LMFDB - Embedded newform 5054.2.a.x.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, 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("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.151572.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 10x^{2} + 8x + 4 $ x^4 - x^3 - 10x^2 + 8x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$3.21578$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +3.21578 q^{3} +1.00000 q^{4} +1.59385 q^{5} +3.21578 q^{6} +1.00000 q^{7} +1.00000 q^{8} +7.34125 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.21578 q^{3} +1.00000 q^{4} +1.59385 q^{5} +3.21578 q^{6} +1.00000 q^{7} +1.00000 q^{8} +7.34125 q^{9} +1.59385 q^{10} -1.21578 q^{11} +3.21578 q^{12} +4.71932 q^{13} +1.00000 q^{14} +5.12547 q^{15} +1.00000 q^{16} -7.55703 q^{17} +7.34125 q^{18} +1.59385 q^{20} +3.21578 q^{21} -1.21578 q^{22} -6.52895 q^{23} +3.21578 q^{24} -2.45965 q^{25} +4.71932 q^{26} +13.9605 q^{27} +1.00000 q^{28} +0.118397 q^{29} +5.12547 q^{30} +6.31317 q^{31} +1.00000 q^{32} -3.90969 q^{33} -7.55703 q^{34} +1.59385 q^{35} +7.34125 q^{36} -5.18770 q^{37} +15.1763 q^{39} +1.59385 q^{40} +7.21578 q^{41} +3.21578 q^{42} -0.313165 q^{43} -1.21578 q^{44} +11.7008 q^{45} -6.52895 q^{46} +0.118397 q^{47} +3.21578 q^{48} +1.00000 q^{49} -2.45965 q^{50} -24.3018 q^{51} +4.71932 q^{52} -2.31317 q^{53} +13.9605 q^{54} -1.93777 q^{55} +1.00000 q^{56} +0.118397 q^{58} +1.25260 q^{59} +5.12547 q^{60} +7.84478 q^{61} +6.31317 q^{62} +7.34125 q^{63} +1.00000 q^{64} +7.52188 q^{65} -3.90969 q^{66} +12.7728 q^{67} -7.55703 q^{68} -20.9957 q^{69} +1.59385 q^{70} -4.97192 q^{71} +7.34125 q^{72} +13.5851 q^{73} -5.18770 q^{74} -7.90969 q^{75} -1.21578 q^{77} +15.1763 q^{78} -6.25094 q^{79} +1.59385 q^{80} +22.8702 q^{81} +7.21578 q^{82} -9.99127 q^{83} +3.21578 q^{84} -12.0448 q^{85} -0.313165 q^{86} +0.380740 q^{87} -1.21578 q^{88} -14.4316 q^{89} +11.7008 q^{90} +4.71932 q^{91} -6.52895 q^{92} +20.3018 q^{93} +0.118397 q^{94} +3.21578 q^{96} +7.64734 q^{97} +1.00000 q^{98} -8.92535 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{7} + 4 q^{8} + 9 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^7 + 4 * q^8 + 9 * q^9	\( 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{7} + 4 q^{8} + 9 q^{9} + q^{10} + 7 q^{11} + q^{12} + 5 q^{13} + 4 q^{14} + 12 q^{15} + 4 q^{16} + 2 q^{17} + 9 q^{18} + q^{20} + q^{21} + 7 q^{22} + 5 q^{23} + q^{24} + 15 q^{25} + 5 q^{26} + q^{27} + 4 q^{28} - 4 q^{29} + 12 q^{30} + 6 q^{31} + 4 q^{32} - 19 q^{33} + 2 q^{34} + q^{35} + 9 q^{36} - 10 q^{37} - 6 q^{39} + q^{40} + 17 q^{41} + q^{42} + 18 q^{43} + 7 q^{44} - 19 q^{45} + 5 q^{46} - 4 q^{47} + q^{48} + 4 q^{49} + 15 q^{50} - 22 q^{51} + 5 q^{52} + 10 q^{53} + q^{54} - 10 q^{55} + 4 q^{56} - 4 q^{58} + 20 q^{59} + 12 q^{60} + 9 q^{61} + 6 q^{62} + 9 q^{63} + 4 q^{64} + 3 q^{65} - 19 q^{66} + 7 q^{67} + 2 q^{68} - 24 q^{69} + q^{70} - 21 q^{71} + 9 q^{72} + 21 q^{73} - 10 q^{74} - 35 q^{75} + 7 q^{77} - 6 q^{78} - 8 q^{79} + q^{80} + 40 q^{81} + 17 q^{82} - 12 q^{83} + q^{84} + 10 q^{85} + 18 q^{86} + 36 q^{87} + 7 q^{88} - 34 q^{89} - 19 q^{90} + 5 q^{91} + 5 q^{92} + 6 q^{93} - 4 q^{94} + q^{96} - 5 q^{97} + 4 q^{98} + 14 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^7 + 4 * q^8 + 9 * q^9 + q^10 + 7 * q^11 + q^12 + 5 * q^13 + 4 * q^14 + 12 * q^15 + 4 * q^16 + 2 * q^17 + 9 * q^18 + q^20 + q^21 + 7 * q^22 + 5 * q^23 + q^24 + 15 * q^25 + 5 * q^26 + q^27 + 4 * q^28 - 4 * q^29 + 12 * q^30 + 6 * q^31 + 4 * q^32 - 19 * q^33 + 2 * q^34 + q^35 + 9 * q^36 - 10 * q^37 - 6 * q^39 + q^40 + 17 * q^41 + q^42 + 18 * q^43 + 7 * q^44 - 19 * q^45 + 5 * q^46 - 4 * q^47 + q^48 + 4 * q^49 + 15 * q^50 - 22 * q^51 + 5 * q^52 + 10 * q^53 + q^54 - 10 * q^55 + 4 * q^56 - 4 * q^58 + 20 * q^59 + 12 * q^60 + 9 * q^61 + 6 * q^62 + 9 * q^63 + 4 * q^64 + 3 * q^65 - 19 * q^66 + 7 * q^67 + 2 * q^68 - 24 * q^69 + q^70 - 21 * q^71 + 9 * q^72 + 21 * q^73 - 10 * q^74 - 35 * q^75 + 7 * q^77 - 6 * q^78 - 8 * q^79 + q^80 + 40 * q^81 + 17 * q^82 - 12 * q^83 + q^84 + 10 * q^85 + 18 * q^86 + 36 * q^87 + 7 * q^88 - 34 * q^89 - 19 * q^90 + 5 * q^91 + 5 * q^92 + 6 * q^93 - 4 * q^94 + q^96 - 5 * q^97 + 4 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	3.21578	1.85663	0.928316	−	0.371792i	$-0.121257\pi$
$3$	3.21578	1.85663	0.928316	+	0.371792i	$0.121257\pi$
$4$	1.00000	0.500000
$5$	1.59385	0.712791	0.356395	−	0.934335i	$-0.384006\pi$
$5$	1.59385	0.712791	0.356395	+	0.934335i	$0.384006\pi$
$6$	3.21578	1.31284
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	7.34125	2.44708
$10$	1.59385	0.504019
$11$	−1.21578	−0.366572	−0.183286	−	0.983060i	$-0.558673\pi$
$11$	−1.21578	−0.366572	−0.183286	+	0.983060i	$0.558673\pi$
$12$	3.21578	0.928316
$13$	4.71932	1.30890	0.654451	−	0.756104i	$-0.272900\pi$
$13$	4.71932	1.30890	0.654451	+	0.756104i	$0.272900\pi$
$14$	1.00000	0.267261
$15$	5.12547	1.32339
$16$	1.00000	0.250000
$17$	−7.55703	−1.83285	−0.916425	−	0.400207i	$-0.868938\pi$
$17$	−7.55703	−1.83285	−0.916425	+	0.400207i	$0.868938\pi$
$18$	7.34125	1.73035
$19$	0	0
$19$	0	0
$20$	1.59385	0.356395
$21$	3.21578	0.701741
$22$	−1.21578	−0.259205
$23$	−6.52895	−1.36138	−0.680690	−	0.732572i	$-0.738320\pi$
$23$	−6.52895	−1.36138	−0.680690	+	0.732572i	$0.738320\pi$
$24$	3.21578	0.656419
$25$	−2.45965	−0.491929
$26$	4.71932	0.925534
$27$	13.9605	2.68670
$28$	1.00000	0.188982
$29$	0.118397	0.0219859	0.0109929	−	0.999940i	$-0.496501\pi$
$29$	0.118397	0.0219859	0.0109929	+	0.999940i	$0.496501\pi$
$30$	5.12547	0.935778
$31$	6.31317	1.13388	0.566939	−	0.823760i	$-0.308128\pi$
$31$	6.31317	1.13388	0.566939	+	0.823760i	$0.308128\pi$
$32$	1.00000	0.176777
$33$	−3.90969	−0.680589
$34$	−7.55703	−1.29602
$35$	1.59385	0.269410
$36$	7.34125	1.22354
$37$	−5.18770	−0.852852	−0.426426	−	0.904522i	$-0.640228\pi$
$37$	−5.18770	−0.852852	−0.426426	+	0.904522i	$0.640228\pi$
$38$	0	0
$39$	15.1763	2.43015
$40$	1.59385	0.252010
$41$	7.21578	1.12692	0.563458	−	0.826145i	$-0.309471\pi$
$41$	7.21578	1.12692	0.563458	+	0.826145i	$0.309471\pi$
$42$	3.21578	0.496206
$43$	−0.313165	−0.0477572	−0.0238786	−	0.999715i	$-0.507602\pi$
$43$	−0.313165	−0.0477572	−0.0238786	+	0.999715i	$0.507602\pi$
$44$	−1.21578	−0.183286
$45$	11.7008	1.74426
$46$	−6.52895	−0.962641
$47$	0.118397	0.0172700	0.00863502	−	0.999963i	$-0.497251\pi$
$47$	0.118397	0.0172700	0.00863502	+	0.999963i	$0.497251\pi$
$48$	3.21578	0.464158
$49$	1.00000	0.142857
$50$	−2.45965	−0.347847
$51$	−24.3018	−3.40293
$52$	4.71932	0.654451
$53$	−2.31317	−0.317738	−0.158869	−	0.987300i	$-0.550785\pi$
$53$	−2.31317	−0.317738	−0.158869	+	0.987300i	$0.550785\pi$
$54$	13.9605	1.89978
$55$	−1.93777	−0.261289
$56$	1.00000	0.133631
$57$	0	0
$58$	0.118397	0.0155463
$59$	1.25260	0.163074	0.0815372	−	0.996670i	$-0.474017\pi$
$59$	1.25260	0.163074	0.0815372	+	0.996670i	$0.474017\pi$
$60$	5.12547	0.661695
$61$	7.84478	1.00442	0.502211	−	0.864745i	$-0.332520\pi$
$61$	7.84478	1.00442	0.502211	+	0.864745i	$0.332520\pi$
$62$	6.31317	0.801773
$63$	7.34125	0.924911
$64$	1.00000	0.125000
$65$	7.52188	0.932974
$66$	−3.90969	−0.481249
$67$	12.7728	1.56045	0.780224	−	0.625501i	$-0.215105\pi$
$67$	12.7728	1.56045	0.780224	+	0.625501i	$0.215105\pi$
$68$	−7.55703	−0.916425
$69$	−20.9957	−2.52758
$70$	1.59385	0.190501
$71$	−4.97192	−0.590058	−0.295029	−	0.955488i	$-0.595329\pi$
$71$	−4.97192	−0.590058	−0.295029	+	0.955488i	$0.595329\pi$
$72$	7.34125	0.865175
$73$	13.5851	1.59002	0.795009	−	0.606598i	$-0.207466\pi$
$73$	13.5851	1.59002	0.795009	+	0.606598i	$0.207466\pi$
$74$	−5.18770	−0.603058
$75$	−7.90969	−0.913332
$76$	0	0
$77$	−1.21578	−0.138551
$78$	15.1763	1.71838
$79$	−6.25094	−0.703285	−0.351643	−	0.936134i	$-0.614377\pi$
$79$	−6.25094	−0.703285	−0.351643	+	0.936134i	$0.614377\pi$
$80$	1.59385	0.178198
$81$	22.8702	2.54113
$82$	7.21578	0.796850
$83$	−9.99127	−1.09668	−0.548342	−	0.836254i	$-0.684741\pi$
$83$	−9.99127	−1.09668	−0.548342	+	0.836254i	$0.684741\pi$
$84$	3.21578	0.350871
$85$	−12.0448	−1.30644
$86$	−0.313165	−0.0337695
$87$	0.380740	0.0408197
$88$	−1.21578	−0.129603
$89$	−14.4316	−1.52974	−0.764871	−	0.644183i	$-0.777197\pi$
$89$	−14.4316	−1.52974	−0.764871	+	0.644183i	$0.777197\pi$
$90$	11.7008	1.23338
$91$	4.71932	0.494719
$92$	−6.52895	−0.680690
$93$	20.3018	2.10519
$94$	0.118397	0.0122118
$95$	0	0
$96$	3.21578	0.328209
$97$	7.64734	0.776470	0.388235	−	0.921560i	$-0.373085\pi$
$97$	7.64734	0.776470	0.388235	+	0.921560i	$0.373085\pi$
$98$	1.00000	0.101015
$99$	−8.92535	−0.897032
$100$	−2.45965	−0.245965
$101$	−5.12547	−0.510003	−0.255002	−	0.966941i	$-0.582076\pi$
$101$	−5.12547	−0.510003	−0.255002	+	0.966941i	$0.582076\pi$
$102$	−24.3018	−2.40623
$103$	4.87453	0.480302	0.240151	−	0.970736i	$-0.422803\pi$
$103$	4.87453	0.480302	0.240151	+	0.970736i	$0.422803\pi$
$104$	4.71932	0.462767
$105$	5.12547	0.500194
$106$	−2.31317	−0.224674
$107$	2.05617	0.198777	0.0993887	−	0.995049i	$-0.468311\pi$
$107$	2.05617	0.198777	0.0993887	+	0.995049i	$0.468311\pi$
$108$	13.9605	1.34335
$109$	−12.9815	−1.24340	−0.621702	−	0.783254i	$-0.713559\pi$
$109$	−12.9815	−1.24340	−0.621702	+	0.783254i	$0.713559\pi$
$110$	−1.93777	−0.184759
$111$	−16.6825	−1.58343
$112$	1.00000	0.0944911
$113$	−8.12547	−0.764380	−0.382190	−	0.924084i	$-0.624830\pi$
$113$	−8.12547	−0.764380	−0.382190	+	0.924084i	$0.624830\pi$
$114$	0	0
$115$	−10.4062	−0.970379
$116$	0.118397	0.0109929
$117$	34.6457	3.20299
$118$	1.25260	0.115311
$119$	−7.55703	−0.692752
$120$	5.12547	0.467889
$121$	−9.52188	−0.865625
$122$	7.84478	0.710233
$123$	23.2044	2.09227
$124$	6.31317	0.566939
$125$	−11.8895	−1.06343
$126$	7.34125	0.654010
$127$	−16.5851	−1.47169	−0.735845	−	0.677149i	$-0.763215\pi$
$127$	−16.5851	−1.47169	−0.735845	+	0.677149i	$0.763215\pi$
$128$	1.00000	0.0883883
$129$	−1.00707	−0.0886676
$130$	7.52188	0.659712
$131$	−3.80256	−0.332231	−0.166116	−	0.986106i	$-0.553122\pi$
$131$	−3.80256	−0.332231	−0.166116	+	0.986106i	$0.553122\pi$
$132$	−3.90969	−0.340295
$133$	0	0
$134$	12.7728	1.10340
$135$	22.2509	1.91506
$136$	−7.55703	−0.648010
$137$	−4.43863	−0.379218	−0.189609	−	0.981860i	$-0.560722\pi$
$137$	−4.43863	−0.379218	−0.189609	+	0.981860i	$0.560722\pi$
$138$	−20.9957	−1.78727
$139$	−18.2737	−1.54995	−0.774976	−	0.631990i	$-0.782238\pi$
$139$	−18.2737	−1.54995	−0.774976	+	0.631990i	$0.782238\pi$
$140$	1.59385	0.134705
$141$	0.380740	0.0320641
$142$	−4.97192	−0.417234
$143$	−5.73766	−0.479807
$144$	7.34125	0.611771
$145$	0.188708	0.0156713
$146$	13.5851	1.12431
$147$	3.21578	0.265233
$148$	−5.18770	−0.426426
$149$	9.18770	0.752685	0.376343	−	0.926481i	$-0.377182\pi$
$149$	9.18770	0.752685	0.376343	+	0.926481i	$0.377182\pi$
$150$	−7.90969	−0.645823
$151$	−9.52188	−0.774879	−0.387440	−	0.921895i	$-0.626640\pi$
$151$	−9.52188	−0.774879	−0.387440	+	0.921895i	$0.626640\pi$
$152$	0	0
$153$	−55.4780	−4.48513
$154$	−1.21578	−0.0979705
$155$	10.0622	0.808218
$156$	15.1763	1.21508
$157$	−1.90701	−0.152196	−0.0760981	−	0.997100i	$-0.524246\pi$
$157$	−1.90701	−0.152196	−0.0760981	+	0.997100i	$0.524246\pi$
$158$	−6.25094	−0.497298
$159$	−7.43863	−0.589922
$160$	1.59385	0.126005
$161$	−6.52895	−0.514553
$162$	22.8702	1.79685
$163$	5.79129	0.453609	0.226804	−	0.973940i	$-0.427172\pi$
$163$	5.79129	0.453609	0.226804	+	0.973940i	$0.427172\pi$
$164$	7.21578	0.563458
$165$	−6.23145	−0.485118
$166$	−9.99127	−0.775473
$167$	−13.6754	−1.05824	−0.529118	−	0.848548i	$-0.677477\pi$
$167$	−13.6754	−1.05824	−0.529118	+	0.848548i	$0.677477\pi$
$168$	3.21578	0.248103
$169$	9.27195	0.713227
$170$	−12.0448	−0.923791
$171$	0	0
$172$	−0.313165	−0.0238786
$173$	−1.96924	−0.149719	−0.0748594	−	0.997194i	$-0.523851\pi$
$173$	−1.96924	−0.149719	−0.0748594	+	0.997194i	$0.523851\pi$
$174$	0.380740	0.0288639
$175$	−2.45965	−0.185932
$176$	−1.21578	−0.0916430
$177$	4.02808	0.302769
$178$	−14.4316	−1.08169
$179$	5.46672	0.408602	0.204301	−	0.978908i	$-0.434508\pi$
$179$	5.46672	0.408602	0.204301	+	0.978908i	$0.434508\pi$
$180$	11.7008	0.872129
$181$	−13.8448	−1.02907	−0.514537	−	0.857468i	$-0.672036\pi$
$181$	−13.8448	−1.02907	−0.514537	+	0.857468i	$0.672036\pi$
$182$	4.71932	0.349819
$183$	25.2271	1.86484
$184$	−6.52895	−0.481320
$185$	−8.26840	−0.607905
$186$	20.3018	1.48860
$187$	9.18770	0.671871
$188$	0.118397	0.00863502
$189$	13.9605	1.01548
$190$	0	0
$191$	−21.0789	−1.52522	−0.762608	−	0.646861i	$-0.776081\pi$
$191$	−21.0789	−1.52522	−0.762608	+	0.646861i	$0.776081\pi$
$192$	3.21578	0.232079
$193$	−1.35266	−0.0973663	−0.0486832	−	0.998814i	$-0.515502\pi$
$193$	−1.35266	−0.0973663	−0.0486832	+	0.998814i	$0.515502\pi$
$194$	7.64734	0.549047
$195$	24.1887	1.73219
$196$	1.00000	0.0714286
$197$	18.0448	1.28564	0.642818	−	0.766019i	$-0.277765\pi$
$197$	18.0448	1.28564	0.642818	+	0.766019i	$0.277765\pi$
$198$	−8.92535	−0.634297
$199$	10.3132	0.731081	0.365540	−	0.930795i	$-0.380884\pi$
$199$	10.3132	0.731081	0.365540	+	0.930795i	$0.380884\pi$
$200$	−2.45965	−0.173923
$201$	41.0746	2.89718
$202$	−5.12547	−0.360627
$203$	0.118397	0.00830987
$204$	−24.3018	−1.70146
$205$	11.5009	0.803255
$206$	4.87453	0.339625
$207$	−47.9306	−3.33141
$208$	4.71932	0.327226
$209$	0	0
$210$	5.12547	0.353691
$211$	4.00000	0.275371	0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000	0.275371	0.137686	+	0.990476i	$0.456034\pi$
$212$	−2.31317	−0.158869
$213$	−15.9886	−1.09552
$214$	2.05617	0.140557
$215$	−0.499138	−0.0340409
$216$	13.9605	0.949892
$217$	6.31317	0.428566
$218$	−12.9815	−0.879220
$219$	43.6868	2.95208
$220$	−1.93777	−0.130645
$221$	−35.6640	−2.39902
$222$	−16.6825	−1.11966
$223$	14.6263	0.979452	0.489726	−	0.871877i	$-0.337097\pi$
$223$	14.6263	0.979452	0.489726	+	0.871877i	$0.337097\pi$
$224$	1.00000	0.0668153
$225$	−18.0569	−1.20379
$226$	−8.12547	−0.540498
$227$	27.7491	1.84177	0.920887	−	0.389829i	$-0.127466\pi$
$227$	27.7491	1.84177	0.920887	+	0.389829i	$0.127466\pi$
$228$	0	0
$229$	19.3904	1.28135	0.640677	−	0.767810i	$-0.278654\pi$
$229$	19.3904	1.28135	0.640677	+	0.767810i	$0.278654\pi$
$230$	−10.4062	−0.686161
$231$	−3.90969	−0.257239
$232$	0.118397	0.00777317
$233$	−10.4386	−0.683858	−0.341929	−	0.939726i	$-0.611080\pi$
$233$	−10.4386	−0.683858	−0.341929	+	0.939726i	$0.611080\pi$
$234$	34.6457	2.26486
$235$	0.188708	0.0123099
$236$	1.25260	0.0815372
$237$	−20.1016	−1.30574
$238$	−7.55703	−0.489850
$239$	12.8361	0.830295	0.415148	−	0.909754i	$-0.363730\pi$
$239$	12.8361	0.830295	0.415148	+	0.909754i	$0.363730\pi$
$240$	5.12547	0.330848
$241$	19.6473	1.26560	0.632798	−	0.774317i	$-0.281906\pi$
$241$	19.6473	1.26560	0.632798	+	0.774317i	$0.281906\pi$
$242$	−9.52188	−0.612089
$243$	31.6640	2.03125
$244$	7.84478	0.502211
$245$	1.59385	0.101827
$246$	23.2044	1.47946
$247$	0	0
$248$	6.31317	0.400886
$249$	−32.1297	−2.03614
$250$	−11.8895	−0.751961
$251$	−4.10966	−0.259400	−0.129700	−	0.991553i	$-0.541401\pi$
$251$	−4.10966	−0.259400	−0.129700	+	0.991553i	$0.541401\pi$
$252$	7.34125	0.462455
$253$	7.93777	0.499043
$254$	−16.5851	−1.04064
$255$	−38.7333	−2.42557
$256$	1.00000	0.0625000
$257$	−28.7052	−1.79058	−0.895292	−	0.445480i	$-0.853033\pi$
$257$	−28.7052	−1.79058	−0.895292	+	0.445480i	$0.853033\pi$
$258$	−1.00707	−0.0626975
$259$	−5.18770	−0.322348
$260$	7.52188	0.466487
$261$	0.869185	0.0538012
$262$	−3.80256	−0.234923
$263$	5.65441	0.348666	0.174333	−	0.984687i	$-0.444223\pi$
$263$	5.65441	0.348666	0.174333	+	0.984687i	$0.444223\pi$
$264$	−3.90969	−0.240625
$265$	−3.68683	−0.226480
$266$	0	0
$267$	−46.4087	−2.84017
$268$	12.7728	0.780224
$269$	16.7447	1.02094	0.510472	−	0.859894i	$-0.329471\pi$
$269$	16.7447	1.02094	0.510472	+	0.859894i	$0.329471\pi$
$270$	22.2509	1.35415
$271$	29.7518	1.80729	0.903647	−	0.428279i	$-0.140880\pi$
$271$	29.7518	1.80729	0.903647	+	0.428279i	$0.140880\pi$
$272$	−7.55703	−0.458212
$273$	15.1763	0.918511
$274$	−4.43863	−0.268148
$275$	2.99039	0.180327
$276$	−20.9957	−1.26379
$277$	−3.68957	−0.221685	−0.110842	−	0.993838i	$-0.535355\pi$
$277$	−3.68957	−0.221685	−0.110842	+	0.993838i	$0.535355\pi$
$278$	−18.2737	−1.09598
$279$	46.3465	2.77469
$280$	1.59385	0.0952507
$281$	−12.3412	−0.736217	−0.368109	−	0.929783i	$-0.619995\pi$
$281$	−12.3412	−0.736217	−0.368109	+	0.929783i	$0.619995\pi$
$282$	0.380740	0.0226728
$283$	19.2860	1.14643	0.573216	−	0.819405i	$-0.305696\pi$
$283$	19.2860	1.14643	0.573216	+	0.819405i	$0.305696\pi$
$284$	−4.97192	−0.295029
$285$	0	0
$286$	−5.73766	−0.339275
$287$	7.21578	0.425934
$288$	7.34125	0.432587
$289$	40.1087	2.35934
$290$	0.188708	0.0110813
$291$	24.5922	1.44162
$292$	13.5851	0.795009
$293$	−26.5781	−1.55271	−0.776355	−	0.630296i	$-0.782933\pi$
$293$	−26.5781	−1.55271	−0.776355	+	0.630296i	$0.782933\pi$
$294$	3.21578	0.187548
$295$	1.99645	0.116238
$296$	−5.18770	−0.301529
$297$	−16.9729	−0.984869
$298$	9.18770	0.532229
$299$	−30.8122	−1.78191
$300$	−7.90969	−0.456666
$301$	−0.313165	−0.0180505
$302$	−9.52188	−0.547922
$303$	−16.4824	−0.946888
$304$	0	0
$305$	12.5034	0.715943
$306$	−55.4780	−3.17147
$307$	31.0378	1.77142	0.885709	−	0.464241i	$-0.153673\pi$
$307$	31.0378	1.77142	0.885709	+	0.464241i	$0.153673\pi$
$308$	−1.21578	−0.0692756
$309$	15.6754	0.891744
$310$	10.0622	0.571496
$311$	17.6193	0.999097	0.499548	−	0.866286i	$-0.333499\pi$
$311$	17.6193	0.999097	0.499548	+	0.866286i	$0.333499\pi$
$312$	15.1763	0.859188
$313$	−19.1482	−1.08232	−0.541160	−	0.840919i	$-0.682015\pi$
$313$	−19.1482	−1.08232	−0.541160	+	0.840919i	$0.682015\pi$
$314$	−1.90701	−0.107619
$315$	11.7008	0.659268
$316$	−6.25094	−0.351643
$317$	11.7579	0.660387	0.330194	−	0.943913i	$-0.392886\pi$
$317$	11.7579	0.660387	0.330194	+	0.943913i	$0.392886\pi$
$318$	−7.43863	−0.417138
$319$	−0.143945	−0.00805940
$320$	1.59385	0.0890988
$321$	6.61219	0.369056
$322$	−6.52895	−0.363844
$323$	0	0
$324$	22.8702	1.27057
$325$	−11.6079	−0.643888
$326$	5.79129	0.320750
$327$	−41.7457	−2.30854
$328$	7.21578	0.398425
$329$	0.118397	0.00652746
$330$	−6.23145	−0.343030
$331$	−8.08425	−0.444351	−0.222175	−	0.975007i	$-0.571316\pi$
$331$	−8.08425	−0.444351	−0.222175	+	0.975007i	$0.571316\pi$
$332$	−9.99127	−0.548342
$333$	−38.0842	−2.08700
$334$	−13.6754	−0.748286
$335$	20.3579	1.11227
$336$	3.21578	0.175435
$337$	8.41843	0.458581	0.229291	−	0.973358i	$-0.426359\pi$
$337$	8.41843	0.458581	0.229291	+	0.973358i	$0.426359\pi$
$338$	9.27195	0.504328
$339$	−26.1297	−1.41917
$340$	−12.0448	−0.653219
$341$	−7.67543	−0.415648
$342$	0	0
$343$	1.00000	0.0539949
$344$	−0.313165	−0.0168847
$345$	−33.4639	−1.80164
$346$	−1.96924	−0.105867
$347$	−22.8939	−1.22901	−0.614506	−	0.788912i	$-0.710645\pi$
$347$	−22.8939	−1.22901	−0.614506	+	0.788912i	$0.710645\pi$
$348$	0.380740	0.0204098
$349$	−13.7518	−0.736117	−0.368058	−	0.929803i	$-0.619977\pi$
$349$	−13.7518	−0.736117	−0.368058	+	0.929803i	$0.619977\pi$
$350$	−2.45965	−0.131474
$351$	65.8841	3.51663
$352$	−1.21578	−0.0648014
$353$	12.0789	0.642895	0.321448	−	0.946927i	$-0.395831\pi$
$353$	12.0789	0.642895	0.321448	+	0.946927i	$0.395831\pi$
$354$	4.02808	0.214090
$355$	−7.92448	−0.420588
$356$	−14.4316	−0.764871
$357$	−24.3018	−1.28619
$358$	5.46672	0.288925
$359$	−3.56309	−0.188053	−0.0940264	−	0.995570i	$-0.529974\pi$
$359$	−3.56309	−0.188053	−0.0940264	+	0.995570i	$0.529974\pi$
$360$	11.7008	0.616688
$361$	0	0
$362$	−13.8448	−0.727666
$363$	−30.6203	−1.60715
$364$	4.71932	0.247359
$365$	21.6526	1.13335
$366$	25.2271	1.31864
$367$	18.9815	0.990827	0.495414	−	0.868657i	$-0.335016\pi$
$367$	18.9815	0.990827	0.495414	+	0.868657i	$0.335016\pi$
$368$	−6.52895	−0.340345
$369$	52.9729	2.75766
$370$	−8.26840	−0.429854
$371$	−2.31317	−0.120094
$372$	20.3018	1.05260
$373$	−23.6868	−1.22646	−0.613229	−	0.789905i	$-0.710130\pi$
$373$	−23.6868	−1.22646	−0.613229	+	0.789905i	$0.710130\pi$
$374$	9.18770	0.475085
$375$	−38.2342	−1.97440
$376$	0.118397	0.00610588
$377$	0.558755	0.0287774
$378$	13.9605	0.718051
$379$	−22.6886	−1.16543	−0.582717	−	0.812676i	$-0.698010\pi$
$379$	−22.6886	−1.16543	−0.582717	+	0.812676i	$0.698010\pi$
$380$	0	0
$381$	−53.3341	−2.73239
$382$	−21.0789	−1.07849
$383$	−14.7333	−0.752838	−0.376419	−	0.926450i	$-0.622845\pi$
$383$	−14.7333	−0.752838	−0.376419	+	0.926450i	$0.622845\pi$
$384$	3.21578	0.164105
$385$	−1.93777	−0.0987580
$386$	−1.35266	−0.0688484
$387$	−2.29902	−0.116866
$388$	7.64734	0.388235
$389$	18.8745	0.956977	0.478488	−	0.878094i	$-0.341185\pi$
$389$	18.8745	0.956977	0.478488	+	0.878094i	$0.341185\pi$
$390$	24.1887	1.22484
$391$	49.3395	2.49520
$392$	1.00000	0.0505076
$393$	−12.2282	−0.616831
$394$	18.0448	0.909082
$395$	−9.96305	−0.501295
$396$	−8.92535	−0.448516
$397$	−16.4202	−0.824104	−0.412052	−	0.911160i	$-0.635188\pi$
$397$	−16.4202	−0.824104	−0.412052	+	0.911160i	$0.635188\pi$
$398$	10.3132	0.516952
$399$	0	0
$400$	−2.45965	−0.122982
$401$	13.0622	0.652297	0.326148	−	0.945319i	$-0.394249\pi$
$401$	13.0622	0.652297	0.326148	+	0.945319i	$0.394249\pi$
$402$	41.0746	2.04861
$403$	29.7938	1.48414
$404$	−5.12547	−0.255002
$405$	36.4516	1.81130
$406$	0.118397	0.00587597
$407$	6.30711	0.312632
$408$	−24.3018	−1.20312
$409$	−0.976251	−0.0482725	−0.0241363	−	0.999709i	$-0.507684\pi$
$409$	−0.976251	−0.0482725	−0.0241363	+	0.999709i	$0.507684\pi$
$410$	11.5009	0.567987
$411$	−14.2737	−0.704068
$412$	4.87453	0.240151
$413$	1.25260	0.0616364
$414$	−47.9306	−2.35566
$415$	−15.9246	−0.781706
$416$	4.71932	0.231384
$417$	−58.7641	−2.87769
$418$	0	0
$419$	−5.43590	−0.265561	−0.132781	−	0.991145i	$-0.542391\pi$
$419$	−5.43590	−0.265561	−0.132781	+	0.991145i	$0.542391\pi$
$420$	5.12547	0.250097
$421$	−4.68856	−0.228506	−0.114253	−	0.993452i	$-0.536448\pi$
$421$	−4.68856	−0.228506	−0.114253	+	0.993452i	$0.536448\pi$
$422$	4.00000	0.194717
$423$	0.869185	0.0422612
$424$	−2.31317	−0.112337
$425$	18.5876	0.901632
$426$	−15.9886	−0.774650
$427$	7.84478	0.379636
$428$	2.05617	0.0993887
$429$	−18.4511	−0.890825
$430$	−0.499138	−0.0240706
$431$	9.18770	0.442556	0.221278	−	0.975211i	$-0.428977\pi$
$431$	9.18770	0.442556	0.221278	+	0.975211i	$0.428977\pi$
$432$	13.9605	0.671675
$433$	−29.0885	−1.39790	−0.698952	−	0.715168i	$-0.746350\pi$
$433$	−29.0885	−1.39790	−0.698952	+	0.715168i	$0.746350\pi$
$434$	6.31317	0.303042
$435$	0.606842	0.0290959
$436$	−12.9815	−0.621702
$437$	0	0
$438$	43.6868	2.08743
$439$	27.5658	1.31565	0.657823	−	0.753173i	$-0.271478\pi$
$439$	27.5658	1.31565	0.657823	+	0.753173i	$0.271478\pi$
$440$	−1.93777	−0.0923796
$441$	7.34125	0.349583
$442$	−35.6640	−1.69636
$443$	−13.9464	−0.662612	−0.331306	−	0.943523i	$-0.607489\pi$
$443$	−13.9464	−0.662612	−0.331306	+	0.943523i	$0.607489\pi$
$444$	−16.6825	−0.791716
$445$	−23.0017	−1.09039
$446$	14.6263	0.692577
$447$	29.5456	1.39746
$448$	1.00000	0.0472456
$449$	24.2527	1.14455	0.572277	−	0.820060i	$-0.306060\pi$
$449$	24.2527	1.14455	0.572277	+	0.820060i	$0.306060\pi$
$450$	−18.0569	−0.851210
$451$	−8.77281	−0.413096
$452$	−8.12547	−0.382190
$453$	−30.6203	−1.43867
$454$	27.7491	1.30233
$455$	7.52188	0.352631
$456$	0	0
$457$	20.2325	0.946435	0.473217	−	0.880946i	$-0.343093\pi$
$457$	20.2325	0.946435	0.473217	+	0.880946i	$0.343093\pi$
$458$	19.3904	0.906054
$459$	−105.500	−4.92432
$460$	−10.4062	−0.485189
$461$	0.649007	0.0302272	0.0151136	−	0.999886i	$-0.495189\pi$
$461$	0.649007	0.0302272	0.0151136	+	0.999886i	$0.495189\pi$
$462$	−3.90969	−0.181895
$463$	−10.3369	−0.480397	−0.240199	−	0.970724i	$-0.577213\pi$
$463$	−10.3369	−0.480397	−0.240199	+	0.970724i	$0.577213\pi$
$464$	0.118397	0.00549646
$465$	32.3579	1.50056
$466$	−10.4386	−0.483560
$467$	−12.2229	−0.565606	−0.282803	−	0.959178i	$-0.591264\pi$
$467$	−12.2229	−0.565606	−0.282803	+	0.959178i	$0.591264\pi$
$468$	34.6457	1.60150
$469$	12.7728	0.589794
$470$	0.188708	0.00870443
$471$	−6.13254	−0.282572
$472$	1.25260	0.0576555
$473$	0.380740	0.0175065
$474$	−20.1016	−0.923299
$475$	0	0
$476$	−7.55703	−0.346376
$477$	−16.9815	−0.777531
$478$	12.8361	0.587107
$479$	31.1080	1.42136	0.710680	−	0.703515i	$-0.248387\pi$
$479$	31.1080	1.42136	0.710680	+	0.703515i	$0.248387\pi$
$480$	5.12547	0.233945
$481$	−24.4824	−1.11630
$482$	19.6473	0.894912
$483$	−20.9957	−0.955336
$484$	−9.52188	−0.432813
$485$	12.1887	0.553461
$486$	31.6640	1.43631
$487$	−10.8123	−0.489952	−0.244976	−	0.969529i	$-0.578780\pi$
$487$	−10.8123	−0.489952	−0.244976	+	0.969529i	$0.578780\pi$
$488$	7.84478	0.355117
$489$	18.6235	0.842185
$490$	1.59385	0.0720027
$491$	−27.1141	−1.22364	−0.611820	−	0.790997i	$-0.709562\pi$
$491$	−27.1141	−1.22364	−0.611820	+	0.790997i	$0.709562\pi$
$492$	23.2044	1.04613
$493$	−0.894733	−0.0402968
$494$	0	0
$495$	−14.2257	−0.639396
$496$	6.31317	0.283469
$497$	−4.97192	−0.223021
$498$	−32.1297	−1.43977
$499$	−3.39641	−0.152044	−0.0760220	−	0.997106i	$-0.524222\pi$
$499$	−3.39641	−0.152044	−0.0760220	+	0.997106i	$0.524222\pi$
$500$	−11.8895	−0.531717
$501$	−43.9772	−1.96476
$502$	−4.10966	−0.183423
$503$	−23.2886	−1.03839	−0.519194	−	0.854656i	$-0.673768\pi$
$503$	−23.2886	−1.03839	−0.519194	+	0.854656i	$0.673768\pi$
$504$	7.34125	0.327005
$505$	−8.16922	−0.363526
$506$	7.93777	0.352877
$507$	29.8166	1.32420
$508$	−16.5851	−0.735845
$509$	33.5229	1.48588	0.742939	−	0.669359i	$-0.233431\pi$
$509$	33.5229	1.48588	0.742939	+	0.669359i	$0.233431\pi$
$510$	−38.7333	−1.71514
$511$	13.5851	0.600970
$512$	1.00000	0.0441942
$513$	0	0
$514$	−28.7052	−1.26613
$515$	7.76927	0.342355
$516$	−1.00707	−0.0443338
$517$	−0.143945	−0.00633071
$518$	−5.18770	−0.227934
$519$	−6.33265	−0.277973
$520$	7.52188	0.329856
$521$	−16.2851	−0.713462	−0.356731	−	0.934207i	$-0.616109\pi$
$521$	−16.2851	−0.713462	−0.356731	+	0.934207i	$0.616109\pi$
$522$	0.869185	0.0380432
$523$	−2.56410	−0.112120	−0.0560602	−	0.998427i	$-0.517854\pi$
$523$	−2.56410	−0.112120	−0.0560602	+	0.998427i	$0.517854\pi$
$524$	−3.80256	−0.166116
$525$	−7.90969	−0.345207
$526$	5.65441	0.246544
$527$	−47.7088	−2.07823
$528$	−3.90969	−0.170147
$529$	19.6271	0.853354
$530$	−3.68683	−0.160146
$531$	9.19564	0.399057
$532$	0	0
$533$	34.0536	1.47502
$534$	−46.4087	−2.00830
$535$	3.27722	0.141687
$536$	12.7728	0.551701
$537$	17.5798	0.758623
$538$	16.7447	0.721916
$539$	−1.21578	−0.0523674
$540$	22.2509	0.957528
$541$	−17.1282	−0.736399	−0.368199	−	0.929747i	$-0.620026\pi$
$541$	−17.1282	−0.736399	−0.368199	+	0.929747i	$0.620026\pi$
$542$	29.7518	1.27795
$543$	−44.5218	−1.91061
$544$	−7.55703	−0.324005
$545$	−20.6906	−0.886287
$546$	15.1763	0.649485
$547$	−12.4376	−0.531794	−0.265897	−	0.964001i	$-0.585668\pi$
$547$	−12.4376	−0.531794	−0.265897	+	0.964001i	$0.585668\pi$
$548$	−4.43863	−0.189609
$549$	57.5905	2.45790
$550$	2.99039	0.127511
$551$	0	0
$552$	−20.9957	−0.893635
$553$	−6.25094	−0.265817
$554$	−3.68957	−0.156755
$555$	−26.5894	−1.12866
$556$	−18.2737	−0.774976
$557$	−7.06324	−0.299279	−0.149640	−	0.988741i	$-0.547811\pi$
$557$	−7.06324	−0.299279	−0.149640	+	0.988741i	$0.547811\pi$
$558$	46.3465	1.96200
$559$	−1.47793	−0.0625096
$560$	1.59385	0.0673524
$561$	29.5456	1.24742
$562$	−12.3412	−0.520584
$563$	26.6657	1.12382	0.561912	−	0.827197i	$-0.310066\pi$
$563$	26.6657	1.12382	0.561912	+	0.827197i	$0.310066\pi$
$564$	0.380740	0.0160321
$565$	−12.9508	−0.544843
$566$	19.2860	0.810649
$567$	22.8702	0.960458
$568$	−4.97192	−0.208617
$569$	25.3298	1.06188	0.530941	−	0.847409i	$-0.321839\pi$
$569$	25.3298	1.06188	0.530941	+	0.847409i	$0.321839\pi$
$570$	0	0
$571$	14.4149	0.603244	0.301622	−	0.953428i	$-0.402472\pi$
$571$	14.4149	0.603244	0.301622	+	0.953428i	$0.402472\pi$
$572$	−5.73766	−0.239903
$573$	−67.7852	−2.83177
$574$	7.21578	0.301181
$575$	16.0589	0.669703
$576$	7.34125	0.305885
$577$	26.8798	1.11902	0.559510	−	0.828823i	$-0.310989\pi$
$577$	26.8798	1.11902	0.559510	+	0.828823i	$0.310989\pi$
$578$	40.1087	1.66830
$579$	−4.34985	−0.180773
$580$	0.188708	0.00783566
$581$	−9.99127	−0.414508
$582$	24.5922	1.01938
$583$	2.81230	0.116474
$584$	13.5851	0.562156
$585$	55.2200	2.28306
$586$	−26.5781	−1.09793
$587$	33.7710	1.39388	0.696939	−	0.717130i	$-0.254545\pi$
$587$	33.7710	1.39388	0.696939	+	0.717130i	$0.254545\pi$
$588$	3.21578	0.132617
$589$	0	0
$590$	1.99645	0.0821927
$591$	58.0280	2.38695
$592$	−5.18770	−0.213213
$593$	4.70524	0.193221	0.0966105	−	0.995322i	$-0.469200\pi$
$593$	4.70524	0.193221	0.0966105	+	0.995322i	$0.469200\pi$
$594$	−16.9729	−0.696408
$595$	−12.0448	−0.493787
$596$	9.18770	0.376343
$597$	33.1649	1.35735
$598$	−30.8122	−1.26000
$599$	10.3789	0.424072	0.212036	−	0.977262i	$-0.431991\pi$
$599$	10.3789	0.424072	0.212036	+	0.977262i	$0.431991\pi$
$600$	−7.90969	−0.322912
$601$	−40.1297	−1.63693	−0.818463	−	0.574559i	$-0.805173\pi$
$601$	−40.1297	−1.63693	−0.818463	+	0.574559i	$0.805173\pi$
$602$	−0.313165	−0.0127637
$603$	93.7684	3.81854
$604$	−9.52188	−0.387440
$605$	−15.1764	−0.617010
$606$	−16.4824	−0.669551
$607$	8.62633	0.350132	0.175066	−	0.984557i	$-0.443986\pi$
$607$	8.62633	0.350132	0.175066	+	0.984557i	$0.443986\pi$
$608$	0	0
$609$	0.380740	0.0154284
$610$	12.5034	0.506248
$611$	0.558755	0.0226048
$612$	−55.4780	−2.24257
$613$	32.8605	1.32722	0.663612	−	0.748077i	$-0.269023\pi$
$613$	32.8605	1.32722	0.663612	+	0.748077i	$0.269023\pi$
$614$	31.0378	1.25258
$615$	36.9843	1.49135
$616$	−1.21578	−0.0489852
$617$	0.444693	0.0179027	0.00895134	−	0.999960i	$-0.497151\pi$
$617$	0.444693	0.0179027	0.00895134	+	0.999960i	$0.497151\pi$
$618$	15.6754	0.630558
$619$	−36.0140	−1.44753	−0.723763	−	0.690049i	$-0.757589\pi$
$619$	−36.0140	−1.44753	−0.723763	+	0.690049i	$0.757589\pi$
$620$	10.0622	0.404109
$621$	−91.1474	−3.65762
$622$	17.6193	0.706468
$623$	−14.4316	−0.578188
$624$	15.1763	0.607538
$625$	−6.65190	−0.266076
$626$	−19.1482	−0.765316
$627$	0	0
$628$	−1.90701	−0.0760981
$629$	39.2036	1.56315
$630$	11.7008	0.466173
$631$	−25.2527	−1.00529	−0.502646	−	0.864492i	$-0.667640\pi$
$631$	−25.2527	−1.00529	−0.502646	+	0.864492i	$0.667640\pi$
$632$	−6.25094	−0.248649
$633$	12.8631	0.511263
$634$	11.7579	0.466964
$635$	−26.4342	−1.04901
$636$	−7.43863	−0.294961
$637$	4.71932	0.186986
$638$	−0.143945	−0.00569885
$639$	−36.5001	−1.44392
$640$	1.59385	0.0630024
$641$	−40.4077	−1.59601	−0.798005	−	0.602651i	$-0.794111\pi$
$641$	−40.4077	−1.59601	−0.798005	+	0.602651i	$0.794111\pi$
$642$	6.61219	0.260962
$643$	−4.11572	−0.162308	−0.0811542	−	0.996702i	$-0.525861\pi$
$643$	−4.11572	−0.162308	−0.0811542	+	0.996702i	$0.525861\pi$
$644$	−6.52895	−0.257277
$645$	−1.60512	−0.0632015
$646$	0	0
$647$	24.0394	0.945087	0.472543	−	0.881307i	$-0.343336\pi$
$647$	24.0394	0.945087	0.472543	+	0.881307i	$0.343336\pi$
$648$	22.8702	0.898426
$649$	−1.52289	−0.0597785
$650$	−11.6079	−0.455297
$651$	20.3018	0.795689
$652$	5.79129	0.226804
$653$	−44.9167	−1.75773	−0.878863	−	0.477075i	$-0.841697\pi$
$653$	−44.9167	−1.75773	−0.878863	+	0.477075i	$0.841697\pi$
$654$	−41.7457	−1.63239
$655$	−6.06070	−0.236811
$656$	7.21578	0.281729
$657$	99.7317	3.89090
$658$	0.118397	0.00461561
$659$	29.6842	1.15633	0.578167	−	0.815919i	$-0.303768\pi$
$659$	29.6842	1.15633	0.578167	+	0.815919i	$0.303768\pi$
$660$	−6.23145	−0.242559
$661$	−8.59557	−0.334329	−0.167165	−	0.985929i	$-0.553461\pi$
$661$	−8.59557	−0.334329	−0.167165	+	0.985929i	$0.553461\pi$
$662$	−8.08425	−0.314203
$663$	−114.688	−4.45410
$664$	−9.99127	−0.387736
$665$	0	0
$666$	−38.0842	−1.47573
$667$	−0.773011	−0.0299311
$668$	−13.6754	−0.529118
$669$	47.0351	1.81848
$670$	20.3579	0.786495
$671$	−9.53754	−0.368193
$672$	3.21578	0.124051
$673$	8.85352	0.341278	0.170639	−	0.985334i	$-0.445417\pi$
$673$	8.85352	0.341278	0.170639	+	0.985334i	$0.445417\pi$
$674$	8.41843	0.324266
$675$	−34.3379	−1.32167
$676$	9.27195	0.356613
$677$	14.0764	0.540999	0.270499	−	0.962720i	$-0.412811\pi$
$677$	14.0764	0.540999	0.270499	+	0.962720i	$0.412811\pi$
$678$	−26.1297	−1.00351
$679$	7.64734	0.293478
$680$	−12.0448	−0.461896
$681$	89.2351	3.41950
$682$	−7.67543	−0.293907
$683$	−20.3324	−0.777997	−0.388998	−	0.921238i	$-0.627179\pi$
$683$	−20.3324	−0.777997	−0.388998	+	0.921238i	$0.627179\pi$
$684$	0	0
$685$	−7.07451	−0.270303
$686$	1.00000	0.0381802
$687$	62.3553	2.37900
$688$	−0.313165	−0.0119393
$689$	−10.9166	−0.415888
$690$	−33.4639	−1.27395
$691$	−26.7473	−1.01752	−0.508758	−	0.860910i	$-0.669895\pi$
$691$	−26.7473	−1.01752	−0.508758	+	0.860910i	$0.669895\pi$
$692$	−1.96924	−0.0748594
$693$	−8.92535	−0.339046
$694$	−22.8939	−0.869042
$695$	−29.1255	−1.10479
$696$	0.380740	0.0144319
$697$	−54.5299	−2.06547
$698$	−13.7518	−0.520513
$699$	−33.5684	−1.26967
$700$	−2.45965	−0.0929659
$701$	34.2702	1.29437	0.647183	−	0.762335i	$-0.275947\pi$
$701$	34.2702	1.29437	0.647183	+	0.762335i	$0.275947\pi$
$702$	65.8841	2.48663
$703$	0	0
$704$	−1.21578	−0.0458215
$705$	0.606842	0.0228550
$706$	12.0789	0.454596
$707$	−5.12547	−0.192763
$708$	4.02808	0.151385
$709$	14.9395	0.561065	0.280532	−	0.959845i	$-0.409489\pi$
$709$	14.9395	0.561065	0.280532	+	0.959845i	$0.409489\pi$
$710$	−7.92448	−0.297400
$711$	−45.8897	−1.72100
$712$	−14.4316	−0.540846
$713$	−41.2183	−1.54364
$714$	−24.3018	−0.909470
$715$	−9.14496	−0.342002
$716$	5.46672	0.204301
$717$	41.2779	1.54155
$718$	−3.56309	−0.132973
$719$	29.0912	1.08492	0.542460	−	0.840081i	$-0.317493\pi$
$719$	29.0912	1.08492	0.542460	+	0.840081i	$0.317493\pi$
$720$	11.7008	0.436065
$721$	4.87453	0.181537
$722$	0	0
$723$	63.1816	2.34975
$724$	−13.8448	−0.514537
$725$	−0.291216	−0.0108155
$726$	−30.6203	−1.13642
$727$	−40.9843	−1.52002	−0.760011	−	0.649910i	$-0.774806\pi$
$727$	−40.9843	−1.52002	−0.760011	+	0.649910i	$0.774806\pi$
$728$	4.71932	0.174910
$729$	33.2140	1.23015
$730$	21.6526	0.801399
$731$	2.36660	0.0875318
$732$	25.2271	0.932421
$733$	−21.5121	−0.794569	−0.397284	−	0.917696i	$-0.630047\pi$
$733$	−21.5121	−0.794569	−0.397284	+	0.917696i	$0.630047\pi$
$734$	18.9815	0.700621
$735$	5.12547	0.189056
$736$	−6.52895	−0.240660
$737$	−15.5289	−0.572016
$738$	52.9729	1.94996
$739$	5.41590	0.199227	0.0996135	−	0.995026i	$-0.468239\pi$
$739$	5.41590	0.199227	0.0996135	+	0.995026i	$0.468239\pi$
$740$	−8.26840	−0.303953
$741$	0	0
$742$	−2.31317	−0.0849190
$743$	−34.9377	−1.28174	−0.640870	−	0.767650i	$-0.721426\pi$
$743$	−34.9377	−1.28174	−0.640870	+	0.767650i	$0.721426\pi$
$744$	20.3018	0.744299
$745$	14.6438	0.536507
$746$	−23.6868	−0.867237
$747$	−73.3484	−2.68368
$748$	9.18770	0.335935
$749$	2.05617	0.0751308
$750$	−38.2342	−1.39611
$751$	−45.7596	−1.66979	−0.834896	−	0.550408i	$-0.814472\pi$
$751$	−45.7596	−1.66979	−0.834896	+	0.550408i	$0.814472\pi$
$752$	0.118397	0.00431751
$753$	−13.2158	−0.481610
$754$	0.558755	0.0203487
$755$	−15.1764	−0.552327
$756$	13.9605	0.507739
$757$	48.8578	1.77577	0.887883	−	0.460069i	$-0.152175\pi$
$757$	48.8578	1.77577	0.887883	+	0.460069i	$0.152175\pi$
$758$	−22.6886	−0.824086
$759$	25.5261	0.926540
$760$	0	0
$761$	−28.5613	−1.03535	−0.517673	−	0.855579i	$-0.673202\pi$
$761$	−28.5613	−1.03535	−0.517673	+	0.855579i	$0.673202\pi$
$762$	−53.3341	−1.93209
$763$	−12.9815	−0.469963
$764$	−21.0789	−0.762608
$765$	−88.4236	−3.19696
$766$	−14.7333	−0.532337
$767$	5.91141	0.213449
$768$	3.21578	0.116040
$769$	−5.18496	−0.186975	−0.0934873	−	0.995620i	$-0.529801\pi$
$769$	−5.18496	−0.186975	−0.0934873	+	0.995620i	$0.529801\pi$
$770$	−1.93777	−0.0698324
$771$	−92.3098	−3.32445
$772$	−1.35266	−0.0486832
$773$	7.76235	0.279192	0.139596	−	0.990209i	$-0.455420\pi$
$773$	7.76235	0.279192	0.139596	+	0.990209i	$0.455420\pi$
$774$	−2.29902	−0.0826367
$775$	−15.5282	−0.557788
$776$	7.64734	0.274524
$777$	−16.6825	−0.598481
$778$	18.8745	0.676685
$779$	0	0
$780$	24.1887	0.866095
$781$	6.04476	0.216299
$782$	49.3395	1.76438
$783$	1.65289	0.0590694
$784$	1.00000	0.0357143
$785$	−3.03949	−0.108484
$786$	−12.2282	−0.436165
$787$	−11.6788	−0.416305	−0.208152	−	0.978096i	$-0.566745\pi$
$787$	−11.6788	−0.416305	−0.208152	+	0.978096i	$0.566745\pi$
$788$	18.0448	0.642818
$789$	18.1834	0.647345
$790$	−9.96305	−0.354469
$791$	−8.12547	−0.288908
$792$	−8.92535	−0.317149
$793$	37.0220	1.31469
$794$	−16.4202	−0.582730
$795$	−11.8561	−0.420491
$796$	10.3132	0.365540
$797$	7.94904	0.281569	0.140785	−	0.990040i	$-0.455037\pi$
$797$	7.94904	0.281569	0.140785	+	0.990040i	$0.455037\pi$
$798$	0	0
$799$	−0.894733	−0.0316534
$800$	−2.45965	−0.0869617
$801$	−105.946	−3.74341
$802$	13.0622	0.461243
$803$	−16.5165	−0.582856
$804$	41.0746	1.44859
$805$	−10.4062	−0.366769
$806$	29.7938	1.04944
$807$	53.8474	1.89552
$808$	−5.12547	−0.180313
$809$	38.8729	1.36670	0.683350	−	0.730091i	$-0.260522\pi$
$809$	38.8729	1.36670	0.683350	+	0.730091i	$0.260522\pi$
$810$	36.4516	1.28078
$811$	−16.1692	−0.567778	−0.283889	−	0.958857i	$-0.591625\pi$
$811$	−16.1692	−0.567778	−0.283889	+	0.958857i	$0.591625\pi$
$812$	0.118397	0.00415494
$813$	95.6753	3.35548
$814$	6.30711	0.221064
$815$	9.23044	0.323328
$816$	−24.3018	−0.850732
$817$	0	0
$818$	−0.976251	−0.0341338
$819$	34.6457	1.21062
$820$	11.5009	0.401628
$821$	−30.8211	−1.07566	−0.537832	−	0.843052i	$-0.680756\pi$
$821$	−30.8211	−1.07566	−0.537832	+	0.843052i	$0.680756\pi$
$822$	−14.2737	−0.497852
$823$	31.0668	1.08292	0.541460	−	0.840726i	$-0.317872\pi$
$823$	31.0668	1.08292	0.541460	+	0.840726i	$0.317872\pi$
$824$	4.87453	0.169812
$825$	9.61645	0.334802
$826$	1.25260	0.0435835
$827$	20.7473	0.721453	0.360727	−	0.932672i	$-0.382529\pi$
$827$	20.7473	0.721453	0.360727	+	0.932672i	$0.382529\pi$
$828$	−47.9306	−1.66570
$829$	−22.3446	−0.776061	−0.388031	−	0.921646i	$-0.626845\pi$
$829$	−22.3446	−0.776061	−0.388031	+	0.921646i	$0.626845\pi$
$830$	−15.9246	−0.552750
$831$	−11.8648	−0.411587
$832$	4.71932	0.163613
$833$	−7.55703	−0.261836
$834$	−58.7641	−2.03484
$835$	−21.7966	−0.754301
$836$	0	0
$837$	88.1350	3.04639
$838$	−5.43590	−0.187780
$839$	30.3018	1.04613	0.523066	−	0.852292i	$-0.324788\pi$
$839$	30.3018	1.04613	0.523066	+	0.852292i	$0.324788\pi$
$840$	5.12547	0.176845
$841$	−28.9860	−0.999517
$842$	−4.68856	−0.161578
$843$	−39.6868	−1.36688
$844$	4.00000	0.137686
$845$	14.7781	0.508382
$846$	0.869185	0.0298832
$847$	−9.52188	−0.327176
$848$	−2.31317	−0.0794344
$849$	62.0194	2.12850
$850$	18.5876	0.637550
$851$	33.8702	1.16106
$852$	−15.9886	−0.547760
$853$	51.1730	1.75213	0.876064	−	0.482194i	$-0.160160\pi$
$853$	51.1730	1.75213	0.876064	+	0.482194i	$0.160160\pi$
$854$	7.84478	0.268443
$855$	0	0
$856$	2.05617	0.0702784
$857$	7.09738	0.242442	0.121221	−	0.992626i	$-0.461319\pi$
$857$	7.09738	0.242442	0.121221	+	0.992626i	$0.461319\pi$
$858$	−18.4511	−0.629908
$859$	−10.8350	−0.369687	−0.184843	−	0.982768i	$-0.559178\pi$
$859$	−10.8350	−0.369687	−0.184843	+	0.982768i	$0.559178\pi$
$860$	−0.499138	−0.0170205
$861$	23.2044	0.790803
$862$	9.18770	0.312934
$863$	−11.4070	−0.388300	−0.194150	−	0.980972i	$-0.562195\pi$
$863$	−11.4070	−0.388300	−0.194150	+	0.980972i	$0.562195\pi$
$864$	13.9605	0.474946
$865$	−3.13867	−0.106718
$866$	−29.0885	−0.988468
$867$	128.981	4.38042
$868$	6.31317	0.214283
$869$	7.59977	0.257805
$870$	0.606842	0.0205739
$871$	60.2789	2.04247
$872$	−12.9815	−0.439610
$873$	56.1411	1.90009
$874$	0	0
$875$	−11.8895	−0.401940
$876$	43.6868	1.47604
$877$	45.9658	1.55215	0.776077	−	0.630638i	$-0.217207\pi$
$877$	45.9658	1.55215	0.776077	+	0.630638i	$0.217207\pi$
$878$	27.5658	0.930302
$879$	−85.4694	−2.88281
$880$	−1.93777	−0.0653223
$881$	34.2562	1.15412	0.577060	−	0.816701i	$-0.304200\pi$
$881$	34.2562	1.15412	0.577060	+	0.816701i	$0.304200\pi$
$882$	7.34125	0.247193
$883$	14.6484	0.492956	0.246478	−	0.969148i	$-0.420727\pi$
$883$	14.6484	0.492956	0.246478	+	0.969148i	$0.420727\pi$
$884$	−35.6640	−1.19951
$885$	6.42016	0.215811
$886$	−13.9464	−0.468537
$887$	5.69492	0.191217	0.0956083	−	0.995419i	$-0.469520\pi$
$887$	5.69492	0.191217	0.0956083	+	0.995419i	$0.469520\pi$
$888$	−16.6825	−0.559828
$889$	−16.5851	−0.556247
$890$	−23.0017	−0.771020
$891$	−27.8052	−0.931508
$892$	14.6263	0.489726
$893$	0	0
$894$	29.5456	0.988153
$895$	8.71312	0.291247
$896$	1.00000	0.0334077
$897$	−99.0852	−3.30836
$898$	24.2527	0.809322
$899$	0.747463	0.0249293
$900$	−18.0569	−0.601896
$901$	17.4807	0.582365
$902$	−8.77281	−0.292103
$903$	−1.00707	−0.0335132
$904$	−8.12547	−0.270249
$905$	−22.0665	−0.733515
$906$	−30.6203	−1.01729
$907$	−23.7571	−0.788841	−0.394420	−	0.918930i	$-0.629055\pi$
$907$	−23.7571	−0.788841	−0.394420	+	0.918930i	$0.629055\pi$
$908$	27.7491	0.920887
$909$	−37.6273	−1.24802
$910$	7.52188	0.249348
$911$	36.5236	1.21008	0.605040	−	0.796195i	$-0.293157\pi$
$911$	36.5236	1.21008	0.605040	+	0.796195i	$0.293157\pi$
$912$	0	0
$913$	12.1472	0.402013
$914$	20.2325	0.669230
$915$	40.2082	1.32924
$916$	19.3904	0.640677
$917$	−3.80256	−0.125572
$918$	−105.500	−3.48202
$919$	28.7738	0.949161	0.474580	−	0.880212i	$-0.342600\pi$
$919$	28.7738	0.949161	0.474580	+	0.880212i	$0.342600\pi$
$920$	−10.4062	−0.343081
$921$	99.8106	3.28887
$922$	0.649007	0.0213739
$923$	−23.4640	−0.772328
$924$	−3.90969	−0.128619
$925$	12.7599	0.419543
$926$	−10.3369	−0.339692
$927$	35.7852	1.17534
$928$	0.118397	0.00388659
$929$	39.0692	1.28182	0.640910	−	0.767616i	$-0.278557\pi$
$929$	39.0692	1.28182	0.640910	+	0.767616i	$0.278557\pi$
$930$	32.3579	1.06106
$931$	0	0
$932$	−10.4386	−0.341929
$933$	56.6597	1.85495
$934$	−12.2229	−0.399944
$935$	14.6438	0.478903
$936$	34.6457	1.13243
$937$	16.3184	0.533100	0.266550	−	0.963821i	$-0.414116\pi$
$937$	16.3184	0.533100	0.266550	+	0.963821i	$0.414116\pi$
$938$	12.7728	0.417047
$939$	−61.5764	−2.00947
$940$	0.188708	0.00615496
$941$	−4.36139	−0.142177	−0.0710886	−	0.997470i	$-0.522647\pi$
$941$	−4.36139	−0.142177	−0.0710886	+	0.997470i	$0.522647\pi$
$942$	−6.13254	−0.199809
$943$	−47.1115	−1.53416
$944$	1.25260	0.0407686
$945$	22.2509	0.723823
$946$	0.380740	0.0123789
$947$	2.14902	0.0698337	0.0349169	−	0.999390i	$-0.488883\pi$
$947$	2.14902	0.0698337	0.0349169	+	0.999390i	$0.488883\pi$
$948$	−20.1016	−0.652871
$949$	64.1125	2.08118
$950$	0	0
$951$	37.8107	1.22610
$952$	−7.55703	−0.244925
$953$	49.9323	1.61747	0.808734	−	0.588175i	$-0.200153\pi$
$953$	49.9323	1.61747	0.808734	+	0.588175i	$0.200153\pi$
$954$	−16.9815	−0.549797
$955$	−33.5966	−1.08716
$956$	12.8361	0.415148
$957$	−0.462897	−0.0149633
$958$	31.1080	1.00505
$959$	−4.43863	−0.143331
$960$	5.12547	0.165424
$961$	8.85605	0.285679
$962$	−24.4824	−0.789344
$963$	15.0948	0.486425
$964$	19.6473	0.632798
$965$	−2.15593	−0.0694018
$966$	−20.9957	−0.675524
$967$	34.6501	1.11427	0.557136	−	0.830421i	$-0.311900\pi$
$967$	34.6501	1.11427	0.557136	+	0.830421i	$0.311900\pi$
$968$	−9.52188	−0.306045
$969$	0	0
$970$	12.1887	0.391356
$971$	29.6411	0.951230	0.475615	−	0.879654i	$-0.342226\pi$
$971$	29.6411	0.951230	0.475615	+	0.879654i	$0.342226\pi$
$972$	31.6640	1.01562
$973$	−18.2737	−0.585827
$974$	−10.8123	−0.346449
$975$	−37.3283	−1.19546
$976$	7.84478	0.251105
$977$	10.3404	0.330820	0.165410	−	0.986225i	$-0.447105\pi$
$977$	10.3404	0.330820	0.165410	+	0.986225i	$0.447105\pi$
$978$	18.6235	0.595515
$979$	17.5456	0.560761
$980$	1.59385	0.0509136
$981$	−95.3006	−3.04271
$982$	−27.1141	−0.865244
$983$	8.43156	0.268925	0.134463	−	0.990919i	$-0.457069\pi$
$983$	8.43156	0.268925	0.134463	+	0.990919i	$0.457069\pi$
$984$	23.2044	0.739728
$985$	28.7606	0.916389
$986$	−0.894733	−0.0284941
$987$	0.380740	0.0121191
$988$	0	0
$989$	2.04464	0.0650157
$990$	−14.2257	−0.452121
$991$	4.48086	0.142339	0.0711696	−	0.997464i	$-0.477327\pi$
$991$	4.48086	0.142339	0.0711696	+	0.997464i	$0.477327\pi$
$992$	6.31317	0.200443
$993$	−25.9972	−0.824996
$994$	−4.97192	−0.157700
$995$	16.4376	0.521108
$996$	−32.1297	−1.01807
$997$	−61.1647	−1.93711	−0.968553	−	0.248805i	$-0.919962\pi$
$997$	−61.1647	−1.93711	−0.968553	+	0.248805i	$0.919962\pi$
$998$	−3.39641	−0.107511
$999$	−72.4229	−2.29136

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.x.1.4		4
19.8	odd	6		266.2.f.d.197.4	✓	8
19.12	odd	6		266.2.f.d.239.4	yes	8
19.18	odd	2		5054.2.a.w.1.1		4
57.8	even	6		2394.2.o.v.1261.3		8
57.50	even	6		2394.2.o.v.505.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.f.d.197.4	✓	8	19.8	odd	6
266.2.f.d.239.4	yes	8	19.12	odd	6
2394.2.o.v.505.3		8	57.50	even	6
2394.2.o.v.1261.3		8	57.8	even	6
5054.2.a.w.1.1		4	19.18	odd	2
5054.2.a.x.1.4		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.21578 q^{3} +1.00000 q^{4} +1.59385 q^{5} +3.21578 q^{6} +1.00000 q^{7} +1.00000 q^{8} +7.34125 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.21578 q^{3} +1.00000 q^{4} +1.59385 q^{5} +3.21578 q^{6} +1.00000 q^{7} +1.00000 q^{8} +7.34125 q^{9} +1.59385 q^{10} -1.21578 q^{11} +3.21578 q^{12} +4.71932 q^{13} +1.00000 q^{14} +5.12547 q^{15} +1.00000 q^{16} -7.55703 q^{17} +7.34125 q^{18} +1.59385 q^{20} +3.21578 q^{21} -1.21578 q^{22} -6.52895 q^{23} +3.21578 q^{24} -2.45965 q^{25} +4.71932 q^{26} +13.9605 q^{27} +1.00000 q^{28} +0.118397 q^{29} +5.12547 q^{30} +6.31317 q^{31} +1.00000 q^{32} -3.90969 q^{33} -7.55703 q^{34} +1.59385 q^{35} +7.34125 q^{36} -5.18770 q^{37} +15.1763 q^{39} +1.59385 q^{40} +7.21578 q^{41} +3.21578 q^{42} -0.313165 q^{43} -1.21578 q^{44} +11.7008 q^{45} -6.52895 q^{46} +0.118397 q^{47} +3.21578 q^{48} +1.00000 q^{49} -2.45965 q^{50} -24.3018 q^{51} +4.71932 q^{52} -2.31317 q^{53} +13.9605 q^{54} -1.93777 q^{55} +1.00000 q^{56} +0.118397 q^{58} +1.25260 q^{59} +5.12547 q^{60} +7.84478 q^{61} +6.31317 q^{62} +7.34125 q^{63} +1.00000 q^{64} +7.52188 q^{65} -3.90969 q^{66} +12.7728 q^{67} -7.55703 q^{68} -20.9957 q^{69} +1.59385 q^{70} -4.97192 q^{71} +7.34125 q^{72} +13.5851 q^{73} -5.18770 q^{74} -7.90969 q^{75} -1.21578 q^{77} +15.1763 q^{78} -6.25094 q^{79} +1.59385 q^{80} +22.8702 q^{81} +7.21578 q^{82} -9.99127 q^{83} +3.21578 q^{84} -12.0448 q^{85} -0.313165 q^{86} +0.380740 q^{87} -1.21578 q^{88} -14.4316 q^{89} +11.7008 q^{90} +4.71932 q^{91} -6.52895 q^{92} +20.3018 q^{93} +0.118397 q^{94} +3.21578 q^{96} +7.64734 q^{97} +1.00000 q^{98} -8.92535 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{7} + 4 q^{8} + 9 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^7 + 4 * q^8 + 9 * q^9	\( 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{7} + 4 q^{8} + 9 q^{9} + q^{10} + 7 q^{11} + q^{12} + 5 q^{13} + 4 q^{14} + 12 q^{15} + 4 q^{16} + 2 q^{17} + 9 q^{18} + q^{20} + q^{21} + 7 q^{22} + 5 q^{23} + q^{24} + 15 q^{25} + 5 q^{26} + q^{27} + 4 q^{28} - 4 q^{29} + 12 q^{30} + 6 q^{31} + 4 q^{32} - 19 q^{33} + 2 q^{34} + q^{35} + 9 q^{36} - 10 q^{37} - 6 q^{39} + q^{40} + 17 q^{41} + q^{42} + 18 q^{43} + 7 q^{44} - 19 q^{45} + 5 q^{46} - 4 q^{47} + q^{48} + 4 q^{49} + 15 q^{50} - 22 q^{51} + 5 q^{52} + 10 q^{53} + q^{54} - 10 q^{55} + 4 q^{56} - 4 q^{58} + 20 q^{59} + 12 q^{60} + 9 q^{61} + 6 q^{62} + 9 q^{63} + 4 q^{64} + 3 q^{65} - 19 q^{66} + 7 q^{67} + 2 q^{68} - 24 q^{69} + q^{70} - 21 q^{71} + 9 q^{72} + 21 q^{73} - 10 q^{74} - 35 q^{75} + 7 q^{77} - 6 q^{78} - 8 q^{79} + q^{80} + 40 q^{81} + 17 q^{82} - 12 q^{83} + q^{84} + 10 q^{85} + 18 q^{86} + 36 q^{87} + 7 q^{88} - 34 q^{89} - 19 q^{90} + 5 q^{91} + 5 q^{92} + 6 q^{93} - 4 q^{94} + q^{96} - 5 q^{97} + 4 q^{98} + 14 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^7 + 4 * q^8 + 9 * q^9 + q^10 + 7 * q^11 + q^12 + 5 * q^13 + 4 * q^14 + 12 * q^15 + 4 * q^16 + 2 * q^17 + 9 * q^18 + q^20 + q^21 + 7 * q^22 + 5 * q^23 + q^24 + 15 * q^25 + 5 * q^26 + q^27 + 4 * q^28 - 4 * q^29 + 12 * q^30 + 6 * q^31 + 4 * q^32 - 19 * q^33 + 2 * q^34 + q^35 + 9 * q^36 - 10 * q^37 - 6 * q^39 + q^40 + 17 * q^41 + q^42 + 18 * q^43 + 7 * q^44 - 19 * q^45 + 5 * q^46 - 4 * q^47 + q^48 + 4 * q^49 + 15 * q^50 - 22 * q^51 + 5 * q^52 + 10 * q^53 + q^54 - 10 * q^55 + 4 * q^56 - 4 * q^58 + 20 * q^59 + 12 * q^60 + 9 * q^61 + 6 * q^62 + 9 * q^63 + 4 * q^64 + 3 * q^65 - 19 * q^66 + 7 * q^67 + 2 * q^68 - 24 * q^69 + q^70 - 21 * q^71 + 9 * q^72 + 21 * q^73 - 10 * q^74 - 35 * q^75 + 7 * q^77 - 6 * q^78 - 8 * q^79 + q^80 + 40 * q^81 + 17 * q^82 - 12 * q^83 + q^84 + 10 * q^85 + 18 * q^86 + 36 * q^87 + 7 * q^88 - 34 * q^89 - 19 * q^90 + 5 * q^91 + 5 * q^92 + 6 * q^93 - 4 * q^94 + q^96 - 5 * q^97 + 4 * q^98 + 14 * q^99

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