LMFDB - Embedded newform 4002.2.a.bh.1.6

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			1.6
Root			$-3.61135$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.16777 q^{5} +1.00000 q^{6} -1.07153 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.16777 q^{5} +1.00000 q^{6} -1.07153 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.16777 q^{10} +3.63917 q^{11} +1.00000 q^{12} -1.89173 q^{13} -1.07153 q^{14} +3.16777 q^{15} +1.00000 q^{16} +3.52860 q^{17} +1.00000 q^{18} +8.15117 q^{19} +3.16777 q^{20} -1.07153 q^{21} +3.63917 q^{22} +1.00000 q^{23} +1.00000 q^{24} +5.03478 q^{25} -1.89173 q^{26} +1.00000 q^{27} -1.07153 q^{28} -1.00000 q^{29} +3.16777 q^{30} -5.55878 q^{31} +1.00000 q^{32} +3.63917 q^{33} +3.52860 q^{34} -3.39436 q^{35} +1.00000 q^{36} -5.88115 q^{37} +8.15117 q^{38} -1.89173 q^{39} +3.16777 q^{40} -11.0791 q^{41} -1.07153 q^{42} -1.20998 q^{43} +3.63917 q^{44} +3.16777 q^{45} +1.00000 q^{46} -9.27673 q^{47} +1.00000 q^{48} -5.85183 q^{49} +5.03478 q^{50} +3.52860 q^{51} -1.89173 q^{52} +2.41575 q^{53} +1.00000 q^{54} +11.5281 q^{55} -1.07153 q^{56} +8.15117 q^{57} -1.00000 q^{58} -10.2273 q^{59} +3.16777 q^{60} +4.69638 q^{61} -5.55878 q^{62} -1.07153 q^{63} +1.00000 q^{64} -5.99256 q^{65} +3.63917 q^{66} +2.61568 q^{67} +3.52860 q^{68} +1.00000 q^{69} -3.39436 q^{70} +10.7436 q^{71} +1.00000 q^{72} +3.30079 q^{73} -5.88115 q^{74} +5.03478 q^{75} +8.15117 q^{76} -3.89947 q^{77} -1.89173 q^{78} -9.55404 q^{79} +3.16777 q^{80} +1.00000 q^{81} -11.0791 q^{82} -7.82283 q^{83} -1.07153 q^{84} +11.1778 q^{85} -1.20998 q^{86} -1.00000 q^{87} +3.63917 q^{88} +4.52717 q^{89} +3.16777 q^{90} +2.02704 q^{91} +1.00000 q^{92} -5.55878 q^{93} -9.27673 q^{94} +25.8210 q^{95} +1.00000 q^{96} +11.0616 q^{97} -5.85183 q^{98} +3.63917 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	3.16777	1.41667	0.708335	−	0.705876i	$-0.249446\pi$
$5$	3.16777	1.41667	0.708335	+	0.705876i	$0.249446\pi$
$6$	1.00000	0.408248
$7$	−1.07153	−0.404999	−0.202500	−	0.979282i	$-0.564907\pi$
$7$	−1.07153	−0.404999	−0.202500	+	0.979282i	$0.564907\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.16777	1.00174
$11$	3.63917	1.09725	0.548625	−	0.836068i	$-0.315151\pi$
$11$	3.63917	1.09725	0.548625	+	0.836068i	$0.315151\pi$
$12$	1.00000	0.288675
$13$	−1.89173	−0.524671	−0.262335	−	0.964977i	$-0.584493\pi$
$13$	−1.89173	−0.524671	−0.262335	+	0.964977i	$0.584493\pi$
$14$	−1.07153	−0.286378
$15$	3.16777	0.817915
$16$	1.00000	0.250000
$17$	3.52860	0.855812	0.427906	−	0.903823i	$-0.359251\pi$
$17$	3.52860	0.855812	0.427906	+	0.903823i	$0.359251\pi$
$18$	1.00000	0.235702
$19$	8.15117	1.87001	0.935003	−	0.354639i	$-0.115396\pi$
$19$	8.15117	1.87001	0.935003	+	0.354639i	$0.115396\pi$
$20$	3.16777	0.708335
$21$	−1.07153	−0.233827
$22$	3.63917	0.775874
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	5.03478	1.00696
$26$	−1.89173	−0.370998
$27$	1.00000	0.192450
$28$	−1.07153	−0.202500
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	3.16777	0.578353
$31$	−5.55878	−0.998387	−0.499193	−	0.866491i	$-0.666370\pi$
$31$	−5.55878	−0.998387	−0.499193	+	0.866491i	$0.666370\pi$
$32$	1.00000	0.176777
$33$	3.63917	0.633498
$34$	3.52860	0.605150
$35$	−3.39436	−0.573751
$36$	1.00000	0.166667
$37$	−5.88115	−0.966855	−0.483427	−	0.875384i	$-0.660608\pi$
$37$	−5.88115	−0.966855	−0.483427	+	0.875384i	$0.660608\pi$
$38$	8.15117	1.32229
$39$	−1.89173	−0.302919
$40$	3.16777	0.500869
$41$	−11.0791	−1.73026	−0.865132	−	0.501544i	$-0.832766\pi$
$41$	−11.0791	−1.73026	−0.865132	+	0.501544i	$0.832766\pi$
$42$	−1.07153	−0.165340
$43$	−1.20998	−0.184520	−0.0922602	−	0.995735i	$-0.529409\pi$
$43$	−1.20998	−0.184520	−0.0922602	+	0.995735i	$0.529409\pi$
$44$	3.63917	0.548625
$45$	3.16777	0.472224
$46$	1.00000	0.147442
$47$	−9.27673	−1.35315	−0.676575	−	0.736373i	$-0.736537\pi$
$47$	−9.27673	−1.35315	−0.676575	+	0.736373i	$0.736537\pi$
$48$	1.00000	0.144338
$49$	−5.85183	−0.835975
$50$	5.03478	0.712026
$51$	3.52860	0.494103
$52$	−1.89173	−0.262335
$53$	2.41575	0.331829	0.165915	−	0.986140i	$-0.446942\pi$
$53$	2.41575	0.331829	0.165915	+	0.986140i	$0.446942\pi$
$54$	1.00000	0.136083
$55$	11.5281	1.55444
$56$	−1.07153	−0.143189
$57$	8.15117	1.07965
$58$	−1.00000	−0.131306
$59$	−10.2273	−1.33148	−0.665739	−	0.746185i	$-0.731883\pi$
$59$	−10.2273	−1.33148	−0.665739	+	0.746185i	$0.731883\pi$
$60$	3.16777	0.408958
$61$	4.69638	0.601309	0.300655	−	0.953733i	$-0.402795\pi$
$61$	4.69638	0.601309	0.300655	+	0.953733i	$0.402795\pi$
$62$	−5.55878	−0.705966
$63$	−1.07153	−0.135000
$64$	1.00000	0.125000
$65$	−5.99256	−0.743286
$66$	3.63917	0.447951
$67$	2.61568	0.319556	0.159778	−	0.987153i	$-0.448922\pi$
$67$	2.61568	0.319556	0.159778	+	0.987153i	$0.448922\pi$
$68$	3.52860	0.427906
$69$	1.00000	0.120386
$70$	−3.39436	−0.405703
$71$	10.7436	1.27503	0.637513	−	0.770440i	$-0.279963\pi$
$71$	10.7436	1.27503	0.637513	+	0.770440i	$0.279963\pi$
$72$	1.00000	0.117851
$73$	3.30079	0.386328	0.193164	−	0.981166i	$-0.438125\pi$
$73$	3.30079	0.386328	0.193164	+	0.981166i	$0.438125\pi$
$74$	−5.88115	−0.683670
$75$	5.03478	0.581367
$76$	8.15117	0.935003
$77$	−3.89947	−0.444386
$78$	−1.89173	−0.214196
$79$	−9.55404	−1.07491	−0.537456	−	0.843291i	$-0.680615\pi$
$79$	−9.55404	−1.07491	−0.537456	+	0.843291i	$0.680615\pi$
$80$	3.16777	0.354168
$81$	1.00000	0.111111
$82$	−11.0791	−1.22348
$83$	−7.82283	−0.858667	−0.429333	−	0.903146i	$-0.641251\pi$
$83$	−7.82283	−0.858667	−0.429333	+	0.903146i	$0.641251\pi$
$84$	−1.07153	−0.116913
$85$	11.1778	1.21240
$86$	−1.20998	−0.130476
$87$	−1.00000	−0.107211
$88$	3.63917	0.387937
$89$	4.52717	0.479879	0.239939	−	0.970788i	$-0.422872\pi$
$89$	4.52717	0.479879	0.239939	+	0.970788i	$0.422872\pi$
$90$	3.16777	0.333913
$91$	2.02704	0.212491
$92$	1.00000	0.104257
$93$	−5.55878	−0.576419
$94$	−9.27673	−0.956822
$95$	25.8210	2.64918
$96$	1.00000	0.102062
$97$	11.0616	1.12314	0.561570	−	0.827430i	$-0.310198\pi$
$97$	11.0616	1.12314	0.561570	+	0.827430i	$0.310198\pi$
$98$	−5.85183	−0.591124
$99$	3.63917	0.365750
$100$	5.03478	0.503478
$101$	−0.883955	−0.0879568	−0.0439784	−	0.999032i	$-0.514003\pi$
$101$	−0.883955	−0.0879568	−0.0439784	+	0.999032i	$0.514003\pi$
$102$	3.52860	0.349384
$103$	10.7757	1.06176	0.530879	−	0.847448i	$-0.321862\pi$
$103$	10.7757	1.06176	0.530879	+	0.847448i	$0.321862\pi$
$104$	−1.89173	−0.185499
$105$	−3.39436	−0.331255
$106$	2.41575	0.234639
$107$	9.79579	0.946995	0.473497	−	0.880795i	$-0.342991\pi$
$107$	9.79579	0.946995	0.473497	+	0.880795i	$0.342991\pi$
$108$	1.00000	0.0962250
$109$	14.0648	1.34716	0.673582	−	0.739112i	$-0.264755\pi$
$109$	14.0648	1.34716	0.673582	+	0.739112i	$0.264755\pi$
$110$	11.5281	1.09916
$111$	−5.88115	−0.558214
$112$	−1.07153	−0.101250
$113$	−4.10773	−0.386423	−0.193211	−	0.981157i	$-0.561890\pi$
$113$	−4.10773	−0.386423	−0.193211	+	0.981157i	$0.561890\pi$
$114$	8.15117	0.763427
$115$	3.16777	0.295396
$116$	−1.00000	−0.0928477
$117$	−1.89173	−0.174890
$118$	−10.2273	−0.941497
$119$	−3.78100	−0.346603
$120$	3.16777	0.289177
$121$	2.24356	0.203960
$122$	4.69638	0.425190
$123$	−11.0791	−0.998969
$124$	−5.55878	−0.499193
$125$	0.110185	0.00985524
$126$	−1.07153	−0.0954593
$127$	−0.750106	−0.0665611	−0.0332806	−	0.999446i	$-0.510595\pi$
$127$	−0.750106	−0.0665611	−0.0332806	+	0.999446i	$0.510595\pi$
$128$	1.00000	0.0883883
$129$	−1.20998	−0.106533
$130$	−5.99256	−0.525582
$131$	1.49068	0.130241	0.0651206	−	0.997877i	$-0.479257\pi$
$131$	1.49068	0.130241	0.0651206	+	0.997877i	$0.479257\pi$
$132$	3.63917	0.316749
$133$	−8.73421	−0.757352
$134$	2.61568	0.225961
$135$	3.16777	0.272638
$136$	3.52860	0.302575
$137$	10.5438	0.900818	0.450409	−	0.892822i	$-0.351278\pi$
$137$	10.5438	0.900818	0.450409	+	0.892822i	$0.351278\pi$
$138$	1.00000	0.0851257
$139$	11.9307	1.01195	0.505975	−	0.862548i	$-0.331133\pi$
$139$	11.9307	1.01195	0.505975	+	0.862548i	$0.331133\pi$
$140$	−3.39436	−0.286875
$141$	−9.27673	−0.781242
$142$	10.7436	0.901579
$143$	−6.88432	−0.575695
$144$	1.00000	0.0833333
$145$	−3.16777	−0.263069
$146$	3.30079	0.273175
$147$	−5.85183	−0.482651
$148$	−5.88115	−0.483427
$149$	−5.46713	−0.447885	−0.223942	−	0.974602i	$-0.571893\pi$
$149$	−5.46713	−0.447885	−0.223942	+	0.974602i	$0.571893\pi$
$150$	5.03478	0.411088
$151$	−4.28611	−0.348799	−0.174399	−	0.984675i	$-0.555798\pi$
$151$	−4.28611	−0.348799	−0.174399	+	0.984675i	$0.555798\pi$
$152$	8.15117	0.661147
$153$	3.52860	0.285271
$154$	−3.89947	−0.314228
$155$	−17.6090	−1.41439
$156$	−1.89173	−0.151459
$157$	14.8149	1.18236	0.591179	−	0.806541i	$-0.298663\pi$
$157$	14.8149	1.18236	0.591179	+	0.806541i	$0.298663\pi$
$158$	−9.55404	−0.760078
$159$	2.41575	0.191582
$160$	3.16777	0.250434
$161$	−1.07153	−0.0844482
$162$	1.00000	0.0785674
$163$	5.55618	0.435194	0.217597	−	0.976039i	$-0.430178\pi$
$163$	5.55618	0.435194	0.217597	+	0.976039i	$0.430178\pi$
$164$	−11.0791	−0.865132
$165$	11.5281	0.897458
$166$	−7.82283	−0.607169
$167$	−23.2409	−1.79843	−0.899216	−	0.437504i	$-0.855862\pi$
$167$	−23.2409	−1.79843	−0.899216	+	0.437504i	$0.855862\pi$
$168$	−1.07153	−0.0826702
$169$	−9.42137	−0.724721
$170$	11.1778	0.857299
$171$	8.15117	0.623335
$172$	−1.20998	−0.0922602
$173$	−24.7968	−1.88527	−0.942633	−	0.333830i	$-0.891659\pi$
$173$	−24.7968	−1.88527	−0.942633	+	0.333830i	$0.891659\pi$
$174$	−1.00000	−0.0758098
$175$	−5.39491	−0.407817
$176$	3.63917	0.274313
$177$	−10.2273	−0.768729
$178$	4.52717	0.339326
$179$	−0.695146	−0.0519577	−0.0259788	−	0.999662i	$-0.508270\pi$
$179$	−0.695146	−0.0519577	−0.0259788	+	0.999662i	$0.508270\pi$
$180$	3.16777	0.236112
$181$	−9.07573	−0.674594	−0.337297	−	0.941398i	$-0.609513\pi$
$181$	−9.07573	−0.674594	−0.337297	+	0.941398i	$0.609513\pi$
$182$	2.02704	0.150254
$183$	4.69638	0.347166
$184$	1.00000	0.0737210
$185$	−18.6301	−1.36972
$186$	−5.55878	−0.407590
$187$	12.8412	0.939040
$188$	−9.27673	−0.676575
$189$	−1.07153	−0.0779422
$190$	25.8210	1.87326
$191$	14.9984	1.08525	0.542624	−	0.839976i	$-0.317431\pi$
$191$	14.9984	1.08525	0.542624	+	0.839976i	$0.317431\pi$
$192$	1.00000	0.0721688
$193$	19.8398	1.42810	0.714048	−	0.700096i	$-0.246860\pi$
$193$	19.8398	1.42810	0.714048	+	0.700096i	$0.246860\pi$
$194$	11.0616	0.794179
$195$	−5.99256	−0.429136
$196$	−5.85183	−0.417988
$197$	15.2303	1.08511	0.542556	−	0.840019i	$-0.317456\pi$
$197$	15.2303	1.08511	0.542556	+	0.840019i	$0.317456\pi$
$198$	3.63917	0.258625
$199$	−14.5545	−1.03174	−0.515872	−	0.856666i	$-0.672532\pi$
$199$	−14.5545	−1.03174	−0.515872	+	0.856666i	$0.672532\pi$
$200$	5.03478	0.356013
$201$	2.61568	0.184496
$202$	−0.883955	−0.0621949
$203$	1.07153	0.0752065
$204$	3.52860	0.247052
$205$	−35.0961	−2.45122
$206$	10.7757	0.750776
$207$	1.00000	0.0695048
$208$	−1.89173	−0.131168
$209$	29.6635	2.05187
$210$	−3.39436	−0.234233
$211$	−17.4823	−1.20353	−0.601766	−	0.798672i	$-0.705536\pi$
$211$	−17.4823	−1.20353	−0.601766	+	0.798672i	$0.705536\pi$
$212$	2.41575	0.165915
$213$	10.7436	0.736136
$214$	9.79579	0.669626
$215$	−3.83294	−0.261405
$216$	1.00000	0.0680414
$217$	5.95639	0.404346
$218$	14.0648	0.952589
$219$	3.30079	0.223047
$220$	11.5281	0.777222
$221$	−6.67515	−0.449019
$222$	−5.88115	−0.394717
$223$	−19.1068	−1.27949	−0.639743	−	0.768589i	$-0.720959\pi$
$223$	−19.1068	−1.27949	−0.639743	+	0.768589i	$0.720959\pi$
$224$	−1.07153	−0.0715945
$225$	5.03478	0.335652
$226$	−4.10773	−0.273242
$227$	−14.2428	−0.945327	−0.472664	−	0.881243i	$-0.656707\pi$
$227$	−14.2428	−0.945327	−0.472664	+	0.881243i	$0.656707\pi$
$228$	8.15117	0.539824
$229$	−1.19395	−0.0788981	−0.0394491	−	0.999222i	$-0.512560\pi$
$229$	−1.19395	−0.0788981	−0.0394491	+	0.999222i	$0.512560\pi$
$230$	3.16777	0.208877
$231$	−3.89947	−0.256566
$232$	−1.00000	−0.0656532
$233$	−11.9798	−0.784824	−0.392412	−	0.919789i	$-0.628359\pi$
$233$	−11.9798	−0.784824	−0.392412	+	0.919789i	$0.628359\pi$
$234$	−1.89173	−0.123666
$235$	−29.3866	−1.91697
$236$	−10.2273	−0.665739
$237$	−9.55404	−0.620601
$238$	−3.78100	−0.245086
$239$	16.3276	1.05614	0.528071	−	0.849200i	$-0.322915\pi$
$239$	16.3276	1.05614	0.528071	+	0.849200i	$0.322915\pi$
$240$	3.16777	0.204479
$241$	2.46784	0.158968	0.0794839	−	0.996836i	$-0.474673\pi$
$241$	2.46784	0.158968	0.0794839	+	0.996836i	$0.474673\pi$
$242$	2.24356	0.144221
$243$	1.00000	0.0641500
$244$	4.69638	0.300655
$245$	−18.5373	−1.18430
$246$	−11.0791	−0.706378
$247$	−15.4198	−0.981138
$248$	−5.55878	−0.352983
$249$	−7.82283	−0.495752
$250$	0.110185	0.00696871
$251$	18.2409	1.15135	0.575677	−	0.817678i	$-0.304739\pi$
$251$	18.2409	1.15135	0.575677	+	0.817678i	$0.304739\pi$
$252$	−1.07153	−0.0674999
$253$	3.63917	0.228793
$254$	−0.750106	−0.0470658
$255$	11.1778	0.699982
$256$	1.00000	0.0625000
$257$	19.8663	1.23922	0.619612	−	0.784908i	$-0.287290\pi$
$257$	19.8663	1.23922	0.619612	+	0.784908i	$0.287290\pi$
$258$	−1.20998	−0.0753301
$259$	6.30181	0.391576
$260$	−5.99256	−0.371643
$261$	−1.00000	−0.0618984
$262$	1.49068	0.0920944
$263$	−26.0757	−1.60790	−0.803948	−	0.594700i	$-0.797271\pi$
$263$	−26.0757	−1.60790	−0.803948	+	0.594700i	$0.797271\pi$
$264$	3.63917	0.223975
$265$	7.65256	0.470093
$266$	−8.73421	−0.535528
$267$	4.52717	0.277058
$268$	2.61568	0.159778
$269$	0.398448	0.0242938	0.0121469	−	0.999926i	$-0.496133\pi$
$269$	0.398448	0.0242938	0.0121469	+	0.999926i	$0.496133\pi$
$270$	3.16777	0.192784
$271$	−4.35025	−0.264259	−0.132129	−	0.991232i	$-0.542181\pi$
$271$	−4.35025	−0.264259	−0.132129	+	0.991232i	$0.542181\pi$
$272$	3.52860	0.213953
$273$	2.02704	0.122682
$274$	10.5438	0.636975
$275$	18.3224	1.10488
$276$	1.00000	0.0601929
$277$	1.72467	0.103625	0.0518127	−	0.998657i	$-0.483500\pi$
$277$	1.72467	0.103625	0.0518127	+	0.998657i	$0.483500\pi$
$278$	11.9307	0.715557
$279$	−5.55878	−0.332796
$280$	−3.39436	−0.202852
$281$	0.250945	0.0149701	0.00748506	−	0.999972i	$-0.497617\pi$
$281$	0.250945	0.0149701	0.00748506	+	0.999972i	$0.497617\pi$
$282$	−9.27673	−0.552421
$283$	22.5636	1.34126	0.670632	−	0.741790i	$-0.266023\pi$
$283$	22.5636	1.34126	0.670632	+	0.741790i	$0.266023\pi$
$284$	10.7436	0.637513
$285$	25.8210	1.52951
$286$	−6.88432	−0.407078
$287$	11.8716	0.700756
$288$	1.00000	0.0589256
$289$	−4.54896	−0.267586
$290$	−3.16777	−0.186018
$291$	11.0616	0.648445
$292$	3.30079	0.193164
$293$	−5.09098	−0.297418	−0.148709	−	0.988881i	$-0.547512\pi$
$293$	−5.09098	−0.297418	−0.148709	+	0.988881i	$0.547512\pi$
$294$	−5.85183	−0.341286
$295$	−32.3977	−1.88627
$296$	−5.88115	−0.341835
$297$	3.63917	0.211166
$298$	−5.46713	−0.316702
$299$	−1.89173	−0.109401
$300$	5.03478	0.290683
$301$	1.29653	0.0747306
$302$	−4.28611	−0.246638
$303$	−0.883955	−0.0507819
$304$	8.15117	0.467502
$305$	14.8770	0.851857
$306$	3.52860	0.201717
$307$	−8.49325	−0.484735	−0.242368	−	0.970184i	$-0.577924\pi$
$307$	−8.49325	−0.484735	−0.242368	+	0.970184i	$0.577924\pi$
$308$	−3.89947	−0.222193
$309$	10.7757	0.613006
$310$	−17.6090	−1.00012
$311$	−23.0400	−1.30648	−0.653240	−	0.757151i	$-0.726591\pi$
$311$	−23.0400	−1.30648	−0.653240	+	0.757151i	$0.726591\pi$
$312$	−1.89173	−0.107098
$313$	26.6122	1.50421	0.752106	−	0.659042i	$-0.229038\pi$
$313$	26.6122	1.50421	0.752106	+	0.659042i	$0.229038\pi$
$314$	14.8149	0.836053
$315$	−3.39436	−0.191250
$316$	−9.55404	−0.537456
$317$	7.31848	0.411047	0.205523	−	0.978652i	$-0.434110\pi$
$317$	7.31848	0.411047	0.205523	+	0.978652i	$0.434110\pi$
$318$	2.41575	0.135469
$319$	−3.63917	−0.203754
$320$	3.16777	0.177084
$321$	9.79579	0.546748
$322$	−1.07153	−0.0597139
$323$	28.7622	1.60037
$324$	1.00000	0.0555556
$325$	−9.52444	−0.528321
$326$	5.55618	0.307728
$327$	14.0648	0.777786
$328$	−11.0791	−0.611741
$329$	9.94028	0.548025
$330$	11.5281	0.634599
$331$	−30.4754	−1.67508	−0.837540	−	0.546376i	$-0.816007\pi$
$331$	−30.4754	−1.67508	−0.837540	+	0.546376i	$0.816007\pi$
$332$	−7.82283	−0.429333
$333$	−5.88115	−0.322285
$334$	−23.2409	−1.27168
$335$	8.28589	0.452706
$336$	−1.07153	−0.0584566
$337$	−8.52456	−0.464362	−0.232181	−	0.972673i	$-0.574586\pi$
$337$	−8.52456	−0.464362	−0.232181	+	0.972673i	$0.574586\pi$
$338$	−9.42137	−0.512455
$339$	−4.10773	−0.223101
$340$	11.1778	0.606202
$341$	−20.2294	−1.09548
$342$	8.15117	0.440765
$343$	13.7711	0.743569
$344$	−1.20998	−0.0652378
$345$	3.16777	0.170547
$346$	−24.7968	−1.33308
$347$	−21.9325	−1.17740	−0.588699	−	0.808353i	$-0.700359\pi$
$347$	−21.9325	−1.17740	−0.588699	+	0.808353i	$0.700359\pi$
$348$	−1.00000	−0.0536056
$349$	−32.9163	−1.76197	−0.880983	−	0.473147i	$-0.843118\pi$
$349$	−32.9163	−1.76197	−0.880983	+	0.473147i	$0.843118\pi$
$350$	−5.39491	−0.288370
$351$	−1.89173	−0.100973
$352$	3.63917	0.193968
$353$	27.4399	1.46048	0.730239	−	0.683192i	$-0.239409\pi$
$353$	27.4399	1.46048	0.730239	+	0.683192i	$0.239409\pi$
$354$	−10.2273	−0.543573
$355$	34.0331	1.80629
$356$	4.52717	0.239939
$357$	−3.78100	−0.200112
$358$	−0.695146	−0.0367396
$359$	27.2519	1.43830	0.719150	−	0.694855i	$-0.244531\pi$
$359$	27.2519	1.43830	0.719150	+	0.694855i	$0.244531\pi$
$360$	3.16777	0.166956
$361$	47.4416	2.49692
$362$	−9.07573	−0.477010
$363$	2.24356	0.117756
$364$	2.02704	0.106246
$365$	10.4562	0.547300
$366$	4.69638	0.245483
$367$	−25.0428	−1.30722	−0.653611	−	0.756831i	$-0.726747\pi$
$367$	−25.0428	−1.30722	−0.653611	+	0.756831i	$0.726747\pi$
$368$	1.00000	0.0521286
$369$	−11.0791	−0.576755
$370$	−18.6301	−0.968535
$371$	−2.58855	−0.134391
$372$	−5.55878	−0.288209
$373$	−27.9579	−1.44761	−0.723804	−	0.690006i	$-0.757608\pi$
$373$	−27.9579	−1.44761	−0.723804	+	0.690006i	$0.757608\pi$
$374$	12.8412	0.664002
$375$	0.110185	0.00568993
$376$	−9.27673	−0.478411
$377$	1.89173	0.0974289
$378$	−1.07153	−0.0551134
$379$	−31.5955	−1.62295	−0.811475	−	0.584386i	$-0.801335\pi$
$379$	−31.5955	−1.62295	−0.811475	+	0.584386i	$0.801335\pi$
$380$	25.8210	1.32459
$381$	−0.750106	−0.0384291
$382$	14.9984	0.767386
$383$	−10.1269	−0.517463	−0.258731	−	0.965949i	$-0.583304\pi$
$383$	−10.1269	−0.517463	−0.258731	+	0.965949i	$0.583304\pi$
$384$	1.00000	0.0510310
$385$	−12.3526	−0.629549
$386$	19.8398	1.00982
$387$	−1.20998	−0.0615068
$388$	11.0616	0.561570
$389$	29.5884	1.50019	0.750097	−	0.661328i	$-0.230007\pi$
$389$	29.5884	1.50019	0.750097	+	0.661328i	$0.230007\pi$
$390$	−5.99256	−0.303445
$391$	3.52860	0.178449
$392$	−5.85183	−0.295562
$393$	1.49068	0.0751948
$394$	15.2303	0.767291
$395$	−30.2650	−1.52280
$396$	3.63917	0.182875
$397$	12.9248	0.648675	0.324338	−	0.945941i	$-0.394859\pi$
$397$	12.9248	0.648675	0.324338	+	0.945941i	$0.394859\pi$
$398$	−14.5545	−0.729553
$399$	−8.73421	−0.437257
$400$	5.03478	0.251739
$401$	−31.5711	−1.57659	−0.788293	−	0.615300i	$-0.789035\pi$
$401$	−31.5711	−1.57659	−0.788293	+	0.615300i	$0.789035\pi$
$402$	2.61568	0.130458
$403$	10.5157	0.523824
$404$	−0.883955	−0.0439784
$405$	3.16777	0.157408
$406$	1.07153	0.0531790
$407$	−21.4025	−1.06088
$408$	3.52860	0.174692
$409$	15.0390	0.743632	0.371816	−	0.928306i	$-0.378735\pi$
$409$	15.0390	0.743632	0.371816	+	0.928306i	$0.378735\pi$
$410$	−35.0961	−1.73327
$411$	10.5438	0.520088
$412$	10.7757	0.530879
$413$	10.9588	0.539248
$414$	1.00000	0.0491473
$415$	−24.7809	−1.21645
$416$	−1.89173	−0.0927496
$417$	11.9307	0.584250
$418$	29.6635	1.45089
$419$	17.7260	0.865974	0.432987	−	0.901400i	$-0.357460\pi$
$419$	17.7260	0.865974	0.432987	+	0.901400i	$0.357460\pi$
$420$	−3.39436	−0.165628
$421$	−4.01734	−0.195793	−0.0978966	−	0.995197i	$-0.531211\pi$
$421$	−4.01734	−0.195793	−0.0978966	+	0.995197i	$0.531211\pi$
$422$	−17.4823	−0.851026
$423$	−9.27673	−0.451050
$424$	2.41575	0.117319
$425$	17.7657	0.861765
$426$	10.7436	0.520527
$427$	−5.03230	−0.243530
$428$	9.79579	0.473497
$429$	−6.88432	−0.332378
$430$	−3.83294	−0.184841
$431$	−12.2481	−0.589971	−0.294986	−	0.955502i	$-0.595315\pi$
$431$	−12.2481	−0.589971	−0.294986	+	0.955502i	$0.595315\pi$
$432$	1.00000	0.0481125
$433$	−0.285954	−0.0137421	−0.00687104	−	0.999976i	$-0.502187\pi$
$433$	−0.285954	−0.0137421	−0.00687104	+	0.999976i	$0.502187\pi$
$434$	5.95639	0.285916
$435$	−3.16777	−0.151883
$436$	14.0648	0.673582
$437$	8.15117	0.389923
$438$	3.30079	0.157718
$439$	−24.8470	−1.18588	−0.592941	−	0.805246i	$-0.702033\pi$
$439$	−24.8470	−1.18588	−0.592941	+	0.805246i	$0.702033\pi$
$440$	11.5281	0.549579
$441$	−5.85183	−0.278658
$442$	−6.67515	−0.317505
$443$	−15.0536	−0.715220	−0.357610	−	0.933871i	$-0.616408\pi$
$443$	−15.0536	−0.715220	−0.357610	+	0.933871i	$0.616408\pi$
$444$	−5.88115	−0.279107
$445$	14.3410	0.679831
$446$	−19.1068	−0.904734
$447$	−5.46713	−0.258586
$448$	−1.07153	−0.0506249
$449$	−22.9321	−1.08223	−0.541117	−	0.840947i	$-0.681998\pi$
$449$	−22.9321	−1.08223	−0.541117	+	0.840947i	$0.681998\pi$
$450$	5.03478	0.237342
$451$	−40.3187	−1.89853
$452$	−4.10773	−0.193211
$453$	−4.28611	−0.201379
$454$	−14.2428	−0.668447
$455$	6.42120	0.301030
$456$	8.15117	0.381713
$457$	−13.3140	−0.622804	−0.311402	−	0.950278i	$-0.600799\pi$
$457$	−13.3140	−0.622804	−0.311402	+	0.950278i	$0.600799\pi$
$458$	−1.19395	−0.0557894
$459$	3.52860	0.164701
$460$	3.16777	0.147698
$461$	−3.59065	−0.167233	−0.0836166	−	0.996498i	$-0.526647\pi$
$461$	−3.59065	−0.167233	−0.0836166	+	0.996498i	$0.526647\pi$
$462$	−3.89947	−0.181420
$463$	27.5059	1.27831	0.639155	−	0.769078i	$-0.279284\pi$
$463$	27.5059	1.27831	0.639155	+	0.769078i	$0.279284\pi$
$464$	−1.00000	−0.0464238
$465$	−17.6090	−0.816596
$466$	−11.9798	−0.554955
$467$	−21.5269	−0.996146	−0.498073	−	0.867135i	$-0.665959\pi$
$467$	−21.5269	−0.996146	−0.498073	+	0.867135i	$0.665959\pi$
$468$	−1.89173	−0.0874451
$469$	−2.80278	−0.129420
$470$	−29.3866	−1.35550
$471$	14.8149	0.682634
$472$	−10.2273	−0.470748
$473$	−4.40332	−0.202465
$474$	−9.55404	−0.438831
$475$	41.0394	1.88302
$476$	−3.78100	−0.173302
$477$	2.41575	0.110610
$478$	16.3276	0.746805
$479$	−1.86011	−0.0849904	−0.0424952	−	0.999097i	$-0.513531\pi$
$479$	−1.86011	−0.0849904	−0.0424952	+	0.999097i	$0.513531\pi$
$480$	3.16777	0.144588
$481$	11.1255	0.507280
$482$	2.46784	0.112407
$483$	−1.07153	−0.0487562
$484$	2.24356	0.101980
$485$	35.0407	1.59112
$486$	1.00000	0.0453609
$487$	−19.9103	−0.902224	−0.451112	−	0.892467i	$-0.648972\pi$
$487$	−19.9103	−0.902224	−0.451112	+	0.892467i	$0.648972\pi$
$488$	4.69638	0.212595
$489$	5.55618	0.251259
$490$	−18.5373	−0.837428
$491$	9.42708	0.425438	0.212719	−	0.977113i	$-0.431768\pi$
$491$	9.42708	0.425438	0.212719	+	0.977113i	$0.431768\pi$
$492$	−11.0791	−0.499484
$493$	−3.52860	−0.158920
$494$	−15.4198	−0.693769
$495$	11.5281	0.518148
$496$	−5.55878	−0.249597
$497$	−11.5120	−0.516385
$498$	−7.82283	−0.350549
$499$	8.44564	0.378079	0.189039	−	0.981970i	$-0.439463\pi$
$499$	8.44564	0.378079	0.189039	+	0.981970i	$0.439463\pi$
$500$	0.110185	0.00492762
$501$	−23.2409	−1.03833
$502$	18.2409	0.814130
$503$	40.5016	1.80588	0.902939	−	0.429769i	$-0.141405\pi$
$503$	40.5016	1.80588	0.902939	+	0.429769i	$0.141405\pi$
$504$	−1.07153	−0.0477296
$505$	−2.80017	−0.124606
$506$	3.63917	0.161781
$507$	−9.42137	−0.418418
$508$	−0.750106	−0.0332806
$509$	−1.86022	−0.0824529	−0.0412265	−	0.999150i	$-0.513127\pi$
$509$	−1.86022	−0.0824529	−0.0412265	+	0.999150i	$0.513127\pi$
$510$	11.1778	0.494962
$511$	−3.53689	−0.156463
$512$	1.00000	0.0441942
$513$	8.15117	0.359883
$514$	19.8663	0.876263
$515$	34.1348	1.50416
$516$	−1.20998	−0.0532664
$517$	−33.7596	−1.48475
$518$	6.30181	0.276886
$519$	−24.7968	−1.08846
$520$	−5.99256	−0.262791
$521$	15.1016	0.661612	0.330806	−	0.943699i	$-0.392679\pi$
$521$	15.1016	0.661612	0.330806	+	0.943699i	$0.392679\pi$
$522$	−1.00000	−0.0437688
$523$	−21.0381	−0.919934	−0.459967	−	0.887936i	$-0.652139\pi$
$523$	−21.0381	−0.919934	−0.459967	+	0.887936i	$0.652139\pi$
$524$	1.49068	0.0651206
$525$	−5.39491	−0.235453
$526$	−26.0757	−1.13695
$527$	−19.6147	−0.854431
$528$	3.63917	0.158375
$529$	1.00000	0.0434783
$530$	7.65256	0.332406
$531$	−10.2273	−0.443826
$532$	−8.73421	−0.378676
$533$	20.9586	0.907819
$534$	4.52717	0.195910
$535$	31.0308	1.34158
$536$	2.61568	0.112980
$537$	−0.695146	−0.0299978
$538$	0.398448	0.0171783
$539$	−21.2958	−0.917275
$540$	3.16777	0.136319
$541$	−9.36077	−0.402451	−0.201225	−	0.979545i	$-0.564492\pi$
$541$	−9.36077	−0.402451	−0.201225	+	0.979545i	$0.564492\pi$
$542$	−4.35025	−0.186859
$543$	−9.07573	−0.389477
$544$	3.52860	0.151288
$545$	44.5541	1.90849
$546$	2.02704	0.0867492
$547$	33.7317	1.44226	0.721131	−	0.692798i	$-0.243622\pi$
$547$	33.7317	1.44226	0.721131	+	0.692798i	$0.243622\pi$
$548$	10.5438	0.450409
$549$	4.69638	0.200436
$550$	18.3224	0.781271
$551$	−8.15117	−0.347251
$552$	1.00000	0.0425628
$553$	10.2374	0.435339
$554$	1.72467	0.0732742
$555$	−18.6301	−0.790805
$556$	11.9307	0.505975
$557$	40.1959	1.70316	0.851578	−	0.524228i	$-0.175646\pi$
$557$	40.1959	1.70316	0.851578	+	0.524228i	$0.175646\pi$
$558$	−5.55878	−0.235322
$559$	2.28895	0.0968124
$560$	−3.39436	−0.143438
$561$	12.8412	0.542155
$562$	0.250945	0.0105855
$563$	−31.6951	−1.33579	−0.667895	−	0.744255i	$-0.732805\pi$
$563$	−31.6951	−1.33579	−0.667895	+	0.744255i	$0.732805\pi$
$564$	−9.27673	−0.390621
$565$	−13.0124	−0.547434
$566$	22.5636	0.948417
$567$	−1.07153	−0.0449999
$568$	10.7436	0.450790
$569$	3.53150	0.148048	0.0740241	−	0.997256i	$-0.476416\pi$
$569$	3.53150	0.148048	0.0740241	+	0.997256i	$0.476416\pi$
$570$	25.8210	1.08152
$571$	−25.5164	−1.06783	−0.533914	−	0.845539i	$-0.679279\pi$
$571$	−25.5164	−1.06783	−0.533914	+	0.845539i	$0.679279\pi$
$572$	−6.88432	−0.287848
$573$	14.9984	0.626568
$574$	11.8716	0.495510
$575$	5.03478	0.209965
$576$	1.00000	0.0416667
$577$	39.5095	1.64480	0.822400	−	0.568909i	$-0.192634\pi$
$577$	39.5095	1.64480	0.822400	+	0.568909i	$0.192634\pi$
$578$	−4.54896	−0.189212
$579$	19.8398	0.824512
$580$	−3.16777	−0.131535
$581$	8.38238	0.347760
$582$	11.0616	0.458520
$583$	8.79134	0.364100
$584$	3.30079	0.136588
$585$	−5.99256	−0.247762
$586$	−5.09098	−0.210306
$587$	24.6968	1.01935	0.509674	−	0.860368i	$-0.329766\pi$
$587$	24.6968	1.01935	0.509674	+	0.860368i	$0.329766\pi$
$588$	−5.85183	−0.241325
$589$	−45.3106	−1.86699
$590$	−32.3977	−1.33379
$591$	15.2303	0.626490
$592$	−5.88115	−0.241714
$593$	22.2000	0.911644	0.455822	−	0.890071i	$-0.349345\pi$
$593$	22.2000	0.911644	0.455822	+	0.890071i	$0.349345\pi$
$594$	3.63917	0.149317
$595$	−11.9773	−0.491023
$596$	−5.46713	−0.223942
$597$	−14.5545	−0.595677
$598$	−1.89173	−0.0773585
$599$	−34.9132	−1.42652	−0.713258	−	0.700901i	$-0.752781\pi$
$599$	−34.9132	−1.42652	−0.713258	+	0.700901i	$0.752781\pi$
$600$	5.03478	0.205544
$601$	41.6504	1.69896	0.849478	−	0.527625i	$-0.176917\pi$
$601$	41.6504	1.69896	0.849478	+	0.527625i	$0.176917\pi$
$602$	1.29653	0.0528425
$603$	2.61568	0.106519
$604$	−4.28611	−0.174399
$605$	7.10708	0.288944
$606$	−0.883955	−0.0359082
$607$	4.34923	0.176530	0.0882648	−	0.996097i	$-0.471868\pi$
$607$	4.34923	0.176530	0.0882648	+	0.996097i	$0.471868\pi$
$608$	8.15117	0.330574
$609$	1.07153	0.0434205
$610$	14.8770	0.602354
$611$	17.5491	0.709959
$612$	3.52860	0.142635
$613$	−5.65613	−0.228449	−0.114224	−	0.993455i	$-0.536438\pi$
$613$	−5.65613	−0.228449	−0.114224	+	0.993455i	$0.536438\pi$
$614$	−8.49325	−0.342760
$615$	−35.0961	−1.41521
$616$	−3.89947	−0.157114
$617$	20.7340	0.834721	0.417361	−	0.908741i	$-0.362955\pi$
$617$	20.7340	0.834721	0.417361	+	0.908741i	$0.362955\pi$
$618$	10.7757	0.433461
$619$	−29.8216	−1.19863	−0.599315	−	0.800513i	$-0.704560\pi$
$619$	−29.8216	−1.19863	−0.599315	+	0.800513i	$0.704560\pi$
$620$	−17.6090	−0.707193
$621$	1.00000	0.0401286
$622$	−23.0400	−0.923820
$623$	−4.85099	−0.194351
$624$	−1.89173	−0.0757297
$625$	−24.8249	−0.992995
$626$	26.6122	1.06364
$627$	29.6635	1.18465
$628$	14.8149	0.591179
$629$	−20.7522	−0.827446
$630$	−3.39436	−0.135234
$631$	−26.5511	−1.05698	−0.528492	−	0.848938i	$-0.677242\pi$
$631$	−26.5511	−1.05698	−0.528492	+	0.848938i	$0.677242\pi$
$632$	−9.55404	−0.380039
$633$	−17.4823	−0.694860
$634$	7.31848	0.290654
$635$	−2.37616	−0.0942952
$636$	2.41575	0.0957909
$637$	11.0701	0.438612
$638$	−3.63917	−0.144076
$639$	10.7436	0.425008
$640$	3.16777	0.125217
$641$	20.2531	0.799951	0.399976	−	0.916526i	$-0.369019\pi$
$641$	20.2531	0.799951	0.399976	+	0.916526i	$0.369019\pi$
$642$	9.79579	0.386609
$643$	16.8565	0.664757	0.332378	−	0.943146i	$-0.392149\pi$
$643$	16.8565	0.664757	0.332378	+	0.943146i	$0.392149\pi$
$644$	−1.07153	−0.0422241
$645$	−3.83294	−0.150922
$646$	28.7622	1.13164
$647$	−22.1899	−0.872373	−0.436187	−	0.899856i	$-0.643671\pi$
$647$	−22.1899	−0.872373	−0.436187	+	0.899856i	$0.643671\pi$
$648$	1.00000	0.0392837
$649$	−37.2188	−1.46096
$650$	−9.52444	−0.373579
$651$	5.95639	0.233449
$652$	5.55618	0.217597
$653$	20.0844	0.785963	0.392981	−	0.919546i	$-0.371444\pi$
$653$	20.0844	0.785963	0.392981	+	0.919546i	$0.371444\pi$
$654$	14.0648	0.549977
$655$	4.72213	0.184509
$656$	−11.0791	−0.432566
$657$	3.30079	0.128776
$658$	9.94028	0.387512
$659$	15.4246	0.600857	0.300429	−	0.953804i	$-0.402870\pi$
$659$	15.4246	0.600857	0.300429	+	0.953804i	$0.402870\pi$
$660$	11.5281	0.448729
$661$	−37.8069	−1.47052	−0.735258	−	0.677787i	$-0.762939\pi$
$661$	−37.8069	−1.47052	−0.735258	+	0.677787i	$0.762939\pi$
$662$	−30.4754	−1.18446
$663$	−6.67515	−0.259242
$664$	−7.82283	−0.303585
$665$	−27.6680	−1.07292
$666$	−5.88115	−0.227890
$667$	−1.00000	−0.0387202
$668$	−23.2409	−0.899216
$669$	−19.1068	−0.738712
$670$	8.28589	0.320112
$671$	17.0909	0.659787
$672$	−1.07153	−0.0413351
$673$	27.2091	1.04883	0.524417	−	0.851461i	$-0.324283\pi$
$673$	27.2091	1.04883	0.524417	+	0.851461i	$0.324283\pi$
$674$	−8.52456	−0.328354
$675$	5.03478	0.193789
$676$	−9.42137	−0.362360
$677$	28.8747	1.10975	0.554873	−	0.831935i	$-0.312767\pi$
$677$	28.8747	1.10975	0.554873	+	0.831935i	$0.312767\pi$
$678$	−4.10773	−0.157756
$679$	−11.8529	−0.454871
$680$	11.1778	0.428649
$681$	−14.2428	−0.545785
$682$	−20.2294	−0.774622
$683$	−9.91183	−0.379266	−0.189633	−	0.981855i	$-0.560730\pi$
$683$	−9.91183	−0.379266	−0.189633	+	0.981855i	$0.560730\pi$
$684$	8.15117	0.311668
$685$	33.4004	1.27616
$686$	13.7711	0.525783
$687$	−1.19395	−0.0455519
$688$	−1.20998	−0.0461301
$689$	−4.56995	−0.174101
$690$	3.16777	0.120595
$691$	−12.7848	−0.486358	−0.243179	−	0.969981i	$-0.578190\pi$
$691$	−12.7848	−0.486358	−0.243179	+	0.969981i	$0.578190\pi$
$692$	−24.7968	−0.942633
$693$	−3.89947	−0.148129
$694$	−21.9325	−0.832546
$695$	37.7938	1.43360
$696$	−1.00000	−0.0379049
$697$	−39.0937	−1.48078
$698$	−32.9163	−1.24590
$699$	−11.9798	−0.453119
$700$	−5.39491	−0.203908
$701$	13.8449	0.522915	0.261457	−	0.965215i	$-0.415797\pi$
$701$	13.8449	0.522915	0.261457	+	0.965215i	$0.415797\pi$
$702$	−1.89173	−0.0713986
$703$	−47.9382	−1.80802
$704$	3.63917	0.137156
$705$	−29.3866	−1.10676
$706$	27.4399	1.03271
$707$	0.947183	0.0356225
$708$	−10.2273	−0.384364
$709$	2.41468	0.0906851	0.0453425	−	0.998971i	$-0.485562\pi$
$709$	2.41468	0.0906851	0.0453425	+	0.998971i	$0.485562\pi$
$710$	34.0331	1.27724
$711$	−9.55404	−0.358304
$712$	4.52717	0.169663
$713$	−5.55878	−0.208178
$714$	−3.78100	−0.141500
$715$	−21.8080	−0.815571
$716$	−0.695146	−0.0259788
$717$	16.3276	0.609764
$718$	27.2519	1.01703
$719$	−16.2152	−0.604726	−0.302363	−	0.953193i	$-0.597775\pi$
$719$	−16.2152	−0.604726	−0.302363	+	0.953193i	$0.597775\pi$
$720$	3.16777	0.118056
$721$	−11.5464	−0.430011
$722$	47.4416	1.76559
$723$	2.46784	0.0917801
$724$	−9.07573	−0.337297
$725$	−5.03478	−0.186987
$726$	2.24356	0.0832662
$727$	−21.9576	−0.814361	−0.407181	−	0.913348i	$-0.633488\pi$
$727$	−21.9576	−0.814361	−0.407181	+	0.913348i	$0.633488\pi$
$728$	2.02704	0.0751270
$729$	1.00000	0.0370370
$730$	10.4562	0.387000
$731$	−4.26954	−0.157915
$732$	4.69638	0.173583
$733$	−2.38615	−0.0881344	−0.0440672	−	0.999029i	$-0.514032\pi$
$733$	−2.38615	−0.0881344	−0.0440672	+	0.999029i	$0.514032\pi$
$734$	−25.0428	−0.924345
$735$	−18.5373	−0.683757
$736$	1.00000	0.0368605
$737$	9.51891	0.350634
$738$	−11.0791	−0.407827
$739$	16.3076	0.599886	0.299943	−	0.953957i	$-0.403032\pi$
$739$	16.3076	0.599886	0.299943	+	0.953957i	$0.403032\pi$
$740$	−18.6301	−0.684858
$741$	−15.4198	−0.566460
$742$	−2.58855	−0.0950286
$743$	0.815049	0.0299012	0.0149506	−	0.999888i	$-0.495241\pi$
$743$	0.815049	0.0299012	0.0149506	+	0.999888i	$0.495241\pi$
$744$	−5.55878	−0.203795
$745$	−17.3186	−0.634505
$746$	−27.9579	−1.02361
$747$	−7.82283	−0.286222
$748$	12.8412	0.469520
$749$	−10.4965	−0.383532
$750$	0.110185	0.00402339
$751$	14.1584	0.516648	0.258324	−	0.966058i	$-0.416830\pi$
$751$	14.1584	0.516648	0.258324	+	0.966058i	$0.416830\pi$
$752$	−9.27673	−0.338288
$753$	18.2409	0.664734
$754$	1.89173	0.0688926
$755$	−13.5774	−0.494133
$756$	−1.07153	−0.0389711
$757$	−8.42896	−0.306356	−0.153178	−	0.988199i	$-0.548951\pi$
$757$	−8.42896	−0.306356	−0.153178	+	0.988199i	$0.548951\pi$
$758$	−31.5955	−1.14760
$759$	3.63917	0.132093
$760$	25.8210	0.936628
$761$	−3.91794	−0.142025	−0.0710127	−	0.997475i	$-0.522623\pi$
$761$	−3.91794	−0.142025	−0.0710127	+	0.997475i	$0.522623\pi$
$762$	−0.750106	−0.0271735
$763$	−15.0708	−0.545601
$764$	14.9984	0.542624
$765$	11.1778	0.404135
$766$	−10.1269	−0.365901
$767$	19.3472	0.698587
$768$	1.00000	0.0360844
$769$	−1.56115	−0.0562965	−0.0281482	−	0.999604i	$-0.508961\pi$
$769$	−1.56115	−0.0562965	−0.0281482	+	0.999604i	$0.508961\pi$
$770$	−12.3526	−0.445158
$771$	19.8663	0.715466
$772$	19.8398	0.714048
$773$	26.8568	0.965970	0.482985	−	0.875629i	$-0.339553\pi$
$773$	26.8568	0.965970	0.482985	+	0.875629i	$0.339553\pi$
$774$	−1.20998	−0.0434919
$775$	−27.9873	−1.00533
$776$	11.0616	0.397090
$777$	6.30181	0.226076
$778$	29.5884	1.06080
$779$	−90.3076	−3.23561
$780$	−5.99256	−0.214568
$781$	39.0976	1.39902
$782$	3.52860	0.126183
$783$	−1.00000	−0.0357371
$784$	−5.85183	−0.208994
$785$	46.9302	1.67501
$786$	1.49068	0.0531707
$787$	−29.0265	−1.03468	−0.517341	−	0.855779i	$-0.673078\pi$
$787$	−29.0265	−1.03468	−0.517341	+	0.855779i	$0.673078\pi$
$788$	15.2303	0.542556
$789$	−26.0757	−0.928319
$790$	−30.2650	−1.07678
$791$	4.40155	0.156501
$792$	3.63917	0.129312
$793$	−8.88426	−0.315489
$794$	12.9248	0.458683
$795$	7.65256	0.271408
$796$	−14.5545	−0.515872
$797$	−11.2451	−0.398321	−0.199161	−	0.979967i	$-0.563822\pi$
$797$	−11.2451	−0.398321	−0.199161	+	0.979967i	$0.563822\pi$
$798$	−8.73421	−0.309188
$799$	−32.7339	−1.15804
$800$	5.03478	0.178006
$801$	4.52717	0.159960
$802$	−31.5711	−1.11481
$803$	12.0121	0.423899
$804$	2.61568	0.0922480
$805$	−3.39436	−0.119635
$806$	10.5157	0.370400
$807$	0.398448	0.0140260
$808$	−0.883955	−0.0310974
$809$	−44.1325	−1.55162	−0.775809	−	0.630968i	$-0.782658\pi$
$809$	−44.1325	−1.55162	−0.775809	+	0.630968i	$0.782658\pi$
$810$	3.16777	0.111304
$811$	28.7236	1.00862	0.504312	−	0.863522i	$-0.331746\pi$
$811$	28.7236	1.00862	0.504312	+	0.863522i	$0.331746\pi$
$812$	1.07153	0.0376033
$813$	−4.35025	−0.152570
$814$	−21.4025	−0.750157
$815$	17.6007	0.616526
$816$	3.52860	0.123526
$817$	−9.86276	−0.345054
$818$	15.0390	0.525827
$819$	2.02704	0.0708305
$820$	−35.0961	−1.22561
$821$	2.05790	0.0718213	0.0359107	−	0.999355i	$-0.488567\pi$
$821$	2.05790	0.0718213	0.0359107	+	0.999355i	$0.488567\pi$
$822$	10.5438	0.367757
$823$	45.8728	1.59902	0.799512	−	0.600650i	$-0.205091\pi$
$823$	45.8728	1.59902	0.799512	+	0.600650i	$0.205091\pi$
$824$	10.7757	0.375388
$825$	18.3224	0.637905
$826$	10.9588	0.381306
$827$	51.7492	1.79950	0.899748	−	0.436411i	$-0.143751\pi$
$827$	51.7492	1.79950	0.899748	+	0.436411i	$0.143751\pi$
$828$	1.00000	0.0347524
$829$	−22.4671	−0.780314	−0.390157	−	0.920748i	$-0.627579\pi$
$829$	−22.4671	−0.780314	−0.390157	+	0.920748i	$0.627579\pi$
$830$	−24.7809	−0.860159
$831$	1.72467	0.0598282
$832$	−1.89173	−0.0655838
$833$	−20.6488	−0.715438
$834$	11.9307	0.413127
$835$	−73.6218	−2.54779
$836$	29.6635	1.02593
$837$	−5.55878	−0.192140
$838$	17.7260	0.612336
$839$	−1.08313	−0.0373939	−0.0186969	−	0.999825i	$-0.505952\pi$
$839$	−1.08313	−0.0373939	−0.0186969	+	0.999825i	$0.505952\pi$
$840$	−3.39436	−0.117116
$841$	1.00000	0.0344828
$842$	−4.01734	−0.138447
$843$	0.250945	0.00864301
$844$	−17.4823	−0.601766
$845$	−29.8448	−1.02669
$846$	−9.27673	−0.318941
$847$	−2.40403	−0.0826036
$848$	2.41575	0.0829574
$849$	22.5636	0.774379
$850$	17.7657	0.609360
$851$	−5.88115	−0.201603
$852$	10.7436	0.368068
$853$	41.9878	1.43763	0.718817	−	0.695200i	$-0.244684\pi$
$853$	41.9878	1.43763	0.718817	+	0.695200i	$0.244684\pi$
$854$	−5.03230	−0.172202
$855$	25.8210	0.883061
$856$	9.79579	0.334813
$857$	−50.7063	−1.73209	−0.866047	−	0.499962i	$-0.833347\pi$
$857$	−50.7063	−1.73209	−0.866047	+	0.499962i	$0.833347\pi$
$858$	−6.88432	−0.235027
$859$	−52.9105	−1.80528	−0.902641	−	0.430394i	$-0.858374\pi$
$859$	−52.9105	−1.80528	−0.902641	+	0.430394i	$0.858374\pi$
$860$	−3.83294	−0.130702
$861$	11.8716	0.404582
$862$	−12.2481	−0.417173
$863$	−1.74546	−0.0594161	−0.0297081	−	0.999559i	$-0.509458\pi$
$863$	−1.74546	−0.0594161	−0.0297081	+	0.999559i	$0.509458\pi$
$864$	1.00000	0.0340207
$865$	−78.5507	−2.67080
$866$	−0.285954	−0.00971712
$867$	−4.54896	−0.154491
$868$	5.95639	0.202173
$869$	−34.7688	−1.17945
$870$	−3.16777	−0.107398
$871$	−4.94816	−0.167662
$872$	14.0648	0.476294
$873$	11.0616	0.374380
$874$	8.15117	0.275717
$875$	−0.118066	−0.00399137
$876$	3.30079	0.111523
$877$	−20.4708	−0.691251	−0.345625	−	0.938373i	$-0.612333\pi$
$877$	−20.4708	−0.691251	−0.345625	+	0.938373i	$0.612333\pi$
$878$	−24.8470	−0.838546
$879$	−5.09098	−0.171715
$880$	11.5281	0.388611
$881$	−36.0813	−1.21561	−0.607805	−	0.794086i	$-0.707950\pi$
$881$	−36.0813	−1.21561	−0.607805	+	0.794086i	$0.707950\pi$
$882$	−5.85183	−0.197041
$883$	2.45759	0.0827044	0.0413522	−	0.999145i	$-0.486833\pi$
$883$	2.45759	0.0827044	0.0413522	+	0.999145i	$0.486833\pi$
$884$	−6.67515	−0.224510
$885$	−32.3977	−1.08904
$886$	−15.0536	−0.505737
$887$	−10.1075	−0.339376	−0.169688	−	0.985498i	$-0.554276\pi$
$887$	−10.1075	−0.339376	−0.169688	+	0.985498i	$0.554276\pi$
$888$	−5.88115	−0.197358
$889$	0.803759	0.0269572
$890$	14.3410	0.480713
$891$	3.63917	0.121917
$892$	−19.1068	−0.639743
$893$	−75.6162	−2.53040
$894$	−5.46713	−0.182848
$895$	−2.20207	−0.0736069
$896$	−1.07153	−0.0357972
$897$	−1.89173	−0.0631629
$898$	−22.9321	−0.765255
$899$	5.55878	0.185396
$900$	5.03478	0.167826
$901$	8.52424	0.283984
$902$	−40.3187	−1.34247
$903$	1.29653	0.0431457
$904$	−4.10773	−0.136621
$905$	−28.7499	−0.955678
$906$	−4.28611	−0.142397
$907$	−41.4053	−1.37484	−0.687420	−	0.726260i	$-0.741257\pi$
$907$	−41.4053	−1.37484	−0.687420	+	0.726260i	$0.741257\pi$
$908$	−14.2428	−0.472664
$909$	−0.883955	−0.0293189
$910$	6.42120	0.212861
$911$	45.3506	1.50253	0.751266	−	0.660000i	$-0.229444\pi$
$911$	45.3506	1.50253	0.751266	+	0.660000i	$0.229444\pi$
$912$	8.15117	0.269912
$913$	−28.4686	−0.942173
$914$	−13.3140	−0.440389
$915$	14.8770	0.491820
$916$	−1.19395	−0.0394491
$917$	−1.59730	−0.0527476
$918$	3.52860	0.116461
$919$	59.1785	1.95212	0.976059	−	0.217504i	$-0.0697915\pi$
$919$	59.1785	1.95212	0.976059	+	0.217504i	$0.0697915\pi$
$920$	3.16777	0.104438
$921$	−8.49325	−0.279862
$922$	−3.59065	−0.118252
$923$	−20.3239	−0.668969
$924$	−3.89947	−0.128283
$925$	−29.6103	−0.973581
$926$	27.5059	0.903901
$927$	10.7757	0.353919
$928$	−1.00000	−0.0328266
$929$	16.8045	0.551337	0.275669	−	0.961253i	$-0.411101\pi$
$929$	16.8045	0.551337	0.275669	+	0.961253i	$0.411101\pi$
$930$	−17.6090	−0.577421
$931$	−47.6992	−1.56328
$932$	−11.9798	−0.392412
$933$	−23.0400	−0.754296
$934$	−21.5269	−0.704382
$935$	40.6780	1.33031
$936$	−1.89173	−0.0618330
$937$	49.5632	1.61916	0.809580	−	0.587010i	$-0.199695\pi$
$937$	49.5632	1.61916	0.809580	+	0.587010i	$0.199695\pi$
$938$	−2.80278	−0.0915139
$939$	26.6122	0.868457
$940$	−29.3866	−0.958485
$941$	37.9929	1.23853	0.619266	−	0.785181i	$-0.287430\pi$
$941$	37.9929	1.23853	0.619266	+	0.785181i	$0.287430\pi$
$942$	14.8149	0.482695
$943$	−11.0791	−0.360785
$944$	−10.2273	−0.332869
$945$	−3.39436	−0.110418
$946$	−4.40332	−0.143164
$947$	18.8057	0.611103	0.305552	−	0.952176i	$-0.401159\pi$
$947$	18.8057	0.611103	0.305552	+	0.952176i	$0.401159\pi$
$948$	−9.55404	−0.310301
$949$	−6.24419	−0.202695
$950$	41.0394	1.33149
$951$	7.31848	0.237318
$952$	−3.78100	−0.122543
$953$	−38.2070	−1.23765	−0.618823	−	0.785530i	$-0.712390\pi$
$953$	−38.2070	−1.23765	−0.618823	+	0.785530i	$0.712390\pi$
$954$	2.41575	0.0782129
$955$	47.5116	1.53744
$956$	16.3276	0.528071
$957$	−3.63917	−0.117638
$958$	−1.86011	−0.0600973
$959$	−11.2980	−0.364831
$960$	3.16777	0.102239
$961$	−0.0999326	−0.00322363
$962$	11.1255	0.358701
$963$	9.79579	0.315665
$964$	2.46784	0.0794839
$965$	62.8478	2.02314
$966$	−1.07153	−0.0344758
$967$	22.4810	0.722939	0.361469	−	0.932384i	$-0.382275\pi$
$967$	22.4810	0.722939	0.361469	+	0.932384i	$0.382275\pi$
$968$	2.24356	0.0721106
$969$	28.7622	0.923976
$970$	35.0407	1.12509
$971$	51.1429	1.64125	0.820627	−	0.571464i	$-0.193624\pi$
$971$	51.1429	1.64125	0.820627	+	0.571464i	$0.193624\pi$
$972$	1.00000	0.0320750
$973$	−12.7841	−0.409839
$974$	−19.9103	−0.637969
$975$	−9.52444	−0.305026
$976$	4.69638	0.150327
$977$	22.1807	0.709623	0.354811	−	0.934938i	$-0.384545\pi$
$977$	22.1807	0.709623	0.354811	+	0.934938i	$0.384545\pi$
$978$	5.55618	0.177667
$979$	16.4751	0.526548
$980$	−18.5373	−0.592151
$981$	14.0648	0.449055
$982$	9.42708	0.300830
$983$	26.1725	0.834774	0.417387	−	0.908729i	$-0.362946\pi$
$983$	26.1725	0.834774	0.417387	+	0.908729i	$0.362946\pi$
$984$	−11.0791	−0.353189
$985$	48.2461	1.53725
$986$	−3.52860	−0.112374
$987$	9.94028	0.316403
$988$	−15.4198	−0.490569
$989$	−1.20998	−0.0384751
$990$	11.5281	0.366386
$991$	−11.8096	−0.375146	−0.187573	−	0.982251i	$-0.560062\pi$
$991$	−11.8096	−0.375146	−0.187573	+	0.982251i	$0.560062\pi$
$992$	−5.55878	−0.176492
$993$	−30.4754	−0.967108
$994$	−11.5120	−0.365139
$995$	−46.1054	−1.46164
$996$	−7.82283	−0.247876
$997$	−43.3367	−1.37249	−0.686244	−	0.727371i	$-0.740742\pi$
$997$	−43.3367	−1.37249	−0.686244	+	0.727371i	$0.740742\pi$
$998$	8.44564	0.267342
$999$	−5.88115	−0.186071

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4002.2.a.bh.1.6	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4002.2.a.bh.1.6	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.16777 q^{5} +1.00000 q^{6} -1.07153 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.16777 q^{5} +1.00000 q^{6} -1.07153 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.16777 q^{10} +3.63917 q^{11} +1.00000 q^{12} -1.89173 q^{13} -1.07153 q^{14} +3.16777 q^{15} +1.00000 q^{16} +3.52860 q^{17} +1.00000 q^{18} +8.15117 q^{19} +3.16777 q^{20} -1.07153 q^{21} +3.63917 q^{22} +1.00000 q^{23} +1.00000 q^{24} +5.03478 q^{25} -1.89173 q^{26} +1.00000 q^{27} -1.07153 q^{28} -1.00000 q^{29} +3.16777 q^{30} -5.55878 q^{31} +1.00000 q^{32} +3.63917 q^{33} +3.52860 q^{34} -3.39436 q^{35} +1.00000 q^{36} -5.88115 q^{37} +8.15117 q^{38} -1.89173 q^{39} +3.16777 q^{40} -11.0791 q^{41} -1.07153 q^{42} -1.20998 q^{43} +3.63917 q^{44} +3.16777 q^{45} +1.00000 q^{46} -9.27673 q^{47} +1.00000 q^{48} -5.85183 q^{49} +5.03478 q^{50} +3.52860 q^{51} -1.89173 q^{52} +2.41575 q^{53} +1.00000 q^{54} +11.5281 q^{55} -1.07153 q^{56} +8.15117 q^{57} -1.00000 q^{58} -10.2273 q^{59} +3.16777 q^{60} +4.69638 q^{61} -5.55878 q^{62} -1.07153 q^{63} +1.00000 q^{64} -5.99256 q^{65} +3.63917 q^{66} +2.61568 q^{67} +3.52860 q^{68} +1.00000 q^{69} -3.39436 q^{70} +10.7436 q^{71} +1.00000 q^{72} +3.30079 q^{73} -5.88115 q^{74} +5.03478 q^{75} +8.15117 q^{76} -3.89947 q^{77} -1.89173 q^{78} -9.55404 q^{79} +3.16777 q^{80} +1.00000 q^{81} -11.0791 q^{82} -7.82283 q^{83} -1.07153 q^{84} +11.1778 q^{85} -1.20998 q^{86} -1.00000 q^{87} +3.63917 q^{88} +4.52717 q^{89} +3.16777 q^{90} +2.02704 q^{91} +1.00000 q^{92} -5.55878 q^{93} -9.27673 q^{94} +25.8210 q^{95} +1.00000 q^{96} +11.0616 q^{97} -5.85183 q^{98} +3.63917 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) \) 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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