LMFDB - Embedded newform 8007.2.a.j.1.18

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			1.18
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.55552 q^{2} -1.00000 q^{3} +0.419651 q^{4} -2.03554 q^{5} +1.55552 q^{6} -4.57317 q^{7} +2.45827 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.55552 q^{2} -1.00000 q^{3} +0.419651 q^{4} -2.03554 q^{5} +1.55552 q^{6} -4.57317 q^{7} +2.45827 q^{8} +1.00000 q^{9} +3.16632 q^{10} +3.90117 q^{11} -0.419651 q^{12} -2.99785 q^{13} +7.11366 q^{14} +2.03554 q^{15} -4.66320 q^{16} +1.00000 q^{17} -1.55552 q^{18} +7.30910 q^{19} -0.854216 q^{20} +4.57317 q^{21} -6.06836 q^{22} +3.66963 q^{23} -2.45827 q^{24} -0.856587 q^{25} +4.66322 q^{26} -1.00000 q^{27} -1.91913 q^{28} +0.0200199 q^{29} -3.16632 q^{30} -8.38816 q^{31} +2.33717 q^{32} -3.90117 q^{33} -1.55552 q^{34} +9.30885 q^{35} +0.419651 q^{36} -0.292369 q^{37} -11.3695 q^{38} +2.99785 q^{39} -5.00390 q^{40} -5.24937 q^{41} -7.11366 q^{42} +9.50720 q^{43} +1.63713 q^{44} -2.03554 q^{45} -5.70819 q^{46} +10.0553 q^{47} +4.66320 q^{48} +13.9138 q^{49} +1.33244 q^{50} -1.00000 q^{51} -1.25805 q^{52} +12.8571 q^{53} +1.55552 q^{54} -7.94099 q^{55} -11.2421 q^{56} -7.30910 q^{57} -0.0311414 q^{58} +8.07056 q^{59} +0.854216 q^{60} -12.6110 q^{61} +13.0480 q^{62} -4.57317 q^{63} +5.69087 q^{64} +6.10223 q^{65} +6.06836 q^{66} +10.2107 q^{67} +0.419651 q^{68} -3.66963 q^{69} -14.4801 q^{70} -0.437604 q^{71} +2.45827 q^{72} -7.02387 q^{73} +0.454787 q^{74} +0.856587 q^{75} +3.06727 q^{76} -17.8407 q^{77} -4.66322 q^{78} +8.59159 q^{79} +9.49211 q^{80} +1.00000 q^{81} +8.16551 q^{82} +2.89402 q^{83} +1.91913 q^{84} -2.03554 q^{85} -14.7887 q^{86} -0.0200199 q^{87} +9.59013 q^{88} -9.08276 q^{89} +3.16632 q^{90} +13.7096 q^{91} +1.53996 q^{92} +8.38816 q^{93} -15.6413 q^{94} -14.8779 q^{95} -2.33717 q^{96} -15.4111 q^{97} -21.6433 q^{98} +3.90117 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.55552	−1.09992	−0.549960	−	0.835191i	$-0.685357\pi$
$2$	−1.55552	−1.09992	−0.549960	+	0.835191i	$0.685357\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.419651	0.209826
$5$	−2.03554	−0.910320	−0.455160	−	0.890410i	$-0.650418\pi$
$5$	−2.03554	−0.910320	−0.455160	+	0.890410i	$0.650418\pi$
$6$	1.55552	0.635040
$7$	−4.57317	−1.72849	−0.864247	−	0.503068i	$-0.832205\pi$
$7$	−4.57317	−1.72849	−0.864247	+	0.503068i	$0.832205\pi$
$8$	2.45827	0.869129
$9$	1.00000	0.333333
$10$	3.16632	1.00128
$11$	3.90117	1.17625	0.588124	−	0.808771i	$-0.299867\pi$
$11$	3.90117	1.17625	0.588124	+	0.808771i	$0.299867\pi$
$12$	−0.419651	−0.121143
$13$	−2.99785	−0.831453	−0.415726	−	0.909490i	$-0.636473\pi$
$13$	−2.99785	−0.831453	−0.415726	+	0.909490i	$0.636473\pi$
$14$	7.11366	1.90121
$15$	2.03554	0.525574
$16$	−4.66320	−1.16580
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.55552	−0.366640
$19$	7.30910	1.67682	0.838411	−	0.545038i	$-0.183485\pi$
$19$	7.30910	1.67682	0.838411	+	0.545038i	$0.183485\pi$
$20$	−0.854216	−0.191008
$21$	4.57317	0.997946
$22$	−6.06836	−1.29378
$23$	3.66963	0.765171	0.382585	−	0.923920i	$-0.375034\pi$
$23$	3.66963	0.765171	0.382585	+	0.923920i	$0.375034\pi$
$24$	−2.45827	−0.501792
$25$	−0.856587	−0.171317
$26$	4.66322	0.914532
$27$	−1.00000	−0.192450
$28$	−1.91913	−0.362682
$29$	0.0200199	0.00371761	0.00185880	−	0.999998i	$-0.499408\pi$
$29$	0.0200199	0.00371761	0.00185880	+	0.999998i	$0.499408\pi$
$30$	−3.16632	−0.578089
$31$	−8.38816	−1.50656	−0.753279	−	0.657701i	$-0.771529\pi$
$31$	−8.38816	−1.50656	−0.753279	+	0.657701i	$0.771529\pi$
$32$	2.33717	0.413157
$33$	−3.90117	−0.679107
$34$	−1.55552	−0.266770
$35$	9.30885	1.57348
$36$	0.419651	0.0699419
$37$	−0.292369	−0.0480652	−0.0240326	−	0.999711i	$-0.507651\pi$
$37$	−0.292369	−0.0480652	−0.0240326	+	0.999711i	$0.507651\pi$
$38$	−11.3695	−1.84437
$39$	2.99785	0.480040
$40$	−5.00390	−0.791186
$41$	−5.24937	−0.819814	−0.409907	−	0.912127i	$-0.634439\pi$
$41$	−5.24937	−0.819814	−0.409907	+	0.912127i	$0.634439\pi$
$42$	−7.11366	−1.09766
$43$	9.50720	1.44983	0.724917	−	0.688836i	$-0.241878\pi$
$43$	9.50720	1.44983	0.724917	+	0.688836i	$0.241878\pi$
$44$	1.63713	0.246807
$45$	−2.03554	−0.303440
$46$	−5.70819	−0.841627
$47$	10.0553	1.46672	0.733361	−	0.679839i	$-0.237950\pi$
$47$	10.0553	1.46672	0.733361	+	0.679839i	$0.237950\pi$
$48$	4.66320	0.673074
$49$	13.9138	1.98769
$50$	1.33244	0.188436
$51$	−1.00000	−0.140028
$52$	−1.25805	−0.174460
$53$	12.8571	1.76606	0.883031	−	0.469314i	$-0.155499\pi$
$53$	12.8571	1.76606	0.883031	+	0.469314i	$0.155499\pi$
$54$	1.55552	0.211680
$55$	−7.94099	−1.07076
$56$	−11.2421	−1.50228
$57$	−7.30910	−0.968114
$58$	−0.0311414	−0.00408907
$59$	8.07056	1.05070	0.525349	−	0.850887i	$-0.323935\pi$
$59$	8.07056	1.05070	0.525349	+	0.850887i	$0.323935\pi$
$60$	0.854216	0.110279
$61$	−12.6110	−1.61467	−0.807335	−	0.590094i	$-0.799091\pi$
$61$	−12.6110	−1.61467	−0.807335	+	0.590094i	$0.799091\pi$
$62$	13.0480	1.65709
$63$	−4.57317	−0.576165
$64$	5.69087	0.711359
$65$	6.10223	0.756888
$66$	6.06836	0.746964
$67$	10.2107	1.24744	0.623720	−	0.781648i	$-0.285621\pi$
$67$	10.2107	1.24744	0.623720	+	0.781648i	$0.285621\pi$
$68$	0.419651	0.0508902
$69$	−3.66963	−0.441771
$70$	−14.4801	−1.73071
$71$	−0.437604	−0.0519340	−0.0259670	−	0.999663i	$-0.508266\pi$
$71$	−0.437604	−0.0519340	−0.0259670	+	0.999663i	$0.508266\pi$
$72$	2.45827	0.289710
$73$	−7.02387	−0.822082	−0.411041	−	0.911617i	$-0.634835\pi$
$73$	−7.02387	−0.822082	−0.411041	+	0.911617i	$0.634835\pi$
$74$	0.454787	0.0528679
$75$	0.856587	0.0989102
$76$	3.06727	0.351840
$77$	−17.8407	−2.03314
$78$	−4.66322	−0.528005
$79$	8.59159	0.966629	0.483314	−	0.875447i	$-0.339433\pi$
$79$	8.59159	0.966629	0.483314	+	0.875447i	$0.339433\pi$
$80$	9.49211	1.06125
$81$	1.00000	0.111111
$82$	8.16551	0.901730
$83$	2.89402	0.317660	0.158830	−	0.987306i	$-0.449228\pi$
$83$	2.89402	0.317660	0.158830	+	0.987306i	$0.449228\pi$
$84$	1.91913	0.209395
$85$	−2.03554	−0.220785
$86$	−14.7887	−1.59470
$87$	−0.0200199	−0.00214636
$88$	9.59013	1.02231
$89$	−9.08276	−0.962771	−0.481385	−	0.876509i	$-0.659866\pi$
$89$	−9.08276	−0.962771	−0.481385	+	0.876509i	$0.659866\pi$
$90$	3.16632	0.333760
$91$	13.7096	1.43716
$92$	1.53996	0.160552
$93$	8.38816	0.869812
$94$	−15.6413	−1.61328
$95$	−14.8779	−1.52645
$96$	−2.33717	−0.238536
$97$	−15.4111	−1.56476	−0.782382	−	0.622799i	$-0.785995\pi$
$97$	−15.4111	−1.56476	−0.782382	+	0.622799i	$0.785995\pi$
$98$	−21.6433	−2.18630
$99$	3.90117	0.392083
$100$	−0.359468	−0.0359468
$101$	−12.8823	−1.28184	−0.640919	−	0.767609i	$-0.721447\pi$
$101$	−12.8823	−1.28184	−0.640919	+	0.767609i	$0.721447\pi$
$102$	1.55552	0.154020
$103$	−6.60272	−0.650585	−0.325293	−	0.945613i	$-0.605463\pi$
$103$	−6.60272	−0.650585	−0.325293	+	0.945613i	$0.605463\pi$
$104$	−7.36951	−0.722640
$105$	−9.30885	−0.908451
$106$	−19.9996	−1.94253
$107$	11.9939	1.15950	0.579748	−	0.814796i	$-0.303151\pi$
$107$	11.9939	1.15950	0.579748	+	0.814796i	$0.303151\pi$
$108$	−0.419651	−0.0403810
$109$	−18.4739	−1.76948	−0.884739	−	0.466087i	$-0.845663\pi$
$109$	−18.4739	−1.76948	−0.884739	+	0.466087i	$0.845663\pi$
$110$	12.3524	1.17775
$111$	0.292369	0.0277504
$112$	21.3256	2.01508
$113$	16.2992	1.53330	0.766650	−	0.642065i	$-0.221922\pi$
$113$	16.2992	1.53330	0.766650	+	0.642065i	$0.221922\pi$
$114$	11.3695	1.06485
$115$	−7.46967	−0.696550
$116$	0.00840138	0.000780049 0
$117$	−2.99785	−0.277151
$118$	−12.5539	−1.15568
$119$	−4.57317	−0.419221
$120$	5.00390	0.456791
$121$	4.21915	0.383560
$122$	19.6167	1.77601
$123$	5.24937	0.473320
$124$	−3.52010	−0.316114
$125$	11.9213	1.06627
$126$	7.11366	0.633735
$127$	−0.143771	−0.0127576	−0.00637882	−	0.999980i	$-0.502030\pi$
$127$	−0.143771	−0.0127576	−0.00637882	+	0.999980i	$0.502030\pi$
$128$	−13.5266	−1.19560
$129$	−9.50720	−0.837063
$130$	−9.49216	−0.832517
$131$	−19.5325	−1.70656	−0.853280	−	0.521453i	$-0.825390\pi$
$131$	−19.5325	−1.70656	−0.853280	+	0.521453i	$0.825390\pi$
$132$	−1.63713	−0.142494
$133$	−33.4257	−2.89838
$134$	−15.8830	−1.37208
$135$	2.03554	0.175191
$136$	2.45827	0.210795
$137$	−12.6038	−1.07681	−0.538406	−	0.842686i	$-0.680973\pi$
$137$	−12.6038	−1.07681	−0.538406	+	0.842686i	$0.680973\pi$
$138$	5.70819	0.485914
$139$	7.63118	0.647268	0.323634	−	0.946182i	$-0.395095\pi$
$139$	7.63118	0.647268	0.323634	+	0.946182i	$0.395095\pi$
$140$	3.90647	0.330157
$141$	−10.0553	−0.846813
$142$	0.680703	0.0571233
$143$	−11.6951	−0.977995
$144$	−4.66320	−0.388600
$145$	−0.0407513	−0.00338421
$146$	10.9258	0.904225
$147$	−13.9138	−1.14759
$148$	−0.122693	−0.0100853
$149$	−11.3207	−0.927429	−0.463714	−	0.885985i	$-0.653484\pi$
$149$	−11.3207	−0.927429	−0.463714	+	0.885985i	$0.653484\pi$
$150$	−1.33244	−0.108793
$151$	4.35225	0.354181	0.177091	−	0.984195i	$-0.443331\pi$
$151$	4.35225	0.354181	0.177091	+	0.984195i	$0.443331\pi$
$152$	17.9677	1.45738
$153$	1.00000	0.0808452
$154$	27.7516	2.23629
$155$	17.0744	1.37145
$156$	1.25805	0.100725
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−13.3644	−1.06322
$159$	−12.8571	−1.01964
$160$	−4.75740	−0.376105
$161$	−16.7818	−1.32259
$162$	−1.55552	−0.122213
$163$	−6.81731	−0.533973	−0.266987	−	0.963700i	$-0.586028\pi$
$163$	−6.81731	−0.533973	−0.266987	+	0.963700i	$0.586028\pi$
$164$	−2.20290	−0.172018
$165$	7.94099	0.618205
$166$	−4.50172	−0.349401
$167$	−21.0854	−1.63164	−0.815819	−	0.578307i	$-0.803713\pi$
$167$	−21.0854	−1.63164	−0.815819	+	0.578307i	$0.803713\pi$
$168$	11.2421	0.867344
$169$	−4.01292	−0.308686
$170$	3.16632	0.242846
$171$	7.30910	0.558941
$172$	3.98971	0.304212
$173$	−22.7687	−1.73107	−0.865536	−	0.500847i	$-0.833022\pi$
$173$	−22.7687	−1.73107	−0.865536	+	0.500847i	$0.833022\pi$
$174$	0.0311414	0.00236083
$175$	3.91731	0.296121
$176$	−18.1919	−1.37127
$177$	−8.07056	−0.606621
$178$	14.1284	1.05897
$179$	10.9699	0.819929	0.409965	−	0.912101i	$-0.365541\pi$
$179$	10.9699	0.819929	0.409965	+	0.912101i	$0.365541\pi$
$180$	−0.854216	−0.0636695
$181$	10.5405	0.783467	0.391733	−	0.920079i	$-0.371876\pi$
$181$	10.5405	0.783467	0.391733	+	0.920079i	$0.371876\pi$
$182$	−21.3257	−1.58076
$183$	12.6110	0.932230
$184$	9.02094	0.665032
$185$	0.595128	0.0437547
$186$	−13.0480	−0.956724
$187$	3.90117	0.285282
$188$	4.21974	0.307756
$189$	4.57317	0.332649
$190$	23.1430	1.67897
$191$	−12.2544	−0.886696	−0.443348	−	0.896350i	$-0.646209\pi$
$191$	−12.2544	−0.886696	−0.443348	+	0.896350i	$0.646209\pi$
$192$	−5.69087	−0.410703
$193$	2.36320	0.170107	0.0850533	−	0.996376i	$-0.472894\pi$
$193$	2.36320	0.170107	0.0850533	+	0.996376i	$0.472894\pi$
$194$	23.9724	1.72112
$195$	−6.10223	−0.436990
$196$	5.83896	0.417068
$197$	14.7699	1.05231	0.526156	−	0.850388i	$-0.323633\pi$
$197$	14.7699	1.05231	0.526156	+	0.850388i	$0.323633\pi$
$198$	−6.06836	−0.431260
$199$	2.29742	0.162860	0.0814299	−	0.996679i	$-0.474051\pi$
$199$	2.29742	0.162860	0.0814299	+	0.996679i	$0.474051\pi$
$200$	−2.10572	−0.148897
$201$	−10.2107	−0.720209
$202$	20.0387	1.40992
$203$	−0.0915544	−0.00642586
$204$	−0.419651	−0.0293815
$205$	10.6853	0.746293
$206$	10.2707	0.715592
$207$	3.66963	0.255057
$208$	13.9795	0.969307
$209$	28.5141	1.97236
$210$	14.4801	0.999224
$211$	−9.90698	−0.682024	−0.341012	−	0.940059i	$-0.610770\pi$
$211$	−9.90698	−0.682024	−0.341012	+	0.940059i	$0.610770\pi$
$212$	5.39551	0.370565
$213$	0.437604	0.0299841
$214$	−18.6568	−1.27535
$215$	−19.3523	−1.31981
$216$	−2.45827	−0.167264
$217$	38.3604	2.60408
$218$	28.7366	1.94629
$219$	7.02387	0.474629
$220$	−3.33244	−0.224673
$221$	−2.99785	−0.201657
$222$	−0.454787	−0.0305233
$223$	1.74311	0.116727	0.0583637	−	0.998295i	$-0.481412\pi$
$223$	1.74311	0.116727	0.0583637	+	0.998295i	$0.481412\pi$
$224$	−10.6883	−0.714139
$225$	−0.856587	−0.0571058
$226$	−25.3538	−1.68651
$227$	−15.4763	−1.02720	−0.513599	−	0.858031i	$-0.671688\pi$
$227$	−15.4763	−1.02720	−0.513599	+	0.858031i	$0.671688\pi$
$228$	−3.06727	−0.203135
$229$	22.2233	1.46855	0.734277	−	0.678850i	$-0.237521\pi$
$229$	22.2233	1.46855	0.734277	+	0.678850i	$0.237521\pi$
$230$	11.6192	0.766150
$231$	17.8407	1.17383
$232$	0.0492144	0.00323108
$233$	−1.48059	−0.0969966	−0.0484983	−	0.998823i	$-0.515444\pi$
$233$	−1.48059	−0.0969966	−0.0484983	+	0.998823i	$0.515444\pi$
$234$	4.66322	0.304844
$235$	−20.4680	−1.33519
$236$	3.38682	0.220463
$237$	−8.59159	−0.558083
$238$	7.11366	0.461110
$239$	−28.7088	−1.85702	−0.928510	−	0.371308i	$-0.878909\pi$
$239$	−28.7088	−1.85702	−0.928510	+	0.371308i	$0.878909\pi$
$240$	−9.49211	−0.612713
$241$	18.9584	1.22122	0.610610	−	0.791931i	$-0.290924\pi$
$241$	18.9584	1.22122	0.610610	+	0.791931i	$0.290924\pi$
$242$	−6.56299	−0.421885
$243$	−1.00000	−0.0641500
$244$	−5.29221	−0.338799
$245$	−28.3221	−1.80944
$246$	−8.16551	−0.520614
$247$	−21.9116	−1.39420
$248$	−20.6204	−1.30939
$249$	−2.89402	−0.183401
$250$	−18.5439	−1.17282
$251$	−9.85301	−0.621916	−0.310958	−	0.950424i	$-0.600650\pi$
$251$	−9.85301	−0.621916	−0.310958	+	0.950424i	$0.600650\pi$
$252$	−1.91913	−0.120894
$253$	14.3159	0.900031
$254$	0.223639	0.0140324
$255$	2.03554	0.127470
$256$	9.65922	0.603701
$257$	22.6093	1.41033	0.705164	−	0.709045i	$-0.250874\pi$
$257$	22.6093	1.41033	0.705164	+	0.709045i	$0.250874\pi$
$258$	14.7887	0.920702
$259$	1.33705	0.0830804
$260$	2.56081	0.158815
$261$	0.0200199	0.00123920
$262$	30.3832	1.87708
$263$	24.3146	1.49930	0.749652	−	0.661832i	$-0.230221\pi$
$263$	24.3146	1.49930	0.749652	+	0.661832i	$0.230221\pi$
$264$	−9.59013	−0.590232
$265$	−26.1712	−1.60768
$266$	51.9945	3.18799
$267$	9.08276	0.555856
$268$	4.28494	0.261745
$269$	8.21607	0.500943	0.250471	−	0.968124i	$-0.419414\pi$
$269$	8.21607	0.500943	0.250471	+	0.968124i	$0.419414\pi$
$270$	−3.16632	−0.192696
$271$	−22.6957	−1.37867	−0.689333	−	0.724445i	$-0.742096\pi$
$271$	−22.6957	−1.37867	−0.689333	+	0.724445i	$0.742096\pi$
$272$	−4.66320	−0.282748
$273$	−13.7096	−0.829746
$274$	19.6054	1.18441
$275$	−3.34169	−0.201512
$276$	−1.53996	−0.0926950
$277$	16.4110	0.986041	0.493020	−	0.870018i	$-0.335893\pi$
$277$	16.4110	0.986041	0.493020	+	0.870018i	$0.335893\pi$
$278$	−11.8705	−0.711944
$279$	−8.38816	−0.502186
$280$	22.8837	1.36756
$281$	−31.3631	−1.87096	−0.935482	−	0.353375i	$-0.885034\pi$
$281$	−31.3631	−1.87096	−0.935482	+	0.353375i	$0.885034\pi$
$282$	15.6413	0.931427
$283$	−7.24052	−0.430404	−0.215202	−	0.976570i	$-0.569041\pi$
$283$	−7.24052	−0.430404	−0.215202	+	0.976570i	$0.569041\pi$
$284$	−0.183641	−0.0108971
$285$	14.8779	0.881294
$286$	18.1920	1.07572
$287$	24.0062	1.41704
$288$	2.33717	0.137719
$289$	1.00000	0.0588235
$290$	0.0633896	0.00372236
$291$	15.4111	0.903417
$292$	−2.94758	−0.172494
$293$	27.1349	1.58524	0.792620	−	0.609716i	$-0.208716\pi$
$293$	27.1349	1.58524	0.792620	+	0.609716i	$0.208716\pi$
$294$	21.6433	1.26226
$295$	−16.4279	−0.956471
$296$	−0.718722	−0.0417748
$297$	−3.90117	−0.226369
$298$	17.6096	1.02010
$299$	−11.0010	−0.636203
$300$	0.359468	0.0207539
$301$	−43.4780	−2.50603
$302$	−6.77002	−0.389571
$303$	12.8823	0.740069
$304$	−34.0838	−1.95484
$305$	25.6701	1.46987
$306$	−1.55552	−0.0889233
$307$	23.6325	1.34878	0.674388	−	0.738377i	$-0.264408\pi$
$307$	23.6325	1.34878	0.674388	+	0.738377i	$0.264408\pi$
$308$	−7.48687	−0.426604
$309$	6.60272	0.375615
$310$	−26.5596	−1.50849
$311$	3.33390	0.189048	0.0945240	−	0.995523i	$-0.469867\pi$
$311$	3.33390	0.189048	0.0945240	+	0.995523i	$0.469867\pi$
$312$	7.36951	0.417216
$313$	23.0077	1.30047	0.650236	−	0.759732i	$-0.274670\pi$
$313$	23.0077	1.30047	0.650236	+	0.759732i	$0.274670\pi$
$314$	1.55552	0.0877832
$315$	9.30885	0.524494
$316$	3.60547	0.202823
$317$	−8.74775	−0.491323	−0.245661	−	0.969356i	$-0.579005\pi$
$317$	−8.74775	−0.491323	−0.245661	+	0.969356i	$0.579005\pi$
$318$	19.9996	1.12152
$319$	0.0781012	0.00437283
$320$	−11.5840	−0.647564
$321$	−11.9939	−0.669436
$322$	26.1045	1.45475
$323$	7.30910	0.406689
$324$	0.419651	0.0233140
$325$	2.56792	0.142442
$326$	10.6045	0.587328
$327$	18.4739	1.02161
$328$	−12.9044	−0.712524
$329$	−45.9848	−2.53522
$330$	−12.3524	−0.679976
$331$	27.0704	1.48792	0.743962	−	0.668222i	$-0.232944\pi$
$331$	27.0704	1.48792	0.743962	+	0.668222i	$0.232944\pi$
$332$	1.21448	0.0666532
$333$	−0.292369	−0.0160217
$334$	32.7988	1.79467
$335$	−20.7843	−1.13557
$336$	−21.3256	−1.16340
$337$	−0.0116226	−0.000633126 0	−0.000316563	−	1.00000i	$-0.500101\pi$
$337$	−0.0116226	−0.000633126 0	−0.000316563		1.00000i	$0.500101\pi$
$338$	6.24218	0.339530
$339$	−16.2992	−0.885251
$340$	−0.854216	−0.0463263
$341$	−32.7237	−1.77209
$342$	−11.3695	−0.614791
$343$	−31.6181	−1.70722
$344$	23.3713	1.26009
$345$	7.46967	0.402153
$346$	35.4172	1.90404
$347$	29.9886	1.60987	0.804936	−	0.593362i	$-0.202200\pi$
$347$	29.9886	1.60987	0.804936	+	0.593362i	$0.202200\pi$
$348$	−0.00840138	−0.000450361 0
$349$	17.8530	0.955651	0.477826	−	0.878455i	$-0.341425\pi$
$349$	17.8530	0.955651	0.477826	+	0.878455i	$0.341425\pi$
$350$	−6.09347	−0.325710
$351$	2.99785	0.160013
$352$	9.11770	0.485975
$353$	8.74485	0.465442	0.232721	−	0.972544i	$-0.425237\pi$
$353$	8.74485	0.465442	0.232721	+	0.972544i	$0.425237\pi$
$354$	12.5539	0.667235
$355$	0.890759	0.0472766
$356$	−3.81159	−0.202014
$357$	4.57317	0.242038
$358$	−17.0639	−0.901857
$359$	−9.22375	−0.486811	−0.243405	−	0.969925i	$-0.578265\pi$
$359$	−9.22375	−0.486811	−0.243405	+	0.969925i	$0.578265\pi$
$360$	−5.00390	−0.263729
$361$	34.4229	1.81173
$362$	−16.3959	−0.861751
$363$	−4.21915	−0.221448
$364$	5.75327	0.301553
$365$	14.2974	0.748358
$366$	−19.6167	−1.02538
$367$	−24.6412	−1.28626	−0.643131	−	0.765756i	$-0.722365\pi$
$367$	−24.6412	−1.28626	−0.643131	+	0.765756i	$0.722365\pi$
$368$	−17.1122	−0.892035
$369$	−5.24937	−0.273271
$370$	−0.925735	−0.0481267
$371$	−58.7978	−3.05263
$372$	3.52010	0.182509
$373$	17.3678	0.899268	0.449634	−	0.893213i	$-0.351554\pi$
$373$	17.3678	0.899268	0.449634	+	0.893213i	$0.351554\pi$
$374$	−6.06836	−0.313788
$375$	−11.9213	−0.615613
$376$	24.7187	1.27477
$377$	−0.0600167	−0.00309102
$378$	−7.11366	−0.365887
$379$	2.10251	0.107999	0.0539994	−	0.998541i	$-0.482803\pi$
$379$	2.10251	0.107999	0.0539994	+	0.998541i	$0.482803\pi$
$380$	−6.24355	−0.320287
$381$	0.143771	0.00736562
$382$	19.0620	0.975295
$383$	−17.7158	−0.905237	−0.452619	−	0.891704i	$-0.649510\pi$
$383$	−17.7158	−0.905237	−0.452619	+	0.891704i	$0.649510\pi$
$384$	13.5266	0.690277
$385$	36.3154	1.85081
$386$	−3.67601	−0.187104
$387$	9.50720	0.483278
$388$	−6.46730	−0.328327
$389$	−7.01741	−0.355797	−0.177898	−	0.984049i	$-0.556930\pi$
$389$	−7.01741	−0.355797	−0.177898	+	0.984049i	$0.556930\pi$
$390$	9.49216	0.480654
$391$	3.66963	0.185581
$392$	34.2040	1.72756
$393$	19.5325	0.985283
$394$	−22.9749	−1.15746
$395$	−17.4885	−0.879942
$396$	1.63713	0.0822690
$397$	−6.33329	−0.317859	−0.158929	−	0.987290i	$-0.550804\pi$
$397$	−6.33329	−0.317859	−0.158929	+	0.987290i	$0.550804\pi$
$398$	−3.57369	−0.179133
$399$	33.4257	1.67338
$400$	3.99443	0.199722
$401$	22.9700	1.14707	0.573533	−	0.819182i	$-0.305572\pi$
$401$	22.9700	1.14707	0.573533	+	0.819182i	$0.305572\pi$
$402$	15.8830	0.792173
$403$	25.1464	1.25263
$404$	−5.40608	−0.268962
$405$	−2.03554	−0.101147
$406$	0.142415	0.00706794
$407$	−1.14058	−0.0565366
$408$	−2.45827	−0.121702
$409$	−26.3680	−1.30381	−0.651907	−	0.758299i	$-0.726031\pi$
$409$	−26.3680	−1.30381	−0.651907	+	0.758299i	$0.726031\pi$
$410$	−16.6212	−0.820863
$411$	12.6038	0.621697
$412$	−2.77084	−0.136509
$413$	−36.9080	−1.81613
$414$	−5.70819	−0.280542
$415$	−5.89089	−0.289172
$416$	−7.00647	−0.343521
$417$	−7.63118	−0.373701
$418$	−44.3543	−2.16944
$419$	−3.87461	−0.189287	−0.0946436	−	0.995511i	$-0.530171\pi$
$419$	−3.87461	−0.189287	−0.0946436	+	0.995511i	$0.530171\pi$
$420$	−3.90647	−0.190616
$421$	18.7232	0.912515	0.456258	−	0.889848i	$-0.349190\pi$
$421$	18.7232	0.912515	0.456258	+	0.889848i	$0.349190\pi$
$422$	15.4105	0.750173
$423$	10.0553	0.488908
$424$	31.6063	1.53494
$425$	−0.856587	−0.0415506
$426$	−0.680703	−0.0329801
$427$	57.6721	2.79095
$428$	5.03327	0.243292
$429$	11.6951	0.564646
$430$	30.1029	1.45169
$431$	10.1227	0.487592	0.243796	−	0.969827i	$-0.421607\pi$
$431$	10.1227	0.487592	0.243796	+	0.969827i	$0.421607\pi$
$432$	4.66320	0.224358
$433$	14.5325	0.698386	0.349193	−	0.937051i	$-0.386456\pi$
$433$	14.5325	0.698386	0.349193	+	0.937051i	$0.386456\pi$
$434$	−59.6706	−2.86428
$435$	0.0407513	0.00195388
$436$	−7.75259	−0.371282
$437$	26.8217	1.28306
$438$	−10.9258	−0.522055
$439$	7.05792	0.336856	0.168428	−	0.985714i	$-0.446131\pi$
$439$	7.05792	0.336856	0.168428	+	0.985714i	$0.446131\pi$
$440$	−19.5211	−0.930631
$441$	13.9138	0.662564
$442$	4.66322	0.221807
$443$	18.0831	0.859155	0.429577	−	0.903030i	$-0.358663\pi$
$443$	18.0831	0.859155	0.429577	+	0.903030i	$0.358663\pi$
$444$	0.122693	0.00582275
$445$	18.4883	0.876429
$446$	−2.71145	−0.128391
$447$	11.3207	0.535451
$448$	−26.0253	−1.22958
$449$	29.8017	1.40643	0.703214	−	0.710978i	$-0.251748\pi$
$449$	29.8017	1.40643	0.703214	+	0.710978i	$0.251748\pi$
$450$	1.33244	0.0628119
$451$	−20.4787	−0.964304
$452$	6.83998	0.321725
$453$	−4.35225	−0.204487
$454$	24.0737	1.12984
$455$	−27.9065	−1.30828
$456$	−17.9677	−0.841416
$457$	−8.18031	−0.382659	−0.191329	−	0.981526i	$-0.561280\pi$
$457$	−8.18031	−0.382659	−0.191329	+	0.981526i	$0.561280\pi$
$458$	−34.5688	−1.61529
$459$	−1.00000	−0.0466760
$460$	−3.13466	−0.146154
$461$	−37.4805	−1.74564	−0.872821	−	0.488040i	$-0.837712\pi$
$461$	−37.4805	−1.74564	−0.872821	+	0.488040i	$0.837712\pi$
$462$	−27.7516	−1.29112
$463$	−18.9114	−0.878889	−0.439444	−	0.898270i	$-0.644825\pi$
$463$	−18.9114	−0.878889	−0.439444	+	0.898270i	$0.644825\pi$
$464$	−0.0933568	−0.00433398
$465$	−17.0744	−0.791807
$466$	2.30309	0.106689
$467$	16.1399	0.746867	0.373434	−	0.927657i	$-0.378180\pi$
$467$	16.1399	0.746867	0.373434	+	0.927657i	$0.378180\pi$
$468$	−1.25805	−0.0581534
$469$	−46.6954	−2.15619
$470$	31.8385	1.46860
$471$	1.00000	0.0460776
$472$	19.8396	0.913192
$473$	37.0892	1.70537
$474$	13.3644	0.613848
$475$	−6.26088	−0.287269
$476$	−1.91913	−0.0879634
$477$	12.8571	0.588688
$478$	44.6572	2.04257
$479$	−36.8349	−1.68303	−0.841514	−	0.540235i	$-0.818335\pi$
$479$	−36.8349	−1.68303	−0.841514	+	0.540235i	$0.818335\pi$
$480$	4.75740	0.217144
$481$	0.876477	0.0399639
$482$	−29.4903	−1.34325
$483$	16.7818	0.763599
$484$	1.77057	0.0804806
$485$	31.3699	1.42444
$486$	1.55552	0.0705599
$487$	33.6704	1.52575	0.762876	−	0.646545i	$-0.223787\pi$
$487$	33.6704	1.52575	0.762876	+	0.646545i	$0.223787\pi$
$488$	−31.0012	−1.40336
$489$	6.81731	0.308290
$490$	44.0557	1.99024
$491$	−4.69357	−0.211818	−0.105909	−	0.994376i	$-0.533775\pi$
$491$	−4.69357	−0.211818	−0.105909	+	0.994376i	$0.533775\pi$
$492$	2.20290	0.0993146
$493$	0.0200199	0.000901652 0
$494$	34.0839	1.53351
$495$	−7.94099	−0.356921
$496$	39.1156	1.75634
$497$	2.00123	0.0897676
$498$	4.50172	0.201727
$499$	0.881169	0.0394465	0.0197233	−	0.999805i	$-0.493721\pi$
$499$	0.881169	0.0394465	0.0197233	+	0.999805i	$0.493721\pi$
$500$	5.00279	0.223732
$501$	21.0854	0.942027
$502$	15.3266	0.684059
$503$	−25.8710	−1.15353	−0.576767	−	0.816909i	$-0.695686\pi$
$503$	−25.8710	−1.15353	−0.576767	+	0.816909i	$0.695686\pi$
$504$	−11.2421	−0.500762
$505$	26.2224	1.16688
$506$	−22.2686	−0.989962
$507$	4.01292	0.178220
$508$	−0.0603338	−0.00267688
$509$	23.4381	1.03887	0.519437	−	0.854509i	$-0.326142\pi$
$509$	23.4381	1.03887	0.519437	+	0.854509i	$0.326142\pi$
$510$	−3.16632	−0.140207
$511$	32.1213	1.42096
$512$	12.0281	0.531572
$513$	−7.30910	−0.322705
$514$	−35.1692	−1.55125
$515$	13.4401	0.592241
$516$	−3.98971	−0.175637
$517$	39.2276	1.72523
$518$	−2.07981	−0.0913818
$519$	22.7687	0.999435
$520$	15.0009	0.657834
$521$	−17.2047	−0.753752	−0.376876	−	0.926264i	$-0.623002\pi$
$521$	−17.2047	−0.753752	−0.376876	+	0.926264i	$0.623002\pi$
$522$	−0.0311414	−0.00136302
$523$	43.1495	1.88680	0.943398	−	0.331663i	$-0.107610\pi$
$523$	43.1495	1.88680	0.943398	+	0.331663i	$0.107610\pi$
$524$	−8.19683	−0.358080
$525$	−3.91731	−0.170966
$526$	−37.8220	−1.64912
$527$	−8.38816	−0.365394
$528$	18.1919	0.791702
$529$	−9.53382	−0.414514
$530$	40.7099	1.76832
$531$	8.07056	0.350233
$532$	−14.0271	−0.608154
$533$	15.7368	0.681636
$534$	−14.1284	−0.611397
$535$	−24.4141	−1.05551
$536$	25.1007	1.08419
$537$	−10.9699	−0.473386
$538$	−12.7803	−0.550997
$539$	54.2803	2.33802
$540$	0.854216	0.0367596
$541$	39.7907	1.71074	0.855369	−	0.518020i	$-0.173331\pi$
$541$	39.7907	1.71074	0.855369	+	0.518020i	$0.173331\pi$
$542$	35.3037	1.51642
$543$	−10.5405	−0.452335
$544$	2.33717	0.100205
$545$	37.6043	1.61079
$546$	21.3257	0.912654
$547$	24.3389	1.04066	0.520328	−	0.853966i	$-0.325810\pi$
$547$	24.3389	1.04066	0.520328	+	0.853966i	$0.325810\pi$
$548$	−5.28918	−0.225943
$549$	−12.6110	−0.538223
$550$	5.19808	0.221647
$551$	0.146328	0.00623377
$552$	−9.02094	−0.383957
$553$	−39.2907	−1.67081
$554$	−25.5277	−1.08457
$555$	−0.595128	−0.0252618
$556$	3.20243	0.135813
$557$	20.6363	0.874386	0.437193	−	0.899368i	$-0.355973\pi$
$557$	20.6363	0.874386	0.437193	+	0.899368i	$0.355973\pi$
$558$	13.0480	0.552365
$559$	−28.5011	−1.20547
$560$	−43.4090	−1.83436
$561$	−3.90117	−0.164708
$562$	48.7860	2.05791
$563$	30.1633	1.27123	0.635615	−	0.772006i	$-0.280747\pi$
$563$	30.1633	1.27123	0.635615	+	0.772006i	$0.280747\pi$
$564$	−4.21974	−0.177683
$565$	−33.1776	−1.39579
$566$	11.2628	0.473410
$567$	−4.57317	−0.192055
$568$	−1.07575	−0.0451374
$569$	−27.6164	−1.15774	−0.578870	−	0.815420i	$-0.696506\pi$
$569$	−27.6164	−1.15774	−0.578870	+	0.815420i	$0.696506\pi$
$570$	−23.1430	−0.969353
$571$	0.901806	0.0377394	0.0188697	−	0.999822i	$-0.493993\pi$
$571$	0.901806	0.0377394	0.0188697	+	0.999822i	$0.493993\pi$
$572$	−4.90787	−0.205208
$573$	12.2544	0.511934
$574$	−37.3422	−1.55863
$575$	−3.14336	−0.131087
$576$	5.69087	0.237120
$577$	−30.3879	−1.26506	−0.632531	−	0.774535i	$-0.717984\pi$
$577$	−30.3879	−1.26506	−0.632531	+	0.774535i	$0.717984\pi$
$578$	−1.55552	−0.0647012
$579$	−2.36320	−0.0982111
$580$	−0.0171013	−0.000710094 0
$581$	−13.2348	−0.549074
$582$	−23.9724	−0.993687
$583$	50.1579	2.07733
$584$	−17.2666	−0.714496
$585$	6.10223	0.252296
$586$	−42.2090	−1.74364
$587$	1.30714	0.0539513	0.0269756	−	0.999636i	$-0.491412\pi$
$587$	1.30714	0.0539513	0.0269756	+	0.999636i	$0.491412\pi$
$588$	−5.83896	−0.240795
$589$	−61.3099	−2.52623
$590$	25.5540	1.05204
$591$	−14.7699	−0.607552
$592$	1.36337	0.0560343
$593$	−9.28720	−0.381380	−0.190690	−	0.981650i	$-0.561072\pi$
$593$	−9.28720	−0.381380	−0.190690	+	0.981650i	$0.561072\pi$
$594$	6.06836	0.248988
$595$	9.30885	0.381626
$596$	−4.75075	−0.194598
$597$	−2.29742	−0.0940271
$598$	17.1123	0.699773
$599$	−1.51023	−0.0617065	−0.0308533	−	0.999524i	$-0.509822\pi$
$599$	−1.51023	−0.0617065	−0.0308533	+	0.999524i	$0.509822\pi$
$600$	2.10572	0.0859657
$601$	−17.2911	−0.705319	−0.352660	−	0.935752i	$-0.614723\pi$
$601$	−17.2911	−0.705319	−0.352660	+	0.935752i	$0.614723\pi$
$602$	67.6310	2.75644
$603$	10.2107	0.415813
$604$	1.82643	0.0743163
$605$	−8.58825	−0.349162
$606$	−20.0387	−0.814018
$607$	−32.5581	−1.32149	−0.660747	−	0.750609i	$-0.729760\pi$
$607$	−32.5581	−1.32149	−0.660747	+	0.750609i	$0.729760\pi$
$608$	17.0826	0.692791
$609$	0.0915544	0.00370997
$610$	−39.9304	−1.61674
$611$	−30.1444	−1.21951
$612$	0.419651	0.0169634
$613$	−26.5098	−1.07072	−0.535361	−	0.844623i	$-0.679824\pi$
$613$	−26.5098	−1.07072	−0.535361	+	0.844623i	$0.679824\pi$
$614$	−36.7608	−1.48355
$615$	−10.6853	−0.430872
$616$	−43.8573	−1.76706
$617$	−5.76815	−0.232217	−0.116108	−	0.993237i	$-0.537042\pi$
$617$	−5.76815	−0.232217	−0.116108	+	0.993237i	$0.537042\pi$
$618$	−10.2707	−0.413147
$619$	7.31853	0.294157	0.147078	−	0.989125i	$-0.453013\pi$
$619$	7.31853	0.294157	0.147078	+	0.989125i	$0.453013\pi$
$620$	7.16530	0.287765
$621$	−3.66963	−0.147257
$622$	−5.18595	−0.207938
$623$	41.5370	1.66414
$624$	−13.9795	−0.559630
$625$	−19.9833	−0.799333
$626$	−35.7890	−1.43042
$627$	−28.5141	−1.13874
$628$	−0.419651	−0.0167459
$629$	−0.292369	−0.0116575
$630$	−14.4801	−0.576902
$631$	3.29006	0.130975	0.0654875	−	0.997853i	$-0.479140\pi$
$631$	3.29006	0.130975	0.0654875	+	0.997853i	$0.479140\pi$
$632$	21.1204	0.840125
$633$	9.90698	0.393767
$634$	13.6073	0.540416
$635$	0.292652	0.0116135
$636$	−5.39551	−0.213946
$637$	−41.7115	−1.65267
$638$	−0.121488	−0.00480976
$639$	−0.437604	−0.0173113
$640$	27.5339	1.08837
$641$	−0.187578	−0.00740889	−0.00370444	−	0.999993i	$-0.501179\pi$
$641$	−0.187578	−0.00740889	−0.00370444	+	0.999993i	$0.501179\pi$
$642$	18.6568	0.736326
$643$	31.9532	1.26011	0.630056	−	0.776550i	$-0.283032\pi$
$643$	31.9532	1.26011	0.630056	+	0.776550i	$0.283032\pi$
$644$	−7.04251	−0.277514
$645$	19.3523	0.761995
$646$	−11.3695	−0.447326
$647$	−30.0127	−1.17992	−0.589961	−	0.807432i	$-0.700857\pi$
$647$	−30.0127	−1.17992	−0.589961	+	0.807432i	$0.700857\pi$
$648$	2.45827	0.0965699
$649$	31.4847	1.23588
$650$	−3.99445	−0.156675
$651$	−38.3604	−1.50346
$652$	−2.86089	−0.112041
$653$	1.78674	0.0699207	0.0349604	−	0.999389i	$-0.488870\pi$
$653$	1.78674	0.0699207	0.0349604	+	0.999389i	$0.488870\pi$
$654$	−28.7366	−1.12369
$655$	39.7591	1.55352
$656$	24.4788	0.955738
$657$	−7.02387	−0.274027
$658$	71.5303	2.78854
$659$	−26.4067	−1.02866	−0.514329	−	0.857593i	$-0.671959\pi$
$659$	−26.4067	−1.02866	−0.514329	+	0.857593i	$0.671959\pi$
$660$	3.33244	0.129715
$661$	12.5774	0.489203	0.244602	−	0.969624i	$-0.421343\pi$
$661$	12.5774	0.489203	0.244602	+	0.969624i	$0.421343\pi$
$662$	−42.1086	−1.63660
$663$	2.99785	0.116427
$664$	7.11429	0.276088
$665$	68.0393	2.63845
$666$	0.454787	0.0176226
$667$	0.0734657	0.00284460
$668$	−8.84852	−0.342359
$669$	−1.74311	−0.0673926
$670$	32.3305	1.24904
$671$	−49.1976	−1.89925
$672$	10.6883	0.412309
$673$	−24.0994	−0.928963	−0.464481	−	0.885583i	$-0.653759\pi$
$673$	−24.0994	−0.928963	−0.464481	+	0.885583i	$0.653759\pi$
$674$	0.0180793	0.000696388 0
$675$	0.856587	0.0329701
$676$	−1.68403	−0.0647702
$677$	14.9500	0.574576	0.287288	−	0.957844i	$-0.407246\pi$
$677$	14.9500	0.574576	0.287288	+	0.957844i	$0.407246\pi$
$678$	25.3538	0.973706
$679$	70.4777	2.70468
$680$	−5.00390	−0.191891
$681$	15.4763	0.593053
$682$	50.9024	1.94915
$683$	−25.5419	−0.977332	−0.488666	−	0.872471i	$-0.662516\pi$
$683$	−25.5419	−0.977332	−0.488666	+	0.872471i	$0.662516\pi$
$684$	3.06727	0.117280
$685$	25.6554	0.980243
$686$	49.1827	1.87780
$687$	−22.2233	−0.847870
$688$	−44.3339	−1.69022
$689$	−38.5437	−1.46840
$690$	−11.6192	−0.442337
$691$	17.3517	0.660090	0.330045	−	0.943965i	$-0.392936\pi$
$691$	17.3517	0.660090	0.330045	+	0.943965i	$0.392936\pi$
$692$	−9.55491	−0.363223
$693$	−17.8407	−0.677713
$694$	−46.6479	−1.77073
$695$	−15.5336	−0.589221
$696$	−0.0492144	−0.00186547
$697$	−5.24937	−0.198834
$698$	−27.7708	−1.05114
$699$	1.48059	0.0560010
$700$	1.64391	0.0621338
$701$	1.33976	0.0506021	0.0253010	−	0.999680i	$-0.491946\pi$
$701$	1.33976	0.0506021	0.0253010	+	0.999680i	$0.491946\pi$
$702$	−4.66322	−0.176002
$703$	−2.13695	−0.0805968
$704$	22.2011	0.836734
$705$	20.4680	0.770871
$706$	−13.6028	−0.511949
$707$	58.9129	2.21565
$708$	−3.38682	−0.127285
$709$	−39.3559	−1.47804	−0.739021	−	0.673683i	$-0.764712\pi$
$709$	−39.3559	−1.47804	−0.739021	+	0.673683i	$0.764712\pi$
$710$	−1.38560	−0.0520005
$711$	8.59159	0.322210
$712$	−22.3279	−0.836772
$713$	−30.7814	−1.15277
$714$	−7.11366	−0.266222
$715$	23.8059	0.890288
$716$	4.60353	0.172042
$717$	28.7088	1.07215
$718$	14.3478	0.535453
$719$	5.94444	0.221690	0.110845	−	0.993838i	$-0.464644\pi$
$719$	5.94444	0.221690	0.110845	+	0.993838i	$0.464644\pi$
$720$	9.49211	0.353750
$721$	30.1953	1.12453
$722$	−53.5457	−1.99276
$723$	−18.9584	−0.705072
$724$	4.42332	0.164391
$725$	−0.0171488	−0.000636891 0
$726$	6.56299	0.243575
$727$	20.6021	0.764090	0.382045	−	0.924144i	$-0.375220\pi$
$727$	20.6021	0.764090	0.382045	+	0.924144i	$0.375220\pi$
$728$	33.7020	1.24908
$729$	1.00000	0.0370370
$730$	−22.2399	−0.823134
$731$	9.50720	0.351637
$732$	5.29221	0.195606
$733$	14.8374	0.548031	0.274015	−	0.961725i	$-0.411648\pi$
$733$	14.8374	0.548031	0.274015	+	0.961725i	$0.411648\pi$
$734$	38.3300	1.41479
$735$	28.3221	1.04468
$736$	8.57655	0.316136
$737$	39.8338	1.46730
$738$	8.16551	0.300577
$739$	12.3645	0.454835	0.227418	−	0.973797i	$-0.426972\pi$
$739$	12.3645	0.454835	0.227418	+	0.973797i	$0.426972\pi$
$740$	0.249746	0.00918085
$741$	21.9116	0.804941
$742$	91.4613	3.35765
$743$	33.1650	1.21670	0.608352	−	0.793667i	$-0.291831\pi$
$743$	33.1650	1.21670	0.608352	+	0.793667i	$0.291831\pi$
$744$	20.6204	0.755979
$745$	23.0437	0.844257
$746$	−27.0159	−0.989124
$747$	2.89402	0.105887
$748$	1.63713	0.0598595
$749$	−54.8502	−2.00418
$750$	18.5439	0.677126
$751$	−7.12050	−0.259831	−0.129915	−	0.991525i	$-0.541471\pi$
$751$	−7.12050	−0.259831	−0.129915	+	0.991525i	$0.541471\pi$
$752$	−46.8900	−1.70990
$753$	9.85301	0.359064
$754$	0.0933573	0.00339987
$755$	−8.85917	−0.322418
$756$	1.91913	0.0697982
$757$	−19.1231	−0.695040	−0.347520	−	0.937673i	$-0.612976\pi$
$757$	−19.1231	−0.695040	−0.347520	+	0.937673i	$0.612976\pi$
$758$	−3.27050	−0.118790
$759$	−14.3159	−0.519633
$760$	−36.5740	−1.32668
$761$	0.227241	0.00823748	0.00411874	−	0.999992i	$-0.498689\pi$
$761$	0.227241	0.00823748	0.00411874	+	0.999992i	$0.498689\pi$
$762$	−0.223639	−0.00810160
$763$	84.4842	3.05853
$764$	−5.14256	−0.186051
$765$	−2.03554	−0.0735950
$766$	27.5574	0.995689
$767$	−24.1943	−0.873606
$768$	−9.65922	−0.348547
$769$	−50.3546	−1.81583	−0.907917	−	0.419150i	$-0.862328\pi$
$769$	−50.3546	−1.81583	−0.907917	+	0.419150i	$0.862328\pi$
$770$	−56.4895	−2.03574
$771$	−22.6093	−0.814253
$772$	0.991718	0.0356927
$773$	40.3326	1.45066	0.725331	−	0.688400i	$-0.241687\pi$
$773$	40.3326	1.45066	0.725331	+	0.688400i	$0.241687\pi$
$774$	−14.7887	−0.531568
$775$	7.18519	0.258100
$776$	−37.8847	−1.35998
$777$	−1.33705	−0.0479665
$778$	10.9157	0.391348
$779$	−38.3682	−1.37468
$780$	−2.56081	−0.0916916
$781$	−1.70717	−0.0610873
$782$	−5.70819	−0.204125
$783$	−0.0200199	−0.000715454 0
$784$	−64.8829	−2.31725
$785$	2.03554	0.0726514
$786$	−30.3832	−1.08373
$787$	−50.3999	−1.79656	−0.898282	−	0.439420i	$-0.855184\pi$
$787$	−50.3999	−1.79656	−0.898282	+	0.439420i	$0.855184\pi$
$788$	6.19820	0.220802
$789$	−24.3146	−0.865624
$790$	27.2038	0.967866
$791$	−74.5389	−2.65030
$792$	9.59013	0.340771
$793$	37.8058	1.34252
$794$	9.85158	0.349619
$795$	26.1712	0.928196
$796$	0.964115	0.0341722
$797$	4.47487	0.158508	0.0792540	−	0.996854i	$-0.474746\pi$
$797$	4.47487	0.158508	0.0792540	+	0.996854i	$0.474746\pi$
$798$	−51.9945	−1.84058
$799$	10.0553	0.355733
$800$	−2.00199	−0.0707810
$801$	−9.08276	−0.320924
$802$	−35.7303	−1.26168
$803$	−27.4014	−0.966973
$804$	−4.28494	−0.151118
$805$	34.1600	1.20398
$806$	−39.1158	−1.37780
$807$	−8.21607	−0.289219
$808$	−31.6682	−1.11408
$809$	53.5951	1.88430	0.942152	−	0.335185i	$-0.108799\pi$
$809$	53.5951	1.88430	0.942152	+	0.335185i	$0.108799\pi$
$810$	3.16632	0.111253
$811$	17.6500	0.619777	0.309888	−	0.950773i	$-0.399708\pi$
$811$	17.6500	0.619777	0.309888	+	0.950773i	$0.399708\pi$
$812$	−0.0384209	−0.00134831
$813$	22.6957	0.795973
$814$	1.77420	0.0621857
$815$	13.8769	0.486087
$816$	4.66320	0.163244
$817$	69.4891	2.43112
$818$	41.0161	1.43409
$819$	13.7096	0.479054
$820$	4.48409	0.156591
$821$	8.85028	0.308877	0.154438	−	0.988002i	$-0.450643\pi$
$821$	8.85028	0.308877	0.154438	+	0.988002i	$0.450643\pi$
$822$	−19.6054	−0.683818
$823$	−32.6985	−1.13980	−0.569899	−	0.821715i	$-0.693018\pi$
$823$	−32.6985	−1.13980	−0.569899	+	0.821715i	$0.693018\pi$
$824$	−16.2313	−0.565443
$825$	3.34169	0.116343
$826$	57.4113	1.99759
$827$	4.70982	0.163777	0.0818883	−	0.996642i	$-0.473905\pi$
$827$	4.70982	0.163777	0.0818883	+	0.996642i	$0.473905\pi$
$828$	1.53996	0.0535175
$829$	14.3182	0.497292	0.248646	−	0.968594i	$-0.420014\pi$
$829$	14.3182	0.497292	0.248646	+	0.968594i	$0.420014\pi$
$830$	9.16342	0.318067
$831$	−16.4110	−0.569291
$832$	−17.0604	−0.591461
$833$	13.9138	0.482086
$834$	11.8705	0.411041
$835$	42.9201	1.48531
$836$	11.9660	0.413851
$837$	8.38816	0.289937
$838$	6.02705	0.208201
$839$	16.1658	0.558106	0.279053	−	0.960276i	$-0.409980\pi$
$839$	16.1658	0.558106	0.279053	+	0.960276i	$0.409980\pi$
$840$	−22.8837	−0.789561
$841$	−28.9996	−0.999986
$842$	−29.1244	−1.00369
$843$	31.3631	1.08020
$844$	−4.15747	−0.143106
$845$	8.16844	0.281003
$846$	−15.6413	−0.537760
$847$	−19.2949	−0.662980
$848$	−59.9553	−2.05887
$849$	7.24052	0.248494
$850$	1.33244	0.0457023
$851$	−1.07289	−0.0367781
$852$	0.183641	0.00629143
$853$	29.2751	1.00236	0.501180	−	0.865343i	$-0.332899\pi$
$853$	29.2751	1.00236	0.501180	+	0.865343i	$0.332899\pi$
$854$	−89.7102	−3.06982
$855$	−14.8779	−0.508815
$856$	29.4843	1.00775
$857$	−25.2945	−0.864044	−0.432022	−	0.901863i	$-0.642200\pi$
$857$	−25.2945	−0.864044	−0.432022	+	0.901863i	$0.642200\pi$
$858$	−18.1920	−0.621065
$859$	−18.6871	−0.637597	−0.318798	−	0.947823i	$-0.603279\pi$
$859$	−18.6871	−0.637597	−0.318798	+	0.947823i	$0.603279\pi$
$860$	−8.12120	−0.276931
$861$	−24.0062	−0.818130
$862$	−15.7460	−0.536312
$863$	20.3477	0.692642	0.346321	−	0.938116i	$-0.387431\pi$
$863$	20.3477	0.692642	0.346321	+	0.938116i	$0.387431\pi$
$864$	−2.33717	−0.0795121
$865$	46.3465	1.57583
$866$	−22.6056	−0.768169
$867$	−1.00000	−0.0339618
$868$	16.0980	0.546402
$869$	33.5173	1.13700
$870$	−0.0633896	−0.00214911
$871$	−30.6102	−1.03719
$872$	−45.4138	−1.53790
$873$	−15.4111	−0.521588
$874$	−41.7217	−1.41126
$875$	−54.5181	−1.84305
$876$	2.94758	0.0995894
$877$	13.6123	0.459656	0.229828	−	0.973231i	$-0.426184\pi$
$877$	13.6123	0.459656	0.229828	+	0.973231i	$0.426184\pi$
$878$	−10.9788	−0.370515
$879$	−27.1349	−0.915239
$880$	37.0304	1.24829
$881$	11.0251	0.371443	0.185722	−	0.982602i	$-0.440538\pi$
$881$	11.0251	0.371443	0.185722	+	0.982602i	$0.440538\pi$
$882$	−21.6433	−0.728768
$883$	−53.5863	−1.80332	−0.901661	−	0.432444i	$-0.857651\pi$
$883$	−53.5863	−1.80332	−0.901661	+	0.432444i	$0.857651\pi$
$884$	−1.25805	−0.0423128
$885$	16.4279	0.552219
$886$	−28.1287	−0.945002
$887$	9.04956	0.303854	0.151927	−	0.988392i	$-0.451452\pi$
$887$	9.04956	0.303854	0.151927	+	0.988392i	$0.451452\pi$
$888$	0.718722	0.0241187
$889$	0.657490	0.0220515
$890$	−28.7590	−0.964003
$891$	3.90117	0.130694
$892$	0.731499	0.0244924
$893$	73.4955	2.45943
$894$	−17.6096	−0.588954
$895$	−22.3297	−0.746398
$896$	61.8595	2.06658
$897$	11.0010	0.367312
$898$	−46.3572	−1.54696
$899$	−0.167930	−0.00560079
$900$	−0.359468	−0.0119823
$901$	12.8571	0.428333
$902$	31.8551	1.06066
$903$	43.4780	1.44686
$904$	40.0678	1.33264
$905$	−21.4555	−0.713205
$906$	6.77002	0.224919
$907$	−24.3664	−0.809073	−0.404536	−	0.914522i	$-0.632567\pi$
$907$	−24.3664	−0.809073	−0.404536	+	0.914522i	$0.632567\pi$
$908$	−6.49464	−0.215532
$909$	−12.8823	−0.427279
$910$	43.4092	1.43900
$911$	29.3668	0.972964	0.486482	−	0.873691i	$-0.338280\pi$
$911$	29.3668	0.972964	0.486482	+	0.873691i	$0.338280\pi$
$912$	34.0838	1.12863
$913$	11.2901	0.373647
$914$	12.7247	0.420894
$915$	−25.6701	−0.848627
$916$	9.32601	0.308140
$917$	89.3252	2.94978
$918$	1.55552	0.0513399
$919$	31.8257	1.04983	0.524916	−	0.851154i	$-0.324097\pi$
$919$	31.8257	1.04983	0.524916	+	0.851154i	$0.324097\pi$
$920$	−18.3625	−0.605392
$921$	−23.6325	−0.778716
$922$	58.3018	1.92007
$923$	1.31187	0.0431807
$924$	7.48687	0.246300
$925$	0.250440	0.00823440
$926$	29.4172	0.966708
$927$	−6.60272	−0.216862
$928$	0.0467900	0.00153596
$929$	4.19586	0.137662	0.0688308	−	0.997628i	$-0.478073\pi$
$929$	4.19586	0.137662	0.0688308	+	0.997628i	$0.478073\pi$
$930$	26.5596	0.870925
$931$	101.698	3.33301
$932$	−0.621331	−0.0203524
$933$	−3.33390	−0.109147
$934$	−25.1060	−0.821495
$935$	−7.94099	−0.259698
$936$	−7.36951	−0.240880
$937$	7.21006	0.235542	0.117771	−	0.993041i	$-0.462425\pi$
$937$	7.21006	0.235542	0.117771	+	0.993041i	$0.462425\pi$
$938$	72.6357	2.37164
$939$	−23.0077	−0.750828
$940$	−8.58943	−0.280156
$941$	−13.4599	−0.438780	−0.219390	−	0.975637i	$-0.570407\pi$
$941$	−13.4599	−0.438780	−0.219390	+	0.975637i	$0.570407\pi$
$942$	−1.55552	−0.0506817
$943$	−19.2632	−0.627297
$944$	−37.6346	−1.22490
$945$	−9.30885	−0.302817
$946$	−57.6932	−1.87577
$947$	−34.3024	−1.11468	−0.557340	−	0.830285i	$-0.688178\pi$
$947$	−34.3024	−1.11468	−0.557340	+	0.830285i	$0.688178\pi$
$948$	−3.60547	−0.117100
$949$	21.0565	0.683523
$950$	9.73894	0.315973
$951$	8.74775	0.283665
$952$	−11.2421	−0.364358
$953$	−17.8045	−0.576744	−0.288372	−	0.957518i	$-0.593114\pi$
$953$	−17.8045	−0.576744	−0.288372	+	0.957518i	$0.593114\pi$
$954$	−19.9996	−0.647510
$955$	24.9443	0.807177
$956$	−12.0477	−0.389650
$957$	−0.0781012	−0.00252465
$958$	57.2975	1.85120
$959$	57.6391	1.86126
$960$	11.5840	0.373871
$961$	39.3613	1.26972
$962$	−1.36338	−0.0439572
$963$	11.9939	0.386499
$964$	7.95593	0.256243
$965$	−4.81038	−0.154851
$966$	−26.1045	−0.839899
$967$	43.4496	1.39724	0.698622	−	0.715491i	$-0.253797\pi$
$967$	43.4496	1.39724	0.698622	+	0.715491i	$0.253797\pi$
$968$	10.3718	0.333363
$969$	−7.30910	−0.234802
$970$	−48.7967	−1.56677
$971$	51.7609	1.66108	0.830542	−	0.556955i	$-0.188031\pi$
$971$	51.7609	1.66108	0.830542	+	0.556955i	$0.188031\pi$
$972$	−0.419651	−0.0134603
$973$	−34.8987	−1.11880
$974$	−52.3751	−1.67821
$975$	−2.56792	−0.0822391
$976$	58.8074	1.88238
$977$	−22.4290	−0.717568	−0.358784	−	0.933421i	$-0.616809\pi$
$977$	−22.4290	−0.717568	−0.358784	+	0.933421i	$0.616809\pi$
$978$	−10.6045	−0.339094
$979$	−35.4334	−1.13246
$980$	−11.8854	−0.379666
$981$	−18.4739	−0.589826
$982$	7.30095	0.232983
$983$	15.4291	0.492113	0.246057	−	0.969255i	$-0.420865\pi$
$983$	15.4291	0.492113	0.246057	+	0.969255i	$0.420865\pi$
$984$	12.9044	0.411376
$985$	−30.0647	−0.957940
$986$	−0.0311414	−0.000991746 0
$987$	45.9848	1.46371
$988$	−9.19521	−0.292539
$989$	34.8879	1.10937
$990$	12.3524	0.392585
$991$	26.9603	0.856424	0.428212	−	0.903678i	$-0.359144\pi$
$991$	26.9603	0.856424	0.428212	+	0.903678i	$0.359144\pi$
$992$	−19.6046	−0.622445
$993$	−27.0704	−0.859053
$994$	−3.11296	−0.0987373
$995$	−4.67648	−0.148255
$996$	−1.21448	−0.0384823
$997$	−2.52224	−0.0798802	−0.0399401	−	0.999202i	$-0.512717\pi$
$997$	−2.52224	−0.0798802	−0.0399401	+	0.999202i	$0.512717\pi$
$998$	−1.37068	−0.0433880
$999$	0.292369	0.00925015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.18	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-1.55552 q^{2} -1.00000 q^{3} +0.419651 q^{4} -2.03554 q^{5} +1.55552 q^{6} -4.57317 q^{7} +2.45827 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.55552 q^{2} -1.00000 q^{3} +0.419651 q^{4} -2.03554 q^{5} +1.55552 q^{6} -4.57317 q^{7} +2.45827 q^{8} +1.00000 q^{9} +3.16632 q^{10} +3.90117 q^{11} -0.419651 q^{12} -2.99785 q^{13} +7.11366 q^{14} +2.03554 q^{15} -4.66320 q^{16} +1.00000 q^{17} -1.55552 q^{18} +7.30910 q^{19} -0.854216 q^{20} +4.57317 q^{21} -6.06836 q^{22} +3.66963 q^{23} -2.45827 q^{24} -0.856587 q^{25} +4.66322 q^{26} -1.00000 q^{27} -1.91913 q^{28} +0.0200199 q^{29} -3.16632 q^{30} -8.38816 q^{31} +2.33717 q^{32} -3.90117 q^{33} -1.55552 q^{34} +9.30885 q^{35} +0.419651 q^{36} -0.292369 q^{37} -11.3695 q^{38} +2.99785 q^{39} -5.00390 q^{40} -5.24937 q^{41} -7.11366 q^{42} +9.50720 q^{43} +1.63713 q^{44} -2.03554 q^{45} -5.70819 q^{46} +10.0553 q^{47} +4.66320 q^{48} +13.9138 q^{49} +1.33244 q^{50} -1.00000 q^{51} -1.25805 q^{52} +12.8571 q^{53} +1.55552 q^{54} -7.94099 q^{55} -11.2421 q^{56} -7.30910 q^{57} -0.0311414 q^{58} +8.07056 q^{59} +0.854216 q^{60} -12.6110 q^{61} +13.0480 q^{62} -4.57317 q^{63} +5.69087 q^{64} +6.10223 q^{65} +6.06836 q^{66} +10.2107 q^{67} +0.419651 q^{68} -3.66963 q^{69} -14.4801 q^{70} -0.437604 q^{71} +2.45827 q^{72} -7.02387 q^{73} +0.454787 q^{74} +0.856587 q^{75} +3.06727 q^{76} -17.8407 q^{77} -4.66322 q^{78} +8.59159 q^{79} +9.49211 q^{80} +1.00000 q^{81} +8.16551 q^{82} +2.89402 q^{83} +1.91913 q^{84} -2.03554 q^{85} -14.7887 q^{86} -0.0200199 q^{87} +9.59013 q^{88} -9.08276 q^{89} +3.16632 q^{90} +13.7096 q^{91} +1.53996 q^{92} +8.38816 q^{93} -15.6413 q^{94} -14.8779 q^{95} -2.33717 q^{96} -15.4111 q^{97} -21.6433 q^{98} +3.90117 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 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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