LMFDB - Embedded newform 8007.2.a.f.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$48$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.38255 q^{2} -1.00000 q^{3} -0.0885651 q^{4} +2.12725 q^{5} +1.38255 q^{6} -0.203962 q^{7} +2.88754 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.38255 q^{2} -1.00000 q^{3} -0.0885651 q^{4} +2.12725 q^{5} +1.38255 q^{6} -0.203962 q^{7} +2.88754 q^{8} +1.00000 q^{9} -2.94103 q^{10} -1.88271 q^{11} +0.0885651 q^{12} +3.56447 q^{13} +0.281986 q^{14} -2.12725 q^{15} -3.81503 q^{16} -1.00000 q^{17} -1.38255 q^{18} -0.0124475 q^{19} -0.188400 q^{20} +0.203962 q^{21} +2.60293 q^{22} +6.58314 q^{23} -2.88754 q^{24} -0.474791 q^{25} -4.92804 q^{26} -1.00000 q^{27} +0.0180639 q^{28} +0.647363 q^{29} +2.94103 q^{30} +0.398581 q^{31} -0.500626 q^{32} +1.88271 q^{33} +1.38255 q^{34} -0.433878 q^{35} -0.0885651 q^{36} +4.09354 q^{37} +0.0172092 q^{38} -3.56447 q^{39} +6.14253 q^{40} -12.2874 q^{41} -0.281986 q^{42} -8.80499 q^{43} +0.166742 q^{44} +2.12725 q^{45} -9.10150 q^{46} +5.83223 q^{47} +3.81503 q^{48} -6.95840 q^{49} +0.656421 q^{50} +1.00000 q^{51} -0.315687 q^{52} -1.05821 q^{53} +1.38255 q^{54} -4.00500 q^{55} -0.588947 q^{56} +0.0124475 q^{57} -0.895010 q^{58} -14.7742 q^{59} +0.188400 q^{60} +2.57004 q^{61} -0.551057 q^{62} -0.203962 q^{63} +8.32219 q^{64} +7.58252 q^{65} -2.60293 q^{66} +6.56955 q^{67} +0.0885651 q^{68} -6.58314 q^{69} +0.599857 q^{70} +3.69245 q^{71} +2.88754 q^{72} +0.453140 q^{73} -5.65951 q^{74} +0.474791 q^{75} +0.00110241 q^{76} +0.384001 q^{77} +4.92804 q^{78} -2.56543 q^{79} -8.11553 q^{80} +1.00000 q^{81} +16.9879 q^{82} +8.30907 q^{83} -0.0180639 q^{84} -2.12725 q^{85} +12.1733 q^{86} -0.647363 q^{87} -5.43640 q^{88} -15.5694 q^{89} -2.94103 q^{90} -0.727014 q^{91} -0.583036 q^{92} -0.398581 q^{93} -8.06333 q^{94} -0.0264789 q^{95} +0.500626 q^{96} -12.1019 q^{97} +9.62031 q^{98} -1.88271 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) $ 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * 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 $

$2$	−1.38255	−0.977608	−0.488804	−	0.872394i	$-0.662567\pi$
$2$	−1.38255	−0.977608	−0.488804	+	0.872394i	$0.662567\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.0885651	−0.0442825
$5$	2.12725	0.951337	0.475668	−	0.879625i	$-0.342206\pi$
$5$	2.12725	0.951337	0.475668	+	0.879625i	$0.342206\pi$
$6$	1.38255	0.564422
$7$	−0.203962	−0.0770903	−0.0385451	−	0.999257i	$-0.512272\pi$
$7$	−0.203962	−0.0770903	−0.0385451	+	0.999257i	$0.512272\pi$
$8$	2.88754	1.02090
$9$	1.00000	0.333333
$10$	−2.94103	−0.930035
$11$	−1.88271	−0.567658	−0.283829	−	0.958875i	$-0.591605\pi$
$11$	−1.88271	−0.567658	−0.283829	+	0.958875i	$0.591605\pi$
$12$	0.0885651	0.0255665
$13$	3.56447	0.988605	0.494302	−	0.869290i	$-0.335424\pi$
$13$	3.56447	0.988605	0.494302	+	0.869290i	$0.335424\pi$
$14$	0.281986	0.0753641
$15$	−2.12725	−0.549255
$16$	−3.81503	−0.953757
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.38255	−0.325869
$19$	−0.0124475	−0.00285564	−0.00142782	−	0.999999i	$-0.500454\pi$
$19$	−0.0124475	−0.00285564	−0.00142782	+	0.999999i	$0.500454\pi$
$20$	−0.188400	−0.0421276
$21$	0.203962	0.0445081
$22$	2.60293	0.554947
$23$	6.58314	1.37268	0.686340	−	0.727281i	$-0.259216\pi$
$23$	6.58314	1.37268	0.686340	+	0.727281i	$0.259216\pi$
$24$	−2.88754	−0.589416
$25$	−0.474791	−0.0949582
$26$	−4.92804	−0.966468
$27$	−1.00000	−0.192450
$28$	0.0180639	0.00341375
$29$	0.647363	0.120212	0.0601062	−	0.998192i	$-0.480856\pi$
$29$	0.647363	0.120212	0.0601062	+	0.998192i	$0.480856\pi$
$30$	2.94103	0.536956
$31$	0.398581	0.0715873	0.0357936	−	0.999359i	$-0.488604\pi$
$31$	0.398581	0.0715873	0.0357936	+	0.999359i	$0.488604\pi$
$32$	−0.500626	−0.0884990
$33$	1.88271	0.327738
$34$	1.38255	0.237105
$35$	−0.433878	−0.0733388
$36$	−0.0885651	−0.0147608
$37$	4.09354	0.672974	0.336487	−	0.941688i	$-0.390761\pi$
$37$	4.09354	0.672974	0.336487	+	0.941688i	$0.390761\pi$
$38$	0.0172092	0.00279170
$39$	−3.56447	−0.570771
$40$	6.14253	0.971219
$41$	−12.2874	−1.91897	−0.959486	−	0.281756i	$-0.909083\pi$
$41$	−12.2874	−1.91897	−0.959486	+	0.281756i	$0.909083\pi$
$42$	−0.281986	−0.0435115
$43$	−8.80499	−1.34275	−0.671374	−	0.741118i	$-0.734296\pi$
$43$	−8.80499	−1.34275	−0.671374	+	0.741118i	$0.734296\pi$
$44$	0.166742	0.0251374
$45$	2.12725	0.317112
$46$	−9.10150	−1.34194
$47$	5.83223	0.850718	0.425359	−	0.905025i	$-0.360148\pi$
$47$	5.83223	0.850718	0.425359	+	0.905025i	$0.360148\pi$
$48$	3.81503	0.550652
$49$	−6.95840	−0.994057
$50$	0.656421	0.0928319
$51$	1.00000	0.140028
$52$	−0.315687	−0.0437779
$53$	−1.05821	−0.145356	−0.0726778	−	0.997355i	$-0.523154\pi$
$53$	−1.05821	−0.145356	−0.0726778	+	0.997355i	$0.523154\pi$
$54$	1.38255	0.188141
$55$	−4.00500	−0.540034
$56$	−0.588947	−0.0787014
$57$	0.0124475	0.00164871
$58$	−0.895010	−0.117521
$59$	−14.7742	−1.92344	−0.961720	−	0.274034i	$-0.911642\pi$
$59$	−14.7742	−1.92344	−0.961720	+	0.274034i	$0.911642\pi$
$60$	0.188400	0.0243224
$61$	2.57004	0.329060	0.164530	−	0.986372i	$-0.447389\pi$
$61$	2.57004	0.329060	0.164530	+	0.986372i	$0.447389\pi$
$62$	−0.551057	−0.0699843
$63$	−0.203962	−0.0256968
$64$	8.32219	1.04027
$65$	7.58252	0.940496
$66$	−2.60293	−0.320399
$67$	6.56955	0.802598	0.401299	−	0.915947i	$-0.368559\pi$
$67$	6.56955	0.802598	0.401299	+	0.915947i	$0.368559\pi$
$68$	0.0885651	0.0107401
$69$	−6.58314	−0.792517
$70$	0.599857	0.0716966
$71$	3.69245	0.438214	0.219107	−	0.975701i	$-0.429686\pi$
$71$	3.69245	0.438214	0.219107	+	0.975701i	$0.429686\pi$
$72$	2.88754	0.340300
$73$	0.453140	0.0530360	0.0265180	−	0.999648i	$-0.491558\pi$
$73$	0.453140	0.0530360	0.0265180	+	0.999648i	$0.491558\pi$
$74$	−5.65951	−0.657905
$75$	0.474791	0.0548241
$76$	0.00110241	0.000126455 0
$77$	0.384001	0.0437609
$78$	4.92804	0.557991
$79$	−2.56543	−0.288634	−0.144317	−	0.989532i	$-0.546098\pi$
$79$	−2.56543	−0.288634	−0.144317	+	0.989532i	$0.546098\pi$
$80$	−8.11553	−0.907344
$81$	1.00000	0.111111
$82$	16.9879	1.87600
$83$	8.30907	0.912039	0.456020	−	0.889970i	$-0.349275\pi$
$83$	8.30907	0.912039	0.456020	+	0.889970i	$0.349275\pi$
$84$	−0.0180639	−0.00197093
$85$	−2.12725	−0.230733
$86$	12.1733	1.31268
$87$	−0.647363	−0.0694046
$88$	−5.43640	−0.579522
$89$	−15.5694	−1.65035	−0.825175	−	0.564877i	$-0.808924\pi$
$89$	−15.5694	−1.65035	−0.825175	+	0.564877i	$0.808924\pi$
$90$	−2.94103	−0.310012
$91$	−0.727014	−0.0762118
$92$	−0.583036	−0.0607857
$93$	−0.398581	−0.0413309
$94$	−8.06333	−0.831669
$95$	−0.0264789	−0.00271668
$96$	0.500626	0.0510949
$97$	−12.1019	−1.22876	−0.614380	−	0.789010i	$-0.710594\pi$
$97$	−12.1019	−1.22876	−0.614380	+	0.789010i	$0.710594\pi$
$98$	9.62031	0.971798
$99$	−1.88271	−0.189219
$100$	0.0420499	0.00420499
$101$	−3.19743	−0.318157	−0.159078	−	0.987266i	$-0.550852\pi$
$101$	−3.19743	−0.318157	−0.159078	+	0.987266i	$0.550852\pi$
$102$	−1.38255	−0.136893
$103$	10.5170	1.03628	0.518138	−	0.855297i	$-0.326625\pi$
$103$	10.5170	1.03628	0.518138	+	0.855297i	$0.326625\pi$
$104$	10.2925	1.00927
$105$	0.433878	0.0423422
$106$	1.46302	0.142101
$107$	−1.18955	−0.114998	−0.0574988	−	0.998346i	$-0.518313\pi$
$107$	−1.18955	−0.114998	−0.0574988	+	0.998346i	$0.518313\pi$
$108$	0.0885651	0.00852218
$109$	−0.401268	−0.0384345	−0.0192173	−	0.999815i	$-0.506117\pi$
$109$	−0.401268	−0.0384345	−0.0192173	+	0.999815i	$0.506117\pi$
$110$	5.53710	0.527942
$111$	−4.09354	−0.388542
$112$	0.778119	0.0735253
$113$	2.21505	0.208375	0.104187	−	0.994558i	$-0.466776\pi$
$113$	2.21505	0.208375	0.104187	+	0.994558i	$0.466776\pi$
$114$	−0.0172092	−0.00161179
$115$	14.0040	1.30588
$116$	−0.0573338	−0.00532331
$117$	3.56447	0.329535
$118$	20.4260	1.88037
$119$	0.203962	0.0186971
$120$	−6.14253	−0.560733
$121$	−7.45540	−0.677764
$122$	−3.55320	−0.321692
$123$	12.2874	1.10792
$124$	−0.0353004	−0.00317007
$125$	−11.6463	−1.04167
$126$	0.281986	0.0251214
$127$	−14.0283	−1.24481	−0.622404	−	0.782696i	$-0.713844\pi$
$127$	−14.0283	−1.24481	−0.622404	+	0.782696i	$0.713844\pi$
$128$	−10.5046	−0.928481
$129$	8.80499	0.775236
$130$	−10.4832	−0.919437
$131$	−12.8106	−1.11926	−0.559632	−	0.828741i	$-0.689058\pi$
$131$	−12.8106	−1.11926	−0.559632	+	0.828741i	$0.689058\pi$
$132$	−0.166742	−0.0145131
$133$	0.00253880	0.000220142 0
$134$	−9.08271	−0.784626
$135$	−2.12725	−0.183085
$136$	−2.88754	−0.247604
$137$	−9.88512	−0.844543	−0.422272	−	0.906469i	$-0.638767\pi$
$137$	−9.88512	−0.844543	−0.422272	+	0.906469i	$0.638767\pi$
$138$	9.10150	0.774771
$139$	−18.5865	−1.57649	−0.788245	−	0.615362i	$-0.789010\pi$
$139$	−18.5865	−1.57649	−0.788245	+	0.615362i	$0.789010\pi$
$140$	0.0384265	0.00324763
$141$	−5.83223	−0.491162
$142$	−5.10499	−0.428401
$143$	−6.71086	−0.561190
$144$	−3.81503	−0.317919
$145$	1.37711	0.114362
$146$	−0.626487	−0.0518484
$147$	6.95840	0.573919
$148$	−0.362545	−0.0298010
$149$	4.36739	0.357791	0.178895	−	0.983868i	$-0.442748\pi$
$149$	4.36739	0.357791	0.178895	+	0.983868i	$0.442748\pi$
$150$	−0.656421	−0.0535965
$151$	−3.13523	−0.255142	−0.127571	−	0.991829i	$-0.540718\pi$
$151$	−3.13523	−0.255142	−0.127571	+	0.991829i	$0.540718\pi$
$152$	−0.0359425	−0.00291532
$153$	−1.00000	−0.0808452
$154$	−0.530899	−0.0427810
$155$	0.847883	0.0681036
$156$	0.315687	0.0252752
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	3.54683	0.282171
$159$	1.05821	0.0839211
$160$	−1.06496	−0.0841923
$161$	−1.34271	−0.105820
$162$	−1.38255	−0.108623
$163$	2.29919	0.180086	0.0900432	−	0.995938i	$-0.471299\pi$
$163$	2.29919	0.180086	0.0900432	+	0.995938i	$0.471299\pi$
$164$	1.08824	0.0849770
$165$	4.00500	0.311789
$166$	−11.4877	−0.891617
$167$	16.6030	1.28478	0.642388	−	0.766380i	$-0.277944\pi$
$167$	16.6030	1.28478	0.642388	+	0.766380i	$0.277944\pi$
$168$	0.588947	0.0454383
$169$	−0.294584	−0.0226603
$170$	2.94103	0.225567
$171$	−0.0124475	−0.000951881 0
$172$	0.779815	0.0594603
$173$	−5.74478	−0.436767	−0.218384	−	0.975863i	$-0.570078\pi$
$173$	−5.74478	−0.436767	−0.218384	+	0.975863i	$0.570078\pi$
$174$	0.895010	0.0678505
$175$	0.0968392	0.00732035
$176$	7.18259	0.541408
$177$	14.7742	1.11050
$178$	21.5254	1.61340
$179$	7.63031	0.570316	0.285158	−	0.958480i	$-0.407954\pi$
$179$	7.63031	0.570316	0.285158	+	0.958480i	$0.407954\pi$
$180$	−0.188400	−0.0140425
$181$	8.05234	0.598525	0.299263	−	0.954171i	$-0.403259\pi$
$181$	8.05234	0.598525	0.299263	+	0.954171i	$0.403259\pi$
$182$	1.00513	0.0745053
$183$	−2.57004	−0.189983
$184$	19.0091	1.40137
$185$	8.70800	0.640225
$186$	0.551057	0.0404055
$187$	1.88271	0.137677
$188$	−0.516532	−0.0376719
$189$	0.203962	0.0148360
$190$	0.0366083	0.00265585
$191$	−4.14413	−0.299859	−0.149930	−	0.988697i	$-0.547905\pi$
$191$	−4.14413	−0.299859	−0.149930	+	0.988697i	$0.547905\pi$
$192$	−8.32219	−0.600602
$193$	10.1962	0.733937	0.366969	−	0.930233i	$-0.380396\pi$
$193$	10.1962	0.733937	0.366969	+	0.930233i	$0.380396\pi$
$194$	16.7314	1.20125
$195$	−7.58252	−0.542996
$196$	0.616271	0.0440194
$197$	−7.93699	−0.565487	−0.282744	−	0.959196i	$-0.591245\pi$
$197$	−7.93699	−0.565487	−0.282744	+	0.959196i	$0.591245\pi$
$198$	2.60293	0.184982
$199$	−1.58998	−0.112711	−0.0563553	−	0.998411i	$-0.517948\pi$
$199$	−1.58998	−0.112711	−0.0563553	+	0.998411i	$0.517948\pi$
$200$	−1.37098	−0.0969427
$201$	−6.56955	−0.463380
$202$	4.42060	0.311032
$203$	−0.132037	−0.00926720
$204$	−0.0885651	−0.00620080
$205$	−26.1385	−1.82559
$206$	−14.5403	−1.01307
$207$	6.58314	0.457560
$208$	−13.5985	−0.942888
$209$	0.0234350	0.00162103
$210$	−0.599857	−0.0413941
$211$	−0.650575	−0.0447874	−0.0223937	−	0.999749i	$-0.507129\pi$
$211$	−0.650575	−0.0447874	−0.0223937	+	0.999749i	$0.507129\pi$
$212$	0.0937200	0.00643672
$213$	−3.69245	−0.253003
$214$	1.64460	0.112423
$215$	−18.7305	−1.27741
$216$	−2.88754	−0.196472
$217$	−0.0812953	−0.00551868
$218$	0.554772	0.0375739
$219$	−0.453140	−0.0306204
$220$	0.354703	0.0239141
$221$	−3.56447	−0.239772
$222$	5.65951	0.379842
$223$	−10.6846	−0.715491	−0.357745	−	0.933819i	$-0.616454\pi$
$223$	−10.6846	−0.715491	−0.357745	+	0.933819i	$0.616454\pi$
$224$	0.102108	0.00682241
$225$	−0.474791	−0.0316527
$226$	−3.06241	−0.203709
$227$	14.6258	0.970751	0.485375	−	0.874306i	$-0.338683\pi$
$227$	14.6258	0.970751	0.485375	+	0.874306i	$0.338683\pi$
$228$	−0.00110241	−7.30089e−5 0
$229$	0.419946	0.0277508	0.0138754	−	0.999904i	$-0.495583\pi$
$229$	0.419946	0.0277508	0.0138754	+	0.999904i	$0.495583\pi$
$230$	−19.3612	−1.27664
$231$	−0.384001	−0.0252654
$232$	1.86929	0.122725
$233$	21.0978	1.38216	0.691080	−	0.722778i	$-0.257135\pi$
$233$	21.0978	1.38216	0.691080	+	0.722778i	$0.257135\pi$
$234$	−4.92804	−0.322156
$235$	12.4066	0.809319
$236$	1.30848	0.0851748
$237$	2.56543	0.166643
$238$	−0.281986	−0.0182785
$239$	22.6592	1.46570	0.732851	−	0.680389i	$-0.238189\pi$
$239$	22.6592	1.46570	0.732851	+	0.680389i	$0.238189\pi$
$240$	8.11553	0.523855
$241$	25.3959	1.63590	0.817948	−	0.575292i	$-0.195112\pi$
$241$	25.3959	1.63590	0.817948	+	0.575292i	$0.195112\pi$
$242$	10.3074	0.662587
$243$	−1.00000	−0.0641500
$244$	−0.227616	−0.0145716
$245$	−14.8023	−0.945683
$246$	−16.9879	−1.08311
$247$	−0.0443685	−0.00282310
$248$	1.15092	0.0730834
$249$	−8.30907	−0.526566
$250$	16.1015	1.01835
$251$	1.76138	0.111178	0.0555888	−	0.998454i	$-0.482296\pi$
$251$	1.76138	0.111178	0.0555888	+	0.998454i	$0.482296\pi$
$252$	0.0180639	0.00113792
$253$	−12.3941	−0.779213
$254$	19.3947	1.21693
$255$	2.12725	0.133214
$256$	−2.12133	−0.132583
$257$	8.52815	0.531971	0.265986	−	0.963977i	$-0.414303\pi$
$257$	8.52815	0.531971	0.265986	+	0.963977i	$0.414303\pi$
$258$	−12.1733	−0.757877
$259$	−0.834925	−0.0518797
$260$	−0.671547	−0.0416476
$261$	0.647363	0.0400708
$262$	17.7112	1.09420
$263$	9.05067	0.558088	0.279044	−	0.960278i	$-0.409982\pi$
$263$	9.05067	0.558088	0.279044	+	0.960278i	$0.409982\pi$
$264$	5.43640	0.334587
$265$	−2.25107	−0.138282
$266$	−0.00351001	−0.000215213 0
$267$	15.5694	0.952830
$268$	−0.581832	−0.0355411
$269$	10.5853	0.645399	0.322699	−	0.946502i	$-0.395410\pi$
$269$	10.5853	0.645399	0.322699	+	0.946502i	$0.395410\pi$
$270$	2.94103	0.178985
$271$	9.18533	0.557969	0.278984	−	0.960296i	$-0.410002\pi$
$271$	9.18533	0.557969	0.278984	+	0.960296i	$0.410002\pi$
$272$	3.81503	0.231320
$273$	0.727014	0.0440009
$274$	13.6666	0.825632
$275$	0.893894	0.0539038
$276$	0.583036	0.0350947
$277$	−4.83846	−0.290715	−0.145358	−	0.989379i	$-0.546433\pi$
$277$	−4.83846	−0.290715	−0.145358	+	0.989379i	$0.546433\pi$
$278$	25.6968	1.54119
$279$	0.398581	0.0238624
$280$	−1.25284	−0.0748715
$281$	−16.5815	−0.989171	−0.494585	−	0.869129i	$-0.664680\pi$
$281$	−16.5815	−0.989171	−0.494585	+	0.869129i	$0.664680\pi$
$282$	8.06333	0.480164
$283$	19.2054	1.14164	0.570820	−	0.821075i	$-0.306625\pi$
$283$	19.2054	1.14164	0.570820	+	0.821075i	$0.306625\pi$
$284$	−0.327022	−0.0194052
$285$	0.0264789	0.00156847
$286$	9.27807	0.548624
$287$	2.50616	0.147934
$288$	−0.500626	−0.0294997
$289$	1.00000	0.0588235
$290$	−1.90391	−0.111802
$291$	12.1019	0.709425
$292$	−0.0401324	−0.00234857
$293$	−21.3155	−1.24527	−0.622633	−	0.782514i	$-0.713937\pi$
$293$	−21.3155	−1.24527	−0.622633	+	0.782514i	$0.713937\pi$
$294$	−9.62031	−0.561068
$295$	−31.4285	−1.82984
$296$	11.8203	0.687039
$297$	1.88271	0.109246
$298$	−6.03812	−0.349779
$299$	23.4654	1.35704
$300$	−0.0420499	−0.00242775
$301$	1.79588	0.103513
$302$	4.33461	0.249429
$303$	3.19743	0.183688
$304$	0.0474874	0.00272359
$305$	5.46713	0.313047
$306$	1.38255	0.0790349
$307$	16.5041	0.941939	0.470970	−	0.882149i	$-0.343904\pi$
$307$	16.5041	0.941939	0.470970	+	0.882149i	$0.343904\pi$
$308$	−0.0340091	−0.00193785
$309$	−10.5170	−0.598294
$310$	−1.17224	−0.0665787
$311$	0.315638	0.0178982	0.00894909	−	0.999960i	$-0.497151\pi$
$311$	0.315638	0.0178982	0.00894909	+	0.999960i	$0.497151\pi$
$312$	−10.2925	−0.582700
$313$	30.8499	1.74374	0.871870	−	0.489738i	$-0.162907\pi$
$313$	30.8499	1.74374	0.871870	+	0.489738i	$0.162907\pi$
$314$	1.38255	0.0780216
$315$	−0.433878	−0.0244463
$316$	0.227208	0.0127814
$317$	−10.5058	−0.590066	−0.295033	−	0.955487i	$-0.595331\pi$
$317$	−10.5058	−0.590066	−0.295033	+	0.955487i	$0.595331\pi$
$318$	−1.46302	−0.0820420
$319$	−1.21880	−0.0682395
$320$	17.7034	0.989651
$321$	1.18955	0.0663939
$322$	1.85636	0.103451
$323$	0.0124475	0.000692595 0
$324$	−0.0885651	−0.00492028
$325$	−1.69238	−0.0938761
$326$	−3.17874	−0.176054
$327$	0.401268	0.0221902
$328$	−35.4804	−1.95908
$329$	−1.18955	−0.0655821
$330$	−5.53710	−0.304807
$331$	−33.7794	−1.85668	−0.928342	−	0.371728i	$-0.878765\pi$
$331$	−33.7794	−1.85668	−0.928342	+	0.371728i	$0.878765\pi$
$332$	−0.735894	−0.0403874
$333$	4.09354	0.224325
$334$	−22.9544	−1.25601
$335$	13.9751	0.763541
$336$	−0.778119	−0.0424499
$337$	−35.5128	−1.93450	−0.967252	−	0.253819i	$-0.918313\pi$
$337$	−35.5128	−1.93450	−0.967252	+	0.253819i	$0.918313\pi$
$338$	0.407276	0.0221529
$339$	−2.21505	−0.120305
$340$	0.188400	0.0102174
$341$	−0.750413	−0.0406371
$342$	0.0172092	0.000930566 0
$343$	2.84698	0.153722
$344$	−25.4248	−1.37081
$345$	−14.0040	−0.753951
$346$	7.94242	0.426987
$347$	9.64863	0.517966	0.258983	−	0.965882i	$-0.416613\pi$
$347$	9.64863	0.517966	0.258983	+	0.965882i	$0.416613\pi$
$348$	0.0573338	0.00307341
$349$	−20.8693	−1.11711	−0.558553	−	0.829469i	$-0.688643\pi$
$349$	−20.8693	−1.11711	−0.558553	+	0.829469i	$0.688643\pi$
$350$	−0.133885	−0.00715644
$351$	−3.56447	−0.190257
$352$	0.942533	0.0502372
$353$	−18.8427	−1.00290	−0.501448	−	0.865188i	$-0.667199\pi$
$353$	−18.8427	−1.00290	−0.501448	+	0.865188i	$0.667199\pi$
$354$	−20.4260	−1.08563
$355$	7.85478	0.416889
$356$	1.37890	0.0730817
$357$	−0.203962	−0.0107948
$358$	−10.5493	−0.557546
$359$	−8.50792	−0.449031	−0.224515	−	0.974471i	$-0.572080\pi$
$359$	−8.50792	−0.449031	−0.224515	+	0.974471i	$0.572080\pi$
$360$	6.14253	0.323740
$361$	−18.9998	−0.999992
$362$	−11.1327	−0.585123
$363$	7.45540	0.391307
$364$	0.0643881	0.00337485
$365$	0.963943	0.0504551
$366$	3.55320	0.185729
$367$	26.1719	1.36616	0.683081	−	0.730343i	$-0.260640\pi$
$367$	26.1719	1.36616	0.683081	+	0.730343i	$0.260640\pi$
$368$	−25.1149	−1.30920
$369$	−12.2874	−0.639657
$370$	−12.0392	−0.625889
$371$	0.215833	0.0112055
$372$	0.0353004	0.00183024
$373$	25.9925	1.34584	0.672921	−	0.739714i	$-0.265039\pi$
$373$	25.9925	1.34584	0.672921	+	0.739714i	$0.265039\pi$
$374$	−2.60293	−0.134595
$375$	11.6463	0.601411
$376$	16.8408	0.868497
$377$	2.30750	0.118842
$378$	−0.281986	−0.0145038
$379$	−24.8000	−1.27389	−0.636944	−	0.770910i	$-0.719802\pi$
$379$	−24.8000	−1.27389	−0.636944	+	0.770910i	$0.719802\pi$
$380$	0.00234511	0.000120301 0
$381$	14.0283	0.718690
$382$	5.72946	0.293145
$383$	28.0135	1.43142	0.715712	−	0.698395i	$-0.246102\pi$
$383$	28.0135	1.43142	0.715712	+	0.698395i	$0.246102\pi$
$384$	10.5046	0.536059
$385$	0.816867	0.0416314
$386$	−14.0967	−0.717503
$387$	−8.80499	−0.447583
$388$	1.07180	0.0544126
$389$	−27.4137	−1.38993	−0.694965	−	0.719043i	$-0.744580\pi$
$389$	−27.4137	−1.38993	−0.694965	+	0.719043i	$0.744580\pi$
$390$	10.4832	0.530837
$391$	−6.58314	−0.332924
$392$	−20.0926	−1.01483
$393$	12.8106	0.646208
$394$	10.9733	0.552825
$395$	−5.45733	−0.274588
$396$	0.166742	0.00837912
$397$	−31.1240	−1.56207	−0.781034	−	0.624489i	$-0.785307\pi$
$397$	−31.1240	−1.56207	−0.781034	+	0.624489i	$0.785307\pi$
$398$	2.19822	0.110187
$399$	−0.00253880	−0.000127099 0
$400$	1.81134	0.0905670
$401$	37.7419	1.88474	0.942369	−	0.334574i	$-0.108593\pi$
$401$	37.7419	1.88474	0.942369	+	0.334574i	$0.108593\pi$
$402$	9.08271	0.453004
$403$	1.42073	0.0707716
$404$	0.283181	0.0140888
$405$	2.12725	0.105704
$406$	0.182548	0.00905969
$407$	−7.70695	−0.382019
$408$	2.88754	0.142954
$409$	−20.7562	−1.02633	−0.513165	−	0.858290i	$-0.671527\pi$
$409$	−20.7562	−1.02633	−0.513165	+	0.858290i	$0.671527\pi$
$410$	36.1376	1.78471
$411$	9.88512	0.487597
$412$	−0.931443	−0.0458889
$413$	3.01337	0.148278
$414$	−9.10150	−0.447314
$415$	17.6755	0.867656
$416$	−1.78446	−0.0874905
$417$	18.5865	0.910187
$418$	−0.0323999	−0.00158473
$419$	−3.11619	−0.152236	−0.0761179	−	0.997099i	$-0.524253\pi$
$419$	−3.11619	−0.152236	−0.0761179	+	0.997099i	$0.524253\pi$
$420$	−0.0384265	−0.00187502
$421$	10.8003	0.526374	0.263187	−	0.964745i	$-0.415226\pi$
$421$	10.8003	0.526374	0.263187	+	0.964745i	$0.415226\pi$
$422$	0.899450	0.0437846
$423$	5.83223	0.283573
$424$	−3.05561	−0.148393
$425$	0.474791	0.0230307
$426$	5.10499	0.247337
$427$	−0.524190	−0.0253673
$428$	0.105352	0.00509239
$429$	6.71086	0.324003
$430$	25.8957	1.24880
$431$	4.07885	0.196471	0.0982357	−	0.995163i	$-0.468680\pi$
$431$	4.07885	0.196471	0.0982357	+	0.995163i	$0.468680\pi$
$432$	3.81503	0.183551
$433$	−28.1269	−1.35169	−0.675845	−	0.737043i	$-0.736221\pi$
$433$	−28.1269	−1.35169	−0.675845	+	0.737043i	$0.736221\pi$
$434$	0.112395	0.00539511
$435$	−1.37711	−0.0660272
$436$	0.0355383	0.00170198
$437$	−0.0819434	−0.00391988
$438$	0.626487	0.0299347
$439$	−26.1788	−1.24944	−0.624722	−	0.780847i	$-0.714788\pi$
$439$	−26.1788	−1.24944	−0.624722	+	0.780847i	$0.714788\pi$
$440$	−11.5646	−0.551321
$441$	−6.95840	−0.331352
$442$	4.92804	0.234403
$443$	−18.6227	−0.884790	−0.442395	−	0.896820i	$-0.645871\pi$
$443$	−18.6227	−0.884790	−0.442395	+	0.896820i	$0.645871\pi$
$444$	0.362545	0.0172056
$445$	−33.1200	−1.57004
$446$	14.7719	0.699470
$447$	−4.36739	−0.206570
$448$	−1.69741	−0.0801950
$449$	16.9928	0.801941	0.400971	−	0.916091i	$-0.368673\pi$
$449$	16.9928	0.801941	0.400971	+	0.916091i	$0.368673\pi$
$450$	0.656421	0.0309440
$451$	23.1336	1.08932
$452$	−0.196176	−0.00922735
$453$	3.13523	0.147306
$454$	−20.2209	−0.949014
$455$	−1.54654	−0.0725031
$456$	0.0359425	0.00168316
$457$	−30.4744	−1.42553	−0.712765	−	0.701403i	$-0.752557\pi$
$457$	−30.4744	−1.42553	−0.712765	+	0.701403i	$0.752557\pi$
$458$	−0.580596	−0.0271294
$459$	1.00000	0.0466760
$460$	−1.24027	−0.0578277
$461$	14.7883	0.688762	0.344381	−	0.938830i	$-0.388089\pi$
$461$	14.7883	0.688762	0.344381	+	0.938830i	$0.388089\pi$
$462$	0.530899	0.0246996
$463$	22.7388	1.05676	0.528382	−	0.849007i	$-0.322799\pi$
$463$	22.7388	1.05676	0.528382	+	0.849007i	$0.322799\pi$
$464$	−2.46971	−0.114653
$465$	−0.847883	−0.0393197
$466$	−29.1686	−1.35121
$467$	22.5443	1.04323	0.521613	−	0.853182i	$-0.325330\pi$
$467$	22.5443	1.04323	0.521613	+	0.853182i	$0.325330\pi$
$468$	−0.315687	−0.0145926
$469$	−1.33994	−0.0618725
$470$	−17.1527	−0.791197
$471$	1.00000	0.0460776
$472$	−42.6611	−1.96364
$473$	16.5772	0.762223
$474$	−3.54683	−0.162911
$475$	0.00590994	0.000271167 0
$476$	−0.0180639	−0.000827957 0
$477$	−1.05821	−0.0484519
$478$	−31.3274	−1.43288
$479$	−16.4861	−0.753269	−0.376635	−	0.926362i	$-0.622919\pi$
$479$	−16.4861	−0.753269	−0.376635	+	0.926362i	$0.622919\pi$
$480$	1.06496	0.0486085
$481$	14.5913	0.665305
$482$	−35.1111	−1.59927
$483$	1.34271	0.0610953
$484$	0.660288	0.0300131
$485$	−25.7438	−1.16896
$486$	1.38255	0.0627136
$487$	−38.4656	−1.74304	−0.871521	−	0.490357i	$-0.836866\pi$
$487$	−38.4656	−1.74304	−0.871521	+	0.490357i	$0.836866\pi$
$488$	7.42109	0.335937
$489$	−2.29919	−0.103973
$490$	20.4648	0.924507
$491$	35.9939	1.62438	0.812191	−	0.583392i	$-0.198275\pi$
$491$	35.9939	1.62438	0.812191	+	0.583392i	$0.198275\pi$
$492$	−1.08824	−0.0490615
$493$	−0.647363	−0.0291558
$494$	0.0613416	0.00275989
$495$	−4.00500	−0.180011
$496$	−1.52060	−0.0682769
$497$	−0.753119	−0.0337820
$498$	11.4877	0.514775
$499$	−3.18705	−0.142672	−0.0713359	−	0.997452i	$-0.522726\pi$
$499$	−3.18705	−0.142672	−0.0713359	+	0.997452i	$0.522726\pi$
$500$	1.03145	0.0461280
$501$	−16.6030	−0.741766
$502$	−2.43519	−0.108688
$503$	−34.4157	−1.53452	−0.767260	−	0.641336i	$-0.778380\pi$
$503$	−34.4157	−1.53452	−0.767260	+	0.641336i	$0.778380\pi$
$504$	−0.588947	−0.0262338
$505$	−6.80175	−0.302674
$506$	17.1355	0.761765
$507$	0.294584	0.0130829
$508$	1.24242	0.0551233
$509$	−5.63897	−0.249943	−0.124972	−	0.992160i	$-0.539884\pi$
$509$	−5.63897	−0.249943	−0.124972	+	0.992160i	$0.539884\pi$
$510$	−2.94103	−0.130231
$511$	−0.0924232	−0.00408856
$512$	23.9420	1.05810
$513$	0.0124475	0.000549569 0
$514$	−11.7906	−0.520059
$515$	22.3724	0.985847
$516$	−0.779815	−0.0343294
$517$	−10.9804	−0.482917
$518$	1.15432	0.0507181
$519$	5.74478	0.252168
$520$	21.8948	0.960152
$521$	−6.52922	−0.286051	−0.143025	−	0.989719i	$-0.545683\pi$
$521$	−6.52922	−0.286051	−0.143025	+	0.989719i	$0.545683\pi$
$522$	−0.895010	−0.0391735
$523$	16.4664	0.720025	0.360012	−	0.932948i	$-0.382772\pi$
$523$	16.4664	0.720025	0.360012	+	0.932948i	$0.382772\pi$
$524$	1.13457	0.0495639
$525$	−0.0968392	−0.00422641
$526$	−12.5130	−0.545591
$527$	−0.398581	−0.0173625
$528$	−7.18259	−0.312582
$529$	20.3377	0.884249
$530$	3.11221	0.135186
$531$	−14.7742	−0.641147
$532$	−0.000224849 0	−9.74846e−6 0
$533$	−43.7981	−1.89711
$534$	−21.5254	−0.931495
$535$	−2.53046	−0.109402
$536$	18.9698	0.819371
$537$	−7.63031	−0.329272
$538$	−14.6347	−0.630947
$539$	13.1006	0.564285
$540$	0.188400	0.00810746
$541$	−40.9238	−1.75945	−0.879726	−	0.475481i	$-0.842274\pi$
$541$	−40.9238	−1.75945	−0.879726	+	0.475481i	$0.842274\pi$
$542$	−12.6991	−0.545475
$543$	−8.05234	−0.345559
$544$	0.500626	0.0214642
$545$	−0.853599	−0.0365642
$546$	−1.00513	−0.0430156
$547$	−36.0457	−1.54120	−0.770600	−	0.637319i	$-0.780044\pi$
$547$	−36.0457	−1.54120	−0.770600	+	0.637319i	$0.780044\pi$
$548$	0.875477	0.0373985
$549$	2.57004	0.109687
$550$	−1.23585	−0.0526968
$551$	−0.00805802	−0.000343283 0
$552$	−19.0091	−0.809080
$553$	0.523250	0.0222509
$554$	6.68940	0.284205
$555$	−8.70800	−0.369634
$556$	1.64612	0.0698110
$557$	−1.03825	−0.0439919	−0.0219959	−	0.999758i	$-0.507002\pi$
$557$	−1.03825	−0.0439919	−0.0219959	+	0.999758i	$0.507002\pi$
$558$	−0.551057	−0.0233281
$559$	−31.3851	−1.32745
$560$	1.65526	0.0699474
$561$	−1.88271	−0.0794881
$562$	22.9247	0.967021
$563$	9.70404	0.408976	0.204488	−	0.978869i	$-0.434447\pi$
$563$	9.70404	0.408976	0.204488	+	0.978869i	$0.434447\pi$
$564$	0.516532	0.0217499
$565$	4.71198	0.198234
$566$	−26.5523	−1.11608
$567$	−0.203962	−0.00856558
$568$	10.6621	0.447372
$569$	19.6552	0.823988	0.411994	−	0.911187i	$-0.364832\pi$
$569$	19.6552	0.823988	0.411994	+	0.911187i	$0.364832\pi$
$570$	−0.0366083	−0.00153335
$571$	−11.3464	−0.474833	−0.237417	−	0.971408i	$-0.576301\pi$
$571$	−11.3464	−0.474833	−0.237417	+	0.971408i	$0.576301\pi$
$572$	0.594347	0.0248509
$573$	4.14413	0.173124
$574$	−3.46489	−0.144622
$575$	−3.12562	−0.130347
$576$	8.32219	0.346758
$577$	−14.6785	−0.611072	−0.305536	−	0.952181i	$-0.598836\pi$
$577$	−14.6785	−0.611072	−0.305536	+	0.952181i	$0.598836\pi$
$578$	−1.38255	−0.0575064
$579$	−10.1962	−0.423739
$580$	−0.121963	−0.00506426
$581$	−1.69473	−0.0703093
$582$	−16.7314	−0.693539
$583$	1.99229	0.0825124
$584$	1.30846	0.0541444
$585$	7.58252	0.313499
$586$	29.4697	1.21738
$587$	23.0412	0.951014	0.475507	−	0.879712i	$-0.342265\pi$
$587$	23.0412	0.951014	0.475507	+	0.879712i	$0.342265\pi$
$588$	−0.616271	−0.0254146
$589$	−0.00496132	−0.000204428 0
$590$	43.4514	1.78887
$591$	7.93699	0.326484
$592$	−15.6170	−0.641853
$593$	13.6537	0.560689	0.280345	−	0.959899i	$-0.409551\pi$
$593$	13.6537	0.560689	0.280345	+	0.959899i	$0.409551\pi$
$594$	−2.60293	−0.106800
$595$	0.433878	0.0177873
$596$	−0.386798	−0.0158439
$597$	1.58998	0.0650735
$598$	−32.4420	−1.32665
$599$	−11.5452	−0.471724	−0.235862	−	0.971787i	$-0.575791\pi$
$599$	−11.5452	−0.471724	−0.235862	+	0.971787i	$0.575791\pi$
$600$	1.37098	0.0559699
$601$	−3.24584	−0.132401	−0.0662003	−	0.997806i	$-0.521088\pi$
$601$	−3.24584	−0.132401	−0.0662003	+	0.997806i	$0.521088\pi$
$602$	−2.48289	−0.101195
$603$	6.56955	0.267533
$604$	0.277672	0.0112983
$605$	−15.8595	−0.644782
$606$	−4.42060	−0.179575
$607$	−31.7395	−1.28827	−0.644133	−	0.764913i	$-0.722782\pi$
$607$	−31.7395	−1.28827	−0.644133	+	0.764913i	$0.722782\pi$
$608$	0.00623152	0.000252721 0
$609$	0.132037	0.00535042
$610$	−7.55856	−0.306037
$611$	20.7888	0.841024
$612$	0.0885651	0.00358003
$613$	−13.0712	−0.527939	−0.263969	−	0.964531i	$-0.585032\pi$
$613$	−13.0712	−0.527939	−0.263969	+	0.964531i	$0.585032\pi$
$614$	−22.8177	−0.920847
$615$	26.1385	1.05400
$616$	1.10882	0.0446755
$617$	−21.2147	−0.854071	−0.427036	−	0.904235i	$-0.640442\pi$
$617$	−21.2147	−0.854071	−0.427036	+	0.904235i	$0.640442\pi$
$618$	14.5403	0.584897
$619$	−48.3407	−1.94298	−0.971488	−	0.237090i	$-0.923806\pi$
$619$	−48.3407	−1.94298	−0.971488	+	0.237090i	$0.923806\pi$
$620$	−0.0750929	−0.00301580
$621$	−6.58314	−0.264172
$622$	−0.436384	−0.0174974
$623$	3.17556	0.127226
$624$	13.5985	0.544377
$625$	−22.4006	−0.896025
$626$	−42.6514	−1.70469
$627$	−0.0234350	−0.000935902 0
$628$	0.0885651	0.00353413
$629$	−4.09354	−0.163220
$630$	0.599857	0.0238989
$631$	−28.7219	−1.14340	−0.571700	−	0.820463i	$-0.693716\pi$
$631$	−28.7219	−1.14340	−0.571700	+	0.820463i	$0.693716\pi$
$632$	−7.40779	−0.294666
$633$	0.650575	0.0258580
$634$	14.5248	0.576853
$635$	−29.8417	−1.18423
$636$	−0.0937200	−0.00371624
$637$	−24.8030	−0.982730
$638$	1.68504	0.0667115
$639$	3.69245	0.146071
$640$	−22.3459	−0.883298
$641$	30.4386	1.20225	0.601126	−	0.799154i	$-0.294719\pi$
$641$	30.4386	1.20225	0.601126	+	0.799154i	$0.294719\pi$
$642$	−1.64460	−0.0649072
$643$	43.0852	1.69912	0.849558	−	0.527496i	$-0.176869\pi$
$643$	43.0852	1.69912	0.849558	+	0.527496i	$0.176869\pi$
$644$	0.118917	0.00468599
$645$	18.7305	0.737511
$646$	−0.0172092	−0.000677086 0
$647$	1.33198	0.0523656	0.0261828	−	0.999657i	$-0.491665\pi$
$647$	1.33198	0.0523656	0.0261828	+	0.999657i	$0.491665\pi$
$648$	2.88754	0.113433
$649$	27.8156	1.09186
$650$	2.33979	0.0917741
$651$	0.0812953	0.00318621
$652$	−0.203628	−0.00797469
$653$	−28.3679	−1.11012	−0.555061	−	0.831810i	$-0.687305\pi$
$653$	−28.3679	−1.11012	−0.555061	+	0.831810i	$0.687305\pi$
$654$	−0.554772	−0.0216933
$655$	−27.2513	−1.06480
$656$	46.8768	1.83023
$657$	0.453140	0.0176787
$658$	1.64461	0.0641136
$659$	34.9333	1.36081	0.680403	−	0.732838i	$-0.261805\pi$
$659$	34.9333	1.36081	0.680403	+	0.732838i	$0.261805\pi$
$660$	−0.354703	−0.0138068
$661$	47.8486	1.86109	0.930547	−	0.366173i	$-0.119332\pi$
$661$	47.8486	1.86109	0.930547	+	0.366173i	$0.119332\pi$
$662$	46.7016	1.81511
$663$	3.56447	0.138432
$664$	23.9928	0.931100
$665$	0.00540068	0.000209429 0
$666$	−5.65951	−0.219302
$667$	4.26168	0.165013
$668$	−1.47044	−0.0568931
$669$	10.6846	0.413089
$670$	−19.3212	−0.746444
$671$	−4.83864	−0.186794
$672$	−0.102108	−0.00393892
$673$	−28.1217	−1.08401	−0.542007	−	0.840374i	$-0.682335\pi$
$673$	−28.1217	−1.08401	−0.542007	+	0.840374i	$0.682335\pi$
$674$	49.0980	1.89119
$675$	0.474791	0.0182747
$676$	0.0260899	0.00100346
$677$	−50.6480	−1.94656	−0.973281	−	0.229618i	$-0.926252\pi$
$677$	−50.6480	−1.94656	−0.973281	+	0.229618i	$0.926252\pi$
$678$	3.06241	0.117611
$679$	2.46832	0.0947254
$680$	−6.14253	−0.235555
$681$	−14.6258	−0.560463
$682$	1.03748	0.0397272
$683$	−26.7424	−1.02327	−0.511635	−	0.859203i	$-0.670960\pi$
$683$	−26.7424	−1.02327	−0.511635	+	0.859203i	$0.670960\pi$
$684$	0.00110241	4.21517e−5 0
$685$	−21.0282	−0.803445
$686$	−3.93608	−0.150280
$687$	−0.419946	−0.0160220
$688$	33.5913	1.28066
$689$	−3.77194	−0.143699
$690$	19.3612	0.737068
$691$	−43.5596	−1.65709	−0.828543	−	0.559925i	$-0.810830\pi$
$691$	−43.5596	−1.65709	−0.828543	+	0.559925i	$0.810830\pi$
$692$	0.508786	0.0193412
$693$	0.384001	0.0145870
$694$	−13.3397	−0.506367
$695$	−39.5383	−1.49977
$696$	−1.86929	−0.0708551
$697$	12.2874	0.465419
$698$	28.8527	1.09209
$699$	−21.0978	−0.797991
$700$	−0.00857657	−0.000324164 0
$701$	−15.9742	−0.603337	−0.301669	−	0.953413i	$-0.597544\pi$
$701$	−15.9742	−0.603337	−0.301669	+	0.953413i	$0.597544\pi$
$702$	4.92804	0.185997
$703$	−0.0509542	−0.00192177
$704$	−15.6683	−0.590520
$705$	−12.4066	−0.467261
$706$	26.0509	0.980439
$707$	0.652154	0.0245268
$708$	−1.30848	−0.0491757
$709$	−44.6106	−1.67539	−0.837693	−	0.546142i	$-0.816096\pi$
$709$	−44.6106	−1.67539	−0.837693	+	0.546142i	$0.816096\pi$
$710$	−10.8596	−0.407554
$711$	−2.56543	−0.0962113
$712$	−44.9572	−1.68484
$713$	2.62392	0.0982664
$714$	0.281986	0.0105531
$715$	−14.2757	−0.533881
$716$	−0.675779	−0.0252551
$717$	−22.6592	−0.846224
$718$	11.7626	0.438976
$719$	−23.9914	−0.894729	−0.447365	−	0.894352i	$-0.647637\pi$
$719$	−23.9914	−0.894729	−0.447365	+	0.894352i	$0.647637\pi$
$720$	−8.11553	−0.302448
$721$	−2.14507	−0.0798868
$722$	26.2682	0.977600
$723$	−25.3959	−0.944485
$724$	−0.713156	−0.0265042
$725$	−0.307362	−0.0114151
$726$	−10.3074	−0.382545
$727$	−27.8456	−1.03273	−0.516367	−	0.856367i	$-0.672716\pi$
$727$	−27.8456	−1.03273	−0.516367	+	0.856367i	$0.672716\pi$
$728$	−2.09928	−0.0778046
$729$	1.00000	0.0370370
$730$	−1.33270	−0.0493253
$731$	8.80499	0.325664
$732$	0.227616	0.00841292
$733$	36.3146	1.34131	0.670655	−	0.741769i	$-0.266013\pi$
$733$	36.3146	1.34131	0.670655	+	0.741769i	$0.266013\pi$
$734$	−36.1838	−1.33557
$735$	14.8023	0.545990
$736$	−3.29569	−0.121481
$737$	−12.3686	−0.455602
$738$	16.9879	0.625334
$739$	11.2275	0.413012	0.206506	−	0.978445i	$-0.433791\pi$
$739$	11.2275	0.413012	0.206506	+	0.978445i	$0.433791\pi$
$740$	−0.771225	−0.0283508
$741$	0.0443685	0.00162992
$742$	−0.298400	−0.0109546
$743$	−5.17852	−0.189982	−0.0949908	−	0.995478i	$-0.530282\pi$
$743$	−5.17852	−0.189982	−0.0949908	+	0.995478i	$0.530282\pi$
$744$	−1.15092	−0.0421947
$745$	9.29055	0.340379
$746$	−35.9359	−1.31571
$747$	8.30907	0.304013
$748$	−0.166742	−0.00609670
$749$	0.242622	0.00886520
$750$	−16.1015	−0.587944
$751$	29.4141	1.07333	0.536667	−	0.843794i	$-0.319683\pi$
$751$	29.4141	1.07333	0.536667	+	0.843794i	$0.319683\pi$
$752$	−22.2501	−0.811378
$753$	−1.76138	−0.0641884
$754$	−3.19023	−0.116181
$755$	−6.66944	−0.242726
$756$	−0.0180639	−0.000656977 0
$757$	−8.97631	−0.326249	−0.163125	−	0.986605i	$-0.552157\pi$
$757$	−8.97631	−0.326249	−0.163125	+	0.986605i	$0.552157\pi$
$758$	34.2871	1.24536
$759$	12.3941	0.449879
$760$	−0.0764588	−0.00277345
$761$	−22.4232	−0.812840	−0.406420	−	0.913686i	$-0.633223\pi$
$761$	−22.4232	−0.812840	−0.406420	+	0.913686i	$0.633223\pi$
$762$	−19.3947	−0.702597
$763$	0.0818433	0.00296293
$764$	0.367026	0.0132785
$765$	−2.12725	−0.0769110
$766$	−38.7300	−1.39937
$767$	−52.6622	−1.90152
$768$	2.12133	0.0765470
$769$	26.6961	0.962686	0.481343	−	0.876532i	$-0.340149\pi$
$769$	26.6961	0.962686	0.481343	+	0.876532i	$0.340149\pi$
$770$	−1.12936	−0.0406992
$771$	−8.52815	−0.307134
$772$	−0.903026	−0.0325006
$773$	−5.73569	−0.206298	−0.103149	−	0.994666i	$-0.532892\pi$
$773$	−5.73569	−0.206298	−0.103149	+	0.994666i	$0.532892\pi$
$774$	12.1733	0.437561
$775$	−0.189243	−0.00679780
$776$	−34.9446	−1.25444
$777$	0.834925	0.0299528
$778$	37.9007	1.35881
$779$	0.152947	0.00547990
$780$	0.671547	0.0240452
$781$	−6.95182	−0.248756
$782$	9.10150	0.325469
$783$	−0.647363	−0.0231349
$784$	26.5465	0.948088
$785$	−2.12725	−0.0759249
$786$	−17.7112	−0.631738
$787$	36.1386	1.28820	0.644101	−	0.764941i	$-0.277232\pi$
$787$	36.1386	1.28820	0.644101	+	0.764941i	$0.277232\pi$
$788$	0.702940	0.0250412
$789$	−9.05067	−0.322212
$790$	7.54501	0.268439
$791$	−0.451786	−0.0160636
$792$	−5.43640	−0.193174
$793$	9.16082	0.325310
$794$	43.0304	1.52709
$795$	2.25107	0.0798373
$796$	0.140816	0.00499111
$797$	−30.4504	−1.07861	−0.539303	−	0.842112i	$-0.681312\pi$
$797$	−30.4504	−1.07861	−0.539303	+	0.842112i	$0.681312\pi$
$798$	0.00351001	0.000124253 0
$799$	−5.83223	−0.206329
$800$	0.237693	0.00840370
$801$	−15.5694	−0.550117
$802$	−52.1799	−1.84254
$803$	−0.853131	−0.0301063
$804$	0.581832	0.0205196
$805$	−2.85628	−0.100671
$806$	−1.96422	−0.0691868
$807$	−10.5853	−0.372621
$808$	−9.23271	−0.324806
$809$	52.2120	1.83568	0.917839	−	0.396953i	$-0.129932\pi$
$809$	52.2120	1.83568	0.917839	+	0.396953i	$0.129932\pi$
$810$	−2.94103	−0.103337
$811$	−38.6079	−1.35571	−0.677854	−	0.735196i	$-0.737090\pi$
$811$	−38.6079	−1.35571	−0.677854	+	0.735196i	$0.737090\pi$
$812$	0.0116939	0.000410375 0
$813$	−9.18533	−0.322144
$814$	10.6552	0.373465
$815$	4.89096	0.171323
$816$	−3.81503	−0.133553
$817$	0.109600	0.00383441
$818$	28.6965	1.00335
$819$	−0.727014	−0.0254039
$820$	2.31495	0.0808417
$821$	−32.4910	−1.13394	−0.566972	−	0.823737i	$-0.691885\pi$
$821$	−32.4910	−1.13394	−0.566972	+	0.823737i	$0.691885\pi$
$822$	−13.6666	−0.476679
$823$	−30.8316	−1.07472	−0.537360	−	0.843353i	$-0.680579\pi$
$823$	−30.8316	−1.07472	−0.537360	+	0.843353i	$0.680579\pi$
$824$	30.3684	1.05793
$825$	−0.893894	−0.0311214
$826$	−4.16613	−0.144958
$827$	22.1948	0.771790	0.385895	−	0.922543i	$-0.373893\pi$
$827$	22.1948	0.771790	0.385895	+	0.922543i	$0.373893\pi$
$828$	−0.583036	−0.0202619
$829$	−36.2820	−1.26012	−0.630062	−	0.776545i	$-0.716971\pi$
$829$	−36.2820	−1.26012	−0.630062	+	0.776545i	$0.716971\pi$
$830$	−24.4372	−0.848228
$831$	4.83846	0.167844
$832$	29.6642	1.02842
$833$	6.95840	0.241094
$834$	−25.6968	−0.889806
$835$	35.3187	1.22225
$836$	−0.00207552	−7.17833e−5 0
$837$	−0.398581	−0.0137770
$838$	4.30828	0.148827
$839$	39.9576	1.37949	0.689744	−	0.724053i	$-0.257723\pi$
$839$	39.9576	1.37949	0.689744	+	0.724053i	$0.257723\pi$
$840$	1.25284	0.0432271
$841$	−28.5809	−0.985549
$842$	−14.9319	−0.514587
$843$	16.5815	0.571098
$844$	0.0576182	0.00198330
$845$	−0.626655	−0.0215576
$846$	−8.06333	−0.277223
$847$	1.52062	0.0522490
$848$	4.03708	0.138634
$849$	−19.2054	−0.659126
$850$	−0.656421	−0.0225150
$851$	26.9484	0.923778
$852$	0.327022	0.0112036
$853$	11.3176	0.387507	0.193753	−	0.981050i	$-0.437934\pi$
$853$	11.3176	0.387507	0.193753	+	0.981050i	$0.437934\pi$
$854$	0.724717	0.0247993
$855$	−0.0264789	−0.000905559 0
$856$	−3.43486	−0.117401
$857$	30.1121	1.02861	0.514305	−	0.857607i	$-0.328050\pi$
$857$	30.1121	1.02861	0.514305	+	0.857607i	$0.328050\pi$
$858$	−9.27807	−0.316748
$859$	−8.17691	−0.278993	−0.139496	−	0.990223i	$-0.544548\pi$
$859$	−8.17691	−0.278993	−0.139496	+	0.990223i	$0.544548\pi$
$860$	1.65886	0.0565668
$861$	−2.50616	−0.0854098
$862$	−5.63920	−0.192072
$863$	47.6091	1.62063	0.810317	−	0.585992i	$-0.199295\pi$
$863$	47.6091	1.62063	0.810317	+	0.585992i	$0.199295\pi$
$864$	0.500626	0.0170316
$865$	−12.2206	−0.415513
$866$	38.8867	1.32142
$867$	−1.00000	−0.0339618
$868$	0.00719992	0.000244381 0
$869$	4.82997	0.163845
$870$	1.90391	0.0645487
$871$	23.4169	0.793452
$872$	−1.15868	−0.0392378
$873$	−12.1019	−0.409587
$874$	0.113291	0.00383211
$875$	2.37539	0.0803029
$876$	0.0401324	0.00135595
$877$	29.2718	0.988438	0.494219	−	0.869338i	$-0.335454\pi$
$877$	29.2718	0.988438	0.494219	+	0.869338i	$0.335454\pi$
$878$	36.1934	1.22147
$879$	21.3155	0.718955
$880$	15.2792	0.515061
$881$	−18.7555	−0.631890	−0.315945	−	0.948777i	$-0.602322\pi$
$881$	−18.7555	−0.631890	−0.315945	+	0.948777i	$0.602322\pi$
$882$	9.62031	0.323933
$883$	17.7396	0.596986	0.298493	−	0.954412i	$-0.403516\pi$
$883$	17.7396	0.596986	0.298493	+	0.954412i	$0.403516\pi$
$884$	0.315687	0.0106177
$885$	31.4285	1.05646
$886$	25.7467	0.864978
$887$	35.7410	1.20006	0.600032	−	0.799976i	$-0.295154\pi$
$887$	35.7410	1.20006	0.600032	+	0.799976i	$0.295154\pi$
$888$	−11.8203	−0.396662
$889$	2.86123	0.0959626
$890$	45.7900	1.53488
$891$	−1.88271	−0.0630732
$892$	0.946279	0.0316838
$893$	−0.0725964	−0.00242935
$894$	6.03812	0.201945
$895$	16.2316	0.542563
$896$	2.14253	0.0715768
$897$	−23.4654	−0.783486
$898$	−23.4934	−0.783984
$899$	0.258027	0.00860567
$900$	0.0420499	0.00140166
$901$	1.05821	0.0352539
$902$	−31.9833	−1.06493
$903$	−1.79588	−0.0597632
$904$	6.39605	0.212729
$905$	17.1294	0.569399
$906$	−4.33461	−0.144008
$907$	−48.8728	−1.62280	−0.811398	−	0.584494i	$-0.801293\pi$
$907$	−48.8728	−1.62280	−0.811398	+	0.584494i	$0.801293\pi$
$908$	−1.29534	−0.0429873
$909$	−3.19743	−0.106052
$910$	2.13817	0.0708796
$911$	−30.3594	−1.00585	−0.502926	−	0.864329i	$-0.667743\pi$
$911$	−30.3594	−1.00585	−0.502926	+	0.864329i	$0.667743\pi$
$912$	−0.0474874	−0.00157246
$913$	−15.6436	−0.517727
$914$	42.1322	1.39361
$915$	−5.46713	−0.180738
$916$	−0.0371926	−0.00122888
$917$	2.61287	0.0862844
$918$	−1.38255	−0.0456308
$919$	−39.7439	−1.31103	−0.655515	−	0.755182i	$-0.727548\pi$
$919$	−39.7439	−1.31103	−0.655515	+	0.755182i	$0.727548\pi$
$920$	40.4371	1.33317
$921$	−16.5041	−0.543829
$922$	−20.4456	−0.673339
$923$	13.1616	0.433220
$924$	0.0340091	0.00111882
$925$	−1.94358	−0.0639044
$926$	−31.4375	−1.03310
$927$	10.5170	0.345425
$928$	−0.324087	−0.0106387
$929$	−7.96176	−0.261217	−0.130608	−	0.991434i	$-0.541693\pi$
$929$	−7.96176	−0.261217	−0.130608	+	0.991434i	$0.541693\pi$
$930$	1.17224	0.0384392
$931$	0.0866144	0.00283867
$932$	−1.86852	−0.0612056
$933$	−0.315638	−0.0103335
$934$	−31.1686	−1.01987
$935$	4.00500	0.130978
$936$	10.2925	0.336422
$937$	0.958798	0.0313226	0.0156613	−	0.999877i	$-0.495015\pi$
$937$	0.958798	0.0313226	0.0156613	+	0.999877i	$0.495015\pi$
$938$	1.85252	0.0604870
$939$	−30.8499	−1.00675
$940$	−1.09879	−0.0358387
$941$	−15.1533	−0.493985	−0.246992	−	0.969017i	$-0.579442\pi$
$941$	−15.1533	−0.493985	−0.246992	+	0.969017i	$0.579442\pi$
$942$	−1.38255	−0.0450458
$943$	−80.8898	−2.63413
$944$	56.3640	1.83449
$945$	0.433878	0.0141141
$946$	−22.9188	−0.745155
$947$	7.54635	0.245223	0.122612	−	0.992455i	$-0.460873\pi$
$947$	7.54635	0.245223	0.122612	+	0.992455i	$0.460873\pi$
$948$	−0.227208	−0.00737937
$949$	1.61520	0.0524317
$950$	−0.00817077	−0.000265095 0
$951$	10.5058	0.340675
$952$	0.588947	0.0190879
$953$	−21.8241	−0.706951	−0.353475	−	0.935444i	$-0.615000\pi$
$953$	−21.8241	−0.706951	−0.353475	+	0.935444i	$0.615000\pi$
$954$	1.46302	0.0473670
$955$	−8.81563	−0.285267
$956$	−2.00682	−0.0649050
$957$	1.21880	0.0393981
$958$	22.7928	0.736402
$959$	2.01619	0.0651061
$960$	−17.7034	−0.571375
$961$	−30.8411	−0.994875
$962$	−20.1731	−0.650408
$963$	−1.18955	−0.0383326
$964$	−2.24919	−0.0724416
$965$	21.6899	0.698221
$966$	−1.85636	−0.0597273
$967$	−28.6063	−0.919916	−0.459958	−	0.887941i	$-0.652135\pi$
$967$	−28.6063	−0.919916	−0.459958	+	0.887941i	$0.652135\pi$
$968$	−21.5278	−0.691928
$969$	−0.0124475	−0.000399870 0
$970$	35.5920	1.14279
$971$	−11.0532	−0.354714	−0.177357	−	0.984147i	$-0.556755\pi$
$971$	−11.0532	−0.354714	−0.177357	+	0.984147i	$0.556755\pi$
$972$	0.0885651	0.00284073
$973$	3.79094	0.121532
$974$	53.1805	1.70401
$975$	1.69238	0.0541994
$976$	−9.80477	−0.313843
$977$	−2.85988	−0.0914956	−0.0457478	−	0.998953i	$-0.514567\pi$
$977$	−2.85988	−0.0914956	−0.0457478	+	0.998953i	$0.514567\pi$
$978$	3.17874	0.101645
$979$	29.3126	0.936835
$980$	1.31097	0.0418773
$981$	−0.401268	−0.0128115
$982$	−49.7632	−1.58801
$983$	−12.8749	−0.410647	−0.205323	−	0.978694i	$-0.565825\pi$
$983$	−12.8749	−0.410647	−0.205323	+	0.978694i	$0.565825\pi$
$984$	35.4804	1.13107
$985$	−16.8840	−0.537969
$986$	0.895010	0.0285029
$987$	1.18955	0.0378638
$988$	0.00392950	0.000125014 0
$989$	−57.9645	−1.84316
$990$	5.53710	0.175981
$991$	−1.74510	−0.0554349	−0.0277174	−	0.999616i	$-0.508824\pi$
$991$	−1.74510	−0.0554349	−0.0277174	+	0.999616i	$0.508824\pi$
$992$	−0.199540	−0.00633540
$993$	33.7794	1.07196
$994$	1.04122	0.0330256
$995$	−3.38229	−0.107226
$996$	0.735894	0.0233177
$997$	−3.28316	−0.103979	−0.0519894	−	0.998648i	$-0.516556\pi$
$997$	−3.28316	−0.103979	−0.0519894	+	0.998648i	$0.516556\pi$
$998$	4.40624	0.139477
$999$	−4.09354	−0.129514

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.f.1.15	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.f.1.15	✓	48	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.38255 q^{2} -1.00000 q^{3} -0.0885651 q^{4} +2.12725 q^{5} +1.38255 q^{6} -0.203962 q^{7} +2.88754 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.38255 q^{2} -1.00000 q^{3} -0.0885651 q^{4} +2.12725 q^{5} +1.38255 q^{6} -0.203962 q^{7} +2.88754 q^{8} +1.00000 q^{9} -2.94103 q^{10} -1.88271 q^{11} +0.0885651 q^{12} +3.56447 q^{13} +0.281986 q^{14} -2.12725 q^{15} -3.81503 q^{16} -1.00000 q^{17} -1.38255 q^{18} -0.0124475 q^{19} -0.188400 q^{20} +0.203962 q^{21} +2.60293 q^{22} +6.58314 q^{23} -2.88754 q^{24} -0.474791 q^{25} -4.92804 q^{26} -1.00000 q^{27} +0.0180639 q^{28} +0.647363 q^{29} +2.94103 q^{30} +0.398581 q^{31} -0.500626 q^{32} +1.88271 q^{33} +1.38255 q^{34} -0.433878 q^{35} -0.0885651 q^{36} +4.09354 q^{37} +0.0172092 q^{38} -3.56447 q^{39} +6.14253 q^{40} -12.2874 q^{41} -0.281986 q^{42} -8.80499 q^{43} +0.166742 q^{44} +2.12725 q^{45} -9.10150 q^{46} +5.83223 q^{47} +3.81503 q^{48} -6.95840 q^{49} +0.656421 q^{50} +1.00000 q^{51} -0.315687 q^{52} -1.05821 q^{53} +1.38255 q^{54} -4.00500 q^{55} -0.588947 q^{56} +0.0124475 q^{57} -0.895010 q^{58} -14.7742 q^{59} +0.188400 q^{60} +2.57004 q^{61} -0.551057 q^{62} -0.203962 q^{63} +8.32219 q^{64} +7.58252 q^{65} -2.60293 q^{66} +6.56955 q^{67} +0.0885651 q^{68} -6.58314 q^{69} +0.599857 q^{70} +3.69245 q^{71} +2.88754 q^{72} +0.453140 q^{73} -5.65951 q^{74} +0.474791 q^{75} +0.00110241 q^{76} +0.384001 q^{77} +4.92804 q^{78} -2.56543 q^{79} -8.11553 q^{80} +1.00000 q^{81} +16.9879 q^{82} +8.30907 q^{83} -0.0180639 q^{84} -2.12725 q^{85} +12.1733 q^{86} -0.647363 q^{87} -5.43640 q^{88} -15.5694 q^{89} -2.94103 q^{90} -0.727014 q^{91} -0.583036 q^{92} -0.398581 q^{93} -8.06333 q^{94} -0.0264789 q^{95} +0.500626 q^{96} -12.1019 q^{97} +9.62031 q^{98} -1.88271 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * q^99

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