	0.845918i	$0.320947\pi$
$728$	−23.6505	−0.876546
$729$	1.00000	0.0370370
$730$	−3.11239	−0.115195
$731$	−15.5754	−0.576077
$732$	16.0430	0.592965
$733$	13.0152	0.480728	0.240364	−	0.970683i	$-0.422733\pi$
$733$	13.0152	0.480728	0.240364	+	0.970683i	$0.422733\pi$
$734$	−0.888998	−0.0328135
$735$	10.7927	0.398096
$736$	5.96102	0.219726
$737$	10.8259	0.398779
$738$	−4.46933	−0.164518
$739$	−16.8127	−0.618465	−0.309232	−	0.950986i	$-0.600072\pi$
$739$	−16.8127	−0.618465	−0.309232	+	0.950986i	$0.600072\pi$
$740$	0.551002	0.0202552
$741$	−24.5598	−0.902228
$742$	5.42658	0.199216
$743$	−25.4838	−0.934909	−0.467455	−	0.884017i	$-0.654829\pi$
$743$	−25.4838	−0.934909	−0.467455	+	0.884017i	$0.654829\pi$
$744$	−10.1355	−0.371585
$745$	−14.7012	−0.538610
$746$	−2.79741	−0.102420
$747$	4.71458	0.172497
$748$	−27.5021	−1.00557
$749$	37.5762	1.37300
$750$	3.14015	0.114662
$751$	−20.4685	−0.746907	−0.373453	−	0.927649i	$-0.621826\pi$
$751$	−20.4685	−0.746907	−0.373453	+	0.927649i	$0.621826\pi$
$752$	−35.0188	−1.27700
$753$	29.4697	1.07394
$754$	−11.5327	−0.419996
$755$	16.4966	0.600372
$756$	8.04387	0.292553
$757$	−22.2413	−0.808373	−0.404187	−	0.914677i	$-0.632445\pi$
$757$	−22.2413	−0.808373	−0.404187	+	0.914677i	$0.632445\pi$
$758$	8.51088	0.309129
$759$	−4.16349	−0.151125
$760$	8.52324	0.309170
$761$	8.27553	0.299988	0.149994	−	0.988687i	$-0.452075\pi$
$761$	8.27553	0.299988	0.149994	+	0.988687i	$0.452075\pi$
$762$	−0.370865	−0.0134350
$763$	7.65750	0.277220
$764$	−18.5620	−0.671549
$765$	4.83549	0.174828
$766$	−1.88479	−0.0681001
$767$	32.1136	1.15955
$768$	−6.09572	−0.219960
$769$	19.1216	0.689543	0.344772	−	0.938687i	$-0.387956\pi$
$769$	19.1216	0.689543	0.344772	+	0.938687i	$0.387956\pi$
$770$	−4.19561	−0.151199
$771$	23.0196	0.829031
$772$	9.53575	0.343199
$773$	−18.4443	−0.663394	−0.331697	−	0.943386i	$-0.607621\pi$
$773$	−18.4443	−0.663394	−0.331697	+	0.943386i	$0.607621\pi$
$774$	−1.10636	−0.0397673
$775$	−29.3090	−1.05281
$776$	24.2994	0.872299
$777$	−1.37963	−0.0494940
$778$	−0.744234	−0.0266821
$779$	−77.4229	−2.77396
$780$	6.59403	0.236104
$781$	39.0418	1.39703
$782$	−2.85044	−0.101932
$783$	8.13453	0.290704
$784$	37.2169	1.32918
$785$	2.47250	0.0882475
$786$	5.67098	0.202277
$787$	23.0220	0.820644	0.410322	−	0.911941i	$-0.365416\pi$
$787$	23.0220	0.820644	0.410322	+	0.911941i	$0.365416\pi$
$788$	−15.8155	−0.563402
$789$	13.4607	0.479214
$790$	−3.18248	−0.113228
$791$	13.7197	0.487815
$792$	−4.05134	−0.143958
$793$	−32.9291	−1.16935
$794$	1.08466	0.0384933
$795$	−3.13772	−0.111283
$796$	−21.8227	−0.773487
$797$	27.1253	0.960829	0.480414	−	0.877042i	$-0.340486\pi$
$797$	27.1253	0.960829	0.480414	+	0.877042i	$0.340486\pi$
$798$	−10.2905	−0.364280
$799$	57.2492	2.02533
$800$	16.7733	0.593025
$801$	5.47029	0.193283
$802$	5.64815	0.199443
$803$	25.6281	0.904396
$804$	−7.12908	−0.251423
$805$	5.88841	0.207539
$806$	10.0314	0.353342
$807$	−10.8413	−0.381632
$808$	−19.4589	−0.684563
$809$	−7.19268	−0.252881	−0.126441	−	0.991974i	$-0.540355\pi$
$809$	−7.19268	−0.252881	−0.126441	+	0.991974i	$0.540355\pi$
$810$	0.343477	0.0120685
$811$	−45.8828	−1.61116	−0.805581	−	0.592485i	$-0.798147\pi$
$811$	−45.8828	−1.61116	−0.805581	+	0.592485i	$0.798147\pi$
$812$	65.4331	2.29625
$813$	0.439860	0.0154266
$814$	0.335058	0.0117438
$815$	8.96653	0.314084
$816$	16.6744	0.583719
$817$	−19.1657	−0.670522
$818$	0.195500	0.00683551
$819$	−16.5105	−0.576924
$820$	20.7872	0.725919
$821$	−22.4595	−0.783842	−0.391921	−	0.919999i	$-0.628189\pi$
$821$	−22.4595	−0.783842	−0.391921	+	0.919999i	$0.628189\pi$
$822$	4.14100	0.144434
$823$	26.0346	0.907509	0.453755	−	0.891127i	$-0.350084\pi$
$823$	26.0346	0.907509	0.453755	+	0.891127i	$0.350084\pi$
$824$	21.3231	0.742825
$825$	−11.7154	−0.407876
$826$	13.4555	0.468177
$827$	22.3403	0.776849	0.388425	−	0.921481i	$-0.373019\pi$
$827$	22.3403	0.776849	0.388425	+	0.921481i	$0.373019\pi$
$828$	2.74173	0.0952817
$829$	−56.1725	−1.95095	−0.975475	−	0.220110i	$-0.929359\pi$
$829$	−56.1725	−1.95095	−0.975475	+	0.220110i	$0.929359\pi$
$830$	1.61935	0.0562084
$831$	−12.8943	−0.447299
$832$	18.6767	0.647498
$833$	−60.8427	−2.10808
$834$	−0.611863	−0.0211871
$835$	−4.55184	−0.157523
$836$	−33.8415	−1.17043
$837$	−7.07562	−0.244569
$838$	−4.45497	−0.153894
$839$	51.1554	1.76608	0.883041	−	0.469296i	$-0.155492\pi$
$839$	51.1554	1.76608	0.883041	+	0.469296i	$0.155492\pi$
$840$	5.72980	0.197697
$841$	37.1706	1.28174
$842$	−0.531361	−0.0183119
$843$	−1.31486	−0.0452861
$844$	−0.437082	−0.0150450
$845$	−1.49468	−0.0514185
$846$	4.06655	0.139811
$847$	−12.9609	−0.445342
$848$	−10.8199	−0.371557
$849$	25.5939	0.878381
$850$	−8.02066	−0.275106
$851$	−0.470243	−0.0161197
$852$	−25.7097	−0.880801
$853$	44.6238	1.52789	0.763946	−	0.645280i	$-0.223259\pi$
$853$	44.6238	1.52789	0.763946	+	0.645280i	$0.223259\pi$
$854$	−13.7972	−0.472131
$855$	5.95011	0.203489
$856$	12.4628	0.425968
$857$	18.6109	0.635738	0.317869	−	0.948135i	$-0.397033\pi$
$857$	18.6109	0.635738	0.317869	+	0.948135i	$0.397033\pi$
$858$	4.00975	0.136891
$859$	−19.7988	−0.675528	−0.337764	−	0.941231i	$-0.609671\pi$
$859$	−19.7988	−0.675528	−0.337764	+	0.941231i	$0.609671\pi$
$860$	5.14576	0.175469
$861$	−52.0481	−1.77379
$862$	−1.33085	−0.0453288
$863$	−35.2187	−1.19886	−0.599429	−	0.800428i	$-0.704606\pi$
$863$	−35.2187	−1.19886	−0.599429	+	0.800428i	$0.704606\pi$
$864$	4.04932	0.137761
$865$	−9.83579	−0.334427
$866$	−14.0283	−0.476700
$867$	−10.2595	−0.348430
$868$	−56.9154	−1.93183
$869$	26.2053	0.888952
$870$	2.79402	0.0947262
$871$	14.6328	0.495815
$872$	2.53973	0.0860062
$873$	16.9635	0.574129
$874$	−3.50749	−0.118643
$875$	36.5690	1.23626
$876$	−16.8766	−0.570206
$877$	17.8375	0.602331	0.301165	−	0.953572i	$-0.402624\pi$
$877$	17.8375	0.602331	0.301165	+	0.953572i	$0.402624\pi$
$878$	0.563121	0.0190044
$879$	−4.89612	−0.165142
$880$	8.36550	0.282001
$881$	53.0217	1.78635	0.893173	−	0.449714i	$-0.148474\pi$
$881$	53.0217	1.78635	0.893173	+	0.449714i	$0.148474\pi$
$882$	−4.32181	−0.145523
$883$	−24.3069	−0.817993	−0.408996	−	0.912536i	$-0.634121\pi$
$883$	−24.3069	−0.817993	−0.408996	+	0.912536i	$0.634121\pi$
$884$	−37.1730	−1.25026
$885$	−7.78014	−0.261527
$886$	−3.55095	−0.119297
$887$	11.0880	0.372299	0.186149	−	0.982521i	$-0.440399\pi$
$887$	11.0880	0.372299	0.186149	+	0.982521i	$0.440399\pi$
$888$	−0.457577	−0.0153553
$889$	−4.31895	−0.144853
$890$	1.87892	0.0629815
$891$	−2.82826	−0.0947503
$892$	44.8885	1.50298
$893$	70.4456	2.35737
$894$	5.88689	0.196887
$895$	10.1838	0.340408
$896$	42.8031	1.42995
$897$	−5.62756	−0.187899
$898$	0.290232	0.00968517
$899$	−57.5569	−1.91963
$900$	7.71476	0.257159
$901$	17.6885	0.589290
$902$	12.6404	0.420880
$903$	−12.8842	−0.428761
$904$	4.55035	0.151343
$905$	−2.77940	−0.0923903
$906$	−6.60584	−0.219464
$907$	3.09372	0.102725	0.0513627	−	0.998680i	$-0.483644\pi$
$907$	3.09372	0.102725	0.0513627	+	0.998680i	$0.483644\pi$
$908$	−38.8961	−1.29081
$909$	−13.5844	−0.450565
$910$	−5.67098	−0.187991
$911$	0.822844	0.0272620	0.0136310	−	0.999907i	$-0.495661\pi$
$911$	0.822844	0.0272620	0.0136310	+	0.999907i	$0.495661\pi$
$912$	20.5179	0.679416
$913$	−13.3341	−0.441293
$914$	9.91412	0.327930
$915$	7.97773	0.263736
$916$	14.5964	0.482280
$917$	66.0421	2.18090
$918$	−1.93631	−0.0639077
$919$	5.22694	0.172421	0.0862105	−	0.996277i	$-0.472524\pi$
$919$	5.22694	0.172421	0.0862105	+	0.996277i	$0.472524\pi$
$920$	1.95299	0.0643881
$921$	30.3388	0.999696
$922$	1.74017	0.0573095
$923$	52.7707	1.73697
$924$	−22.7502	−0.748425
$925$	−1.32318	−0.0435060
$926$	−1.54835	−0.0508820
$927$	14.8857	0.488912
$928$	32.9393	1.08129
$929$	−0.790482	−0.0259349	−0.0129674	−	0.999916i	$-0.504128\pi$
$929$	−0.790482	−0.0259349	−0.0129674	+	0.999916i	$0.504128\pi$
$930$	−2.43031	−0.0796931
$931$	−74.8675	−2.45368
$932$	14.3477	0.469974
$933$	27.8232	0.910890
$934$	−0.938648	−0.0307135
$935$	−13.6760	−0.447254
$936$	−5.47598	−0.178988
$937$	−0.218494	−0.00713790	−0.00356895	−	0.999994i	$-0.501136\pi$
$937$	−0.218494	−0.00713790	−0.00356895	+	0.999994i	$0.501136\pi$
$938$	6.13113	0.200188
$939$	−33.7179	−1.10034
$940$	−18.9138	−0.616901
$941$	−2.19880	−0.0716787	−0.0358393	−	0.999358i	$-0.511410\pi$
$941$	−2.19880	−0.0716787	−0.0358393	+	0.999358i	$0.511410\pi$
$942$	−0.990082	−0.0322586
$943$	−17.7404	−0.577708
$944$	−26.8285	−0.873193
$945$	4.00000	0.130120
$946$	3.12908	0.101735
$947$	19.3998	0.630407	0.315204	−	0.949024i	$-0.397927\pi$
$947$	19.3998	0.630407	0.315204	+	0.949024i	$0.397927\pi$
$948$	−17.2566	−0.560469
$949$	34.6401	1.12447
$950$	−9.86949	−0.320208
$951$	−11.2137	−0.363630
$952$	−32.3010	−1.04688
$953$	24.0211	0.778121	0.389060	−	0.921212i	$-0.372800\pi$
$953$	24.0211	0.778121	0.389060	+	0.921212i	$0.372800\pi$
$954$	1.25646	0.0406794
$955$	−9.23037	−0.298688
$956$	36.8757	1.19265
$957$	−23.0066	−0.743697
$958$	5.80540	0.187564
$959$	48.2245	1.55725
$960$	−4.52480	−0.146037
$961$	19.0645	0.614983
$962$	0.452880	0.0146014
$963$	8.70031	0.280364
$964$	7.90527	0.254611
$965$	4.74187	0.152646
$966$	−2.35793	−0.0758653
$967$	−23.5414	−0.757041	−0.378521	−	0.925593i	$-0.623567\pi$
$967$	−23.5414	−0.757041	−0.378521	+	0.925593i	$0.623567\pi$
$968$	−4.29869	−0.138165
$969$	−33.5430	−1.07756
$970$	5.82659	0.187080
$971$	−30.3654	−0.974472	−0.487236	−	0.873270i	$-0.661995\pi$
$971$	−30.3654	−0.974472	−0.487236	+	0.873270i	$0.661995\pi$
$972$	1.86246	0.0597384
$973$	−7.12552	−0.228434
$974$	8.41742	0.269711
$975$	−15.8350	−0.507126
$976$	27.5099	0.880569
$977$	−31.2725	−1.00050	−0.500248	−	0.865882i	$-0.666758\pi$
$977$	−31.2725	−1.00050	−0.500248	+	0.865882i	$0.666758\pi$
$978$	−3.59053	−0.114812
$979$	−15.4714	−0.494468
$980$	20.1010	0.642104
$981$	1.77300	0.0566075
$982$	−2.93595	−0.0936898
$983$	−34.2489	−1.09237	−0.546186	−	0.837664i	$-0.683921\pi$
$983$	−34.2489	−1.09237	−0.546186	+	0.837664i	$0.683921\pi$
$984$	−17.2626	−0.550312
$985$	−7.86460	−0.250587
$986$	−15.7510	−0.501613
$987$	47.3575	1.50741
$988$	−45.7417	−1.45524
$989$	−4.39156	−0.139643
$990$	−0.971443	−0.0308745
$991$	−23.2901	−0.739834	−0.369917	−	0.929065i	$-0.620614\pi$
$991$	−23.2901	−0.739834	−0.369917	+	0.929065i	$0.620614\pi$
$992$	−28.6515	−0.909686
$993$	28.4207	0.901903
$994$	22.1108	0.701312
$995$	−10.8519	−0.344027
$996$	8.78071	0.278228
$997$	39.4698	1.25002	0.625010	−	0.780617i	$-0.285095\pi$
$997$	39.4698	1.25002	0.625010	+	0.780617i	$0.285095\pi$
$998$	−13.4594	−0.426050
$999$	−0.319436	−0.0101065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	381.2.a.c.1.3	✓	5
3.2	odd	2		1143.2.a.h.1.3		5
4.3	odd	2		6096.2.a.be.1.3		5
5.4	even	2		9525.2.a.k.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
381.2.a.c.1.3	✓	5	1.1	even	1	trivial
1143.2.a.h.1.3		5	3.2	odd	2
6096.2.a.be.1.3		5	4.3	odd	2
9525.2.a.k.1.3		5	5.4	even	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:	\( N \)	\(=\)	\( 381 = 3 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	381.a (trivial)

\(f(q)\)	\(=\)	\(q-0.370865 q^{2} -1.00000 q^{3} -1.86246 q^{4} -0.926151 q^{5} +0.370865 q^{6} +4.31895 q^{7} +1.43245 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.370865 q^{2} -1.00000 q^{3} -1.86246 q^{4} -0.926151 q^{5} +0.370865 q^{6} +4.31895 q^{7} +1.43245 q^{8} +1.00000 q^{9} +0.343477 q^{10} -2.82826 q^{11} +1.86246 q^{12} -3.82281 q^{13} -1.60175 q^{14} +0.926151 q^{15} +3.19367 q^{16} -5.22106 q^{17} -0.370865 q^{18} -6.42455 q^{19} +1.72492 q^{20} -4.31895 q^{21} +1.04890 q^{22} -1.47210 q^{23} -1.43245 q^{24} -4.14224 q^{25} +1.41775 q^{26} -1.00000 q^{27} -8.04387 q^{28} -8.13453 q^{29} -0.343477 q^{30} +7.07562 q^{31} -4.04932 q^{32} +2.82826 q^{33} +1.93631 q^{34} -4.00000 q^{35} -1.86246 q^{36} +0.319436 q^{37} +2.38264 q^{38} +3.82281 q^{39} -1.32667 q^{40} +12.0511 q^{41} +1.60175 q^{42} +2.98319 q^{43} +5.26752 q^{44} -0.926151 q^{45} +0.545951 q^{46} -10.9651 q^{47} -3.19367 q^{48} +11.6533 q^{49} +1.53621 q^{50} +5.22106 q^{51} +7.11982 q^{52} -3.38792 q^{53} +0.370865 q^{54} +2.61940 q^{55} +6.18668 q^{56} +6.42455 q^{57} +3.01681 q^{58} -8.40051 q^{59} -1.72492 q^{60} +8.61386 q^{61} -2.62410 q^{62} +4.31895 q^{63} -4.88559 q^{64} +3.54050 q^{65} -1.04890 q^{66} -3.82778 q^{67} +9.72401 q^{68} +1.47210 q^{69} +1.48346 q^{70} -13.8042 q^{71} +1.43245 q^{72} -9.06144 q^{73} -0.118468 q^{74} +4.14224 q^{75} +11.9655 q^{76} -12.2151 q^{77} -1.41775 q^{78} -9.26550 q^{79} -2.95782 q^{80} +1.00000 q^{81} -4.46933 q^{82} +4.71458 q^{83} +8.04387 q^{84} +4.83549 q^{85} -1.10636 q^{86} +8.13453 q^{87} -4.05134 q^{88} +5.47029 q^{89} +0.343477 q^{90} -16.5105 q^{91} +2.74173 q^{92} -7.07562 q^{93} +4.06655 q^{94} +5.95011 q^{95} +4.04932 q^{96} +16.9635 q^{97} -4.32181 q^{98} -2.82826 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} - 5 q^{3} + q^{4} - 5 q^{5} + q^{6} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - q^2 - 5 * q^3 + q^4 - 5 * q^5 + q^6 - 3 * q^8 + 5 * q^9	\( 5 q - q^{2} - 5 q^{3} + q^{4} - 5 q^{5} + q^{6} - 3 q^{8} + 5 q^{9} - 2 q^{10} - 16 q^{11} - q^{12} + 3 q^{13} - 6 q^{14} + 5 q^{15} - 7 q^{16} - 6 q^{17} - q^{18} - 8 q^{19} - 12 q^{20} - 8 q^{22} - 9 q^{23} + 3 q^{24} + 4 q^{25} - 2 q^{26} - 5 q^{27} + 2 q^{28} - 17 q^{29} + 2 q^{30} - 9 q^{31} - 2 q^{32} + 16 q^{33} - q^{34} - 20 q^{35} + q^{36} - q^{37} + q^{38} - 3 q^{39} + 16 q^{40} - 2 q^{41} + 6 q^{42} - 4 q^{43} + 3 q^{44} - 5 q^{45} + 4 q^{46} - 8 q^{47} + 7 q^{48} + 13 q^{49} + 15 q^{50} + 6 q^{51} + 13 q^{52} - 15 q^{53} + q^{54} + 20 q^{55} + 8 q^{56} + 8 q^{57} + 34 q^{58} - 19 q^{59} + 12 q^{60} + q^{61} + 15 q^{62} + q^{64} - 5 q^{65} + 8 q^{66} - 2 q^{67} + 14 q^{68} + 9 q^{69} + 4 q^{70} - 3 q^{72} + 13 q^{73} - 17 q^{74} - 4 q^{75} + 8 q^{76} + 2 q^{77} + 2 q^{78} - 28 q^{79} + 12 q^{80} + 5 q^{81} + 30 q^{82} - q^{83} - 2 q^{84} + 6 q^{85} + 32 q^{86} + 17 q^{87} + 3 q^{88} + q^{89} - 2 q^{90} - 18 q^{91} + 12 q^{92} + 9 q^{93} + 16 q^{94} + 4 q^{95} + 2 q^{96} + 28 q^{97} + 15 q^{98} - 16 q^{99}+O(q^{100}) \) 5 * q - q^2 - 5 * q^3 + q^4 - 5 * q^5 + q^6 - 3 * q^8 + 5 * q^9 - 2 * q^10 - 16 * q^11 - q^12 + 3 * q^13 - 6 * q^14 + 5 * q^15 - 7 * q^16 - 6 * q^17 - q^18 - 8 * q^19 - 12 * q^20 - 8 * q^22 - 9 * q^23 + 3 * q^24 + 4 * q^25 - 2 * q^26 - 5 * q^27 + 2 * q^28 - 17 * q^29 + 2 * q^30 - 9 * q^31 - 2 * q^32 + 16 * q^33 - q^34 - 20 * q^35 + q^36 - q^37 + q^38 - 3 * q^39 + 16 * q^40 - 2 * q^41 + 6 * q^42 - 4 * q^43 + 3 * q^44 - 5 * q^45 + 4 * q^46 - 8 * q^47 + 7 * q^48 + 13 * q^49 + 15 * q^50 + 6 * q^51 + 13 * q^52 - 15 * q^53 + q^54 + 20 * q^55 + 8 * q^56 + 8 * q^57 + 34 * q^58 - 19 * q^59 + 12 * q^60 + q^61 + 15 * q^62 + q^64 - 5 * q^65 + 8 * q^66 - 2 * q^67 + 14 * q^68 + 9 * q^69 + 4 * q^70 - 3 * q^72 + 13 * q^73 - 17 * q^74 - 4 * q^75 + 8 * q^76 + 2 * q^77 + 2 * q^78 - 28 * q^79 + 12 * q^80 + 5 * q^81 + 30 * q^82 - q^83 - 2 * q^84 + 6 * q^85 + 32 * q^86 + 17 * q^87 + 3 * q^88 + q^89 - 2 * q^90 - 18 * q^91 + 12 * q^92 + 9 * q^93 + 16 * q^94 + 4 * q^95 + 2 * q^96 + 28 * q^97 + 15 * q^98 - 16 * q^99

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