LMFDB - Embedded newform 4031.2.a.e.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.75205 q^{2} +2.78767 q^{3} +5.57380 q^{4} -3.50027 q^{5} -7.67183 q^{6} +2.04758 q^{7} -9.83529 q^{8} +4.77113 q^{9} +O(q^{10})$	\(q-2.75205 q^{2} +2.78767 q^{3} +5.57380 q^{4} -3.50027 q^{5} -7.67183 q^{6} +2.04758 q^{7} -9.83529 q^{8} +4.77113 q^{9} +9.63294 q^{10} -6.53525 q^{11} +15.5379 q^{12} -4.33443 q^{13} -5.63504 q^{14} -9.75762 q^{15} +15.9197 q^{16} +5.70925 q^{17} -13.1304 q^{18} +0.237291 q^{19} -19.5098 q^{20} +5.70798 q^{21} +17.9854 q^{22} +4.18886 q^{23} -27.4176 q^{24} +7.25191 q^{25} +11.9286 q^{26} +4.93732 q^{27} +11.4128 q^{28} -1.00000 q^{29} +26.8535 q^{30} -0.235964 q^{31} -24.1412 q^{32} -18.2181 q^{33} -15.7122 q^{34} -7.16708 q^{35} +26.5933 q^{36} +2.27795 q^{37} -0.653038 q^{38} -12.0830 q^{39} +34.4262 q^{40} +0.630586 q^{41} -15.7087 q^{42} +6.69072 q^{43} -36.4262 q^{44} -16.7002 q^{45} -11.5280 q^{46} +13.3463 q^{47} +44.3788 q^{48} -2.80743 q^{49} -19.9577 q^{50} +15.9155 q^{51} -24.1592 q^{52} -12.2790 q^{53} -13.5878 q^{54} +22.8752 q^{55} -20.1385 q^{56} +0.661490 q^{57} +2.75205 q^{58} +0.196344 q^{59} -54.3870 q^{60} -1.82609 q^{61} +0.649387 q^{62} +9.76925 q^{63} +34.5985 q^{64} +15.1717 q^{65} +50.1373 q^{66} -10.0296 q^{67} +31.8222 q^{68} +11.6772 q^{69} +19.7242 q^{70} -11.7165 q^{71} -46.9254 q^{72} +6.70228 q^{73} -6.26905 q^{74} +20.2160 q^{75} +1.32261 q^{76} -13.3814 q^{77} +33.2530 q^{78} +1.90372 q^{79} -55.7232 q^{80} -0.549729 q^{81} -1.73541 q^{82} +3.64550 q^{83} +31.8151 q^{84} -19.9839 q^{85} -18.4132 q^{86} -2.78767 q^{87} +64.2761 q^{88} -2.30004 q^{89} +45.9600 q^{90} -8.87508 q^{91} +23.3479 q^{92} -0.657792 q^{93} -36.7296 q^{94} -0.830584 q^{95} -67.2977 q^{96} -5.42734 q^{97} +7.72620 q^{98} -31.1805 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.75205	−1.94600	−0.972998	−	0.230813i	$-0.925861\pi$
$2$	−2.75205	−1.94600	−0.972998	+	0.230813i	$0.925861\pi$
$3$	2.78767	1.60946	0.804732	−	0.593638i	$-0.202309\pi$
$3$	2.78767	1.60946	0.804732	+	0.593638i	$0.202309\pi$
$4$	5.57380	2.78690
$5$	−3.50027	−1.56537	−0.782685	−	0.622418i	$-0.786150\pi$
$5$	−3.50027	−1.56537	−0.782685	+	0.622418i	$0.786150\pi$
$6$	−7.67183	−3.13201
$7$	2.04758	0.773911	0.386956	−	0.922098i	$-0.373527\pi$
$7$	2.04758	0.773911	0.386956	+	0.922098i	$0.373527\pi$
$8$	−9.83529	−3.47730
$9$	4.77113	1.59038
$10$	9.63294	3.04620
$11$	−6.53525	−1.97045	−0.985226	−	0.171259i	$-0.945216\pi$
$11$	−6.53525	−1.97045	−0.985226	+	0.171259i	$0.945216\pi$
$12$	15.5379	4.48542
$13$	−4.33443	−1.20215	−0.601077	−	0.799191i	$-0.705262\pi$
$13$	−4.33443	−1.20215	−0.601077	+	0.799191i	$0.705262\pi$
$14$	−5.63504	−1.50603
$15$	−9.75762	−2.51941
$16$	15.9197	3.97991
$17$	5.70925	1.38470	0.692349	−	0.721563i	$-0.256576\pi$
$17$	5.70925	1.38470	0.692349	+	0.721563i	$0.256576\pi$
$18$	−13.1304	−3.09486
$19$	0.237291	0.0544383	0.0272192	−	0.999629i	$-0.491335\pi$
$19$	0.237291	0.0544383	0.0272192	+	0.999629i	$0.491335\pi$
$20$	−19.5098	−4.36253
$21$	5.70798	1.24558
$22$	17.9854	3.83449
$23$	4.18886	0.873437	0.436718	−	0.899598i	$-0.356141\pi$
$23$	4.18886	0.873437	0.436718	+	0.899598i	$0.356141\pi$
$24$	−27.4176	−5.59659
$25$	7.25191	1.45038
$26$	11.9286	2.33939
$27$	4.93732	0.950189
$28$	11.4128	2.15681
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	26.8535	4.90276
$31$	−0.235964	−0.0423805	−0.0211902	−	0.999775i	$-0.506746\pi$
$31$	−0.235964	−0.0423805	−0.0211902	+	0.999775i	$0.506746\pi$
$32$	−24.1412	−4.26760
$33$	−18.2181	−3.17137
$34$	−15.7122	−2.69462
$35$	−7.16708	−1.21146
$36$	26.5933	4.43222
$37$	2.27795	0.374493	0.187246	−	0.982313i	$-0.440044\pi$
$37$	2.27795	0.374493	0.187246	+	0.982313i	$0.440044\pi$
$38$	−0.653038	−0.105937
$39$	−12.0830	−1.93482
$40$	34.4262	5.44326
$41$	0.630586	0.0984809	0.0492405	−	0.998787i	$-0.484320\pi$
$41$	0.630586	0.0984809	0.0492405	+	0.998787i	$0.484320\pi$
$42$	−15.7087	−2.42390
$43$	6.69072	1.02033	0.510163	−	0.860078i	$-0.329585\pi$
$43$	6.69072	1.02033	0.510163	+	0.860078i	$0.329585\pi$
$44$	−36.4262	−5.49145
$45$	−16.7002	−2.48953
$46$	−11.5280	−1.69970
$47$	13.3463	1.94675	0.973376	−	0.229216i	$-0.0736162\pi$
$47$	13.3463	1.94675	0.973376	+	0.229216i	$0.0736162\pi$
$48$	44.3788	6.40553
$49$	−2.80743	−0.401061
$50$	−19.9577	−2.82244
$51$	15.9155	2.22862
$52$	−24.1592	−3.35028
$53$	−12.2790	−1.68665	−0.843326	−	0.537403i	$-0.819405\pi$
$53$	−12.2790	−1.68665	−0.843326	+	0.537403i	$0.819405\pi$
$54$	−13.5878	−1.84906
$55$	22.8752	3.08449
$56$	−20.1385	−2.69112
$57$	0.661490	0.0876165
$58$	2.75205	0.361362
$59$	0.196344	0.0255619	0.0127809	−	0.999918i	$-0.495932\pi$
$59$	0.196344	0.0255619	0.0127809	+	0.999918i	$0.495932\pi$
$60$	−54.3870	−7.02134
$61$	−1.82609	−0.233807	−0.116904	−	0.993143i	$-0.537297\pi$
$61$	−1.82609	−0.233807	−0.116904	+	0.993143i	$0.537297\pi$
$62$	0.649387	0.0824722
$63$	9.76925	1.23081
$64$	34.5985	4.32481
$65$	15.1717	1.88182
$66$	50.1373	6.17148
$67$	−10.0296	−1.22532	−0.612658	−	0.790348i	$-0.709900\pi$
$67$	−10.0296	−1.22532	−0.612658	+	0.790348i	$0.709900\pi$
$68$	31.8222	3.85901
$69$	11.6772	1.40577
$70$	19.7242	2.35749
$71$	−11.7165	−1.39049	−0.695246	−	0.718772i	$-0.744704\pi$
$71$	−11.7165	−1.39049	−0.695246	+	0.718772i	$0.744704\pi$
$72$	−46.9254	−5.53022
$73$	6.70228	0.784442	0.392221	−	0.919871i	$-0.371707\pi$
$73$	6.70228	0.784442	0.392221	+	0.919871i	$0.371707\pi$
$74$	−6.26905	−0.728762
$75$	20.2160	2.33434
$76$	1.32261	0.151714
$77$	−13.3814	−1.52496
$78$	33.2530	3.76516
$79$	1.90372	0.214185	0.107093	−	0.994249i	$-0.465846\pi$
$79$	1.90372	0.214185	0.107093	+	0.994249i	$0.465846\pi$
$80$	−55.7232	−6.23004
$81$	−0.549729	−0.0610810
$82$	−1.73541	−0.191644
$83$	3.64550	0.400145	0.200073	−	0.979781i	$-0.435882\pi$
$83$	3.64550	0.400145	0.200073	+	0.979781i	$0.435882\pi$
$84$	31.8151	3.47132
$85$	−19.9839	−2.16756
$86$	−18.4132	−1.98555
$87$	−2.78767	−0.298870
$88$	64.2761	6.85186
$89$	−2.30004	−0.243804	−0.121902	−	0.992542i	$-0.538899\pi$
$89$	−2.30004	−0.243804	−0.121902	+	0.992542i	$0.538899\pi$
$90$	45.9600	4.84461
$91$	−8.87508	−0.930361
$92$	23.3479	2.43418
$93$	−0.657792	−0.0682098
$94$	−36.7296	−3.78837
$95$	−0.830584	−0.0852161
$96$	−67.2977	−6.86855
$97$	−5.42734	−0.551063	−0.275531	−	0.961292i	$-0.588854\pi$
$97$	−5.42734	−0.551063	−0.275531	+	0.961292i	$0.588854\pi$
$98$	7.72620	0.780464
$99$	−31.1805	−3.13376
$100$	40.4207	4.04207
$101$	−9.22336	−0.917758	−0.458879	−	0.888499i	$-0.651749\pi$
$101$	−9.22336	−0.917758	−0.458879	+	0.888499i	$0.651749\pi$
$102$	−43.8004	−4.33689
$103$	6.99459	0.689198	0.344599	−	0.938750i	$-0.388015\pi$
$103$	6.99459	0.689198	0.344599	+	0.938750i	$0.388015\pi$
$104$	42.6304	4.18025
$105$	−19.9795	−1.94980
$106$	33.7925	3.28222
$107$	4.61477	0.446127	0.223063	−	0.974804i	$-0.428394\pi$
$107$	4.61477	0.446127	0.223063	+	0.974804i	$0.428394\pi$
$108$	27.5197	2.64808
$109$	9.45791	0.905904	0.452952	−	0.891535i	$-0.350371\pi$
$109$	9.45791	0.905904	0.452952	+	0.891535i	$0.350371\pi$
$110$	−62.9537	−6.00240
$111$	6.35019	0.602733
$112$	32.5967	3.08010
$113$	18.4980	1.74014	0.870071	−	0.492927i	$-0.164073\pi$
$113$	18.4980	1.74014	0.870071	+	0.492927i	$0.164073\pi$
$114$	−1.82046	−0.170501
$115$	−14.6621	−1.36725
$116$	−5.57380	−0.517514
$117$	−20.6801	−1.91188
$118$	−0.540350	−0.0497433
$119$	11.6901	1.07163
$120$	95.9691	8.76074
$121$	31.7095	2.88268
$122$	5.02551	0.454988
$123$	1.75787	0.158502
$124$	−1.31522	−0.118110
$125$	−7.88231	−0.705015
$126$	−26.8855	−2.39515
$127$	−17.0884	−1.51635	−0.758177	−	0.652048i	$-0.773910\pi$
$127$	−17.0884	−1.51635	−0.758177	+	0.652048i	$0.773910\pi$
$128$	−46.9346	−4.14847
$129$	18.6515	1.64218
$130$	−41.7533	−3.66201
$131$	10.0003	0.873726	0.436863	−	0.899528i	$-0.356089\pi$
$131$	10.0003	0.873726	0.436863	+	0.899528i	$0.356089\pi$
$132$	−101.544	−8.83830
$133$	0.485872	0.0421304
$134$	27.6021	2.38446
$135$	−17.2820	−1.48740
$136$	−56.1522	−4.81501
$137$	2.44085	0.208536	0.104268	−	0.994549i	$-0.466750\pi$
$137$	2.44085	0.208536	0.104268	+	0.994549i	$0.466750\pi$
$138$	−32.1362	−2.73561
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	−39.9479	−3.37621
$141$	37.2050	3.13323
$142$	32.2444	2.70589
$143$	28.3266	2.36879
$144$	75.9547	6.32956
$145$	3.50027	0.290682
$146$	−18.4450	−1.52652
$147$	−7.82620	−0.645494
$148$	12.6969	1.04367
$149$	19.9552	1.63479	0.817397	−	0.576075i	$-0.195417\pi$
$149$	19.9552	1.63479	0.817397	+	0.576075i	$0.195417\pi$
$150$	−55.6354	−4.54261
$151$	22.7767	1.85354	0.926770	−	0.375630i	$-0.122574\pi$
$151$	22.7767	1.85354	0.926770	+	0.375630i	$0.122574\pi$
$152$	−2.33383	−0.189298
$153$	27.2396	2.20219
$154$	36.8264	2.96756
$155$	0.825940	0.0663411
$156$	−67.3481	−5.39216
$157$	7.62400	0.608461	0.304231	−	0.952598i	$-0.401601\pi$
$157$	7.62400	0.608461	0.304231	+	0.952598i	$0.401601\pi$
$158$	−5.23914	−0.416803
$159$	−34.2299	−2.71461
$160$	84.5007	6.68037
$161$	8.57700	0.675963
$162$	1.51288	0.118863
$163$	23.1390	1.81239	0.906193	−	0.422865i	$-0.138976\pi$
$163$	23.1390	1.81239	0.906193	+	0.422865i	$0.138976\pi$
$164$	3.51476	0.274457
$165$	63.7685	4.96437
$166$	−10.0326	−0.778682
$167$	22.4226	1.73511	0.867556	−	0.497340i	$-0.165690\pi$
$167$	22.4226	1.73511	0.867556	+	0.497340i	$0.165690\pi$
$168$	−56.1396	−4.33127
$169$	5.78728	0.445175
$170$	54.9969	4.21807
$171$	1.13215	0.0865774
$172$	37.2927	2.84354
$173$	−0.628340	−0.0477718	−0.0238859	−	0.999715i	$-0.507604\pi$
$173$	−0.628340	−0.0477718	−0.0238859	+	0.999715i	$0.507604\pi$
$174$	7.67183	0.581600
$175$	14.8488	1.12247
$176$	−104.039	−7.84223
$177$	0.547344	0.0411409
$178$	6.32984	0.474442
$179$	24.5283	1.83333	0.916664	−	0.399659i	$-0.130871\pi$
$179$	24.5283	1.83333	0.916664	+	0.399659i	$0.130871\pi$
$180$	−93.0839	−6.93806
$181$	−1.68721	−0.125409	−0.0627047	−	0.998032i	$-0.519973\pi$
$181$	−1.68721	−0.125409	−0.0627047	+	0.998032i	$0.519973\pi$
$182$	24.4247	1.81048
$183$	−5.09056	−0.376305
$184$	−41.1986	−3.03720
$185$	−7.97345	−0.586220
$186$	1.81028	0.132736
$187$	−37.3114	−2.72848
$188$	74.3894	5.42540
$189$	10.1096	0.735362
$190$	2.28581	0.165830
$191$	−9.83936	−0.711951	−0.355975	−	0.934495i	$-0.615851\pi$
$191$	−9.83936	−0.711951	−0.355975	+	0.934495i	$0.615851\pi$
$192$	96.4493	6.96063
$193$	12.1679	0.875864	0.437932	−	0.899008i	$-0.355711\pi$
$193$	12.1679	0.875864	0.437932	+	0.899008i	$0.355711\pi$
$194$	14.9363	1.07237
$195$	42.2937	3.02872
$196$	−15.6481	−1.11772
$197$	2.57088	0.183167	0.0915837	−	0.995797i	$-0.470807\pi$
$197$	2.57088	0.183167	0.0915837	+	0.995797i	$0.470807\pi$
$198$	85.8104	6.09828
$199$	8.50893	0.603182	0.301591	−	0.953437i	$-0.402482\pi$
$199$	8.50893	0.603182	0.301591	+	0.953437i	$0.402482\pi$
$200$	−71.3247	−5.04342
$201$	−27.9594	−1.97210
$202$	25.3832	1.78595
$203$	−2.04758	−0.143712
$204$	88.7101	6.21095
$205$	−2.20722	−0.154159
$206$	−19.2495	−1.34118
$207$	19.9856	1.38909
$208$	−69.0026	−4.78447
$209$	−1.55076	−0.107268
$210$	54.9846	3.79430
$211$	5.67024	0.390355	0.195178	−	0.980768i	$-0.437472\pi$
$211$	5.67024	0.390355	0.195178	+	0.980768i	$0.437472\pi$
$212$	−68.4407	−4.70053
$213$	−32.6618	−2.23795
$214$	−12.7001	−0.868161
$215$	−23.4193	−1.59719
$216$	−48.5600	−3.30409
$217$	−0.483155	−0.0327987
$218$	−26.0287	−1.76289
$219$	18.6838	1.26253
$220$	127.502	8.59616
$221$	−24.7464	−1.66462
$222$	−17.4761	−1.17292
$223$	3.28360	0.219886	0.109943	−	0.993938i	$-0.464933\pi$
$223$	3.28360	0.219886	0.109943	+	0.993938i	$0.464933\pi$
$224$	−49.4309	−3.30274
$225$	34.5998	2.30665
$226$	−50.9074	−3.38631
$227$	1.78324	0.118358	0.0591788	−	0.998247i	$-0.481152\pi$
$227$	1.78324	0.118358	0.0591788	+	0.998247i	$0.481152\pi$
$228$	3.68702	0.244179
$229$	−13.5746	−0.897038	−0.448519	−	0.893773i	$-0.648048\pi$
$229$	−13.5746	−0.897038	−0.448519	+	0.893773i	$0.648048\pi$
$230$	40.3510	2.66067
$231$	−37.3031	−2.45436
$232$	9.83529	0.645719
$233$	2.13451	0.139837	0.0699183	−	0.997553i	$-0.477726\pi$
$233$	2.13451	0.139837	0.0699183	+	0.997553i	$0.477726\pi$
$234$	56.9128	3.72051
$235$	−46.7155	−3.04739
$236$	1.09438	0.0712384
$237$	5.30695	0.344723
$238$	−32.1719	−2.08539
$239$	−13.3030	−0.860503	−0.430251	−	0.902709i	$-0.641575\pi$
$239$	−13.3030	−0.860503	−0.430251	+	0.902709i	$0.641575\pi$
$240$	−155.338	−10.0270
$241$	28.5195	1.83710	0.918550	−	0.395305i	$-0.129361\pi$
$241$	28.5195	1.83710	0.918550	+	0.395305i	$0.129361\pi$
$242$	−87.2662	−5.60969
$243$	−16.3444	−1.04850
$244$	−10.1783	−0.651598
$245$	9.82677	0.627809
$246$	−4.83775	−0.308443
$247$	−1.02852	−0.0654432
$248$	2.32078	0.147370
$249$	10.1625	0.644020
$250$	21.6925	1.37196
$251$	−9.01419	−0.568971	−0.284485	−	0.958680i	$-0.591823\pi$
$251$	−9.01419	−0.568971	−0.284485	+	0.958680i	$0.591823\pi$
$252$	54.4519	3.43014
$253$	−27.3752	−1.72107
$254$	47.0283	2.95082
$255$	−55.7087	−3.48862
$256$	59.9695	3.74810
$257$	−11.8761	−0.740810	−0.370405	−	0.928870i	$-0.620781\pi$
$257$	−11.8761	−0.740810	−0.370405	+	0.928870i	$0.620781\pi$
$258$	−51.3301	−3.19567
$259$	4.66428	0.289824
$260$	84.5640	5.24443
$261$	−4.77113	−0.295325
$262$	−27.5212	−1.70027
$263$	7.57516	0.467104	0.233552	−	0.972344i	$-0.424965\pi$
$263$	7.57516	0.467104	0.233552	+	0.972344i	$0.424965\pi$
$264$	179.181	11.0278
$265$	42.9799	2.64023
$266$	−1.33715	−0.0819856
$267$	−6.41177	−0.392394
$268$	−55.9032	−3.41483
$269$	0.707577	0.0431417	0.0215709	−	0.999767i	$-0.493133\pi$
$269$	0.707577	0.0431417	0.0215709	+	0.999767i	$0.493133\pi$
$270$	47.5610	2.89447
$271$	28.1739	1.71145	0.855723	−	0.517435i	$-0.173113\pi$
$271$	28.1739	1.71145	0.855723	+	0.517435i	$0.173113\pi$
$272$	90.8894	5.51098
$273$	−24.7408	−1.49738
$274$	−6.71735	−0.405810
$275$	−47.3931	−2.85791
$276$	65.0862	3.91773
$277$	17.4922	1.05101	0.525503	−	0.850791i	$-0.323877\pi$
$277$	17.4922	1.05101	0.525503	+	0.850791i	$0.323877\pi$
$278$	−2.75205	−0.165057
$279$	−1.12582	−0.0674008
$280$	70.4903	4.21260
$281$	22.3826	1.33523	0.667616	−	0.744505i	$-0.267315\pi$
$281$	22.3826	1.33523	0.667616	+	0.744505i	$0.267315\pi$
$282$	−102.390	−6.09725
$283$	2.09375	0.124461	0.0622304	−	0.998062i	$-0.480179\pi$
$283$	2.09375	0.124461	0.0622304	+	0.998062i	$0.480179\pi$
$284$	−65.3054	−3.87516
$285$	−2.31540	−0.137152
$286$	−77.9563	−4.60965
$287$	1.29117	0.0762155
$288$	−115.181	−6.78708
$289$	15.5956	0.917387
$290$	−9.63294	−0.565666
$291$	−15.1297	−0.886916
$292$	37.3572	2.18616
$293$	−3.05753	−0.178623	−0.0893113	−	0.996004i	$-0.528467\pi$
$293$	−3.05753	−0.178623	−0.0893113	+	0.996004i	$0.528467\pi$
$294$	21.5381	1.25613
$295$	−0.687259	−0.0400138
$296$	−22.4043	−1.30222
$297$	−32.2667	−1.87230
$298$	−54.9178	−3.18130
$299$	−18.1563	−1.05001
$300$	112.680	6.50557
$301$	13.6998	0.789641
$302$	−62.6826	−3.60698
$303$	−25.7117	−1.47710
$304$	3.77759	0.216660
$305$	6.39183	0.365995
$306$	−74.9648	−4.28545
$307$	−24.2465	−1.38382	−0.691911	−	0.721983i	$-0.743231\pi$
$307$	−24.2465	−1.38382	−0.691911	+	0.721983i	$0.743231\pi$
$308$	−74.5854	−4.24990
$309$	19.4987	1.10924
$310$	−2.27303	−0.129099
$311$	−20.0409	−1.13642	−0.568209	−	0.822885i	$-0.692363\pi$
$311$	−20.0409	−1.13642	−0.568209	+	0.822885i	$0.692363\pi$
$312$	118.840	6.72797
$313$	9.88682	0.558836	0.279418	−	0.960170i	$-0.409859\pi$
$313$	9.88682	0.558836	0.279418	+	0.960170i	$0.409859\pi$
$314$	−20.9817	−1.18406
$315$	−34.1950	−1.92667
$316$	10.6109	0.596912
$317$	6.97117	0.391540	0.195770	−	0.980650i	$-0.437279\pi$
$317$	6.97117	0.391540	0.195770	+	0.980650i	$0.437279\pi$
$318$	94.2024	5.28261
$319$	6.53525	0.365904
$320$	−121.104	−6.76993
$321$	12.8645	0.718025
$322$	−23.6044	−1.31542
$323$	1.35476	0.0753806
$324$	−3.06408	−0.170227
$325$	−31.4329	−1.74358
$326$	−63.6797	−3.52689
$327$	26.3656	1.45802
$328$	−6.20200	−0.342448
$329$	27.3275	1.50661
$330$	−175.494	−9.66065
$331$	−18.0348	−0.991280	−0.495640	−	0.868528i	$-0.665066\pi$
$331$	−18.0348	−0.991280	−0.495640	+	0.868528i	$0.665066\pi$
$332$	20.3193	1.11517
$333$	10.8684	0.595584
$334$	−61.7082	−3.37652
$335$	35.1065	1.91807
$336$	90.8691	4.95731
$337$	6.61658	0.360428	0.180214	−	0.983627i	$-0.442321\pi$
$337$	6.61658	0.360428	0.180214	+	0.983627i	$0.442321\pi$
$338$	−15.9269	−0.866309
$339$	51.5663	2.80070
$340$	−111.387	−6.04078
$341$	1.54209	0.0835087
$342$	−3.11573	−0.168479
$343$	−20.0815	−1.08430
$344$	−65.8052	−3.54798
$345$	−40.8733	−2.20054
$346$	1.72923	0.0929638
$347$	−3.33046	−0.178789	−0.0893943	−	0.995996i	$-0.528493\pi$
$347$	−3.33046	−0.178789	−0.0893943	+	0.995996i	$0.528493\pi$
$348$	−15.5379	−0.832921
$349$	30.0619	1.60918	0.804589	−	0.593833i	$-0.202386\pi$
$349$	30.0619	1.60918	0.804589	+	0.593833i	$0.202386\pi$
$350$	−40.8648	−2.18432
$351$	−21.4005	−1.14227
$352$	157.769	8.40910
$353$	34.9736	1.86145	0.930727	−	0.365714i	$-0.119175\pi$
$353$	34.9736	1.86145	0.930727	+	0.365714i	$0.119175\pi$
$354$	−1.50632	−0.0800601
$355$	41.0109	2.17663
$356$	−12.8200	−0.679458
$357$	32.5883	1.72476
$358$	−67.5031	−3.56765
$359$	7.94794	0.419476	0.209738	−	0.977758i	$-0.432739\pi$
$359$	7.94794	0.419476	0.209738	+	0.977758i	$0.432739\pi$
$360$	164.252	8.65683
$361$	−18.9437	−0.997036
$362$	4.64330	0.244046
$363$	88.3957	4.63957
$364$	−49.4679	−2.59282
$365$	−23.4598	−1.22794
$366$	14.0095	0.732287
$367$	−11.6073	−0.605894	−0.302947	−	0.953007i	$-0.597971\pi$
$367$	−11.6073	−0.605894	−0.302947	+	0.953007i	$0.597971\pi$
$368$	66.6852	3.47620
$369$	3.00860	0.156622
$370$	21.9434	1.14078
$371$	−25.1422	−1.30532
$372$	−3.66640	−0.190094
$373$	−14.2013	−0.735317	−0.367659	−	0.929961i	$-0.619840\pi$
$373$	−14.2013	−0.735317	−0.367659	+	0.929961i	$0.619840\pi$
$374$	102.683	5.30961
$375$	−21.9733	−1.13470
$376$	−131.264	−6.76944
$377$	4.33443	0.223234
$378$	−27.8220	−1.43101
$379$	−2.23816	−0.114966	−0.0574832	−	0.998346i	$-0.518308\pi$
$379$	−2.23816	−0.114966	−0.0574832	+	0.998346i	$0.518308\pi$
$380$	−4.62951	−0.237489
$381$	−47.6370	−2.44052
$382$	27.0784	1.38545
$383$	0.977662	0.0499562	0.0249781	−	0.999688i	$-0.492048\pi$
$383$	0.977662	0.0499562	0.0249781	+	0.999688i	$0.492048\pi$
$384$	−130.838	−6.67682
$385$	46.8386	2.38712
$386$	−33.4867	−1.70443
$387$	31.9223	1.62270
$388$	−30.2509	−1.53576
$389$	−10.1072	−0.512456	−0.256228	−	0.966616i	$-0.582480\pi$
$389$	−10.1072	−0.512456	−0.256228	+	0.966616i	$0.582480\pi$
$390$	−116.395	−5.89387
$391$	23.9152	1.20945
$392$	27.6119	1.39461
$393$	27.8775	1.40623
$394$	−7.07519	−0.356443
$395$	−6.66353	−0.335279
$396$	−173.794	−8.73348
$397$	−36.8407	−1.84898	−0.924491	−	0.381205i	$-0.875509\pi$
$397$	−36.8407	−1.84898	−0.924491	+	0.381205i	$0.875509\pi$
$398$	−23.4170	−1.17379
$399$	1.35445	0.0678074
$400$	115.448	5.77240
$401$	28.1325	1.40487	0.702436	−	0.711747i	$-0.252096\pi$
$401$	28.1325	1.40487	0.702436	+	0.711747i	$0.252096\pi$
$402$	76.9457	3.83770
$403$	1.02277	0.0509479
$404$	−51.4092	−2.55770
$405$	1.92420	0.0956143
$406$	5.63504	0.279662
$407$	−14.8870	−0.737920
$408$	−156.534	−7.74959
$409$	−13.8740	−0.686027	−0.343014	−	0.939330i	$-0.611448\pi$
$409$	−13.8740	−0.686027	−0.343014	+	0.939330i	$0.611448\pi$
$410$	6.07439	0.299993
$411$	6.80430	0.335631
$412$	38.9865	1.92073
$413$	0.402030	0.0197826
$414$	−55.0013	−2.70317
$415$	−12.7602	−0.626376
$416$	104.638	5.13031
$417$	2.78767	0.136513
$418$	4.26777	0.208743
$419$	36.9922	1.80719	0.903594	−	0.428391i	$-0.140919\pi$
$419$	36.9922	1.80719	0.903594	+	0.428391i	$0.140919\pi$
$420$	−111.362	−5.43389
$421$	3.10251	0.151207	0.0756037	−	0.997138i	$-0.475912\pi$
$421$	3.10251	0.151207	0.0756037	+	0.997138i	$0.475912\pi$
$422$	−15.6048	−0.759630
$423$	63.6767	3.09607
$424$	120.768	5.86500
$425$	41.4030	2.00834
$426$	89.8869	4.35504
$427$	−3.73907	−0.180946
$428$	25.7218	1.24331
$429$	78.9653	3.81248
$430$	64.4513	3.10812
$431$	−28.9204	−1.39304	−0.696522	−	0.717535i	$-0.745270\pi$
$431$	−28.9204	−1.39304	−0.696522	+	0.717535i	$0.745270\pi$
$432$	78.6005	3.78167
$433$	−31.5131	−1.51442	−0.757211	−	0.653171i	$-0.773438\pi$
$433$	−31.5131	−1.51442	−0.757211	+	0.653171i	$0.773438\pi$
$434$	1.32967	0.0638262
$435$	9.75762	0.467842
$436$	52.7165	2.52466
$437$	0.993978	0.0475484
$438$	−51.4187	−2.45688
$439$	−18.2602	−0.871512	−0.435756	−	0.900065i	$-0.643519\pi$
$439$	−18.2602	−0.871512	−0.435756	+	0.900065i	$0.643519\pi$
$440$	−224.984	−10.7257
$441$	−13.3946	−0.637838
$442$	68.1033	3.23934
$443$	25.9092	1.23098	0.615490	−	0.788144i	$-0.288958\pi$
$443$	25.9092	1.23098	0.615490	+	0.788144i	$0.288958\pi$
$444$	35.3947	1.67976
$445$	8.05078	0.381643
$446$	−9.03665	−0.427898
$447$	55.6286	2.63114
$448$	70.8431	3.34702
$449$	−15.6457	−0.738367	−0.369183	−	0.929357i	$-0.620363\pi$
$449$	−15.6457	−0.738367	−0.369183	+	0.929357i	$0.620363\pi$
$450$	−95.2205	−4.48874
$451$	−4.12104	−0.194052
$452$	103.104	4.84960
$453$	63.4940	2.98321
$454$	−4.90757	−0.230323
$455$	31.0652	1.45636
$456$	−6.50595	−0.304669
$457$	−20.0218	−0.936581	−0.468291	−	0.883574i	$-0.655130\pi$
$457$	−20.0218	−0.936581	−0.468291	+	0.883574i	$0.655130\pi$
$458$	37.3582	1.74563
$459$	28.1884	1.31572
$460$	−81.7239	−3.81039
$461$	−0.727906	−0.0339020	−0.0169510	−	0.999856i	$-0.505396\pi$
$461$	−0.727906	−0.0339020	−0.0169510	+	0.999856i	$0.505396\pi$
$462$	102.660	4.77618
$463$	0.274591	0.0127613	0.00638067	−	0.999980i	$-0.497969\pi$
$463$	0.274591	0.0127613	0.00638067	+	0.999980i	$0.497969\pi$
$464$	−15.9197	−0.739052
$465$	2.30245	0.106774
$466$	−5.87430	−0.272122
$467$	14.8460	0.686991	0.343495	−	0.939154i	$-0.388389\pi$
$467$	14.8460	0.686991	0.343495	+	0.939154i	$0.388389\pi$
$468$	−115.267	−5.32821
$469$	−20.5365	−0.948285
$470$	128.564	5.93020
$471$	21.2532	0.979297
$472$	−1.93111	−0.0888863
$473$	−43.7255	−2.01050
$474$	−14.6050	−0.670830
$475$	1.72081	0.0789564
$476$	65.1585	2.98653
$477$	−58.5847	−2.68241
$478$	36.6107	1.67453
$479$	7.39500	0.337886	0.168943	−	0.985626i	$-0.445965\pi$
$479$	7.39500	0.337886	0.168943	+	0.985626i	$0.445965\pi$
$480$	235.560	10.7518
$481$	−9.87362	−0.450198
$482$	−78.4871	−3.57499
$483$	23.9099	1.08794
$484$	176.742	8.03375
$485$	18.9972	0.862617
$486$	44.9808	2.04037
$487$	−3.26706	−0.148045	−0.0740224	−	0.997257i	$-0.523584\pi$
$487$	−3.26706	−0.148045	−0.0740224	+	0.997257i	$0.523584\pi$
$488$	17.9602	0.813019
$489$	64.5039	2.91697
$490$	−27.0438	−1.22171
$491$	28.9645	1.30715	0.653575	−	0.756862i	$-0.273268\pi$
$491$	28.9645	1.30715	0.653575	+	0.756862i	$0.273268\pi$
$492$	9.79800	0.441728
$493$	−5.70925	−0.257132
$494$	2.83055	0.127352
$495$	109.140	4.90549
$496$	−3.75647	−0.168671
$497$	−23.9904	−1.07612
$498$	−27.9676	−1.25326
$499$	9.58704	0.429175	0.214587	−	0.976705i	$-0.431159\pi$
$499$	9.58704	0.429175	0.214587	+	0.976705i	$0.431159\pi$
$500$	−43.9344	−1.96481
$501$	62.5068	2.79260
$502$	24.8075	1.10722
$503$	6.56882	0.292889	0.146445	−	0.989219i	$-0.453217\pi$
$503$	6.56882	0.292889	0.146445	+	0.989219i	$0.453217\pi$
$504$	−96.0834	−4.27990
$505$	32.2843	1.43663
$506$	75.3381	3.34919
$507$	16.1330	0.716494
$508$	−95.2476	−4.22593
$509$	18.7343	0.830383	0.415192	−	0.909734i	$-0.363715\pi$
$509$	18.7343	0.830383	0.415192	+	0.909734i	$0.363715\pi$
$510$	153.313	6.78883
$511$	13.7234	0.607089
$512$	−71.1702	−3.14531
$513$	1.17158	0.0517267
$514$	32.6836	1.44161
$515$	−24.4830	−1.07885
$516$	103.960	4.57658
$517$	−87.2211	−3.83598
$518$	−12.8364	−0.563997
$519$	−1.75161	−0.0768870
$520$	−149.218	−6.54364
$521$	−13.0811	−0.573094	−0.286547	−	0.958066i	$-0.592507\pi$
$521$	−13.0811	−0.573094	−0.286547	+	0.958066i	$0.592507\pi$
$522$	13.1304	0.574702
$523$	0.720253	0.0314945	0.0157472	−	0.999876i	$-0.494987\pi$
$523$	0.720253	0.0314945	0.0157472	+	0.999876i	$0.494987\pi$
$524$	55.7394	2.43499
$525$	41.3937	1.80657
$526$	−20.8472	−0.908983
$527$	−1.34718	−0.0586841
$528$	−290.027	−12.6218
$529$	−5.45349	−0.237108
$530$	−118.283	−5.13788
$531$	0.936784	0.0406530
$532$	2.70815	0.117413
$533$	−2.73323	−0.118389
$534$	17.6455	0.763597
$535$	−16.1530	−0.698353
$536$	98.6445	4.26079
$537$	68.3768	2.95068
$538$	−1.94729	−0.0839536
$539$	18.3473	0.790272
$540$	−96.3264	−4.14523
$541$	−32.2603	−1.38698	−0.693490	−	0.720466i	$-0.743928\pi$
$541$	−32.2603	−1.38698	−0.693490	+	0.720466i	$0.743928\pi$
$542$	−77.5362	−3.33047
$543$	−4.70340	−0.201842
$544$	−137.828	−5.90933
$545$	−33.1053	−1.41807
$546$	68.0881	2.91390
$547$	15.1540	0.647940	0.323970	−	0.946067i	$-0.394982\pi$
$547$	15.1540	0.647940	0.323970	+	0.946067i	$0.394982\pi$
$548$	13.6048	0.581169
$549$	−8.71253	−0.371842
$550$	130.428	5.56148
$551$	−0.237291	−0.0101089
$552$	−114.848	−4.88827
$553$	3.89801	0.165760
$554$	−48.1396	−2.04526
$555$	−22.2274	−0.943500
$556$	5.57380	0.236382
$557$	6.61009	0.280078	0.140039	−	0.990146i	$-0.455277\pi$
$557$	6.61009	0.280078	0.140039	+	0.990146i	$0.455277\pi$
$558$	3.09831	0.131162
$559$	−29.0004	−1.22659
$560$	−114.097	−4.82150
$561$	−104.012	−4.39139
$562$	−61.5981	−2.59836
$563$	29.2766	1.23386	0.616930	−	0.787018i	$-0.288376\pi$
$563$	29.2766	1.23386	0.616930	+	0.787018i	$0.288376\pi$
$564$	207.373	8.73199
$565$	−64.7479	−2.72397
$566$	−5.76212	−0.242200
$567$	−1.12561	−0.0472713
$568$	115.235	4.83516
$569$	−38.0574	−1.59545	−0.797725	−	0.603022i	$-0.793963\pi$
$569$	−38.0574	−1.59545	−0.797725	+	0.603022i	$0.793963\pi$
$570$	6.37210	0.266898
$571$	26.2984	1.10055	0.550276	−	0.834983i	$-0.314522\pi$
$571$	26.2984	1.10055	0.550276	+	0.834983i	$0.314522\pi$
$572$	157.887	6.60158
$573$	−27.4289	−1.14586
$574$	−3.55338	−0.148315
$575$	30.3772	1.26682
$576$	165.074	6.87808
$577$	−20.0776	−0.835840	−0.417920	−	0.908484i	$-0.637241\pi$
$577$	−20.0776	−0.835840	−0.417920	+	0.908484i	$0.637241\pi$
$578$	−42.9199	−1.78523
$579$	33.9201	1.40967
$580$	19.5098	0.810102
$581$	7.46444	0.309677
$582$	41.6376	1.72593
$583$	80.2464	3.32347
$584$	−65.9189	−2.72774
$585$	72.3860	2.99279
$586$	8.41448	0.347599
$587$	27.2099	1.12307	0.561536	−	0.827452i	$-0.310211\pi$
$587$	27.2099	1.12307	0.561536	+	0.827452i	$0.310211\pi$
$588$	−43.6217	−1.79893
$589$	−0.0559922	−0.00230712
$590$	1.89137	0.0778666
$591$	7.16677	0.294801
$592$	36.2642	1.49045
$593$	17.6711	0.725666	0.362833	−	0.931854i	$-0.381809\pi$
$593$	17.6711	0.725666	0.362833	+	0.931854i	$0.381809\pi$
$594$	88.7996	3.64349
$595$	−40.9187	−1.67750
$596$	111.226	4.55601
$597$	23.7201	0.970800
$598$	49.9671	2.04331
$599$	−39.6598	−1.62046	−0.810229	−	0.586114i	$-0.800657\pi$
$599$	−39.6598	−1.62046	−0.810229	+	0.586114i	$0.800657\pi$
$600$	−198.830	−8.11720
$601$	5.46974	0.223115	0.111558	−	0.993758i	$-0.464416\pi$
$601$	5.46974	0.223115	0.111558	+	0.993758i	$0.464416\pi$
$602$	−37.7025	−1.53664
$603$	−47.8527	−1.94871
$604$	126.953	5.16563
$605$	−110.992	−4.51246
$606$	70.7600	2.87443
$607$	−30.4358	−1.23535	−0.617675	−	0.786433i	$-0.711925\pi$
$607$	−30.4358	−1.23535	−0.617675	+	0.786433i	$0.711925\pi$
$608$	−5.72849	−0.232321
$609$	−5.70798	−0.231299
$610$	−17.5907	−0.712225
$611$	−57.8484	−2.34030
$612$	151.828	6.13728
$613$	−22.4910	−0.908401	−0.454201	−	0.890899i	$-0.650075\pi$
$613$	−22.4910	−0.908401	−0.454201	+	0.890899i	$0.650075\pi$
$614$	66.7277	2.69291
$615$	−6.15302	−0.248114
$616$	131.610	5.30273
$617$	−6.50917	−0.262049	−0.131025	−	0.991379i	$-0.541827\pi$
$617$	−6.50917	−0.262049	−0.131025	+	0.991379i	$0.541827\pi$
$618$	−53.6613	−2.15858
$619$	36.7007	1.47513	0.737564	−	0.675278i	$-0.235976\pi$
$619$	36.7007	1.47513	0.737564	+	0.675278i	$0.235976\pi$
$620$	4.60362	0.184886
$621$	20.6817	0.829930
$622$	55.1537	2.21146
$623$	−4.70951	−0.188683
$624$	−192.357	−7.70044
$625$	−8.66933	−0.346773
$626$	−27.2091	−1.08749
$627$	−4.32300	−0.172644
$628$	42.4946	1.69572
$629$	13.0054	0.518559
$630$	94.1066	3.74930
$631$	29.8990	1.19026	0.595130	−	0.803629i	$-0.297100\pi$
$631$	29.8990	1.19026	0.595130	+	0.803629i	$0.297100\pi$
$632$	−18.7236	−0.744786
$633$	15.8068	0.628263
$634$	−19.1850	−0.761935
$635$	59.8142	2.37366
$636$	−190.790	−7.56534
$637$	12.1686	0.482138
$638$	−17.9854	−0.712047
$639$	−55.9009	−2.21140
$640$	164.284	6.49389
$641$	33.8764	1.33804	0.669019	−	0.743246i	$-0.266715\pi$
$641$	33.8764	1.33804	0.669019	+	0.743246i	$0.266715\pi$
$642$	−35.4037	−1.39727
$643$	−28.9439	−1.14144	−0.570719	−	0.821146i	$-0.693335\pi$
$643$	−28.9439	−1.14144	−0.570719	+	0.821146i	$0.693335\pi$
$644$	47.8065	1.88384
$645$	−65.2855	−2.57061
$646$	−3.72836	−0.146690
$647$	6.15112	0.241826	0.120913	−	0.992663i	$-0.461418\pi$
$647$	6.15112	0.241826	0.120913	+	0.992663i	$0.461418\pi$
$648$	5.40675	0.212397
$649$	−1.28316	−0.0503684
$650$	86.5050	3.39301
$651$	−1.34688	−0.0527884
$652$	128.972	5.05094
$653$	−2.58871	−0.101304	−0.0506521	−	0.998716i	$-0.516130\pi$
$653$	−2.58871	−0.101304	−0.0506521	+	0.998716i	$0.516130\pi$
$654$	−72.5595	−2.83730
$655$	−35.0036	−1.36770
$656$	10.0387	0.391946
$657$	31.9774	1.24756
$658$	−75.2067	−2.93186
$659$	−22.6222	−0.881236	−0.440618	−	0.897695i	$-0.645241\pi$
$659$	−22.6222	−0.881236	−0.440618	+	0.897695i	$0.645241\pi$
$660$	355.433	13.8352
$661$	32.4602	1.26255	0.631277	−	0.775557i	$-0.282531\pi$
$661$	32.4602	1.26255	0.631277	+	0.775557i	$0.282531\pi$
$662$	49.6326	1.92903
$663$	−68.9848	−2.67915
$664$	−35.8546	−1.39143
$665$	−1.70068	−0.0659497
$666$	−29.9104	−1.15900
$667$	−4.18886	−0.162193
$668$	124.979	4.83558
$669$	9.15361	0.353899
$670$	−96.6149	−3.73256
$671$	11.9340	0.460706
$672$	−137.797	−5.31565
$673$	−44.0575	−1.69829	−0.849145	−	0.528159i	$-0.822882\pi$
$673$	−44.0575	−1.69829	−0.849145	+	0.528159i	$0.822882\pi$
$674$	−18.2092	−0.701392
$675$	35.8050	1.37814
$676$	32.2571	1.24066
$677$	−15.7668	−0.605968	−0.302984	−	0.952996i	$-0.597983\pi$
$677$	−15.7668	−0.605968	−0.302984	+	0.952996i	$0.597983\pi$
$678$	−141.913	−5.45014
$679$	−11.1129	−0.426474
$680$	196.548	7.53727
$681$	4.97108	0.190492
$682$	−4.24391	−0.162508
$683$	14.0924	0.539230	0.269615	−	0.962968i	$-0.413104\pi$
$683$	14.0924	0.539230	0.269615	+	0.962968i	$0.413104\pi$
$684$	6.31036	0.241283
$685$	−8.54365	−0.326436
$686$	55.2653	2.11004
$687$	−37.8417	−1.44375
$688$	106.514	4.06081
$689$	53.2225	2.02762
$690$	112.485	4.28225
$691$	39.0186	1.48434	0.742169	−	0.670213i	$-0.233797\pi$
$691$	39.0186	1.48434	0.742169	+	0.670213i	$0.233797\pi$
$692$	−3.50224	−0.133135
$693$	−63.8445	−2.42525
$694$	9.16561	0.347922
$695$	−3.50027	−0.132773
$696$	27.4176	1.03926
$697$	3.60017	0.136366
$698$	−82.7320	−3.13145
$699$	5.95033	0.225062
$700$	82.7645	3.12821
$701$	6.91596	0.261212	0.130606	−	0.991434i	$-0.458308\pi$
$701$	6.91596	0.261212	0.130606	+	0.991434i	$0.458308\pi$
$702$	58.8953	2.22286
$703$	0.540538	0.0203868
$704$	−226.110	−8.52184
$705$	−130.228	−4.90466
$706$	−96.2491	−3.62238
$707$	−18.8855	−0.710264
$708$	3.05079	0.114656
$709$	−1.27852	−0.0480160	−0.0240080	−	0.999712i	$-0.507643\pi$
$709$	−1.27852	−0.0480160	−0.0240080	+	0.999712i	$0.507643\pi$
$710$	−112.864	−4.23572
$711$	9.08288	0.340635
$712$	22.6216	0.847780
$713$	−0.988421	−0.0370167
$714$	−89.6847	−3.35637
$715$	−99.1508	−3.70803
$716$	136.716	5.10930
$717$	−37.0846	−1.38495
$718$	−21.8732	−0.816299
$719$	−19.7412	−0.736223	−0.368111	−	0.929782i	$-0.619996\pi$
$719$	−19.7412	−0.736223	−0.368111	+	0.929782i	$0.619996\pi$
$720$	−265.862	−9.90810
$721$	14.3220	0.533378
$722$	52.1341	1.94023
$723$	79.5030	2.95675
$724$	−9.40418	−0.349504
$725$	−7.25191	−0.269329
$726$	−243.270	−9.02859
$727$	6.21787	0.230608	0.115304	−	0.993330i	$-0.463216\pi$
$727$	6.21787	0.230608	0.115304	+	0.993330i	$0.463216\pi$
$728$	87.2890	3.23515
$729$	−43.9138	−1.62644
$730$	64.5626	2.38957
$731$	38.1990	1.41284
$732$	−28.3737	−1.04872
$733$	19.7871	0.730853	0.365426	−	0.930840i	$-0.380923\pi$
$733$	19.7871	0.730853	0.365426	+	0.930840i	$0.380923\pi$
$734$	31.9438	1.17907
$735$	27.3938	1.01044
$736$	−101.124	−3.72748
$737$	65.5462	2.41443
$738$	−8.27984	−0.304785
$739$	−19.3389	−0.711395	−0.355697	−	0.934601i	$-0.615757\pi$
$739$	−19.3389	−0.711395	−0.355697	+	0.934601i	$0.615757\pi$
$740$	−44.4424	−1.63374
$741$	−2.86718	−0.105329
$742$	69.1927	2.54014
$743$	−16.2265	−0.595292	−0.297646	−	0.954676i	$-0.596202\pi$
$743$	−16.2265	−0.595292	−0.297646	+	0.954676i	$0.596202\pi$
$744$	6.46958	0.237186
$745$	−69.8486	−2.55906
$746$	39.0828	1.43092
$747$	17.3931	0.636382
$748$	−207.966	−7.60400
$749$	9.44910	0.345262
$750$	60.4717	2.20812
$751$	−6.89081	−0.251449	−0.125725	−	0.992065i	$-0.540126\pi$
$751$	−6.89081	−0.251449	−0.125725	+	0.992065i	$0.540126\pi$
$752$	212.468	7.74790
$753$	−25.1286	−0.915738
$754$	−11.9286	−0.434413
$755$	−79.7246	−2.90147
$756$	56.3486	2.04938
$757$	−33.4814	−1.21690	−0.608452	−	0.793591i	$-0.708209\pi$
$757$	−33.4814	−1.21690	−0.608452	+	0.793591i	$0.708209\pi$
$758$	6.15953	0.223724
$759$	−76.3132	−2.76999
$760$	8.16903	0.296322
$761$	2.10846	0.0764315	0.0382158	−	0.999270i	$-0.487833\pi$
$761$	2.10846	0.0764315	0.0382158	+	0.999270i	$0.487833\pi$
$762$	131.100	4.74924
$763$	19.3658	0.701089
$764$	−54.8426	−1.98414
$765$	−95.3460	−3.44724
$766$	−2.69058	−0.0972145
$767$	−0.851041	−0.0307293
$768$	167.175	6.03243
$769$	−28.2290	−1.01797	−0.508983	−	0.860777i	$-0.669978\pi$
$769$	−28.2290	−1.01797	−0.508983	+	0.860777i	$0.669978\pi$
$770$	−128.902	−4.64532
$771$	−33.1067	−1.19231
$772$	67.8214	2.44095
$773$	−22.8131	−0.820530	−0.410265	−	0.911966i	$-0.634564\pi$
$773$	−22.8131	−0.820530	−0.410265	+	0.911966i	$0.634564\pi$
$774$	−87.8518	−3.15777
$775$	−1.71119	−0.0614679
$776$	53.3795	1.91621
$777$	13.0025	0.466462
$778$	27.8156	0.997238
$779$	0.149632	0.00536114
$780$	235.737	8.44073
$781$	76.5702	2.73990
$782$	−65.8160	−2.35358
$783$	−4.93732	−0.176446
$784$	−44.6933	−1.59619
$785$	−26.6861	−0.952467
$786$	−76.7203	−2.73652
$787$	37.8497	1.34920	0.674598	−	0.738186i	$-0.264317\pi$
$787$	37.8497	1.34920	0.674598	+	0.738186i	$0.264317\pi$
$788$	14.3296	0.510469
$789$	21.1171	0.751787
$790$	18.3384	0.652451
$791$	37.8760	1.34672
$792$	306.669	10.8970
$793$	7.91508	0.281073
$794$	101.388	3.59811
$795$	119.814	4.24936
$796$	47.4271	1.68101
$797$	32.7031	1.15840	0.579202	−	0.815184i	$-0.303364\pi$
$797$	32.7031	1.15840	0.579202	+	0.815184i	$0.303364\pi$
$798$	−3.72753	−0.131953
$799$	76.1972	2.69566
$800$	−175.070	−6.18965
$801$	−10.9738	−0.387740
$802$	−77.4223	−2.73388
$803$	−43.8011	−1.54571
$804$	−155.840	−5.49605
$805$	−30.0219	−1.05813
$806$	−2.81472	−0.0991443
$807$	1.97249	0.0694350
$808$	90.7144	3.19132
$809$	27.9256	0.981813	0.490907	−	0.871212i	$-0.336666\pi$
$809$	27.9256	0.981813	0.490907	+	0.871212i	$0.336666\pi$
$810$	−5.29551	−0.186065
$811$	−29.4125	−1.03281	−0.516407	−	0.856343i	$-0.672731\pi$
$811$	−29.4125	−1.03281	−0.516407	+	0.856343i	$0.672731\pi$
$812$	−11.4128	−0.400510
$813$	78.5398	2.75451
$814$	40.9698	1.43599
$815$	−80.9928	−2.83705
$816$	253.370	8.86972
$817$	1.58765	0.0555448
$818$	38.1821	1.33501
$819$	−42.3441	−1.47962
$820$	−12.3026	−0.429626
$821$	−0.622506	−0.0217256	−0.0108628	−	0.999941i	$-0.503458\pi$
$821$	−0.622506	−0.0217256	−0.0108628	+	0.999941i	$0.503458\pi$
$822$	−18.7258	−0.653137
$823$	9.00271	0.313815	0.156907	−	0.987613i	$-0.449848\pi$
$823$	9.00271	0.313815	0.156907	+	0.987613i	$0.449848\pi$
$824$	−68.7939	−2.39655
$825$	−132.116	−4.59970
$826$	−1.10641	−0.0384969
$827$	−2.93596	−0.102093	−0.0510467	−	0.998696i	$-0.516256\pi$
$827$	−2.93596	−0.102093	−0.0510467	+	0.998696i	$0.516256\pi$
$828$	111.396	3.87126
$829$	5.45293	0.189388	0.0946940	−	0.995506i	$-0.469813\pi$
$829$	5.45293	0.189388	0.0946940	+	0.995506i	$0.469813\pi$
$830$	35.1169	1.21892
$831$	48.7627	1.69156
$832$	−149.965	−5.19909
$833$	−16.0283	−0.555349
$834$	−7.67183	−0.265654
$835$	−78.4852	−2.71609
$836$	−8.64361	−0.298945
$837$	−1.16503	−0.0402694
$838$	−101.805	−3.51678
$839$	−40.0744	−1.38352	−0.691760	−	0.722127i	$-0.743165\pi$
$839$	−40.0744	−1.38352	−0.691760	+	0.722127i	$0.743165\pi$
$840$	196.504	6.78003
$841$	1.00000	0.0344828
$842$	−8.53829	−0.294249
$843$	62.3953	2.14901
$844$	31.6048	1.08788
$845$	−20.2570	−0.696864
$846$	−175.242	−6.02493
$847$	64.9276	2.23094
$848$	−195.478	−6.71273
$849$	5.83670	0.200315
$850$	−113.943	−3.90822
$851$	9.54201	0.327096
$852$	−182.050	−6.23693
$853$	−24.8328	−0.850259	−0.425129	−	0.905133i	$-0.639771\pi$
$853$	−24.8328	−0.850259	−0.425129	+	0.905133i	$0.639771\pi$
$854$	10.2901	0.352121
$855$	−3.96282	−0.135526
$856$	−45.3876	−1.55132
$857$	50.0358	1.70919	0.854595	−	0.519295i	$-0.173805\pi$
$857$	50.0358	1.70919	0.854595	+	0.519295i	$0.173805\pi$
$858$	−217.317	−7.41907
$859$	9.90011	0.337787	0.168894	−	0.985634i	$-0.445981\pi$
$859$	9.90011	0.337787	0.168894	+	0.985634i	$0.445981\pi$
$860$	−130.535	−4.45120
$861$	3.59937	0.122666
$862$	79.5904	2.71086
$863$	12.8491	0.437387	0.218693	−	0.975794i	$-0.429821\pi$
$863$	12.8491	0.437387	0.218693	+	0.975794i	$0.429821\pi$
$864$	−119.193	−4.05502
$865$	2.19936	0.0747806
$866$	86.7257	2.94706
$867$	43.4754	1.47650
$868$	−2.69301	−0.0914068
$869$	−12.4413	−0.422041
$870$	−26.8535	−0.910419
$871$	43.4728	1.47302
$872$	−93.0214	−3.15010
$873$	−25.8945	−0.876397
$874$	−2.73548	−0.0925290
$875$	−16.1396	−0.545619
$876$	104.140	3.51855
$877$	−40.5764	−1.37017	−0.685084	−	0.728464i	$-0.740234\pi$
$877$	−40.5764	−1.37017	−0.685084	+	0.728464i	$0.740234\pi$
$878$	50.2531	1.69596
$879$	−8.52339	−0.287487
$880$	364.165	12.2760
$881$	−6.09154	−0.205229	−0.102615	−	0.994721i	$-0.532721\pi$
$881$	−6.09154	−0.205229	−0.102615	+	0.994721i	$0.532721\pi$
$882$	36.8627	1.24123
$883$	19.0595	0.641402	0.320701	−	0.947181i	$-0.396082\pi$
$883$	19.0595	0.641402	0.320701	+	0.947181i	$0.396082\pi$
$884$	−137.931	−4.63913
$885$	−1.91585	−0.0644007
$886$	−71.3034	−2.39548
$887$	25.3583	0.851448	0.425724	−	0.904853i	$-0.360019\pi$
$887$	25.3583	0.851448	0.425724	+	0.904853i	$0.360019\pi$
$888$	−62.4560	−2.09588
$889$	−34.9899	−1.17352
$890$	−22.1562	−0.742677
$891$	3.59262	0.120357
$892$	18.3021	0.612801
$893$	3.16695	0.105978
$894$	−153.093	−5.12019
$895$	−85.8556	−2.86984
$896$	−96.1022	−3.21055
$897$	−50.6138	−1.68995
$898$	43.0579	1.43686
$899$	0.235964	0.00786985
$900$	192.852	6.42841
$901$	−70.1040	−2.33550
$902$	11.3413	0.377624
$903$	38.1905	1.27090
$904$	−181.933	−6.05100
$905$	5.90570	0.196312
$906$	−174.739	−5.80531
$907$	−43.5584	−1.44633	−0.723167	−	0.690674i	$-0.757314\pi$
$907$	−43.5584	−1.44633	−0.723167	+	0.690674i	$0.757314\pi$
$908$	9.93941	0.329851
$909$	−44.0058	−1.45958
$910$	−85.4931	−2.83407
$911$	−16.1311	−0.534448	−0.267224	−	0.963634i	$-0.586106\pi$
$911$	−16.1311	−0.534448	−0.267224	+	0.963634i	$0.586106\pi$
$912$	10.5307	0.348706
$913$	−23.8242	−0.788467
$914$	55.1011	1.82258
$915$	17.8183	0.589056
$916$	−75.6624	−2.49996
$917$	20.4763	0.676187
$918$	−77.5761	−2.56039
$919$	41.4228	1.36641	0.683205	−	0.730226i	$-0.260585\pi$
$919$	41.4228	1.36641	0.683205	+	0.730226i	$0.260585\pi$
$920$	144.206	4.75435
$921$	−67.5914	−2.22721
$922$	2.00324	0.0659731
$923$	50.7843	1.67159
$924$	−207.920	−6.84006
$925$	16.5195	0.543158
$926$	−0.755690	−0.0248335
$927$	33.3721	1.09608
$928$	24.1412	0.792473
$929$	−12.4714	−0.409175	−0.204587	−	0.978848i	$-0.565585\pi$
$929$	−12.4714	−0.409175	−0.204587	+	0.978848i	$0.565585\pi$
$930$	−6.33647	−0.207781
$931$	−0.666178	−0.0218331
$932$	11.8974	0.389711
$933$	−55.8676	−1.82902
$934$	−40.8570	−1.33688
$935$	130.600	4.27108
$936$	203.395	6.64817
$937$	25.4125	0.830189	0.415095	−	0.909778i	$-0.363748\pi$
$937$	25.4125	0.830189	0.415095	+	0.909778i	$0.363748\pi$
$938$	56.5174	1.84536
$939$	27.5612	0.899426
$940$	−260.383	−8.49276
$941$	48.3187	1.57515	0.787573	−	0.616222i	$-0.211338\pi$
$941$	48.3187	1.57515	0.787573	+	0.616222i	$0.211338\pi$
$942$	−58.4900	−1.90571
$943$	2.64143	0.0860169
$944$	3.12574	0.101734
$945$	−35.3862	−1.15111
$946$	120.335	3.91243
$947$	−40.7031	−1.32267	−0.661337	−	0.750089i	$-0.730011\pi$
$947$	−40.7031	−1.32267	−0.661337	+	0.750089i	$0.730011\pi$
$948$	29.5799	0.960709
$949$	−29.0505	−0.943021
$950$	−4.73577	−0.153649
$951$	19.4333	0.630169
$952$	−114.976	−3.72639
$953$	−44.2904	−1.43471	−0.717354	−	0.696709i	$-0.754647\pi$
$953$	−44.2904	−1.43471	−0.717354	+	0.696709i	$0.754647\pi$
$954$	161.228	5.21996
$955$	34.4404	1.11447
$956$	−74.1485	−2.39814
$957$	18.2181	0.588909
$958$	−20.3514	−0.657525
$959$	4.99783	0.161388
$960$	−337.599	−10.8960
$961$	−30.9443	−0.998204
$962$	27.1727	0.876084
$963$	22.0177	0.709509
$964$	158.962	5.11982
$965$	−42.5910	−1.37105
$966$	−65.8013	−2.11712
$967$	6.03585	0.194100	0.0970498	−	0.995280i	$-0.469059\pi$
$967$	6.03585	0.194100	0.0970498	+	0.995280i	$0.469059\pi$
$968$	−311.872	−10.0240
$969$	3.77662	0.121322
$970$	−52.2812	−1.67865
$971$	−20.7197	−0.664928	−0.332464	−	0.943116i	$-0.607880\pi$
$971$	−20.7197	−0.664928	−0.332464	+	0.943116i	$0.607880\pi$
$972$	−91.1007	−2.92205
$973$	2.04758	0.0656423
$974$	8.99113	0.288095
$975$	−87.6247	−2.80624
$976$	−29.0708	−0.930534
$977$	−45.7596	−1.46398	−0.731989	−	0.681317i	$-0.761408\pi$
$977$	−45.7596	−1.46398	−0.731989	+	0.681317i	$0.761408\pi$
$978$	−177.518	−5.67641
$979$	15.0314	0.480404
$980$	54.7725	1.74964
$981$	45.1249	1.44073
$982$	−79.7119	−2.54371
$983$	9.20716	0.293663	0.146831	−	0.989162i	$-0.453093\pi$
$983$	9.20716	0.293663	0.146831	+	0.989162i	$0.453093\pi$
$984$	−17.2891	−0.551158
$985$	−8.99877	−0.286725
$986$	15.7122	0.500378
$987$	76.1801	2.42484
$988$	−5.73277	−0.182384
$989$	28.0265	0.891189
$990$	−300.360	−9.54607
$991$	−4.07484	−0.129441	−0.0647207	−	0.997903i	$-0.520616\pi$
$991$	−4.07484	−0.129441	−0.0647207	+	0.997903i	$0.520616\pi$
$992$	5.69646	0.180863
$993$	−50.2750	−1.59543
$994$	66.0229	2.09412
$995$	−29.7836	−0.944203
$996$	56.6435	1.79482
$997$	−33.4045	−1.05793	−0.528965	−	0.848644i	$-0.677420\pi$
$997$	−33.4045	−1.05793	−0.528965	+	0.848644i	$0.677420\pi$
$998$	−26.3840	−0.835172
$999$	11.2470	0.355839

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.e.1.3	✓	103

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.e.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.75205 q^{2} +2.78767 q^{3} +5.57380 q^{4} -3.50027 q^{5} -7.67183 q^{6} +2.04758 q^{7} -9.83529 q^{8} +4.77113 q^{9} +O(q^{10})\)	\(q-2.75205 q^{2} +2.78767 q^{3} +5.57380 q^{4} -3.50027 q^{5} -7.67183 q^{6} +2.04758 q^{7} -9.83529 q^{8} +4.77113 q^{9} +9.63294 q^{10} -6.53525 q^{11} +15.5379 q^{12} -4.33443 q^{13} -5.63504 q^{14} -9.75762 q^{15} +15.9197 q^{16} +5.70925 q^{17} -13.1304 q^{18} +0.237291 q^{19} -19.5098 q^{20} +5.70798 q^{21} +17.9854 q^{22} +4.18886 q^{23} -27.4176 q^{24} +7.25191 q^{25} +11.9286 q^{26} +4.93732 q^{27} +11.4128 q^{28} -1.00000 q^{29} +26.8535 q^{30} -0.235964 q^{31} -24.1412 q^{32} -18.2181 q^{33} -15.7122 q^{34} -7.16708 q^{35} +26.5933 q^{36} +2.27795 q^{37} -0.653038 q^{38} -12.0830 q^{39} +34.4262 q^{40} +0.630586 q^{41} -15.7087 q^{42} +6.69072 q^{43} -36.4262 q^{44} -16.7002 q^{45} -11.5280 q^{46} +13.3463 q^{47} +44.3788 q^{48} -2.80743 q^{49} -19.9577 q^{50} +15.9155 q^{51} -24.1592 q^{52} -12.2790 q^{53} -13.5878 q^{54} +22.8752 q^{55} -20.1385 q^{56} +0.661490 q^{57} +2.75205 q^{58} +0.196344 q^{59} -54.3870 q^{60} -1.82609 q^{61} +0.649387 q^{62} +9.76925 q^{63} +34.5985 q^{64} +15.1717 q^{65} +50.1373 q^{66} -10.0296 q^{67} +31.8222 q^{68} +11.6772 q^{69} +19.7242 q^{70} -11.7165 q^{71} -46.9254 q^{72} +6.70228 q^{73} -6.26905 q^{74} +20.2160 q^{75} +1.32261 q^{76} -13.3814 q^{77} +33.2530 q^{78} +1.90372 q^{79} -55.7232 q^{80} -0.549729 q^{81} -1.73541 q^{82} +3.64550 q^{83} +31.8151 q^{84} -19.9839 q^{85} -18.4132 q^{86} -2.78767 q^{87} +64.2761 q^{88} -2.30004 q^{89} +45.9600 q^{90} -8.87508 q^{91} +23.3479 q^{92} -0.657792 q^{93} -36.7296 q^{94} -0.830584 q^{95} -67.2977 q^{96} -5.42734 q^{97} +7.72620 q^{98} -31.1805 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) \) 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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