LMFDB - Embedded newform 8007.2.a.j.1.57

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:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.57
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)

$f(q)$	$=$	$q+2.35033 q^{2} -1.00000 q^{3} +3.52404 q^{4} +2.14411 q^{5} -2.35033 q^{6} +1.95991 q^{7} +3.58199 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.35033 q^{2} -1.00000 q^{3} +3.52404 q^{4} +2.14411 q^{5} -2.35033 q^{6} +1.95991 q^{7} +3.58199 q^{8} +1.00000 q^{9} +5.03937 q^{10} +4.74824 q^{11} -3.52404 q^{12} +3.81414 q^{13} +4.60643 q^{14} -2.14411 q^{15} +1.37077 q^{16} +1.00000 q^{17} +2.35033 q^{18} +0.385846 q^{19} +7.55594 q^{20} -1.95991 q^{21} +11.1599 q^{22} +8.94546 q^{23} -3.58199 q^{24} -0.402780 q^{25} +8.96447 q^{26} -1.00000 q^{27} +6.90680 q^{28} +9.04768 q^{29} -5.03937 q^{30} -8.87607 q^{31} -3.94222 q^{32} -4.74824 q^{33} +2.35033 q^{34} +4.20227 q^{35} +3.52404 q^{36} -3.63496 q^{37} +0.906864 q^{38} -3.81414 q^{39} +7.68019 q^{40} -0.823068 q^{41} -4.60643 q^{42} +0.447683 q^{43} +16.7330 q^{44} +2.14411 q^{45} +21.0248 q^{46} -12.9147 q^{47} -1.37077 q^{48} -3.15876 q^{49} -0.946664 q^{50} -1.00000 q^{51} +13.4412 q^{52} +10.6831 q^{53} -2.35033 q^{54} +10.1808 q^{55} +7.02037 q^{56} -0.385846 q^{57} +21.2650 q^{58} -8.72674 q^{59} -7.55594 q^{60} -11.9042 q^{61} -20.8617 q^{62} +1.95991 q^{63} -12.0071 q^{64} +8.17794 q^{65} -11.1599 q^{66} -5.94480 q^{67} +3.52404 q^{68} -8.94546 q^{69} +9.87670 q^{70} +7.13079 q^{71} +3.58199 q^{72} -0.486955 q^{73} -8.54335 q^{74} +0.402780 q^{75} +1.35973 q^{76} +9.30613 q^{77} -8.96447 q^{78} -15.2283 q^{79} +2.93908 q^{80} +1.00000 q^{81} -1.93448 q^{82} -10.3424 q^{83} -6.90680 q^{84} +2.14411 q^{85} +1.05220 q^{86} -9.04768 q^{87} +17.0081 q^{88} -5.73034 q^{89} +5.03937 q^{90} +7.47536 q^{91} +31.5241 q^{92} +8.87607 q^{93} -30.3538 q^{94} +0.827297 q^{95} +3.94222 q^{96} -7.63148 q^{97} -7.42411 q^{98} +4.74824 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * 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 $

$2$	2.35033	1.66193	0.830966	−	0.556323i	$-0.187788\pi$
$2$	2.35033	1.66193	0.830966	+	0.556323i	$0.187788\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.52404	1.76202
$5$	2.14411	0.958876	0.479438	−	0.877576i	$-0.340840\pi$
$5$	2.14411	0.958876	0.479438	+	0.877576i	$0.340840\pi$
$6$	−2.35033	−0.959517
$7$	1.95991	0.740776	0.370388	−	0.928877i	$-0.379225\pi$
$7$	1.95991	0.740776	0.370388	+	0.928877i	$0.379225\pi$
$8$	3.58199	1.26642
$9$	1.00000	0.333333
$10$	5.03937	1.59359
$11$	4.74824	1.43165	0.715825	−	0.698280i	$-0.246051\pi$
$11$	4.74824	1.43165	0.715825	+	0.698280i	$0.246051\pi$
$12$	−3.52404	−1.01730
$13$	3.81414	1.05785	0.528925	−	0.848668i	$-0.322595\pi$
$13$	3.81414	1.05785	0.528925	+	0.848668i	$0.322595\pi$
$14$	4.60643	1.23112
$15$	−2.14411	−0.553608
$16$	1.37077	0.342692
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.35033	0.553977
$19$	0.385846	0.0885191	0.0442595	−	0.999020i	$-0.485907\pi$
$19$	0.385846	0.0885191	0.0442595	+	0.999020i	$0.485907\pi$
$20$	7.55594	1.68956
$21$	−1.95991	−0.427687
$22$	11.1599	2.37930
$23$	8.94546	1.86526	0.932629	−	0.360837i	$-0.117509\pi$
$23$	8.94546	1.86526	0.932629	+	0.360837i	$0.117509\pi$
$24$	−3.58199	−0.731170
$25$	−0.402780	−0.0805559
$26$	8.96447	1.75808
$27$	−1.00000	−0.192450
$28$	6.90680	1.30526
$29$	9.04768	1.68011	0.840056	−	0.542499i	$-0.182522\pi$
$29$	9.04768	1.68011	0.840056	+	0.542499i	$0.182522\pi$
$30$	−5.03937	−0.920058
$31$	−8.87607	−1.59419	−0.797095	−	0.603854i	$-0.793631\pi$
$31$	−8.87607	−1.59419	−0.797095	+	0.603854i	$0.793631\pi$
$32$	−3.94222	−0.696893
$33$	−4.74824	−0.826563
$34$	2.35033	0.403078
$35$	4.20227	0.710313
$36$	3.52404	0.587340
$37$	−3.63496	−0.597584	−0.298792	−	0.954318i	$-0.596584\pi$
$37$	−3.63496	−0.597584	−0.298792	+	0.954318i	$0.596584\pi$
$38$	0.906864	0.147113
$39$	−3.81414	−0.610750
$40$	7.68019	1.21434
$41$	−0.823068	−0.128542	−0.0642708	−	0.997932i	$-0.520472\pi$
$41$	−0.823068	−0.128542	−0.0642708	+	0.997932i	$0.520472\pi$
$42$	−4.60643	−0.710787
$43$	0.447683	0.0682711	0.0341355	−	0.999417i	$-0.489132\pi$
$43$	0.447683	0.0682711	0.0341355	+	0.999417i	$0.489132\pi$
$44$	16.7330	2.52259
$45$	2.14411	0.319625
$46$	21.0248	3.09993
$47$	−12.9147	−1.88381	−0.941903	−	0.335885i	$-0.890965\pi$
$47$	−12.9147	−1.88381	−0.941903	+	0.335885i	$0.890965\pi$
$48$	−1.37077	−0.197853
$49$	−3.15876	−0.451251
$50$	−0.946664	−0.133878
$51$	−1.00000	−0.140028
$52$	13.4412	1.86395
$53$	10.6831	1.46744	0.733719	−	0.679453i	$-0.237783\pi$
$53$	10.6831	1.46744	0.733719	+	0.679453i	$0.237783\pi$
$54$	−2.35033	−0.319839
$55$	10.1808	1.37277
$56$	7.02037	0.938137
$57$	−0.385846	−0.0511065
$58$	21.2650	2.79223
$59$	−8.72674	−1.13612	−0.568062	−	0.822985i	$-0.692307\pi$
$59$	−8.72674	−1.13612	−0.568062	+	0.822985i	$0.692307\pi$
$60$	−7.55594	−0.975467
$61$	−11.9042	−1.52418	−0.762088	−	0.647473i	$-0.775826\pi$
$61$	−11.9042	−1.52418	−0.762088	+	0.647473i	$0.775826\pi$
$62$	−20.8617	−2.64943
$63$	1.95991	0.246925
$64$	−12.0071	−1.50088
$65$	8.17794	1.01435
$66$	−11.1599	−1.37369
$67$	−5.94480	−0.726273	−0.363137	−	0.931736i	$-0.618294\pi$
$67$	−5.94480	−0.726273	−0.363137	+	0.931736i	$0.618294\pi$
$68$	3.52404	0.427352
$69$	−8.94546	−1.07691
$70$	9.87670	1.18049
$71$	7.13079	0.846269	0.423134	−	0.906067i	$-0.360930\pi$
$71$	7.13079	0.846269	0.423134	+	0.906067i	$0.360930\pi$
$72$	3.58199	0.422141
$73$	−0.486955	−0.0569937	−0.0284969	−	0.999594i	$-0.509072\pi$
$73$	−0.486955	−0.0569937	−0.0284969	+	0.999594i	$0.509072\pi$
$74$	−8.54335	−0.993144
$75$	0.402780	0.0465090
$76$	1.35973	0.155972
$77$	9.30613	1.06053
$78$	−8.96447	−1.01503
$79$	−15.2283	−1.71332	−0.856661	−	0.515880i	$-0.827465\pi$
$79$	−15.2283	−1.71332	−0.856661	+	0.515880i	$0.827465\pi$
$80$	2.93908	0.328599
$81$	1.00000	0.111111
$82$	−1.93448	−0.213628
$83$	−10.3424	−1.13523	−0.567615	−	0.823294i	$-0.692134\pi$
$83$	−10.3424	−1.13523	−0.567615	+	0.823294i	$0.692134\pi$
$84$	−6.90680	−0.753593
$85$	2.14411	0.232562
$86$	1.05220	0.113462
$87$	−9.04768	−0.970014
$88$	17.0081	1.81307
$89$	−5.73034	−0.607415	−0.303707	−	0.952765i	$-0.598225\pi$
$89$	−5.73034	−0.607415	−0.303707	+	0.952765i	$0.598225\pi$
$90$	5.03937	0.531196
$91$	7.47536	0.783631
$92$	31.5241	3.28662
$93$	8.87607	0.920406
$94$	−30.3538	−3.13076
$95$	0.827297	0.0848789
$96$	3.94222	0.402352
$97$	−7.63148	−0.774860	−0.387430	−	0.921899i	$-0.626637\pi$
$97$	−7.63148	−0.774860	−0.387430	+	0.921899i	$0.626637\pi$
$98$	−7.42411	−0.749948
$99$	4.74824	0.477216
$100$	−1.41941	−0.141941
$101$	18.3682	1.82771	0.913853	−	0.406045i	$-0.133092\pi$
$101$	18.3682	1.82771	0.913853	+	0.406045i	$0.133092\pi$
$102$	−2.35033	−0.232717
$103$	3.68703	0.363294	0.181647	−	0.983364i	$-0.441857\pi$
$103$	3.68703	0.363294	0.181647	+	0.983364i	$0.441857\pi$
$104$	13.6622	1.33969
$105$	−4.20227	−0.410099
$106$	25.1088	2.43878
$107$	15.1620	1.46577	0.732884	−	0.680354i	$-0.238174\pi$
$107$	15.1620	1.46577	0.732884	+	0.680354i	$0.238174\pi$
$108$	−3.52404	−0.339101
$109$	−9.94549	−0.952605	−0.476302	−	0.879282i	$-0.658023\pi$
$109$	−9.94549	−0.952605	−0.476302	+	0.879282i	$0.658023\pi$
$110$	23.9281	2.28146
$111$	3.63496	0.345015
$112$	2.68658	0.253858
$113$	19.1989	1.80608	0.903042	−	0.429552i	$-0.141329\pi$
$113$	19.1989	1.80608	0.903042	+	0.429552i	$0.141329\pi$
$114$	−0.906864	−0.0849356
$115$	19.1801	1.78855
$116$	31.8844	2.96039
$117$	3.81414	0.352617
$118$	−20.5107	−1.88816
$119$	1.95991	0.179665
$120$	−7.68019	−0.701102
$121$	11.5458	1.04962
$122$	−27.9788	−2.53308
$123$	0.823068	0.0742136
$124$	−31.2796	−2.80899
$125$	−11.5842	−1.03612
$126$	4.60643	0.410373
$127$	−9.81759	−0.871170	−0.435585	−	0.900148i	$-0.643459\pi$
$127$	−9.81759	−0.871170	−0.435585	+	0.900148i	$0.643459\pi$
$128$	−20.3360	−1.79747
$129$	−0.447683	−0.0394163
$130$	19.2208	1.68578
$131$	15.0016	1.31069	0.655347	−	0.755328i	$-0.272522\pi$
$131$	15.0016	1.31069	0.655347	+	0.755328i	$0.272522\pi$
$132$	−16.7330	−1.45642
$133$	0.756223	0.0655728
$134$	−13.9722	−1.20702
$135$	−2.14411	−0.184536
$136$	3.58199	0.307153
$137$	−0.925406	−0.0790628	−0.0395314	−	0.999218i	$-0.512587\pi$
$137$	−0.925406	−0.0790628	−0.0395314	+	0.999218i	$0.512587\pi$
$138$	−21.0248	−1.78975
$139$	−2.07491	−0.175991	−0.0879956	−	0.996121i	$-0.528046\pi$
$139$	−2.07491	−0.175991	−0.0879956	+	0.996121i	$0.528046\pi$
$140$	14.8089	1.25158
$141$	12.9147	1.08762
$142$	16.7597	1.40644
$143$	18.1104	1.51447
$144$	1.37077	0.114231
$145$	19.3993	1.61102
$146$	−1.14450	−0.0947197
$147$	3.15876	0.260530
$148$	−12.8097	−1.05295
$149$	−2.70743	−0.221801	−0.110901	−	0.993832i	$-0.535373\pi$
$149$	−2.70743	−0.221801	−0.110901	+	0.993832i	$0.535373\pi$
$150$	0.946664	0.0772948
$151$	−21.4446	−1.74514	−0.872570	−	0.488490i	$-0.837548\pi$
$151$	−21.4446	−1.74514	−0.872570	+	0.488490i	$0.837548\pi$
$152$	1.38209	0.112103
$153$	1.00000	0.0808452
$154$	21.8724	1.76253
$155$	−19.0313	−1.52863
$156$	−13.4412	−1.07615
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−35.7916	−2.84742
$159$	−10.6831	−0.847226
$160$	−8.45257	−0.668235
$161$	17.5323	1.38174
$162$	2.35033	0.184659
$163$	2.01855	0.158105	0.0790526	−	0.996870i	$-0.474810\pi$
$163$	2.01855	0.158105	0.0790526	+	0.996870i	$0.474810\pi$
$164$	−2.90052	−0.226493
$165$	−10.1808	−0.792572
$166$	−24.3081	−1.88667
$167$	−10.5631	−0.817399	−0.408700	−	0.912669i	$-0.634018\pi$
$167$	−10.5631	−0.817399	−0.408700	+	0.912669i	$0.634018\pi$
$168$	−7.02037	−0.541633
$169$	1.54763	0.119048
$170$	5.03937	0.386502
$171$	0.385846	0.0295064
$172$	1.57765	0.120295
$173$	−9.65805	−0.734288	−0.367144	−	0.930164i	$-0.619664\pi$
$173$	−9.65805	−0.734288	−0.367144	+	0.930164i	$0.619664\pi$
$174$	−21.2650	−1.61210
$175$	−0.789411	−0.0596739
$176$	6.50874	0.490614
$177$	8.72674	0.655942
$178$	−13.4682	−1.00948
$179$	18.5515	1.38661	0.693303	−	0.720646i	$-0.256155\pi$
$179$	18.5515	1.38661	0.693303	+	0.720646i	$0.256155\pi$
$180$	7.55594	0.563186
$181$	4.79693	0.356553	0.178276	−	0.983980i	$-0.442948\pi$
$181$	4.79693	0.356553	0.178276	+	0.983980i	$0.442948\pi$
$182$	17.5695	1.30234
$183$	11.9042	0.879984
$184$	32.0425	2.36221
$185$	−7.79377	−0.573009
$186$	20.8617	1.52965
$187$	4.74824	0.347226
$188$	−45.5120	−3.31930
$189$	−1.95991	−0.142562
$190$	1.94442	0.141063
$191$	−12.3896	−0.896480	−0.448240	−	0.893913i	$-0.647949\pi$
$191$	−12.3896	−0.896480	−0.448240	+	0.893913i	$0.647949\pi$
$192$	12.0071	0.866534
$193$	20.9661	1.50917	0.754587	−	0.656200i	$-0.227837\pi$
$193$	20.9661	1.50917	0.754587	+	0.656200i	$0.227837\pi$
$194$	−17.9365	−1.28776
$195$	−8.17794	−0.585634
$196$	−11.1316	−0.795112
$197$	−16.6780	−1.18826	−0.594128	−	0.804370i	$-0.702503\pi$
$197$	−16.6780	−1.18826	−0.594128	+	0.804370i	$0.702503\pi$
$198$	11.1599	0.793101
$199$	13.6737	0.969303	0.484651	−	0.874707i	$-0.338946\pi$
$199$	13.6737	0.969303	0.484651	+	0.874707i	$0.338946\pi$
$200$	−1.44275	−0.102018
$201$	5.94480	0.419314
$202$	43.1713	3.03752
$203$	17.7326	1.24459
$204$	−3.52404	−0.246732
$205$	−1.76475	−0.123256
$206$	8.66574	0.603770
$207$	8.94546	0.621753
$208$	5.22829	0.362517
$209$	1.83209	0.126728
$210$	−9.87670	−0.681557
$211$	26.0869	1.79590	0.897949	−	0.440099i	$-0.145057\pi$
$211$	26.0869	1.79590	0.897949	+	0.440099i	$0.145057\pi$
$212$	37.6477	2.58565
$213$	−7.13079	−0.488593
$214$	35.6357	2.43601
$215$	0.959883	0.0654635
$216$	−3.58199	−0.243723
$217$	−17.3963	−1.18094
$218$	−23.3751	−1.58316
$219$	0.486955	0.0329053
$220$	35.8774	2.41886
$221$	3.81414	0.256567
$222$	8.54335	0.573392
$223$	−8.48367	−0.568109	−0.284054	−	0.958808i	$-0.591680\pi$
$223$	−8.48367	−0.568109	−0.284054	+	0.958808i	$0.591680\pi$
$224$	−7.72640	−0.516242
$225$	−0.402780	−0.0268520
$226$	45.1238	3.00159
$227$	−12.9833	−0.861732	−0.430866	−	0.902416i	$-0.641792\pi$
$227$	−12.9833	−0.861732	−0.430866	+	0.902416i	$0.641792\pi$
$228$	−1.35973	−0.0900506
$229$	−1.79772	−0.118797	−0.0593983	−	0.998234i	$-0.518918\pi$
$229$	−1.79772	−0.118797	−0.0593983	+	0.998234i	$0.518918\pi$
$230$	45.0795	2.97245
$231$	−9.30613	−0.612298
$232$	32.4087	2.12773
$233$	−26.7000	−1.74917	−0.874587	−	0.484869i	$-0.838867\pi$
$233$	−26.7000	−1.74917	−0.874587	+	0.484869i	$0.838867\pi$
$234$	8.96447	0.586025
$235$	−27.6906	−1.80634
$236$	−30.7534	−2.00187
$237$	15.2283	0.989187
$238$	4.60643	0.298590
$239$	20.8160	1.34647	0.673237	−	0.739427i	$-0.264903\pi$
$239$	20.8160	1.34647	0.673237	+	0.739427i	$0.264903\pi$
$240$	−2.93908	−0.189717
$241$	−2.37912	−0.153253	−0.0766263	−	0.997060i	$-0.524415\pi$
$241$	−2.37912	−0.153253	−0.0766263	+	0.997060i	$0.524415\pi$
$242$	27.1364	1.74440
$243$	−1.00000	−0.0641500
$244$	−41.9509	−2.68563
$245$	−6.77273	−0.432694
$246$	1.93448	0.123338
$247$	1.47167	0.0936400
$248$	−31.7940	−2.01892
$249$	10.3424	0.655425
$250$	−27.2266	−1.72196
$251$	10.0558	0.634716	0.317358	−	0.948306i	$-0.397204\pi$
$251$	10.0558	0.634716	0.317358	+	0.948306i	$0.397204\pi$
$252$	6.90680	0.435087
$253$	42.4752	2.67040
$254$	−23.0745	−1.44783
$255$	−2.14411	−0.134270
$256$	−23.7823	−1.48639
$257$	−14.5649	−0.908531	−0.454266	−	0.890866i	$-0.650098\pi$
$257$	−14.5649	−0.908531	−0.454266	+	0.890866i	$0.650098\pi$
$258$	−1.05220	−0.0655072
$259$	−7.12420	−0.442676
$260$	28.8194	1.78730
$261$	9.04768	0.560038
$262$	35.2586	2.17829
$263$	3.35532	0.206898	0.103449	−	0.994635i	$-0.467012\pi$
$263$	3.35532	0.206898	0.103449	+	0.994635i	$0.467012\pi$
$264$	−17.0081	−1.04678
$265$	22.9058	1.40709
$266$	1.77737	0.108978
$267$	5.73034	0.350691
$268$	−20.9497	−1.27971
$269$	20.4704	1.24810	0.624051	−	0.781383i	$-0.285486\pi$
$269$	20.4704	1.24810	0.624051	+	0.781383i	$0.285486\pi$
$270$	−5.03937	−0.306686
$271$	−24.5550	−1.49161	−0.745806	−	0.666163i	$-0.767935\pi$
$271$	−24.5550	−1.49161	−0.745806	+	0.666163i	$0.767935\pi$
$272$	1.37077	0.0831150
$273$	−7.47536	−0.452429
$274$	−2.17501	−0.131397
$275$	−1.91250	−0.115328
$276$	−31.5241	−1.89753
$277$	−3.36874	−0.202408	−0.101204	−	0.994866i	$-0.532269\pi$
$277$	−3.36874	−0.202408	−0.101204	+	0.994866i	$0.532269\pi$
$278$	−4.87671	−0.292486
$279$	−8.87607	−0.531396
$280$	15.0525	0.899557
$281$	2.90164	0.173097	0.0865486	−	0.996248i	$-0.472416\pi$
$281$	2.90164	0.173097	0.0865486	+	0.996248i	$0.472416\pi$
$282$	30.3538	1.80754
$283$	1.06442	0.0632732	0.0316366	−	0.999499i	$-0.489928\pi$
$283$	1.06442	0.0632732	0.0316366	+	0.999499i	$0.489928\pi$
$284$	25.1292	1.49114
$285$	−0.827297	−0.0490048
$286$	42.5655	2.51695
$287$	−1.61314	−0.0952206
$288$	−3.94222	−0.232298
$289$	1.00000	0.0588235
$290$	45.5946	2.67741
$291$	7.63148	0.447366
$292$	−1.71605	−0.100424
$293$	20.7680	1.21328	0.606641	−	0.794976i	$-0.292517\pi$
$293$	20.7680	1.21328	0.606641	+	0.794976i	$0.292517\pi$
$294$	7.42411	0.432983
$295$	−18.7111	−1.08940
$296$	−13.0204	−0.756795
$297$	−4.74824	−0.275521
$298$	−6.36334	−0.368618
$299$	34.1192	1.97316
$300$	1.41941	0.0819497
$301$	0.877419	0.0505736
$302$	−50.4019	−2.90030
$303$	−18.3682	−1.05523
$304$	0.528905	0.0303348
$305$	−25.5240	−1.46150
$306$	2.35033	0.134359
$307$	14.6030	0.833437	0.416719	−	0.909035i	$-0.363180\pi$
$307$	14.6030	0.833437	0.416719	+	0.909035i	$0.363180\pi$
$308$	32.7951	1.86868
$309$	−3.68703	−0.209748
$310$	−44.7298	−2.54048
$311$	21.6421	1.22721	0.613604	−	0.789614i	$-0.289719\pi$
$311$	21.6421	1.22721	0.613604	+	0.789614i	$0.289719\pi$
$312$	−13.6622	−0.773469
$313$	1.60593	0.0907724	0.0453862	−	0.998970i	$-0.485548\pi$
$313$	1.60593	0.0907724	0.0453862	+	0.998970i	$0.485548\pi$
$314$	−2.35033	−0.132637
$315$	4.20227	0.236771
$316$	−53.6652	−3.01891
$317$	−21.5274	−1.20910	−0.604551	−	0.796566i	$-0.706647\pi$
$317$	−21.5274	−1.20910	−0.604551	+	0.796566i	$0.706647\pi$
$318$	−25.1088	−1.40803
$319$	42.9606	2.40533
$320$	−25.7445	−1.43916
$321$	−15.1620	−0.846262
$322$	41.2066	2.29636
$323$	0.385846	0.0214690
$324$	3.52404	0.195780
$325$	−1.53626	−0.0852161
$326$	4.74426	0.262760
$327$	9.94549	0.549987
$328$	−2.94822	−0.162788
$329$	−25.3117	−1.39548
$330$	−23.9281	−1.31720
$331$	−12.6455	−0.695061	−0.347530	−	0.937669i	$-0.612980\pi$
$331$	−12.6455	−0.695061	−0.347530	+	0.937669i	$0.612980\pi$
$332$	−36.4471	−2.00030
$333$	−3.63496	−0.199195
$334$	−24.8268	−1.35846
$335$	−12.7463	−0.696406
$336$	−2.68658	−0.146565
$337$	−0.729160	−0.0397199	−0.0198600	−	0.999803i	$-0.506322\pi$
$337$	−0.729160	−0.0397199	−0.0198600	+	0.999803i	$0.506322\pi$
$338$	3.63743	0.197850
$339$	−19.1989	−1.04274
$340$	7.55594	0.409778
$341$	−42.1457	−2.28232
$342$	0.906864	0.0490376
$343$	−19.9102	−1.07505
$344$	1.60360	0.0864601
$345$	−19.1801	−1.03262
$346$	−22.6996	−1.22034
$347$	11.1479	0.598450	0.299225	−	0.954183i	$-0.403272\pi$
$347$	11.1479	0.598450	0.299225	+	0.954183i	$0.403272\pi$
$348$	−31.8844	−1.70918
$349$	17.4623	0.934733	0.467366	−	0.884064i	$-0.345203\pi$
$349$	17.4623	0.934733	0.467366	+	0.884064i	$0.345203\pi$
$350$	−1.85538	−0.0991740
$351$	−3.81414	−0.203583
$352$	−18.7186	−0.997707
$353$	−15.8078	−0.841365	−0.420682	−	0.907208i	$-0.638209\pi$
$353$	−15.8078	−0.841365	−0.420682	+	0.907208i	$0.638209\pi$
$354$	20.5107	1.09013
$355$	15.2892	0.811467
$356$	−20.1939	−1.07028
$357$	−1.95991	−0.103729
$358$	43.6021	2.30444
$359$	32.7088	1.72631	0.863153	−	0.504943i	$-0.168486\pi$
$359$	32.7088	1.72631	0.863153	+	0.504943i	$0.168486\pi$
$360$	7.68019	0.404781
$361$	−18.8511	−0.992164
$362$	11.2743	0.592567
$363$	−11.5458	−0.605998
$364$	26.3435	1.38077
$365$	−1.04409	−0.0546499
$366$	27.9788	1.46247
$367$	−28.3165	−1.47811	−0.739056	−	0.673644i	$-0.764728\pi$
$367$	−28.3165	−1.47811	−0.739056	+	0.673644i	$0.764728\pi$
$368$	12.2621	0.639209
$369$	−0.823068	−0.0428472
$370$	−18.3179	−0.952303
$371$	20.9379	1.08704
$372$	31.2796	1.62177
$373$	20.1042	1.04096	0.520478	−	0.853875i	$-0.325754\pi$
$373$	20.1042	1.04096	0.520478	+	0.853875i	$0.325754\pi$
$374$	11.1599	0.577066
$375$	11.5842	0.598204
$376$	−46.2604	−2.38570
$377$	34.5091	1.77731
$378$	−4.60643	−0.236929
$379$	37.0100	1.90108	0.950538	−	0.310609i	$-0.100533\pi$
$379$	37.0100	1.90108	0.950538	+	0.310609i	$0.100533\pi$
$380$	2.91543	0.149558
$381$	9.81759	0.502970
$382$	−29.1196	−1.48989
$383$	−13.5400	−0.691861	−0.345931	−	0.938260i	$-0.612437\pi$
$383$	−13.5400	−0.691861	−0.345931	+	0.938260i	$0.612437\pi$
$384$	20.3360	1.03777
$385$	19.9534	1.01692
$386$	49.2772	2.50815
$387$	0.447683	0.0227570
$388$	−26.8936	−1.36532
$389$	22.7804	1.15501	0.577505	−	0.816387i	$-0.304026\pi$
$389$	22.7804	1.15501	0.577505	+	0.816387i	$0.304026\pi$
$390$	−19.2208	−0.973284
$391$	8.94546	0.452392
$392$	−11.3146	−0.571475
$393$	−15.0016	−0.756730
$394$	−39.1987	−1.97480
$395$	−32.6513	−1.64286
$396$	16.7330	0.840864
$397$	−3.06192	−0.153673	−0.0768367	−	0.997044i	$-0.524482\pi$
$397$	−3.06192	−0.153673	−0.0768367	+	0.997044i	$0.524482\pi$
$398$	32.1377	1.61092
$399$	−0.756223	−0.0378585
$400$	−0.552117	−0.0276058
$401$	−9.59098	−0.478951	−0.239475	−	0.970902i	$-0.576975\pi$
$401$	−9.59098	−0.478951	−0.239475	+	0.970902i	$0.576975\pi$
$402$	13.9722	0.696871
$403$	−33.8545	−1.68641
$404$	64.7303	3.22045
$405$	2.14411	0.106542
$406$	41.6775	2.06842
$407$	−17.2597	−0.855531
$408$	−3.58199	−0.177335
$409$	31.9162	1.57816	0.789078	−	0.614293i	$-0.210559\pi$
$409$	31.9162	1.57816	0.789078	+	0.614293i	$0.210559\pi$
$410$	−4.14774	−0.204842
$411$	0.925406	0.0456469
$412$	12.9932	0.640131
$413$	−17.1036	−0.841614
$414$	21.0248	1.03331
$415$	−22.1753	−1.08854
$416$	−15.0362	−0.737209
$417$	2.07491	0.101609
$418$	4.30601	0.210614
$419$	−19.7947	−0.967034	−0.483517	−	0.875335i	$-0.660641\pi$
$419$	−19.7947	−0.967034	−0.483517	+	0.875335i	$0.660641\pi$
$420$	−14.8089	−0.722603
$421$	6.95367	0.338901	0.169451	−	0.985539i	$-0.445801\pi$
$421$	6.95367	0.338901	0.169451	+	0.985539i	$0.445801\pi$
$422$	61.3128	2.98466
$423$	−12.9147	−0.627935
$424$	38.2668	1.85840
$425$	−0.402780	−0.0195377
$426$	−16.7597	−0.812009
$427$	−23.3312	−1.12907
$428$	53.4315	2.58271
$429$	−18.1104	−0.874380
$430$	2.25604	0.108796
$431$	−20.1497	−0.970575	−0.485288	−	0.874355i	$-0.661285\pi$
$431$	−20.1497	−0.970575	−0.485288	+	0.874355i	$0.661285\pi$
$432$	−1.37077	−0.0659511
$433$	−17.7563	−0.853313	−0.426657	−	0.904414i	$-0.640309\pi$
$433$	−17.7563	−0.853313	−0.426657	+	0.904414i	$0.640309\pi$
$434$	−40.8870	−1.96264
$435$	−19.3993	−0.930123
$436$	−35.0483	−1.67851
$437$	3.45157	0.165111
$438$	1.14450	0.0546864
$439$	−15.9290	−0.760251	−0.380125	−	0.924935i	$-0.624119\pi$
$439$	−15.9290	−0.760251	−0.380125	+	0.924935i	$0.624119\pi$
$440$	36.4674	1.73851
$441$	−3.15876	−0.150417
$442$	8.96447	0.426396
$443$	−12.6659	−0.601777	−0.300888	−	0.953659i	$-0.597283\pi$
$443$	−12.6659	−0.601777	−0.300888	+	0.953659i	$0.597283\pi$
$444$	12.8097	0.607924
$445$	−12.2865	−0.582436
$446$	−19.9394	−0.944158
$447$	2.70743	0.128057
$448$	−23.5327	−1.11182
$449$	−12.9572	−0.611488	−0.305744	−	0.952114i	$-0.598905\pi$
$449$	−12.9572	−0.611488	−0.305744	+	0.952114i	$0.598905\pi$
$450$	−0.946664	−0.0446262
$451$	−3.90813	−0.184027
$452$	67.6578	3.18235
$453$	21.4446	1.00756
$454$	−30.5150	−1.43214
$455$	16.0280	0.751405
$456$	−1.38209	−0.0647225
$457$	31.9619	1.49512	0.747558	−	0.664196i	$-0.231226\pi$
$457$	31.9619	1.49512	0.747558	+	0.664196i	$0.231226\pi$
$458$	−4.22523	−0.197432
$459$	−1.00000	−0.0466760
$460$	67.5913	3.15146
$461$	30.2146	1.40724	0.703618	−	0.710579i	$-0.251567\pi$
$461$	30.2146	1.40724	0.703618	+	0.710579i	$0.251567\pi$
$462$	−21.8724	−1.01760
$463$	17.1756	0.798217	0.399108	−	0.916904i	$-0.369320\pi$
$463$	17.1756	0.798217	0.399108	+	0.916904i	$0.369320\pi$
$464$	12.4023	0.575761
$465$	19.0313	0.882555
$466$	−62.7537	−2.90701
$467$	16.1109	0.745523	0.372761	−	0.927927i	$-0.378411\pi$
$467$	16.1109	0.745523	0.372761	+	0.927927i	$0.378411\pi$
$468$	13.4412	0.621318
$469$	−11.6513	−0.538006
$470$	−65.0820	−3.00201
$471$	1.00000	0.0460776
$472$	−31.2591	−1.43882
$473$	2.12571	0.0977402
$474$	35.7916	1.64396
$475$	−0.155411	−0.00713073
$476$	6.90680	0.316572
$477$	10.6831	0.489146
$478$	48.9244	2.23775
$479$	20.9694	0.958118	0.479059	−	0.877783i	$-0.340978\pi$
$479$	20.9694	0.958118	0.479059	+	0.877783i	$0.340978\pi$
$480$	8.45257	0.385805
$481$	−13.8642	−0.632155
$482$	−5.59171	−0.254695
$483$	−17.5323	−0.797747
$484$	40.6879	1.84945
$485$	−16.3628	−0.742995
$486$	−2.35033	−0.106613
$487$	−8.80642	−0.399057	−0.199528	−	0.979892i	$-0.563941\pi$
$487$	−8.80642	−0.399057	−0.199528	+	0.979892i	$0.563941\pi$
$488$	−42.6407	−1.93025
$489$	−2.01855	−0.0912821
$490$	−15.9181	−0.719108
$491$	−21.7237	−0.980377	−0.490189	−	0.871616i	$-0.663072\pi$
$491$	−21.7237	−0.980377	−0.490189	+	0.871616i	$0.663072\pi$
$492$	2.90052	0.130766
$493$	9.04768	0.407487
$494$	3.45890	0.155623
$495$	10.1808	0.457592
$496$	−12.1670	−0.546315
$497$	13.9757	0.626896
$498$	24.3081	1.08927
$499$	12.6410	0.565887	0.282943	−	0.959137i	$-0.408689\pi$
$499$	12.6410	0.565887	0.282943	+	0.959137i	$0.408689\pi$
$500$	−40.8231	−1.82566
$501$	10.5631	0.471926
$502$	23.6344	1.05486
$503$	22.2181	0.990657	0.495328	−	0.868706i	$-0.335048\pi$
$503$	22.2181	0.990657	0.495328	+	0.868706i	$0.335048\pi$
$504$	7.02037	0.312712
$505$	39.3835	1.75254
$506$	99.8307	4.43802
$507$	−1.54763	−0.0687326
$508$	−34.5976	−1.53502
$509$	−1.54301	−0.0683929	−0.0341965	−	0.999415i	$-0.510887\pi$
$509$	−1.54301	−0.0683929	−0.0341965	+	0.999415i	$0.510887\pi$
$510$	−5.03937	−0.223147
$511$	−0.954387	−0.0422196
$512$	−15.2240	−0.672813
$513$	−0.385846	−0.0170355
$514$	−34.2322	−1.50992
$515$	7.90542	0.348354
$516$	−1.57765	−0.0694523
$517$	−61.3223	−2.69695
$518$	−16.7442	−0.735698
$519$	9.65805	0.423941
$520$	29.2933	1.28459
$521$	25.2260	1.10517	0.552586	−	0.833456i	$-0.313641\pi$
$521$	25.2260	1.10517	0.552586	+	0.833456i	$0.313641\pi$
$522$	21.2650	0.930745
$523$	32.0987	1.40358	0.701789	−	0.712385i	$-0.252385\pi$
$523$	32.0987	1.40358	0.701789	+	0.712385i	$0.252385\pi$
$524$	52.8661	2.30947
$525$	0.789411	0.0344527
$526$	7.88610	0.343850
$527$	−8.87607	−0.386648
$528$	−6.50874	−0.283256
$529$	57.0213	2.47919
$530$	53.8361	2.33849
$531$	−8.72674	−0.378708
$532$	2.66496	0.115541
$533$	−3.13929	−0.135978
$534$	13.4682	0.582825
$535$	32.5091	1.40549
$536$	−21.2942	−0.919769
$537$	−18.5515	−0.800557
$538$	48.1121	2.07426
$539$	−14.9985	−0.646033
$540$	−7.55594	−0.325156
$541$	−9.45833	−0.406645	−0.203323	−	0.979112i	$-0.565174\pi$
$541$	−9.45833	−0.406645	−0.203323	+	0.979112i	$0.565174\pi$
$542$	−57.7124	−2.47896
$543$	−4.79693	−0.205856
$544$	−3.94222	−0.169021
$545$	−21.3242	−0.913430
$546$	−17.5695	−0.751907
$547$	−13.8798	−0.593455	−0.296728	−	0.954962i	$-0.595895\pi$
$547$	−13.8798	−0.593455	−0.296728	+	0.954962i	$0.595895\pi$
$548$	−3.26117	−0.139310
$549$	−11.9042	−0.508059
$550$	−4.49499	−0.191667
$551$	3.49101	0.148722
$552$	−32.0425	−1.36382
$553$	−29.8462	−1.26919
$554$	−7.91763	−0.336388
$555$	7.79377	0.330827
$556$	−7.31205	−0.310100
$557$	6.11587	0.259138	0.129569	−	0.991570i	$-0.458641\pi$
$557$	6.11587	0.259138	0.129569	+	0.991570i	$0.458641\pi$
$558$	−20.8617	−0.883145
$559$	1.70752	0.0722206
$560$	5.76033	0.243418
$561$	−4.74824	−0.200471
$562$	6.81980	0.287676
$563$	−13.6767	−0.576405	−0.288203	−	0.957569i	$-0.593058\pi$
$563$	−13.6767	−0.576405	−0.288203	+	0.957569i	$0.593058\pi$
$564$	45.5120	1.91640
$565$	41.1647	1.73181
$566$	2.50173	0.105156
$567$	1.95991	0.0823085
$568$	25.5424	1.07173
$569$	−36.5876	−1.53383	−0.766915	−	0.641748i	$-0.778209\pi$
$569$	−36.5876	−1.53383	−0.766915	+	0.641748i	$0.778209\pi$
$570$	−1.94442	−0.0814427
$571$	−23.3135	−0.975641	−0.487821	−	0.872944i	$-0.662208\pi$
$571$	−23.3135	−0.975641	−0.487821	+	0.872944i	$0.662208\pi$
$572$	63.8219	2.66853
$573$	12.3896	0.517583
$574$	−3.79140	−0.158250
$575$	−3.60305	−0.150258
$576$	−12.0071	−0.500294
$577$	−10.3944	−0.432723	−0.216362	−	0.976313i	$-0.569419\pi$
$577$	−10.3944	−0.432723	−0.216362	+	0.976313i	$0.569419\pi$
$578$	2.35033	0.0977607
$579$	−20.9661	−0.871322
$580$	68.3637	2.83865
$581$	−20.2702	−0.840951
$582$	17.9365	0.743491
$583$	50.7260	2.10086
$584$	−1.74427	−0.0721782
$585$	8.17794	0.338116
$586$	48.8117	2.01639
$587$	22.5685	0.931502	0.465751	−	0.884916i	$-0.345784\pi$
$587$	22.5685	0.931502	0.465751	+	0.884916i	$0.345784\pi$
$588$	11.1316	0.459058
$589$	−3.42479	−0.141116
$590$	−43.9772	−1.81051
$591$	16.6780	0.686040
$592$	−4.98269	−0.204787
$593$	26.0722	1.07066	0.535329	−	0.844644i	$-0.320188\pi$
$593$	26.0722	1.07066	0.535329	+	0.844644i	$0.320188\pi$
$594$	−11.1599	−0.457897
$595$	4.20227	0.172276
$596$	−9.54107	−0.390818
$597$	−13.6737	−0.559627
$598$	80.1913	3.27927
$599$	13.8028	0.563966	0.281983	−	0.959419i	$-0.409008\pi$
$599$	13.8028	0.563966	0.281983	+	0.959419i	$0.409008\pi$
$600$	1.44275	0.0589001
$601$	−36.2247	−1.47764	−0.738819	−	0.673904i	$-0.764616\pi$
$601$	−36.2247	−1.47764	−0.738819	+	0.673904i	$0.764616\pi$
$602$	2.06222	0.0840498
$603$	−5.94480	−0.242091
$604$	−75.5717	−3.07497
$605$	24.7555	1.00646
$606$	−43.1713	−1.75372
$607$	35.4951	1.44070	0.720350	−	0.693610i	$-0.243981\pi$
$607$	35.4951	1.44070	0.720350	+	0.693610i	$0.243981\pi$
$608$	−1.52109	−0.0616884
$609$	−17.7326	−0.718563
$610$	−59.9896	−2.42891
$611$	−49.2585	−1.99279
$612$	3.52404	0.142451
$613$	−31.4984	−1.27221	−0.636104	−	0.771603i	$-0.719455\pi$
$613$	−31.4984	−1.27221	−0.636104	+	0.771603i	$0.719455\pi$
$614$	34.3218	1.38512
$615$	1.76475	0.0711616
$616$	33.3344	1.34308
$617$	−2.71210	−0.109185	−0.0545926	−	0.998509i	$-0.517386\pi$
$617$	−2.71210	−0.109185	−0.0545926	+	0.998509i	$0.517386\pi$
$618$	−8.66574	−0.348587
$619$	−6.75390	−0.271462	−0.135731	−	0.990746i	$-0.543338\pi$
$619$	−6.75390	−0.271462	−0.135731	+	0.990746i	$0.543338\pi$
$620$	−67.0670	−2.69348
$621$	−8.94546	−0.358969
$622$	50.8659	2.03954
$623$	−11.2309	−0.449958
$624$	−5.22829	−0.209299
$625$	−22.8239	−0.912955
$626$	3.77445	0.150858
$627$	−1.83209	−0.0731666
$628$	−3.52404	−0.140624
$629$	−3.63496	−0.144935
$630$	9.87670	0.393497
$631$	−13.6106	−0.541827	−0.270914	−	0.962604i	$-0.587326\pi$
$631$	−13.6106	−0.541827	−0.270914	+	0.962604i	$0.587326\pi$
$632$	−54.5477	−2.16979
$633$	−26.0869	−1.03686
$634$	−50.5965	−2.00945
$635$	−21.0500	−0.835345
$636$	−37.6477	−1.49283
$637$	−12.0479	−0.477356
$638$	100.971	3.99750
$639$	7.13079	0.282090
$640$	−43.6028	−1.72355
$641$	44.9448	1.77521	0.887606	−	0.460603i	$-0.152367\pi$
$641$	44.9448	1.77521	0.887606	+	0.460603i	$0.152367\pi$
$642$	−35.6357	−1.40643
$643$	11.2668	0.444321	0.222161	−	0.975010i	$-0.428689\pi$
$643$	11.2668	0.444321	0.222161	+	0.975010i	$0.428689\pi$
$644$	61.7845	2.43465
$645$	−0.959883	−0.0377954
$646$	0.906864	0.0356801
$647$	−2.98556	−0.117374	−0.0586872	−	0.998276i	$-0.518691\pi$
$647$	−2.98556	−0.117374	−0.0586872	+	0.998276i	$0.518691\pi$
$648$	3.58199	0.140714
$649$	−41.4367	−1.62653
$650$	−3.61070	−0.141623
$651$	17.3963	0.681814
$652$	7.11345	0.278584
$653$	−8.26622	−0.323482	−0.161741	−	0.986833i	$-0.551711\pi$
$653$	−8.26622	−0.323482	−0.161741	+	0.986833i	$0.551711\pi$
$654$	23.3751	0.914041
$655$	32.1651	1.25679
$656$	−1.12823	−0.0440502
$657$	−0.486955	−0.0189979
$658$	−59.4908	−2.31919
$659$	5.37103	0.209226	0.104613	−	0.994513i	$-0.466640\pi$
$659$	5.37103	0.209226	0.104613	+	0.994513i	$0.466640\pi$
$660$	−35.8774	−1.39653
$661$	−39.9676	−1.55456	−0.777281	−	0.629154i	$-0.783401\pi$
$661$	−39.9676	−1.55456	−0.777281	+	0.629154i	$0.783401\pi$
$662$	−29.7211	−1.15514
$663$	−3.81414	−0.148129
$664$	−37.0465	−1.43768
$665$	1.62143	0.0628762
$666$	−8.54335	−0.331048
$667$	80.9357	3.13384
$668$	−37.2249	−1.44027
$669$	8.48367	0.327998
$670$	−29.9580	−1.15738
$671$	−56.5240	−2.18209
$672$	7.72640	0.298052
$673$	−27.7088	−1.06810	−0.534048	−	0.845454i	$-0.679330\pi$
$673$	−27.7088	−1.06810	−0.534048	+	0.845454i	$0.679330\pi$
$674$	−1.71377	−0.0660118
$675$	0.402780	0.0155030
$676$	5.45390	0.209765
$677$	−3.11965	−0.119898	−0.0599489	−	0.998201i	$-0.519094\pi$
$677$	−3.11965	−0.119898	−0.0599489	+	0.998201i	$0.519094\pi$
$678$	−45.1238	−1.73297
$679$	−14.9570	−0.573998
$680$	7.68019	0.294522
$681$	12.9833	0.497521
$682$	−99.0563	−3.79306
$683$	−33.0607	−1.26503	−0.632516	−	0.774547i	$-0.717978\pi$
$683$	−33.0607	−1.26503	−0.632516	+	0.774547i	$0.717978\pi$
$684$	1.35973	0.0519908
$685$	−1.98418	−0.0758114
$686$	−46.7956	−1.78666
$687$	1.79772	0.0685872
$688$	0.613669	0.0233959
$689$	40.7468	1.55233
$690$	−45.0795	−1.71615
$691$	−21.2953	−0.810113	−0.405056	−	0.914292i	$-0.632748\pi$
$691$	−21.2953	−0.810113	−0.405056	+	0.914292i	$0.632748\pi$
$692$	−34.0353	−1.29383
$693$	9.30613	0.353511
$694$	26.2012	0.994584
$695$	−4.44883	−0.168754
$696$	−32.4087	−1.22845
$697$	−0.823068	−0.0311759
$698$	41.0420	1.55346
$699$	26.7000	1.00989
$700$	−2.78192	−0.105147
$701$	38.9978	1.47293	0.736464	−	0.676477i	$-0.236494\pi$
$701$	38.9978	1.47293	0.736464	+	0.676477i	$0.236494\pi$
$702$	−8.96447	−0.338342
$703$	−1.40253	−0.0528976
$704$	−57.0124	−2.14874
$705$	27.6906	1.04289
$706$	−37.1535	−1.39829
$707$	36.0001	1.35392
$708$	30.7534	1.15578
$709$	−8.23805	−0.309387	−0.154693	−	0.987963i	$-0.549439\pi$
$709$	−8.23805	−0.309387	−0.154693	+	0.987963i	$0.549439\pi$
$710$	35.9347	1.34860
$711$	−15.2283	−0.571107
$712$	−20.5260	−0.769244
$713$	−79.4006	−2.97357
$714$	−4.60643	−0.172391
$715$	38.8308	1.45219
$716$	65.3762	2.44323
$717$	−20.8160	−0.777387
$718$	76.8764	2.86900
$719$	−6.41735	−0.239327	−0.119663	−	0.992815i	$-0.538182\pi$
$719$	−6.41735	−0.239327	−0.119663	+	0.992815i	$0.538182\pi$
$720$	2.93908	0.109533
$721$	7.22625	0.269120
$722$	−44.3063	−1.64891
$723$	2.37912	0.0884804
$724$	16.9046	0.628253
$725$	−3.64422	−0.135343
$726$	−27.1364	−1.00713
$727$	−10.8411	−0.402072	−0.201036	−	0.979584i	$-0.564431\pi$
$727$	−10.8411	−0.402072	−0.201036	+	0.979584i	$0.564431\pi$
$728$	26.7766	0.992409
$729$	1.00000	0.0370370
$730$	−2.45394	−0.0908245
$731$	0.447683	0.0165582
$732$	41.9509	1.55055
$733$	46.2055	1.70664	0.853320	−	0.521388i	$-0.174585\pi$
$733$	46.2055	1.70664	0.853320	+	0.521388i	$0.174585\pi$
$734$	−66.5531	−2.45652
$735$	6.77273	0.249816
$736$	−35.2650	−1.29989
$737$	−28.2274	−1.03977
$738$	−1.93448	−0.0712092
$739$	−21.9885	−0.808860	−0.404430	−	0.914569i	$-0.632530\pi$
$739$	−21.9885	−0.808860	−0.404430	+	0.914569i	$0.632530\pi$
$740$	−27.4655	−1.00965
$741$	−1.47167	−0.0540631
$742$	49.2110	1.80659
$743$	−21.1110	−0.774487	−0.387243	−	0.921978i	$-0.626573\pi$
$743$	−21.1110	−0.774487	−0.387243	+	0.921978i	$0.626573\pi$
$744$	31.7940	1.16562
$745$	−5.80503	−0.212680
$746$	47.2514	1.73000
$747$	−10.3424	−0.378410
$748$	16.7330	0.611819
$749$	29.7162	1.08581
$750$	27.2266	0.994174
$751$	−51.1351	−1.86595	−0.932974	−	0.359945i	$-0.882795\pi$
$751$	−51.1351	−1.86595	−0.932974	+	0.359945i	$0.882795\pi$
$752$	−17.7031	−0.645565
$753$	−10.0558	−0.366454
$754$	81.1077	2.95377
$755$	−45.9797	−1.67337
$756$	−6.90680	−0.251198
$757$	17.3171	0.629402	0.314701	−	0.949191i	$-0.398096\pi$
$757$	17.3171	0.629402	0.314701	+	0.949191i	$0.398096\pi$
$758$	86.9856	3.15946
$759$	−42.4752	−1.54175
$760$	2.96337	0.107493
$761$	−34.4184	−1.24767	−0.623833	−	0.781557i	$-0.714426\pi$
$761$	−34.4184	−1.24767	−0.623833	+	0.781557i	$0.714426\pi$
$762$	23.0745	0.835903
$763$	−19.4923	−0.705667
$764$	−43.6614	−1.57961
$765$	2.14411	0.0775206
$766$	−31.8234	−1.14983
$767$	−33.2850	−1.20185
$768$	23.7823	0.858169
$769$	−5.54995	−0.200136	−0.100068	−	0.994981i	$-0.531906\pi$
$769$	−5.54995	−0.200136	−0.100068	+	0.994981i	$0.531906\pi$
$770$	46.8970	1.69005
$771$	14.5649	0.524541
$772$	73.8854	2.65919
$773$	16.7196	0.601361	0.300680	−	0.953725i	$-0.402786\pi$
$773$	16.7196	0.601361	0.300680	+	0.953725i	$0.402786\pi$
$774$	1.05220	0.0378206
$775$	3.57510	0.128421
$776$	−27.3359	−0.981301
$777$	7.12420	0.255579
$778$	53.5413	1.91955
$779$	−0.317577	−0.0113784
$780$	−28.8194	−1.03190
$781$	33.8587	1.21156
$782$	21.0248	0.751844
$783$	−9.04768	−0.323338
$784$	−4.32992	−0.154640
$785$	−2.14411	−0.0765267
$786$	−35.2586	−1.25763
$787$	10.8633	0.387235	0.193617	−	0.981077i	$-0.437978\pi$
$787$	10.8633	0.387235	0.193617	+	0.981077i	$0.437978\pi$
$788$	−58.7738	−2.09373
$789$	−3.35532	−0.119452
$790$	−76.7412	−2.73033
$791$	37.6282	1.33790
$792$	17.0081	0.604358
$793$	−45.4042	−1.61235
$794$	−7.19651	−0.255395
$795$	−22.9058	−0.812385
$796$	48.1866	1.70793
$797$	39.1010	1.38503	0.692514	−	0.721404i	$-0.256503\pi$
$797$	39.1010	1.38503	0.692514	+	0.721404i	$0.256503\pi$
$798$	−1.77737	−0.0629182
$799$	−12.9147	−0.456890
$800$	1.58785	0.0561389
$801$	−5.73034	−0.202472
$802$	−22.5419	−0.795984
$803$	−2.31218	−0.0815950
$804$	20.9497	0.738839
$805$	37.5912	1.32492
$806$	−79.5692	−2.80271
$807$	−20.4704	−0.720592
$808$	65.7947	2.31465
$809$	−0.0722984	−0.00254188	−0.00127094	−	0.999999i	$-0.500405\pi$
$809$	−0.0722984	−0.00254188	−0.00127094	+	0.999999i	$0.500405\pi$
$810$	5.03937	0.177065
$811$	15.5827	0.547182	0.273591	−	0.961846i	$-0.411788\pi$
$811$	15.5827	0.547182	0.273591	+	0.961846i	$0.411788\pi$
$812$	62.4905	2.19299
$813$	24.5550	0.861183
$814$	−40.5659	−1.42183
$815$	4.32800	0.151603
$816$	−1.37077	−0.0479864
$817$	0.172737	0.00604329
$818$	75.0136	2.62279
$819$	7.47536	0.261210
$820$	−6.21905	−0.217179
$821$	49.0990	1.71357	0.856783	−	0.515677i	$-0.172460\pi$
$821$	49.0990	1.71357	0.856783	+	0.515677i	$0.172460\pi$
$822$	2.17501	0.0758621
$823$	−35.4334	−1.23513	−0.617566	−	0.786519i	$-0.711881\pi$
$823$	−35.4334	−1.23513	−0.617566	+	0.786519i	$0.711881\pi$
$824$	13.2069	0.460084
$825$	1.91250	0.0665845
$826$	−40.1991	−1.39871
$827$	4.19469	0.145864	0.0729318	−	0.997337i	$-0.476764\pi$
$827$	4.19469	0.145864	0.0729318	+	0.997337i	$0.476764\pi$
$828$	31.5241	1.09554
$829$	34.2760	1.19046	0.595228	−	0.803557i	$-0.297062\pi$
$829$	34.2760	1.19046	0.595228	+	0.803557i	$0.297062\pi$
$830$	−52.1193	−1.80909
$831$	3.36874	0.116860
$832$	−45.7965	−1.58771
$833$	−3.15876	−0.109444
$834$	4.87671	0.168867
$835$	−22.6485	−0.783785
$836$	6.45635	0.223298
$837$	8.87607	0.306802
$838$	−46.5240	−1.60714
$839$	7.55748	0.260913	0.130457	−	0.991454i	$-0.458356\pi$
$839$	7.55748	0.260913	0.130457	+	0.991454i	$0.458356\pi$
$840$	−15.0525	−0.519360
$841$	52.8606	1.82278
$842$	16.3434	0.563231
$843$	−2.90164	−0.0999377
$844$	91.9313	3.16441
$845$	3.31829	0.114153
$846$	−30.3538	−1.04359
$847$	22.6288	0.777533
$848$	14.6441	0.502879
$849$	−1.06442	−0.0365308
$850$	−0.946664	−0.0324703
$851$	−32.5164	−1.11465
$852$	−25.1292	−0.860911
$853$	−39.9674	−1.36846	−0.684228	−	0.729268i	$-0.739861\pi$
$853$	−39.9674	−1.36846	−0.684228	+	0.729268i	$0.739861\pi$
$854$	−54.8359	−1.87644
$855$	0.827297	0.0282930
$856$	54.3102	1.85628
$857$	21.3091	0.727907	0.363953	−	0.931417i	$-0.381427\pi$
$857$	21.3091	0.727907	0.363953	+	0.931417i	$0.381427\pi$
$858$	−42.5655	−1.45316
$859$	−17.5845	−0.599977	−0.299988	−	0.953943i	$-0.596983\pi$
$859$	−17.5845	−0.599977	−0.299988	+	0.953943i	$0.596983\pi$
$860$	3.38267	0.115348
$861$	1.61314	0.0549756
$862$	−47.3583	−1.61303
$863$	16.1652	0.550271	0.275135	−	0.961405i	$-0.411277\pi$
$863$	16.1652	0.550271	0.275135	+	0.961405i	$0.411277\pi$
$864$	3.94222	0.134117
$865$	−20.7080	−0.704092
$866$	−41.7331	−1.41815
$867$	−1.00000	−0.0339618
$868$	−61.3052	−2.08083
$869$	−72.3079	−2.45288
$870$	−45.5946	−1.54580
$871$	−22.6743	−0.768288
$872$	−35.6246	−1.20640
$873$	−7.63148	−0.258287
$874$	8.11232	0.274403
$875$	−22.7039	−0.767533
$876$	1.71605	0.0579798
$877$	19.6694	0.664187	0.332094	−	0.943246i	$-0.392245\pi$
$877$	19.6694	0.664187	0.332094	+	0.943246i	$0.392245\pi$
$878$	−37.4384	−1.26349
$879$	−20.7680	−0.700489
$880$	13.9555	0.470439
$881$	8.60690	0.289974	0.144987	−	0.989434i	$-0.453686\pi$
$881$	8.60690	0.289974	0.144987	+	0.989434i	$0.453686\pi$
$882$	−7.42411	−0.249983
$883$	23.2501	0.782427	0.391214	−	0.920300i	$-0.372055\pi$
$883$	23.2501	0.782427	0.391214	+	0.920300i	$0.372055\pi$
$884$	13.4412	0.452075
$885$	18.7111	0.628967
$886$	−29.7691	−1.00011
$887$	−44.1788	−1.48338	−0.741689	−	0.670744i	$-0.765975\pi$
$887$	−44.1788	−1.48338	−0.741689	+	0.670744i	$0.765975\pi$
$888$	13.0204	0.436936
$889$	−19.2416	−0.645342
$890$	−28.8773	−0.967969
$891$	4.74824	0.159072
$892$	−29.8968	−1.00102
$893$	−4.98309	−0.166753
$894$	6.36334	0.212822
$895$	39.7765	1.32958
$896$	−39.8568	−1.33152
$897$	−34.1192	−1.13921
$898$	−30.4536	−1.01625
$899$	−80.3079	−2.67842
$900$	−1.41941	−0.0473137
$901$	10.6831	0.355906
$902$	−9.18538	−0.305840
$903$	−0.877419	−0.0291987
$904$	68.7704	2.28727
$905$	10.2852	0.341890
$906$	50.4019	1.67449
$907$	−39.4330	−1.30935	−0.654675	−	0.755911i	$-0.727194\pi$
$907$	−39.4330	−1.30935	−0.654675	+	0.755911i	$0.727194\pi$
$908$	−45.7536	−1.51839
$909$	18.3682	0.609235
$910$	37.6711	1.24878
$911$	3.27136	0.108385	0.0541925	−	0.998531i	$-0.482742\pi$
$911$	3.27136	0.108385	0.0541925	+	0.998531i	$0.482742\pi$
$912$	−0.528905	−0.0175138
$913$	−49.1084	−1.62525
$914$	75.1210	2.48478
$915$	25.5240	0.843796
$916$	−6.33523	−0.209322
$917$	29.4017	0.970931
$918$	−2.35033	−0.0775724
$919$	−10.2147	−0.336953	−0.168477	−	0.985706i	$-0.553885\pi$
$919$	−10.2147	−0.336953	−0.168477	+	0.985706i	$0.553885\pi$
$920$	68.7028	2.26506
$921$	−14.6030	−0.481185
$922$	71.0143	2.33873
$923$	27.1978	0.895226
$924$	−32.7951	−1.07888
$925$	1.46409	0.0481389
$926$	40.3682	1.32658
$927$	3.68703	0.121098
$928$	−35.6680	−1.17086
$929$	−52.0247	−1.70687	−0.853437	−	0.521196i	$-0.825486\pi$
$929$	−52.0247	−1.70687	−0.853437	+	0.521196i	$0.825486\pi$
$930$	44.7298	1.46675
$931$	−1.21879	−0.0399443
$932$	−94.0917	−3.08208
$933$	−21.6421	−0.708529
$934$	37.8658	1.23901
$935$	10.1808	0.332947
$936$	13.6622	0.446563
$937$	38.6174	1.26158	0.630788	−	0.775955i	$-0.282732\pi$
$937$	38.6174	1.26158	0.630788	+	0.775955i	$0.282732\pi$
$938$	−27.3843	−0.894129
$939$	−1.60593	−0.0524074
$940$	−97.5828	−3.18280
$941$	3.66983	0.119633	0.0598165	−	0.998209i	$-0.480948\pi$
$941$	3.66983	0.119633	0.0598165	+	0.998209i	$0.480948\pi$
$942$	2.35033	0.0765778
$943$	−7.36273	−0.239763
$944$	−11.9623	−0.389341
$945$	−4.20227	−0.136700
$946$	4.99611	0.162438
$947$	9.67108	0.314268	0.157134	−	0.987577i	$-0.449775\pi$
$947$	9.67108	0.314268	0.157134	+	0.987577i	$0.449775\pi$
$948$	53.6652	1.74297
$949$	−1.85731	−0.0602908
$950$	−0.365266	−0.0118508
$951$	21.5274	0.698075
$952$	7.02037	0.227532
$953$	−46.3333	−1.50088	−0.750441	−	0.660938i	$-0.770159\pi$
$953$	−46.3333	−1.50088	−0.750441	+	0.660938i	$0.770159\pi$
$954$	25.1088	0.812928
$955$	−26.5647	−0.859614
$956$	73.3563	2.37251
$957$	−42.9606	−1.38872
$958$	49.2850	1.59233
$959$	−1.81371	−0.0585678
$960$	25.7445	0.830899
$961$	47.7846	1.54144
$962$	−32.5855	−1.05060
$963$	15.1620	0.488589
$964$	−8.38411	−0.270034
$965$	44.9537	1.44711
$966$	−41.2066	−1.32580
$967$	−46.5213	−1.49602	−0.748011	−	0.663686i	$-0.768991\pi$
$967$	−46.5213	−1.49602	−0.748011	+	0.663686i	$0.768991\pi$
$968$	41.3570	1.32926
$969$	−0.385846	−0.0123951
$970$	−38.4579	−1.23481
$971$	−15.0930	−0.484356	−0.242178	−	0.970232i	$-0.577862\pi$
$971$	−15.0930	−0.484356	−0.242178	+	0.970232i	$0.577862\pi$
$972$	−3.52404	−0.113034
$973$	−4.06663	−0.130370
$974$	−20.6980	−0.663206
$975$	1.53626	0.0491996
$976$	−16.3179	−0.522323
$977$	22.7935	0.729230	0.364615	−	0.931158i	$-0.381201\pi$
$977$	22.7935	0.729230	0.364615	+	0.931158i	$0.381201\pi$
$978$	−4.74426	−0.151705
$979$	−27.2090	−0.869605
$980$	−23.8673	−0.762414
$981$	−9.94549	−0.317535
$982$	−51.0578	−1.62932
$983$	34.7439	1.10816	0.554080	−	0.832464i	$-0.313070\pi$
$983$	34.7439	1.10816	0.554080	+	0.832464i	$0.313070\pi$
$984$	2.94822	0.0939858
$985$	−35.7595	−1.13939
$986$	21.2650	0.677216
$987$	25.3117	0.805680
$988$	5.18621	0.164995
$989$	4.00473	0.127343
$990$	23.9281	0.760486
$991$	21.5703	0.685202	0.342601	−	0.939481i	$-0.388692\pi$
$991$	21.5703	0.685202	0.342601	+	0.939481i	$0.388692\pi$
$992$	34.9915	1.11098
$993$	12.6455	0.401294
$994$	32.8475	1.04186
$995$	29.3180	0.929442
$996$	36.4471	1.15487
$997$	−0.407779	−0.0129145	−0.00645725	−	0.999979i	$-0.502055\pi$
$997$	−0.407779	−0.0129145	−0.00645725	+	0.999979i	$0.502055\pi$
$998$	29.7104	0.940465
$999$	3.63496	0.115005

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.57	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.57	✓	64	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)

\(f(q)\)	\(=\)	\(q+2.35033 q^{2} -1.00000 q^{3} +3.52404 q^{4} +2.14411 q^{5} -2.35033 q^{6} +1.95991 q^{7} +3.58199 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.35033 q^{2} -1.00000 q^{3} +3.52404 q^{4} +2.14411 q^{5} -2.35033 q^{6} +1.95991 q^{7} +3.58199 q^{8} +1.00000 q^{9} +5.03937 q^{10} +4.74824 q^{11} -3.52404 q^{12} +3.81414 q^{13} +4.60643 q^{14} -2.14411 q^{15} +1.37077 q^{16} +1.00000 q^{17} +2.35033 q^{18} +0.385846 q^{19} +7.55594 q^{20} -1.95991 q^{21} +11.1599 q^{22} +8.94546 q^{23} -3.58199 q^{24} -0.402780 q^{25} +8.96447 q^{26} -1.00000 q^{27} +6.90680 q^{28} +9.04768 q^{29} -5.03937 q^{30} -8.87607 q^{31} -3.94222 q^{32} -4.74824 q^{33} +2.35033 q^{34} +4.20227 q^{35} +3.52404 q^{36} -3.63496 q^{37} +0.906864 q^{38} -3.81414 q^{39} +7.68019 q^{40} -0.823068 q^{41} -4.60643 q^{42} +0.447683 q^{43} +16.7330 q^{44} +2.14411 q^{45} +21.0248 q^{46} -12.9147 q^{47} -1.37077 q^{48} -3.15876 q^{49} -0.946664 q^{50} -1.00000 q^{51} +13.4412 q^{52} +10.6831 q^{53} -2.35033 q^{54} +10.1808 q^{55} +7.02037 q^{56} -0.385846 q^{57} +21.2650 q^{58} -8.72674 q^{59} -7.55594 q^{60} -11.9042 q^{61} -20.8617 q^{62} +1.95991 q^{63} -12.0071 q^{64} +8.17794 q^{65} -11.1599 q^{66} -5.94480 q^{67} +3.52404 q^{68} -8.94546 q^{69} +9.87670 q^{70} +7.13079 q^{71} +3.58199 q^{72} -0.486955 q^{73} -8.54335 q^{74} +0.402780 q^{75} +1.35973 q^{76} +9.30613 q^{77} -8.96447 q^{78} -15.2283 q^{79} +2.93908 q^{80} +1.00000 q^{81} -1.93448 q^{82} -10.3424 q^{83} -6.90680 q^{84} +2.14411 q^{85} +1.05220 q^{86} -9.04768 q^{87} +17.0081 q^{88} -5.73034 q^{89} +5.03937 q^{90} +7.47536 q^{91} +31.5241 q^{92} +8.87607 q^{93} -30.3538 q^{94} +0.827297 q^{95} +3.94222 q^{96} -7.63148 q^{97} -7.42411 q^{98} +4.74824 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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