LMFDB - Embedded newform 8029.2.a.g.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, 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("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.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:	$64.1118877829$
Analytic rank:	$0$
Dimension:	$70$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.74189 q^{2} +1.96861 q^{3} +1.03416 q^{4} +1.87277 q^{5} -3.42909 q^{6} +1.00000 q^{7} +1.68238 q^{8} +0.875422 q^{9} +O(q^{10})$	\(q-1.74189 q^{2} +1.96861 q^{3} +1.03416 q^{4} +1.87277 q^{5} -3.42909 q^{6} +1.00000 q^{7} +1.68238 q^{8} +0.875422 q^{9} -3.26215 q^{10} +5.70350 q^{11} +2.03586 q^{12} +2.08470 q^{13} -1.74189 q^{14} +3.68675 q^{15} -4.99883 q^{16} +2.77174 q^{17} -1.52488 q^{18} -0.0123365 q^{19} +1.93675 q^{20} +1.96861 q^{21} -9.93484 q^{22} +3.69596 q^{23} +3.31194 q^{24} -1.49273 q^{25} -3.63131 q^{26} -4.18246 q^{27} +1.03416 q^{28} -9.45413 q^{29} -6.42190 q^{30} +1.00000 q^{31} +5.34264 q^{32} +11.2280 q^{33} -4.82805 q^{34} +1.87277 q^{35} +0.905330 q^{36} +1.00000 q^{37} +0.0214888 q^{38} +4.10396 q^{39} +3.15070 q^{40} -0.408999 q^{41} -3.42909 q^{42} +9.52973 q^{43} +5.89835 q^{44} +1.63946 q^{45} -6.43794 q^{46} -6.61932 q^{47} -9.84075 q^{48} +1.00000 q^{49} +2.60017 q^{50} +5.45647 q^{51} +2.15592 q^{52} -11.1090 q^{53} +7.28537 q^{54} +10.6813 q^{55} +1.68238 q^{56} -0.0242858 q^{57} +16.4680 q^{58} +12.0509 q^{59} +3.81270 q^{60} +12.0568 q^{61} -1.74189 q^{62} +0.875422 q^{63} +0.691397 q^{64} +3.90417 q^{65} -19.5578 q^{66} -14.5037 q^{67} +2.86643 q^{68} +7.27590 q^{69} -3.26215 q^{70} +13.4553 q^{71} +1.47279 q^{72} -0.906662 q^{73} -1.74189 q^{74} -2.93861 q^{75} -0.0127580 q^{76} +5.70350 q^{77} -7.14863 q^{78} +15.5847 q^{79} -9.36166 q^{80} -10.8599 q^{81} +0.712429 q^{82} +14.8055 q^{83} +2.03586 q^{84} +5.19083 q^{85} -16.5997 q^{86} -18.6115 q^{87} +9.59543 q^{88} +16.3004 q^{89} -2.85576 q^{90} +2.08470 q^{91} +3.82223 q^{92} +1.96861 q^{93} +11.5301 q^{94} -0.0231035 q^{95} +10.5176 q^{96} -6.09014 q^{97} -1.74189 q^{98} +4.99297 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9}+O(q^{10}) $ 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9} + 4 q^{10} + 61 q^{11} + 49 q^{12} + 28 q^{13} + 5 q^{14} + 22 q^{15} + 73 q^{16} + 37 q^{17} + 8 q^{18} + 23 q^{19} + 45 q^{20} + 22 q^{21} - 10 q^{22} + 26 q^{23} + 3 q^{24} + 66 q^{25} + 57 q^{26} + 76 q^{27} + 71 q^{28} + 38 q^{29} - 14 q^{30} + 70 q^{31} - 2 q^{32} + 44 q^{33} + 34 q^{34} + 24 q^{35} + 46 q^{36} + 70 q^{37} + 21 q^{38} + 10 q^{39} + 13 q^{40} + 71 q^{41} + 9 q^{42} + 30 q^{43} + 108 q^{44} + 13 q^{45} - 14 q^{46} + 78 q^{47} + 85 q^{48} + 70 q^{49} - 12 q^{50} + 21 q^{51} + 23 q^{52} + 47 q^{53} + 17 q^{54} + 5 q^{55} + 9 q^{56} + 9 q^{57} + 8 q^{58} + 109 q^{59} - q^{60} + 41 q^{61} + 5 q^{62} + 78 q^{63} + 29 q^{64} + 36 q^{65} + 5 q^{66} + 23 q^{67} + 47 q^{68} + 8 q^{69} + 4 q^{70} + 99 q^{71} + 8 q^{72} + 33 q^{73} + 5 q^{74} + 94 q^{75} - 19 q^{76} + 61 q^{77} + 37 q^{78} + 52 q^{79} + 78 q^{80} + 102 q^{81} + 118 q^{83} + 49 q^{84} - 21 q^{85} + 74 q^{86} + 11 q^{87} - 21 q^{88} + 86 q^{89} - 7 q^{90} + 28 q^{91} + 14 q^{92} + 22 q^{93} + 35 q^{94} + 24 q^{95} - 40 q^{96} + 9 q^{97} + 5 q^{98} + 92 q^{99}+O(q^{100}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9 + 4 * q^10 + 61 * q^11 + 49 * q^12 + 28 * q^13 + 5 * q^14 + 22 * q^15 + 73 * q^16 + 37 * q^17 + 8 * q^18 + 23 * q^19 + 45 * q^20 + 22 * q^21 - 10 * q^22 + 26 * q^23 + 3 * q^24 + 66 * q^25 + 57 * q^26 + 76 * q^27 + 71 * q^28 + 38 * q^29 - 14 * q^30 + 70 * q^31 - 2 * q^32 + 44 * q^33 + 34 * q^34 + 24 * q^35 + 46 * q^36 + 70 * q^37 + 21 * q^38 + 10 * q^39 + 13 * q^40 + 71 * q^41 + 9 * q^42 + 30 * q^43 + 108 * q^44 + 13 * q^45 - 14 * q^46 + 78 * q^47 + 85 * q^48 + 70 * q^49 - 12 * q^50 + 21 * q^51 + 23 * q^52 + 47 * q^53 + 17 * q^54 + 5 * q^55 + 9 * q^56 + 9 * q^57 + 8 * q^58 + 109 * q^59 - q^60 + 41 * q^61 + 5 * q^62 + 78 * q^63 + 29 * q^64 + 36 * q^65 + 5 * q^66 + 23 * q^67 + 47 * q^68 + 8 * q^69 + 4 * q^70 + 99 * q^71 + 8 * q^72 + 33 * q^73 + 5 * q^74 + 94 * q^75 - 19 * q^76 + 61 * q^77 + 37 * q^78 + 52 * q^79 + 78 * q^80 + 102 * q^81 + 118 * q^83 + 49 * q^84 - 21 * q^85 + 74 * q^86 + 11 * q^87 - 21 * q^88 + 86 * q^89 - 7 * q^90 + 28 * q^91 + 14 * q^92 + 22 * q^93 + 35 * q^94 + 24 * q^95 - 40 * q^96 + 9 * q^97 + 5 * q^98 + 92 * 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 $

$2$	−1.74189	−1.23170	−0.615849	−	0.787864i	$-0.711187\pi$
$2$	−1.74189	−1.23170	−0.615849	+	0.787864i	$0.711187\pi$
$3$	1.96861	1.13658	0.568289	−	0.822829i	$-0.307606\pi$
$3$	1.96861	1.13658	0.568289	+	0.822829i	$0.307606\pi$
$4$	1.03416	0.517082
$5$	1.87277	0.837528	0.418764	−	0.908095i	$-0.362463\pi$
$5$	1.87277	0.837528	0.418764	+	0.908095i	$0.362463\pi$
$6$	−3.42909	−1.39992
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.68238	0.594810
$9$	0.875422	0.291807
$10$	−3.26215	−1.03158
$11$	5.70350	1.71967	0.859835	−	0.510572i	$-0.170566\pi$
$11$	5.70350	1.71967	0.859835	+	0.510572i	$0.170566\pi$
$12$	2.03586	0.587703
$13$	2.08470	0.578192	0.289096	−	0.957300i	$-0.406645\pi$
$13$	2.08470	0.578192	0.289096	+	0.957300i	$0.406645\pi$
$14$	−1.74189	−0.465538
$15$	3.68675	0.951915
$16$	−4.99883	−1.24971
$17$	2.77174	0.672246	0.336123	−	0.941818i	$-0.390884\pi$
$17$	2.77174	0.672246	0.336123	+	0.941818i	$0.390884\pi$
$18$	−1.52488	−0.359419
$19$	−0.0123365	−0.00283020	−0.00141510	−	0.999999i	$-0.500450\pi$
$19$	−0.0123365	−0.00283020	−0.00141510	+	0.999999i	$0.500450\pi$
$20$	1.93675	0.433071
$21$	1.96861	0.429586
$22$	−9.93484	−2.11812
$23$	3.69596	0.770661	0.385330	−	0.922779i	$-0.374087\pi$
$23$	3.69596	0.770661	0.385330	+	0.922779i	$0.374087\pi$
$24$	3.31194	0.676047
$25$	−1.49273	−0.298547
$26$	−3.63131	−0.712159
$27$	−4.18246	−0.804916
$28$	1.03416	0.195439
$29$	−9.45413	−1.75559	−0.877794	−	0.479038i	$-0.840986\pi$
$29$	−9.45413	−1.75559	−0.877794	+	0.479038i	$0.840986\pi$
$30$	−6.42190	−1.17247
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	5.34264	0.944455
$33$	11.2280	1.95454
$34$	−4.82805	−0.828005
$35$	1.87277	0.316556
$36$	0.905330	0.150888
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	0.0214888	0.00348595
$39$	4.10396	0.657160
$40$	3.15070	0.498170
$41$	−0.408999	−0.0638749	−0.0319375	−	0.999490i	$-0.510168\pi$
$41$	−0.408999	−0.0638749	−0.0319375	+	0.999490i	$0.510168\pi$
$42$	−3.42909	−0.529120
$43$	9.52973	1.45327	0.726635	−	0.687024i	$-0.241083\pi$
$43$	9.52973	1.45327	0.726635	+	0.687024i	$0.241083\pi$
$44$	5.89835	0.889210
$45$	1.63946	0.244397
$46$	−6.43794	−0.949222
$47$	−6.61932	−0.965527	−0.482763	−	0.875751i	$-0.660367\pi$
$47$	−6.61932	−0.965527	−0.482763	+	0.875751i	$0.660367\pi$
$48$	−9.84075	−1.42039
$49$	1.00000	0.142857
$50$	2.60017	0.367720
$51$	5.45647	0.764059
$52$	2.15592	0.298973
$53$	−11.1090	−1.52594	−0.762968	−	0.646436i	$-0.776259\pi$
$53$	−11.1090	−1.52594	−0.762968	+	0.646436i	$0.776259\pi$
$54$	7.28537	0.991413
$55$	10.6813	1.44027
$56$	1.68238	0.224817
$57$	−0.0242858	−0.00321674
$58$	16.4680	2.16236
$59$	12.0509	1.56889	0.784444	−	0.620200i	$-0.212949\pi$
$59$	12.0509	1.56889	0.784444	+	0.620200i	$0.212949\pi$
$60$	3.81270	0.492218
$61$	12.0568	1.54371	0.771856	−	0.635797i	$-0.219328\pi$
$61$	12.0568	1.54371	0.771856	+	0.635797i	$0.219328\pi$
$62$	−1.74189	−0.221220
$63$	0.875422	0.110293
$64$	0.691397	0.0864247
$65$	3.90417	0.484252
$66$	−19.5578	−2.40740
$67$	−14.5037	−1.77191	−0.885957	−	0.463768i	$-0.846497\pi$
$67$	−14.5037	−1.77191	−0.885957	+	0.463768i	$0.846497\pi$
$68$	2.86643	0.347606
$69$	7.27590	0.875915
$70$	−3.26215	−0.389901
$71$	13.4553	1.59686	0.798428	−	0.602091i	$-0.205665\pi$
$71$	13.4553	1.59686	0.798428	+	0.602091i	$0.205665\pi$
$72$	1.47279	0.173570
$73$	−0.906662	−0.106117	−0.0530584	−	0.998591i	$-0.516897\pi$
$73$	−0.906662	−0.106117	−0.0530584	+	0.998591i	$0.516897\pi$
$74$	−1.74189	−0.202490
$75$	−2.93861	−0.339322
$76$	−0.0127580	−0.00146344
$77$	5.70350	0.649974
$78$	−7.14863	−0.809423
$79$	15.5847	1.75342	0.876708	−	0.481024i	$-0.159735\pi$
$79$	15.5847	1.75342	0.876708	+	0.481024i	$0.159735\pi$
$80$	−9.36166	−1.04667
$81$	−10.8599	−1.20666
$82$	0.712429	0.0786747
$83$	14.8055	1.62512	0.812560	−	0.582877i	$-0.198073\pi$
$83$	14.8055	1.62512	0.812560	+	0.582877i	$0.198073\pi$
$84$	2.03586	0.222131
$85$	5.19083	0.563025
$86$	−16.5997	−1.78999
$87$	−18.6115	−1.99536
$88$	9.59543	1.02288
$89$	16.3004	1.72784	0.863918	−	0.503633i	$-0.168004\pi$
$89$	16.3004	1.72784	0.863918	+	0.503633i	$0.168004\pi$
$90$	−2.85576	−0.301023
$91$	2.08470	0.218536
$92$	3.82223	0.398495
$93$	1.96861	0.204135
$94$	11.5301	1.18924
$95$	−0.0231035	−0.00237037
$96$	10.5176	1.07345
$97$	−6.09014	−0.618360	−0.309180	−	0.951004i	$-0.600054\pi$
$97$	−6.09014	−0.618360	−0.309180	+	0.951004i	$0.600054\pi$
$98$	−1.74189	−0.175957
$99$	4.99297	0.501812
$100$	−1.54373	−0.154373
$101$	−11.6472	−1.15894	−0.579469	−	0.814994i	$-0.696740\pi$
$101$	−11.6472	−1.15894	−0.579469	+	0.814994i	$0.696740\pi$
$102$	−9.50455	−0.941091
$103$	−7.56390	−0.745294	−0.372647	−	0.927973i	$-0.621550\pi$
$103$	−7.56390	−0.745294	−0.372647	+	0.927973i	$0.621550\pi$
$104$	3.50725	0.343914
$105$	3.68675	0.359790
$106$	19.3506	1.87949
$107$	−10.4246	−1.00778	−0.503890	−	0.863768i	$-0.668098\pi$
$107$	−10.4246	−1.00778	−0.503890	+	0.863768i	$0.668098\pi$
$108$	−4.32535	−0.416207
$109$	16.3873	1.56962	0.784809	−	0.619738i	$-0.212761\pi$
$109$	16.3873	1.56962	0.784809	+	0.619738i	$0.212761\pi$
$110$	−18.6057	−1.77398
$111$	1.96861	0.186852
$112$	−4.99883	−0.472345
$113$	12.0059	1.12942	0.564711	−	0.825289i	$-0.308988\pi$
$113$	12.0059	1.12942	0.564711	+	0.825289i	$0.308988\pi$
$114$	0.0423031	0.00396205
$115$	6.92168	0.645450
$116$	−9.77712	−0.907783
$117$	1.82499	0.168721
$118$	−20.9912	−1.93240
$119$	2.77174	0.254085
$120$	6.20250	0.566208
$121$	21.5299	1.95726
$122$	−21.0015	−1.90139
$123$	−0.805159	−0.0725988
$124$	1.03416	0.0928707
$125$	−12.1594	−1.08757
$126$	−1.52488	−0.135848
$127$	11.1733	0.991467	0.495734	−	0.868475i	$-0.334899\pi$
$127$	11.1733	0.991467	0.495734	+	0.868475i	$0.334899\pi$
$128$	−11.8896	−1.05090
$129$	18.7603	1.65175
$130$	−6.80061	−0.596453
$131$	−18.7862	−1.64136	−0.820680	−	0.571388i	$-0.806405\pi$
$131$	−18.7862	−1.64136	−0.820680	+	0.571388i	$0.806405\pi$
$132$	11.6116	1.01066
$133$	−0.0123365	−0.00106971
$134$	25.2638	2.18246
$135$	−7.83279	−0.674139
$136$	4.66311	0.399858
$137$	21.2641	1.81672	0.908358	−	0.418194i	$-0.137337\pi$
$137$	21.2641	1.81672	0.908358	+	0.418194i	$0.137337\pi$
$138$	−12.6738	−1.07886
$139$	0.0915456	0.00776480	0.00388240	−	0.999992i	$-0.498764\pi$
$139$	0.0915456	0.00776480	0.00388240	+	0.999992i	$0.498764\pi$
$140$	1.93675	0.163685
$141$	−13.0308	−1.09740
$142$	−23.4377	−1.96685
$143$	11.8901	0.994300
$144$	−4.37609	−0.364674
$145$	−17.7054	−1.47035
$146$	1.57930	0.130704
$147$	1.96861	0.162368
$148$	1.03416	0.0850078
$149$	−1.71760	−0.140711	−0.0703555	−	0.997522i	$-0.522413\pi$
$149$	−1.71760	−0.140711	−0.0703555	+	0.997522i	$0.522413\pi$
$150$	5.11872	0.417942
$151$	−21.7401	−1.76918	−0.884592	−	0.466367i	$-0.845563\pi$
$151$	−21.7401	−1.76918	−0.884592	+	0.466367i	$0.845563\pi$
$152$	−0.0207547	−0.00168343
$153$	2.42644	0.196166
$154$	−9.93484	−0.800572
$155$	1.87277	0.150424
$156$	4.24417	0.339806
$157$	−1.78582	−0.142524	−0.0712620	−	0.997458i	$-0.522703\pi$
$157$	−1.78582	−0.142524	−0.0712620	+	0.997458i	$0.522703\pi$
$158$	−27.1467	−2.15968
$159$	−21.8692	−1.73434
$160$	10.0055	0.791007
$161$	3.69596	0.291282
$162$	18.9167	1.48624
$163$	−4.53138	−0.354925	−0.177463	−	0.984128i	$-0.556789\pi$
$163$	−4.53138	−0.354925	−0.177463	+	0.984128i	$0.556789\pi$
$164$	−0.422972	−0.0330286
$165$	21.0274	1.63698
$166$	−25.7896	−2.00166
$167$	−21.4704	−1.66143	−0.830714	−	0.556699i	$-0.812068\pi$
$167$	−21.4704	−1.66143	−0.830714	+	0.556699i	$0.812068\pi$
$168$	3.31194	0.255522
$169$	−8.65402	−0.665694
$170$	−9.04183	−0.693477
$171$	−0.0107997	−0.000825872 0
$172$	9.85530	0.751460
$173$	14.8008	1.12528	0.562642	−	0.826701i	$-0.309785\pi$
$173$	14.8008	1.12528	0.562642	+	0.826701i	$0.309785\pi$
$174$	32.4191	2.45768
$175$	−1.49273	−0.112840
$176$	−28.5108	−2.14909
$177$	23.7234	1.78316
$178$	−28.3934	−2.12817
$179$	−25.3028	−1.89122	−0.945610	−	0.325304i	$-0.894533\pi$
$179$	−25.3028	−1.89122	−0.945610	+	0.325304i	$0.894533\pi$
$180$	1.69547	0.126373
$181$	23.7540	1.76562	0.882812	−	0.469727i	$-0.155647\pi$
$181$	23.7540	1.76562	0.882812	+	0.469727i	$0.155647\pi$
$182$	−3.63131	−0.269171
$183$	23.7351	1.75455
$184$	6.21799	0.458396
$185$	1.87277	0.137689
$186$	−3.42909	−0.251433
$187$	15.8086	1.15604
$188$	−6.84546	−0.499256
$189$	−4.18246	−0.304229
$190$	0.0402436	0.00291958
$191$	−11.7175	−0.847852	−0.423926	−	0.905697i	$-0.639348\pi$
$191$	−11.7175	−0.847852	−0.423926	+	0.905697i	$0.639348\pi$
$192$	1.36109	0.0982283
$193$	6.80407	0.489767	0.244884	−	0.969552i	$-0.421250\pi$
$193$	6.80407	0.489767	0.244884	+	0.969552i	$0.421250\pi$
$194$	10.6083	0.761633
$195$	7.68578	0.550390
$196$	1.03416	0.0738689
$197$	−3.69823	−0.263488	−0.131744	−	0.991284i	$-0.542058\pi$
$197$	−3.69823	−0.263488	−0.131744	+	0.991284i	$0.542058\pi$
$198$	−8.69718	−0.618082
$199$	−0.550919	−0.0390536	−0.0195268	−	0.999809i	$-0.506216\pi$
$199$	−0.550919	−0.0390536	−0.0195268	+	0.999809i	$0.506216\pi$
$200$	−2.51134	−0.177579
$201$	−28.5522	−2.01392
$202$	20.2881	1.42746
$203$	−9.45413	−0.663550
$204$	5.64289	0.395081
$205$	−0.765961	−0.0534970
$206$	13.1755	0.917977
$207$	3.23552	0.224884
$208$	−10.4211	−0.722571
$209$	−0.0703615	−0.00486700
$210$	−6.42190	−0.443153
$211$	23.2335	1.59946	0.799731	−	0.600359i	$-0.204976\pi$
$211$	23.2335	1.59946	0.799731	+	0.600359i	$0.204976\pi$
$212$	−11.4885	−0.789034
$213$	26.4883	1.81495
$214$	18.1584	1.24128
$215$	17.8470	1.21715
$216$	−7.03647	−0.478771
$217$	1.00000	0.0678844
$218$	−28.5448	−1.93330
$219$	−1.78486	−0.120610
$220$	11.0463	0.744738
$221$	5.77825	0.388687
$222$	−3.42909	−0.230146
$223$	2.99318	0.200438	0.100219	−	0.994965i	$-0.468046\pi$
$223$	2.99318	0.200438	0.100219	+	0.994965i	$0.468046\pi$
$224$	5.34264	0.356970
$225$	−1.30677	−0.0871182
$226$	−20.9129	−1.39111
$227$	3.57256	0.237119	0.118560	−	0.992947i	$-0.462172\pi$
$227$	3.57256	0.237119	0.118560	+	0.992947i	$0.462172\pi$
$228$	−0.0251155	−0.00166332
$229$	−1.44201	−0.0952907	−0.0476454	−	0.998864i	$-0.515172\pi$
$229$	−1.44201	−0.0952907	−0.0476454	+	0.998864i	$0.515172\pi$
$230$	−12.0568	−0.795000
$231$	11.2280	0.738746
$232$	−15.9054	−1.04424
$233$	−0.654900	−0.0429039	−0.0214519	−	0.999770i	$-0.506829\pi$
$233$	−0.654900	−0.0429039	−0.0214519	+	0.999770i	$0.506829\pi$
$234$	−3.17893	−0.207813
$235$	−12.3965	−0.808656
$236$	12.4626	0.811243
$237$	30.6802	1.99289
$238$	−4.82805	−0.312956
$239$	16.8651	1.09091	0.545456	−	0.838139i	$-0.316356\pi$
$239$	16.8651	1.09091	0.545456	+	0.838139i	$0.316356\pi$
$240$	−18.4295	−1.18962
$241$	−3.45881	−0.222802	−0.111401	−	0.993776i	$-0.535534\pi$
$241$	−3.45881	−0.222802	−0.111401	+	0.993776i	$0.535534\pi$
$242$	−37.5026	−2.41076
$243$	−8.83151	−0.566542
$244$	12.4687	0.798226
$245$	1.87277	0.119647
$246$	1.40250	0.0894198
$247$	−0.0257180	−0.00163640
$248$	1.68238	0.106831
$249$	29.1463	1.84707
$250$	21.1803	1.33956
$251$	−15.4192	−0.973250	−0.486625	−	0.873611i	$-0.661772\pi$
$251$	−15.4192	−0.973250	−0.486625	+	0.873611i	$0.661772\pi$
$252$	0.905330	0.0570304
$253$	21.0799	1.32528
$254$	−19.4626	−1.22119
$255$	10.2187	0.639921
$256$	19.3276	1.20797
$257$	8.34152	0.520330	0.260165	−	0.965564i	$-0.416223\pi$
$257$	8.34152	0.520330	0.260165	+	0.965564i	$0.416223\pi$
$258$	−32.6783	−2.03446
$259$	1.00000	0.0621370
$260$	4.03755	0.250398
$261$	−8.27636	−0.512294
$262$	32.7235	2.02166
$263$	−5.07384	−0.312866	−0.156433	−	0.987689i	$-0.550000\pi$
$263$	−5.07384	−0.312866	−0.156433	+	0.987689i	$0.550000\pi$
$264$	18.8896	1.16258
$265$	−20.8046	−1.27801
$266$	0.0214888	0.00131757
$267$	32.0891	1.96382
$268$	−14.9992	−0.916224
$269$	−14.7622	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$269$	−14.7622	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$270$	13.6438	0.830336
$271$	−16.8258	−1.02209	−0.511046	−	0.859553i	$-0.670742\pi$
$271$	−16.8258	−1.02209	−0.511046	+	0.859553i	$0.670742\pi$
$272$	−13.8555	−0.840111
$273$	4.10396	0.248383
$274$	−37.0396	−2.23765
$275$	−8.51381	−0.513402
$276$	7.52447	0.452920
$277$	−15.0159	−0.902217	−0.451109	−	0.892469i	$-0.648971\pi$
$277$	−15.0159	−0.902217	−0.451109	+	0.892469i	$0.648971\pi$
$278$	−0.159462	−0.00956389
$279$	0.875422	0.0524101
$280$	3.15070	0.188290
$281$	3.44933	0.205770	0.102885	−	0.994693i	$-0.467193\pi$
$281$	3.44933	0.205770	0.102885	+	0.994693i	$0.467193\pi$
$282$	22.6982	1.35166
$283$	25.4741	1.51428	0.757138	−	0.653255i	$-0.226597\pi$
$283$	25.4741	1.51428	0.757138	+	0.653255i	$0.226597\pi$
$284$	13.9150	0.825705
$285$	−0.0454817	−0.00269411
$286$	−20.7112	−1.22468
$287$	−0.408999	−0.0241425
$288$	4.67707	0.275599
$289$	−9.31745	−0.548085
$290$	30.8408	1.81103
$291$	−11.9891	−0.702813
$292$	−0.937637	−0.0548711
$293$	−5.96352	−0.348393	−0.174196	−	0.984711i	$-0.555733\pi$
$293$	−5.96352	−0.348393	−0.174196	+	0.984711i	$0.555733\pi$
$294$	−3.42909	−0.199989
$295$	22.5685	1.31399
$296$	1.68238	0.0977861
$297$	−23.8547	−1.38419
$298$	2.99185	0.173313
$299$	7.70497	0.445590
$300$	−3.03901	−0.175457
$301$	9.52973	0.549284
$302$	37.8687	2.17910
$303$	−22.9288	−1.31722
$304$	0.0616683	0.00353692
$305$	22.5796	1.29290
$306$	−4.22659	−0.241618
$307$	9.79964	0.559295	0.279647	−	0.960103i	$-0.409782\pi$
$307$	9.79964	0.559295	0.279647	+	0.960103i	$0.409782\pi$
$308$	5.89835	0.336090
$309$	−14.8904	−0.847084
$310$	−3.26215	−0.185278
$311$	−13.2957	−0.753928	−0.376964	−	0.926228i	$-0.623032\pi$
$311$	−13.2957	−0.753928	−0.376964	+	0.926228i	$0.623032\pi$
$312$	6.90441	0.390885
$313$	0.587277	0.0331949	0.0165974	−	0.999862i	$-0.494717\pi$
$313$	0.587277	0.0331949	0.0165974	+	0.999862i	$0.494717\pi$
$314$	3.11069	0.175547
$315$	1.63946	0.0923733
$316$	16.1171	0.906659
$317$	5.51532	0.309771	0.154886	−	0.987932i	$-0.450499\pi$
$317$	5.51532	0.309771	0.154886	+	0.987932i	$0.450499\pi$
$318$	38.0937	2.13619
$319$	−53.9216	−3.01903
$320$	1.29483	0.0723831
$321$	−20.5219	−1.14542
$322$	−6.43794	−0.358772
$323$	−0.0341937	−0.00190259
$324$	−11.2309	−0.623940
$325$	−3.11191	−0.172618
$326$	7.89314	0.437161
$327$	32.2602	1.78399
$328$	−0.688090	−0.0379934
$329$	−6.61932	−0.364935
$330$	−36.6273	−2.01627
$331$	−10.0411	−0.551907	−0.275953	−	0.961171i	$-0.588994\pi$
$331$	−10.0411	−0.551907	−0.275953	+	0.961171i	$0.588994\pi$
$332$	15.3114	0.840320
$333$	0.875422	0.0479728
$334$	37.3989	2.04638
$335$	−27.1621	−1.48403
$336$	−9.84075	−0.536857
$337$	25.7409	1.40219	0.701097	−	0.713065i	$-0.252694\pi$
$337$	25.7409	1.40219	0.701097	+	0.713065i	$0.252694\pi$
$338$	15.0743	0.819934
$339$	23.6350	1.28367
$340$	5.36817	0.291130
$341$	5.70350	0.308862
$342$	0.0188118	0.00101723
$343$	1.00000	0.0539949
$344$	16.0326	0.864419
$345$	13.6261	0.733604
$346$	−25.7813	−1.38601
$347$	−2.97310	−0.159604	−0.0798021	−	0.996811i	$-0.525429\pi$
$347$	−2.97310	−0.159604	−0.0798021	+	0.996811i	$0.525429\pi$
$348$	−19.2473	−1.03177
$349$	18.2147	0.975013	0.487506	−	0.873119i	$-0.337907\pi$
$349$	18.2147	0.975013	0.487506	+	0.873119i	$0.337907\pi$
$350$	2.60017	0.138985
$351$	−8.71919	−0.465396
$352$	30.4718	1.62415
$353$	8.63215	0.459443	0.229722	−	0.973256i	$-0.426218\pi$
$353$	8.63215	0.459443	0.229722	+	0.973256i	$0.426218\pi$
$354$	−41.3235	−2.19632
$355$	25.1988	1.33741
$356$	16.8573	0.893433
$357$	5.45647	0.288787
$358$	44.0745	2.32941
$359$	11.3772	0.600464	0.300232	−	0.953866i	$-0.402936\pi$
$359$	11.3772	0.600464	0.300232	+	0.953866i	$0.402936\pi$
$360$	2.75819	0.145370
$361$	−18.9998	−0.999992
$362$	−41.3768	−2.17472
$363$	42.3840	2.22458
$364$	2.15592	0.113001
$365$	−1.69797	−0.0888758
$366$	−41.3438	−2.16107
$367$	−24.8744	−1.29843	−0.649217	−	0.760604i	$-0.724903\pi$
$367$	−24.8744	−1.29843	−0.649217	+	0.760604i	$0.724903\pi$
$368$	−18.4755	−0.963101
$369$	−0.358047	−0.0186392
$370$	−3.26215	−0.169591
$371$	−11.1090	−0.576750
$372$	2.03586	0.105555
$373$	6.61452	0.342487	0.171243	−	0.985229i	$-0.445222\pi$
$373$	6.61452	0.342487	0.171243	+	0.985229i	$0.445222\pi$
$374$	−27.5368	−1.42389
$375$	−23.9371	−1.23611
$376$	−11.1362	−0.574305
$377$	−19.7090	−1.01507
$378$	7.28537	0.374719
$379$	−2.36354	−0.121407	−0.0607035	−	0.998156i	$-0.519334\pi$
$379$	−2.36354	−0.121407	−0.0607035	+	0.998156i	$0.519334\pi$
$380$	−0.0238928	−0.00122567
$381$	21.9958	1.12688
$382$	20.4106	1.04430
$383$	−18.4091	−0.940660	−0.470330	−	0.882491i	$-0.655865\pi$
$383$	−18.4091	−0.940660	−0.470330	+	0.882491i	$0.655865\pi$
$384$	−23.4060	−1.19443
$385$	10.6813	0.544372
$386$	−11.8519	−0.603246
$387$	8.34253	0.424075
$388$	−6.29820	−0.319743
$389$	27.4229	1.39040	0.695198	−	0.718818i	$-0.255317\pi$
$389$	27.4229	1.39040	0.695198	+	0.718818i	$0.255317\pi$
$390$	−13.3877	−0.677914
$391$	10.2442	0.518074
$392$	1.68238	0.0849728
$393$	−36.9828	−1.86553
$394$	6.44189	0.324538
$395$	29.1865	1.46853
$396$	5.16355	0.259478
$397$	26.8319	1.34665	0.673326	−	0.739346i	$-0.264865\pi$
$397$	26.8319	1.34665	0.673326	+	0.739346i	$0.264865\pi$
$398$	0.959638	0.0481023
$399$	−0.0242858	−0.00121581
$400$	7.46193	0.373097
$401$	7.60640	0.379846	0.189923	−	0.981799i	$-0.439176\pi$
$401$	7.60640	0.379846	0.189923	+	0.981799i	$0.439176\pi$
$402$	49.7346	2.48054
$403$	2.08470	0.103846
$404$	−12.0451	−0.599266
$405$	−20.3381	−1.01061
$406$	16.4680	0.817294
$407$	5.70350	0.282712
$408$	9.17984	0.454470
$409$	−10.7057	−0.529364	−0.264682	−	0.964336i	$-0.585267\pi$
$409$	−10.7057	−0.529364	−0.264682	+	0.964336i	$0.585267\pi$
$410$	1.33422	0.0658922
$411$	41.8607	2.06484
$412$	−7.82232	−0.385378
$413$	12.0509	0.592984
$414$	−5.63591	−0.276990
$415$	27.7274	1.36108
$416$	11.1378	0.546076
$417$	0.180217	0.00882529
$418$	0.122562	0.00599468
$419$	−3.65174	−0.178399	−0.0891997	−	0.996014i	$-0.528431\pi$
$419$	−3.65174	−0.178399	−0.0891997	+	0.996014i	$0.528431\pi$
$420$	3.81270	0.186041
$421$	−8.46134	−0.412380	−0.206190	−	0.978512i	$-0.566107\pi$
$421$	−8.46134	−0.412380	−0.206190	+	0.978512i	$0.566107\pi$
$422$	−40.4701	−1.97005
$423$	−5.79470	−0.281748
$424$	−18.6895	−0.907642
$425$	−4.13747	−0.200697
$426$	−46.1396	−2.23547
$427$	12.0568	0.583468
$428$	−10.7807	−0.521105
$429$	23.4069	1.13010
$430$	−31.0874	−1.49917
$431$	36.0852	1.73816	0.869082	−	0.494668i	$-0.164710\pi$
$431$	36.0852	1.73816	0.869082	+	0.494668i	$0.164710\pi$
$432$	20.9074	1.00591
$433$	−20.3726	−0.979046	−0.489523	−	0.871990i	$-0.662829\pi$
$433$	−20.3726	−0.979046	−0.489523	+	0.871990i	$0.662829\pi$
$434$	−1.74189	−0.0836132
$435$	−34.8550	−1.67117
$436$	16.9471	0.811621
$437$	−0.0455953	−0.00218112
$438$	3.10903	0.148555
$439$	−0.169217	−0.00807627	−0.00403814	−	0.999992i	$-0.501285\pi$
$439$	−0.169217	−0.00807627	−0.00403814	+	0.999992i	$0.501285\pi$
$440$	17.9700	0.856687
$441$	0.875422	0.0416868
$442$	−10.0651	−0.478746
$443$	32.5273	1.54542	0.772710	−	0.634760i	$-0.218901\pi$
$443$	32.5273	1.54542	0.772710	+	0.634760i	$0.218901\pi$
$444$	2.03586	0.0966179
$445$	30.5268	1.44711
$446$	−5.21378	−0.246879
$447$	−3.38127	−0.159929
$448$	0.691397	0.0326655
$449$	−40.9869	−1.93429	−0.967145	−	0.254224i	$-0.918180\pi$
$449$	−40.9869	−1.93429	−0.967145	+	0.254224i	$0.918180\pi$
$450$	2.27625	0.107303
$451$	−2.33273	−0.109844
$452$	12.4161	0.584003
$453$	−42.7977	−2.01081
$454$	−6.22299	−0.292059
$455$	3.90417	0.183030
$456$	−0.0408579	−0.00191335
$457$	−1.53764	−0.0719279	−0.0359639	−	0.999353i	$-0.511450\pi$
$457$	−1.53764	−0.0719279	−0.0359639	+	0.999353i	$0.511450\pi$
$458$	2.51182	0.117369
$459$	−11.5927	−0.541101
$460$	7.15815	0.333751
$461$	−3.88176	−0.180792	−0.0903958	−	0.995906i	$-0.528813\pi$
$461$	−3.88176	−0.180792	−0.0903958	+	0.995906i	$0.528813\pi$
$462$	−19.5578	−0.909912
$463$	−5.71562	−0.265627	−0.132814	−	0.991141i	$-0.542401\pi$
$463$	−5.71562	−0.265627	−0.132814	+	0.991141i	$0.542401\pi$
$464$	47.2596	2.19397
$465$	3.68675	0.170969
$466$	1.14076	0.0528447
$467$	34.4930	1.59615	0.798074	−	0.602560i	$-0.205853\pi$
$467$	34.4930	1.59615	0.798074	+	0.602560i	$0.205853\pi$
$468$	1.88734	0.0872424
$469$	−14.5037	−0.669720
$470$	21.5932	0.996020
$471$	−3.51558	−0.161989
$472$	20.2741	0.933189
$473$	54.3528	2.49914
$474$	−53.4413	−2.45464
$475$	0.0184152	0.000844946 0
$476$	2.86643	0.131383
$477$	−9.72505	−0.445279
$478$	−29.3771	−1.34368
$479$	−24.1250	−1.10230	−0.551150	−	0.834406i	$-0.685811\pi$
$479$	−24.1250	−1.10230	−0.551150	+	0.834406i	$0.685811\pi$
$480$	19.6970	0.899040
$481$	2.08470	0.0950542
$482$	6.02485	0.274425
$483$	7.27590	0.331065
$484$	22.2655	1.01207
$485$	−11.4054	−0.517893
$486$	15.3835	0.697809
$487$	−16.9192	−0.766681	−0.383340	−	0.923607i	$-0.625226\pi$
$487$	−16.9192	−0.766681	−0.383340	+	0.923607i	$0.625226\pi$
$488$	20.2840	0.918215
$489$	−8.92051	−0.403400
$490$	−3.26215	−0.147369
$491$	−3.16890	−0.143011	−0.0715053	−	0.997440i	$-0.522780\pi$
$491$	−3.16890	−0.143011	−0.0715053	+	0.997440i	$0.522780\pi$
$492$	−0.832667	−0.0375395
$493$	−26.2044	−1.18019
$494$	0.0447978	0.00201555
$495$	9.35068	0.420282
$496$	−4.99883	−0.224454
$497$	13.4553	0.603555
$498$	−50.7696	−2.27504
$499$	−33.6948	−1.50839	−0.754193	−	0.656652i	$-0.771972\pi$
$499$	−33.6948	−1.50839	−0.754193	+	0.656652i	$0.771972\pi$
$500$	−12.5748	−0.562362
$501$	−42.2668	−1.88834
$502$	26.8584	1.19875
$503$	4.72136	0.210515	0.105258	−	0.994445i	$-0.466433\pi$
$503$	4.72136	0.210515	0.105258	+	0.994445i	$0.466433\pi$
$504$	1.47279	0.0656032
$505$	−21.8125	−0.970643
$506$	−36.7188	−1.63235
$507$	−17.0364	−0.756612
$508$	11.5550	0.512670
$509$	12.0759	0.535254	0.267627	−	0.963523i	$-0.413760\pi$
$509$	12.0759	0.535254	0.267627	+	0.963523i	$0.413760\pi$
$510$	−17.7998	−0.788190
$511$	−0.906662	−0.0401084
$512$	−9.88714	−0.436954
$513$	0.0515971	0.00227807
$514$	−14.5300	−0.640890
$515$	−14.1654	−0.624204
$516$	19.4012	0.854092
$517$	−37.7533	−1.66039
$518$	−1.74189	−0.0765340
$519$	29.1370	1.27897
$520$	6.56827	0.288038
$521$	18.2108	0.797831	0.398916	−	0.916988i	$-0.369387\pi$
$521$	18.2108	0.797831	0.398916	+	0.916988i	$0.369387\pi$
$522$	14.4165	0.630991
$523$	−19.2652	−0.842410	−0.421205	−	0.906965i	$-0.638393\pi$
$523$	−19.2652	−0.842410	−0.421205	+	0.906965i	$0.638393\pi$
$524$	−19.4280	−0.848718
$525$	−2.93861	−0.128252
$526$	8.83804	0.385357
$527$	2.77174	0.120739
$528$	−56.1267	−2.44260
$529$	−9.33989	−0.406082
$530$	36.2392	1.57413
$531$	10.5496	0.457813
$532$	−0.0127580	−0.000553130 0
$533$	−0.852641	−0.0369320
$534$	−55.8954	−2.41883
$535$	−19.5228	−0.844043
$536$	−24.4007	−1.05395
$537$	−49.8113	−2.14952
$538$	25.7141	1.10862
$539$	5.70350	0.245667
$540$	−8.10039	−0.348585
$541$	−31.0904	−1.33668	−0.668339	−	0.743856i	$-0.732995\pi$
$541$	−31.0904	−1.33668	−0.668339	+	0.743856i	$0.732995\pi$
$542$	29.3085	1.25891
$543$	46.7624	2.00677
$544$	14.8084	0.634906
$545$	30.6896	1.31460
$546$	−7.14863	−0.305933
$547$	−35.2850	−1.50868	−0.754339	−	0.656485i	$-0.772042\pi$
$547$	−35.2850	−1.50868	−0.754339	+	0.656485i	$0.772042\pi$
$548$	21.9906	0.939391
$549$	10.5548	0.450467
$550$	14.8301	0.632357
$551$	0.116631	0.00496866
$552$	12.2408	0.521003
$553$	15.5847	0.662729
$554$	26.1559	1.11126
$555$	3.68675	0.156494
$556$	0.0946731	0.00401504
$557$	−39.8300	−1.68765	−0.843825	−	0.536618i	$-0.819702\pi$
$557$	−39.8300	−1.68765	−0.843825	+	0.536618i	$0.819702\pi$
$558$	−1.52488	−0.0645535
$559$	19.8666	0.840269
$560$	−9.36166	−0.395602
$561$	31.1210	1.31393
$562$	−6.00834	−0.253446
$563$	4.21645	0.177702	0.0888511	−	0.996045i	$-0.471680\pi$
$563$	4.21645	0.177702	0.0888511	+	0.996045i	$0.471680\pi$
$564$	−13.4760	−0.567443
$565$	22.4843	0.945922
$566$	−44.3729	−1.86513
$567$	−10.8599	−0.456073
$568$	22.6369	0.949825
$569$	−6.14249	−0.257507	−0.128753	−	0.991677i	$-0.541098\pi$
$569$	−6.14249	−0.257507	−0.128753	+	0.991677i	$0.541098\pi$
$570$	0.0792240	0.00331833
$571$	14.0483	0.587902	0.293951	−	0.955821i	$-0.405030\pi$
$571$	14.0483	0.587902	0.293951	+	0.955821i	$0.405030\pi$
$572$	12.2963	0.514134
$573$	−23.0673	−0.963649
$574$	0.712429	0.0297362
$575$	−5.51709	−0.230078
$576$	0.605264	0.0252194
$577$	8.18158	0.340604	0.170302	−	0.985392i	$-0.445526\pi$
$577$	8.18158	0.340604	0.170302	+	0.985392i	$0.445526\pi$
$578$	16.2299	0.675076
$579$	13.3945	0.556658
$580$	−18.3103	−0.760294
$581$	14.8055	0.614238
$582$	20.8836	0.865654
$583$	−63.3601	−2.62411
$584$	−1.52535	−0.0631193
$585$	3.41779	0.141308
$586$	10.3878	0.429115
$587$	−8.45285	−0.348887	−0.174443	−	0.984667i	$-0.555813\pi$
$587$	−8.45285	−0.348887	−0.174443	+	0.984667i	$0.555813\pi$
$588$	2.03586	0.0839576
$589$	−0.0123365	−0.000508318 0
$590$	−39.3117	−1.61844
$591$	−7.28037	−0.299474
$592$	−4.99883	−0.205451
$593$	−26.9805	−1.10796	−0.553979	−	0.832531i	$-0.686891\pi$
$593$	−26.9805	−1.10796	−0.553979	+	0.832531i	$0.686891\pi$
$594$	41.5521	1.70490
$595$	5.19083	0.212803
$596$	−1.77628	−0.0727591
$597$	−1.08454	−0.0443875
$598$	−13.4212	−0.548833
$599$	−16.8830	−0.689822	−0.344911	−	0.938635i	$-0.612091\pi$
$599$	−16.8830	−0.689822	−0.344911	+	0.938635i	$0.612091\pi$
$600$	−4.94385	−0.201832
$601$	11.5439	0.470884	0.235442	−	0.971888i	$-0.424346\pi$
$601$	11.5439	0.470884	0.235442	+	0.971888i	$0.424346\pi$
$602$	−16.5997	−0.676553
$603$	−12.6969	−0.517057
$604$	−22.4828	−0.914813
$605$	40.3206	1.63926
$606$	39.9393	1.62242
$607$	28.9703	1.17587	0.587933	−	0.808910i	$-0.299942\pi$
$607$	28.9703	1.17587	0.587933	+	0.808910i	$0.299942\pi$
$608$	−0.0659097	−0.00267299
$609$	−18.6115	−0.754176
$610$	−39.3310	−1.59247
$611$	−13.7993	−0.558260
$612$	2.50934	0.101434
$613$	−26.0130	−1.05065	−0.525327	−	0.850901i	$-0.676057\pi$
$613$	−26.0130	−1.05065	−0.525327	+	0.850901i	$0.676057\pi$
$614$	−17.0698	−0.688883
$615$	−1.50788	−0.0608035
$616$	9.59543	0.386611
$617$	25.0492	1.00844	0.504221	−	0.863575i	$-0.331780\pi$
$617$	25.0492	1.00844	0.504221	+	0.863575i	$0.331780\pi$
$618$	25.9373	1.04335
$619$	−0.939042	−0.0377433	−0.0188717	−	0.999822i	$-0.506007\pi$
$619$	−0.939042	−0.0377433	−0.0188717	+	0.999822i	$0.506007\pi$
$620$	1.93675	0.0777818
$621$	−15.4582	−0.620317
$622$	23.1595	0.928612
$623$	16.3004	0.653060
$624$	−20.5150	−0.821258
$625$	−15.3081	−0.612323
$626$	−1.02297	−0.0408861
$627$	−0.138514	−0.00553172
$628$	−1.84683	−0.0736966
$629$	2.77174	0.110517
$630$	−2.85576	−0.113776
$631$	17.6487	0.702584	0.351292	−	0.936266i	$-0.385742\pi$
$631$	17.6487	0.702584	0.351292	+	0.936266i	$0.385742\pi$
$632$	26.2193	1.04295
$633$	45.7377	1.81791
$634$	−9.60706	−0.381545
$635$	20.9250	0.830382
$636$	−22.6164	−0.896798
$637$	2.08470	0.0825989
$638$	93.9253	3.71854
$639$	11.7791	0.465974
$640$	−22.2665	−0.880161
$641$	26.5484	1.04860	0.524299	−	0.851534i	$-0.324327\pi$
$641$	26.5484	1.04860	0.524299	+	0.851534i	$0.324327\pi$
$642$	35.7467	1.41081
$643$	44.2957	1.74685	0.873425	−	0.486958i	$-0.161894\pi$
$643$	44.2957	1.74685	0.873425	+	0.486958i	$0.161894\pi$
$644$	3.82223	0.150617
$645$	35.1337	1.38339
$646$	0.0595615	0.00234342
$647$	17.1703	0.675032	0.337516	−	0.941320i	$-0.390413\pi$
$647$	17.1703	0.675032	0.337516	+	0.941320i	$0.390413\pi$
$648$	−18.2704	−0.717730
$649$	68.7320	2.69797
$650$	5.42058	0.212613
$651$	1.96861	0.0771559
$652$	−4.68619	−0.183525
$653$	−24.2862	−0.950391	−0.475196	−	0.879880i	$-0.657623\pi$
$653$	−24.2862	−0.950391	−0.475196	+	0.879880i	$0.657623\pi$
$654$	−56.1935	−2.19734
$655$	−35.1823	−1.37469
$656$	2.04452	0.0798250
$657$	−0.793712	−0.0309657
$658$	11.5301	0.449490
$659$	8.55510	0.333259	0.166630	−	0.986020i	$-0.446712\pi$
$659$	8.55510	0.333259	0.166630	+	0.986020i	$0.446712\pi$
$660$	21.7458	0.846453
$661$	−26.4296	−1.02799	−0.513997	−	0.857792i	$-0.671836\pi$
$661$	−26.4296	−1.02799	−0.513997	+	0.857792i	$0.671836\pi$
$662$	17.4904	0.679783
$663$	11.3751	0.441773
$664$	24.9085	0.966637
$665$	−0.0231035	−0.000895915 0
$666$	−1.52488	−0.0590881
$667$	−34.9421	−1.35296
$668$	−22.2039	−0.859094
$669$	5.89240	0.227813
$670$	47.3133	1.82787
$671$	68.7658	2.65468
$672$	10.5176	0.405724
$673$	24.3683	0.939328	0.469664	−	0.882845i	$-0.344375\pi$
$673$	24.3683	0.939328	0.469664	+	0.882845i	$0.344375\pi$
$674$	−44.8377	−1.72708
$675$	6.24331	0.240305
$676$	−8.94968	−0.344218
$677$	7.13077	0.274058	0.137029	−	0.990567i	$-0.456245\pi$
$677$	7.13077	0.274058	0.137029	+	0.990567i	$0.456245\pi$
$678$	−41.1694	−1.58110
$679$	−6.09014	−0.233718
$680$	8.73293	0.334893
$681$	7.03297	0.269504
$682$	−9.93484	−0.380425
$683$	12.6660	0.484652	0.242326	−	0.970195i	$-0.422090\pi$
$683$	12.6660	0.484652	0.242326	+	0.970195i	$0.422090\pi$
$684$	−0.0111686	−0.000427044 0
$685$	39.8228	1.52155
$686$	−1.74189	−0.0665055
$687$	−2.83875	−0.108305
$688$	−47.6375	−1.81616
$689$	−23.1589	−0.882284
$690$	−23.7351	−0.903579
$691$	29.7501	1.13175	0.565873	−	0.824492i	$-0.308539\pi$
$691$	29.7501	1.13175	0.565873	+	0.824492i	$0.308539\pi$
$692$	15.3065	0.581864
$693$	4.99297	0.189667
$694$	5.17879	0.196584
$695$	0.171444	0.00650323
$696$	−31.3115	−1.18686
$697$	−1.13364	−0.0429397
$698$	−31.7280	−1.20092
$699$	−1.28924	−0.0487636
$700$	−1.54373	−0.0583476
$701$	−4.93607	−0.186433	−0.0932163	−	0.995646i	$-0.529715\pi$
$701$	−4.93607	−0.186433	−0.0932163	+	0.995646i	$0.529715\pi$
$702$	15.1878	0.573227
$703$	−0.0123365	−0.000465281 0
$704$	3.94338	0.148622
$705$	−24.4038	−0.919099
$706$	−15.0362	−0.565895
$707$	−11.6472	−0.438037
$708$	24.5339	0.922041
$709$	−4.97530	−0.186851	−0.0934257	−	0.995626i	$-0.529782\pi$
$709$	−4.97530	−0.186851	−0.0934257	+	0.995626i	$0.529782\pi$
$710$	−43.8933	−1.64729
$711$	13.6432	0.511659
$712$	27.4233	1.02773
$713$	3.69596	0.138415
$714$	−9.50455	−0.355699
$715$	22.2674	0.832754
$716$	−26.1672	−0.977915
$717$	33.2008	1.23991
$718$	−19.8177	−0.739591
$719$	2.13455	0.0796053	0.0398026	−	0.999208i	$-0.487327\pi$
$719$	2.13455	0.0796053	0.0398026	+	0.999208i	$0.487327\pi$
$720$	−8.19540	−0.305425
$721$	−7.56390	−0.281695
$722$	33.0956	1.23169
$723$	−6.80905	−0.253231
$724$	24.5656	0.912972
$725$	14.1125	0.524126
$726$	−73.8280	−2.74002
$727$	−32.5869	−1.20858	−0.604290	−	0.796765i	$-0.706543\pi$
$727$	−32.5869	−1.20858	−0.604290	+	0.796765i	$0.706543\pi$
$728$	3.50725	0.129987
$729$	15.1939	0.562737
$730$	2.95767	0.109468
$731$	26.4139	0.976955
$732$	24.5460	0.907245
$733$	−23.2574	−0.859031	−0.429515	−	0.903060i	$-0.641316\pi$
$733$	−23.2574	−0.859031	−0.429515	+	0.903060i	$0.641316\pi$
$734$	43.3284	1.59928
$735$	3.68675	0.135988
$736$	19.7462	0.727854
$737$	−82.7220	−3.04711
$738$	0.623676	0.0229578
$739$	11.1348	0.409599	0.204800	−	0.978804i	$-0.434346\pi$
$739$	11.1348	0.409599	0.204800	+	0.978804i	$0.434346\pi$
$740$	1.93675	0.0711964
$741$	−0.0506287	−0.00185989
$742$	19.3506	0.710382
$743$	−17.6632	−0.647999	−0.323999	−	0.946057i	$-0.605028\pi$
$743$	−17.6632	−0.647999	−0.323999	+	0.946057i	$0.605028\pi$
$744$	3.31194	0.121422
$745$	−3.21666	−0.117849
$746$	−11.5217	−0.421840
$747$	12.9611	0.474222
$748$	16.3487	0.597768
$749$	−10.4246	−0.380905
$750$	41.6957	1.52251
$751$	−44.9465	−1.64012	−0.820061	−	0.572276i	$-0.806061\pi$
$751$	−44.9465	−1.64012	−0.820061	+	0.572276i	$0.806061\pi$
$752$	33.0889	1.20663
$753$	−30.3543	−1.10617
$754$	34.3309	1.25026
$755$	−40.7142	−1.48174
$756$	−4.32535	−0.157312
$757$	21.5383	0.782822	0.391411	−	0.920216i	$-0.371987\pi$
$757$	21.5383	0.782822	0.391411	+	0.920216i	$0.371987\pi$
$758$	4.11702	0.149537
$759$	41.4981	1.50629
$760$	−0.0388688	−0.00140992
$761$	−42.5291	−1.54168	−0.770839	−	0.637030i	$-0.780163\pi$
$761$	−42.5291	−1.54168	−0.770839	+	0.637030i	$0.780163\pi$
$762$	−38.3142	−1.38798
$763$	16.3873	0.593260
$764$	−12.1179	−0.438409
$765$	4.54417	0.164295
$766$	32.0665	1.15861
$767$	25.1224	0.907118
$768$	38.0484	1.37295
$769$	−38.8424	−1.40069	−0.700347	−	0.713803i	$-0.746971\pi$
$769$	−38.8424	−1.40069	−0.700347	+	0.713803i	$0.746971\pi$
$770$	−18.6057	−0.670502
$771$	16.4212	0.591395
$772$	7.03652	0.253250
$773$	33.6442	1.21010	0.605048	−	0.796189i	$-0.293154\pi$
$773$	33.6442	1.21010	0.605048	+	0.796189i	$0.293154\pi$
$774$	−14.5317	−0.522333
$775$	−1.49273	−0.0536206
$776$	−10.2459	−0.367806
$777$	1.96861	0.0706235
$778$	−47.7675	−1.71255
$779$	0.00504563	0.000180779 0
$780$	7.94835	0.284597
$781$	76.7426	2.74606
$782$	−17.8443	−0.638111
$783$	39.5416	1.41310
$784$	−4.99883	−0.178530
$785$	−3.34443	−0.119368
$786$	64.4197	2.29777
$787$	−17.8474	−0.636193	−0.318096	−	0.948058i	$-0.603044\pi$
$787$	−17.8474	−0.636193	−0.318096	+	0.948058i	$0.603044\pi$
$788$	−3.82458	−0.136245
$789$	−9.98841	−0.355597
$790$	−50.8396	−1.80879
$791$	12.0059	0.426881
$792$	8.40005	0.298483
$793$	25.1348	0.892562
$794$	−46.7380	−1.65867
$795$	−40.9561	−1.45256
$796$	−0.569741	−0.0201939
$797$	8.10317	0.287029	0.143515	−	0.989648i	$-0.454160\pi$
$797$	8.10317	0.287029	0.143515	+	0.989648i	$0.454160\pi$
$798$	0.0423031	0.00149751
$799$	−18.3470	−0.649071
$800$	−7.97515	−0.281964
$801$	14.2697	0.504195
$802$	−13.2495	−0.467856
$803$	−5.17115	−0.182486
$804$	−29.5276	−1.04136
$805$	6.92168	0.243957
$806$	−3.63131	−0.127907
$807$	−29.0611	−1.02300
$808$	−19.5949	−0.689348
$809$	33.6796	1.18411	0.592056	−	0.805897i	$-0.298316\pi$
$809$	33.6796	1.18411	0.592056	+	0.805897i	$0.298316\pi$
$810$	35.4266	1.24476
$811$	−25.1324	−0.882516	−0.441258	−	0.897380i	$-0.645468\pi$
$811$	−25.1324	−0.882516	−0.441258	+	0.897380i	$0.645468\pi$
$812$	−9.77712	−0.343110
$813$	−33.1233	−1.16169
$814$	−9.93484	−0.348216
$815$	−8.48623	−0.297260
$816$	−27.2760	−0.954851
$817$	−0.117564	−0.00411304
$818$	18.6481	0.652017
$819$	1.82499	0.0637704
$820$	−0.792129	−0.0276624
$821$	−22.6062	−0.788963	−0.394482	−	0.918904i	$-0.629076\pi$
$821$	−22.6062	−0.788963	−0.394482	+	0.918904i	$0.629076\pi$
$822$	−72.9166	−2.54326
$823$	−16.0750	−0.560340	−0.280170	−	0.959950i	$-0.590391\pi$
$823$	−16.0750	−0.560340	−0.280170	+	0.959950i	$0.590391\pi$
$824$	−12.7253	−0.443308
$825$	−16.7604	−0.583521
$826$	−20.9912	−0.730377
$827$	22.1673	0.770833	0.385416	−	0.922743i	$-0.374058\pi$
$827$	22.1673	0.770833	0.385416	+	0.922743i	$0.374058\pi$
$828$	3.34606	0.116284
$829$	−31.5161	−1.09460	−0.547299	−	0.836937i	$-0.684344\pi$
$829$	−31.5161	−1.09460	−0.547299	+	0.836937i	$0.684344\pi$
$830$	−48.2979	−1.67644
$831$	−29.5604	−1.02544
$832$	1.44136	0.0499701
$833$	2.77174	0.0960351
$834$	−0.313918	−0.0108701
$835$	−40.2091	−1.39149
$836$	−0.0727653	−0.00251664
$837$	−4.18246	−0.144567
$838$	6.36092	0.219734
$839$	48.6380	1.67917	0.839585	−	0.543229i	$-0.182798\pi$
$839$	48.6380	1.67917	0.839585	+	0.543229i	$0.182798\pi$
$840$	6.20250	0.214007
$841$	60.3806	2.08209
$842$	14.7387	0.507928
$843$	6.79038	0.233873
$844$	24.0273	0.827052
$845$	−16.2070	−0.557537
$846$	10.0937	0.347028
$847$	21.5299	0.739777
$848$	55.5320	1.90698
$849$	50.1485	1.72109
$850$	7.20700	0.247198
$851$	3.69596	0.126696
$852$	27.3933	0.938478
$853$	−45.2834	−1.55047	−0.775236	−	0.631671i	$-0.782369\pi$
$853$	−45.2834	−1.55047	−0.775236	+	0.631671i	$0.782369\pi$
$854$	−21.0015	−0.718657
$855$	−0.0202253	−0.000691691 0
$856$	−17.5380	−0.599437
$857$	40.9947	1.40035	0.700176	−	0.713970i	$-0.253105\pi$
$857$	40.9947	1.40035	0.700176	+	0.713970i	$0.253105\pi$
$858$	−40.7722	−1.39194
$859$	−22.1689	−0.756393	−0.378196	−	0.925725i	$-0.623456\pi$
$859$	−22.1689	−0.756393	−0.378196	+	0.925725i	$0.623456\pi$
$860$	18.4567	0.629369
$861$	−0.805159	−0.0274398
$862$	−62.8563	−2.14090
$863$	−18.3890	−0.625970	−0.312985	−	0.949758i	$-0.601329\pi$
$863$	−18.3890	−0.625970	−0.312985	+	0.949758i	$0.601329\pi$
$864$	−22.3454	−0.760206
$865$	27.7185	0.942457
$866$	35.4868	1.20589
$867$	−18.3424	−0.622941
$868$	1.03416	0.0351018
$869$	88.8873	3.01530
$870$	60.7135	2.05838
$871$	−30.2360	−1.02451
$872$	27.5696	0.933624
$873$	−5.33144	−0.180442
$874$	0.0794219	0.00268648
$875$	−12.1594	−0.411063
$876$	−1.84584	−0.0623652
$877$	18.9568	0.640127	0.320063	−	0.947396i	$-0.396296\pi$
$877$	18.9568	0.640127	0.320063	+	0.947396i	$0.396296\pi$
$878$	0.294756	0.00994754
$879$	−11.7398	−0.395975
$880$	−53.3942	−1.79992
$881$	−0.296187	−0.00997878	−0.00498939	−	0.999988i	$-0.501588\pi$
$881$	−0.296187	−0.00997878	−0.00498939	+	0.999988i	$0.501588\pi$
$882$	−1.52488	−0.0513455
$883$	−22.9026	−0.770733	−0.385367	−	0.922764i	$-0.625925\pi$
$883$	−22.9026	−0.770733	−0.385367	+	0.922764i	$0.625925\pi$
$884$	5.97566	0.200983
$885$	44.4285	1.49345
$886$	−56.6589	−1.90349
$887$	16.7959	0.563950	0.281975	−	0.959422i	$-0.409010\pi$
$887$	16.7959	0.563950	0.281975	+	0.959422i	$0.409010\pi$
$888$	3.31194	0.111141
$889$	11.1733	0.374739
$890$	−53.1742	−1.78240
$891$	−61.9395	−2.07505
$892$	3.09544	0.103643
$893$	0.0816595	0.00273263
$894$	5.88979	0.196984
$895$	−47.3863	−1.58395
$896$	−11.8896	−0.397204
$897$	15.1681	0.506447
$898$	71.3944	2.38246
$899$	−9.45413	−0.315313
$900$	−1.35142	−0.0450472
$901$	−30.7912	−1.02580
$902$	4.06334	0.135294
$903$	18.7603	0.624304
$904$	20.1985	0.671791
$905$	44.4858	1.47876
$906$	74.5487	2.47672
$907$	−25.0659	−0.832300	−0.416150	−	0.909296i	$-0.636621\pi$
$907$	−25.0659	−0.832300	−0.416150	+	0.909296i	$0.636621\pi$
$908$	3.69461	0.122610
$909$	−10.1962	−0.338187
$910$	−6.80061	−0.225438
$911$	35.9630	1.19151	0.595754	−	0.803167i	$-0.296853\pi$
$911$	35.9630	1.19151	0.595754	+	0.803167i	$0.296853\pi$
$912$	0.121401	0.00401998
$913$	84.4434	2.79467
$914$	2.67840	0.0885935
$915$	44.4503	1.46948
$916$	−1.49128	−0.0492731
$917$	−18.7862	−0.620376
$918$	20.1932	0.666474
$919$	−49.2660	−1.62514	−0.812568	−	0.582866i	$-0.801931\pi$
$919$	−49.2660	−1.62514	−0.812568	+	0.582866i	$0.801931\pi$
$920$	11.6449	0.383920
$921$	19.2917	0.635682
$922$	6.76158	0.222681
$923$	28.0504	0.923289
$924$	11.6116	0.381992
$925$	−1.49273	−0.0490808
$926$	9.95596	0.327173
$927$	−6.62161	−0.217482
$928$	−50.5100	−1.65807
$929$	−29.8100	−0.978034	−0.489017	−	0.872274i	$-0.662644\pi$
$929$	−29.8100	−0.978034	−0.489017	+	0.872274i	$0.662644\pi$
$930$	−6.42190	−0.210582
$931$	−0.0123365	−0.000404314 0
$932$	−0.677274	−0.0221848
$933$	−26.1740	−0.856897
$934$	−60.0829	−1.96597
$935$	29.6059	0.968217
$936$	3.07032	0.100357
$937$	−19.6770	−0.642819	−0.321410	−	0.946940i	$-0.604157\pi$
$937$	−19.6770	−0.642819	−0.321410	+	0.946940i	$0.604157\pi$
$938$	25.2638	0.824894
$939$	1.15612	0.0377285
$940$	−12.8200	−0.418141
$941$	−9.03898	−0.294662	−0.147331	−	0.989087i	$-0.547068\pi$
$941$	−9.03898	−0.294662	−0.147331	+	0.989087i	$0.547068\pi$
$942$	6.12374	0.199522
$943$	−1.51164	−0.0492259
$944$	−60.2402	−1.96065
$945$	−7.83279	−0.254801
$946$	−94.6764	−3.07819
$947$	−9.94030	−0.323016	−0.161508	−	0.986871i	$-0.551636\pi$
$947$	−9.94030	−0.323016	−0.161508	+	0.986871i	$0.551636\pi$
$948$	31.7283	1.03049
$949$	−1.89012	−0.0613559
$950$	−0.0320771	−0.00104072
$951$	10.8575	0.352079
$952$	4.66311	0.151132
$953$	8.27717	0.268124	0.134062	−	0.990973i	$-0.457198\pi$
$953$	8.27717	0.268124	0.134062	+	0.990973i	$0.457198\pi$
$954$	16.9399	0.548450
$955$	−21.9443	−0.710099
$956$	17.4413	0.564091
$957$	−106.151	−3.43136
$958$	42.0230	1.35770
$959$	21.2641	0.686654
$960$	2.54901	0.0822689
$961$	1.00000	0.0322581
$962$	−3.63131	−0.117078
$963$	−9.12588	−0.294077
$964$	−3.57698	−0.115207
$965$	12.7424	0.410194
$966$	−12.6738	−0.407772
$967$	11.5941	0.372842	0.186421	−	0.982470i	$-0.440311\pi$
$967$	11.5941	0.372842	0.186421	+	0.982470i	$0.440311\pi$
$968$	36.2214	1.16420
$969$	−0.0673140	−0.00216244
$970$	19.8669	0.637889
$971$	38.5963	1.23861	0.619307	−	0.785149i	$-0.287414\pi$
$971$	38.5963	1.23861	0.619307	+	0.785149i	$0.287414\pi$
$972$	−9.13323	−0.292949
$973$	0.0915456	0.00293482
$974$	29.4712	0.944319
$975$	−6.12613	−0.196193
$976$	−60.2698	−1.92919
$977$	−19.6157	−0.627561	−0.313780	−	0.949496i	$-0.601596\pi$
$977$	−19.6157	−0.627561	−0.313780	+	0.949496i	$0.601596\pi$
$978$	15.5385	0.496867
$979$	92.9691	2.97131
$980$	1.93675	0.0618672
$981$	14.3458	0.458026
$982$	5.51987	0.176146
$983$	−22.8806	−0.729779	−0.364890	−	0.931051i	$-0.618893\pi$
$983$	−22.8806	−0.729779	−0.364890	+	0.931051i	$0.618893\pi$
$984$	−1.35458	−0.0431824
$985$	−6.92593	−0.220679
$986$	45.6451	1.45364
$987$	−13.0308	−0.414776
$988$	−0.0265966	−0.000846152 0
$989$	35.2215	1.11998
$990$	−16.2878	−0.517661
$991$	−14.4104	−0.457761	−0.228880	−	0.973455i	$-0.573506\pi$
$991$	−14.4104	−0.457761	−0.228880	+	0.973455i	$0.573506\pi$
$992$	5.34264	0.169629
$993$	−19.7669	−0.627284
$994$	−23.4377	−0.743398
$995$	−1.03174	−0.0327085
$996$	30.1421	0.955089
$997$	−37.4204	−1.18512	−0.592558	−	0.805528i	$-0.701882\pi$
$997$	−37.4204	−1.18512	−0.592558	+	0.805528i	$0.701882\pi$
$998$	58.6925	1.85788
$999$	−4.18246	−0.132327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.g.1.16	✓	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.g.1.16	✓	70	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.74189 q^{2} +1.96861 q^{3} +1.03416 q^{4} +1.87277 q^{5} -3.42909 q^{6} +1.00000 q^{7} +1.68238 q^{8} +0.875422 q^{9} +O(q^{10})\)	\(q-1.74189 q^{2} +1.96861 q^{3} +1.03416 q^{4} +1.87277 q^{5} -3.42909 q^{6} +1.00000 q^{7} +1.68238 q^{8} +0.875422 q^{9} -3.26215 q^{10} +5.70350 q^{11} +2.03586 q^{12} +2.08470 q^{13} -1.74189 q^{14} +3.68675 q^{15} -4.99883 q^{16} +2.77174 q^{17} -1.52488 q^{18} -0.0123365 q^{19} +1.93675 q^{20} +1.96861 q^{21} -9.93484 q^{22} +3.69596 q^{23} +3.31194 q^{24} -1.49273 q^{25} -3.63131 q^{26} -4.18246 q^{27} +1.03416 q^{28} -9.45413 q^{29} -6.42190 q^{30} +1.00000 q^{31} +5.34264 q^{32} +11.2280 q^{33} -4.82805 q^{34} +1.87277 q^{35} +0.905330 q^{36} +1.00000 q^{37} +0.0214888 q^{38} +4.10396 q^{39} +3.15070 q^{40} -0.408999 q^{41} -3.42909 q^{42} +9.52973 q^{43} +5.89835 q^{44} +1.63946 q^{45} -6.43794 q^{46} -6.61932 q^{47} -9.84075 q^{48} +1.00000 q^{49} +2.60017 q^{50} +5.45647 q^{51} +2.15592 q^{52} -11.1090 q^{53} +7.28537 q^{54} +10.6813 q^{55} +1.68238 q^{56} -0.0242858 q^{57} +16.4680 q^{58} +12.0509 q^{59} +3.81270 q^{60} +12.0568 q^{61} -1.74189 q^{62} +0.875422 q^{63} +0.691397 q^{64} +3.90417 q^{65} -19.5578 q^{66} -14.5037 q^{67} +2.86643 q^{68} +7.27590 q^{69} -3.26215 q^{70} +13.4553 q^{71} +1.47279 q^{72} -0.906662 q^{73} -1.74189 q^{74} -2.93861 q^{75} -0.0127580 q^{76} +5.70350 q^{77} -7.14863 q^{78} +15.5847 q^{79} -9.36166 q^{80} -10.8599 q^{81} +0.712429 q^{82} +14.8055 q^{83} +2.03586 q^{84} +5.19083 q^{85} -16.5997 q^{86} -18.6115 q^{87} +9.59543 q^{88} +16.3004 q^{89} -2.85576 q^{90} +2.08470 q^{91} +3.82223 q^{92} +1.96861 q^{93} +11.5301 q^{94} -0.0231035 q^{95} +10.5176 q^{96} -6.09014 q^{97} -1.74189 q^{98} +4.99297 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9}+O(q^{10}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9} + 4 q^{10} + 61 q^{11} + 49 q^{12} + 28 q^{13} + 5 q^{14} + 22 q^{15} + 73 q^{16} + 37 q^{17} + 8 q^{18} + 23 q^{19} + 45 q^{20} + 22 q^{21} - 10 q^{22} + 26 q^{23} + 3 q^{24} + 66 q^{25} + 57 q^{26} + 76 q^{27} + 71 q^{28} + 38 q^{29} - 14 q^{30} + 70 q^{31} - 2 q^{32} + 44 q^{33} + 34 q^{34} + 24 q^{35} + 46 q^{36} + 70 q^{37} + 21 q^{38} + 10 q^{39} + 13 q^{40} + 71 q^{41} + 9 q^{42} + 30 q^{43} + 108 q^{44} + 13 q^{45} - 14 q^{46} + 78 q^{47} + 85 q^{48} + 70 q^{49} - 12 q^{50} + 21 q^{51} + 23 q^{52} + 47 q^{53} + 17 q^{54} + 5 q^{55} + 9 q^{56} + 9 q^{57} + 8 q^{58} + 109 q^{59} - q^{60} + 41 q^{61} + 5 q^{62} + 78 q^{63} + 29 q^{64} + 36 q^{65} + 5 q^{66} + 23 q^{67} + 47 q^{68} + 8 q^{69} + 4 q^{70} + 99 q^{71} + 8 q^{72} + 33 q^{73} + 5 q^{74} + 94 q^{75} - 19 q^{76} + 61 q^{77} + 37 q^{78} + 52 q^{79} + 78 q^{80} + 102 q^{81} + 118 q^{83} + 49 q^{84} - 21 q^{85} + 74 q^{86} + 11 q^{87} - 21 q^{88} + 86 q^{89} - 7 q^{90} + 28 q^{91} + 14 q^{92} + 22 q^{93} + 35 q^{94} + 24 q^{95} - 40 q^{96} + 9 q^{97} + 5 q^{98} + 92 q^{99}+O(q^{100}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9 + 4 * q^10 + 61 * q^11 + 49 * q^12 + 28 * q^13 + 5 * q^14 + 22 * q^15 + 73 * q^16 + 37 * q^17 + 8 * q^18 + 23 * q^19 + 45 * q^20 + 22 * q^21 - 10 * q^22 + 26 * q^23 + 3 * q^24 + 66 * q^25 + 57 * q^26 + 76 * q^27 + 71 * q^28 + 38 * q^29 - 14 * q^30 + 70 * q^31 - 2 * q^32 + 44 * q^33 + 34 * q^34 + 24 * q^35 + 46 * q^36 + 70 * q^37 + 21 * q^38 + 10 * q^39 + 13 * q^40 + 71 * q^41 + 9 * q^42 + 30 * q^43 + 108 * q^44 + 13 * q^45 - 14 * q^46 + 78 * q^47 + 85 * q^48 + 70 * q^49 - 12 * q^50 + 21 * q^51 + 23 * q^52 + 47 * q^53 + 17 * q^54 + 5 * q^55 + 9 * q^56 + 9 * q^57 + 8 * q^58 + 109 * q^59 - q^60 + 41 * q^61 + 5 * q^62 + 78 * q^63 + 29 * q^64 + 36 * q^65 + 5 * q^66 + 23 * q^67 + 47 * q^68 + 8 * q^69 + 4 * q^70 + 99 * q^71 + 8 * q^72 + 33 * q^73 + 5 * q^74 + 94 * q^75 - 19 * q^76 + 61 * q^77 + 37 * q^78 + 52 * q^79 + 78 * q^80 + 102 * q^81 + 118 * q^83 + 49 * q^84 - 21 * q^85 + 74 * q^86 + 11 * q^87 - 21 * q^88 + 86 * q^89 - 7 * q^90 + 28 * q^91 + 14 * q^92 + 22 * q^93 + 35 * q^94 + 24 * q^95 - 40 * q^96 + 9 * q^97 + 5 * q^98 + 92 * q^99

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