LMFDB - Embedded newform 4002.2.a.bh.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4002,2,Mod(1,4002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4002, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4002 = 2 \cdot 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4002.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:	$31.9561308889$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 16x^{5} + 51x^{4} + 45x^{3} - 152x^{2} - 54x + 70 $ x^7 - 3x^6 - 16x^5 + 51x^4 + 45x^3 - 152x^2 - 54x + 70
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.76200$ of defining polynomial
Character	$\chi$	$=$	4002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.888451 q^{5} +1.00000 q^{6} +4.32361 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.888451 q^{5} +1.00000 q^{6} +4.32361 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.888451 q^{10} -3.02625 q^{11} +1.00000 q^{12} -3.43657 q^{13} +4.32361 q^{14} +0.888451 q^{15} +1.00000 q^{16} +7.91470 q^{17} +1.00000 q^{18} +0.799605 q^{19} +0.888451 q^{20} +4.32361 q^{21} -3.02625 q^{22} +1.00000 q^{23} +1.00000 q^{24} -4.21065 q^{25} -3.43657 q^{26} +1.00000 q^{27} +4.32361 q^{28} -1.00000 q^{29} +0.888451 q^{30} -6.85626 q^{31} +1.00000 q^{32} -3.02625 q^{33} +7.91470 q^{34} +3.84132 q^{35} +1.00000 q^{36} +9.31017 q^{37} +0.799605 q^{38} -3.43657 q^{39} +0.888451 q^{40} +9.48015 q^{41} +4.32361 q^{42} +8.81862 q^{43} -3.02625 q^{44} +0.888451 q^{45} +1.00000 q^{46} -7.39512 q^{47} +1.00000 q^{48} +11.6936 q^{49} -4.21065 q^{50} +7.91470 q^{51} -3.43657 q^{52} -1.38621 q^{53} +1.00000 q^{54} -2.68867 q^{55} +4.32361 q^{56} +0.799605 q^{57} -1.00000 q^{58} -7.21347 q^{59} +0.888451 q^{60} +6.80315 q^{61} -6.85626 q^{62} +4.32361 q^{63} +1.00000 q^{64} -3.05322 q^{65} -3.02625 q^{66} +7.98469 q^{67} +7.91470 q^{68} +1.00000 q^{69} +3.84132 q^{70} -5.25705 q^{71} +1.00000 q^{72} -7.90214 q^{73} +9.31017 q^{74} -4.21065 q^{75} +0.799605 q^{76} -13.0843 q^{77} -3.43657 q^{78} -8.50391 q^{79} +0.888451 q^{80} +1.00000 q^{81} +9.48015 q^{82} +5.93292 q^{83} +4.32361 q^{84} +7.03182 q^{85} +8.81862 q^{86} -1.00000 q^{87} -3.02625 q^{88} +12.9772 q^{89} +0.888451 q^{90} -14.8584 q^{91} +1.00000 q^{92} -6.85626 q^{93} -7.39512 q^{94} +0.710410 q^{95} +1.00000 q^{96} -9.12711 q^{97} +11.6936 q^{98} -3.02625 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + q^5 + 7 * q^6 - 2 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9} + q^{10} + 11 q^{11} + 7 q^{12} - q^{13} - 2 q^{14} + q^{15} + 7 q^{16} + 18 q^{17} + 7 q^{18} + 6 q^{19} + q^{20} - 2 q^{21} + 11 q^{22} + 7 q^{23} + 7 q^{24} + 12 q^{25} - q^{26} + 7 q^{27} - 2 q^{28} - 7 q^{29} + q^{30} + 3 q^{31} + 7 q^{32} + 11 q^{33} + 18 q^{34} - 4 q^{35} + 7 q^{36} + 5 q^{37} + 6 q^{38} - q^{39} + q^{40} + 25 q^{41} - 2 q^{42} + 20 q^{43} + 11 q^{44} + q^{45} + 7 q^{46} + 7 q^{48} + 7 q^{49} + 12 q^{50} + 18 q^{51} - q^{52} - 4 q^{53} + 7 q^{54} + 17 q^{55} - 2 q^{56} + 6 q^{57} - 7 q^{58} - 17 q^{59} + q^{60} + 5 q^{61} + 3 q^{62} - 2 q^{63} + 7 q^{64} + 7 q^{65} + 11 q^{66} + 15 q^{67} + 18 q^{68} + 7 q^{69} - 4 q^{70} + 15 q^{71} + 7 q^{72} + 14 q^{73} + 5 q^{74} + 12 q^{75} + 6 q^{76} - 12 q^{77} - q^{78} - 4 q^{79} + q^{80} + 7 q^{81} + 25 q^{82} + 14 q^{83} - 2 q^{84} + 34 q^{85} + 20 q^{86} - 7 q^{87} + 11 q^{88} + 8 q^{89} + q^{90} - 6 q^{91} + 7 q^{92} + 3 q^{93} - 18 q^{95} + 7 q^{96} - 18 q^{97} + 7 q^{98} + 11 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + q^5 + 7 * q^6 - 2 * q^7 + 7 * q^8 + 7 * q^9 + q^10 + 11 * q^11 + 7 * q^12 - q^13 - 2 * q^14 + q^15 + 7 * q^16 + 18 * q^17 + 7 * q^18 + 6 * q^19 + q^20 - 2 * q^21 + 11 * q^22 + 7 * q^23 + 7 * q^24 + 12 * q^25 - q^26 + 7 * q^27 - 2 * q^28 - 7 * q^29 + q^30 + 3 * q^31 + 7 * q^32 + 11 * q^33 + 18 * q^34 - 4 * q^35 + 7 * q^36 + 5 * q^37 + 6 * q^38 - q^39 + q^40 + 25 * q^41 - 2 * q^42 + 20 * q^43 + 11 * q^44 + q^45 + 7 * q^46 + 7 * q^48 + 7 * q^49 + 12 * q^50 + 18 * q^51 - q^52 - 4 * q^53 + 7 * q^54 + 17 * q^55 - 2 * q^56 + 6 * q^57 - 7 * q^58 - 17 * q^59 + q^60 + 5 * q^61 + 3 * q^62 - 2 * q^63 + 7 * q^64 + 7 * q^65 + 11 * q^66 + 15 * q^67 + 18 * q^68 + 7 * q^69 - 4 * q^70 + 15 * q^71 + 7 * q^72 + 14 * q^73 + 5 * q^74 + 12 * q^75 + 6 * q^76 - 12 * q^77 - q^78 - 4 * q^79 + q^80 + 7 * q^81 + 25 * q^82 + 14 * q^83 - 2 * q^84 + 34 * q^85 + 20 * q^86 - 7 * q^87 + 11 * q^88 + 8 * q^89 + q^90 - 6 * q^91 + 7 * q^92 + 3 * q^93 - 18 * q^95 + 7 * q^96 - 18 * q^97 + 7 * q^98 + 11 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.888451	0.397327	0.198664	−	0.980068i	$-0.436340\pi$
$5$	0.888451	0.397327	0.198664	+	0.980068i	$0.436340\pi$
$6$	1.00000	0.408248
$7$	4.32361	1.63417	0.817086	−	0.576516i	$-0.195588\pi$
$7$	4.32361	1.63417	0.817086	+	0.576516i	$0.195588\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.888451	0.280953
$11$	−3.02625	−0.912447	−0.456224	−	0.889865i	$-0.650798\pi$
$11$	−3.02625	−0.912447	−0.456224	+	0.889865i	$0.650798\pi$
$12$	1.00000	0.288675
$13$	−3.43657	−0.953133	−0.476567	−	0.879138i	$-0.658119\pi$
$13$	−3.43657	−0.953133	−0.476567	+	0.879138i	$0.658119\pi$
$14$	4.32361	1.15553
$15$	0.888451	0.229397
$16$	1.00000	0.250000
$17$	7.91470	1.91960	0.959798	−	0.280692i	$-0.0905638\pi$
$17$	7.91470	1.91960	0.959798	+	0.280692i	$0.0905638\pi$
$18$	1.00000	0.235702
$19$	0.799605	0.183442	0.0917210	−	0.995785i	$-0.470763\pi$
$19$	0.799605	0.183442	0.0917210	+	0.995785i	$0.470763\pi$
$20$	0.888451	0.198664
$21$	4.32361	0.943490
$22$	−3.02625	−0.645198
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	−4.21065	−0.842131
$26$	−3.43657	−0.673967
$27$	1.00000	0.192450
$28$	4.32361	0.817086
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0.888451	0.162208
$31$	−6.85626	−1.23142	−0.615711	−	0.787972i	$-0.711131\pi$
$31$	−6.85626	−1.23142	−0.615711	+	0.787972i	$0.711131\pi$
$32$	1.00000	0.176777
$33$	−3.02625	−0.526802
$34$	7.91470	1.35736
$35$	3.84132	0.649301
$36$	1.00000	0.166667
$37$	9.31017	1.53058	0.765291	−	0.643684i	$-0.222595\pi$
$37$	9.31017	1.53058	0.765291	+	0.643684i	$0.222595\pi$
$38$	0.799605	0.129713
$39$	−3.43657	−0.550292
$40$	0.888451	0.140476
$41$	9.48015	1.48055	0.740275	−	0.672304i	$-0.234695\pi$
$41$	9.48015	1.48055	0.740275	+	0.672304i	$0.234695\pi$
$42$	4.32361	0.667148
$43$	8.81862	1.34483	0.672413	−	0.740176i	$-0.265258\pi$
$43$	8.81862	1.34483	0.672413	+	0.740176i	$0.265258\pi$
$44$	−3.02625	−0.456224
$45$	0.888451	0.132442
$46$	1.00000	0.147442
$47$	−7.39512	−1.07869	−0.539345	−	0.842085i	$-0.681328\pi$
$47$	−7.39512	−1.07869	−0.539345	+	0.842085i	$0.681328\pi$
$48$	1.00000	0.144338
$49$	11.6936	1.67052
$50$	−4.21065	−0.595476
$51$	7.91470	1.10828
$52$	−3.43657	−0.476567
$53$	−1.38621	−0.190411	−0.0952055	−	0.995458i	$-0.530351\pi$
$53$	−1.38621	−0.190411	−0.0952055	+	0.995458i	$0.530351\pi$
$54$	1.00000	0.136083
$55$	−2.68867	−0.362540
$56$	4.32361	0.577767
$57$	0.799605	0.105910
$58$	−1.00000	−0.131306
$59$	−7.21347	−0.939114	−0.469557	−	0.882902i	$-0.655586\pi$
$59$	−7.21347	−0.939114	−0.469557	+	0.882902i	$0.655586\pi$
$60$	0.888451	0.114699
$61$	6.80315	0.871054	0.435527	−	0.900176i	$-0.356562\pi$
$61$	6.80315	0.871054	0.435527	+	0.900176i	$0.356562\pi$
$62$	−6.85626	−0.870746
$63$	4.32361	0.544724
$64$	1.00000	0.125000
$65$	−3.05322	−0.378706
$66$	−3.02625	−0.372505
$67$	7.98469	0.975485	0.487743	−	0.872988i	$-0.337820\pi$
$67$	7.98469	0.975485	0.487743	+	0.872988i	$0.337820\pi$
$68$	7.91470	0.959798
$69$	1.00000	0.120386
$70$	3.84132	0.459125
$71$	−5.25705	−0.623897	−0.311949	−	0.950099i	$-0.600982\pi$
$71$	−5.25705	−0.623897	−0.311949	+	0.950099i	$0.600982\pi$
$72$	1.00000	0.117851
$73$	−7.90214	−0.924876	−0.462438	−	0.886652i	$-0.653025\pi$
$73$	−7.90214	−0.924876	−0.462438	+	0.886652i	$0.653025\pi$
$74$	9.31017	1.08229
$75$	−4.21065	−0.486204
$76$	0.799605	0.0917210
$77$	−13.0843	−1.49110
$78$	−3.43657	−0.389115
$79$	−8.50391	−0.956765	−0.478383	−	0.878152i	$-0.658777\pi$
$79$	−8.50391	−0.956765	−0.478383	+	0.878152i	$0.658777\pi$
$80$	0.888451	0.0993319
$81$	1.00000	0.111111
$82$	9.48015	1.04691
$83$	5.93292	0.651223	0.325611	−	0.945504i	$-0.394430\pi$
$83$	5.93292	0.651223	0.325611	+	0.945504i	$0.394430\pi$
$84$	4.32361	0.471745
$85$	7.03182	0.762708
$86$	8.81862	0.950936
$87$	−1.00000	−0.107211
$88$	−3.02625	−0.322599
$89$	12.9772	1.37558	0.687789	−	0.725910i	$-0.258581\pi$
$89$	12.9772	1.37558	0.687789	+	0.725910i	$0.258581\pi$
$90$	0.888451	0.0936510
$91$	−14.8584	−1.55758
$92$	1.00000	0.104257
$93$	−6.85626	−0.710961
$94$	−7.39512	−0.762749
$95$	0.710410	0.0728865
$96$	1.00000	0.102062
$97$	−9.12711	−0.926718	−0.463359	−	0.886171i	$-0.653356\pi$
$97$	−9.12711	−0.926718	−0.463359	+	0.886171i	$0.653356\pi$
$98$	11.6936	1.18123
$99$	−3.02625	−0.304149
$100$	−4.21065	−0.421065
$101$	−10.6785	−1.06255	−0.531277	−	0.847198i	$-0.678288\pi$
$101$	−10.6785	−1.06255	−0.531277	+	0.847198i	$0.678288\pi$
$102$	7.91470	0.783672
$103$	−13.6189	−1.34191	−0.670957	−	0.741496i	$-0.734117\pi$
$103$	−13.6189	−1.34191	−0.670957	+	0.741496i	$0.734117\pi$
$104$	−3.43657	−0.336983
$105$	3.84132	0.374874
$106$	−1.38621	−0.134641
$107$	12.9255	1.24955	0.624776	−	0.780804i	$-0.285190\pi$
$107$	12.9255	1.24955	0.624776	+	0.780804i	$0.285190\pi$
$108$	1.00000	0.0962250
$109$	−8.21685	−0.787031	−0.393516	−	0.919318i	$-0.628741\pi$
$109$	−8.21685	−0.787031	−0.393516	+	0.919318i	$0.628741\pi$
$110$	−2.68867	−0.256355
$111$	9.31017	0.883682
$112$	4.32361	0.408543
$113$	16.0399	1.50891	0.754455	−	0.656351i	$-0.227901\pi$
$113$	16.0399	1.50891	0.754455	+	0.656351i	$0.227901\pi$
$114$	0.799605	0.0748899
$115$	0.888451	0.0828485
$116$	−1.00000	−0.0928477
$117$	−3.43657	−0.317711
$118$	−7.21347	−0.664054
$119$	34.2201	3.13695
$120$	0.888451	0.0811041
$121$	−1.84184	−0.167440
$122$	6.80315	0.615928
$123$	9.48015	0.854796
$124$	−6.85626	−0.615711
$125$	−8.18322	−0.731929
$126$	4.32361	0.385178
$127$	−9.02131	−0.800512	−0.400256	−	0.916403i	$-0.631079\pi$
$127$	−9.02131	−0.800512	−0.400256	+	0.916403i	$0.631079\pi$
$128$	1.00000	0.0883883
$129$	8.81862	0.776436
$130$	−3.05322	−0.267786
$131$	1.32539	0.115800	0.0578998	−	0.998322i	$-0.481560\pi$
$131$	1.32539	0.115800	0.0578998	+	0.998322i	$0.481560\pi$
$132$	−3.02625	−0.263401
$133$	3.45718	0.299776
$134$	7.98469	0.689772
$135$	0.888451	0.0764657
$136$	7.91470	0.678680
$137$	−23.3473	−1.99470	−0.997349	−	0.0727618i	$-0.976819\pi$
$137$	−23.3473	−1.99470	−0.997349	+	0.0727618i	$0.976819\pi$
$138$	1.00000	0.0851257
$139$	−12.0251	−1.01996	−0.509978	−	0.860187i	$-0.670346\pi$
$139$	−12.0251	−1.01996	−0.509978	+	0.860187i	$0.670346\pi$
$140$	3.84132	0.324651
$141$	−7.39512	−0.622782
$142$	−5.25705	−0.441162
$143$	10.3999	0.869684
$144$	1.00000	0.0833333
$145$	−0.888451	−0.0737819
$146$	−7.90214	−0.653986
$147$	11.6936	0.964474
$148$	9.31017	0.765291
$149$	3.95121	0.323696	0.161848	−	0.986816i	$-0.448255\pi$
$149$	3.95121	0.323696	0.161848	+	0.986816i	$0.448255\pi$
$150$	−4.21065	−0.343798
$151$	17.2944	1.40740	0.703701	−	0.710496i	$-0.251529\pi$
$151$	17.2944	1.40740	0.703701	+	0.710496i	$0.251529\pi$
$152$	0.799605	0.0648565
$153$	7.91470	0.639865
$154$	−13.0843	−1.05436
$155$	−6.09146	−0.489277
$156$	−3.43657	−0.275146
$157$	−0.638723	−0.0509757	−0.0254878	−	0.999675i	$-0.508114\pi$
$157$	−0.638723	−0.0509757	−0.0254878	+	0.999675i	$0.508114\pi$
$158$	−8.50391	−0.676535
$159$	−1.38621	−0.109934
$160$	0.888451	0.0702382
$161$	4.32361	0.340748
$162$	1.00000	0.0785674
$163$	11.6597	0.913256	0.456628	−	0.889658i	$-0.349057\pi$
$163$	11.6597	0.913256	0.456628	+	0.889658i	$0.349057\pi$
$164$	9.48015	0.740275
$165$	−2.68867	−0.209313
$166$	5.93292	0.460484
$167$	6.60096	0.510798	0.255399	−	0.966836i	$-0.417793\pi$
$167$	6.60096	0.510798	0.255399	+	0.966836i	$0.417793\pi$
$168$	4.32361	0.333574
$169$	−1.18998	−0.0915373
$170$	7.03182	0.539316
$171$	0.799605	0.0611473
$172$	8.81862	0.672413
$173$	−7.26665	−0.552473	−0.276237	−	0.961090i	$-0.589087\pi$
$173$	−7.26665	−0.552473	−0.276237	+	0.961090i	$0.589087\pi$
$174$	−1.00000	−0.0758098
$175$	−18.2052	−1.37619
$176$	−3.02625	−0.228112
$177$	−7.21347	−0.542198
$178$	12.9772	0.972681
$179$	17.7435	1.32621	0.663104	−	0.748527i	$-0.269239\pi$
$179$	17.7435	1.32621	0.663104	+	0.748527i	$0.269239\pi$
$180$	0.888451	0.0662212
$181$	12.5746	0.934665	0.467332	−	0.884082i	$-0.345215\pi$
$181$	12.5746	0.934665	0.467332	+	0.884082i	$0.345215\pi$
$182$	−14.8584	−1.10138
$183$	6.80315	0.502903
$184$	1.00000	0.0737210
$185$	8.27163	0.608142
$186$	−6.85626	−0.502726
$187$	−23.9518	−1.75153
$188$	−7.39512	−0.539345
$189$	4.32361	0.314497
$190$	0.710410	0.0515386
$191$	−20.9658	−1.51703	−0.758515	−	0.651656i	$-0.774075\pi$
$191$	−20.9658	−1.51703	−0.758515	+	0.651656i	$0.774075\pi$
$192$	1.00000	0.0721688
$193$	−12.8893	−0.927795	−0.463897	−	0.885889i	$-0.653549\pi$
$193$	−12.8893	−0.927795	−0.463897	+	0.885889i	$0.653549\pi$
$194$	−9.12711	−0.655288
$195$	−3.05322	−0.218646
$196$	11.6936	0.835259
$197$	−11.2374	−0.800629	−0.400314	−	0.916378i	$-0.631099\pi$
$197$	−11.2374	−0.800629	−0.400314	+	0.916378i	$0.631099\pi$
$198$	−3.02625	−0.215066
$199$	−12.2629	−0.869297	−0.434648	−	0.900600i	$-0.643127\pi$
$199$	−12.2629	−0.869297	−0.434648	+	0.900600i	$0.643127\pi$
$200$	−4.21065	−0.297738
$201$	7.98469	0.563197
$202$	−10.6785	−0.751339
$203$	−4.32361	−0.303458
$204$	7.91470	0.554140
$205$	8.42265	0.588264
$206$	−13.6189	−0.948877
$207$	1.00000	0.0695048
$208$	−3.43657	−0.238283
$209$	−2.41980	−0.167381
$210$	3.84132	0.265076
$211$	−27.7695	−1.91173	−0.955865	−	0.293808i	$-0.905077\pi$
$211$	−27.7695	−1.91173	−0.955865	+	0.293808i	$0.905077\pi$
$212$	−1.38621	−0.0952055
$213$	−5.25705	−0.360207
$214$	12.9255	0.883567
$215$	7.83491	0.534336
$216$	1.00000	0.0680414
$217$	−29.6438	−2.01235
$218$	−8.21685	−0.556515
$219$	−7.90214	−0.533977
$220$	−2.68867	−0.181270
$221$	−27.1994	−1.82963
$222$	9.31017	0.624858
$223$	−13.6852	−0.916428	−0.458214	−	0.888842i	$-0.651511\pi$
$223$	−13.6852	−0.916428	−0.458214	+	0.888842i	$0.651511\pi$
$224$	4.32361	0.288884
$225$	−4.21065	−0.280710
$226$	16.0399	1.06696
$227$	19.5702	1.29892	0.649458	−	0.760397i	$-0.274996\pi$
$227$	19.5702	1.29892	0.649458	+	0.760397i	$0.274996\pi$
$228$	0.799605	0.0529551
$229$	11.1938	0.739707	0.369853	−	0.929090i	$-0.379408\pi$
$229$	11.1938	0.739707	0.369853	+	0.929090i	$0.379408\pi$
$230$	0.888451	0.0585827
$231$	−13.0843	−0.860885
$232$	−1.00000	−0.0656532
$233$	23.9754	1.57068	0.785341	−	0.619063i	$-0.212487\pi$
$233$	23.9754	1.57068	0.785341	+	0.619063i	$0.212487\pi$
$234$	−3.43657	−0.224656
$235$	−6.57021	−0.428593
$236$	−7.21347	−0.469557
$237$	−8.50391	−0.552389
$238$	34.2201	2.21816
$239$	10.3371	0.668651	0.334326	−	0.942458i	$-0.391491\pi$
$239$	10.3371	0.668651	0.334326	+	0.942458i	$0.391491\pi$
$240$	0.888451	0.0573493
$241$	−20.8977	−1.34614	−0.673069	−	0.739580i	$-0.735024\pi$
$241$	−20.8977	−1.34614	−0.673069	+	0.739580i	$0.735024\pi$
$242$	−1.84184	−0.118398
$243$	1.00000	0.0641500
$244$	6.80315	0.435527
$245$	10.3892	0.663743
$246$	9.48015	0.604432
$247$	−2.74790	−0.174845
$248$	−6.85626	−0.435373
$249$	5.93292	0.375984
$250$	−8.18322	−0.517552
$251$	−10.2667	−0.648028	−0.324014	−	0.946052i	$-0.605033\pi$
$251$	−10.2667	−0.648028	−0.324014	+	0.946052i	$0.605033\pi$
$252$	4.32361	0.272362
$253$	−3.02625	−0.190258
$254$	−9.02131	−0.566047
$255$	7.03182	0.440350
$256$	1.00000	0.0625000
$257$	18.9066	1.17936	0.589681	−	0.807636i	$-0.299253\pi$
$257$	18.9066	1.17936	0.589681	+	0.807636i	$0.299253\pi$
$258$	8.81862	0.549023
$259$	40.2536	2.50123
$260$	−3.05322	−0.189353
$261$	−1.00000	−0.0618984
$262$	1.32539	0.0818827
$263$	−25.2309	−1.55580	−0.777901	−	0.628387i	$-0.783715\pi$
$263$	−25.2309	−1.55580	−0.777901	+	0.628387i	$0.783715\pi$
$264$	−3.02625	−0.186253
$265$	−1.23158	−0.0756555
$266$	3.45718	0.211973
$267$	12.9772	0.794191
$268$	7.98469	0.487743
$269$	6.91459	0.421590	0.210795	−	0.977530i	$-0.432395\pi$
$269$	6.91459	0.421590	0.210795	+	0.977530i	$0.432395\pi$
$270$	0.888451	0.0540694
$271$	5.72049	0.347495	0.173748	−	0.984790i	$-0.444412\pi$
$271$	5.72049	0.347495	0.173748	+	0.984790i	$0.444412\pi$
$272$	7.91470	0.479899
$273$	−14.8584	−0.899271
$274$	−23.3473	−1.41046
$275$	12.7425	0.768400
$276$	1.00000	0.0601929
$277$	−8.39834	−0.504607	−0.252304	−	0.967648i	$-0.581188\pi$
$277$	−8.39834	−0.504607	−0.252304	+	0.967648i	$0.581188\pi$
$278$	−12.0251	−0.721218
$279$	−6.85626	−0.410474
$280$	3.84132	0.229563
$281$	−20.7394	−1.23721	−0.618605	−	0.785702i	$-0.712302\pi$
$281$	−20.7394	−1.23721	−0.618605	+	0.785702i	$0.712302\pi$
$282$	−7.39512	−0.440373
$283$	−14.8458	−0.882490	−0.441245	−	0.897387i	$-0.645463\pi$
$283$	−14.8458	−0.882490	−0.441245	+	0.897387i	$0.645463\pi$
$284$	−5.25705	−0.311949
$285$	0.710410	0.0420811
$286$	10.3999	0.614959
$287$	40.9885	2.41947
$288$	1.00000	0.0589256
$289$	45.6424	2.68485
$290$	−0.888451	−0.0521717
$291$	−9.12711	−0.535041
$292$	−7.90214	−0.462438
$293$	3.46866	0.202641	0.101321	−	0.994854i	$-0.467693\pi$
$293$	3.46866	0.202641	0.101321	+	0.994854i	$0.467693\pi$
$294$	11.6936	0.681986
$295$	−6.40882	−0.373136
$296$	9.31017	0.541143
$297$	−3.02625	−0.175601
$298$	3.95121	0.228887
$299$	−3.43657	−0.198742
$300$	−4.21065	−0.243102
$301$	38.1283	2.19768
$302$	17.2944	0.995184
$303$	−10.6785	−0.613465
$304$	0.799605	0.0458605
$305$	6.04427	0.346094
$306$	7.91470	0.452453
$307$	−19.4117	−1.10788	−0.553942	−	0.832555i	$-0.686877\pi$
$307$	−19.4117	−1.10788	−0.553942	+	0.832555i	$0.686877\pi$
$308$	−13.0843	−0.745548
$309$	−13.6189	−0.774755
$310$	−6.09146	−0.345971
$311$	11.7072	0.663852	0.331926	−	0.943305i	$-0.392302\pi$
$311$	11.7072	0.663852	0.331926	+	0.943305i	$0.392302\pi$
$312$	−3.43657	−0.194557
$313$	28.1210	1.58949	0.794746	−	0.606942i	$-0.207604\pi$
$313$	28.1210	1.58949	0.794746	+	0.606942i	$0.207604\pi$
$314$	−0.638723	−0.0360452
$315$	3.84132	0.216434
$316$	−8.50391	−0.478383
$317$	−16.9607	−0.952606	−0.476303	−	0.879281i	$-0.658023\pi$
$317$	−16.9607	−0.952606	−0.476303	+	0.879281i	$0.658023\pi$
$318$	−1.38621	−0.0777350
$319$	3.02625	0.169437
$320$	0.888451	0.0496659
$321$	12.9255	0.721430
$322$	4.32361	0.240945
$323$	6.32863	0.352134
$324$	1.00000	0.0555556
$325$	14.4702	0.802663
$326$	11.6597	0.645769
$327$	−8.21685	−0.454393
$328$	9.48015	0.523454
$329$	−31.9736	−1.76276
$330$	−2.68867	−0.148007
$331$	19.4675	1.07003	0.535016	−	0.844842i	$-0.320305\pi$
$331$	19.4675	1.07003	0.535016	+	0.844842i	$0.320305\pi$
$332$	5.93292	0.325611
$333$	9.31017	0.510194
$334$	6.60096	0.361188
$335$	7.09401	0.387587
$336$	4.32361	0.235872
$337$	4.82730	0.262960	0.131480	−	0.991319i	$-0.458027\pi$
$337$	4.82730	0.262960	0.131480	+	0.991319i	$0.458027\pi$
$338$	−1.18998	−0.0647266
$339$	16.0399	0.871170
$340$	7.03182	0.381354
$341$	20.7487	1.12361
$342$	0.799605	0.0432377
$343$	20.2934	1.09574
$344$	8.81862	0.475468
$345$	0.888451	0.0478326
$346$	−7.26665	−0.390657
$347$	−21.9303	−1.17728	−0.588641	−	0.808395i	$-0.700337\pi$
$347$	−21.9303	−1.17728	−0.588641	+	0.808395i	$0.700337\pi$
$348$	−1.00000	−0.0536056
$349$	15.5661	0.833233	0.416617	−	0.909082i	$-0.363216\pi$
$349$	15.5661	0.833233	0.416617	+	0.909082i	$0.363216\pi$
$350$	−18.2052	−0.973111
$351$	−3.43657	−0.183431
$352$	−3.02625	−0.161299
$353$	−23.6311	−1.25776	−0.628879	−	0.777503i	$-0.716486\pi$
$353$	−23.6311	−1.25776	−0.628879	+	0.777503i	$0.716486\pi$
$354$	−7.21347	−0.383392
$355$	−4.67064	−0.247892
$356$	12.9772	0.687789
$357$	34.2201	1.81112
$358$	17.7435	0.937771
$359$	33.7103	1.77916	0.889581	−	0.456778i	$-0.150997\pi$
$359$	33.7103	1.77916	0.889581	+	0.456778i	$0.150997\pi$
$360$	0.888451	0.0468255
$361$	−18.3606	−0.966349
$362$	12.5746	0.660908
$363$	−1.84184	−0.0966714
$364$	−14.8584	−0.778792
$365$	−7.02067	−0.367479
$366$	6.80315	0.355606
$367$	19.4578	1.01569	0.507845	−	0.861449i	$-0.330442\pi$
$367$	19.4578	1.01569	0.507845	+	0.861449i	$0.330442\pi$
$368$	1.00000	0.0521286
$369$	9.48015	0.493517
$370$	8.27163	0.430022
$371$	−5.99345	−0.311164
$372$	−6.85626	−0.355481
$373$	−19.0469	−0.986213	−0.493107	−	0.869969i	$-0.664139\pi$
$373$	−19.0469	−0.986213	−0.493107	+	0.869969i	$0.664139\pi$
$374$	−23.9518	−1.23852
$375$	−8.18322	−0.422580
$376$	−7.39512	−0.381374
$377$	3.43657	0.176992
$378$	4.32361	0.222383
$379$	14.6247	0.751221	0.375611	−	0.926778i	$-0.377433\pi$
$379$	14.6247	0.751221	0.375611	+	0.926778i	$0.377433\pi$
$380$	0.710410	0.0364433
$381$	−9.02131	−0.462176
$382$	−20.9658	−1.07270
$383$	6.97705	0.356510	0.178255	−	0.983984i	$-0.442955\pi$
$383$	6.97705	0.356510	0.178255	+	0.983984i	$0.442955\pi$
$384$	1.00000	0.0510310
$385$	−11.6248	−0.592453
$386$	−12.8893	−0.656050
$387$	8.81862	0.448275
$388$	−9.12711	−0.463359
$389$	19.7638	1.00206	0.501032	−	0.865428i	$-0.332954\pi$
$389$	19.7638	1.00206	0.501032	+	0.865428i	$0.332954\pi$
$390$	−3.05322	−0.154606
$391$	7.91470	0.400263
$392$	11.6936	0.590617
$393$	1.32539	0.0668569
$394$	−11.2374	−0.566130
$395$	−7.55531	−0.380149
$396$	−3.02625	−0.152075
$397$	−10.6071	−0.532356	−0.266178	−	0.963924i	$-0.585761\pi$
$397$	−10.6071	−0.532356	−0.266178	+	0.963924i	$0.585761\pi$
$398$	−12.2629	−0.614686
$399$	3.45718	0.173076
$400$	−4.21065	−0.210533
$401$	5.11262	0.255312	0.127656	−	0.991818i	$-0.459255\pi$
$401$	5.11262	0.255312	0.127656	+	0.991818i	$0.459255\pi$
$402$	7.98469	0.398240
$403$	23.5620	1.17371
$404$	−10.6785	−0.531277
$405$	0.888451	0.0441475
$406$	−4.32361	−0.214577
$407$	−28.1749	−1.39658
$408$	7.91470	0.391836
$409$	−17.2252	−0.851732	−0.425866	−	0.904786i	$-0.640031\pi$
$409$	−17.2252	−0.851732	−0.425866	+	0.904786i	$0.640031\pi$
$410$	8.42265	0.415965
$411$	−23.3473	−1.15164
$412$	−13.6189	−0.670957
$413$	−31.1883	−1.53467
$414$	1.00000	0.0491473
$415$	5.27111	0.258749
$416$	−3.43657	−0.168492
$417$	−12.0251	−0.588872
$418$	−2.41980	−0.118356
$419$	22.9015	1.11881	0.559405	−	0.828894i	$-0.311030\pi$
$419$	22.9015	1.11881	0.559405	+	0.828894i	$0.311030\pi$
$420$	3.84132	0.187437
$421$	−30.8764	−1.50483	−0.752413	−	0.658692i	$-0.771110\pi$
$421$	−30.8764	−1.50483	−0.752413	+	0.658692i	$0.771110\pi$
$422$	−27.7695	−1.35180
$423$	−7.39512	−0.359563
$424$	−1.38621	−0.0673204
$425$	−33.3261	−1.61655
$426$	−5.25705	−0.254705
$427$	29.4142	1.42345
$428$	12.9255	0.624776
$429$	10.3999	0.502112
$430$	7.83491	0.377833
$431$	−5.03912	−0.242726	−0.121363	−	0.992608i	$-0.538726\pi$
$431$	−5.03912	−0.242726	−0.121363	+	0.992608i	$0.538726\pi$
$432$	1.00000	0.0481125
$433$	31.2422	1.50140	0.750702	−	0.660641i	$-0.229715\pi$
$433$	31.2422	1.50140	0.750702	+	0.660641i	$0.229715\pi$
$434$	−29.6438	−1.42295
$435$	−0.888451	−0.0425980
$436$	−8.21685	−0.393516
$437$	0.799605	0.0382503
$438$	−7.90214	−0.377579
$439$	−32.5231	−1.55224	−0.776120	−	0.630585i	$-0.782815\pi$
$439$	−32.5231	−1.55224	−0.776120	+	0.630585i	$0.782815\pi$
$440$	−2.68867	−0.128177
$441$	11.6936	0.556839
$442$	−27.1994	−1.29374
$443$	8.01010	0.380571	0.190286	−	0.981729i	$-0.439059\pi$
$443$	8.01010	0.380571	0.190286	+	0.981729i	$0.439059\pi$
$444$	9.31017	0.441841
$445$	11.5296	0.546555
$446$	−13.6852	−0.648012
$447$	3.95121	0.186886
$448$	4.32361	0.204271
$449$	13.0283	0.614844	0.307422	−	0.951573i	$-0.400534\pi$
$449$	13.0283	0.614844	0.307422	+	0.951573i	$0.400534\pi$
$450$	−4.21065	−0.198492
$451$	−28.6893	−1.35092
$452$	16.0399	0.754455
$453$	17.2944	0.812564
$454$	19.5702	0.918473
$455$	−13.2010	−0.618871
$456$	0.799605	0.0374449
$457$	−16.5526	−0.774300	−0.387150	−	0.922017i	$-0.626540\pi$
$457$	−16.5526	−0.774300	−0.387150	+	0.922017i	$0.626540\pi$
$458$	11.1938	0.523052
$459$	7.91470	0.369426
$460$	0.888451	0.0414243
$461$	37.2188	1.73345	0.866727	−	0.498784i	$-0.166220\pi$
$461$	37.2188	1.73345	0.866727	+	0.498784i	$0.166220\pi$
$462$	−13.0843	−0.608737
$463$	−14.2185	−0.660792	−0.330396	−	0.943842i	$-0.607182\pi$
$463$	−14.2185	−0.660792	−0.330396	+	0.943842i	$0.607182\pi$
$464$	−1.00000	−0.0464238
$465$	−6.09146	−0.282484
$466$	23.9754	1.11064
$467$	−18.5127	−0.856664	−0.428332	−	0.903621i	$-0.640899\pi$
$467$	−18.5127	−0.856664	−0.428332	+	0.903621i	$0.640899\pi$
$468$	−3.43657	−0.158856
$469$	34.5227	1.59411
$470$	−6.57021	−0.303061
$471$	−0.638723	−0.0294308
$472$	−7.21347	−0.332027
$473$	−26.6873	−1.22708
$474$	−8.50391	−0.390598
$475$	−3.36686	−0.154482
$476$	34.2201	1.56847
$477$	−1.38621	−0.0634703
$478$	10.3371	0.472808
$479$	−7.78004	−0.355479	−0.177739	−	0.984078i	$-0.556878\pi$
$479$	−7.78004	−0.355479	−0.177739	+	0.984078i	$0.556878\pi$
$480$	0.888451	0.0405521
$481$	−31.9950	−1.45885
$482$	−20.8977	−0.951863
$483$	4.32361	0.196731
$484$	−1.84184	−0.0837199
$485$	−8.10899	−0.368210
$486$	1.00000	0.0453609
$487$	−37.6755	−1.70724	−0.853620	−	0.520896i	$-0.825598\pi$
$487$	−37.6755	−1.70724	−0.853620	+	0.520896i	$0.825598\pi$
$488$	6.80315	0.307964
$489$	11.6597	0.527268
$490$	10.3892	0.469337
$491$	12.6244	0.569733	0.284866	−	0.958567i	$-0.408051\pi$
$491$	12.6244	0.569733	0.284866	+	0.958567i	$0.408051\pi$
$492$	9.48015	0.427398
$493$	−7.91470	−0.356460
$494$	−2.74790	−0.123634
$495$	−2.68867	−0.120847
$496$	−6.85626	−0.307855
$497$	−22.7295	−1.01956
$498$	5.93292	0.265861
$499$	−23.2560	−1.04108	−0.520540	−	0.853837i	$-0.674269\pi$
$499$	−23.2560	−1.04108	−0.520540	+	0.853837i	$0.674269\pi$
$500$	−8.18322	−0.365965
$501$	6.60096	0.294909
$502$	−10.2667	−0.458225
$503$	4.47137	0.199368	0.0996842	−	0.995019i	$-0.468217\pi$
$503$	4.47137	0.199368	0.0996842	+	0.995019i	$0.468217\pi$
$504$	4.32361	0.192589
$505$	−9.48735	−0.422182
$506$	−3.02625	−0.134533
$507$	−1.18998	−0.0528491
$508$	−9.02131	−0.400256
$509$	32.9012	1.45832	0.729161	−	0.684342i	$-0.239911\pi$
$509$	32.9012	1.45832	0.729161	+	0.684342i	$0.239911\pi$
$510$	7.03182	0.311374
$511$	−34.1658	−1.51141
$512$	1.00000	0.0441942
$513$	0.799605	0.0353034
$514$	18.9066	0.833935
$515$	−12.0998	−0.533180
$516$	8.81862	0.388218
$517$	22.3795	0.984248
$518$	40.2536	1.76864
$519$	−7.26665	−0.318970
$520$	−3.05322	−0.133893
$521$	10.9699	0.480600	0.240300	−	0.970699i	$-0.422754\pi$
$521$	10.9699	0.480600	0.240300	+	0.970699i	$0.422754\pi$
$522$	−1.00000	−0.0437688
$523$	−10.1064	−0.441921	−0.220960	−	0.975283i	$-0.570919\pi$
$523$	−10.1064	−0.441921	−0.220960	+	0.975283i	$0.570919\pi$
$524$	1.32539	0.0578998
$525$	−18.2052	−0.794542
$526$	−25.2309	−1.10012
$527$	−54.2652	−2.36383
$528$	−3.02625	−0.131700
$529$	1.00000	0.0434783
$530$	−1.23158	−0.0534965
$531$	−7.21347	−0.313038
$532$	3.45718	0.149888
$533$	−32.5792	−1.41116
$534$	12.9772	0.561578
$535$	11.4837	0.496482
$536$	7.98469	0.344886
$537$	17.7435	0.765687
$538$	6.91459	0.298109
$539$	−35.3878	−1.52426
$540$	0.888451	0.0382329
$541$	5.26129	0.226200	0.113100	−	0.993584i	$-0.463922\pi$
$541$	5.26129	0.226200	0.113100	+	0.993584i	$0.463922\pi$
$542$	5.72049	0.245716
$543$	12.5746	0.539629
$544$	7.91470	0.339340
$545$	−7.30027	−0.312709
$546$	−14.8584	−0.635881
$547$	−11.6014	−0.496042	−0.248021	−	0.968755i	$-0.579780\pi$
$547$	−11.6014	−0.496042	−0.248021	+	0.968755i	$0.579780\pi$
$548$	−23.3473	−0.997349
$549$	6.80315	0.290351
$550$	12.7425	0.543341
$551$	−0.799605	−0.0340643
$552$	1.00000	0.0425628
$553$	−36.7676	−1.56352
$554$	−8.39834	−0.356811
$555$	8.27163	0.351111
$556$	−12.0251	−0.509978
$557$	−7.38702	−0.312998	−0.156499	−	0.987678i	$-0.550021\pi$
$557$	−7.38702	−0.312998	−0.156499	+	0.987678i	$0.550021\pi$
$558$	−6.85626	−0.290249
$559$	−30.3058	−1.28180
$560$	3.84132	0.162325
$561$	−23.9518	−1.01125
$562$	−20.7394	−0.874839
$563$	−3.98154	−0.167802	−0.0839010	−	0.996474i	$-0.526738\pi$
$563$	−3.98154	−0.167802	−0.0839010	+	0.996474i	$0.526738\pi$
$564$	−7.39512	−0.311391
$565$	14.2507	0.599532
$566$	−14.8458	−0.624015
$567$	4.32361	0.181575
$568$	−5.25705	−0.220581
$569$	−34.8760	−1.46208	−0.731040	−	0.682335i	$-0.760965\pi$
$569$	−34.8760	−1.46208	−0.731040	+	0.682335i	$0.760965\pi$
$570$	0.710410	0.0297558
$571$	−16.6748	−0.697820	−0.348910	−	0.937156i	$-0.613448\pi$
$571$	−16.6748	−0.697820	−0.348910	+	0.937156i	$0.613448\pi$
$572$	10.3999	0.434842
$573$	−20.9658	−0.875857
$574$	40.9885	1.71083
$575$	−4.21065	−0.175596
$576$	1.00000	0.0416667
$577$	−30.0524	−1.25110	−0.625550	−	0.780184i	$-0.715125\pi$
$577$	−30.0524	−1.25110	−0.625550	+	0.780184i	$0.715125\pi$
$578$	45.6424	1.89847
$579$	−12.8893	−0.535662
$580$	−0.888451	−0.0368909
$581$	25.6517	1.06421
$582$	−9.12711	−0.378331
$583$	4.19502	0.173740
$584$	−7.90214	−0.326993
$585$	−3.05322	−0.126235
$586$	3.46866	0.143289
$587$	30.0385	1.23982	0.619912	−	0.784672i	$-0.287168\pi$
$587$	30.0385	1.23982	0.619912	+	0.784672i	$0.287168\pi$
$588$	11.6936	0.482237
$589$	−5.48230	−0.225894
$590$	−6.40882	−0.263847
$591$	−11.2374	−0.462243
$592$	9.31017	0.382646
$593$	−33.3754	−1.37056	−0.685281	−	0.728279i	$-0.740321\pi$
$593$	−33.3754	−1.37056	−0.685281	+	0.728279i	$0.740321\pi$
$594$	−3.02625	−0.124168
$595$	30.4029	1.24640
$596$	3.95121	0.161848
$597$	−12.2629	−0.501889
$598$	−3.43657	−0.140532
$599$	13.9457	0.569805	0.284903	−	0.958556i	$-0.408039\pi$
$599$	13.9457	0.569805	0.284903	+	0.958556i	$0.408039\pi$
$600$	−4.21065	−0.171899
$601$	−41.6451	−1.69874	−0.849369	−	0.527800i	$-0.823017\pi$
$601$	−41.6451	−1.69874	−0.849369	+	0.527800i	$0.823017\pi$
$602$	38.1283	1.55399
$603$	7.98469	0.325162
$604$	17.2944	0.703701
$605$	−1.63638	−0.0665284
$606$	−10.6785	−0.433786
$607$	−20.3054	−0.824172	−0.412086	−	0.911145i	$-0.635200\pi$
$607$	−20.3054	−0.824172	−0.412086	+	0.911145i	$0.635200\pi$
$608$	0.799605	0.0324283
$609$	−4.32361	−0.175202
$610$	6.04427	0.244725
$611$	25.4139	1.02813
$612$	7.91470	0.319933
$613$	37.2066	1.50276	0.751381	−	0.659869i	$-0.229388\pi$
$613$	37.2066	1.50276	0.751381	+	0.659869i	$0.229388\pi$
$614$	−19.4117	−0.783392
$615$	8.42265	0.339634
$616$	−13.0843	−0.527182
$617$	−7.76392	−0.312564	−0.156282	−	0.987713i	$-0.549951\pi$
$617$	−7.76392	−0.312564	−0.156282	+	0.987713i	$0.549951\pi$
$618$	−13.6189	−0.547834
$619$	−11.9004	−0.478319	−0.239160	−	0.970980i	$-0.576872\pi$
$619$	−11.9004	−0.478319	−0.239160	+	0.970980i	$0.576872\pi$
$620$	−6.09146	−0.244639
$621$	1.00000	0.0401286
$622$	11.7072	0.469415
$623$	56.1083	2.24793
$624$	−3.43657	−0.137573
$625$	13.7829	0.551315
$626$	28.1210	1.12394
$627$	−2.41980	−0.0966375
$628$	−0.638723	−0.0254878
$629$	73.6872	2.93810
$630$	3.84132	0.153042
$631$	−17.9949	−0.716366	−0.358183	−	0.933651i	$-0.616604\pi$
$631$	−17.9949	−0.716366	−0.358183	+	0.933651i	$0.616604\pi$
$632$	−8.50391	−0.338268
$633$	−27.7695	−1.10374
$634$	−16.9607	−0.673594
$635$	−8.01499	−0.318065
$636$	−1.38621	−0.0549669
$637$	−40.1860	−1.59223
$638$	3.02625	0.119810
$639$	−5.25705	−0.207966
$640$	0.888451	0.0351191
$641$	−9.28263	−0.366642	−0.183321	−	0.983053i	$-0.558685\pi$
$641$	−9.28263	−0.366642	−0.183321	+	0.983053i	$0.558685\pi$
$642$	12.9255	0.510128
$643$	41.2403	1.62636	0.813179	−	0.582013i	$-0.197735\pi$
$643$	41.2403	1.62636	0.813179	+	0.582013i	$0.197735\pi$
$644$	4.32361	0.170374
$645$	7.83491	0.308499
$646$	6.32863	0.248997
$647$	−25.2868	−0.994127	−0.497063	−	0.867714i	$-0.665588\pi$
$647$	−25.2868	−0.994127	−0.497063	+	0.867714i	$0.665588\pi$
$648$	1.00000	0.0392837
$649$	21.8297	0.856892
$650$	14.4702	0.567568
$651$	−29.6438	−1.16183
$652$	11.6597	0.456628
$653$	−3.35487	−0.131286	−0.0656430	−	0.997843i	$-0.520910\pi$
$653$	−3.35487	−0.131286	−0.0656430	+	0.997843i	$0.520910\pi$
$654$	−8.21685	−0.321304
$655$	1.17754	0.0460104
$656$	9.48015	0.370138
$657$	−7.90214	−0.308292
$658$	−31.9736	−1.24646
$659$	36.8482	1.43540	0.717701	−	0.696351i	$-0.245194\pi$
$659$	36.8482	1.43540	0.717701	+	0.696351i	$0.245194\pi$
$660$	−2.68867	−0.104656
$661$	19.0332	0.740306	0.370153	−	0.928971i	$-0.379305\pi$
$661$	19.0332	0.740306	0.370153	+	0.928971i	$0.379305\pi$
$662$	19.4675	0.756628
$663$	−27.1994	−1.05634
$664$	5.93292	0.230242
$665$	3.07154	0.119109
$666$	9.31017	0.360762
$667$	−1.00000	−0.0387202
$668$	6.60096	0.255399
$669$	−13.6852	−0.529100
$670$	7.09401	0.274065
$671$	−20.5880	−0.794791
$672$	4.32361	0.166787
$673$	−32.7308	−1.26168	−0.630841	−	0.775913i	$-0.717290\pi$
$673$	−32.7308	−1.26168	−0.630841	+	0.775913i	$0.717290\pi$
$674$	4.82730	0.185941
$675$	−4.21065	−0.162068
$676$	−1.18998	−0.0457687
$677$	−9.91577	−0.381094	−0.190547	−	0.981678i	$-0.561026\pi$
$677$	−9.91577	−0.381094	−0.190547	+	0.981678i	$0.561026\pi$
$678$	16.0399	0.616010
$679$	−39.4621	−1.51442
$680$	7.03182	0.269658
$681$	19.5702	0.749930
$682$	20.7487	0.794510
$683$	26.9425	1.03092	0.515462	−	0.856912i	$-0.327620\pi$
$683$	26.9425	1.03092	0.515462	+	0.856912i	$0.327620\pi$
$684$	0.799605	0.0305737
$685$	−20.7430	−0.792549
$686$	20.2934	0.774806
$687$	11.1938	0.427070
$688$	8.81862	0.336207
$689$	4.76382	0.181487
$690$	0.888451	0.0338228
$691$	−43.5901	−1.65824	−0.829122	−	0.559068i	$-0.811159\pi$
$691$	−43.5901	−1.65824	−0.829122	+	0.559068i	$0.811159\pi$
$692$	−7.26665	−0.276237
$693$	−13.0843	−0.497032
$694$	−21.9303	−0.832464
$695$	−10.6837	−0.405257
$696$	−1.00000	−0.0379049
$697$	75.0325	2.84206
$698$	15.5661	0.589185
$699$	23.9754	0.906834
$700$	−18.2052	−0.688093
$701$	−40.0003	−1.51079	−0.755396	−	0.655269i	$-0.772555\pi$
$701$	−40.0003	−1.51079	−0.755396	+	0.655269i	$0.772555\pi$
$702$	−3.43657	−0.129705
$703$	7.44446	0.280773
$704$	−3.02625	−0.114056
$705$	−6.57021	−0.247448
$706$	−23.6311	−0.889370
$707$	−46.1698	−1.73639
$708$	−7.21347	−0.271099
$709$	27.2216	1.02233	0.511164	−	0.859483i	$-0.329214\pi$
$709$	27.2216	1.02233	0.511164	+	0.859483i	$0.329214\pi$
$710$	−4.67064	−0.175286
$711$	−8.50391	−0.318922
$712$	12.9772	0.486340
$713$	−6.85626	−0.256769
$714$	34.2201	1.28065
$715$	9.23981	0.345549
$716$	17.7435	0.663104
$717$	10.3371	0.386046
$718$	33.7103	1.25806
$719$	−36.5293	−1.36231	−0.681156	−	0.732139i	$-0.738522\pi$
$719$	−36.5293	−1.36231	−0.681156	+	0.732139i	$0.738522\pi$
$720$	0.888451	0.0331106
$721$	−58.8830	−2.19292
$722$	−18.3606	−0.683312
$723$	−20.8977	−0.777193
$724$	12.5746	0.467332
$725$	4.21065	0.156380
$726$	−1.84184	−0.0683570
$727$	0.524461	0.0194512	0.00972558	−	0.999953i	$-0.496904\pi$
$727$	0.524461	0.0194512	0.00972558	+	0.999953i	$0.496904\pi$
$728$	−14.8584	−0.550689
$729$	1.00000	0.0370370
$730$	−7.02067	−0.259847
$731$	69.7967	2.58152
$732$	6.80315	0.251452
$733$	−3.05162	−0.112714	−0.0563572	−	0.998411i	$-0.517949\pi$
$733$	−3.05162	−0.112714	−0.0563572	+	0.998411i	$0.517949\pi$
$734$	19.4578	0.718201
$735$	10.3892	0.383212
$736$	1.00000	0.0368605
$737$	−24.1636	−0.890079
$738$	9.48015	0.348969
$739$	−31.8463	−1.17148	−0.585742	−	0.810498i	$-0.699197\pi$
$739$	−31.8463	−1.17148	−0.585742	+	0.810498i	$0.699197\pi$
$740$	8.27163	0.304071
$741$	−2.74790	−0.100947
$742$	−5.99345	−0.220026
$743$	15.4194	0.565682	0.282841	−	0.959167i	$-0.408723\pi$
$743$	15.4194	0.565682	0.282841	+	0.959167i	$0.408723\pi$
$744$	−6.85626	−0.251363
$745$	3.51046	0.128613
$746$	−19.0469	−0.697358
$747$	5.93292	0.217074
$748$	−23.9518	−0.875765
$749$	55.8847	2.04198
$750$	−8.18322	−0.298809
$751$	17.0226	0.621163	0.310581	−	0.950547i	$-0.399476\pi$
$751$	17.0226	0.621163	0.310581	+	0.950547i	$0.399476\pi$
$752$	−7.39512	−0.269672
$753$	−10.2667	−0.374139
$754$	3.43657	0.125153
$755$	15.3653	0.559200
$756$	4.32361	0.157248
$757$	−24.4979	−0.890390	−0.445195	−	0.895434i	$-0.646866\pi$
$757$	−24.4979	−0.890390	−0.445195	+	0.895434i	$0.646866\pi$
$758$	14.6247	0.531194
$759$	−3.02625	−0.109846
$760$	0.710410	0.0257693
$761$	−20.8187	−0.754676	−0.377338	−	0.926076i	$-0.623161\pi$
$761$	−20.8187	−0.754676	−0.377338	+	0.926076i	$0.623161\pi$
$762$	−9.02131	−0.326808
$763$	−35.5265	−1.28614
$764$	−20.9658	−0.758515
$765$	7.03182	0.254236
$766$	6.97705	0.252091
$767$	24.7896	0.895101
$768$	1.00000	0.0360844
$769$	31.9300	1.15142	0.575712	−	0.817653i	$-0.304725\pi$
$769$	31.9300	1.15142	0.575712	+	0.817653i	$0.304725\pi$
$770$	−11.6248	−0.418928
$771$	18.9066	0.680905
$772$	−12.8893	−0.463897
$773$	−33.6387	−1.20990	−0.604950	−	0.796263i	$-0.706807\pi$
$773$	−33.6387	−1.20990	−0.604950	+	0.796263i	$0.706807\pi$
$774$	8.81862	0.316979
$775$	28.8694	1.03702
$776$	−9.12711	−0.327644
$777$	40.2536	1.44409
$778$	19.7638	0.708567
$779$	7.58038	0.271595
$780$	−3.05322	−0.109323
$781$	15.9091	0.569274
$782$	7.91470	0.283029
$783$	−1.00000	−0.0357371
$784$	11.6936	0.417629
$785$	−0.567474	−0.0202540
$786$	1.32539	0.0472750
$787$	10.6824	0.380787	0.190393	−	0.981708i	$-0.439024\pi$
$787$	10.6824	0.380787	0.190393	+	0.981708i	$0.439024\pi$
$788$	−11.2374	−0.400314
$789$	−25.2309	−0.898242
$790$	−7.55531	−0.268806
$791$	69.3505	2.46582
$792$	−3.02625	−0.107533
$793$	−23.3795	−0.830230
$794$	−10.6071	−0.376432
$795$	−1.23158	−0.0436797
$796$	−12.2629	−0.434648
$797$	33.4088	1.18340	0.591700	−	0.806158i	$-0.298457\pi$
$797$	33.4088	1.18340	0.591700	+	0.806158i	$0.298457\pi$
$798$	3.45718	0.122383
$799$	−58.5302	−2.07065
$800$	−4.21065	−0.148869
$801$	12.9772	0.458526
$802$	5.11262	0.180533
$803$	23.9138	0.843901
$804$	7.98469	0.281598
$805$	3.84132	0.135389
$806$	23.5620	0.829937
$807$	6.91459	0.243405
$808$	−10.6785	−0.375669
$809$	30.6166	1.07642	0.538211	−	0.842810i	$-0.319100\pi$
$809$	30.6166	1.07642	0.538211	+	0.842810i	$0.319100\pi$
$810$	0.888451	0.0312170
$811$	46.2148	1.62282	0.811410	−	0.584478i	$-0.198701\pi$
$811$	46.2148	1.62282	0.811410	+	0.584478i	$0.198701\pi$
$812$	−4.32361	−0.151729
$813$	5.72049	0.200626
$814$	−28.1749	−0.987528
$815$	10.3590	0.362862
$816$	7.91470	0.277070
$817$	7.05141	0.246698
$818$	−17.2252	−0.602266
$819$	−14.8584	−0.519194
$820$	8.42265	0.294132
$821$	26.9634	0.941030	0.470515	−	0.882392i	$-0.344068\pi$
$821$	26.9634	0.941030	0.470515	+	0.882392i	$0.344068\pi$
$822$	−23.3473	−0.814332
$823$	−10.9293	−0.380970	−0.190485	−	0.981690i	$-0.561006\pi$
$823$	−10.9293	−0.380970	−0.190485	+	0.981690i	$0.561006\pi$
$824$	−13.6189	−0.474438
$825$	12.7425	0.443636
$826$	−31.1883	−1.08518
$827$	−12.6216	−0.438897	−0.219449	−	0.975624i	$-0.570426\pi$
$827$	−12.6216	−0.438897	−0.219449	+	0.975624i	$0.570426\pi$
$828$	1.00000	0.0347524
$829$	18.2089	0.632421	0.316210	−	0.948689i	$-0.397589\pi$
$829$	18.2089	0.632421	0.316210	+	0.948689i	$0.397589\pi$
$830$	5.27111	0.182963
$831$	−8.39834	−0.291335
$832$	−3.43657	−0.119142
$833$	92.5515	3.20672
$834$	−12.0251	−0.416395
$835$	5.86463	0.202954
$836$	−2.41980	−0.0836906
$837$	−6.85626	−0.236987
$838$	22.9015	0.791119
$839$	−27.0081	−0.932422	−0.466211	−	0.884674i	$-0.654381\pi$
$839$	−27.0081	−0.932422	−0.466211	+	0.884674i	$0.654381\pi$
$840$	3.84132	0.132538
$841$	1.00000	0.0344828
$842$	−30.8764	−1.06407
$843$	−20.7394	−0.714303
$844$	−27.7695	−0.955865
$845$	−1.05724	−0.0363703
$846$	−7.39512	−0.254250
$847$	−7.96339	−0.273625
$848$	−1.38621	−0.0476027
$849$	−14.8458	−0.509506
$850$	−33.3261	−1.14307
$851$	9.31017	0.319148
$852$	−5.25705	−0.180104
$853$	43.3156	1.48310	0.741549	−	0.670899i	$-0.234092\pi$
$853$	43.3156	1.48310	0.741549	+	0.670899i	$0.234092\pi$
$854$	29.4142	1.00653
$855$	0.710410	0.0242955
$856$	12.9255	0.441784
$857$	−7.52747	−0.257133	−0.128567	−	0.991701i	$-0.541038\pi$
$857$	−7.52747	−0.257133	−0.128567	+	0.991701i	$0.541038\pi$
$858$	10.3999	0.355047
$859$	−44.7404	−1.52652	−0.763261	−	0.646090i	$-0.776403\pi$
$859$	−44.7404	−1.52652	−0.763261	+	0.646090i	$0.776403\pi$
$860$	7.83491	0.267168
$861$	40.9885	1.39688
$862$	−5.03912	−0.171633
$863$	−36.9790	−1.25878	−0.629390	−	0.777089i	$-0.716695\pi$
$863$	−36.9790	−1.25878	−0.629390	+	0.777089i	$0.716695\pi$
$864$	1.00000	0.0340207
$865$	−6.45606	−0.219513
$866$	31.2422	1.06165
$867$	45.6424	1.55010
$868$	−29.6438	−1.00618
$869$	25.7349	0.872998
$870$	−0.888451	−0.0301213
$871$	−27.4399	−0.929767
$872$	−8.21685	−0.278258
$873$	−9.12711	−0.308906
$874$	0.799605	0.0270470
$875$	−35.3811	−1.19610
$876$	−7.90214	−0.266989
$877$	10.4588	0.353169	0.176584	−	0.984286i	$-0.443495\pi$
$877$	10.4588	0.353169	0.176584	+	0.984286i	$0.443495\pi$
$878$	−32.5231	−1.09760
$879$	3.46866	0.116995
$880$	−2.68867	−0.0906351
$881$	15.2721	0.514529	0.257264	−	0.966341i	$-0.417179\pi$
$881$	15.2721	0.514529	0.257264	+	0.966341i	$0.417179\pi$
$882$	11.6936	0.393745
$883$	4.74728	0.159759	0.0798793	−	0.996805i	$-0.474546\pi$
$883$	4.74728	0.159759	0.0798793	+	0.996805i	$0.474546\pi$
$884$	−27.1994	−0.914815
$885$	−6.40882	−0.215430
$886$	8.01010	0.269105
$887$	12.2295	0.410625	0.205312	−	0.978696i	$-0.434179\pi$
$887$	12.2295	0.410625	0.205312	+	0.978696i	$0.434179\pi$
$888$	9.31017	0.312429
$889$	−39.0047	−1.30817
$890$	11.5296	0.386473
$891$	−3.02625	−0.101383
$892$	−13.6852	−0.458214
$893$	−5.91318	−0.197877
$894$	3.95121	0.132148
$895$	15.7642	0.526939
$896$	4.32361	0.144442
$897$	−3.43657	−0.114744
$898$	13.0283	0.434761
$899$	6.85626	0.228669
$900$	−4.21065	−0.140355
$901$	−10.9715	−0.365512
$902$	−28.6893	−0.955248
$903$	38.1283	1.26883
$904$	16.0399	0.533480
$905$	11.1719	0.371368
$906$	17.2944	0.574570
$907$	21.0667	0.699508	0.349754	−	0.936842i	$-0.386265\pi$
$907$	21.0667	0.699508	0.349754	+	0.936842i	$0.386265\pi$
$908$	19.5702	0.649458
$909$	−10.6785	−0.354184
$910$	−13.2010	−0.437608
$911$	−39.3039	−1.30220	−0.651099	−	0.758993i	$-0.725692\pi$
$911$	−39.3039	−1.30220	−0.651099	+	0.758993i	$0.725692\pi$
$912$	0.799605	0.0264776
$913$	−17.9545	−0.594207
$914$	−16.5526	−0.547513
$915$	6.04427	0.199817
$916$	11.1938	0.369853
$917$	5.73046	0.189236
$918$	7.91470	0.261224
$919$	−42.3198	−1.39600	−0.698001	−	0.716097i	$-0.745927\pi$
$919$	−42.3198	−1.39600	−0.698001	+	0.716097i	$0.745927\pi$
$920$	0.888451	0.0292914
$921$	−19.4117	−0.639637
$922$	37.2188	1.22574
$923$	18.0662	0.594657
$924$	−13.0843	−0.430442
$925$	−39.2019	−1.28895
$926$	−14.2185	−0.467250
$927$	−13.6189	−0.447305
$928$	−1.00000	−0.0328266
$929$	−36.9614	−1.21266	−0.606332	−	0.795212i	$-0.707360\pi$
$929$	−36.9614	−1.21266	−0.606332	+	0.795212i	$0.707360\pi$
$930$	−6.09146	−0.199747
$931$	9.35028	0.306443
$932$	23.9754	0.785341
$933$	11.7072	0.383275
$934$	−18.5127	−0.605753
$935$	−21.2800	−0.695931
$936$	−3.43657	−0.112328
$937$	−38.9990	−1.27404	−0.637021	−	0.770847i	$-0.719833\pi$
$937$	−38.9990	−1.27404	−0.637021	+	0.770847i	$0.719833\pi$
$938$	34.5227	1.12721
$939$	28.1210	0.917694
$940$	−6.57021	−0.214296
$941$	−42.0590	−1.37108	−0.685542	−	0.728034i	$-0.740435\pi$
$941$	−42.0590	−1.37108	−0.685542	+	0.728034i	$0.740435\pi$
$942$	−0.638723	−0.0208107
$943$	9.48015	0.308716
$944$	−7.21347	−0.234779
$945$	3.84132	0.124958
$946$	−26.6873	−0.867679
$947$	−43.6513	−1.41848	−0.709238	−	0.704969i	$-0.750961\pi$
$947$	−43.6513	−1.41848	−0.709238	+	0.704969i	$0.750961\pi$
$948$	−8.50391	−0.276194
$949$	27.1563	0.881530
$950$	−3.36686	−0.109235
$951$	−16.9607	−0.549987
$952$	34.2201	1.10908
$953$	42.7378	1.38441	0.692207	−	0.721699i	$-0.256639\pi$
$953$	42.7378	1.38441	0.692207	+	0.721699i	$0.256639\pi$
$954$	−1.38621	−0.0448803
$955$	−18.6271	−0.602757
$956$	10.3371	0.334326
$957$	3.02625	0.0978246
$958$	−7.78004	−0.251362
$959$	−100.945	−3.25968
$960$	0.888451	0.0286746
$961$	16.0083	0.516398
$962$	−31.9950	−1.03156
$963$	12.9255	0.416518
$964$	−20.8977	−0.673069
$965$	−11.4515	−0.368638
$966$	4.32361	0.139110
$967$	8.53421	0.274442	0.137221	−	0.990540i	$-0.456183\pi$
$967$	8.53421	0.274442	0.137221	+	0.990540i	$0.456183\pi$
$968$	−1.84184	−0.0591989
$969$	6.32863	0.203305
$970$	−8.10899	−0.260364
$971$	−11.4973	−0.368965	−0.184483	−	0.982836i	$-0.559061\pi$
$971$	−11.4973	−0.368965	−0.184483	+	0.982836i	$0.559061\pi$
$972$	1.00000	0.0320750
$973$	−51.9919	−1.66678
$974$	−37.6755	−1.20720
$975$	14.4702	0.463418
$976$	6.80315	0.217763
$977$	18.9241	0.605435	0.302718	−	0.953080i	$-0.402106\pi$
$977$	18.9241	0.605435	0.302718	+	0.953080i	$0.402106\pi$
$978$	11.6597	0.372835
$979$	−39.2721	−1.25514
$980$	10.3892	0.331871
$981$	−8.21685	−0.262344
$982$	12.6244	0.402862
$983$	0.123191	0.00392920	0.00196460	−	0.999998i	$-0.499375\pi$
$983$	0.123191	0.00392920	0.00196460	+	0.999998i	$0.499375\pi$
$984$	9.48015	0.302216
$985$	−9.98384	−0.318112
$986$	−7.91470	−0.252055
$987$	−31.9736	−1.01773
$988$	−2.74790	−0.0874223
$989$	8.81862	0.280416
$990$	−2.68867	−0.0854516
$991$	54.5261	1.73208	0.866039	−	0.499976i	$-0.166658\pi$
$991$	54.5261	1.73208	0.866039	+	0.499976i	$0.166658\pi$
$992$	−6.85626	−0.217687
$993$	19.4675	0.617784
$994$	−22.7295	−0.720935
$995$	−10.8950	−0.345395
$996$	5.93292	0.187992
$997$	−52.7170	−1.66957	−0.834783	−	0.550579i	$-0.814407\pi$
$997$	−52.7170	−1.66957	−0.834783	+	0.550579i	$0.814407\pi$
$998$	−23.2560	−0.736154
$999$	9.31017	0.294561

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4002.2.a.bh.1.5	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4002.2.a.bh.1.5	✓	7	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:	\( N \)	\(=\)	\( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.888451 q^{5} +1.00000 q^{6} +4.32361 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.888451 q^{5} +1.00000 q^{6} +4.32361 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.888451 q^{10} -3.02625 q^{11} +1.00000 q^{12} -3.43657 q^{13} +4.32361 q^{14} +0.888451 q^{15} +1.00000 q^{16} +7.91470 q^{17} +1.00000 q^{18} +0.799605 q^{19} +0.888451 q^{20} +4.32361 q^{21} -3.02625 q^{22} +1.00000 q^{23} +1.00000 q^{24} -4.21065 q^{25} -3.43657 q^{26} +1.00000 q^{27} +4.32361 q^{28} -1.00000 q^{29} +0.888451 q^{30} -6.85626 q^{31} +1.00000 q^{32} -3.02625 q^{33} +7.91470 q^{34} +3.84132 q^{35} +1.00000 q^{36} +9.31017 q^{37} +0.799605 q^{38} -3.43657 q^{39} +0.888451 q^{40} +9.48015 q^{41} +4.32361 q^{42} +8.81862 q^{43} -3.02625 q^{44} +0.888451 q^{45} +1.00000 q^{46} -7.39512 q^{47} +1.00000 q^{48} +11.6936 q^{49} -4.21065 q^{50} +7.91470 q^{51} -3.43657 q^{52} -1.38621 q^{53} +1.00000 q^{54} -2.68867 q^{55} +4.32361 q^{56} +0.799605 q^{57} -1.00000 q^{58} -7.21347 q^{59} +0.888451 q^{60} +6.80315 q^{61} -6.85626 q^{62} +4.32361 q^{63} +1.00000 q^{64} -3.05322 q^{65} -3.02625 q^{66} +7.98469 q^{67} +7.91470 q^{68} +1.00000 q^{69} +3.84132 q^{70} -5.25705 q^{71} +1.00000 q^{72} -7.90214 q^{73} +9.31017 q^{74} -4.21065 q^{75} +0.799605 q^{76} -13.0843 q^{77} -3.43657 q^{78} -8.50391 q^{79} +0.888451 q^{80} +1.00000 q^{81} +9.48015 q^{82} +5.93292 q^{83} +4.32361 q^{84} +7.03182 q^{85} +8.81862 q^{86} -1.00000 q^{87} -3.02625 q^{88} +12.9772 q^{89} +0.888451 q^{90} -14.8584 q^{91} +1.00000 q^{92} -6.85626 q^{93} -7.39512 q^{94} +0.710410 q^{95} +1.00000 q^{96} -9.12711 q^{97} +11.6936 q^{98} -3.02625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + q^5 + 7 * q^6 - 2 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9} + q^{10} + 11 q^{11} + 7 q^{12} - q^{13} - 2 q^{14} + q^{15} + 7 q^{16} + 18 q^{17} + 7 q^{18} + 6 q^{19} + q^{20} - 2 q^{21} + 11 q^{22} + 7 q^{23} + 7 q^{24} + 12 q^{25} - q^{26} + 7 q^{27} - 2 q^{28} - 7 q^{29} + q^{30} + 3 q^{31} + 7 q^{32} + 11 q^{33} + 18 q^{34} - 4 q^{35} + 7 q^{36} + 5 q^{37} + 6 q^{38} - q^{39} + q^{40} + 25 q^{41} - 2 q^{42} + 20 q^{43} + 11 q^{44} + q^{45} + 7 q^{46} + 7 q^{48} + 7 q^{49} + 12 q^{50} + 18 q^{51} - q^{52} - 4 q^{53} + 7 q^{54} + 17 q^{55} - 2 q^{56} + 6 q^{57} - 7 q^{58} - 17 q^{59} + q^{60} + 5 q^{61} + 3 q^{62} - 2 q^{63} + 7 q^{64} + 7 q^{65} + 11 q^{66} + 15 q^{67} + 18 q^{68} + 7 q^{69} - 4 q^{70} + 15 q^{71} + 7 q^{72} + 14 q^{73} + 5 q^{74} + 12 q^{75} + 6 q^{76} - 12 q^{77} - q^{78} - 4 q^{79} + q^{80} + 7 q^{81} + 25 q^{82} + 14 q^{83} - 2 q^{84} + 34 q^{85} + 20 q^{86} - 7 q^{87} + 11 q^{88} + 8 q^{89} + q^{90} - 6 q^{91} + 7 q^{92} + 3 q^{93} - 18 q^{95} + 7 q^{96} - 18 q^{97} + 7 q^{98} + 11 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + q^5 + 7 * q^6 - 2 * q^7 + 7 * q^8 + 7 * q^9 + q^10 + 11 * q^11 + 7 * q^12 - q^13 - 2 * q^14 + q^15 + 7 * q^16 + 18 * q^17 + 7 * q^18 + 6 * q^19 + q^20 - 2 * q^21 + 11 * q^22 + 7 * q^23 + 7 * q^24 + 12 * q^25 - q^26 + 7 * q^27 - 2 * q^28 - 7 * q^29 + q^30 + 3 * q^31 + 7 * q^32 + 11 * q^33 + 18 * q^34 - 4 * q^35 + 7 * q^36 + 5 * q^37 + 6 * q^38 - q^39 + q^40 + 25 * q^41 - 2 * q^42 + 20 * q^43 + 11 * q^44 + q^45 + 7 * q^46 + 7 * q^48 + 7 * q^49 + 12 * q^50 + 18 * q^51 - q^52 - 4 * q^53 + 7 * q^54 + 17 * q^55 - 2 * q^56 + 6 * q^57 - 7 * q^58 - 17 * q^59 + q^60 + 5 * q^61 + 3 * q^62 - 2 * q^63 + 7 * q^64 + 7 * q^65 + 11 * q^66 + 15 * q^67 + 18 * q^68 + 7 * q^69 - 4 * q^70 + 15 * q^71 + 7 * q^72 + 14 * q^73 + 5 * q^74 + 12 * q^75 + 6 * q^76 - 12 * q^77 - q^78 - 4 * q^79 + q^80 + 7 * q^81 + 25 * q^82 + 14 * q^83 - 2 * q^84 + 34 * q^85 + 20 * q^86 - 7 * q^87 + 11 * q^88 + 8 * q^89 + q^90 - 6 * q^91 + 7 * q^92 + 3 * q^93 - 18 * q^95 + 7 * q^96 - 18 * q^97 + 7 * q^98 + 11 * q^99

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