LMFDB - Embedded newform 4031.2.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$0$
Dimension:	$103$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62778 q^{2} +2.50964 q^{3} +4.90520 q^{4} -0.626861 q^{5} -6.59477 q^{6} +4.88608 q^{7} -7.63422 q^{8} +3.29828 q^{9} +O(q^{10})$	\(q-2.62778 q^{2} +2.50964 q^{3} +4.90520 q^{4} -0.626861 q^{5} -6.59477 q^{6} +4.88608 q^{7} -7.63422 q^{8} +3.29828 q^{9} +1.64725 q^{10} +2.30665 q^{11} +12.3103 q^{12} +2.81227 q^{13} -12.8395 q^{14} -1.57319 q^{15} +10.2506 q^{16} -1.33171 q^{17} -8.66715 q^{18} +7.99575 q^{19} -3.07488 q^{20} +12.2623 q^{21} -6.06137 q^{22} -2.69320 q^{23} -19.1591 q^{24} -4.60705 q^{25} -7.39001 q^{26} +0.748586 q^{27} +23.9672 q^{28} -1.00000 q^{29} +4.13400 q^{30} +7.92946 q^{31} -11.6679 q^{32} +5.78886 q^{33} +3.49943 q^{34} -3.06290 q^{35} +16.1788 q^{36} +7.49776 q^{37} -21.0110 q^{38} +7.05777 q^{39} +4.78560 q^{40} +3.66854 q^{41} -32.2226 q^{42} -11.0583 q^{43} +11.3146 q^{44} -2.06757 q^{45} +7.07713 q^{46} -7.38580 q^{47} +25.7253 q^{48} +16.8738 q^{49} +12.1063 q^{50} -3.34211 q^{51} +13.7947 q^{52} +2.51573 q^{53} -1.96712 q^{54} -1.44595 q^{55} -37.3014 q^{56} +20.0665 q^{57} +2.62778 q^{58} +5.63328 q^{59} -7.71684 q^{60} -2.23274 q^{61} -20.8368 q^{62} +16.1157 q^{63} +10.1593 q^{64} -1.76290 q^{65} -15.2118 q^{66} -1.62101 q^{67} -6.53231 q^{68} -6.75896 q^{69} +8.04860 q^{70} +8.68673 q^{71} -25.1798 q^{72} -9.52275 q^{73} -19.7024 q^{74} -11.5620 q^{75} +39.2208 q^{76} +11.2705 q^{77} -18.5462 q^{78} -4.31486 q^{79} -6.42571 q^{80} -8.01617 q^{81} -9.64011 q^{82} -5.14164 q^{83} +60.1491 q^{84} +0.834797 q^{85} +29.0587 q^{86} -2.50964 q^{87} -17.6095 q^{88} -2.57852 q^{89} +5.43310 q^{90} +13.7410 q^{91} -13.2107 q^{92} +19.9001 q^{93} +19.4082 q^{94} -5.01223 q^{95} -29.2821 q^{96} +0.763117 q^{97} -44.3406 q^{98} +7.60800 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) $ 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.62778	−1.85812	−0.929059	−	0.369932i	$-0.879381\pi$
$2$	−2.62778	−1.85812	−0.929059	+	0.369932i	$0.879381\pi$
$3$	2.50964	1.44894	0.724470	−	0.689306i	$-0.242084\pi$
$3$	2.50964	1.44894	0.724470	+	0.689306i	$0.242084\pi$
$4$	4.90520	2.45260
$5$	−0.626861	−0.280341	−0.140170	−	0.990127i	$-0.544765\pi$
$5$	−0.626861	−0.280341	−0.140170	+	0.990127i	$0.544765\pi$
$6$	−6.59477	−2.69230
$7$	4.88608	1.84677	0.923383	−	0.383880i	$-0.125412\pi$
$7$	4.88608	1.84677	0.923383	+	0.383880i	$0.125412\pi$
$8$	−7.63422	−2.69910
$9$	3.29828	1.09943
$10$	1.64725	0.520906
$11$	2.30665	0.695482	0.347741	−	0.937591i	$-0.386949\pi$
$11$	2.30665	0.695482	0.347741	+	0.937591i	$0.386949\pi$
$12$	12.3103	3.55367
$13$	2.81227	0.779983	0.389991	−	0.920819i	$-0.372478\pi$
$13$	2.81227	0.779983	0.389991	+	0.920819i	$0.372478\pi$
$14$	−12.8395	−3.43151
$15$	−1.57319	−0.406197
$16$	10.2506	2.56265
$17$	−1.33171	−0.322987	−0.161493	−	0.986874i	$-0.551631\pi$
$17$	−1.33171	−0.322987	−0.161493	+	0.986874i	$0.551631\pi$
$18$	−8.66715	−2.04287
$19$	7.99575	1.83435	0.917176	−	0.398483i	$-0.130463\pi$
$19$	7.99575	1.83435	0.917176	+	0.398483i	$0.130463\pi$
$20$	−3.07488	−0.687564
$21$	12.2623	2.67585
$22$	−6.06137	−1.29229
$23$	−2.69320	−0.561571	−0.280786	−	0.959770i	$-0.590595\pi$
$23$	−2.69320	−0.561571	−0.280786	+	0.959770i	$0.590595\pi$
$24$	−19.1591	−3.91084
$25$	−4.60705	−0.921409
$26$	−7.39001	−1.44930
$27$	0.748586	0.144065
$28$	23.9672	4.52938
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	4.13400	0.754762
$31$	7.92946	1.42417	0.712087	−	0.702092i	$-0.247750\pi$
$31$	7.92946	1.42417	0.712087	+	0.702092i	$0.247750\pi$
$32$	−11.6679	−2.06261
$33$	5.78886	1.00771
$34$	3.49943	0.600148
$35$	−3.06290	−0.517724
$36$	16.1788	2.69646
$37$	7.49776	1.23262	0.616312	−	0.787502i	$-0.288626\pi$
$37$	7.49776	1.23262	0.616312	+	0.787502i	$0.288626\pi$
$38$	−21.0110	−3.40844
$39$	7.05777	1.13015
$40$	4.78560	0.756669
$41$	3.66854	0.572930	0.286465	−	0.958091i	$-0.407520\pi$
$41$	3.66854	0.572930	0.286465	+	0.958091i	$0.407520\pi$
$42$	−32.2226	−4.97205
$43$	−11.0583	−1.68637	−0.843187	−	0.537621i	$-0.819323\pi$
$43$	−11.0583	−1.68637	−0.843187	+	0.537621i	$0.819323\pi$
$44$	11.3146	1.70574
$45$	−2.06757	−0.308215
$46$	7.07713	1.04347
$47$	−7.38580	−1.07733	−0.538665	−	0.842520i	$-0.681071\pi$
$47$	−7.38580	−1.07733	−0.538665	+	0.842520i	$0.681071\pi$
$48$	25.7253	3.71313
$49$	16.8738	2.41054
$50$	12.1063	1.71209
$51$	−3.34211	−0.467989
$52$	13.7947	1.91299
$53$	2.51573	0.345563	0.172781	−	0.984960i	$-0.444725\pi$
$53$	2.51573	0.345563	0.172781	+	0.984960i	$0.444725\pi$
$54$	−1.96712	−0.267690
$55$	−1.44595	−0.194972
$56$	−37.3014	−4.98461
$57$	20.0665	2.65787
$58$	2.62778	0.345044
$59$	5.63328	0.733391	0.366695	−	0.930341i	$-0.380489\pi$
$59$	5.63328	0.733391	0.366695	+	0.930341i	$0.380489\pi$
$60$	−7.71684	−0.996240
$61$	−2.23274	−0.285873	−0.142936	−	0.989732i	$-0.545654\pi$
$61$	−2.23274	−0.285873	−0.142936	+	0.989732i	$0.545654\pi$
$62$	−20.8368	−2.64628
$63$	16.1157	2.03039
$64$	10.1593	1.26991
$65$	−1.76290	−0.218661
$66$	−15.2118	−1.87245
$67$	−1.62101	−0.198038	−0.0990188	−	0.995086i	$-0.531570\pi$
$67$	−1.62101	−0.198038	−0.0990188	+	0.995086i	$0.531570\pi$
$68$	−6.53231	−0.792158
$69$	−6.75896	−0.813683
$70$	8.04860	0.961992
$71$	8.68673	1.03093	0.515463	−	0.856912i	$-0.327620\pi$
$71$	8.68673	1.03093	0.515463	+	0.856912i	$0.327620\pi$
$72$	−25.1798	−2.96747
$73$	−9.52275	−1.11455	−0.557277	−	0.830327i	$-0.688154\pi$
$73$	−9.52275	−1.11455	−0.557277	+	0.830327i	$0.688154\pi$
$74$	−19.7024	−2.29036
$75$	−11.5620	−1.33507
$76$	39.2208	4.49893
$77$	11.2705	1.28439
$78$	−18.5462	−2.09995
$79$	−4.31486	−0.485460	−0.242730	−	0.970094i	$-0.578043\pi$
$79$	−4.31486	−0.485460	−0.242730	+	0.970094i	$0.578043\pi$
$80$	−6.42571	−0.718416
$81$	−8.01617	−0.890686
$82$	−9.64011	−1.06457
$83$	−5.14164	−0.564368	−0.282184	−	0.959360i	$-0.591059\pi$
$83$	−5.14164	−0.564368	−0.282184	+	0.959360i	$0.591059\pi$
$84$	60.1491	6.56280
$85$	0.834797	0.0905464
$86$	29.0587	3.13348
$87$	−2.50964	−0.269061
$88$	−17.6095	−1.87718
$89$	−2.57852	−0.273323	−0.136662	−	0.990618i	$-0.543637\pi$
$89$	−2.57852	−0.273323	−0.136662	+	0.990618i	$0.543637\pi$
$90$	5.43310	0.572699
$91$	13.7410	1.44045
$92$	−13.2107	−1.37731
$93$	19.9001	2.06354
$94$	19.4082	2.00181
$95$	−5.01223	−0.514244
$96$	−29.2821	−2.98859
$97$	0.763117	0.0774828	0.0387414	−	0.999249i	$-0.487665\pi$
$97$	0.763117	0.0774828	0.0387414	+	0.999249i	$0.487665\pi$
$98$	−44.3406	−4.47908
$99$	7.60800	0.764632
$100$	−22.5985	−2.25985
$101$	2.42980	0.241774	0.120887	−	0.992666i	$-0.461426\pi$
$101$	2.42980	0.241774	0.120887	+	0.992666i	$0.461426\pi$
$102$	8.78231	0.869578
$103$	2.55645	0.251895	0.125947	−	0.992037i	$-0.459803\pi$
$103$	2.55645	0.251895	0.125947	+	0.992037i	$0.459803\pi$
$104$	−21.4695	−2.10525
$105$	−7.68676	−0.750151
$106$	−6.61078	−0.642096
$107$	−9.82887	−0.950193	−0.475096	−	0.879934i	$-0.657587\pi$
$107$	−9.82887	−0.950193	−0.475096	+	0.879934i	$0.657587\pi$
$108$	3.67197	0.353335
$109$	−9.53858	−0.913631	−0.456815	−	0.889562i	$-0.651010\pi$
$109$	−9.53858	−0.913631	−0.456815	+	0.889562i	$0.651010\pi$
$110$	3.79963	0.362281
$111$	18.8167	1.78600
$112$	50.0853	4.73262
$113$	20.6067	1.93851	0.969256	−	0.246054i	$-0.0791342\pi$
$113$	20.6067	1.93851	0.969256	+	0.246054i	$0.0791342\pi$
$114$	−52.7301	−4.93863
$115$	1.68826	0.157431
$116$	−4.90520	−0.455437
$117$	9.27566	0.857535
$118$	−14.8030	−1.36273
$119$	−6.50684	−0.596481
$120$	12.0101	1.09637
$121$	−5.67935	−0.516305
$122$	5.86713	0.531185
$123$	9.20672	0.830142
$124$	38.8956	3.49293
$125$	6.02228	0.538649
$126$	−42.3484	−3.77270
$127$	−16.2058	−1.43803	−0.719015	−	0.694995i	$-0.755407\pi$
$127$	−16.2058	−1.43803	−0.719015	+	0.694995i	$0.755407\pi$
$128$	−3.36063	−0.297040
$129$	−27.7523	−2.44346
$130$	4.63251	0.406298
$131$	14.8294	1.29565	0.647825	−	0.761789i	$-0.275679\pi$
$131$	14.8294	1.29565	0.647825	+	0.761789i	$0.275679\pi$
$132$	28.3956	2.47152
$133$	39.0679	3.38762
$134$	4.25964	0.367977
$135$	−0.469259	−0.0403874
$136$	10.1666	0.871776
$137$	−10.1347	−0.865862	−0.432931	−	0.901427i	$-0.642521\pi$
$137$	−10.1347	−0.865862	−0.432931	+	0.901427i	$0.642521\pi$
$138$	17.7610	1.51192
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	−15.0241	−1.26977
$141$	−18.5357	−1.56099
$142$	−22.8268	−1.91558
$143$	6.48692	0.542464
$144$	33.8094	2.81745
$145$	0.626861	0.0520580
$146$	25.0236	2.07097
$147$	42.3472	3.49274
$148$	36.7780	3.02313
$149$	10.4178	0.853459	0.426729	−	0.904379i	$-0.359666\pi$
$149$	10.4178	0.853459	0.426729	+	0.904379i	$0.359666\pi$
$150$	30.3824	2.48071
$151$	−3.00752	−0.244749	−0.122374	−	0.992484i	$-0.539051\pi$
$151$	−3.00752	−0.244749	−0.122374	+	0.992484i	$0.539051\pi$
$152$	−61.0414	−4.95111
$153$	−4.39236	−0.355101
$154$	−29.6163	−2.38655
$155$	−4.97067	−0.399254
$156$	34.6198	2.77180
$157$	−7.04961	−0.562620	−0.281310	−	0.959617i	$-0.590769\pi$
$157$	−7.04961	−0.562620	−0.281310	+	0.959617i	$0.590769\pi$
$158$	11.3385	0.902042
$159$	6.31358	0.500700
$160$	7.31413	0.578233
$161$	−13.1592	−1.03709
$162$	21.0647	1.65500
$163$	−14.7063	−1.15189	−0.575944	−	0.817489i	$-0.695366\pi$
$163$	−14.7063	−1.15189	−0.575944	+	0.817489i	$0.695366\pi$
$164$	17.9949	1.40517
$165$	−3.62881	−0.282503
$166$	13.5111	1.04866
$167$	3.42658	0.265157	0.132578	−	0.991173i	$-0.457674\pi$
$167$	3.42658	0.265157	0.132578	+	0.991173i	$0.457674\pi$
$168$	−93.6131	−7.22241
$169$	−5.09115	−0.391627
$170$	−2.19366	−0.168246
$171$	26.3723	2.01674
$172$	−54.2432	−4.13600
$173$	17.1941	1.30724	0.653622	−	0.756821i	$-0.273248\pi$
$173$	17.1941	1.30724	0.653622	+	0.756821i	$0.273248\pi$
$174$	6.59477	0.499948
$175$	−22.5104	−1.70163
$176$	23.6446	1.78228
$177$	14.1375	1.06264
$178$	6.77578	0.507866
$179$	8.59046	0.642081	0.321041	−	0.947065i	$-0.395967\pi$
$179$	8.59046	0.642081	0.321041	+	0.947065i	$0.395967\pi$
$180$	−10.1418	−0.755928
$181$	−5.76629	−0.428605	−0.214303	−	0.976767i	$-0.568748\pi$
$181$	−5.76629	−0.428605	−0.214303	+	0.976767i	$0.568748\pi$
$182$	−36.1082	−2.67652
$183$	−5.60336	−0.414212
$184$	20.5605	1.51574
$185$	−4.70005	−0.345555
$186$	−52.2929	−3.83430
$187$	−3.07179	−0.224632
$188$	−36.2288	−2.64226
$189$	3.65765	0.266055
$190$	13.1710	0.955525
$191$	−19.5050	−1.41134	−0.705668	−	0.708543i	$-0.749353\pi$
$191$	−19.5050	−1.41134	−0.705668	+	0.708543i	$0.749353\pi$
$192$	25.4962	1.84003
$193$	−3.47873	−0.250404	−0.125202	−	0.992131i	$-0.539958\pi$
$193$	−3.47873	−0.250404	−0.125202	+	0.992131i	$0.539958\pi$
$194$	−2.00530	−0.143972
$195$	−4.42424	−0.316827
$196$	82.7695	5.91211
$197$	16.1096	1.14776	0.573881	−	0.818939i	$-0.305437\pi$
$197$	16.1096	1.14776	0.573881	+	0.818939i	$0.305437\pi$
$198$	−19.9921	−1.42078
$199$	12.9300	0.916587	0.458293	−	0.888801i	$-0.348461\pi$
$199$	12.9300	0.916587	0.458293	+	0.888801i	$0.348461\pi$
$200$	35.1712	2.48698
$201$	−4.06814	−0.286945
$202$	−6.38496	−0.449244
$203$	−4.88608	−0.342936
$204$	−16.3937	−1.14779
$205$	−2.29967	−0.160616
$206$	−6.71778	−0.468050
$207$	−8.88294	−0.617407
$208$	28.8275	1.99882
$209$	18.4434	1.27576
$210$	20.1991	1.39387
$211$	13.1304	0.903937	0.451969	−	0.892034i	$-0.350722\pi$
$211$	13.1304	0.903937	0.451969	+	0.892034i	$0.350722\pi$
$212$	12.3402	0.847527
$213$	21.8006	1.49375
$214$	25.8281	1.76557
$215$	6.93201	0.472759
$216$	−5.71487	−0.388848
$217$	38.7440	2.63012
$218$	25.0653	1.69763
$219$	−23.8987	−1.61492
$220$	−7.09268	−0.478189
$221$	−3.74512	−0.251924
$222$	−49.4459	−3.31859
$223$	16.0637	1.07571	0.537853	−	0.843039i	$-0.319236\pi$
$223$	16.0637	1.07571	0.537853	+	0.843039i	$0.319236\pi$
$224$	−57.0102	−3.80915
$225$	−15.1953	−1.01302
$226$	−54.1497	−3.60198
$227$	−19.9340	−1.32306	−0.661532	−	0.749917i	$-0.730093\pi$
$227$	−19.9340	−1.32306	−0.661532	+	0.749917i	$0.730093\pi$
$228$	98.4300	6.51869
$229$	−23.1797	−1.53176	−0.765879	−	0.642985i	$-0.777696\pi$
$229$	−23.1797	−1.53176	−0.765879	+	0.642985i	$0.777696\pi$
$230$	−4.43638	−0.292526
$231$	28.2849	1.86101
$232$	7.63422	0.501211
$233$	−17.7793	−1.16476	−0.582379	−	0.812917i	$-0.697878\pi$
$233$	−17.7793	−1.16476	−0.582379	+	0.812917i	$0.697878\pi$
$234$	−24.3743	−1.59340
$235$	4.62987	0.302019
$236$	27.6324	1.79872
$237$	−10.8287	−0.703403
$238$	17.0985	1.10833
$239$	4.41813	0.285785	0.142892	−	0.989738i	$-0.454360\pi$
$239$	4.41813	0.285785	0.142892	+	0.989738i	$0.454360\pi$
$240$	−16.1262	−1.04094
$241$	−1.21526	−0.0782815	−0.0391407	−	0.999234i	$-0.512462\pi$
$241$	−1.21526	−0.0782815	−0.0391407	+	0.999234i	$0.512462\pi$
$242$	14.9241	0.959355
$243$	−22.3635	−1.43462
$244$	−10.9520	−0.701132
$245$	−10.5775	−0.675774
$246$	−24.1932	−1.54250
$247$	22.4862	1.43076
$248$	−60.5353	−3.84399
$249$	−12.9036	−0.817736
$250$	−15.8252	−1.00087
$251$	−4.39094	−0.277154	−0.138577	−	0.990352i	$-0.544253\pi$
$251$	−4.39094	−0.277154	−0.138577	+	0.990352i	$0.544253\pi$
$252$	79.0507	4.97973
$253$	−6.21228	−0.390563
$254$	42.5851	2.67203
$255$	2.09504	0.131196
$256$	−11.4876	−0.717977
$257$	−5.63933	−0.351772	−0.175886	−	0.984411i	$-0.556279\pi$
$257$	−5.63933	−0.351772	−0.175886	+	0.984411i	$0.556279\pi$
$258$	72.9268	4.54023
$259$	36.6347	2.27637
$260$	−8.64739	−0.536288
$261$	−3.29828	−0.204159
$262$	−38.9683	−2.40747
$263$	−9.11228	−0.561887	−0.280944	−	0.959724i	$-0.590647\pi$
$263$	−9.11228	−0.561887	−0.280944	+	0.959724i	$0.590647\pi$
$264$	−44.1935	−2.71992
$265$	−1.57702	−0.0968753
$266$	−102.662	−6.29459
$267$	−6.47116	−0.396029
$268$	−7.95137	−0.485707
$269$	−31.4462	−1.91731	−0.958654	−	0.284574i	$-0.908148\pi$
$269$	−31.4462	−1.91731	−0.958654	+	0.284574i	$0.908148\pi$
$270$	1.23311	0.0750446
$271$	−13.1319	−0.797703	−0.398852	−	0.917015i	$-0.630591\pi$
$271$	−13.1319	−0.797703	−0.398852	+	0.917015i	$0.630591\pi$
$272$	−13.6508	−0.827704
$273$	34.4849	2.08712
$274$	26.6316	1.60887
$275$	−10.6269	−0.640823
$276$	−33.1541	−1.99564
$277$	−10.5897	−0.636274	−0.318137	−	0.948045i	$-0.603057\pi$
$277$	−10.5897	−0.636274	−0.318137	+	0.948045i	$0.603057\pi$
$278$	−2.62778	−0.157603
$279$	26.1536	1.56578
$280$	23.3828	1.39739
$281$	−5.34372	−0.318779	−0.159390	−	0.987216i	$-0.550953\pi$
$281$	−5.34372	−0.318779	−0.159390	+	0.987216i	$0.550953\pi$
$282$	48.7076	2.90050
$283$	12.9983	0.772668	0.386334	−	0.922359i	$-0.373741\pi$
$283$	12.9983	0.772668	0.386334	+	0.922359i	$0.373741\pi$
$284$	42.6102	2.52845
$285$	−12.5789	−0.745108
$286$	−17.0462	−1.00796
$287$	17.9248	1.05807
$288$	−38.4839	−2.26769
$289$	−15.2265	−0.895679
$290$	−1.64725	−0.0967299
$291$	1.91515	0.112268
$292$	−46.7110	−2.73356
$293$	10.3379	0.603945	0.301973	−	0.953317i	$-0.402355\pi$
$293$	10.3379	0.603945	0.301973	+	0.953317i	$0.402355\pi$
$294$	−111.279	−6.48991
$295$	−3.53128	−0.205599
$296$	−57.2395	−3.32698
$297$	1.72673	0.100195
$298$	−27.3756	−1.58583
$299$	−7.57400	−0.438016
$300$	−56.7140	−3.27439
$301$	−54.0317	−3.11434
$302$	7.90309	0.454772
$303$	6.09791	0.350316
$304$	81.9614	4.70081
$305$	1.39962	0.0801418
$306$	11.5421	0.659819
$307$	14.7559	0.842163	0.421082	−	0.907023i	$-0.361651\pi$
$307$	14.7559	0.842163	0.421082	+	0.907023i	$0.361651\pi$
$308$	55.2841	3.15010
$309$	6.41577	0.364980
$310$	13.0618	0.741861
$311$	−18.9733	−1.07588	−0.537939	−	0.842984i	$-0.680797\pi$
$311$	−18.9733	−1.07588	−0.537939	+	0.842984i	$0.680797\pi$
$312$	−53.8806	−3.05039
$313$	−16.9361	−0.957285	−0.478643	−	0.878010i	$-0.658871\pi$
$313$	−16.9361	−0.957285	−0.478643	+	0.878010i	$0.658871\pi$
$314$	18.5248	1.04541
$315$	−10.1023	−0.569200
$316$	−21.1653	−1.19064
$317$	−33.9945	−1.90932	−0.954662	−	0.297692i	$-0.903783\pi$
$317$	−33.9945	−1.90932	−0.954662	+	0.297692i	$0.903783\pi$
$318$	−16.5907	−0.930359
$319$	−2.30665	−0.129148
$320$	−6.36847	−0.356008
$321$	−24.6669	−1.37677
$322$	34.5794	1.92704
$323$	−10.6480	−0.592472
$324$	−39.3210	−2.18450
$325$	−12.9562	−0.718683
$326$	38.6449	2.14035
$327$	−23.9384	−1.32380
$328$	−28.0065	−1.54640
$329$	−36.0876	−1.98958
$330$	9.53571	0.524923
$331$	−20.6836	−1.13687	−0.568436	−	0.822727i	$-0.692451\pi$
$331$	−20.6836	−1.13687	−0.568436	+	0.822727i	$0.692451\pi$
$332$	−25.2208	−1.38417
$333$	24.7297	1.35518
$334$	−9.00429	−0.492693
$335$	1.01615	0.0555180
$336$	125.696	6.85728
$337$	0.165714	0.00902702	0.00451351	−	0.999990i	$-0.498563\pi$
$337$	0.165714	0.00902702	0.00451351	+	0.999990i	$0.498563\pi$
$338$	13.3784	0.727689
$339$	51.7153	2.80879
$340$	4.09485	0.222074
$341$	18.2905	0.990487
$342$	−69.3004	−3.74734
$343$	48.2443	2.60495
$344$	84.4215	4.55170
$345$	4.23693	0.228109
$346$	−45.1823	−2.42901
$347$	27.3216	1.46670	0.733351	−	0.679850i	$-0.237955\pi$
$347$	27.3216	1.46670	0.733351	+	0.679850i	$0.237955\pi$
$348$	−12.3103	−0.659901
$349$	4.26201	0.228140	0.114070	−	0.993473i	$-0.463611\pi$
$349$	4.26201	0.228140	0.114070	+	0.993473i	$0.463611\pi$
$350$	59.1523	3.16182
$351$	2.10522	0.112369
$352$	−26.9137	−1.43451
$353$	−11.5206	−0.613179	−0.306590	−	0.951842i	$-0.599188\pi$
$353$	−11.5206	−0.613179	−0.306590	+	0.951842i	$0.599188\pi$
$354$	−37.1502	−1.97451
$355$	−5.44538	−0.289011
$356$	−12.6482	−0.670353
$357$	−16.3298	−0.864266
$358$	−22.5738	−1.19306
$359$	34.3735	1.81416	0.907081	−	0.420956i	$-0.138305\pi$
$359$	34.3735	1.81416	0.907081	+	0.420956i	$0.138305\pi$
$360$	15.7843	0.831903
$361$	44.9321	2.36485
$362$	15.1525	0.796399
$363$	−14.2531	−0.748095
$364$	67.4023	3.53284
$365$	5.96944	0.312455
$366$	14.7244	0.769656
$367$	17.3924	0.907874	0.453937	−	0.891034i	$-0.350019\pi$
$367$	17.3924	0.907874	0.453937	+	0.891034i	$0.350019\pi$
$368$	−27.6070	−1.43911
$369$	12.0999	0.629895
$370$	12.3507	0.642081
$371$	12.2921	0.638173
$372$	97.6139	5.06105
$373$	−28.6888	−1.48545	−0.742726	−	0.669595i	$-0.766467\pi$
$373$	−28.6888	−1.48545	−0.742726	+	0.669595i	$0.766467\pi$
$374$	8.07198	0.417392
$375$	15.1138	0.780471
$376$	56.3848	2.90783
$377$	−2.81227	−0.144839
$378$	−9.61149	−0.494362
$379$	−23.1153	−1.18735	−0.593677	−	0.804703i	$-0.702324\pi$
$379$	−23.1153	−1.18735	−0.593677	+	0.804703i	$0.702324\pi$
$380$	−24.5860	−1.26123
$381$	−40.6706	−2.08362
$382$	51.2549	2.62243
$383$	−15.6462	−0.799483	−0.399741	−	0.916628i	$-0.630900\pi$
$383$	−15.6462	−0.799483	−0.399741	+	0.916628i	$0.630900\pi$
$384$	−8.43396	−0.430394
$385$	−7.06504	−0.360068
$386$	9.14131	0.465280
$387$	−36.4734	−1.85405
$388$	3.74324	0.190034
$389$	18.6312	0.944639	0.472320	−	0.881427i	$-0.343417\pi$
$389$	18.6312	0.944639	0.472320	+	0.881427i	$0.343417\pi$
$390$	11.6259	0.588701
$391$	3.58656	0.181380
$392$	−128.818	−6.50631
$393$	37.2164	1.87732
$394$	−42.3324	−2.13268
$395$	2.70482	0.136094
$396$	37.3188	1.87534
$397$	37.9199	1.90314	0.951572	−	0.307426i	$-0.0994675\pi$
$397$	37.9199	1.90314	0.951572	+	0.307426i	$0.0994675\pi$
$398$	−33.9773	−1.70313
$399$	98.0464	4.90846
$400$	−47.2250	−2.36125
$401$	16.3446	0.816213	0.408106	−	0.912934i	$-0.366189\pi$
$401$	16.3446	0.816213	0.408106	+	0.912934i	$0.366189\pi$
$402$	10.6902	0.533177
$403$	22.2998	1.11083
$404$	11.9186	0.592975
$405$	5.02503	0.249696
$406$	12.8395	0.637215
$407$	17.2947	0.857267
$408$	25.5144	1.26315
$409$	19.1627	0.947535	0.473768	−	0.880650i	$-0.342894\pi$
$409$	19.1627	0.947535	0.473768	+	0.880650i	$0.342894\pi$
$410$	6.04301	0.298443
$411$	−25.4343	−1.25458
$412$	12.5399	0.617797
$413$	27.5247	1.35440
$414$	23.3424	1.14722
$415$	3.22309	0.158215
$416$	−32.8131	−1.60880
$417$	2.50964	0.122898
$418$	−48.4652	−2.37051
$419$	7.87172	0.384559	0.192279	−	0.981340i	$-0.438412\pi$
$419$	7.87172	0.384559	0.192279	+	0.981340i	$0.438412\pi$
$420$	−37.7051	−1.83982
$421$	16.0612	0.782773	0.391387	−	0.920226i	$-0.371996\pi$
$421$	16.0612	0.782773	0.391387	+	0.920226i	$0.371996\pi$
$422$	−34.5039	−1.67962
$423$	−24.3605	−1.18445
$424$	−19.2057	−0.932710
$425$	6.13525	0.297603
$426$	−57.2870	−2.77556
$427$	−10.9093	−0.527940
$428$	−48.2126	−2.33044
$429$	16.2798	0.785998
$430$	−18.2158	−0.878443
$431$	16.3167	0.785947	0.392974	−	0.919550i	$-0.371446\pi$
$431$	16.3167	0.785947	0.392974	+	0.919550i	$0.371446\pi$
$432$	7.67346	0.369190
$433$	32.4109	1.55757	0.778785	−	0.627291i	$-0.215836\pi$
$433$	32.4109	1.55757	0.778785	+	0.627291i	$0.215836\pi$
$434$	−101.811	−4.88706
$435$	1.57319	0.0754289
$436$	−46.7887	−2.24077
$437$	−21.5342	−1.03012
$438$	62.8003	3.00071
$439$	17.0594	0.814202	0.407101	−	0.913383i	$-0.366540\pi$
$439$	17.0594	0.814202	0.407101	+	0.913383i	$0.366540\pi$
$440$	11.0387	0.526250
$441$	55.6546	2.65022
$442$	9.84134	0.468105
$443$	−14.5428	−0.690949	−0.345474	−	0.938428i	$-0.612282\pi$
$443$	−14.5428	−0.690949	−0.345474	+	0.938428i	$0.612282\pi$
$444$	92.2995	4.38034
$445$	1.61638	0.0766236
$446$	−42.2118	−1.99879
$447$	26.1449	1.23661
$448$	49.6392	2.34523
$449$	−14.7616	−0.696641	−0.348321	−	0.937375i	$-0.613248\pi$
$449$	−14.7616	−0.696641	−0.348321	+	0.937375i	$0.613248\pi$
$450$	39.9300	1.88232
$451$	8.46205	0.398463
$452$	101.080	4.75440
$453$	−7.54779	−0.354626
$454$	52.3820	2.45841
$455$	−8.61368	−0.403816
$456$	−153.192	−7.17386
$457$	26.5815	1.24343	0.621715	−	0.783243i	$-0.286436\pi$
$457$	26.5815	1.24343	0.621715	+	0.783243i	$0.286436\pi$
$458$	60.9110	2.84619
$459$	−0.996899	−0.0465313
$460$	8.28128	0.386116
$461$	−13.5399	−0.630617	−0.315309	−	0.948989i	$-0.602108\pi$
$461$	−13.5399	−0.630617	−0.315309	+	0.948989i	$0.602108\pi$
$462$	−74.3263	−3.45797
$463$	−10.7607	−0.500090	−0.250045	−	0.968234i	$-0.580445\pi$
$463$	−10.7607	−0.500090	−0.250045	+	0.968234i	$0.580445\pi$
$464$	−10.2506	−0.475873
$465$	−12.4746	−0.578495
$466$	46.7199	2.16426
$467$	14.3006	0.661755	0.330877	−	0.943674i	$-0.392655\pi$
$467$	14.3006	0.661755	0.330877	+	0.943674i	$0.392655\pi$
$468$	45.4990	2.10319
$469$	−7.92038	−0.365729
$470$	−12.1663	−0.561188
$471$	−17.6920	−0.815203
$472$	−43.0057	−1.97950
$473$	−25.5076	−1.17284
$474$	28.4555	1.30701
$475$	−36.8368	−1.69019
$476$	−31.9174	−1.46293
$477$	8.29760	0.379921
$478$	−11.6098	−0.531022
$479$	−12.5689	−0.574286	−0.287143	−	0.957888i	$-0.592705\pi$
$479$	−12.5689	−0.574286	−0.287143	+	0.957888i	$0.592705\pi$
$480$	18.3558	0.837825
$481$	21.0857	0.961425
$482$	3.19342	0.145456
$483$	−33.0249	−1.50268
$484$	−27.8584	−1.26629
$485$	−0.478368	−0.0217216
$486$	58.7661	2.66569
$487$	−1.65899	−0.0751760	−0.0375880	−	0.999293i	$-0.511967\pi$
$487$	−1.65899	−0.0751760	−0.0375880	+	0.999293i	$0.511967\pi$
$488$	17.0452	0.771600
$489$	−36.9076	−1.66902
$490$	27.7954	1.25567
$491$	21.9029	0.988464	0.494232	−	0.869330i	$-0.335449\pi$
$491$	21.9029	0.988464	0.494232	+	0.869330i	$0.335449\pi$
$492$	45.1608	2.03601
$493$	1.33171	0.0599772
$494$	−59.0887	−2.65853
$495$	−4.76916	−0.214358
$496$	81.2818	3.64966
$497$	42.4441	1.90388
$498$	33.9079	1.51945
$499$	36.2216	1.62150	0.810752	−	0.585390i	$-0.199059\pi$
$499$	36.2216	1.62150	0.810752	+	0.585390i	$0.199059\pi$
$500$	29.5405	1.32109
$501$	8.59948	0.384196
$502$	11.5384	0.514984
$503$	23.9261	1.06681	0.533407	−	0.845859i	$-0.320911\pi$
$503$	23.9261	1.06681	0.533407	+	0.845859i	$0.320911\pi$
$504$	−123.031	−5.48023
$505$	−1.52314	−0.0677790
$506$	16.3245	0.725712
$507$	−12.7770	−0.567444
$508$	−79.4926	−3.52691
$509$	36.4811	1.61700	0.808499	−	0.588498i	$-0.200281\pi$
$509$	36.4811	1.61700	0.808499	+	0.588498i	$0.200281\pi$
$510$	−5.50529	−0.243778
$511$	−46.5289	−2.05832
$512$	36.9081	1.63113
$513$	5.98551	0.264267
$514$	14.8189	0.653633
$515$	−1.60254	−0.0706164
$516$	−136.131	−5.99282
$517$	−17.0365	−0.749263
$518$	−96.2677	−4.22976
$519$	43.1510	1.89412
$520$	13.4584	0.590189
$521$	4.44930	0.194927	0.0974637	−	0.995239i	$-0.468927\pi$
$521$	4.44930	0.194927	0.0974637	+	0.995239i	$0.468927\pi$
$522$	8.66715	0.379351
$523$	7.20594	0.315094	0.157547	−	0.987512i	$-0.449641\pi$
$523$	7.20594	0.315094	0.157547	+	0.987512i	$0.449641\pi$
$524$	72.7412	3.17771
$525$	−56.4930	−2.46556
$526$	23.9450	1.04405
$527$	−10.5597	−0.459989
$528$	59.3394	2.58242
$529$	−15.7467	−0.684638
$530$	4.14404	0.180006
$531$	18.5802	0.806310
$532$	191.636	8.30848
$533$	10.3169	0.446875
$534$	17.0048	0.735868
$535$	6.16134	0.266378
$536$	12.3751	0.534524
$537$	21.5589	0.930337
$538$	82.6335	3.56258
$539$	38.9220	1.67649
$540$	−2.30181	−0.0990542
$541$	−30.9088	−1.32887	−0.664436	−	0.747345i	$-0.731328\pi$
$541$	−30.9088	−1.32887	−0.664436	+	0.747345i	$0.731328\pi$
$542$	34.5076	1.48223
$543$	−14.4713	−0.621023
$544$	15.5382	0.666195
$545$	5.97937	0.256128
$546$	−90.6185	−3.87811
$547$	−26.9512	−1.15235	−0.576175	−	0.817326i	$-0.695455\pi$
$547$	−26.9512	−1.15235	−0.576175	+	0.817326i	$0.695455\pi$
$548$	−49.7125	−2.12361
$549$	−7.36420	−0.314296
$550$	27.9250	1.19073
$551$	−7.99575	−0.340631
$552$	51.5994	2.19622
$553$	−21.0828	−0.896531
$554$	27.8274	1.18227
$555$	−11.7954	−0.500688
$556$	4.90520	0.208027
$557$	23.9984	1.01684	0.508422	−	0.861108i	$-0.330229\pi$
$557$	23.9984	1.01684	0.508422	+	0.861108i	$0.330229\pi$
$558$	−68.7258	−2.90940
$559$	−31.0989	−1.31534
$560$	−31.3966	−1.32675
$561$	−7.70908	−0.325478
$562$	14.0421	0.592330
$563$	28.6634	1.20802	0.604008	−	0.796978i	$-0.293569\pi$
$563$	28.6634	1.20802	0.604008	+	0.796978i	$0.293569\pi$
$564$	−90.9213	−3.82848
$565$	−12.9175	−0.543444
$566$	−34.1566	−1.43571
$567$	−39.1677	−1.64489
$568$	−66.3165	−2.78258
$569$	12.1685	0.510128	0.255064	−	0.966924i	$-0.417903\pi$
$569$	12.1685	0.510128	0.255064	+	0.966924i	$0.417903\pi$
$570$	33.0545	1.38450
$571$	31.4577	1.31646	0.658232	−	0.752816i	$-0.271305\pi$
$571$	31.4577	1.31646	0.658232	+	0.752816i	$0.271305\pi$
$572$	31.8197	1.33045
$573$	−48.9506	−2.04494
$574$	−47.1024	−1.96601
$575$	12.4077	0.517437
$576$	33.5083	1.39618
$577$	0.0180414	0.000751073 0	0.000375537	−	1.00000i	$-0.499880\pi$
$577$	0.0180414	0.000751073 0	0.000375537		1.00000i	$0.499880\pi$
$578$	40.0120	1.66428
$579$	−8.73034	−0.362821
$580$	3.07488	0.127677
$581$	−25.1225	−1.04226
$582$	−5.03258	−0.208607
$583$	5.80292	0.240333
$584$	72.6988	3.00830
$585$	−5.81455	−0.240402
$586$	−27.1656	−1.12220
$587$	18.1544	0.749312	0.374656	−	0.927164i	$-0.377761\pi$
$587$	18.1544	0.749312	0.374656	+	0.927164i	$0.377761\pi$
$588$	207.721	8.56629
$589$	63.4020	2.61244
$590$	9.27942	0.382028
$591$	40.4293	1.66304
$592$	76.8566	3.15879
$593$	−23.2362	−0.954195	−0.477097	−	0.878850i	$-0.658311\pi$
$593$	−23.2362	−0.954195	−0.477097	+	0.878850i	$0.658311\pi$
$594$	−4.53745	−0.186174
$595$	4.07889	0.167218
$596$	51.1014	2.09319
$597$	32.4497	1.32808
$598$	19.9028	0.813885
$599$	−46.7527	−1.91026	−0.955131	−	0.296183i	$-0.904286\pi$
$599$	−46.7527	−1.91026	−0.955131	+	0.296183i	$0.904286\pi$
$600$	88.2670	3.60348
$601$	−23.4458	−0.956373	−0.478187	−	0.878258i	$-0.658706\pi$
$601$	−23.4458	−0.956373	−0.478187	+	0.878258i	$0.658706\pi$
$602$	141.983	5.78681
$603$	−5.34654	−0.217728
$604$	−14.7525	−0.600271
$605$	3.56017	0.144741
$606$	−16.0239	−0.650928
$607$	−5.71620	−0.232013	−0.116007	−	0.993248i	$-0.537009\pi$
$607$	−5.71620	−0.232013	−0.116007	+	0.993248i	$0.537009\pi$
$608$	−93.2934	−3.78355
$609$	−12.2623	−0.496894
$610$	−3.67788	−0.148913
$611$	−20.7708	−0.840298
$612$	−21.5454	−0.870921
$613$	30.7277	1.24108	0.620540	−	0.784175i	$-0.286913\pi$
$613$	30.7277	1.24108	0.620540	+	0.784175i	$0.286913\pi$
$614$	−38.7752	−1.56484
$615$	−5.77133	−0.232723
$616$	−86.0415	−3.46671
$617$	−31.0034	−1.24815	−0.624074	−	0.781365i	$-0.714524\pi$
$617$	−31.0034	−1.24815	−0.624074	+	0.781365i	$0.714524\pi$
$618$	−16.8592	−0.678177
$619$	24.4105	0.981139	0.490570	−	0.871402i	$-0.336789\pi$
$619$	24.4105	0.981139	0.490570	+	0.871402i	$0.336789\pi$
$620$	−24.3822	−0.979211
$621$	−2.01609	−0.0809030
$622$	49.8576	1.99911
$623$	−12.5989	−0.504764
$624$	72.3465	2.89618
$625$	19.2601	0.770404
$626$	44.5043	1.77875
$627$	46.2863	1.84850
$628$	−34.5798	−1.37988
$629$	−9.98483	−0.398121
$630$	26.5466	1.05764
$631$	36.8606	1.46740	0.733699	−	0.679475i	$-0.237792\pi$
$631$	36.8606	1.46740	0.733699	+	0.679475i	$0.237792\pi$
$632$	32.9406	1.31031
$633$	32.9527	1.30975
$634$	89.3300	3.54775
$635$	10.1588	0.403138
$636$	30.9694	1.22802
$637$	47.4537	1.88018
$638$	6.06137	0.239972
$639$	28.6513	1.13343
$640$	2.10665	0.0832725
$641$	1.34401	0.0530852	0.0265426	−	0.999648i	$-0.491550\pi$
$641$	1.34401	0.0530852	0.0265426	+	0.999648i	$0.491550\pi$
$642$	64.8191	2.55821
$643$	13.3648	0.527058	0.263529	−	0.964652i	$-0.415114\pi$
$643$	13.3648	0.527058	0.263529	+	0.964652i	$0.415114\pi$
$644$	−64.5486	−2.54357
$645$	17.3968	0.685000
$646$	27.9806	1.10088
$647$	−7.31581	−0.287614	−0.143807	−	0.989606i	$-0.545934\pi$
$647$	−7.31581	−0.287614	−0.143807	+	0.989606i	$0.545934\pi$
$648$	61.1972	2.40405
$649$	12.9940	0.510060
$650$	34.0461	1.33540
$651$	97.2335	3.81088
$652$	−72.1376	−2.82512
$653$	2.61706	0.102413	0.0512067	−	0.998688i	$-0.483693\pi$
$653$	2.61706	0.102413	0.0512067	+	0.998688i	$0.483693\pi$
$654$	62.9047	2.45977
$655$	−9.29597	−0.363224
$656$	37.6048	1.46822
$657$	−31.4087	−1.22537
$658$	94.8302	3.69687
$659$	−10.4326	−0.406395	−0.203197	−	0.979138i	$-0.565133\pi$
$659$	−10.4326	−0.406395	−0.203197	+	0.979138i	$0.565133\pi$
$660$	−17.8001	−0.692867
$661$	−28.8289	−1.12132	−0.560658	−	0.828047i	$-0.689452\pi$
$661$	−28.8289	−1.12132	−0.560658	+	0.828047i	$0.689452\pi$
$662$	54.3518	2.11244
$663$	−9.39890	−0.365023
$664$	39.2524	1.52329
$665$	−24.4902	−0.949688
$666$	−64.9842	−2.51809
$667$	2.69320	0.104281
$668$	16.8081	0.650324
$669$	40.3141	1.55863
$670$	−2.67020	−0.103159
$671$	−5.15015	−0.198819
$672$	−143.075	−5.51923
$673$	29.4157	1.13389	0.566946	−	0.823755i	$-0.308125\pi$
$673$	29.4157	1.13389	0.566946	+	0.823755i	$0.308125\pi$
$674$	−0.435459	−0.0167733
$675$	−3.44877	−0.132743
$676$	−24.9731	−0.960506
$677$	−7.40598	−0.284635	−0.142318	−	0.989821i	$-0.545455\pi$
$677$	−7.40598	−0.284635	−0.142318	+	0.989821i	$0.545455\pi$
$678$	−135.896	−5.21906
$679$	3.72865	0.143093
$680$	−6.37302	−0.244394
$681$	−50.0270	−1.91704
$682$	−48.0634	−1.84044
$683$	13.2521	0.507078	0.253539	−	0.967325i	$-0.418405\pi$
$683$	13.2521	0.507078	0.253539	+	0.967325i	$0.418405\pi$
$684$	129.361	4.94625
$685$	6.35302	0.242736
$686$	−126.775	−4.84030
$687$	−58.1727	−2.21943
$688$	−113.354	−4.32159
$689$	7.07491	0.269533
$690$	−11.1337	−0.423853
$691$	36.1170	1.37396	0.686978	−	0.726678i	$-0.258937\pi$
$691$	36.1170	1.37396	0.686978	+	0.726678i	$0.258937\pi$
$692$	84.3407	3.20615
$693$	37.1733	1.41210
$694$	−71.7951	−2.72530
$695$	−0.626861	−0.0237782
$696$	19.1591	0.726225
$697$	−4.88543	−0.185049
$698$	−11.1996	−0.423911
$699$	−44.6195	−1.68766
$700$	−110.418	−4.17341
$701$	12.4717	0.471049	0.235525	−	0.971868i	$-0.424319\pi$
$701$	12.4717	0.471049	0.235525	+	0.971868i	$0.424319\pi$
$702$	−5.53205	−0.208794
$703$	59.9502	2.26107
$704$	23.4340	0.883201
$705$	11.6193	0.437608
$706$	30.2735	1.13936
$707$	11.8722	0.446499
$708$	69.3473	2.60623
$709$	−43.2551	−1.62448	−0.812240	−	0.583324i	$-0.801752\pi$
$709$	−43.2551	−1.62448	−0.812240	+	0.583324i	$0.801752\pi$
$710$	14.3092	0.537016
$711$	−14.2316	−0.533729
$712$	19.6850	0.737728
$713$	−21.3556	−0.799775
$714$	42.9111	1.60591
$715$	−4.06640	−0.152075
$716$	42.1379	1.57477
$717$	11.0879	0.414085
$718$	−90.3257	−3.37093
$719$	−36.1043	−1.34646	−0.673231	−	0.739432i	$-0.735094\pi$
$719$	−36.1043	−1.34646	−0.673231	+	0.739432i	$0.735094\pi$
$720$	−21.1938	−0.789847
$721$	12.4910	0.465191
$722$	−118.071	−4.39416
$723$	−3.04985	−0.113425
$724$	−28.2848	−1.05120
$725$	4.60705	0.171101
$726$	37.4540	1.39005
$727$	40.1093	1.48757	0.743785	−	0.668418i	$-0.233028\pi$
$727$	40.1093	1.48757	0.743785	+	0.668418i	$0.233028\pi$
$728$	−104.902	−3.88791
$729$	−32.0757	−1.18799
$730$	−15.6863	−0.580578
$731$	14.7264	0.544677
$732$	−27.4856	−1.01590
$733$	−26.7499	−0.988030	−0.494015	−	0.869453i	$-0.664471\pi$
$733$	−26.7499	−0.988030	−0.494015	+	0.869453i	$0.664471\pi$
$734$	−45.7032	−1.68694
$735$	−26.5458	−0.979156
$736$	31.4239	1.15830
$737$	−3.73910	−0.137732
$738$	−31.7958	−1.17042
$739$	−34.5033	−1.26922	−0.634612	−	0.772831i	$-0.718840\pi$
$739$	−34.5033	−1.26922	−0.634612	+	0.772831i	$0.718840\pi$
$740$	−23.0547	−0.847508
$741$	56.4322	2.07309
$742$	−32.3008	−1.18580
$743$	−31.5221	−1.15643	−0.578217	−	0.815883i	$-0.696251\pi$
$743$	−31.5221	−1.15643	−0.578217	+	0.815883i	$0.696251\pi$
$744$	−151.922	−5.56972
$745$	−6.53051	−0.239259
$746$	75.3878	2.76014
$747$	−16.9586	−0.620482
$748$	−15.0678	−0.550932
$749$	−48.0247	−1.75478
$750$	−39.7155	−1.45021
$751$	−41.0836	−1.49916	−0.749581	−	0.661913i	$-0.769745\pi$
$751$	−41.0836	−1.49916	−0.749581	+	0.661913i	$0.769745\pi$
$752$	−75.7090	−2.76082
$753$	−11.0197	−0.401579
$754$	7.39001	0.269128
$755$	1.88530	0.0686131
$756$	17.9415	0.652527
$757$	−38.3158	−1.39261	−0.696305	−	0.717746i	$-0.745174\pi$
$757$	−38.3158	−1.39261	−0.696305	+	0.717746i	$0.745174\pi$
$758$	60.7419	2.20624
$759$	−15.5906	−0.565902
$760$	38.2645	1.38800
$761$	−28.1686	−1.02111	−0.510555	−	0.859845i	$-0.670560\pi$
$761$	−28.1686	−1.02111	−0.510555	+	0.859845i	$0.670560\pi$
$762$	106.873	3.87161
$763$	−46.6063	−1.68726
$764$	−95.6762	−3.46144
$765$	2.75340	0.0995493
$766$	41.1147	1.48553
$767$	15.8423	0.572032
$768$	−28.8298	−1.04031
$769$	20.6056	0.743056	0.371528	−	0.928422i	$-0.378834\pi$
$769$	20.6056	0.743056	0.371528	+	0.928422i	$0.378834\pi$
$770$	18.5653	0.669048
$771$	−14.1527	−0.509696
$772$	−17.0639	−0.614142
$773$	−21.2418	−0.764015	−0.382007	−	0.924159i	$-0.624767\pi$
$773$	−21.2418	−0.764015	−0.382007	+	0.924159i	$0.624767\pi$
$774$	95.8439	3.44504
$775$	−36.5314	−1.31225
$776$	−5.82580	−0.209134
$777$	91.9397	3.29832
$778$	−48.9586	−1.75525
$779$	29.3328	1.05096
$780$	−21.7018	−0.777050
$781$	20.0373	0.716990
$782$	−9.42468	−0.337026
$783$	−0.748586	−0.0267523
$784$	172.967	6.17739
$785$	4.41913	0.157725
$786$	−97.7964	−3.48828
$787$	52.9457	1.88731	0.943654	−	0.330933i	$-0.107363\pi$
$787$	52.9457	1.88731	0.943654	+	0.330933i	$0.107363\pi$
$788$	79.0209	2.81500
$789$	−22.8685	−0.814141
$790$	−7.10766	−0.252879
$791$	100.686	3.57998
$792$	−58.0811	−2.06382
$793$	−6.27905	−0.222976
$794$	−99.6449	−3.53627
$795$	−3.95774	−0.140367
$796$	63.4245	2.24802
$797$	−12.0791	−0.427864	−0.213932	−	0.976849i	$-0.568627\pi$
$797$	−12.0791	−0.427864	−0.213932	+	0.976849i	$0.568627\pi$
$798$	−257.644	−9.12049
$799$	9.83574	0.347963
$800$	53.7544	1.90050
$801$	−8.50471	−0.300499
$802$	−42.9501	−1.51662
$803$	−21.9657	−0.775152
$804$	−19.9551	−0.703761
$805$	8.24900	0.290739
$806$	−58.5988	−2.06405
$807$	−78.9186	−2.77806
$808$	−18.5496	−0.652573
$809$	16.6442	0.585178	0.292589	−	0.956238i	$-0.405483\pi$
$809$	16.6442	0.585178	0.292589	+	0.956238i	$0.405483\pi$
$810$	−13.2046	−0.463964
$811$	17.8505	0.626815	0.313408	−	0.949619i	$-0.398529\pi$
$811$	17.8505	0.626815	0.313408	+	0.949619i	$0.398529\pi$
$812$	−23.9672	−0.841085
$813$	−32.9562	−1.15582
$814$	−45.4466	−1.59290
$815$	9.21883	0.322922
$816$	−34.2587	−1.19929
$817$	−88.4194	−3.09340
$818$	−50.3553	−1.76063
$819$	45.3216	1.58367
$820$	−11.2803	−0.393926
$821$	49.1192	1.71427	0.857136	−	0.515089i	$-0.172241\pi$
$821$	49.1192	1.71427	0.857136	+	0.515089i	$0.172241\pi$
$822$	66.8357	2.33116
$823$	−36.7962	−1.28263	−0.641317	−	0.767276i	$-0.721612\pi$
$823$	−36.7962	−1.28263	−0.641317	+	0.767276i	$0.721612\pi$
$824$	−19.5165	−0.679890
$825$	−26.6696	−0.928515
$826$	−72.3287	−2.51664
$827$	−51.0441	−1.77498	−0.887489	−	0.460830i	$-0.847552\pi$
$827$	−51.0441	−1.77498	−0.887489	+	0.460830i	$0.847552\pi$
$828$	−43.5726	−1.51425
$829$	37.4067	1.29919	0.649594	−	0.760281i	$-0.274939\pi$
$829$	37.4067	1.29919	0.649594	+	0.760281i	$0.274939\pi$
$830$	−8.46956	−0.293983
$831$	−26.5763	−0.921923
$832$	28.5707	0.990509
$833$	−22.4710	−0.778575
$834$	−6.59477	−0.228358
$835$	−2.14799	−0.0743343
$836$	90.4688	3.12893
$837$	5.93588	0.205174
$838$	−20.6851	−0.714556
$839$	50.2701	1.73552	0.867758	−	0.496987i	$-0.165560\pi$
$839$	50.2701	1.73552	0.867758	+	0.496987i	$0.165560\pi$
$840$	58.6824	2.02474
$841$	1.00000	0.0344828
$842$	−42.2051	−1.45448
$843$	−13.4108	−0.461892
$844$	64.4075	2.21700
$845$	3.19145	0.109789
$846$	64.0138	2.20084
$847$	−27.7498	−0.953494
$848$	25.7878	0.885557
$849$	32.6210	1.11955
$850$	−16.1220	−0.552982
$851$	−20.1930	−0.692206
$852$	106.936	3.66357
$853$	−13.0046	−0.445270	−0.222635	−	0.974902i	$-0.571466\pi$
$853$	−13.0046	−0.445270	−0.222635	+	0.974902i	$0.571466\pi$
$854$	28.6673	0.980975
$855$	−16.5318	−0.565374
$856$	75.0358	2.56467
$857$	50.4625	1.72377	0.861884	−	0.507106i	$-0.169285\pi$
$857$	50.4625	1.72377	0.861884	+	0.507106i	$0.169285\pi$
$858$	−42.7797	−1.46048
$859$	46.3122	1.58015	0.790075	−	0.613010i	$-0.210041\pi$
$859$	46.3122	1.58015	0.790075	+	0.613010i	$0.210041\pi$
$860$	34.0029	1.15949
$861$	44.9848	1.53308
$862$	−42.8766	−1.46038
$863$	−14.1567	−0.481900	−0.240950	−	0.970538i	$-0.577459\pi$
$863$	−14.1567	−0.481900	−0.240950	+	0.970538i	$0.577459\pi$
$864$	−8.73440	−0.297150
$865$	−10.7783	−0.366474
$866$	−85.1686	−2.89415
$867$	−38.2131	−1.29779
$868$	190.047	6.45062
$869$	−9.95289	−0.337629
$870$	−4.13400	−0.140156
$871$	−4.55870	−0.154466
$872$	72.8197	2.46599
$873$	2.51698	0.0851867
$874$	56.5870	1.91408
$875$	29.4254	0.994759
$876$	−117.228	−3.96076
$877$	22.1099	0.746598	0.373299	−	0.927711i	$-0.378227\pi$
$877$	22.1099	0.746598	0.373299	+	0.927711i	$0.378227\pi$
$878$	−44.8284	−1.51288
$879$	25.9443	0.875081
$880$	−14.8219	−0.499646
$881$	22.8141	0.768628	0.384314	−	0.923202i	$-0.374438\pi$
$881$	22.8141	0.768628	0.384314	+	0.923202i	$0.374438\pi$
$882$	−146.248	−4.92442
$883$	−42.6929	−1.43673	−0.718366	−	0.695666i	$-0.755110\pi$
$883$	−42.6929	−1.43673	−0.718366	+	0.695666i	$0.755110\pi$
$884$	−18.3706	−0.617870
$885$	−8.86225	−0.297901
$886$	38.2152	1.28386
$887$	−49.5431	−1.66350	−0.831748	−	0.555154i	$-0.812659\pi$
$887$	−49.5431	−1.66350	−0.831748	+	0.555154i	$0.812659\pi$
$888$	−143.651	−4.82060
$889$	−79.1827	−2.65570
$890$	−4.24748	−0.142376
$891$	−18.4905	−0.619456
$892$	78.7957	2.63828
$893$	−59.0550	−1.97620
$894$	−68.7029	−2.29777
$895$	−5.38503	−0.180002
$896$	−16.4203	−0.548564
$897$	−19.0080	−0.634659
$898$	38.7901	1.29444
$899$	−7.92946	−0.264462
$900$	−74.5363	−2.48454
$901$	−3.35023	−0.111612
$902$	−22.2364	−0.740390
$903$	−135.600	−4.51249
$904$	−157.316	−5.23225
$905$	3.61466	0.120155
$906$	19.8339	0.658937
$907$	−3.11298	−0.103365	−0.0516823	−	0.998664i	$-0.516458\pi$
$907$	−3.11298	−0.103365	−0.0516823	+	0.998664i	$0.516458\pi$
$908$	−97.7801	−3.24495
$909$	8.01416	0.265813
$910$	22.6348	0.750337
$911$	43.6020	1.44460	0.722299	−	0.691581i	$-0.243086\pi$
$911$	43.6020	1.44460	0.722299	+	0.691581i	$0.243086\pi$
$912$	205.693	6.81119
$913$	−11.8600	−0.392508
$914$	−69.8502	−2.31044
$915$	3.51253	0.116121
$916$	−113.701	−3.75679
$917$	72.4576	2.39276
$918$	2.61963	0.0864605
$919$	−39.6017	−1.30634	−0.653169	−	0.757212i	$-0.726561\pi$
$919$	−39.6017	−1.30634	−0.653169	+	0.757212i	$0.726561\pi$
$920$	−12.8886	−0.424924
$921$	37.0319	1.22024
$922$	35.5799	1.17176
$923$	24.4294	0.804104
$924$	138.743	4.56431
$925$	−34.5425	−1.13575
$926$	28.2766	0.929226
$927$	8.43191	0.276940
$928$	11.6679	0.383016
$929$	−27.1911	−0.892112	−0.446056	−	0.895005i	$-0.647172\pi$
$929$	−27.1911	−0.892112	−0.446056	+	0.895005i	$0.647172\pi$
$930$	32.7804	1.07491
$931$	134.919	4.42179
$932$	−87.2109	−2.85669
$933$	−47.6161	−1.55888
$934$	−37.5789	−1.22962
$935$	1.92559	0.0629734
$936$	−70.8124	−2.31458
$937$	−53.3776	−1.74377	−0.871885	−	0.489711i	$-0.837102\pi$
$937$	−53.3776	−1.74377	−0.871885	+	0.489711i	$0.837102\pi$
$938$	20.8130	0.679567
$939$	−42.5035	−1.38705
$940$	22.7105	0.740733
$941$	−39.9799	−1.30331	−0.651653	−	0.758517i	$-0.725924\pi$
$941$	−39.9799	−1.30331	−0.651653	+	0.758517i	$0.725924\pi$
$942$	46.4905	1.51474
$943$	−9.88012	−0.321741
$944$	57.7446	1.87943
$945$	−2.29284	−0.0745861
$946$	67.0283	2.17928
$947$	−11.4687	−0.372682	−0.186341	−	0.982485i	$-0.559663\pi$
$947$	−11.4687	−0.372682	−0.186341	+	0.982485i	$0.559663\pi$
$948$	−53.1172	−1.72517
$949$	−26.7805	−0.869332
$950$	96.7988	3.14057
$951$	−85.3140	−2.76650
$952$	49.6747	1.60997
$953$	−47.1125	−1.52612	−0.763061	−	0.646326i	$-0.776304\pi$
$953$	−47.1125	−1.52612	−0.763061	+	0.646326i	$0.776304\pi$
$954$	−21.8042	−0.705938
$955$	12.2270	0.395655
$956$	21.6718	0.700917
$957$	−5.78886	−0.187127
$958$	33.0281	1.06709
$959$	−49.5188	−1.59904
$960$	−15.9826	−0.515835
$961$	31.8764	1.02827
$962$	−55.4085	−1.78644
$963$	−32.4184	−1.04467
$964$	−5.96107	−0.191993
$965$	2.18068	0.0701985
$966$	86.7819	2.79216
$967$	53.9281	1.73421	0.867106	−	0.498124i	$-0.165978\pi$
$967$	53.9281	1.73421	0.867106	+	0.498124i	$0.165978\pi$
$968$	43.3574	1.39356
$969$	−26.7227	−0.858456
$970$	1.25704	0.0403613
$971$	−26.7738	−0.859213	−0.429606	−	0.903016i	$-0.641348\pi$
$971$	−26.7738	−0.859213	−0.429606	+	0.903016i	$0.641348\pi$
$972$	−109.697	−3.51854
$973$	4.88608	0.156641
$974$	4.35945	0.139686
$975$	−32.5155	−1.04133
$976$	−22.8869	−0.732593
$977$	−21.1402	−0.676336	−0.338168	−	0.941086i	$-0.609807\pi$
$977$	−21.1402	−0.676336	−0.338168	+	0.941086i	$0.609807\pi$
$978$	96.9848	3.10123
$979$	−5.94776	−0.190091
$980$	−51.8850	−1.65740
$981$	−31.4610	−1.00447
$982$	−57.5559	−1.83668
$983$	−5.44730	−0.173742	−0.0868709	−	0.996220i	$-0.527687\pi$
$983$	−5.44730	−0.173742	−0.0868709	+	0.996220i	$0.527687\pi$
$984$	−70.2861	−2.24064
$985$	−10.0985	−0.321765
$986$	−3.49943	−0.111445
$987$	−90.5669	−2.88278
$988$	110.299	3.50909
$989$	29.7822	0.947019
$990$	12.5323	0.398302
$991$	40.4451	1.28478	0.642390	−	0.766378i	$-0.277943\pi$
$991$	40.4451	1.28478	0.642390	+	0.766378i	$0.277943\pi$
$992$	−92.5199	−2.93751
$993$	−51.9083	−1.64726
$994$	−111.534	−3.53763
$995$	−8.10534	−0.256957
$996$	−63.2950	−2.00558
$997$	21.9592	0.695456	0.347728	−	0.937596i	$-0.386953\pi$
$997$	21.9592	0.695456	0.347728	+	0.937596i	$0.386953\pi$
$998$	−95.1823	−3.01294
$999$	5.61271	0.177578

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.e.1.7	✓	103

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.e.1.7	✓	103	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62778 q^{2} +2.50964 q^{3} +4.90520 q^{4} -0.626861 q^{5} -6.59477 q^{6} +4.88608 q^{7} -7.63422 q^{8} +3.29828 q^{9} +O(q^{10})\)	\(q-2.62778 q^{2} +2.50964 q^{3} +4.90520 q^{4} -0.626861 q^{5} -6.59477 q^{6} +4.88608 q^{7} -7.63422 q^{8} +3.29828 q^{9} +1.64725 q^{10} +2.30665 q^{11} +12.3103 q^{12} +2.81227 q^{13} -12.8395 q^{14} -1.57319 q^{15} +10.2506 q^{16} -1.33171 q^{17} -8.66715 q^{18} +7.99575 q^{19} -3.07488 q^{20} +12.2623 q^{21} -6.06137 q^{22} -2.69320 q^{23} -19.1591 q^{24} -4.60705 q^{25} -7.39001 q^{26} +0.748586 q^{27} +23.9672 q^{28} -1.00000 q^{29} +4.13400 q^{30} +7.92946 q^{31} -11.6679 q^{32} +5.78886 q^{33} +3.49943 q^{34} -3.06290 q^{35} +16.1788 q^{36} +7.49776 q^{37} -21.0110 q^{38} +7.05777 q^{39} +4.78560 q^{40} +3.66854 q^{41} -32.2226 q^{42} -11.0583 q^{43} +11.3146 q^{44} -2.06757 q^{45} +7.07713 q^{46} -7.38580 q^{47} +25.7253 q^{48} +16.8738 q^{49} +12.1063 q^{50} -3.34211 q^{51} +13.7947 q^{52} +2.51573 q^{53} -1.96712 q^{54} -1.44595 q^{55} -37.3014 q^{56} +20.0665 q^{57} +2.62778 q^{58} +5.63328 q^{59} -7.71684 q^{60} -2.23274 q^{61} -20.8368 q^{62} +16.1157 q^{63} +10.1593 q^{64} -1.76290 q^{65} -15.2118 q^{66} -1.62101 q^{67} -6.53231 q^{68} -6.75896 q^{69} +8.04860 q^{70} +8.68673 q^{71} -25.1798 q^{72} -9.52275 q^{73} -19.7024 q^{74} -11.5620 q^{75} +39.2208 q^{76} +11.2705 q^{77} -18.5462 q^{78} -4.31486 q^{79} -6.42571 q^{80} -8.01617 q^{81} -9.64011 q^{82} -5.14164 q^{83} +60.1491 q^{84} +0.834797 q^{85} +29.0587 q^{86} -2.50964 q^{87} -17.6095 q^{88} -2.57852 q^{89} +5.43310 q^{90} +13.7410 q^{91} -13.2107 q^{92} +19.9001 q^{93} +19.4082 q^{94} -5.01223 q^{95} -29.2821 q^{96} +0.763117 q^{97} -44.3406 q^{98} +7.60800 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * q^99

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