LMFDB - Embedded newform 8007.2.a.g.1.4

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:	$0$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-2.51234 q^{2} -1.00000 q^{3} +4.31187 q^{4} -0.437106 q^{5} +2.51234 q^{6} +0.108032 q^{7} -5.80821 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.51234 q^{2} -1.00000 q^{3} +4.31187 q^{4} -0.437106 q^{5} +2.51234 q^{6} +0.108032 q^{7} -5.80821 q^{8} +1.00000 q^{9} +1.09816 q^{10} -3.33288 q^{11} -4.31187 q^{12} -2.46877 q^{13} -0.271415 q^{14} +0.437106 q^{15} +5.96848 q^{16} -1.00000 q^{17} -2.51234 q^{18} +5.06650 q^{19} -1.88474 q^{20} -0.108032 q^{21} +8.37333 q^{22} -1.92127 q^{23} +5.80821 q^{24} -4.80894 q^{25} +6.20240 q^{26} -1.00000 q^{27} +0.465822 q^{28} +7.75649 q^{29} -1.09816 q^{30} -9.48756 q^{31} -3.37845 q^{32} +3.33288 q^{33} +2.51234 q^{34} -0.0472217 q^{35} +4.31187 q^{36} +10.7903 q^{37} -12.7288 q^{38} +2.46877 q^{39} +2.53880 q^{40} -11.4424 q^{41} +0.271415 q^{42} +8.90451 q^{43} -14.3709 q^{44} -0.437106 q^{45} +4.82689 q^{46} -0.0366194 q^{47} -5.96848 q^{48} -6.98833 q^{49} +12.0817 q^{50} +1.00000 q^{51} -10.6450 q^{52} -8.36806 q^{53} +2.51234 q^{54} +1.45682 q^{55} -0.627475 q^{56} -5.06650 q^{57} -19.4870 q^{58} -0.584001 q^{59} +1.88474 q^{60} +12.0301 q^{61} +23.8360 q^{62} +0.108032 q^{63} -3.44914 q^{64} +1.07911 q^{65} -8.37333 q^{66} +0.0187605 q^{67} -4.31187 q^{68} +1.92127 q^{69} +0.118637 q^{70} -7.34992 q^{71} -5.80821 q^{72} -6.62891 q^{73} -27.1088 q^{74} +4.80894 q^{75} +21.8461 q^{76} -0.360059 q^{77} -6.20240 q^{78} -0.501328 q^{79} -2.60886 q^{80} +1.00000 q^{81} +28.7472 q^{82} +2.23119 q^{83} -0.465822 q^{84} +0.437106 q^{85} -22.3712 q^{86} -7.75649 q^{87} +19.3580 q^{88} -14.5691 q^{89} +1.09816 q^{90} -0.266707 q^{91} -8.28426 q^{92} +9.48756 q^{93} +0.0920004 q^{94} -2.21460 q^{95} +3.37845 q^{96} -10.3803 q^{97} +17.5571 q^{98} -3.33288 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) $ 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * 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 $

$2$	−2.51234	−1.77650	−0.888248	−	0.459365i	$-0.848077\pi$
$2$	−2.51234	−1.77650	−0.888248	+	0.459365i	$0.848077\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.31187	2.15593
$5$	−0.437106	−0.195480	−0.0977399	−	0.995212i	$-0.531161\pi$
$5$	−0.437106	−0.195480	−0.0977399	+	0.995212i	$0.531161\pi$
$6$	2.51234	1.02566
$7$	0.108032	0.0408324	0.0204162	−	0.999792i	$-0.493501\pi$
$7$	0.108032	0.0408324	0.0204162	+	0.999792i	$0.493501\pi$
$8$	−5.80821	−2.05351
$9$	1.00000	0.333333
$10$	1.09816	0.347269
$11$	−3.33288	−1.00490	−0.502450	−	0.864606i	$-0.667568\pi$
$11$	−3.33288	−1.00490	−0.502450	+	0.864606i	$0.667568\pi$
$12$	−4.31187	−1.24473
$13$	−2.46877	−0.684713	−0.342357	−	0.939570i	$-0.611225\pi$
$13$	−2.46877	−0.684713	−0.342357	+	0.939570i	$0.611225\pi$
$14$	−0.271415	−0.0725386
$15$	0.437106	0.112860
$16$	5.96848	1.49212
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.51234	−0.592165
$19$	5.06650	1.16234	0.581168	−	0.813784i	$-0.302596\pi$
$19$	5.06650	1.16234	0.581168	+	0.813784i	$0.302596\pi$
$20$	−1.88474	−0.421442
$21$	−0.108032	−0.0235746
$22$	8.37333	1.78520
$23$	−1.92127	−0.400612	−0.200306	−	0.979733i	$-0.564194\pi$
$23$	−1.92127	−0.400612	−0.200306	+	0.979733i	$0.564194\pi$
$24$	5.80821	1.18560
$25$	−4.80894	−0.961788
$26$	6.20240	1.21639
$27$	−1.00000	−0.192450
$28$	0.465822	0.0880320
$29$	7.75649	1.44034	0.720172	−	0.693796i	$-0.244063\pi$
$29$	7.75649	1.44034	0.720172	+	0.693796i	$0.244063\pi$
$30$	−1.09816	−0.200496
$31$	−9.48756	−1.70402	−0.852008	−	0.523529i	$-0.824615\pi$
$31$	−9.48756	−1.70402	−0.852008	+	0.523529i	$0.824615\pi$
$32$	−3.37845	−0.597231
$33$	3.33288	0.580179
$34$	2.51234	0.430863
$35$	−0.0472217	−0.00798192
$36$	4.31187	0.718645
$37$	10.7903	1.77391	0.886953	−	0.461859i	$-0.152817\pi$
$37$	10.7903	1.77391	0.886953	+	0.461859i	$0.152817\pi$
$38$	−12.7288	−2.06488
$39$	2.46877	0.395319
$40$	2.53880	0.401420
$41$	−11.4424	−1.78700	−0.893502	−	0.449060i	$-0.851759\pi$
$41$	−11.4424	−1.78700	−0.893502	+	0.449060i	$0.851759\pi$
$42$	0.271415	0.0418802
$43$	8.90451	1.35793	0.678963	−	0.734173i	$-0.262430\pi$
$43$	8.90451	1.35793	0.678963	+	0.734173i	$0.262430\pi$
$44$	−14.3709	−2.16650
$45$	−0.437106	−0.0651599
$46$	4.82689	0.711685
$47$	−0.0366194	−0.00534148	−0.00267074	−	0.999996i	$-0.500850\pi$
$47$	−0.0366194	−0.00534148	−0.00267074	+	0.999996i	$0.500850\pi$
$48$	−5.96848	−0.861476
$49$	−6.98833	−0.998333
$50$	12.0817	1.70861
$51$	1.00000	0.140028
$52$	−10.6450	−1.47620
$53$	−8.36806	−1.14944	−0.574720	−	0.818350i	$-0.694889\pi$
$53$	−8.36806	−1.14944	−0.574720	+	0.818350i	$0.694889\pi$
$54$	2.51234	0.341887
$55$	1.45682	0.196438
$56$	−0.627475	−0.0838499
$57$	−5.06650	−0.671075
$58$	−19.4870	−2.55876
$59$	−0.584001	−0.0760304	−0.0380152	−	0.999277i	$-0.512104\pi$
$59$	−0.584001	−0.0760304	−0.0380152	+	0.999277i	$0.512104\pi$
$60$	1.88474	0.243320
$61$	12.0301	1.54030	0.770150	−	0.637863i	$-0.220182\pi$
$61$	12.0301	1.54030	0.770150	+	0.637863i	$0.220182\pi$
$62$	23.8360	3.02718
$63$	0.108032	0.0136108
$64$	−3.44914	−0.431142
$65$	1.07911	0.133848
$66$	−8.37333	−1.03069
$67$	0.0187605	0.00229195	0.00114598	−	0.999999i	$-0.499635\pi$
$67$	0.0187605	0.00229195	0.00114598	+	0.999999i	$0.499635\pi$
$68$	−4.31187	−0.522891
$69$	1.92127	0.231294
$70$	0.118637	0.0141798
$71$	−7.34992	−0.872275	−0.436137	−	0.899880i	$-0.643654\pi$
$71$	−7.34992	−0.872275	−0.436137	+	0.899880i	$0.643654\pi$
$72$	−5.80821	−0.684504
$73$	−6.62891	−0.775856	−0.387928	−	0.921690i	$-0.626809\pi$
$73$	−6.62891	−0.775856	−0.387928	+	0.921690i	$0.626809\pi$
$74$	−27.1088	−3.15134
$75$	4.80894	0.555288
$76$	21.8461	2.50592
$77$	−0.360059	−0.0410325
$78$	−6.20240	−0.702283
$79$	−0.501328	−0.0564038	−0.0282019	−	0.999602i	$-0.508978\pi$
$79$	−0.501328	−0.0564038	−0.0282019	+	0.999602i	$0.508978\pi$
$80$	−2.60886	−0.291679
$81$	1.00000	0.111111
$82$	28.7472	3.17460
$83$	2.23119	0.244905	0.122452	−	0.992474i	$-0.460924\pi$
$83$	2.23119	0.244905	0.122452	+	0.992474i	$0.460924\pi$
$84$	−0.465822	−0.0508253
$85$	0.437106	0.0474108
$86$	−22.3712	−2.41235
$87$	−7.75649	−0.831583
$88$	19.3580	2.06357
$89$	−14.5691	−1.54432	−0.772160	−	0.635428i	$-0.780824\pi$
$89$	−14.5691	−1.54432	−0.772160	+	0.635428i	$0.780824\pi$
$90$	1.09816	0.115756
$91$	−0.266707	−0.0279585
$92$	−8.28426	−0.863694
$93$	9.48756	0.983814
$94$	0.0920004	0.00948912
$95$	−2.21460	−0.227213
$96$	3.37845	0.344811
$97$	−10.3803	−1.05396	−0.526981	−	0.849877i	$-0.676676\pi$
$97$	−10.3803	−1.05396	−0.526981	+	0.849877i	$0.676676\pi$
$98$	17.5571	1.77353
$99$	−3.33288	−0.334967
$100$	−20.7355	−2.07355
$101$	−5.71800	−0.568962	−0.284481	−	0.958682i	$-0.591821\pi$
$101$	−5.71800	−0.568962	−0.284481	+	0.958682i	$0.591821\pi$
$102$	−2.51234	−0.248759
$103$	12.4134	1.22313	0.611563	−	0.791196i	$-0.290541\pi$
$103$	12.4134	1.22313	0.611563	+	0.791196i	$0.290541\pi$
$104$	14.3391	1.40607
$105$	0.0472217	0.00460836
$106$	21.0234	2.04198
$107$	−11.4261	−1.10461	−0.552303	−	0.833644i	$-0.686251\pi$
$107$	−11.4261	−1.10461	−0.552303	+	0.833644i	$0.686251\pi$
$108$	−4.31187	−0.414910
$109$	5.14362	0.492669	0.246335	−	0.969185i	$-0.420774\pi$
$109$	5.14362	0.492669	0.246335	+	0.969185i	$0.420774\pi$
$110$	−3.66004	−0.348971
$111$	−10.7903	−1.02417
$112$	0.644789	0.0609269
$113$	2.21043	0.207940	0.103970	−	0.994580i	$-0.466845\pi$
$113$	2.21043	0.207940	0.103970	+	0.994580i	$0.466845\pi$
$114$	12.7288	1.19216
$115$	0.839798	0.0783116
$116$	33.4450	3.10529
$117$	−2.46877	−0.228238
$118$	1.46721	0.135068
$119$	−0.108032	−0.00990332
$120$	−2.53880	−0.231760
$121$	0.108071	0.00982467
$122$	−30.2238	−2.73633
$123$	11.4424	1.03173
$124$	−40.9091	−3.67375
$125$	4.28755	0.383490
$126$	−0.271415	−0.0241795
$127$	19.2128	1.70486	0.852431	−	0.522840i	$-0.175127\pi$
$127$	19.2128	1.70486	0.852431	+	0.522840i	$0.175127\pi$
$128$	15.4223	1.36315
$129$	−8.90451	−0.783999
$130$	−2.71111	−0.237780
$131$	9.68021	0.845764	0.422882	−	0.906185i	$-0.361018\pi$
$131$	9.68021	0.845764	0.422882	+	0.906185i	$0.361018\pi$
$132$	14.3709	1.25083
$133$	0.547347	0.0474610
$134$	−0.0471327	−0.00407164
$135$	0.437106	0.0376201
$136$	5.80821	0.498050
$137$	−22.7559	−1.94417	−0.972083	−	0.234637i	$-0.924610\pi$
$137$	−22.7559	−1.94417	−0.972083	+	0.234637i	$0.924610\pi$
$138$	−4.82689	−0.410892
$139$	1.51712	0.128680	0.0643401	−	0.997928i	$-0.479506\pi$
$139$	1.51712	0.128680	0.0643401	+	0.997928i	$0.479506\pi$
$140$	−0.203614	−0.0172085
$141$	0.0366194	0.00308391
$142$	18.4655	1.54959
$143$	8.22810	0.688069
$144$	5.96848	0.497373
$145$	−3.39041	−0.281558
$146$	16.6541	1.37830
$147$	6.98833	0.576388
$148$	46.5262	3.82443
$149$	19.2288	1.57529	0.787643	−	0.616132i	$-0.211301\pi$
$149$	19.2288	1.57529	0.787643	+	0.616132i	$0.211301\pi$
$150$	−12.0817	−0.986467
$151$	−12.0625	−0.981632	−0.490816	−	0.871263i	$-0.663301\pi$
$151$	−12.0625	−0.981632	−0.490816	+	0.871263i	$0.663301\pi$
$152$	−29.4273	−2.38687
$153$	−1.00000	−0.0808452
$154$	0.904592	0.0728941
$155$	4.14707	0.333101
$156$	10.6450	0.852283
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	1.25951	0.100201
$159$	8.36806	0.663630
$160$	1.47674	0.116747
$161$	−0.207559	−0.0163580
$162$	−2.51234	−0.197388
$163$	−6.71359	−0.525849	−0.262924	−	0.964816i	$-0.584687\pi$
$163$	−6.71359	−0.525849	−0.262924	+	0.964816i	$0.584687\pi$
$164$	−49.3381	−3.85266
$165$	−1.45682	−0.113413
$166$	−5.60551	−0.435072
$167$	−5.96134	−0.461303	−0.230651	−	0.973036i	$-0.574086\pi$
$167$	−5.96134	−0.461303	−0.230651	+	0.973036i	$0.574086\pi$
$168$	0.627475	0.0484108
$169$	−6.90518	−0.531168
$170$	−1.09816	−0.0842251
$171$	5.06650	0.387445
$172$	38.3951	2.92760
$173$	18.9253	1.43886	0.719432	−	0.694563i	$-0.244402\pi$
$173$	18.9253	1.43886	0.719432	+	0.694563i	$0.244402\pi$
$174$	19.4870	1.47730
$175$	−0.519521	−0.0392721
$176$	−19.8922	−1.49943
$177$	0.584001	0.0438962
$178$	36.6025	2.74348
$179$	−18.3513	−1.37164	−0.685821	−	0.727770i	$-0.740557\pi$
$179$	−18.3513	−1.37164	−0.685821	+	0.727770i	$0.740557\pi$
$180$	−1.88474	−0.140481
$181$	25.8290	1.91985	0.959925	−	0.280255i	$-0.0904192\pi$
$181$	25.8290	1.91985	0.959925	+	0.280255i	$0.0904192\pi$
$182$	0.670060	0.0496682
$183$	−12.0301	−0.889292
$184$	11.1591	0.822662
$185$	−4.71649	−0.346763
$186$	−23.8360	−1.74774
$187$	3.33288	0.243724
$188$	−0.157898	−0.0115159
$189$	−0.108032	−0.00785820
$190$	5.56384	0.403643
$191$	−4.12289	−0.298322	−0.149161	−	0.988813i	$-0.547657\pi$
$191$	−4.12289	−0.298322	−0.149161	+	0.988813i	$0.547657\pi$
$192$	3.44914	0.248920
$193$	18.9401	1.36334	0.681670	−	0.731660i	$-0.261254\pi$
$193$	18.9401	1.36334	0.681670	+	0.731660i	$0.261254\pi$
$194$	26.0789	1.87236
$195$	−1.07911	−0.0772770
$196$	−30.1328	−2.15234
$197$	2.63863	0.187995	0.0939973	−	0.995572i	$-0.470036\pi$
$197$	2.63863	0.187995	0.0939973	+	0.995572i	$0.470036\pi$
$198$	8.37333	0.595067
$199$	2.77193	0.196497	0.0982486	−	0.995162i	$-0.468676\pi$
$199$	2.77193	0.196497	0.0982486	+	0.995162i	$0.468676\pi$
$200$	27.9313	1.97504
$201$	−0.0187605	−0.00132326
$202$	14.3656	1.01076
$203$	0.837952	0.0588127
$204$	4.31187	0.301891
$205$	5.00155	0.349323
$206$	−31.1867	−2.17288
$207$	−1.92127	−0.133537
$208$	−14.7348	−1.02167
$209$	−16.8860	−1.16803
$210$	−0.118637	−0.00818673
$211$	−22.6514	−1.55939	−0.779695	−	0.626160i	$-0.784626\pi$
$211$	−22.6514	−1.55939	−0.779695	+	0.626160i	$0.784626\pi$
$212$	−36.0820	−2.47812
$213$	7.34992	0.503608
$214$	28.7064	1.96233
$215$	−3.89222	−0.265447
$216$	5.80821	0.395199
$217$	−1.02496	−0.0695791
$218$	−12.9225	−0.875224
$219$	6.62891	0.447941
$220$	6.28162	0.423507
$221$	2.46877	0.166067
$222$	27.1088	1.81943
$223$	22.1051	1.48027	0.740133	−	0.672460i	$-0.234762\pi$
$223$	22.1051	1.48027	0.740133	+	0.672460i	$0.234762\pi$
$224$	−0.364982	−0.0243864
$225$	−4.80894	−0.320596
$226$	−5.55336	−0.369404
$227$	−13.5420	−0.898813	−0.449406	−	0.893327i	$-0.648364\pi$
$227$	−13.5420	−0.898813	−0.449406	+	0.893327i	$0.648364\pi$
$228$	−21.8461	−1.44679
$229$	−0.174065	−0.0115025	−0.00575126	−	0.999983i	$-0.501831\pi$
$229$	−0.174065	−0.0115025	−0.00575126	+	0.999983i	$0.501831\pi$
$230$	−2.10986	−0.139120
$231$	0.360059	0.0236901
$232$	−45.0513	−2.95776
$233$	25.1194	1.64563	0.822814	−	0.568311i	$-0.192403\pi$
$233$	25.1194	1.64563	0.822814	+	0.568311i	$0.192403\pi$
$234$	6.20240	0.405463
$235$	0.0160066	0.00104415
$236$	−2.51814	−0.163917
$237$	0.501328	0.0325648
$238$	0.271415	0.0175932
$239$	12.6769	0.819999	0.410000	−	0.912086i	$-0.365529\pi$
$239$	12.6769	0.819999	0.410000	+	0.912086i	$0.365529\pi$
$240$	2.60886	0.168401
$241$	−18.6505	−1.20139	−0.600693	−	0.799480i	$-0.705108\pi$
$241$	−18.6505	−1.20139	−0.600693	+	0.799480i	$0.705108\pi$
$242$	−0.271512	−0.0174535
$243$	−1.00000	−0.0641500
$244$	51.8723	3.32078
$245$	3.05464	0.195154
$246$	−28.7472	−1.83286
$247$	−12.5080	−0.795867
$248$	55.1057	3.49922
$249$	−2.23119	−0.141396
$250$	−10.7718	−0.681268
$251$	−8.08868	−0.510553	−0.255277	−	0.966868i	$-0.582167\pi$
$251$	−8.08868	−0.510553	−0.255277	+	0.966868i	$0.582167\pi$
$252$	0.465822	0.0293440
$253$	6.40335	0.402575
$254$	−48.2692	−3.02868
$255$	−0.437106	−0.0273727
$256$	−31.8479	−1.99049
$257$	1.56978	0.0979200	0.0489600	−	0.998801i	$-0.484409\pi$
$257$	1.56978	0.0979200	0.0489600	+	0.998801i	$0.484409\pi$
$258$	22.3712	1.39277
$259$	1.16570	0.0724329
$260$	4.65300	0.288567
$261$	7.75649	0.480114
$262$	−24.3200	−1.50250
$263$	18.5092	1.14132	0.570662	−	0.821185i	$-0.306687\pi$
$263$	18.5092	1.14132	0.570662	+	0.821185i	$0.306687\pi$
$264$	−19.3580	−1.19141
$265$	3.65773	0.224693
$266$	−1.37512	−0.0843142
$267$	14.5691	0.891613
$268$	0.0808926	0.00494130
$269$	−28.0265	−1.70881	−0.854403	−	0.519611i	$-0.826077\pi$
$269$	−28.0265	−1.70881	−0.854403	+	0.519611i	$0.826077\pi$
$270$	−1.09816	−0.0668319
$271$	−19.3618	−1.17615	−0.588074	−	0.808807i	$-0.700114\pi$
$271$	−19.3618	−1.17615	−0.588074	+	0.808807i	$0.700114\pi$
$272$	−5.96848	−0.361892
$273$	0.266707	0.0161419
$274$	57.1706	3.45380
$275$	16.0276	0.966501
$276$	8.28426	0.498654
$277$	4.02460	0.241815	0.120907	−	0.992664i	$-0.461420\pi$
$277$	4.02460	0.241815	0.120907	+	0.992664i	$0.461420\pi$
$278$	−3.81152	−0.228600
$279$	−9.48756	−0.568005
$280$	0.274273	0.0163910
$281$	−5.30207	−0.316295	−0.158148	−	0.987415i	$-0.550552\pi$
$281$	−5.30207	−0.316295	−0.158148	+	0.987415i	$0.550552\pi$
$282$	−0.0920004	−0.00547855
$283$	−14.8477	−0.882607	−0.441303	−	0.897358i	$-0.645484\pi$
$283$	−14.8477	−0.882607	−0.441303	+	0.897358i	$0.645484\pi$
$284$	−31.6919	−1.88057
$285$	2.21460	0.131182
$286$	−20.6718	−1.22235
$287$	−1.23615	−0.0729677
$288$	−3.37845	−0.199077
$289$	1.00000	0.0588235
$290$	8.51787	0.500187
$291$	10.3803	0.608505
$292$	−28.5830	−1.67269
$293$	10.5887	0.618596	0.309298	−	0.950965i	$-0.399906\pi$
$293$	10.5887	0.618596	0.309298	+	0.950965i	$0.399906\pi$
$294$	−17.5571	−1.02395
$295$	0.255270	0.0148624
$296$	−62.6721	−3.64274
$297$	3.33288	0.193393
$298$	−48.3094	−2.79849
$299$	4.74317	0.274304
$300$	20.7355	1.19717
$301$	0.961976	0.0554474
$302$	30.3051	1.74386
$303$	5.71800	0.328490
$304$	30.2393	1.73434
$305$	−5.25844	−0.301097
$306$	2.51234	0.143621
$307$	−13.5241	−0.771863	−0.385931	−	0.922528i	$-0.626120\pi$
$307$	−13.5241	−0.771863	−0.385931	+	0.922528i	$0.626120\pi$
$308$	−1.55253	−0.0884634
$309$	−12.4134	−0.706172
$310$	−10.4189	−0.591752
$311$	−23.2009	−1.31560	−0.657801	−	0.753192i	$-0.728513\pi$
$311$	−23.2009	−1.31560	−0.657801	+	0.753192i	$0.728513\pi$
$312$	−14.3391	−0.811793
$313$	23.2265	1.31284	0.656419	−	0.754397i	$-0.272071\pi$
$313$	23.2265	1.31284	0.656419	+	0.754397i	$0.272071\pi$
$314$	−2.51234	−0.141780
$315$	−0.0472217	−0.00266064
$316$	−2.16166	−0.121603
$317$	12.9032	0.724716	0.362358	−	0.932039i	$-0.381972\pi$
$317$	12.9032	0.724716	0.362358	+	0.932039i	$0.381972\pi$
$318$	−21.0234	−1.17894
$319$	−25.8514	−1.44740
$320$	1.50764	0.0842796
$321$	11.4261	0.637744
$322$	0.521460	0.0290598
$323$	−5.06650	−0.281908
$324$	4.31187	0.239548
$325$	11.8722	0.658549
$326$	16.8668	0.934168
$327$	−5.14362	−0.284443
$328$	66.4599	3.66963
$329$	−0.00395608	−0.000218106 0
$330$	3.66004	0.201478
$331$	−29.0064	−1.59433	−0.797167	−	0.603759i	$-0.793669\pi$
$331$	−29.0064	−1.59433	−0.797167	+	0.603759i	$0.793669\pi$
$332$	9.62058	0.527998
$333$	10.7903	0.591302
$334$	14.9769	0.819502
$335$	−0.00820031	−0.000448031 0
$336$	−0.644789	−0.0351761
$337$	−19.4798	−1.06113	−0.530567	−	0.847643i	$-0.678021\pi$
$337$	−19.4798	−1.06113	−0.530567	+	0.847643i	$0.678021\pi$
$338$	17.3482	0.943617
$339$	−2.21043	−0.120054
$340$	1.88474	0.102215
$341$	31.6209	1.71237
$342$	−12.7288	−0.688295
$343$	−1.51119	−0.0815968
$344$	−51.7193	−2.78852
$345$	−0.839798	−0.0452132
$346$	−47.5469	−2.55614
$347$	8.89819	0.477680	0.238840	−	0.971059i	$-0.423233\pi$
$347$	8.89819	0.477680	0.238840	+	0.971059i	$0.423233\pi$
$348$	−33.4450	−1.79284
$349$	20.8628	1.11676	0.558379	−	0.829586i	$-0.311423\pi$
$349$	20.8628	1.11676	0.558379	+	0.829586i	$0.311423\pi$
$350$	1.30522	0.0697667
$351$	2.46877	0.131773
$352$	11.2599	0.600157
$353$	−8.52491	−0.453735	−0.226868	−	0.973926i	$-0.572848\pi$
$353$	−8.52491	−0.453735	−0.226868	+	0.973926i	$0.572848\pi$
$354$	−1.46721	−0.0779814
$355$	3.21269	0.170512
$356$	−62.8200	−3.32945
$357$	0.108032	0.00571768
$358$	46.1048	2.43672
$359$	18.2957	0.965611	0.482806	−	0.875728i	$-0.339618\pi$
$359$	18.2957	0.965611	0.482806	+	0.875728i	$0.339618\pi$
$360$	2.53880	0.133807
$361$	6.66947	0.351025
$362$	−64.8912	−3.41061
$363$	−0.108071	−0.00567228
$364$	−1.15001	−0.0602767
$365$	2.89754	0.151664
$366$	30.2238	1.57982
$367$	11.7171	0.611630	0.305815	−	0.952091i	$-0.401071\pi$
$367$	11.7171	0.611630	0.305815	+	0.952091i	$0.401071\pi$
$368$	−11.4670	−0.597761
$369$	−11.4424	−0.595668
$370$	11.8494	0.616023
$371$	−0.904022	−0.0469345
$372$	40.9091	2.12104
$373$	−20.7871	−1.07632	−0.538158	−	0.842844i	$-0.680880\pi$
$373$	−20.7871	−1.07632	−0.538158	+	0.842844i	$0.680880\pi$
$374$	−8.37333	−0.432975
$375$	−4.28755	−0.221408
$376$	0.212693	0.0109688
$377$	−19.1490	−0.986222
$378$	0.271415	0.0139601
$379$	15.5499	0.798746	0.399373	−	0.916789i	$-0.369228\pi$
$379$	15.5499	0.798746	0.399373	+	0.916789i	$0.369228\pi$
$380$	−9.54907	−0.489857
$381$	−19.2128	−0.984303
$382$	10.3581	0.529968
$383$	−28.7863	−1.47091	−0.735457	−	0.677572i	$-0.763032\pi$
$383$	−28.7863	−1.47091	−0.735457	+	0.677572i	$0.763032\pi$
$384$	−15.4223	−0.787016
$385$	0.157384	0.00802103
$386$	−47.5841	−2.42197
$387$	8.90451	0.452642
$388$	−44.7586	−2.27227
$389$	29.8531	1.51361	0.756806	−	0.653640i	$-0.226759\pi$
$389$	29.8531	1.51361	0.756806	+	0.653640i	$0.226759\pi$
$390$	2.71111	0.137282
$391$	1.92127	0.0971627
$392$	40.5897	2.05009
$393$	−9.68021	−0.488302
$394$	−6.62914	−0.333971
$395$	0.219134	0.0110258
$396$	−14.3709	−0.722166
$397$	2.76816	0.138930	0.0694650	−	0.997584i	$-0.477871\pi$
$397$	2.76816	0.138930	0.0694650	+	0.997584i	$0.477871\pi$
$398$	−6.96405	−0.349076
$399$	−0.547347	−0.0274016
$400$	−28.7020	−1.43510
$401$	0.323174	0.0161386	0.00806928	−	0.999967i	$-0.497431\pi$
$401$	0.323174	0.0161386	0.00806928	+	0.999967i	$0.497431\pi$
$402$	0.0471327	0.00235077
$403$	23.4226	1.16676
$404$	−24.6553	−1.22664
$405$	−0.437106	−0.0217200
$406$	−2.10522	−0.104480
$407$	−35.9626	−1.78260
$408$	−5.80821	−0.287549
$409$	−16.4656	−0.814170	−0.407085	−	0.913390i	$-0.633455\pi$
$409$	−16.4656	−0.814170	−0.407085	+	0.913390i	$0.633455\pi$
$410$	−12.5656	−0.620571
$411$	22.7559	1.12246
$412$	53.5248	2.63698
$413$	−0.0630910	−0.00310451
$414$	4.82689	0.237228
$415$	−0.975265	−0.0478739
$416$	8.34061	0.408932
$417$	−1.51712	−0.0742936
$418$	42.4235	2.07500
$419$	5.67002	0.276999	0.138499	−	0.990363i	$-0.455772\pi$
$419$	5.67002	0.276999	0.138499	+	0.990363i	$0.455772\pi$
$420$	0.203614	0.00993533
$421$	1.18201	0.0576076	0.0288038	−	0.999585i	$-0.490830\pi$
$421$	1.18201	0.0576076	0.0288038	+	0.999585i	$0.490830\pi$
$422$	56.9082	2.77025
$423$	−0.0366194	−0.00178049
$424$	48.6034	2.36039
$425$	4.80894	0.233268
$426$	−18.4655	−0.894657
$427$	1.29964	0.0628942
$428$	−49.2680	−2.38146
$429$	−8.22810	−0.397257
$430$	9.77859	0.471565
$431$	32.1784	1.54998	0.774989	−	0.631975i	$-0.217756\pi$
$431$	32.1784	1.54998	0.774989	+	0.631975i	$0.217756\pi$
$432$	−5.96848	−0.287159
$433$	21.9089	1.05287	0.526437	−	0.850214i	$-0.323528\pi$
$433$	21.9089	1.05287	0.526437	+	0.850214i	$0.323528\pi$
$434$	2.57506	0.123607
$435$	3.39041	0.162558
$436$	22.1786	1.06216
$437$	−9.73411	−0.465646
$438$	−16.6541	−0.795764
$439$	3.55830	0.169828	0.0849142	−	0.996388i	$-0.472938\pi$
$439$	3.55830	0.169828	0.0849142	+	0.996388i	$0.472938\pi$
$440$	−8.46152	−0.403387
$441$	−6.98833	−0.332778
$442$	−6.20240	−0.295018
$443$	−5.03557	−0.239247	−0.119624	−	0.992819i	$-0.538169\pi$
$443$	−5.03557	−0.239247	−0.119624	+	0.992819i	$0.538169\pi$
$444$	−46.5262	−2.20803
$445$	6.36824	0.301883
$446$	−55.5356	−2.62969
$447$	−19.2288	−0.909491
$448$	−0.372619	−0.0176046
$449$	10.5999	0.500242	0.250121	−	0.968215i	$-0.419530\pi$
$449$	10.5999	0.500242	0.250121	+	0.968215i	$0.419530\pi$
$450$	12.0817	0.569537
$451$	38.1361	1.79576
$452$	9.53109	0.448305
$453$	12.0625	0.566745
$454$	34.0221	1.59674
$455$	0.116579	0.00546532
$456$	29.4273	1.37806
$457$	15.4525	0.722837	0.361419	−	0.932404i	$-0.382293\pi$
$457$	15.4525	0.722837	0.361419	+	0.932404i	$0.382293\pi$
$458$	0.437310	0.0204342
$459$	1.00000	0.0466760
$460$	3.62110	0.168835
$461$	−34.1344	−1.58980	−0.794899	−	0.606741i	$-0.792476\pi$
$461$	−34.1344	−1.58980	−0.794899	+	0.606741i	$0.792476\pi$
$462$	−0.904592	−0.0420854
$463$	−8.89319	−0.413302	−0.206651	−	0.978415i	$-0.566256\pi$
$463$	−8.89319	−0.413302	−0.206651	+	0.978415i	$0.566256\pi$
$464$	46.2944	2.14916
$465$	−4.14707	−0.192316
$466$	−63.1086	−2.92345
$467$	−18.1261	−0.838776	−0.419388	−	0.907807i	$-0.637755\pi$
$467$	−18.1261	−0.838776	−0.419388	+	0.907807i	$0.637755\pi$
$468$	−10.6450	−0.492066
$469$	0.00202674	9.35860e−5 0
$470$	−0.0402140	−0.00185493
$471$	−1.00000	−0.0460776
$472$	3.39200	0.156129
$473$	−29.6776	−1.36458
$474$	−1.25951	−0.0578511
$475$	−24.3645	−1.11792
$476$	−0.465822	−0.0213509
$477$	−8.36806	−0.383147
$478$	−31.8487	−1.45672
$479$	−10.3317	−0.472065	−0.236033	−	0.971745i	$-0.575847\pi$
$479$	−10.3317	−0.472065	−0.236033	+	0.971745i	$0.575847\pi$
$480$	−1.47674	−0.0674037
$481$	−26.6386	−1.21462
$482$	46.8565	2.13426
$483$	0.207559	0.00944428
$484$	0.465990	0.0211814
$485$	4.53730	0.206028
$486$	2.51234	0.113962
$487$	0.817676	0.0370524	0.0185262	−	0.999828i	$-0.494103\pi$
$487$	0.817676	0.0370524	0.0185262	+	0.999828i	$0.494103\pi$
$488$	−69.8735	−3.16302
$489$	6.71359	0.303599
$490$	−7.67431	−0.346690
$491$	−24.0310	−1.08451	−0.542253	−	0.840216i	$-0.682428\pi$
$491$	−24.0310	−1.08451	−0.542253	+	0.840216i	$0.682428\pi$
$492$	49.3381	2.22434
$493$	−7.75649	−0.349335
$494$	31.4245	1.41385
$495$	1.45682	0.0654793
$496$	−56.6263	−2.54260
$497$	−0.794029	−0.0356171
$498$	5.60551	0.251189
$499$	−2.32187	−0.103941	−0.0519706	−	0.998649i	$-0.516550\pi$
$499$	−2.32187	−0.103941	−0.0519706	+	0.998649i	$0.516550\pi$
$500$	18.4873	0.826779
$501$	5.96134	0.266333
$502$	20.3215	0.906995
$503$	−12.7501	−0.568497	−0.284249	−	0.958751i	$-0.591744\pi$
$503$	−12.7501	−0.568497	−0.284249	+	0.958751i	$0.591744\pi$
$504$	−0.627475	−0.0279500
$505$	2.49937	0.111221
$506$	−16.0874	−0.715173
$507$	6.90518	0.306670
$508$	82.8432	3.67557
$509$	31.5196	1.39708	0.698540	−	0.715571i	$-0.253834\pi$
$509$	31.5196	1.39708	0.698540	+	0.715571i	$0.253834\pi$
$510$	1.09816	0.0486274
$511$	−0.716138	−0.0316801
$512$	49.1682	2.17295
$513$	−5.06650	−0.223692
$514$	−3.94382	−0.173954
$515$	−5.42596	−0.239097
$516$	−38.3951	−1.69025
$517$	0.122048	0.00536766
$518$	−2.92863	−0.128677
$519$	−18.9253	−0.830729
$520$	−6.26772	−0.274858
$521$	20.3723	0.892527	0.446263	−	0.894902i	$-0.352754\pi$
$521$	20.3723	0.892527	0.446263	+	0.894902i	$0.352754\pi$
$522$	−19.4870	−0.852921
$523$	−16.8880	−0.738462	−0.369231	−	0.929338i	$-0.620379\pi$
$523$	−16.8880	−0.738462	−0.369231	+	0.929338i	$0.620379\pi$
$524$	41.7398	1.82341
$525$	0.519521	0.0226738
$526$	−46.5014	−2.02756
$527$	9.48756	0.413285
$528$	19.8922	0.865697
$529$	−19.3087	−0.839510
$530$	−9.18947	−0.399165
$531$	−0.584001	−0.0253435
$532$	2.36009	0.102323
$533$	28.2487	1.22358
$534$	−36.6025	−1.58395
$535$	4.99443	0.215928
$536$	−0.108965	−0.00470655
$537$	18.3513	0.791918
$538$	70.4122	3.03569
$539$	23.2912	1.00322
$540$	1.88474	0.0811065
$541$	7.65519	0.329122	0.164561	−	0.986367i	$-0.447379\pi$
$541$	7.65519	0.329122	0.164561	+	0.986367i	$0.447379\pi$
$542$	48.6436	2.08942
$543$	−25.8290	−1.10843
$544$	3.37845	0.144850
$545$	−2.24831	−0.0963069
$546$	−0.670060	−0.0286759
$547$	−16.4894	−0.705036	−0.352518	−	0.935805i	$-0.614674\pi$
$547$	−16.4894	−0.705036	−0.352518	+	0.935805i	$0.614674\pi$
$548$	−98.1204	−4.19150
$549$	12.0301	0.513433
$550$	−40.2668	−1.71698
$551$	39.2983	1.67416
$552$	−11.1591	−0.474964
$553$	−0.0541597	−0.00230311
$554$	−10.1112	−0.429583
$555$	4.71649	0.200204
$556$	6.54161	0.277426
$557$	−35.7069	−1.51295	−0.756475	−	0.654023i	$-0.773080\pi$
$557$	−35.7069	−1.51295	−0.756475	+	0.654023i	$0.773080\pi$
$558$	23.8360	1.00906
$559$	−21.9832	−0.929790
$560$	−0.281841	−0.0119100
$561$	−3.33288	−0.140714
$562$	13.3206	0.561897
$563$	37.2869	1.57145	0.785727	−	0.618574i	$-0.212289\pi$
$563$	37.2869	1.57145	0.785727	+	0.618574i	$0.212289\pi$
$564$	0.157898	0.00664870
$565$	−0.966193	−0.0406480
$566$	37.3026	1.56795
$567$	0.108032	0.00453694
$568$	42.6899	1.79123
$569$	17.8488	0.748261	0.374131	−	0.927376i	$-0.377941\pi$
$569$	17.8488	0.748261	0.374131	+	0.927376i	$0.377941\pi$
$570$	−5.56384	−0.233044
$571$	29.7841	1.24642	0.623212	−	0.782053i	$-0.285827\pi$
$571$	29.7841	1.24642	0.623212	+	0.782053i	$0.285827\pi$
$572$	35.4785	1.48343
$573$	4.12289	0.172236
$574$	3.10564	0.129627
$575$	9.23926	0.385304
$576$	−3.44914	−0.143714
$577$	−17.8898	−0.744762	−0.372381	−	0.928080i	$-0.621459\pi$
$577$	−17.8898	−0.744762	−0.372381	+	0.928080i	$0.621459\pi$
$578$	−2.51234	−0.104500
$579$	−18.9401	−0.787125
$580$	−14.6190	−0.607021
$581$	0.241041	0.0100000
$582$	−26.0789	−1.08101
$583$	27.8897	1.15507
$584$	38.5021	1.59323
$585$	1.07911	0.0446159
$586$	−26.6023	−1.09893
$587$	24.2026	0.998949	0.499474	−	0.866329i	$-0.333526\pi$
$587$	24.2026	0.998949	0.499474	+	0.866329i	$0.333526\pi$
$588$	30.1328	1.24265
$589$	−48.0688	−1.98064
$590$	−0.641327	−0.0264030
$591$	−2.63863	−0.108539
$592$	64.4014	2.64688
$593$	0.690969	0.0283747	0.0141873	−	0.999899i	$-0.495484\pi$
$593$	0.690969	0.0283747	0.0141873	+	0.999899i	$0.495484\pi$
$594$	−8.37333	−0.343562
$595$	0.0472217	0.00193590
$596$	82.9121	3.39621
$597$	−2.77193	−0.113448
$598$	−11.9165	−0.487301
$599$	28.8118	1.17722	0.588608	−	0.808418i	$-0.299676\pi$
$599$	28.8118	1.17722	0.588608	+	0.808418i	$0.299676\pi$
$600$	−27.9313	−1.14029
$601$	34.1276	1.39209	0.696046	−	0.717997i	$-0.254941\pi$
$601$	34.1276	1.39209	0.696046	+	0.717997i	$0.254941\pi$
$602$	−2.41681	−0.0985020
$603$	0.0187605	0.000763985 0
$604$	−52.0119	−2.11633
$605$	−0.0472387	−0.00192053
$606$	−14.3656	−0.583562
$607$	−37.0247	−1.50279	−0.751394	−	0.659854i	$-0.770618\pi$
$607$	−37.0247	−1.50279	−0.751394	+	0.659854i	$0.770618\pi$
$608$	−17.1169	−0.694183
$609$	−0.837952	−0.0339555
$610$	13.2110	0.534898
$611$	0.0904048	0.00365739
$612$	−4.31187	−0.174297
$613$	22.3444	0.902480	0.451240	−	0.892403i	$-0.350982\pi$
$613$	22.3444	0.902480	0.451240	+	0.892403i	$0.350982\pi$
$614$	33.9772	1.37121
$615$	−5.00155	−0.201682
$616$	2.09130	0.0842608
$617$	16.0260	0.645184	0.322592	−	0.946538i	$-0.395446\pi$
$617$	16.0260	0.645184	0.322592	+	0.946538i	$0.395446\pi$
$618$	31.1867	1.25451
$619$	13.5733	0.545558	0.272779	−	0.962077i	$-0.412057\pi$
$619$	13.5733	0.545558	0.272779	+	0.962077i	$0.412057\pi$
$620$	17.8816	0.718144
$621$	1.92127	0.0770978
$622$	58.2886	2.33716
$623$	−1.57393	−0.0630583
$624$	14.7348	0.589864
$625$	22.1706	0.886823
$626$	−58.3528	−2.33225
$627$	16.8860	0.674363
$628$	4.31187	0.172062
$629$	−10.7903	−0.430236
$630$	0.118637	0.00472661
$631$	−3.39498	−0.135152	−0.0675761	−	0.997714i	$-0.521527\pi$
$631$	−3.39498	−0.135152	−0.0675761	+	0.997714i	$0.521527\pi$
$632$	2.91182	0.115826
$633$	22.6514	0.900314
$634$	−32.4173	−1.28745
$635$	−8.39804	−0.333266
$636$	36.0820	1.43074
$637$	17.2526	0.683572
$638$	64.9476	2.57130
$639$	−7.34992	−0.290758
$640$	−6.74119	−0.266469
$641$	−20.1066	−0.794165	−0.397082	−	0.917783i	$-0.629977\pi$
$641$	−20.1066	−0.794165	−0.397082	+	0.917783i	$0.629977\pi$
$642$	−28.7064	−1.13295
$643$	15.1554	0.597669	0.298834	−	0.954305i	$-0.403402\pi$
$643$	15.1554	0.597669	0.298834	+	0.954305i	$0.403402\pi$
$644$	−0.894969	−0.0352667
$645$	3.89222	0.153256
$646$	12.7288	0.500808
$647$	12.6138	0.495901	0.247950	−	0.968773i	$-0.420243\pi$
$647$	12.6138	0.495901	0.247950	+	0.968773i	$0.420243\pi$
$648$	−5.80821	−0.228168
$649$	1.94640	0.0764030
$650$	−29.8269	−1.16991
$651$	1.02496	0.0401715
$652$	−28.9481	−1.13370
$653$	−0.0165002	−0.000645705 0	−0.000322852	−	1.00000i	$-0.500103\pi$
$653$	−0.0165002	−0.000645705 0	−0.000322852		1.00000i	$0.500103\pi$
$654$	12.9225	0.505311
$655$	−4.23128	−0.165330
$656$	−68.2937	−2.66642
$657$	−6.62891	−0.258619
$658$	0.00993903	0.000387464 0
$659$	37.1176	1.44590	0.722948	−	0.690902i	$-0.242787\pi$
$659$	37.1176	1.44590	0.722948	+	0.690902i	$0.242787\pi$
$660$	−6.28162	−0.244512
$661$	−8.46477	−0.329241	−0.164621	−	0.986357i	$-0.552640\pi$
$661$	−8.46477	−0.329241	−0.164621	+	0.986357i	$0.552640\pi$
$662$	72.8740	2.83233
$663$	−2.46877	−0.0958790
$664$	−12.9592	−0.502914
$665$	−0.239249	−0.00927767
$666$	−27.1088	−1.05045
$667$	−14.9023	−0.577019
$668$	−25.7045	−0.994538
$669$	−22.1051	−0.854632
$670$	0.0206020	0.000795924 0
$671$	−40.0949	−1.54785
$672$	0.364982	0.0140795
$673$	15.9467	0.614700	0.307350	−	0.951597i	$-0.400558\pi$
$673$	15.9467	0.614700	0.307350	+	0.951597i	$0.400558\pi$
$674$	48.9401	1.88510
$675$	4.80894	0.185096
$676$	−29.7742	−1.14516
$677$	1.97543	0.0759220	0.0379610	−	0.999279i	$-0.487914\pi$
$677$	1.97543	0.0759220	0.0379610	+	0.999279i	$0.487914\pi$
$678$	5.55336	0.213276
$679$	−1.12141	−0.0430358
$680$	−2.53880	−0.0973587
$681$	13.5420	0.518930
$682$	−79.4425	−3.04201
$683$	41.2907	1.57995	0.789973	−	0.613142i	$-0.210095\pi$
$683$	41.2907	1.57995	0.789973	+	0.613142i	$0.210095\pi$
$684$	21.8461	0.835307
$685$	9.94674	0.380045
$686$	3.79664	0.144956
$687$	0.174065	0.00664099
$688$	53.1464	2.02619
$689$	20.6588	0.787038
$690$	2.10986	0.0803211
$691$	−8.21369	−0.312463	−0.156232	−	0.987720i	$-0.549935\pi$
$691$	−8.21369	−0.312463	−0.156232	+	0.987720i	$0.549935\pi$
$692$	81.6035	3.10210
$693$	−0.360059	−0.0136775
$694$	−22.3553	−0.848596
$695$	−0.663142	−0.0251544
$696$	45.0513	1.70766
$697$	11.4424	0.433412
$698$	−52.4144	−1.98392
$699$	−25.1194	−0.950103
$700$	−2.24011	−0.0846681
$701$	30.1678	1.13942	0.569712	−	0.821845i	$-0.307055\pi$
$701$	30.1678	1.13942	0.569712	+	0.821845i	$0.307055\pi$
$702$	−6.20240	−0.234094
$703$	54.6689	2.06188
$704$	11.4956	0.433255
$705$	−0.0160066	−0.000602842 0
$706$	21.4175	0.806058
$707$	−0.617729	−0.0232321
$708$	2.51814	0.0946373
$709$	26.4395	0.992956	0.496478	−	0.868049i	$-0.334626\pi$
$709$	26.4395	0.992956	0.496478	+	0.868049i	$0.334626\pi$
$710$	−8.07139	−0.302914
$711$	−0.501328	−0.0188013
$712$	84.6203	3.17128
$713$	18.2281	0.682650
$714$	−0.271415	−0.0101574
$715$	−3.59656	−0.134504
$716$	−79.1285	−2.95717
$717$	−12.6769	−0.473427
$718$	−45.9651	−1.71540
$719$	−22.0964	−0.824055	−0.412027	−	0.911171i	$-0.635179\pi$
$719$	−22.0964	−0.824055	−0.412027	+	0.911171i	$0.635179\pi$
$720$	−2.60886	−0.0972264
$721$	1.34105	0.0499432
$722$	−16.7560	−0.623594
$723$	18.6505	0.693620
$724$	111.371	4.13907
$725$	−37.3005	−1.38530
$726$	0.271512	0.0100768
$727$	−0.866140	−0.0321234	−0.0160617	−	0.999871i	$-0.505113\pi$
$727$	−0.866140	−0.0321234	−0.0160617	+	0.999871i	$0.505113\pi$
$728$	1.54909	0.0574131
$729$	1.00000	0.0370370
$730$	−7.27962	−0.269431
$731$	−8.90451	−0.329345
$732$	−51.8723	−1.91726
$733$	33.9836	1.25521	0.627606	−	0.778531i	$-0.284035\pi$
$733$	33.9836	1.25521	0.627606	+	0.778531i	$0.284035\pi$
$734$	−29.4375	−1.08656
$735$	−3.05464	−0.112672
$736$	6.49090	0.239258
$737$	−0.0625263	−0.00230319
$738$	28.7472	1.05820
$739$	19.9294	0.733116	0.366558	−	0.930395i	$-0.380536\pi$
$739$	19.9294	0.733116	0.366558	+	0.930395i	$0.380536\pi$
$740$	−20.3369	−0.747598
$741$	12.5080	0.459494
$742$	2.27121	0.0833788
$743$	42.1072	1.54476	0.772382	−	0.635158i	$-0.219065\pi$
$743$	42.1072	1.54476	0.772382	+	0.635158i	$0.219065\pi$
$744$	−55.1057	−2.02027
$745$	−8.40503	−0.307937
$746$	52.2243	1.91207
$747$	2.23119	0.0816348
$748$	14.3709	0.525453
$749$	−1.23439	−0.0451037
$750$	10.7718	0.393330
$751$	−40.9200	−1.49319	−0.746596	−	0.665278i	$-0.768313\pi$
$751$	−40.9200	−1.49319	−0.746596	+	0.665278i	$0.768313\pi$
$752$	−0.218562	−0.00797013
$753$	8.08868	0.294768
$754$	48.1088	1.75202
$755$	5.27259	0.191889
$756$	−0.465822	−0.0169418
$757$	19.6785	0.715227	0.357613	−	0.933870i	$-0.383591\pi$
$757$	19.6785	0.715227	0.357613	+	0.933870i	$0.383591\pi$
$758$	−39.0667	−1.41897
$759$	−6.40335	−0.232427
$760$	12.8629	0.466585
$761$	3.25522	0.118002	0.0590008	−	0.998258i	$-0.481209\pi$
$761$	3.25522	0.118002	0.0590008	+	0.998258i	$0.481209\pi$
$762$	48.2692	1.74861
$763$	0.555677	0.0201169
$764$	−17.7774	−0.643163
$765$	0.437106	0.0158036
$766$	72.3212	2.61307
$767$	1.44176	0.0520591
$768$	31.8479	1.14921
$769$	−43.0016	−1.55068	−0.775338	−	0.631546i	$-0.782421\pi$
$769$	−43.0016	−1.55068	−0.775338	+	0.631546i	$0.782421\pi$
$770$	−0.395403	−0.0142493
$771$	−1.56978	−0.0565341
$772$	81.6673	2.93927
$773$	47.9910	1.72612	0.863058	−	0.505106i	$-0.168546\pi$
$773$	47.9910	1.72612	0.863058	+	0.505106i	$0.168546\pi$
$774$	−22.3712	−0.804116
$775$	45.6251	1.63890
$776$	60.2911	2.16432
$777$	−1.16570	−0.0418192
$778$	−75.0012	−2.68892
$779$	−57.9730	−2.07710
$780$	−4.65300	−0.166604
$781$	24.4964	0.876549
$782$	−4.82689	−0.172609
$783$	−7.75649	−0.277194
$784$	−41.7097	−1.48963
$785$	−0.437106	−0.0156010
$786$	24.3200	0.867466
$787$	−15.6480	−0.557792	−0.278896	−	0.960321i	$-0.589968\pi$
$787$	−15.6480	−0.557792	−0.278896	+	0.960321i	$0.589968\pi$
$788$	11.3774	0.405304
$789$	−18.5092	−0.658944
$790$	−0.550539	−0.0195873
$791$	0.238798	0.00849069
$792$	19.3580	0.687858
$793$	−29.6996	−1.05466
$794$	−6.95457	−0.246808
$795$	−3.65773	−0.129726
$796$	11.9522	0.423635
$797$	7.30793	0.258860	0.129430	−	0.991589i	$-0.458685\pi$
$797$	7.30793	0.258860	0.129430	+	0.991589i	$0.458685\pi$
$798$	1.37512	0.0486788
$799$	0.0366194	0.00129550
$800$	16.2467	0.574409
$801$	−14.5691	−0.514773
$802$	−0.811925	−0.0286701
$803$	22.0934	0.779658
$804$	−0.0808926	−0.00285286
$805$	0.0907255	0.00319765
$806$	−58.8456	−2.07275
$807$	28.0265	0.986580
$808$	33.2113	1.16837
$809$	−49.1713	−1.72877	−0.864385	−	0.502831i	$-0.832292\pi$
$809$	−49.1713	−1.72877	−0.864385	+	0.502831i	$0.832292\pi$
$810$	1.09816	0.0385854
$811$	51.9222	1.82324	0.911618	−	0.411038i	$-0.134834\pi$
$811$	51.9222	1.82324	0.911618	+	0.411038i	$0.134834\pi$
$812$	3.61314	0.126796
$813$	19.3618	0.679049
$814$	90.3504	3.16678
$815$	2.93455	0.102793
$816$	5.96848	0.208939
$817$	45.1148	1.57837
$818$	41.3672	1.44637
$819$	−0.266707	−0.00931950
$820$	21.5660	0.753118
$821$	4.34174	0.151528	0.0757639	−	0.997126i	$-0.475860\pi$
$821$	4.34174	0.151528	0.0757639	+	0.997126i	$0.475860\pi$
$822$	−57.1706	−1.99405
$823$	9.68735	0.337680	0.168840	−	0.985643i	$-0.445998\pi$
$823$	9.68735	0.337680	0.168840	+	0.985643i	$0.445998\pi$
$824$	−72.0995	−2.51170
$825$	−16.0276	−0.558009
$826$	0.158506	0.00551514
$827$	19.5242	0.678924	0.339462	−	0.940620i	$-0.389755\pi$
$827$	19.5242	0.678924	0.339462	+	0.940620i	$0.389755\pi$
$828$	−8.28426	−0.287898
$829$	−17.0398	−0.591817	−0.295909	−	0.955216i	$-0.595622\pi$
$829$	−17.0398	−0.591817	−0.295909	+	0.955216i	$0.595622\pi$
$830$	2.45020	0.0850477
$831$	−4.02460	−0.139612
$832$	8.51512	0.295209
$833$	6.98833	0.242131
$834$	3.81152	0.131982
$835$	2.60574	0.0901753
$836$	−72.8104	−2.51820
$837$	9.48756	0.327938
$838$	−14.2450	−0.492087
$839$	20.7595	0.716696	0.358348	−	0.933588i	$-0.383340\pi$
$839$	20.7595	0.716696	0.358348	+	0.933588i	$0.383340\pi$
$840$	−0.274273	−0.00946333
$841$	31.1631	1.07459
$842$	−2.96961	−0.102340
$843$	5.30207	0.182613
$844$	−97.6701	−3.36194
$845$	3.01830	0.103833
$846$	0.0920004	0.00316304
$847$	0.0116752	0.000401165 0
$848$	−49.9446	−1.71510
$849$	14.8477	0.509573
$850$	−12.0817	−0.414399
$851$	−20.7310	−0.710649
$852$	31.6919	1.08575
$853$	−8.95799	−0.306716	−0.153358	−	0.988171i	$-0.549009\pi$
$853$	−8.95799	−0.306716	−0.153358	+	0.988171i	$0.549009\pi$
$854$	−3.26515	−0.111731
$855$	−2.21460	−0.0757377
$856$	66.3653	2.26832
$857$	42.1449	1.43964	0.719822	−	0.694159i	$-0.244223\pi$
$857$	42.1449	1.43964	0.719822	+	0.694159i	$0.244223\pi$
$858$	20.6718	0.705724
$859$	44.4253	1.51577	0.757887	−	0.652386i	$-0.226232\pi$
$859$	44.4253	1.51577	0.757887	+	0.652386i	$0.226232\pi$
$860$	−16.7827	−0.572287
$861$	1.23615	0.0421279
$862$	−80.8431	−2.75353
$863$	−50.1719	−1.70787	−0.853936	−	0.520378i	$-0.825791\pi$
$863$	−50.1719	−1.70787	−0.853936	+	0.520378i	$0.825791\pi$
$864$	3.37845	0.114937
$865$	−8.27237	−0.281269
$866$	−55.0426	−1.87042
$867$	−1.00000	−0.0339618
$868$	−4.41951	−0.150008
$869$	1.67087	0.0566802
$870$	−8.51787	−0.288783
$871$	−0.0463152	−0.00156933
$872$	−29.8752	−1.01170
$873$	−10.3803	−0.351321
$874$	24.4554	0.827218
$875$	0.463194	0.0156588
$876$	28.5830	0.965731
$877$	14.5339	0.490773	0.245387	−	0.969425i	$-0.421085\pi$
$877$	14.5339	0.490773	0.245387	+	0.969425i	$0.421085\pi$
$878$	−8.93967	−0.301699
$879$	−10.5887	−0.357146
$880$	8.69501	0.293109
$881$	8.71664	0.293671	0.146836	−	0.989161i	$-0.453091\pi$
$881$	8.71664	0.293671	0.146836	+	0.989161i	$0.453091\pi$
$882$	17.5571	0.591178
$883$	−22.1317	−0.744790	−0.372395	−	0.928074i	$-0.621463\pi$
$883$	−22.1317	−0.744790	−0.372395	+	0.928074i	$0.621463\pi$
$884$	10.6450	0.358030
$885$	−0.255270	−0.00858082
$886$	12.6511	0.425022
$887$	−7.83620	−0.263114	−0.131557	−	0.991309i	$-0.541998\pi$
$887$	−7.83620	−0.263114	−0.131557	+	0.991309i	$0.541998\pi$
$888$	62.6721	2.10314
$889$	2.07561	0.0696137
$890$	−15.9992	−0.536294
$891$	−3.33288	−0.111656
$892$	95.3143	3.19136
$893$	−0.185532	−0.00620860
$894$	48.3094	1.61571
$895$	8.02148	0.268128
$896$	1.66611	0.0556608
$897$	−4.74317	−0.158370
$898$	−26.6307	−0.888677
$899$	−73.5901	−2.45437
$900$	−20.7355	−0.691184
$901$	8.36806	0.278780
$902$	−95.8110	−3.19016
$903$	−0.961976	−0.0320126
$904$	−12.8386	−0.427007
$905$	−11.2900	−0.375292
$906$	−30.3051	−1.00682
$907$	35.4805	1.17811	0.589056	−	0.808092i	$-0.299500\pi$
$907$	35.4805	1.17811	0.589056	+	0.808092i	$0.299500\pi$
$908$	−58.3912	−1.93778
$909$	−5.71800	−0.189654
$910$	−0.292887	−0.00970912
$911$	−11.4865	−0.380566	−0.190283	−	0.981729i	$-0.560941\pi$
$911$	−11.4865	−0.380566	−0.190283	+	0.981729i	$0.560941\pi$
$912$	−30.2393	−1.00132
$913$	−7.43627	−0.246105
$914$	−38.8220	−1.28412
$915$	5.25844	0.173839
$916$	−0.750545	−0.0247987
$917$	1.04578	0.0345346
$918$	−2.51234	−0.0829197
$919$	24.9647	0.823509	0.411754	−	0.911295i	$-0.364916\pi$
$919$	24.9647	0.823509	0.411754	+	0.911295i	$0.364916\pi$
$920$	−4.87772	−0.160814
$921$	13.5241	0.445635
$922$	85.7574	2.82427
$923$	18.1452	0.597258
$924$	1.55253	0.0510744
$925$	−51.8897	−1.70612
$926$	22.3427	0.734228
$927$	12.4134	0.407709
$928$	−26.2049	−0.860217
$929$	−31.2550	−1.02544	−0.512722	−	0.858555i	$-0.671363\pi$
$929$	−31.2550	−1.02544	−0.512722	+	0.858555i	$0.671363\pi$
$930$	10.4189	0.341648
$931$	−35.4064	−1.16040
$932$	108.312	3.54787
$933$	23.2009	0.759563
$934$	45.5390	1.49008
$935$	−1.45682	−0.0476432
$936$	14.3391	0.468689
$937$	−34.0219	−1.11145	−0.555723	−	0.831367i	$-0.687559\pi$
$937$	−34.0219	−1.11145	−0.555723	+	0.831367i	$0.687559\pi$
$938$	−0.00509186	−0.000166255 0
$939$	−23.2265	−0.757967
$940$	0.0690182	0.00225112
$941$	−11.4973	−0.374802	−0.187401	−	0.982284i	$-0.560006\pi$
$941$	−11.4973	−0.374802	−0.187401	+	0.982284i	$0.560006\pi$
$942$	2.51234	0.0818566
$943$	21.9839	0.715895
$944$	−3.48560	−0.113446
$945$	0.0472217	0.00153612
$946$	74.5604	2.42417
$947$	−4.11215	−0.133627	−0.0668134	−	0.997765i	$-0.521283\pi$
$947$	−4.11215	−0.133627	−0.0668134	+	0.997765i	$0.521283\pi$
$948$	2.16166	0.0702075
$949$	16.3653	0.531239
$950$	61.2120	1.98598
$951$	−12.9032	−0.418415
$952$	0.627475	0.0203366
$953$	14.0640	0.455578	0.227789	−	0.973711i	$-0.426850\pi$
$953$	14.0640	0.455578	0.227789	+	0.973711i	$0.426850\pi$
$954$	21.0234	0.680659
$955$	1.80214	0.0583159
$956$	54.6610	1.76786
$957$	25.8514	0.835658
$958$	25.9567	0.838621
$959$	−2.45837	−0.0793850
$960$	−1.50764	−0.0486588
$961$	59.0138	1.90367
$962$	66.9254	2.15776
$963$	−11.4261	−0.368202
$964$	−80.4186	−2.59011
$965$	−8.27885	−0.266506
$966$	−0.521460	−0.0167777
$967$	40.7126	1.30923	0.654615	−	0.755963i	$-0.272831\pi$
$967$	40.7126	1.30923	0.654615	+	0.755963i	$0.272831\pi$
$968$	−0.627701	−0.0201751
$969$	5.06650	0.162760
$970$	−11.3993	−0.366008
$971$	8.19209	0.262897	0.131448	−	0.991323i	$-0.458037\pi$
$971$	8.19209	0.262897	0.131448	+	0.991323i	$0.458037\pi$
$972$	−4.31187	−0.138303
$973$	0.163898	0.00525433
$974$	−2.05428	−0.0658235
$975$	−11.8722	−0.380213
$976$	71.8015	2.29831
$977$	35.4764	1.13499	0.567495	−	0.823377i	$-0.307912\pi$
$977$	35.4764	1.13499	0.567495	+	0.823377i	$0.307912\pi$
$978$	−16.8668	−0.539342
$979$	48.5570	1.55189
$980$	13.1712	0.420739
$981$	5.14362	0.164223
$982$	60.3742	1.92662
$983$	52.0456	1.66000	0.829999	−	0.557765i	$-0.188341\pi$
$983$	52.0456	1.66000	0.829999	+	0.557765i	$0.188341\pi$
$984$	−66.4599	−2.11866
$985$	−1.15336	−0.0367491
$986$	19.4870	0.620591
$987$	0.00395608	0.000125923 0
$988$	−53.9330	−1.71584
$989$	−17.1080	−0.544001
$990$	−3.66004	−0.116324
$991$	43.9063	1.39473	0.697365	−	0.716716i	$-0.254356\pi$
$991$	43.9063	1.39473	0.697365	+	0.716716i	$0.254356\pi$
$992$	32.0532	1.01769
$993$	29.0064	0.920489
$994$	1.99487	0.0632736
$995$	−1.21163	−0.0384112
$996$	−9.62058	−0.304840
$997$	32.5786	1.03177	0.515887	−	0.856657i	$-0.327462\pi$
$997$	32.5786	1.03177	0.515887	+	0.856657i	$0.327462\pi$
$998$	5.83334	0.184651
$999$	−10.7903	−0.341389

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.g.1.4	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.g.1.4	✓	56	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)

\(f(q)\)	\(=\)	\(q-2.51234 q^{2} -1.00000 q^{3} +4.31187 q^{4} -0.437106 q^{5} +2.51234 q^{6} +0.108032 q^{7} -5.80821 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.51234 q^{2} -1.00000 q^{3} +4.31187 q^{4} -0.437106 q^{5} +2.51234 q^{6} +0.108032 q^{7} -5.80821 q^{8} +1.00000 q^{9} +1.09816 q^{10} -3.33288 q^{11} -4.31187 q^{12} -2.46877 q^{13} -0.271415 q^{14} +0.437106 q^{15} +5.96848 q^{16} -1.00000 q^{17} -2.51234 q^{18} +5.06650 q^{19} -1.88474 q^{20} -0.108032 q^{21} +8.37333 q^{22} -1.92127 q^{23} +5.80821 q^{24} -4.80894 q^{25} +6.20240 q^{26} -1.00000 q^{27} +0.465822 q^{28} +7.75649 q^{29} -1.09816 q^{30} -9.48756 q^{31} -3.37845 q^{32} +3.33288 q^{33} +2.51234 q^{34} -0.0472217 q^{35} +4.31187 q^{36} +10.7903 q^{37} -12.7288 q^{38} +2.46877 q^{39} +2.53880 q^{40} -11.4424 q^{41} +0.271415 q^{42} +8.90451 q^{43} -14.3709 q^{44} -0.437106 q^{45} +4.82689 q^{46} -0.0366194 q^{47} -5.96848 q^{48} -6.98833 q^{49} +12.0817 q^{50} +1.00000 q^{51} -10.6450 q^{52} -8.36806 q^{53} +2.51234 q^{54} +1.45682 q^{55} -0.627475 q^{56} -5.06650 q^{57} -19.4870 q^{58} -0.584001 q^{59} +1.88474 q^{60} +12.0301 q^{61} +23.8360 q^{62} +0.108032 q^{63} -3.44914 q^{64} +1.07911 q^{65} -8.37333 q^{66} +0.0187605 q^{67} -4.31187 q^{68} +1.92127 q^{69} +0.118637 q^{70} -7.34992 q^{71} -5.80821 q^{72} -6.62891 q^{73} -27.1088 q^{74} +4.80894 q^{75} +21.8461 q^{76} -0.360059 q^{77} -6.20240 q^{78} -0.501328 q^{79} -2.60886 q^{80} +1.00000 q^{81} +28.7472 q^{82} +2.23119 q^{83} -0.465822 q^{84} +0.437106 q^{85} -22.3712 q^{86} -7.75649 q^{87} +19.3580 q^{88} -14.5691 q^{89} +1.09816 q^{90} -0.266707 q^{91} -8.28426 q^{92} +9.48756 q^{93} +0.0920004 q^{94} -2.21460 q^{95} +3.37845 q^{96} -10.3803 q^{97} +17.5571 q^{98} -3.33288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * q^99

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