LMFDB - Embedded newform 301.2.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [301,2,Mod(1,301)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(301, 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("301.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 301 = 7 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	301.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:	$2.40349710084$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.1957.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} - x + 1 $ x^4 - 4*x^2 - x + 1
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			1.4
Root			$2.06150$ of defining polynomial
Character	$\chi$	$=$	301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.06150 q^{2} -0.326637 q^{3} -0.873220 q^{4} -3.24978 q^{5} -0.346725 q^{6} +1.00000 q^{7} -3.04992 q^{8} -2.89331 q^{9} +O(q^{10})$	\(q+1.06150 q^{2} -0.326637 q^{3} -0.873220 q^{4} -3.24978 q^{5} -0.346725 q^{6} +1.00000 q^{7} -3.04992 q^{8} -2.89331 q^{9} -3.44964 q^{10} -3.51492 q^{11} +0.285226 q^{12} +3.47947 q^{13} +1.06150 q^{14} +1.06150 q^{15} -1.49105 q^{16} -4.60808 q^{17} -3.07124 q^{18} +4.37278 q^{19} +2.83777 q^{20} -0.326637 q^{21} -3.73108 q^{22} -1.10853 q^{23} +0.996218 q^{24} +5.56105 q^{25} +3.69345 q^{26} +1.92497 q^{27} -0.873220 q^{28} -7.18266 q^{29} +1.12678 q^{30} +1.25952 q^{31} +4.51710 q^{32} +1.14810 q^{33} -4.89147 q^{34} -3.24978 q^{35} +2.52649 q^{36} -7.20275 q^{37} +4.64170 q^{38} -1.13652 q^{39} +9.91156 q^{40} +8.91936 q^{41} -0.346725 q^{42} +1.00000 q^{43} +3.06930 q^{44} +9.40261 q^{45} -1.17670 q^{46} -2.54097 q^{47} +0.487031 q^{48} +1.00000 q^{49} +5.90305 q^{50} +1.50517 q^{51} -3.03834 q^{52} -0.312166 q^{53} +2.04336 q^{54} +11.4227 q^{55} -3.04992 q^{56} -1.42831 q^{57} -7.62439 q^{58} -10.7609 q^{59} -0.926922 q^{60} -2.59467 q^{61} +1.33698 q^{62} -2.89331 q^{63} +7.77698 q^{64} -11.3075 q^{65} +1.21871 q^{66} -8.46411 q^{67} +4.02387 q^{68} +0.362086 q^{69} -3.44964 q^{70} +8.92225 q^{71} +8.82436 q^{72} -8.68818 q^{73} -7.64571 q^{74} -1.81645 q^{75} -3.81840 q^{76} -3.51492 q^{77} -1.20642 q^{78} -12.6878 q^{79} +4.84557 q^{80} +8.05116 q^{81} +9.46789 q^{82} -1.64915 q^{83} +0.285226 q^{84} +14.9752 q^{85} +1.06150 q^{86} +2.34613 q^{87} +10.7202 q^{88} +6.82803 q^{89} +9.98086 q^{90} +3.47947 q^{91} +0.967988 q^{92} -0.411407 q^{93} -2.69723 q^{94} -14.2105 q^{95} -1.47545 q^{96} +0.914286 q^{97} +1.06150 q^{98} +10.1697 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 3 q^{3} + 4 q^{4} - 4 q^{5} + 2 q^{6} + 4 q^{7} - 9 q^{8} + q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 3 * q^3 + 4 * q^4 - 4 * q^5 + 2 * q^6 + 4 * q^7 - 9 * q^8 + q^9	\( 4 q - 4 q^{2} - 3 q^{3} + 4 q^{4} - 4 q^{5} + 2 q^{6} + 4 q^{7} - 9 q^{8} + q^{9} + q^{10} - 15 q^{11} + 6 q^{12} + q^{13} - 4 q^{14} - 4 q^{15} + 12 q^{16} - q^{17} - 11 q^{18} - 8 q^{19} - 10 q^{20} - 3 q^{21} + 19 q^{22} - 5 q^{23} - 20 q^{24} - 4 q^{25} + 8 q^{26} - 15 q^{27} + 4 q^{28} - 16 q^{29} + 12 q^{30} + 3 q^{31} - 22 q^{32} + 14 q^{33} - 19 q^{34} - 4 q^{35} + 6 q^{36} - 11 q^{37} + 27 q^{38} - 19 q^{39} + 34 q^{40} + q^{41} + 2 q^{42} + 4 q^{43} - 25 q^{44} + 14 q^{45} - 9 q^{46} + 11 q^{47} + 37 q^{48} + 4 q^{49} + 18 q^{50} - 14 q^{52} - 20 q^{53} + 41 q^{54} + 17 q^{55} - 9 q^{56} + 11 q^{57} + 16 q^{58} - 11 q^{59} - 17 q^{60} - 10 q^{61} - 5 q^{62} + q^{63} + 47 q^{64} - 4 q^{65} - 13 q^{66} - 2 q^{67} + 35 q^{68} + 17 q^{69} + q^{70} - 11 q^{71} + 31 q^{72} + 13 q^{73} + 14 q^{74} + 16 q^{75} - 28 q^{76} - 15 q^{77} + 37 q^{78} - 32 q^{79} - 31 q^{80} + 36 q^{81} + 30 q^{82} - 15 q^{83} + 6 q^{84} + 5 q^{85} - 4 q^{86} + 25 q^{87} + 43 q^{88} - q^{89} - 3 q^{90} + q^{91} + 43 q^{92} - 33 q^{93} - 28 q^{94} - 10 q^{95} - 46 q^{96} + 22 q^{97} - 4 q^{98} - 22 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 3 * q^3 + 4 * q^4 - 4 * q^5 + 2 * q^6 + 4 * q^7 - 9 * q^8 + q^9 + q^10 - 15 * q^11 + 6 * q^12 + q^13 - 4 * q^14 - 4 * q^15 + 12 * q^16 - q^17 - 11 * q^18 - 8 * q^19 - 10 * q^20 - 3 * q^21 + 19 * q^22 - 5 * q^23 - 20 * q^24 - 4 * q^25 + 8 * q^26 - 15 * q^27 + 4 * q^28 - 16 * q^29 + 12 * q^30 + 3 * q^31 - 22 * q^32 + 14 * q^33 - 19 * q^34 - 4 * q^35 + 6 * q^36 - 11 * q^37 + 27 * q^38 - 19 * q^39 + 34 * q^40 + q^41 + 2 * q^42 + 4 * q^43 - 25 * q^44 + 14 * q^45 - 9 * q^46 + 11 * q^47 + 37 * q^48 + 4 * q^49 + 18 * q^50 - 14 * q^52 - 20 * q^53 + 41 * q^54 + 17 * q^55 - 9 * q^56 + 11 * q^57 + 16 * q^58 - 11 * q^59 - 17 * q^60 - 10 * q^61 - 5 * q^62 + q^63 + 47 * q^64 - 4 * q^65 - 13 * q^66 - 2 * q^67 + 35 * q^68 + 17 * q^69 + q^70 - 11 * q^71 + 31 * q^72 + 13 * q^73 + 14 * q^74 + 16 * q^75 - 28 * q^76 - 15 * q^77 + 37 * q^78 - 32 * q^79 - 31 * q^80 + 36 * q^81 + 30 * q^82 - 15 * q^83 + 6 * q^84 + 5 * q^85 - 4 * q^86 + 25 * q^87 + 43 * q^88 - q^89 - 3 * q^90 + q^91 + 43 * q^92 - 33 * q^93 - 28 * q^94 - 10 * q^95 - 46 * q^96 + 22 * q^97 - 4 * q^98 - 22 * 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 $

$2$	1.06150	0.750593	0.375297	−	0.926905i	$-0.377541\pi$
$2$	1.06150	0.750593	0.375297	+	0.926905i	$0.377541\pi$
$3$	−0.326637	−0.188584	−0.0942921	−	0.995545i	$-0.530059\pi$
$3$	−0.326637	−0.188584	−0.0942921	+	0.995545i	$0.530059\pi$
$4$	−0.873220	−0.436610
$5$	−3.24978	−1.45334	−0.726672	−	0.686984i	$-0.758934\pi$
$5$	−3.24978	−1.45334	−0.726672	+	0.686984i	$0.758934\pi$
$6$	−0.346725	−0.141550
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.04992	−1.07831
$9$	−2.89331	−0.964436
$10$	−3.44964	−1.09087
$11$	−3.51492	−1.05979	−0.529894	−	0.848064i	$-0.677768\pi$
$11$	−3.51492	−1.05979	−0.529894	+	0.848064i	$0.677768\pi$
$12$	0.285226	0.0823378
$13$	3.47947	0.965031	0.482515	−	0.875888i	$-0.339723\pi$
$13$	3.47947	0.965031	0.482515	+	0.875888i	$0.339723\pi$
$14$	1.06150	0.283698
$15$	1.06150	0.274078
$16$	−1.49105	−0.372762
$17$	−4.60808	−1.11762	−0.558812	−	0.829294i	$-0.688743\pi$
$17$	−4.60808	−1.11762	−0.558812	+	0.829294i	$0.688743\pi$
$18$	−3.07124	−0.723899
$19$	4.37278	1.00318	0.501592	−	0.865104i	$-0.332748\pi$
$19$	4.37278	1.00318	0.501592	+	0.865104i	$0.332748\pi$
$20$	2.83777	0.634545
$21$	−0.326637	−0.0712781
$22$	−3.73108	−0.795469
$23$	−1.10853	−0.231144	−0.115572	−	0.993299i	$-0.536870\pi$
$23$	−1.10853	−0.231144	−0.115572	+	0.993299i	$0.536870\pi$
$24$	0.996218	0.203352
$25$	5.56105	1.11221
$26$	3.69345	0.724345
$27$	1.92497	0.370462
$28$	−0.873220	−0.165023
$29$	−7.18266	−1.33379	−0.666893	−	0.745153i	$-0.732376\pi$
$29$	−7.18266	−1.33379	−0.666893	+	0.745153i	$0.732376\pi$
$30$	1.12678	0.205721
$31$	1.25952	0.226217	0.113108	−	0.993583i	$-0.463919\pi$
$31$	1.25952	0.226217	0.113108	+	0.993583i	$0.463919\pi$
$32$	4.51710	0.798517
$33$	1.14810	0.199859
$34$	−4.89147	−0.838881
$35$	−3.24978	−0.549313
$36$	2.52649	0.421082
$37$	−7.20275	−1.18412	−0.592062	−	0.805892i	$-0.701686\pi$
$37$	−7.20275	−1.18412	−0.592062	+	0.805892i	$0.701686\pi$
$38$	4.64170	0.752982
$39$	−1.13652	−0.181990
$40$	9.91156	1.56716
$41$	8.91936	1.39297	0.696485	−	0.717572i	$-0.254746\pi$
$41$	8.91936	1.39297	0.696485	+	0.717572i	$0.254746\pi$
$42$	−0.346725	−0.0535009
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	3.06930	0.462714
$45$	9.40261	1.40166
$46$	−1.17670	−0.173495
$47$	−2.54097	−0.370638	−0.185319	−	0.982678i	$-0.559332\pi$
$47$	−2.54097	−0.370638	−0.185319	+	0.982678i	$0.559332\pi$
$48$	0.487031	0.0702969
$49$	1.00000	0.142857
$50$	5.90305	0.834818
$51$	1.50517	0.210766
$52$	−3.03834	−0.421342
$53$	−0.312166	−0.0428793	−0.0214397	−	0.999770i	$-0.506825\pi$
$53$	−0.312166	−0.0428793	−0.0214397	+	0.999770i	$0.506825\pi$
$54$	2.04336	0.278066
$55$	11.4227	1.54024
$56$	−3.04992	−0.407563
$57$	−1.42831	−0.189185
$58$	−7.62439	−1.00113
$59$	−10.7609	−1.40095	−0.700476	−	0.713676i	$-0.747029\pi$
$59$	−10.7609	−1.40095	−0.700476	+	0.713676i	$0.747029\pi$
$60$	−0.926922	−0.119665
$61$	−2.59467	−0.332213	−0.166107	−	0.986108i	$-0.553120\pi$
$61$	−2.59467	−0.332213	−0.166107	+	0.986108i	$0.553120\pi$
$62$	1.33698	0.169797
$63$	−2.89331	−0.364523
$64$	7.77698	0.972123
$65$	−11.3075	−1.40252
$66$	1.21871	0.150013
$67$	−8.46411	−1.03406	−0.517028	−	0.855969i	$-0.672962\pi$
$67$	−8.46411	−1.03406	−0.517028	+	0.855969i	$0.672962\pi$
$68$	4.02387	0.487966
$69$	0.362086	0.0435901
$70$	−3.44964	−0.412310
$71$	8.92225	1.05888	0.529438	−	0.848349i	$-0.322403\pi$
$71$	8.92225	1.05888	0.529438	+	0.848349i	$0.322403\pi$
$72$	8.82436	1.03996
$73$	−8.68818	−1.01687	−0.508437	−	0.861099i	$-0.669777\pi$
$73$	−8.68818	−1.01687	−0.508437	+	0.861099i	$0.669777\pi$
$74$	−7.64571	−0.888796
$75$	−1.81645	−0.209745
$76$	−3.81840	−0.438000
$77$	−3.51492	−0.400562
$78$	−1.20642	−0.136600
$79$	−12.6878	−1.42749	−0.713746	−	0.700404i	$-0.753003\pi$
$79$	−12.6878	−1.42749	−0.713746	+	0.700404i	$0.753003\pi$
$80$	4.84557	0.541751
$81$	8.05116	0.894573
$82$	9.46789	1.04555
$83$	−1.64915	−0.181017	−0.0905087	−	0.995896i	$-0.528849\pi$
$83$	−1.64915	−0.181017	−0.0905087	+	0.995896i	$0.528849\pi$
$84$	0.285226	0.0311207
$85$	14.9752	1.62429
$86$	1.06150	0.114464
$87$	2.34613	0.251531
$88$	10.7202	1.14278
$89$	6.82803	0.723769	0.361885	−	0.932223i	$-0.382133\pi$
$89$	6.82803	0.723769	0.361885	+	0.932223i	$0.382133\pi$
$90$	9.98086	1.05207
$91$	3.47947	0.364747
$92$	0.967988	0.100920
$93$	−0.411407	−0.0426609
$94$	−2.69723	−0.278198
$95$	−14.2105	−1.45797
$96$	−1.47545	−0.150588
$97$	0.914286	0.0928317	0.0464158	−	0.998922i	$-0.485220\pi$
$97$	0.914286	0.0928317	0.0464158	+	0.998922i	$0.485220\pi$
$98$	1.06150	0.107228
$99$	10.1697	1.02210
$100$	−4.85602	−0.485602
$101$	9.23442	0.918859	0.459429	−	0.888214i	$-0.348054\pi$
$101$	9.23442	0.918859	0.459429	+	0.888214i	$0.348054\pi$
$102$	1.59774	0.158200
$103$	−8.83215	−0.870258	−0.435129	−	0.900368i	$-0.643297\pi$
$103$	−8.83215	−0.870258	−0.435129	+	0.900368i	$0.643297\pi$
$104$	−10.6121	−1.04060
$105$	1.06150	0.103592
$106$	−0.331364	−0.0321849
$107$	12.0964	1.16940	0.584702	−	0.811248i	$-0.301212\pi$
$107$	12.0964	1.16940	0.584702	+	0.811248i	$0.301212\pi$
$108$	−1.68093	−0.161747
$109$	−14.1807	−1.35827	−0.679133	−	0.734015i	$-0.737644\pi$
$109$	−14.1807	−1.35827	−0.679133	+	0.734015i	$0.737644\pi$
$110$	12.1252	1.15609
$111$	2.35269	0.223307
$112$	−1.49105	−0.140891
$113$	−16.8821	−1.58813	−0.794066	−	0.607832i	$-0.792040\pi$
$113$	−16.8821	−1.58813	−0.794066	+	0.607832i	$0.792040\pi$
$114$	−1.51615	−0.142001
$115$	3.60246	0.335932
$116$	6.27205	0.582345
$117$	−10.0672	−0.930710
$118$	−11.4227	−1.05154
$119$	−4.60808	−0.422422
$120$	−3.23749	−0.295541
$121$	1.35463	0.123149
$122$	−2.75424	−0.249357
$123$	−2.91340	−0.262692
$124$	−1.09984	−0.0987685
$125$	−1.82330	−0.163081
$126$	−3.07124	−0.273608
$127$	7.93472	0.704092	0.352046	−	0.935983i	$-0.385486\pi$
$127$	7.93472	0.704092	0.352046	+	0.935983i	$0.385486\pi$
$128$	−0.778932	−0.0688485
$129$	−0.326637	−0.0287588
$130$	−12.0029	−1.05272
$131$	−7.94139	−0.693843	−0.346921	−	0.937894i	$-0.612773\pi$
$131$	−7.94139	−0.693843	−0.346921	+	0.937894i	$0.612773\pi$
$132$	−1.00255	−0.0872605
$133$	4.37278	0.379168
$134$	−8.98464	−0.776155
$135$	−6.25574	−0.538408
$136$	14.0543	1.20514
$137$	18.9398	1.61814	0.809068	−	0.587715i	$-0.199972\pi$
$137$	18.9398	1.61814	0.809068	+	0.587715i	$0.199972\pi$
$138$	0.384354	0.0327184
$139$	−4.62528	−0.392311	−0.196155	−	0.980573i	$-0.562846\pi$
$139$	−4.62528	−0.392311	−0.196155	+	0.980573i	$0.562846\pi$
$140$	2.83777	0.239835
$141$	0.829975	0.0698965
$142$	9.47096	0.794785
$143$	−12.2300	−1.02273
$144$	4.31406	0.359505
$145$	23.3421	1.93845
$146$	−9.22249	−0.763259
$147$	−0.326637	−0.0269406
$148$	6.28959	0.517001
$149$	−5.39410	−0.441902	−0.220951	−	0.975285i	$-0.570916\pi$
$149$	−5.39410	−0.441902	−0.220951	+	0.975285i	$0.570916\pi$
$150$	−1.92816	−0.157433
$151$	3.49772	0.284640	0.142320	−	0.989821i	$-0.454544\pi$
$151$	3.49772	0.284640	0.142320	+	0.989821i	$0.454544\pi$
$152$	−13.3366	−1.08174
$153$	13.3326	1.07788
$154$	−3.73108	−0.300659
$155$	−4.09317	−0.328771
$156$	0.992436	0.0794585
$157$	−5.79258	−0.462298	−0.231149	−	0.972918i	$-0.574248\pi$
$157$	−5.79258	−0.462298	−0.231149	+	0.972918i	$0.574248\pi$
$158$	−13.4681	−1.07147
$159$	0.101965	0.00808637
$160$	−14.6796	−1.16052
$161$	−1.10853	−0.0873641
$162$	8.54629	0.671460
$163$	−17.1337	−1.34201	−0.671007	−	0.741451i	$-0.734138\pi$
$163$	−17.1337	−1.34201	−0.671007	+	0.741451i	$0.734138\pi$
$164$	−7.78856	−0.608185
$165$	−3.73108	−0.290464
$166$	−1.75057	−0.135870
$167$	−15.3961	−1.19139	−0.595693	−	0.803212i	$-0.703123\pi$
$167$	−15.3961	−1.19139	−0.595693	+	0.803212i	$0.703123\pi$
$168$	0.996218	0.0768599
$169$	−0.893308	−0.0687160
$170$	15.8962	1.21918
$171$	−12.6518	−0.967506
$172$	−0.873220	−0.0665824
$173$	25.1608	1.91294	0.956470	−	0.291831i	$-0.0942645\pi$
$173$	25.1608	1.91294	0.956470	+	0.291831i	$0.0942645\pi$
$174$	2.49041	0.188797
$175$	5.56105	0.420376
$176$	5.24090	0.395048
$177$	3.51492	0.264197
$178$	7.24794	0.543256
$179$	−19.2247	−1.43692	−0.718460	−	0.695569i	$-0.755153\pi$
$179$	−19.2247	−1.43692	−0.718460	+	0.695569i	$0.755153\pi$
$180$	−8.21055	−0.611978
$181$	5.05737	0.375911	0.187956	−	0.982178i	$-0.439814\pi$
$181$	5.05737	0.375911	0.187956	+	0.982178i	$0.439814\pi$
$182$	3.69345	0.273777
$183$	0.847516	0.0626502
$184$	3.38092	0.249245
$185$	23.4073	1.72094
$186$	−0.436708	−0.0320210
$187$	16.1970	1.18444
$188$	2.21882	0.161824
$189$	1.92497	0.140021
$190$	−15.0845	−1.09434
$191$	2.99349	0.216602	0.108301	−	0.994118i	$-0.465459\pi$
$191$	2.99349	0.216602	0.108301	+	0.994118i	$0.465459\pi$
$192$	−2.54025	−0.183327
$193$	17.1766	1.23640	0.618199	−	0.786022i	$-0.287863\pi$
$193$	17.1766	1.23640	0.618199	+	0.786022i	$0.287863\pi$
$194$	0.970513	0.0696788
$195$	3.69345	0.264493
$196$	−0.873220	−0.0623729
$197$	−2.27732	−0.162252	−0.0811260	−	0.996704i	$-0.525852\pi$
$197$	−2.27732	−0.162252	−0.0811260	+	0.996704i	$0.525852\pi$
$198$	10.7952	0.767179
$199$	−3.62906	−0.257257	−0.128629	−	0.991693i	$-0.541058\pi$
$199$	−3.62906	−0.257257	−0.128629	+	0.991693i	$0.541058\pi$
$200$	−16.9608	−1.19931
$201$	2.76469	0.195006
$202$	9.80232	0.689689
$203$	−7.18266	−0.504124
$204$	−1.31435	−0.0920227
$205$	−28.9859	−2.02447
$206$	−9.37532	−0.653210
$207$	3.20731	0.222923
$208$	−5.18805	−0.359726
$209$	−15.3699	−1.06316
$210$	1.12678	0.0777552
$211$	−21.3816	−1.47197	−0.735986	−	0.676997i	$-0.763281\pi$
$211$	−21.3816	−1.47197	−0.735986	+	0.676997i	$0.763281\pi$
$212$	0.272590	0.0187216
$213$	−2.91434	−0.199687
$214$	12.8403	0.877746
$215$	−3.24978	−0.221633
$216$	−5.87102	−0.399472
$217$	1.25952	0.0855019
$218$	−15.0528	−1.01951
$219$	2.83788	0.191766
$220$	−9.97453	−0.672483
$221$	−16.0337	−1.07854
$222$	2.49737	0.167613
$223$	26.9635	1.80561	0.902806	−	0.430047i	$-0.141503\pi$
$223$	26.9635	1.80561	0.902806	+	0.430047i	$0.141503\pi$
$224$	4.51710	0.301811
$225$	−16.0898	−1.07266
$226$	−17.9203	−1.19204
$227$	−23.6976	−1.57287	−0.786434	−	0.617675i	$-0.788075\pi$
$227$	−23.6976	−1.57287	−0.786434	+	0.617675i	$0.788075\pi$
$228$	1.24723	0.0825999
$229$	23.9396	1.58197	0.790987	−	0.611833i	$-0.209567\pi$
$229$	23.9396	1.58197	0.790987	+	0.611833i	$0.209567\pi$
$230$	3.82401	0.252148
$231$	1.14810	0.0755396
$232$	21.9065	1.43824
$233$	23.8600	1.56312	0.781562	−	0.623828i	$-0.214423\pi$
$233$	23.8600	1.56312	0.781562	+	0.623828i	$0.214423\pi$
$234$	−10.6863	−0.698585
$235$	8.25757	0.538665
$236$	9.39665	0.611669
$237$	4.14432	0.269203
$238$	−4.89147	−0.317067
$239$	0.908669	0.0587769	0.0293885	−	0.999568i	$-0.490644\pi$
$239$	0.908669	0.0587769	0.0293885	+	0.999568i	$0.490644\pi$
$240$	−1.58274	−0.102166
$241$	12.6582	0.815385	0.407693	−	0.913119i	$-0.366334\pi$
$241$	12.6582	0.815385	0.407693	+	0.913119i	$0.366334\pi$
$242$	1.43794	0.0924345
$243$	−8.40473	−0.539164
$244$	2.26572	0.145048
$245$	−3.24978	−0.207621
$246$	−3.09257	−0.197175
$247$	15.2149	0.968103
$248$	−3.84144	−0.243932
$249$	0.538673	0.0341370
$250$	−1.93543	−0.122407
$251$	−24.5168	−1.54749	−0.773744	−	0.633499i	$-0.781618\pi$
$251$	−24.5168	−1.54749	−0.773744	+	0.633499i	$0.781618\pi$
$252$	2.52649	0.159154
$253$	3.89638	0.244963
$254$	8.42270	0.528487
$255$	−4.89147	−0.306316
$256$	−16.3808	−1.02380
$257$	−19.8934	−1.24091	−0.620457	−	0.784241i	$-0.713053\pi$
$257$	−19.8934	−1.24091	−0.620457	+	0.784241i	$0.713053\pi$
$258$	−0.346725	−0.0215862
$259$	−7.20275	−0.447557
$260$	9.87393	0.612355
$261$	20.7817	1.28635
$262$	−8.42978	−0.520794
$263$	10.8183	0.667084	0.333542	−	0.942735i	$-0.391756\pi$
$263$	10.8183	0.667084	0.333542	+	0.942735i	$0.391756\pi$
$264$	−3.50162	−0.215510
$265$	1.01447	0.0623185
$266$	4.64170	0.284601
$267$	−2.23029	−0.136491
$268$	7.39103	0.451479
$269$	29.1818	1.77924	0.889622	−	0.456698i	$-0.150968\pi$
$269$	29.1818	1.77924	0.889622	+	0.456698i	$0.150968\pi$
$270$	−6.64046	−0.404126
$271$	18.3578	1.11515	0.557577	−	0.830125i	$-0.311731\pi$
$271$	18.3578	1.11515	0.557577	+	0.830125i	$0.311731\pi$
$272$	6.87086	0.416607
$273$	−1.13652	−0.0687856
$274$	20.1046	1.21456
$275$	−19.5466	−1.17871
$276$	−0.316181	−0.0190319
$277$	24.9331	1.49809	0.749043	−	0.662521i	$-0.230514\pi$
$277$	24.9331	1.49809	0.749043	+	0.662521i	$0.230514\pi$
$278$	−4.90973	−0.294466
$279$	−3.64418	−0.218172
$280$	9.91156	0.592329
$281$	3.05439	0.182210	0.0911049	−	0.995841i	$-0.470960\pi$
$281$	3.05439	0.182210	0.0911049	+	0.995841i	$0.470960\pi$
$282$	0.881017	0.0524638
$283$	−23.5353	−1.39903	−0.699516	−	0.714617i	$-0.746601\pi$
$283$	−23.5353	−1.39903	−0.699516	+	0.714617i	$0.746601\pi$
$284$	−7.79109	−0.462316
$285$	4.64170	0.274950
$286$	−12.9822	−0.767652
$287$	8.91936	0.526493
$288$	−13.0694	−0.770119
$289$	4.23442	0.249083
$290$	24.7776	1.45499
$291$	−0.298640	−0.0175066
$292$	7.58669	0.443978
$293$	22.1153	1.29199	0.645994	−	0.763343i	$-0.276443\pi$
$293$	22.1153	1.29199	0.645994	+	0.763343i	$0.276443\pi$
$294$	−0.346725	−0.0202214
$295$	34.9706	2.03607
$296$	21.9678	1.27685
$297$	−6.76612	−0.392610
$298$	−5.72583	−0.331688
$299$	−3.85708	−0.223061
$300$	1.58616	0.0915769
$301$	1.00000	0.0576390
$302$	3.71283	0.213649
$303$	−3.01631	−0.173282
$304$	−6.52001	−0.373948
$305$	8.43209	0.482820
$306$	14.1525	0.809047
$307$	30.7995	1.75782	0.878910	−	0.476988i	$-0.158272\pi$
$307$	30.7995	1.75782	0.878910	+	0.476988i	$0.158272\pi$
$308$	3.06930	0.174889
$309$	2.88491	0.164117
$310$	−4.34489	−0.246773
$311$	−0.955697	−0.0541926	−0.0270963	−	0.999633i	$-0.508626\pi$
$311$	−0.955697	−0.0541926	−0.0270963	+	0.999633i	$0.508626\pi$
$312$	3.46631	0.196241
$313$	−15.7483	−0.890145	−0.445073	−	0.895495i	$-0.646822\pi$
$313$	−15.7483	−0.890145	−0.445073	+	0.895495i	$0.646822\pi$
$314$	−6.14882	−0.346998
$315$	9.40261	0.529777
$316$	11.0793	0.623258
$317$	−19.5125	−1.09593	−0.547967	−	0.836500i	$-0.684598\pi$
$317$	−19.5125	−1.09593	−0.547967	+	0.836500i	$0.684598\pi$
$318$	0.108236	0.00606957
$319$	25.2465	1.41353
$320$	−25.2735	−1.41283
$321$	−3.95114	−0.220531
$322$	−1.17670	−0.0655749
$323$	−20.1501	−1.12118
$324$	−7.03043	−0.390580
$325$	19.3495	1.07332
$326$	−18.1874	−1.00731
$327$	4.63195	0.256148
$328$	−27.2033	−1.50205
$329$	−2.54097	−0.140088
$330$	−3.96054	−0.218020
$331$	6.56200	0.360680	0.180340	−	0.983604i	$-0.442280\pi$
$331$	6.56200	0.360680	0.180340	+	0.983604i	$0.442280\pi$
$332$	1.44007	0.0790340
$333$	20.8398	1.14201
$334$	−16.3429	−0.894246
$335$	27.5065	1.50284
$336$	0.487031	0.0265697
$337$	19.3069	1.05172	0.525858	−	0.850572i	$-0.323744\pi$
$337$	19.3069	1.05172	0.525858	+	0.850572i	$0.323744\pi$
$338$	−0.948245	−0.0515778
$339$	5.51432	0.299497
$340$	−13.0767	−0.709183
$341$	−4.42711	−0.239742
$342$	−13.4299	−0.726203
$343$	1.00000	0.0539949
$344$	−3.04992	−0.164441
$345$	−1.17670	−0.0633514
$346$	26.7082	1.43584
$347$	4.03562	0.216643	0.108322	−	0.994116i	$-0.465452\pi$
$347$	4.03562	0.216643	0.108322	+	0.994116i	$0.465452\pi$
$348$	−2.04868	−0.109821
$349$	−35.1994	−1.88418	−0.942089	−	0.335362i	$-0.891142\pi$
$349$	−35.1994	−1.88418	−0.942089	+	0.335362i	$0.891142\pi$
$350$	5.90305	0.315531
$351$	6.69789	0.357507
$352$	−15.8772	−0.846258
$353$	14.0884	0.749852	0.374926	−	0.927055i	$-0.377668\pi$
$353$	14.0884	0.749852	0.374926	+	0.927055i	$0.377668\pi$
$354$	3.73108	0.198305
$355$	−28.9953	−1.53891
$356$	−5.96237	−0.316005
$357$	1.50517	0.0796621
$358$	−20.4070	−1.07854
$359$	30.9121	1.63148	0.815740	−	0.578419i	$-0.196330\pi$
$359$	30.9121	1.63148	0.815740	+	0.578419i	$0.196330\pi$
$360$	−28.6772	−1.51142
$361$	0.121163	0.00637700
$362$	5.36839	0.282157
$363$	−0.442474	−0.0232239
$364$	−3.03834	−0.159252
$365$	28.2346	1.47787
$366$	0.899637	0.0470248
$367$	−3.08826	−0.161206	−0.0806030	−	0.996746i	$-0.525685\pi$
$367$	−3.08826	−0.161206	−0.0806030	+	0.996746i	$0.525685\pi$
$368$	1.65286	0.0861615
$369$	−25.8065	−1.34343
$370$	24.8469	1.29173
$371$	−0.312166	−0.0162069
$372$	0.359249	0.0186262
$373$	6.00656	0.311008	0.155504	−	0.987835i	$-0.450300\pi$
$373$	6.00656	0.311008	0.155504	+	0.987835i	$0.450300\pi$
$374$	17.1931	0.889035
$375$	0.595558	0.0307545
$376$	7.74974	0.399662
$377$	−24.9918	−1.28715
$378$	2.04336	0.105099
$379$	−27.9772	−1.43709	−0.718546	−	0.695480i	$-0.755192\pi$
$379$	−27.9772	−1.43709	−0.718546	+	0.695480i	$0.755192\pi$
$380$	12.4089	0.636565
$381$	−2.59178	−0.132781
$382$	3.17759	0.162580
$383$	−33.1048	−1.69158	−0.845788	−	0.533519i	$-0.820869\pi$
$383$	−33.1048	−1.69158	−0.845788	+	0.533519i	$0.820869\pi$
$384$	0.254428	0.0129837
$385$	11.4227	0.582154
$386$	18.2329	0.928032
$387$	−2.89331	−0.147075
$388$	−0.798373	−0.0405312
$389$	8.08631	0.409992	0.204996	−	0.978763i	$-0.434282\pi$
$389$	8.08631	0.409992	0.204996	+	0.978763i	$0.434282\pi$
$390$	3.92059	0.198527
$391$	5.10818	0.258332
$392$	−3.04992	−0.154044
$393$	2.59396	0.130848
$394$	−2.41737	−0.121785
$395$	41.2326	2.07464
$396$	−8.88042	−0.446258
$397$	−24.3536	−1.22227	−0.611136	−	0.791526i	$-0.709287\pi$
$397$	−24.3536	−1.22227	−0.611136	+	0.791526i	$0.709287\pi$
$398$	−3.85224	−0.193095
$399$	−1.42831	−0.0715050
$400$	−8.29179	−0.414589
$401$	9.32652	0.465744	0.232872	−	0.972507i	$-0.425188\pi$
$401$	9.32652	0.465744	0.232872	+	0.972507i	$0.425188\pi$
$402$	2.93472	0.146370
$403$	4.38246	0.218306
$404$	−8.06368	−0.401183
$405$	−26.1645	−1.30012
$406$	−7.62439	−0.378392
$407$	25.3171	1.25492
$408$	−4.59065	−0.227271
$409$	−10.5710	−0.522701	−0.261351	−	0.965244i	$-0.584168\pi$
$409$	−10.5710	−0.522701	−0.261351	+	0.965244i	$0.584168\pi$
$410$	−30.7685	−1.51955
$411$	−6.18644	−0.305155
$412$	7.71242	0.379963
$413$	−10.7609	−0.529510
$414$	3.40455	0.167325
$415$	5.35936	0.263081
$416$	15.7171	0.770594
$417$	1.51079	0.0739836
$418$	−16.3152	−0.798001
$419$	−9.30426	−0.454543	−0.227271	−	0.973831i	$-0.572980\pi$
$419$	−9.30426	−0.454543	−0.227271	+	0.973831i	$0.572980\pi$
$420$	−0.926922	−0.0452292
$421$	−33.8955	−1.65197	−0.825984	−	0.563694i	$-0.809380\pi$
$421$	−33.8955	−1.65197	−0.825984	+	0.563694i	$0.809380\pi$
$422$	−22.6966	−1.10485
$423$	7.35180	0.357457
$424$	0.952082	0.0462372
$425$	−25.6258	−1.24303
$426$	−3.09357	−0.149884
$427$	−2.59467	−0.125565
$428$	−10.5628	−0.510573
$429$	3.99479	0.192870
$430$	−3.44964	−0.166356
$431$	39.9234	1.92304	0.961522	−	0.274728i	$-0.0885879\pi$
$431$	39.9234	1.92304	0.961522	+	0.274728i	$0.0885879\pi$
$432$	−2.87023	−0.138094
$433$	8.94463	0.429852	0.214926	−	0.976630i	$-0.431049\pi$
$433$	8.94463	0.429852	0.214926	+	0.976630i	$0.431049\pi$
$434$	1.33698	0.0641771
$435$	−7.62439	−0.365561
$436$	12.3829	0.593033
$437$	−4.84734	−0.231880
$438$	3.01241	0.143939
$439$	27.3739	1.30648	0.653242	−	0.757149i	$-0.273408\pi$
$439$	27.3739	1.30648	0.653242	+	0.757149i	$0.273408\pi$
$440$	−34.8383	−1.66085
$441$	−2.89331	−0.137777
$442$	−17.0197	−0.809546
$443$	−5.16696	−0.245489	−0.122745	−	0.992438i	$-0.539170\pi$
$443$	−5.16696	−0.245489	−0.122745	+	0.992438i	$0.539170\pi$
$444$	−2.05441	−0.0974982
$445$	−22.1896	−1.05189
$446$	28.6218	1.35528
$447$	1.76191	0.0833357
$448$	7.77698	0.367428
$449$	−31.9375	−1.50722	−0.753612	−	0.657320i	$-0.771690\pi$
$449$	−31.9375	−1.50722	−0.753612	+	0.657320i	$0.771690\pi$
$450$	−17.0793	−0.805128
$451$	−31.3508	−1.47625
$452$	14.7418	0.693394
$453$	−1.14249	−0.0536787
$454$	−25.1550	−1.18058
$455$	−11.3075	−0.530104
$456$	4.35624	0.203999
$457$	−1.77653	−0.0831024	−0.0415512	−	0.999136i	$-0.513230\pi$
$457$	−1.77653	−0.0831024	−0.0415512	+	0.999136i	$0.513230\pi$
$458$	25.4119	1.18742
$459$	−8.87044	−0.414037
$460$	−3.14575	−0.146671
$461$	−16.7079	−0.778165	−0.389083	−	0.921203i	$-0.627208\pi$
$461$	−16.7079	−0.778165	−0.389083	+	0.921203i	$0.627208\pi$
$462$	1.21871	0.0566995
$463$	−32.2707	−1.49975	−0.749873	−	0.661582i	$-0.769886\pi$
$463$	−32.2707	−1.49975	−0.749873	+	0.661582i	$0.769886\pi$
$464$	10.7097	0.497184
$465$	1.33698	0.0620010
$466$	25.3274	1.17327
$467$	21.1602	0.979177	0.489589	−	0.871954i	$-0.337147\pi$
$467$	21.1602	0.979177	0.489589	+	0.871954i	$0.337147\pi$
$468$	8.79086	0.406357
$469$	−8.46411	−0.390836
$470$	8.76541	0.404318
$471$	1.89207	0.0871821
$472$	32.8199	1.51066
$473$	−3.51492	−0.161616
$474$	4.39919	0.202062
$475$	24.3172	1.11575
$476$	4.02387	0.184434
$477$	0.903193	0.0413544
$478$	0.964551	0.0441175
$479$	−26.9993	−1.23363	−0.616814	−	0.787109i	$-0.711577\pi$
$479$	−26.9993	−1.23363	−0.616814	+	0.787109i	$0.711577\pi$
$480$	4.79489	0.218856
$481$	−25.0617	−1.14272
$482$	13.4366	0.612022
$483$	0.362086	0.0164755
$484$	−1.18289	−0.0537679
$485$	−2.97123	−0.134916
$486$	−8.92161	−0.404693
$487$	8.74793	0.396407	0.198203	−	0.980161i	$-0.436489\pi$
$487$	8.74793	0.396407	0.198203	+	0.980161i	$0.436489\pi$
$488$	7.91353	0.358229
$489$	5.59650	0.253083
$490$	−3.44964	−0.155839
$491$	−38.4989	−1.73743	−0.868715	−	0.495311i	$-0.835054\pi$
$491$	−38.4989	−1.73743	−0.868715	+	0.495311i	$0.835054\pi$
$492$	2.54404	0.114694
$493$	33.0983	1.49067
$494$	16.1506	0.726651
$495$	−33.0494	−1.48546
$496$	−1.87801	−0.0843249
$497$	8.92225	0.400218
$498$	0.571801	0.0256230
$499$	−8.23335	−0.368575	−0.184288	−	0.982872i	$-0.558998\pi$
$499$	−8.23335	−0.368575	−0.184288	+	0.982872i	$0.558998\pi$
$500$	1.59214	0.0712028
$501$	5.02894	0.224677
$502$	−26.0246	−1.16153
$503$	10.3850	0.463042	0.231521	−	0.972830i	$-0.425630\pi$
$503$	10.3850	0.463042	0.231521	+	0.972830i	$0.425630\pi$
$504$	8.82436	0.393068
$505$	−30.0098	−1.33542
$506$	4.13600	0.183868
$507$	0.291788	0.0129588
$508$	−6.92876	−0.307414
$509$	−42.5450	−1.88578	−0.942888	−	0.333111i	$-0.891902\pi$
$509$	−42.5450	−1.88578	−0.942888	+	0.333111i	$0.891902\pi$
$510$	−5.19229	−0.229919
$511$	−8.68818	−0.384342
$512$	−15.8303	−0.699609
$513$	8.41748	0.371641
$514$	−21.1168	−0.931421
$515$	28.7025	1.26478
$516$	0.285226	0.0125564
$517$	8.93128	0.392797
$518$	−7.64571	−0.335933
$519$	−8.21846	−0.360750
$520$	34.4870	1.51235
$521$	−15.7186	−0.688645	−0.344322	−	0.938851i	$-0.611891\pi$
$521$	−15.7186	−0.688645	−0.344322	+	0.938851i	$0.611891\pi$
$522$	22.0597	0.965527
$523$	−16.6174	−0.726627	−0.363313	−	0.931667i	$-0.618355\pi$
$523$	−16.6174	−0.726627	−0.363313	+	0.931667i	$0.618355\pi$
$524$	6.93458	0.302939
$525$	−1.81645	−0.0792763
$526$	11.4836	0.500709
$527$	−5.80398	−0.252825
$528$	−1.71187	−0.0744998
$529$	−21.7712	−0.946573
$530$	1.07686	0.0467758
$531$	31.1346	1.35113
$532$	−3.81840	−0.165548
$533$	31.0346	1.34426
$534$	−2.36745	−0.102450
$535$	−39.3106	−1.69955
$536$	25.8148	1.11503
$537$	6.27950	0.270980
$538$	30.9764	1.33549
$539$	−3.51492	−0.151398
$540$	5.46264	0.235075
$541$	−15.4954	−0.666200	−0.333100	−	0.942891i	$-0.608095\pi$
$541$	−15.4954	−0.666200	−0.333100	+	0.942891i	$0.608095\pi$
$542$	19.4867	0.837027
$543$	−1.65193	−0.0708910
$544$	−20.8151	−0.892442
$545$	46.0842	1.97403
$546$	−1.20642	−0.0516300
$547$	33.9161	1.45015	0.725074	−	0.688671i	$-0.241806\pi$
$547$	33.9161	1.45015	0.725074	+	0.688671i	$0.241806\pi$
$548$	−16.5386	−0.706494
$549$	7.50717	0.320398
$550$	−20.7487	−0.884729
$551$	−31.4082	−1.33803
$552$	−1.10433	−0.0470036
$553$	−12.6878	−0.539542
$554$	26.4665	1.12445
$555$	−7.64571	−0.324542
$556$	4.03889	0.171287
$557$	15.6390	0.662644	0.331322	−	0.943518i	$-0.392505\pi$
$557$	15.6390	0.662644	0.331322	+	0.943518i	$0.392505\pi$
$558$	−3.86830	−0.163758
$559$	3.47947	0.147166
$560$	4.84557	0.204763
$561$	−5.29055	−0.223367
$562$	3.24223	0.136765
$563$	11.4692	0.483368	0.241684	−	0.970355i	$-0.422300\pi$
$563$	11.4692	0.483368	0.241684	+	0.970355i	$0.422300\pi$
$564$	−0.724751	−0.0305175
$565$	54.8630	2.30810
$566$	−24.9827	−1.05010
$567$	8.05116	0.338117
$568$	−27.2121	−1.14180
$569$	−9.30566	−0.390114	−0.195057	−	0.980792i	$-0.562489\pi$
$569$	−9.30566	−0.390114	−0.195057	+	0.980792i	$0.562489\pi$
$570$	4.92715	0.206376
$571$	−43.1235	−1.80466	−0.902330	−	0.431046i	$-0.858145\pi$
$571$	−43.1235	−1.80466	−0.902330	+	0.431046i	$0.858145\pi$
$572$	10.6795	0.446533
$573$	−0.977787	−0.0408476
$574$	9.46789	0.395182
$575$	−6.16458	−0.257081
$576$	−22.5012	−0.937550
$577$	−16.2387	−0.676026	−0.338013	−	0.941141i	$-0.609755\pi$
$577$	−16.2387	−0.676026	−0.338013	+	0.941141i	$0.609755\pi$
$578$	4.49483	0.186960
$579$	−5.61052	−0.233165
$580$	−20.3828	−0.846348
$581$	−1.64915	−0.0684182
$582$	−0.317006	−0.0131403
$583$	1.09724	0.0454430
$584$	26.4983	1.09651
$585$	32.7161	1.35264
$586$	23.4753	0.969756
$587$	−15.4160	−0.636287	−0.318144	−	0.948043i	$-0.603059\pi$
$587$	−15.4160	−0.636287	−0.318144	+	0.948043i	$0.603059\pi$
$588$	0.285226	0.0117625
$589$	5.50761	0.226937
$590$	37.1212	1.52826
$591$	0.743857	0.0305982
$592$	10.7396	0.441396
$593$	30.2486	1.24216	0.621080	−	0.783747i	$-0.286694\pi$
$593$	30.2486	1.24216	0.621080	+	0.783747i	$0.286694\pi$
$594$	−7.18223	−0.294691
$595$	14.9752	0.613925
$596$	4.71024	0.192939
$597$	1.18539	0.0485146
$598$	−4.09429	−0.167428
$599$	−15.6301	−0.638629	−0.319315	−	0.947649i	$-0.603453\pi$
$599$	−15.6301	−0.638629	−0.319315	+	0.947649i	$0.603453\pi$
$600$	5.54002	0.226170
$601$	26.5005	1.08098	0.540489	−	0.841351i	$-0.318239\pi$
$601$	26.5005	1.08098	0.540489	+	0.841351i	$0.318239\pi$
$602$	1.06150	0.0432635
$603$	24.4893	0.997280
$604$	−3.05428	−0.124277
$605$	−4.40226	−0.178977
$606$	−3.20181	−0.130064
$607$	5.67371	0.230289	0.115144	−	0.993349i	$-0.463267\pi$
$607$	5.67371	0.230289	0.115144	+	0.993349i	$0.463267\pi$
$608$	19.7522	0.801059
$609$	2.34613	0.0950698
$610$	8.95066	0.362402
$611$	−8.84121	−0.357677
$612$	−11.6423	−0.470612
$613$	−1.09938	−0.0444036	−0.0222018	−	0.999754i	$-0.507068\pi$
$613$	−1.09938	−0.0444036	−0.0222018	+	0.999754i	$0.507068\pi$
$614$	32.6936	1.31941
$615$	9.46789	0.381782
$616$	10.7202	0.431930
$617$	−46.2443	−1.86172	−0.930862	−	0.365371i	$-0.880942\pi$
$617$	−46.2443	−1.86172	−0.930862	+	0.365371i	$0.880942\pi$
$618$	3.06233	0.123185
$619$	7.57824	0.304595	0.152298	−	0.988335i	$-0.451333\pi$
$619$	7.57824	0.304595	0.152298	+	0.988335i	$0.451333\pi$
$620$	3.57423	0.143545
$621$	−2.13389	−0.0856299
$622$	−1.01447	−0.0406766
$623$	6.82803	0.273559
$624$	1.69461	0.0678387
$625$	−21.8799	−0.875198
$626$	−16.7168	−0.668137
$627$	5.02040	0.200495
$628$	5.05820	0.201844
$629$	33.1909	1.32341
$630$	9.98086	0.397647
$631$	−28.9525	−1.15258	−0.576290	−	0.817245i	$-0.695500\pi$
$631$	−28.9525	−1.15258	−0.576290	+	0.817245i	$0.695500\pi$
$632$	38.6969	1.53928
$633$	6.98404	0.277591
$634$	−20.7125	−0.822600
$635$	−25.7861	−1.02329
$636$	−0.0890381	−0.00353059
$637$	3.47947	0.137862
$638$	26.7991	1.06099
$639$	−25.8148	−1.02122
$640$	2.53136	0.100061
$641$	−23.4346	−0.925612	−0.462806	−	0.886460i	$-0.653157\pi$
$641$	−23.4346	−0.925612	−0.462806	+	0.886460i	$0.653157\pi$
$642$	−4.19413	−0.165529
$643$	−7.30755	−0.288182	−0.144091	−	0.989564i	$-0.546026\pi$
$643$	−7.30755	−0.288182	−0.144091	+	0.989564i	$0.546026\pi$
$644$	0.967988	0.0381441
$645$	1.06150	0.0417965
$646$	−21.3893	−0.841551
$647$	33.6955	1.32471	0.662354	−	0.749191i	$-0.269558\pi$
$647$	33.6955	1.32471	0.662354	+	0.749191i	$0.269558\pi$
$648$	−24.5554	−0.964626
$649$	37.8237	1.48471
$650$	20.5395	0.805625
$651$	−0.411407	−0.0161243
$652$	14.9615	0.585937
$653$	−8.22974	−0.322055	−0.161027	−	0.986950i	$-0.551481\pi$
$653$	−8.22974	−0.322055	−0.161027	+	0.986950i	$0.551481\pi$
$654$	4.91681	0.192263
$655$	25.8078	1.00839
$656$	−13.2992	−0.519246
$657$	25.1376	0.980710
$658$	−2.69723	−0.105149
$659$	−40.6210	−1.58237	−0.791184	−	0.611578i	$-0.790535\pi$
$659$	−40.6210	−1.58237	−0.791184	+	0.611578i	$0.790535\pi$
$660$	3.25805	0.126820
$661$	28.1121	1.09343	0.546717	−	0.837317i	$-0.315877\pi$
$661$	28.1121	1.09343	0.546717	+	0.837317i	$0.315877\pi$
$662$	6.96555	0.270724
$663$	5.23720	0.203396
$664$	5.02977	0.195193
$665$	−14.2105	−0.551061
$666$	22.1214	0.857187
$667$	7.96217	0.308297
$668$	13.4442	0.520171
$669$	−8.80730	−0.340510
$670$	29.1981	1.12802
$671$	9.12004	0.352075
$672$	−1.47545	−0.0569168
$673$	−27.3098	−1.05272	−0.526359	−	0.850263i	$-0.676443\pi$
$673$	−27.3098	−1.05272	−0.526359	+	0.850263i	$0.676443\pi$
$674$	20.4943	0.789411
$675$	10.7049	0.412031
$676$	0.780055	0.0300021
$677$	35.6166	1.36886	0.684428	−	0.729080i	$-0.260052\pi$
$677$	35.6166	1.36886	0.684428	+	0.729080i	$0.260052\pi$
$678$	5.85344	0.224800
$679$	0.914286	0.0350871
$680$	−45.6733	−1.75149
$681$	7.74053	0.296618
$682$	−4.69938	−0.179948
$683$	42.3482	1.62041	0.810205	−	0.586146i	$-0.199356\pi$
$683$	42.3482	1.62041	0.810205	+	0.586146i	$0.199356\pi$
$684$	11.0478	0.422423
$685$	−61.5501	−2.35171
$686$	1.06150	0.0405282
$687$	−7.81957	−0.298335
$688$	−1.49105	−0.0568456
$689$	−1.08617	−0.0413799
$690$	−1.24907	−0.0475511
$691$	10.5870	0.402748	0.201374	−	0.979514i	$-0.435459\pi$
$691$	10.5870	0.402748	0.201374	+	0.979514i	$0.435459\pi$
$692$	−21.9709	−0.835209
$693$	10.1697	0.386316
$694$	4.28380	0.162611
$695$	15.0311	0.570163
$696$	−7.15550	−0.271228
$697$	−41.1011	−1.55682
$698$	−37.3641	−1.41425
$699$	−7.79358	−0.294780
$700$	−4.85602	−0.183540
$701$	2.12282	0.0801778	0.0400889	−	0.999196i	$-0.487236\pi$
$701$	2.12282	0.0801778	0.0400889	+	0.999196i	$0.487236\pi$
$702$	7.10980	0.268342
$703$	−31.4960	−1.18789
$704$	−27.3354	−1.03024
$705$	−2.69723	−0.101584
$706$	14.9549	0.562834
$707$	9.23442	0.347296
$708$	−3.06930	−0.115351
$709$	24.1455	0.906804	0.453402	−	0.891306i	$-0.350210\pi$
$709$	24.1455	0.906804	0.453402	+	0.891306i	$0.350210\pi$
$710$	−30.7785	−1.15510
$711$	36.7098	1.37673
$712$	−20.8249	−0.780447
$713$	−1.39621	−0.0522886
$714$	1.59774	0.0597938
$715$	39.7449	1.48637
$716$	16.7874	0.627374
$717$	−0.296805	−0.0110844
$718$	32.8132	1.22458
$719$	4.74916	0.177114	0.0885570	−	0.996071i	$-0.471774\pi$
$719$	4.74916	0.177114	0.0885570	+	0.996071i	$0.471774\pi$
$720$	−14.0197	−0.522484
$721$	−8.83215	−0.328927
$722$	0.128614	0.00478653
$723$	−4.13463	−0.153769
$724$	−4.41620	−0.164127
$725$	−39.9432	−1.48345
$726$	−0.469686	−0.0174317
$727$	−1.94901	−0.0722849	−0.0361424	−	0.999347i	$-0.511507\pi$
$727$	−1.94901	−0.0722849	−0.0361424	+	0.999347i	$0.511507\pi$
$728$	−10.6121	−0.393310
$729$	−21.4082	−0.792895
$730$	29.9710	1.10928
$731$	−4.60808	−0.170436
$732$	−0.740068	−0.0273537
$733$	−51.9966	−1.92054	−0.960269	−	0.279075i	$-0.909972\pi$
$733$	−51.9966	−1.92054	−0.960269	+	0.279075i	$0.909972\pi$
$734$	−3.27819	−0.121000
$735$	1.06150	0.0391540
$736$	−5.00732	−0.184572
$737$	29.7506	1.09588
$738$	−27.3935	−1.00837
$739$	15.9633	0.587218	0.293609	−	0.955926i	$-0.405144\pi$
$739$	15.9633	0.587218	0.293609	+	0.955926i	$0.405144\pi$
$740$	−20.4398	−0.751380
$741$	−4.96976	−0.182569
$742$	−0.331364	−0.0121648
$743$	7.63117	0.279961	0.139980	−	0.990154i	$-0.455296\pi$
$743$	7.63117	0.279961	0.139980	+	0.990154i	$0.455296\pi$
$744$	1.25476	0.0460017
$745$	17.5296	0.642236
$746$	6.37596	0.233440
$747$	4.77149	0.174580
$748$	−14.1436	−0.517140
$749$	12.0964	0.441993
$750$	0.632184	0.0230841
$751$	−5.49325	−0.200451	−0.100226	−	0.994965i	$-0.531956\pi$
$751$	−5.49325	−0.200451	−0.100226	+	0.994965i	$0.531956\pi$
$752$	3.78870	0.138160
$753$	8.00811	0.291832
$754$	−26.5288	−0.966122
$755$	−11.3668	−0.413681
$756$	−1.68093	−0.0611347
$757$	−2.74171	−0.0996493	−0.0498246	−	0.998758i	$-0.515866\pi$
$757$	−2.74171	−0.0996493	−0.0498246	+	0.998758i	$0.515866\pi$
$758$	−29.6978	−1.07867
$759$	−1.27270	−0.0461962
$760$	43.3410	1.57214
$761$	14.1691	0.513629	0.256814	−	0.966461i	$-0.417327\pi$
$761$	14.1691	0.513629	0.256814	+	0.966461i	$0.417327\pi$
$762$	−2.75117	−0.0996643
$763$	−14.1807	−0.513376
$764$	−2.61398	−0.0945704
$765$	−43.3280	−1.56653
$766$	−35.1407	−1.26969
$767$	−37.4422	−1.35196
$768$	5.35058	0.193073
$769$	0.339329	0.0122365	0.00611825	−	0.999981i	$-0.498052\pi$
$769$	0.339329	0.0122365	0.00611825	+	0.999981i	$0.498052\pi$
$770$	12.1252	0.436961
$771$	6.49792	0.234017
$772$	−14.9989	−0.539824
$773$	43.8177	1.57601	0.788007	−	0.615666i	$-0.211113\pi$
$773$	43.8177	1.57601	0.788007	+	0.615666i	$0.211113\pi$
$774$	−3.07124	−0.110394
$775$	7.00427	0.251601
$776$	−2.78850	−0.100101
$777$	2.35269	0.0844022
$778$	8.58361	0.307737
$779$	39.0023	1.39740
$780$	−3.22520	−0.115481
$781$	−31.3610	−1.12218
$782$	5.42233	0.193902
$783$	−13.8264	−0.494117
$784$	−1.49105	−0.0532516
$785$	18.8246	0.671878
$786$	2.75348	0.0982134
$787$	−11.0694	−0.394582	−0.197291	−	0.980345i	$-0.563214\pi$
$787$	−11.0694	−0.394582	−0.197291	+	0.980345i	$0.563214\pi$
$788$	1.98860	0.0708409
$789$	−3.53366	−0.125801
$790$	43.7684	1.55721
$791$	−16.8821	−0.600257
$792$	−31.0169	−1.10214
$793$	−9.02806	−0.320596
$794$	−25.8513	−0.917428
$795$	−0.331364	−0.0117523
$796$	3.16897	0.112321
$797$	−13.6175	−0.482356	−0.241178	−	0.970481i	$-0.577534\pi$
$797$	−13.6175	−0.482356	−0.241178	+	0.970481i	$0.577534\pi$
$798$	−1.51615	−0.0536712
$799$	11.7090	0.414234
$800$	25.1198	0.888120
$801$	−19.7556	−0.698029
$802$	9.90010	0.349585
$803$	30.5382	1.07767
$804$	−2.41419	−0.0851418
$805$	3.60246	0.126970
$806$	4.65198	0.163859
$807$	−9.53186	−0.335537
$808$	−28.1642	−0.990814
$809$	28.7414	1.01050	0.505248	−	0.862974i	$-0.331401\pi$
$809$	28.7414	1.01050	0.505248	+	0.862974i	$0.331401\pi$
$810$	−27.7735	−0.975863
$811$	−19.3972	−0.681129	−0.340564	−	0.940221i	$-0.610618\pi$
$811$	−19.3972	−0.681129	−0.340564	+	0.940221i	$0.610618\pi$
$812$	6.27205	0.220106
$813$	−5.99633	−0.210300
$814$	26.8740	0.941934
$815$	55.6807	1.95041
$816$	−2.24428	−0.0785655
$817$	4.37278	0.152984
$818$	−11.2211	−0.392336
$819$	−10.0672	−0.351775
$820$	25.3111	0.883902
$821$	−32.5505	−1.13602	−0.568010	−	0.823022i	$-0.692286\pi$
$821$	−32.5505	−1.13602	−0.568010	+	0.823022i	$0.692286\pi$
$822$	−6.56690	−0.229047
$823$	15.9033	0.554354	0.277177	−	0.960819i	$-0.410601\pi$
$823$	15.9033	0.554354	0.277177	+	0.960819i	$0.410601\pi$
$824$	26.9374	0.938408
$825$	6.38466	0.222285
$826$	−11.4227	−0.397446
$827$	−25.4608	−0.885357	−0.442679	−	0.896680i	$-0.645972\pi$
$827$	−25.4608	−0.885357	−0.442679	+	0.896680i	$0.645972\pi$
$828$	−2.80069	−0.0973306
$829$	−17.4003	−0.604338	−0.302169	−	0.953254i	$-0.597711\pi$
$829$	−17.4003	−0.604338	−0.302169	+	0.953254i	$0.597711\pi$
$830$	5.68896	0.197467
$831$	−8.14409	−0.282515
$832$	27.0598	0.938128
$833$	−4.60808	−0.159661
$834$	1.60370	0.0555316
$835$	50.0339	1.73149
$836$	13.4213	0.464187
$837$	2.42455	0.0838046
$838$	−9.87646	−0.341177
$839$	−37.4422	−1.29265	−0.646325	−	0.763062i	$-0.723695\pi$
$839$	−37.4422	−1.29265	−0.646325	+	0.763062i	$0.723695\pi$
$840$	−3.23749	−0.111704
$841$	22.5906	0.778987
$842$	−35.9801	−1.23996
$843$	−0.997679	−0.0343619
$844$	18.6709	0.642678
$845$	2.90305	0.0998680
$846$	7.80392	0.268304
$847$	1.35463	0.0465458
$848$	0.465454	0.0159838
$849$	7.68753	0.263835
$850$	−27.2017	−0.933012
$851$	7.98444	0.273703
$852$	2.54486	0.0871855
$853$	−34.3713	−1.17685	−0.588426	−	0.808551i	$-0.700252\pi$
$853$	−34.3713	−1.17685	−0.588426	+	0.808551i	$0.700252\pi$
$854$	−2.75424	−0.0942481
$855$	41.1155	1.40612
$856$	−36.8931	−1.26098
$857$	22.3715	0.764194	0.382097	−	0.924122i	$-0.375202\pi$
$857$	22.3715	0.764194	0.382097	+	0.924122i	$0.375202\pi$
$858$	4.24046	0.144767
$859$	−12.8250	−0.437584	−0.218792	−	0.975772i	$-0.570212\pi$
$859$	−12.8250	−0.437584	−0.218792	+	0.975772i	$0.570212\pi$
$860$	2.83777	0.0967672
$861$	−2.91340	−0.0992883
$862$	42.3787	1.44342
$863$	−11.9595	−0.407105	−0.203553	−	0.979064i	$-0.565249\pi$
$863$	−11.9595	−0.407105	−0.203553	+	0.979064i	$0.565249\pi$
$864$	8.69530	0.295820
$865$	−81.7670	−2.78016
$866$	9.49472	0.322644
$867$	−1.38312	−0.0469732
$868$	−1.09984	−0.0373310
$869$	44.5967	1.51284
$870$	−8.09328	−0.274388
$871$	−29.4506	−0.997895
$872$	43.2500	1.46463
$873$	−2.64531	−0.0895302
$874$	−5.14544	−0.174047
$875$	−1.82330	−0.0616388
$876$	−2.47810	−0.0837272
$877$	−3.62811	−0.122513	−0.0612564	−	0.998122i	$-0.519511\pi$
$877$	−3.62811	−0.122513	−0.0612564	+	0.998122i	$0.519511\pi$
$878$	29.0574	0.980638
$879$	−7.22367	−0.243648
$880$	−17.0318	−0.574141
$881$	2.37575	0.0800412	0.0400206	−	0.999199i	$-0.487258\pi$
$881$	2.37575	0.0800412	0.0400206	+	0.999199i	$0.487258\pi$
$882$	−3.07124	−0.103414
$883$	46.4241	1.56230	0.781148	−	0.624346i	$-0.214634\pi$
$883$	46.4241	1.56230	0.781148	+	0.624346i	$0.214634\pi$
$884$	14.0009	0.470902
$885$	−11.4227	−0.383970
$886$	−5.48472	−0.184263
$887$	−2.53446	−0.0850988	−0.0425494	−	0.999094i	$-0.513548\pi$
$887$	−2.53446	−0.0850988	−0.0425494	+	0.999094i	$0.513548\pi$
$888$	−7.17551	−0.240794
$889$	7.93472	0.266122
$890$	−23.5542	−0.789539
$891$	−28.2991	−0.948057
$892$	−23.5451	−0.788349
$893$	−11.1111	−0.371818
$894$	1.87027	0.0625512
$895$	62.4759	2.08834
$896$	−0.778932	−0.0260223
$897$	1.25987	0.0420657
$898$	−33.9016	−1.13131
$899$	−9.04672	−0.301725
$900$	14.0500	0.468332
$901$	1.43849	0.0479230
$902$	−33.2788	−1.10806
$903$	−0.326637	−0.0108698
$904$	51.4890	1.71250
$905$	−16.4353	−0.546329
$906$	−1.21275	−0.0402908
$907$	−4.59484	−0.152569	−0.0762845	−	0.997086i	$-0.524306\pi$
$907$	−4.59484	−0.152569	−0.0762845	+	0.997086i	$0.524306\pi$
$908$	20.6933	0.686730
$909$	−26.7180	−0.886180
$910$	−12.0029	−0.397892
$911$	−46.1008	−1.52739	−0.763693	−	0.645580i	$-0.776616\pi$
$911$	−46.1008	−1.52739	−0.763693	+	0.645580i	$0.776616\pi$
$912$	2.12968	0.0705207
$913$	5.79661	0.191840
$914$	−1.88578	−0.0623761
$915$	−2.75424	−0.0910523
$916$	−20.9046	−0.690706
$917$	−7.94139	−0.262248
$918$	−9.41596	−0.310773
$919$	14.5854	0.481129	0.240565	−	0.970633i	$-0.422667\pi$
$919$	14.5854	0.481129	0.240565	+	0.970633i	$0.422667\pi$
$920$	−10.9872	−0.362238
$921$	−10.0603	−0.331497
$922$	−17.7354	−0.584086
$923$	31.0447	1.02185
$924$	−1.00255	−0.0329814
$925$	−40.0549	−1.31700
$926$	−34.2553	−1.12570
$927$	25.5541	0.839308
$928$	−32.4448	−1.06505
$929$	1.18957	0.0390285	0.0195142	−	0.999810i	$-0.493788\pi$
$929$	1.18957	0.0390285	0.0195142	+	0.999810i	$0.493788\pi$
$930$	1.41920	0.0465375
$931$	4.37278	0.143312
$932$	−20.8351	−0.682475
$933$	0.312166	0.0102199
$934$	22.4615	0.734963
$935$	−52.6367	−1.72140
$936$	30.7041	1.00359
$937$	28.4769	0.930300	0.465150	−	0.885232i	$-0.346000\pi$
$937$	28.4769	0.930300	0.465150	+	0.885232i	$0.346000\pi$
$938$	−8.98464	−0.293359
$939$	5.14398	0.167867
$940$	−7.21068	−0.235186
$941$	33.6825	1.09802	0.549009	−	0.835816i	$-0.315005\pi$
$941$	33.6825	1.09802	0.549009	+	0.835816i	$0.315005\pi$
$942$	2.00843	0.0654383
$943$	−9.88735	−0.321976
$944$	16.0450	0.522221
$945$	−6.25574	−0.203499
$946$	−3.73108	−0.121308
$947$	−32.2123	−1.04676	−0.523379	−	0.852100i	$-0.675329\pi$
$947$	−32.2123	−1.04676	−0.523379	+	0.852100i	$0.675329\pi$
$948$	−3.61890	−0.117537
$949$	−30.2302	−0.981315
$950$	25.8127	0.837475
$951$	6.37352	0.206676
$952$	14.0543	0.455502
$953$	2.47356	0.0801265	0.0400632	−	0.999197i	$-0.487244\pi$
$953$	2.47356	0.0801265	0.0400632	+	0.999197i	$0.487244\pi$
$954$	0.958739	0.0310403
$955$	−9.72819	−0.314797
$956$	−0.793468	−0.0256626
$957$	−8.24644	−0.266569
$958$	−28.6597	−0.925953
$959$	18.9398	0.611598
$960$	8.25526	0.266437
$961$	−29.4136	−0.948826
$962$	−26.6030	−0.857715
$963$	−34.9986	−1.12781
$964$	−11.0534	−0.356005
$965$	−55.8201	−1.79691
$966$	0.384354	0.0123664
$967$	59.2186	1.90434	0.952171	−	0.305564i	$-0.0988451\pi$
$967$	59.2186	1.90434	0.952171	+	0.305564i	$0.0988451\pi$
$968$	−4.13153	−0.132792
$969$	6.58178	0.211437
$970$	−3.15395	−0.101267
$971$	34.6901	1.11326	0.556629	−	0.830761i	$-0.312095\pi$
$971$	34.6901	1.11326	0.556629	+	0.830761i	$0.312095\pi$
$972$	7.33918	0.235404
$973$	−4.62528	−0.148280
$974$	9.28592	0.297540
$975$	−6.32027	−0.202411
$976$	3.86877	0.123836
$977$	−1.28706	−0.0411767	−0.0205884	−	0.999788i	$-0.506554\pi$
$977$	−1.28706	−0.0411767	−0.0205884	+	0.999788i	$0.506554\pi$
$978$	5.94068	0.189962
$979$	−23.9999	−0.767041
$980$	2.83777	0.0906493
$981$	41.0292	1.30996
$982$	−40.8665	−1.30410
$983$	−25.3868	−0.809714	−0.404857	−	0.914380i	$-0.632679\pi$
$983$	−25.3868	−0.809714	−0.404857	+	0.914380i	$0.632679\pi$
$984$	8.88562	0.283263
$985$	7.40077	0.235808
$986$	35.1338	1.11889
$987$	0.829975	0.0264184
$988$	−13.2860	−0.422683
$989$	−1.10853	−0.0352491
$990$	−35.0819	−1.11498
$991$	48.8364	1.55134	0.775670	−	0.631138i	$-0.217412\pi$
$991$	48.8364	1.55134	0.775670	+	0.631138i	$0.217412\pi$
$992$	5.68938	0.180638
$993$	−2.14339	−0.0680186
$994$	9.47096	0.300401
$995$	11.7936	0.373883
$996$	−0.470380	−0.0149046
$997$	−28.5479	−0.904122	−0.452061	−	0.891987i	$-0.649311\pi$
$997$	−28.5479	−0.904122	−0.452061	+	0.891987i	$0.649311\pi$
$998$	−8.73969	−0.276650
$999$	−13.8651	−0.438673

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	301.2.a.a.1.4	✓	4
3.2	odd	2		2709.2.a.h.1.1		4
4.3	odd	2		4816.2.a.p.1.2		4
5.4	even	2		7525.2.a.e.1.1		4
7.6	odd	2		2107.2.a.e.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
301.2.a.a.1.4	✓	4	1.1	even	1	trivial
2107.2.a.e.1.4		4	7.6	odd	2
2709.2.a.h.1.1		4	3.2	odd	2
4816.2.a.p.1.2		4	4.3	odd	2
7525.2.a.e.1.1		4	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:	\( N \)	\(=\)	\( 301 = 7 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	301.a (trivial)

\(f(q)\)	\(=\)	\(q+1.06150 q^{2} -0.326637 q^{3} -0.873220 q^{4} -3.24978 q^{5} -0.346725 q^{6} +1.00000 q^{7} -3.04992 q^{8} -2.89331 q^{9} +O(q^{10})\)	\(q+1.06150 q^{2} -0.326637 q^{3} -0.873220 q^{4} -3.24978 q^{5} -0.346725 q^{6} +1.00000 q^{7} -3.04992 q^{8} -2.89331 q^{9} -3.44964 q^{10} -3.51492 q^{11} +0.285226 q^{12} +3.47947 q^{13} +1.06150 q^{14} +1.06150 q^{15} -1.49105 q^{16} -4.60808 q^{17} -3.07124 q^{18} +4.37278 q^{19} +2.83777 q^{20} -0.326637 q^{21} -3.73108 q^{22} -1.10853 q^{23} +0.996218 q^{24} +5.56105 q^{25} +3.69345 q^{26} +1.92497 q^{27} -0.873220 q^{28} -7.18266 q^{29} +1.12678 q^{30} +1.25952 q^{31} +4.51710 q^{32} +1.14810 q^{33} -4.89147 q^{34} -3.24978 q^{35} +2.52649 q^{36} -7.20275 q^{37} +4.64170 q^{38} -1.13652 q^{39} +9.91156 q^{40} +8.91936 q^{41} -0.346725 q^{42} +1.00000 q^{43} +3.06930 q^{44} +9.40261 q^{45} -1.17670 q^{46} -2.54097 q^{47} +0.487031 q^{48} +1.00000 q^{49} +5.90305 q^{50} +1.50517 q^{51} -3.03834 q^{52} -0.312166 q^{53} +2.04336 q^{54} +11.4227 q^{55} -3.04992 q^{56} -1.42831 q^{57} -7.62439 q^{58} -10.7609 q^{59} -0.926922 q^{60} -2.59467 q^{61} +1.33698 q^{62} -2.89331 q^{63} +7.77698 q^{64} -11.3075 q^{65} +1.21871 q^{66} -8.46411 q^{67} +4.02387 q^{68} +0.362086 q^{69} -3.44964 q^{70} +8.92225 q^{71} +8.82436 q^{72} -8.68818 q^{73} -7.64571 q^{74} -1.81645 q^{75} -3.81840 q^{76} -3.51492 q^{77} -1.20642 q^{78} -12.6878 q^{79} +4.84557 q^{80} +8.05116 q^{81} +9.46789 q^{82} -1.64915 q^{83} +0.285226 q^{84} +14.9752 q^{85} +1.06150 q^{86} +2.34613 q^{87} +10.7202 q^{88} +6.82803 q^{89} +9.98086 q^{90} +3.47947 q^{91} +0.967988 q^{92} -0.411407 q^{93} -2.69723 q^{94} -14.2105 q^{95} -1.47545 q^{96} +0.914286 q^{97} +1.06150 q^{98} +10.1697 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 3 q^{3} + 4 q^{4} - 4 q^{5} + 2 q^{6} + 4 q^{7} - 9 q^{8} + q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 3 * q^3 + 4 * q^4 - 4 * q^5 + 2 * q^6 + 4 * q^7 - 9 * q^8 + q^9	\( 4 q - 4 q^{2} - 3 q^{3} + 4 q^{4} - 4 q^{5} + 2 q^{6} + 4 q^{7} - 9 q^{8} + q^{9} + q^{10} - 15 q^{11} + 6 q^{12} + q^{13} - 4 q^{14} - 4 q^{15} + 12 q^{16} - q^{17} - 11 q^{18} - 8 q^{19} - 10 q^{20} - 3 q^{21} + 19 q^{22} - 5 q^{23} - 20 q^{24} - 4 q^{25} + 8 q^{26} - 15 q^{27} + 4 q^{28} - 16 q^{29} + 12 q^{30} + 3 q^{31} - 22 q^{32} + 14 q^{33} - 19 q^{34} - 4 q^{35} + 6 q^{36} - 11 q^{37} + 27 q^{38} - 19 q^{39} + 34 q^{40} + q^{41} + 2 q^{42} + 4 q^{43} - 25 q^{44} + 14 q^{45} - 9 q^{46} + 11 q^{47} + 37 q^{48} + 4 q^{49} + 18 q^{50} - 14 q^{52} - 20 q^{53} + 41 q^{54} + 17 q^{55} - 9 q^{56} + 11 q^{57} + 16 q^{58} - 11 q^{59} - 17 q^{60} - 10 q^{61} - 5 q^{62} + q^{63} + 47 q^{64} - 4 q^{65} - 13 q^{66} - 2 q^{67} + 35 q^{68} + 17 q^{69} + q^{70} - 11 q^{71} + 31 q^{72} + 13 q^{73} + 14 q^{74} + 16 q^{75} - 28 q^{76} - 15 q^{77} + 37 q^{78} - 32 q^{79} - 31 q^{80} + 36 q^{81} + 30 q^{82} - 15 q^{83} + 6 q^{84} + 5 q^{85} - 4 q^{86} + 25 q^{87} + 43 q^{88} - q^{89} - 3 q^{90} + q^{91} + 43 q^{92} - 33 q^{93} - 28 q^{94} - 10 q^{95} - 46 q^{96} + 22 q^{97} - 4 q^{98} - 22 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 3 * q^3 + 4 * q^4 - 4 * q^5 + 2 * q^6 + 4 * q^7 - 9 * q^8 + q^9 + q^10 - 15 * q^11 + 6 * q^12 + q^13 - 4 * q^14 - 4 * q^15 + 12 * q^16 - q^17 - 11 * q^18 - 8 * q^19 - 10 * q^20 - 3 * q^21 + 19 * q^22 - 5 * q^23 - 20 * q^24 - 4 * q^25 + 8 * q^26 - 15 * q^27 + 4 * q^28 - 16 * q^29 + 12 * q^30 + 3 * q^31 - 22 * q^32 + 14 * q^33 - 19 * q^34 - 4 * q^35 + 6 * q^36 - 11 * q^37 + 27 * q^38 - 19 * q^39 + 34 * q^40 + q^41 + 2 * q^42 + 4 * q^43 - 25 * q^44 + 14 * q^45 - 9 * q^46 + 11 * q^47 + 37 * q^48 + 4 * q^49 + 18 * q^50 - 14 * q^52 - 20 * q^53 + 41 * q^54 + 17 * q^55 - 9 * q^56 + 11 * q^57 + 16 * q^58 - 11 * q^59 - 17 * q^60 - 10 * q^61 - 5 * q^62 + q^63 + 47 * q^64 - 4 * q^65 - 13 * q^66 - 2 * q^67 + 35 * q^68 + 17 * q^69 + q^70 - 11 * q^71 + 31 * q^72 + 13 * q^73 + 14 * q^74 + 16 * q^75 - 28 * q^76 - 15 * q^77 + 37 * q^78 - 32 * q^79 - 31 * q^80 + 36 * q^81 + 30 * q^82 - 15 * q^83 + 6 * q^84 + 5 * q^85 - 4 * q^86 + 25 * q^87 + 43 * q^88 - q^89 - 3 * q^90 + q^91 + 43 * q^92 - 33 * q^93 - 28 * q^94 - 10 * q^95 - 46 * q^96 + 22 * q^97 - 4 * q^98 - 22 * q^99

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