LMFDB - Embedded newform 4031.2.a.b.1.10

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:	$1$
Dimension:	$59$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-2.00564 q^{2} +2.28170 q^{3} +2.02257 q^{4} -4.04874 q^{5} -4.57625 q^{6} -0.876531 q^{7} -0.0452719 q^{8} +2.20615 q^{9} +O(q^{10})$	\(q-2.00564 q^{2} +2.28170 q^{3} +2.02257 q^{4} -4.04874 q^{5} -4.57625 q^{6} -0.876531 q^{7} -0.0452719 q^{8} +2.20615 q^{9} +8.12030 q^{10} +0.376276 q^{11} +4.61490 q^{12} -0.557767 q^{13} +1.75800 q^{14} -9.23800 q^{15} -3.95435 q^{16} +1.05967 q^{17} -4.42472 q^{18} -1.91558 q^{19} -8.18887 q^{20} -1.99998 q^{21} -0.754672 q^{22} +2.31769 q^{23} -0.103297 q^{24} +11.3923 q^{25} +1.11868 q^{26} -1.81134 q^{27} -1.77285 q^{28} +1.00000 q^{29} +18.5281 q^{30} +1.87729 q^{31} +8.02152 q^{32} +0.858548 q^{33} -2.12531 q^{34} +3.54885 q^{35} +4.46209 q^{36} +9.78786 q^{37} +3.84195 q^{38} -1.27266 q^{39} +0.183294 q^{40} +9.58741 q^{41} +4.01123 q^{42} -6.82479 q^{43} +0.761045 q^{44} -8.93211 q^{45} -4.64845 q^{46} +1.94591 q^{47} -9.02262 q^{48} -6.23169 q^{49} -22.8488 q^{50} +2.41784 q^{51} -1.12812 q^{52} +1.94246 q^{53} +3.63288 q^{54} -1.52344 q^{55} +0.0396822 q^{56} -4.37077 q^{57} -2.00564 q^{58} -6.20295 q^{59} -18.6845 q^{60} -6.15824 q^{61} -3.76517 q^{62} -1.93375 q^{63} -8.17955 q^{64} +2.25825 q^{65} -1.72193 q^{66} -1.93736 q^{67} +2.14325 q^{68} +5.28828 q^{69} -7.11769 q^{70} +7.78073 q^{71} -0.0998764 q^{72} -15.7962 q^{73} -19.6309 q^{74} +25.9938 q^{75} -3.87440 q^{76} -0.329818 q^{77} +2.55248 q^{78} -1.28713 q^{79} +16.0101 q^{80} -10.7514 q^{81} -19.2289 q^{82} +1.61753 q^{83} -4.04510 q^{84} -4.29032 q^{85} +13.6880 q^{86} +2.28170 q^{87} -0.0170347 q^{88} +13.6733 q^{89} +17.9146 q^{90} +0.488900 q^{91} +4.68770 q^{92} +4.28342 q^{93} -3.90278 q^{94} +7.75568 q^{95} +18.3027 q^{96} -2.14252 q^{97} +12.4985 q^{98} +0.830119 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) $ 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9	\( 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9} - 18 q^{10} - 27 q^{11} - 8 q^{12} - 22 q^{13} - 24 q^{14} - 18 q^{15} + 5 q^{16} - 23 q^{17} + q^{18} - 32 q^{19} - 14 q^{20} - 36 q^{21} - 6 q^{22} - 3 q^{23} - 18 q^{24} - 8 q^{25} - q^{26} - 12 q^{27} - 9 q^{28} + 59 q^{29} - 18 q^{30} - 32 q^{31} - 39 q^{32} - 12 q^{33} - 18 q^{34} - 9 q^{35} + 10 q^{36} - 44 q^{37} + 5 q^{38} - 27 q^{39} - 68 q^{40} - 44 q^{41} - 25 q^{42} - 40 q^{43} - 56 q^{44} - 39 q^{45} - 40 q^{46} - 20 q^{47} - 9 q^{48} - 39 q^{49} - 21 q^{50} - 28 q^{51} - 49 q^{52} - 31 q^{53} - 32 q^{54} - 32 q^{55} - 48 q^{56} - 58 q^{57} - 5 q^{58} + 6 q^{59} - 44 q^{60} - 88 q^{61} + 35 q^{62} - 22 q^{63} - 10 q^{64} - 43 q^{65} - 31 q^{66} - 45 q^{67} - 29 q^{68} - 60 q^{69} - 14 q^{70} - 20 q^{71} - 4 q^{72} - 90 q^{73} - 25 q^{74} + 15 q^{75} - 64 q^{76} - 39 q^{77} - 28 q^{78} - 120 q^{79} + 24 q^{80} - 77 q^{81} - 71 q^{82} - 33 q^{83} - 14 q^{84} - 71 q^{85} - 61 q^{86} - 6 q^{87} - 34 q^{88} - 78 q^{89} - 88 q^{90} - 28 q^{91} - 31 q^{92} - 36 q^{93} - 4 q^{94} - 12 q^{95} - 29 q^{96} - 48 q^{97} - 4 q^{98} - 43 q^{99}+O(q^{100}) \) 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9 - 18 * q^10 - 27 * q^11 - 8 * q^12 - 22 * q^13 - 24 * q^14 - 18 * q^15 + 5 * q^16 - 23 * q^17 + q^18 - 32 * q^19 - 14 * q^20 - 36 * q^21 - 6 * q^22 - 3 * q^23 - 18 * q^24 - 8 * q^25 - q^26 - 12 * q^27 - 9 * q^28 + 59 * q^29 - 18 * q^30 - 32 * q^31 - 39 * q^32 - 12 * q^33 - 18 * q^34 - 9 * q^35 + 10 * q^36 - 44 * q^37 + 5 * q^38 - 27 * q^39 - 68 * q^40 - 44 * q^41 - 25 * q^42 - 40 * q^43 - 56 * q^44 - 39 * q^45 - 40 * q^46 - 20 * q^47 - 9 * q^48 - 39 * q^49 - 21 * q^50 - 28 * q^51 - 49 * q^52 - 31 * q^53 - 32 * q^54 - 32 * q^55 - 48 * q^56 - 58 * q^57 - 5 * q^58 + 6 * q^59 - 44 * q^60 - 88 * q^61 + 35 * q^62 - 22 * q^63 - 10 * q^64 - 43 * q^65 - 31 * q^66 - 45 * q^67 - 29 * q^68 - 60 * q^69 - 14 * q^70 - 20 * q^71 - 4 * q^72 - 90 * q^73 - 25 * q^74 + 15 * q^75 - 64 * q^76 - 39 * q^77 - 28 * q^78 - 120 * q^79 + 24 * q^80 - 77 * q^81 - 71 * q^82 - 33 * q^83 - 14 * q^84 - 71 * q^85 - 61 * q^86 - 6 * q^87 - 34 * q^88 - 78 * q^89 - 88 * q^90 - 28 * q^91 - 31 * q^92 - 36 * q^93 - 4 * q^94 - 12 * q^95 - 29 * q^96 - 48 * q^97 - 4 * q^98 - 43 * 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 $

$2$	−2.00564	−1.41820	−0.709099	−	0.705109i	$-0.750898\pi$
$2$	−2.00564	−1.41820	−0.709099	+	0.705109i	$0.750898\pi$
$3$	2.28170	1.31734	0.658669	−	0.752432i	$-0.271120\pi$
$3$	2.28170	1.31734	0.658669	+	0.752432i	$0.271120\pi$
$4$	2.02257	1.01129
$5$	−4.04874	−1.81065	−0.905326	−	0.424718i	$-0.860373\pi$
$5$	−4.04874	−1.81065	−0.905326	+	0.424718i	$0.860373\pi$
$6$	−4.57625	−1.86825
$7$	−0.876531	−0.331298	−0.165649	−	0.986185i	$-0.552972\pi$
$7$	−0.876531	−0.331298	−0.165649	+	0.986185i	$0.552972\pi$
$8$	−0.0452719	−0.0160060
$9$	2.20615	0.735382
$10$	8.12030	2.56786
$11$	0.376276	0.113451	0.0567257	−	0.998390i	$-0.481934\pi$
$11$	0.376276	0.113451	0.0567257	+	0.998390i	$0.481934\pi$
$12$	4.61490	1.33221
$13$	−0.557767	−0.154697	−0.0773483	−	0.997004i	$-0.524645\pi$
$13$	−0.557767	−0.154697	−0.0773483	+	0.997004i	$0.524645\pi$
$14$	1.75800	0.469846
$15$	−9.23800	−2.38524
$16$	−3.95435	−0.988586
$17$	1.05967	0.257007	0.128503	−	0.991709i	$-0.458983\pi$
$17$	1.05967	0.257007	0.128503	+	0.991709i	$0.458983\pi$
$18$	−4.42472	−1.04292
$19$	−1.91558	−0.439464	−0.219732	−	0.975560i	$-0.570518\pi$
$19$	−1.91558	−0.439464	−0.219732	+	0.975560i	$0.570518\pi$
$20$	−8.18887	−1.83109
$21$	−1.99998	−0.436431
$22$	−0.754672	−0.160897
$23$	2.31769	0.483273	0.241636	−	0.970367i	$-0.422316\pi$
$23$	2.31769	0.483273	0.241636	+	0.970367i	$0.422316\pi$
$24$	−0.103297	−0.0210854
$25$	11.3923	2.27846
$26$	1.11868	0.219391
$27$	−1.81134	−0.348592
$28$	−1.77285	−0.335037
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	18.5281	3.38275
$31$	1.87729	0.337172	0.168586	−	0.985687i	$-0.446080\pi$
$31$	1.87729	0.337172	0.168586	+	0.985687i	$0.446080\pi$
$32$	8.02152	1.41802
$33$	0.858548	0.149454
$34$	−2.12531	−0.364487
$35$	3.54885	0.599864
$36$	4.46209	0.743681
$37$	9.78786	1.60911	0.804557	−	0.593875i	$-0.202403\pi$
$37$	9.78786	1.60911	0.804557	+	0.593875i	$0.202403\pi$
$38$	3.84195	0.623247
$39$	−1.27266	−0.203788
$40$	0.183294	0.0289813
$41$	9.58741	1.49730	0.748651	−	0.662964i	$-0.230702\pi$
$41$	9.58741	1.49730	0.748651	+	0.662964i	$0.230702\pi$
$42$	4.01123	0.618946
$43$	−6.82479	−1.04077	−0.520385	−	0.853932i	$-0.674212\pi$
$43$	−6.82479	−1.04077	−0.520385	+	0.853932i	$0.674212\pi$
$44$	0.761045	0.114732
$45$	−8.93211	−1.33152
$46$	−4.64845	−0.685376
$47$	1.94591	0.283839	0.141920	−	0.989878i	$-0.454673\pi$
$47$	1.94591	0.283839	0.141920	+	0.989878i	$0.454673\pi$
$48$	−9.02262	−1.30230
$49$	−6.23169	−0.890242
$50$	−22.8488	−3.23131
$51$	2.41784	0.338565
$52$	−1.12812	−0.156443
$53$	1.94246	0.266818	0.133409	−	0.991061i	$-0.457408\pi$
$53$	1.94246	0.266818	0.133409	+	0.991061i	$0.457408\pi$
$54$	3.63288	0.494372
$55$	−1.52344	−0.205421
$56$	0.0396822	0.00530276
$57$	−4.37077	−0.578923
$58$	−2.00564	−0.263353
$59$	−6.20295	−0.807556	−0.403778	−	0.914857i	$-0.632303\pi$
$59$	−6.20295	−0.807556	−0.403778	+	0.914857i	$0.632303\pi$
$60$	−18.6845	−2.41216
$61$	−6.15824	−0.788481	−0.394241	−	0.919007i	$-0.628992\pi$
$61$	−6.15824	−0.788481	−0.394241	+	0.919007i	$0.628992\pi$
$62$	−3.76517	−0.478177
$63$	−1.93375	−0.243630
$64$	−8.17955	−1.02244
$65$	2.25825	0.280102
$66$	−1.72193	−0.211955
$67$	−1.93736	−0.236686	−0.118343	−	0.992973i	$-0.537758\pi$
$67$	−1.93736	−0.236686	−0.118343	+	0.992973i	$0.537758\pi$
$68$	2.14325	0.259908
$69$	5.28828	0.636634
$70$	−7.11769	−0.850727
$71$	7.78073	0.923403	0.461701	−	0.887035i	$-0.347239\pi$
$71$	7.78073	0.923403	0.461701	+	0.887035i	$0.347239\pi$
$72$	−0.0998764	−0.0117705
$73$	−15.7962	−1.84881	−0.924404	−	0.381416i	$-0.875437\pi$
$73$	−15.7962	−1.84881	−0.924404	+	0.381416i	$0.875437\pi$
$74$	−19.6309	−2.28204
$75$	25.9938	3.00150
$76$	−3.87440	−0.444424
$77$	−0.329818	−0.0375862
$78$	2.55248	0.289012
$79$	−1.28713	−0.144813	−0.0724065	−	0.997375i	$-0.523068\pi$
$79$	−1.28713	−0.144813	−0.0724065	+	0.997375i	$0.523068\pi$
$80$	16.0101	1.78999
$81$	−10.7514	−1.19460
$82$	−19.2289	−2.12347
$83$	1.61753	0.177547	0.0887734	−	0.996052i	$-0.471705\pi$
$83$	1.61753	0.177547	0.0887734	+	0.996052i	$0.471705\pi$
$84$	−4.04510	−0.441357
$85$	−4.29032	−0.465350
$86$	13.6880	1.47602
$87$	2.28170	0.244624
$88$	−0.0170347	−0.00181591
$89$	13.6733	1.44937	0.724684	−	0.689081i	$-0.241986\pi$
$89$	13.6733	1.44937	0.724684	+	0.689081i	$0.241986\pi$
$90$	17.9146	1.88836
$91$	0.488900	0.0512506
$92$	4.68770	0.488727
$93$	4.28342	0.444170
$94$	−3.90278	−0.402541
$95$	7.75568	0.795716
$96$	18.3027	1.86801
$97$	−2.14252	−0.217540	−0.108770	−	0.994067i	$-0.534691\pi$
$97$	−2.14252	−0.217540	−0.108770	+	0.994067i	$0.534691\pi$
$98$	12.4985	1.26254
$99$	0.830119	0.0834301
$100$	23.0417	2.30417
$101$	−9.67312	−0.962511	−0.481256	−	0.876580i	$-0.659819\pi$
$101$	−9.67312	−0.962511	−0.481256	+	0.876580i	$0.659819\pi$
$102$	−4.84930	−0.480153
$103$	1.35737	0.133745	0.0668727	−	0.997762i	$-0.478698\pi$
$103$	1.35737	0.133745	0.0668727	+	0.997762i	$0.478698\pi$
$104$	0.0252512	0.00247608
$105$	8.09739	0.790225
$106$	−3.89587	−0.378400
$107$	4.71193	0.455519	0.227760	−	0.973717i	$-0.426860\pi$
$107$	4.71193	0.455519	0.227760	+	0.973717i	$0.426860\pi$
$108$	−3.66356	−0.352526
$109$	2.34541	0.224649	0.112325	−	0.993672i	$-0.464170\pi$
$109$	2.34541	0.224649	0.112325	+	0.993672i	$0.464170\pi$
$110$	3.05547	0.291328
$111$	22.3329	2.11975
$112$	3.46611	0.327516
$113$	−4.55646	−0.428636	−0.214318	−	0.976764i	$-0.568753\pi$
$113$	−4.55646	−0.428636	−0.214318	+	0.976764i	$0.568753\pi$
$114$	8.76618	0.821028
$115$	−9.38374	−0.875038
$116$	2.02257	0.187791
$117$	−1.23051	−0.113761
$118$	12.4409	1.14527
$119$	−0.928831	−0.0851458
$120$	0.418222	0.0381783
$121$	−10.8584	−0.987129
$122$	12.3512	1.11822
$123$	21.8756	1.97245
$124$	3.79696	0.340978
$125$	−25.8807	−2.31484
$126$	3.87841	0.345516
$127$	−4.48376	−0.397869	−0.198935	−	0.980013i	$-0.563748\pi$
$127$	−4.48376	−0.397869	−0.198935	+	0.980013i	$0.563748\pi$
$128$	0.362152	0.0320100
$129$	−15.5721	−1.37105
$130$	−4.52923	−0.397240
$131$	4.69438	0.410150	0.205075	−	0.978746i	$-0.434256\pi$
$131$	4.69438	0.410150	0.205075	+	0.978746i	$0.434256\pi$
$132$	1.73648	0.151141
$133$	1.67906	0.145593
$134$	3.88563	0.335668
$135$	7.33363	0.631178
$136$	−0.0479731	−0.00411366
$137$	−20.7024	−1.76873	−0.884364	−	0.466799i	$-0.845407\pi$
$137$	−20.7024	−1.76873	−0.884364	+	0.466799i	$0.845407\pi$
$138$	−10.6064	−0.902873
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	7.17780	0.606635
$141$	4.43997	0.373913
$142$	−15.6053	−1.30957
$143$	−0.209874	−0.0175506
$144$	−8.72386	−0.726988
$145$	−4.04874	−0.336230
$146$	31.6814	2.62198
$147$	−14.2188	−1.17275
$148$	19.7967	1.62728
$149$	7.30811	0.598704	0.299352	−	0.954143i	$-0.403230\pi$
$149$	7.30811	0.598704	0.299352	+	0.954143i	$0.403230\pi$
$150$	−52.1340	−4.25673
$151$	−3.91146	−0.318310	−0.159155	−	0.987254i	$-0.550877\pi$
$151$	−3.91146	−0.318310	−0.159155	+	0.987254i	$0.550877\pi$
$152$	0.0867219	0.00703407
$153$	2.33778	0.188998
$154$	0.661494	0.0533047
$155$	−7.60068	−0.610501
$156$	−2.57404	−0.206088
$157$	−0.904909	−0.0722196	−0.0361098	−	0.999348i	$-0.511497\pi$
$157$	−0.904909	−0.0722196	−0.0361098	+	0.999348i	$0.511497\pi$
$158$	2.58151	0.205374
$159$	4.43211	0.351489
$160$	−32.4770	−2.56754
$161$	−2.03153	−0.160107
$162$	21.5633	1.69417
$163$	−6.47136	−0.506876	−0.253438	−	0.967352i	$-0.581561\pi$
$163$	−6.47136	−0.506876	−0.253438	+	0.967352i	$0.581561\pi$
$164$	19.3912	1.51420
$165$	−3.47604	−0.270609
$166$	−3.24417	−0.251796
$167$	−10.5062	−0.812993	−0.406497	−	0.913652i	$-0.633250\pi$
$167$	−10.5062	−0.812993	−0.406497	+	0.913652i	$0.633250\pi$
$168$	0.0905428	0.00698553
$169$	−12.6889	−0.976069
$170$	8.60481	0.659959
$171$	−4.22605	−0.323174
$172$	−13.8036	−1.05252
$173$	6.87546	0.522732	0.261366	−	0.965240i	$-0.415827\pi$
$173$	6.87546	0.522732	0.261366	+	0.965240i	$0.415827\pi$
$174$	−4.57625	−0.346925
$175$	−9.98570	−0.754848
$176$	−1.48793	−0.112157
$177$	−14.1533	−1.06382
$178$	−27.4237	−2.05549
$179$	−6.66208	−0.497947	−0.248974	−	0.968510i	$-0.580093\pi$
$179$	−6.66208	−0.497947	−0.248974	+	0.968510i	$0.580093\pi$
$180$	−18.0658	−1.34655
$181$	−1.22984	−0.0914131	−0.0457065	−	0.998955i	$-0.514554\pi$
$181$	−1.22984	−0.0914131	−0.0457065	+	0.998955i	$0.514554\pi$
$182$	−0.980555	−0.0726835
$183$	−14.0512	−1.03870
$184$	−0.104926	−0.00773528
$185$	−39.6285	−2.91355
$186$	−8.59098	−0.629921
$187$	0.398727	0.0291578
$188$	3.93573	0.287043
$189$	1.58769	0.115488
$190$	−15.5551	−1.12848
$191$	11.2577	0.814581	0.407291	−	0.913299i	$-0.366474\pi$
$191$	11.2577	0.814581	0.407291	+	0.913299i	$0.366474\pi$
$192$	−18.6633	−1.34690
$193$	−3.45403	−0.248627	−0.124313	−	0.992243i	$-0.539673\pi$
$193$	−3.45403	−0.248627	−0.124313	+	0.992243i	$0.539673\pi$
$194$	4.29712	0.308515
$195$	5.15265	0.368989
$196$	−12.6041	−0.900289
$197$	−17.6654	−1.25860	−0.629302	−	0.777161i	$-0.716659\pi$
$197$	−17.6654	−1.25860	−0.629302	+	0.777161i	$0.716659\pi$
$198$	−1.66492	−0.118320
$199$	−20.7509	−1.47099	−0.735496	−	0.677529i	$-0.763051\pi$
$199$	−20.7509	−1.47099	−0.735496	+	0.677529i	$0.763051\pi$
$200$	−0.515751	−0.0364691
$201$	−4.42047	−0.311796
$202$	19.4007	1.36503
$203$	−0.876531	−0.0615204
$204$	4.89026	0.342386
$205$	−38.8169	−2.71109
$206$	−2.72239	−0.189678
$207$	5.11317	0.355390
$208$	2.20560	0.152931
$209$	−0.720786	−0.0498578
$210$	−16.2404	−1.12070
$211$	8.41967	0.579634	0.289817	−	0.957082i	$-0.406406\pi$
$211$	8.41967	0.579634	0.289817	+	0.957082i	$0.406406\pi$
$212$	3.92877	0.269829
$213$	17.7533	1.21643
$214$	−9.45041	−0.646017
$215$	27.6318	1.88447
$216$	0.0820026	0.00557957
$217$	−1.64551	−0.111704
$218$	−4.70403	−0.318597
$219$	−36.0422	−2.43551
$220$	−3.08127	−0.207740
$221$	−0.591047	−0.0397581
$222$	−44.7917	−3.00623
$223$	6.23327	0.417411	0.208705	−	0.977979i	$-0.433075\pi$
$223$	6.23327	0.417411	0.208705	+	0.977979i	$0.433075\pi$
$224$	−7.03111	−0.469786
$225$	25.1331	1.67554
$226$	9.13860	0.607891
$227$	−14.1080	−0.936382	−0.468191	−	0.883627i	$-0.655094\pi$
$227$	−14.1080	−0.936382	−0.468191	+	0.883627i	$0.655094\pi$
$228$	−8.84020	−0.585457
$229$	12.6651	0.836933	0.418466	−	0.908232i	$-0.362568\pi$
$229$	12.6651	0.836933	0.418466	+	0.908232i	$0.362568\pi$
$230$	18.8204	1.24098
$231$	−0.752544	−0.0495138
$232$	−0.0452719	−0.00297225
$233$	24.5196	1.60633	0.803167	−	0.595754i	$-0.203147\pi$
$233$	24.5196	1.60633	0.803167	+	0.595754i	$0.203147\pi$
$234$	2.46796	0.161336
$235$	−7.87846	−0.513934
$236$	−12.5459	−0.816670
$237$	−2.93683	−0.190768
$238$	1.86290	0.120754
$239$	−0.311857	−0.0201724	−0.0100862	−	0.999949i	$-0.503211\pi$
$239$	−0.311857	−0.0201724	−0.0100862	+	0.999949i	$0.503211\pi$
$240$	36.5303	2.35802
$241$	−13.9508	−0.898652	−0.449326	−	0.893368i	$-0.648336\pi$
$241$	−13.9508	−0.898652	−0.449326	+	0.893368i	$0.648336\pi$
$242$	21.7780	1.39994
$243$	−19.0973	−1.22510
$244$	−12.4555	−0.797380
$245$	25.2305	1.61192
$246$	−43.8744	−2.79733
$247$	1.06845	0.0679836
$248$	−0.0849887	−0.00539679
$249$	3.69071	0.233889
$250$	51.9073	3.28291
$251$	−21.7918	−1.37549	−0.687743	−	0.725954i	$-0.741398\pi$
$251$	−21.7918	−1.37549	−0.687743	+	0.725954i	$0.741398\pi$
$252$	−3.91116	−0.246380
$253$	0.872093	0.0548280
$254$	8.99278	0.564257
$255$	−9.78921	−0.613024
$256$	15.6328	0.977047
$257$	−7.26433	−0.453137	−0.226568	−	0.973995i	$-0.572751\pi$
$257$	−7.26433	−0.453137	−0.226568	+	0.973995i	$0.572751\pi$
$258$	31.2320	1.94442
$259$	−8.57936	−0.533096
$260$	4.56748	0.283263
$261$	2.20615	0.136557
$262$	−9.41521	−0.581673
$263$	−22.1108	−1.36341	−0.681704	−	0.731628i	$-0.738761\pi$
$263$	−22.1108	−1.36341	−0.681704	+	0.731628i	$0.738761\pi$
$264$	−0.0388681	−0.00239217
$265$	−7.86452	−0.483114
$266$	−3.36759	−0.206480
$267$	31.1984	1.90931
$268$	−3.91845	−0.239357
$269$	8.94753	0.545540	0.272770	−	0.962079i	$-0.412060\pi$
$269$	8.94753	0.545540	0.272770	+	0.962079i	$0.412060\pi$
$270$	−14.7086	−0.895136
$271$	6.06943	0.368692	0.184346	−	0.982861i	$-0.440983\pi$
$271$	6.06943	0.368692	0.184346	+	0.982861i	$0.440983\pi$
$272$	−4.19029	−0.254074
$273$	1.11552	0.0675144
$274$	41.5215	2.50841
$275$	4.28665	0.258495
$276$	10.6959	0.643819
$277$	−6.03173	−0.362411	−0.181206	−	0.983445i	$-0.558000\pi$
$277$	−6.03173	−0.362411	−0.181206	+	0.983445i	$0.558000\pi$
$278$	−2.00564	−0.120290
$279$	4.14159	0.247950
$280$	−0.160663	−0.00960145
$281$	−16.7564	−0.999600	−0.499800	−	0.866141i	$-0.666593\pi$
$281$	−16.7564	−0.999600	−0.499800	+	0.866141i	$0.666593\pi$
$282$	−8.90496	−0.530282
$283$	7.73804	0.459979	0.229989	−	0.973193i	$-0.426131\pi$
$283$	7.73804	0.459979	0.229989	+	0.973193i	$0.426131\pi$
$284$	15.7371	0.933824
$285$	17.6961	1.04823
$286$	0.420931	0.0248902
$287$	−8.40366	−0.496053
$288$	17.6966	1.04278
$289$	−15.8771	−0.933947
$290$	8.12030	0.476840
$291$	−4.88859	−0.286574
$292$	−31.9490	−1.86967
$293$	16.9061	0.987665	0.493832	−	0.869557i	$-0.335596\pi$
$293$	16.9061	0.987665	0.493832	+	0.869557i	$0.335596\pi$
$294$	28.5178	1.66319
$295$	25.1141	1.46220
$296$	−0.443115	−0.0257555
$297$	−0.681562	−0.0395483
$298$	−14.6574	−0.849081
$299$	−1.29273	−0.0747607
$300$	52.5743	3.03538
$301$	5.98214	0.344805
$302$	7.84496	0.451426
$303$	−22.0711	−1.26795
$304$	7.57486	0.434448
$305$	24.9331	1.42766
$306$	−4.68873	−0.268037
$307$	10.8432	0.618851	0.309426	−	0.950924i	$-0.399863\pi$
$307$	10.8432	0.618851	0.309426	+	0.950924i	$0.399863\pi$
$308$	−0.667080	−0.0380104
$309$	3.09710	0.176188
$310$	15.2442	0.865812
$311$	−17.9278	−1.01659	−0.508296	−	0.861183i	$-0.669724\pi$
$311$	−17.9278	−1.01659	−0.508296	+	0.861183i	$0.669724\pi$
$312$	0.0576155	0.00326184
$313$	−18.4606	−1.04345	−0.521726	−	0.853113i	$-0.674712\pi$
$313$	−18.4606	−1.04345	−0.521726	+	0.853113i	$0.674712\pi$
$314$	1.81492	0.102422
$315$	7.82927	0.441129
$316$	−2.60331	−0.146447
$317$	−12.5262	−0.703541	−0.351770	−	0.936086i	$-0.614420\pi$
$317$	−12.5262	−0.703541	−0.351770	+	0.936086i	$0.614420\pi$
$318$	−8.88919	−0.498481
$319$	0.376276	0.0210674
$320$	33.1169	1.85129
$321$	10.7512	0.600073
$322$	4.07451	0.227064
$323$	−2.02988	−0.112945
$324$	−21.7454	−1.20808
$325$	−6.35424	−0.352470
$326$	12.9792	0.718850
$327$	5.35151	0.295939
$328$	−0.434040	−0.0239659
$329$	−1.70565	−0.0940353
$330$	6.97166	0.383777
$331$	18.1960	1.00014	0.500070	−	0.865985i	$-0.333308\pi$
$331$	18.1960	1.00014	0.500070	+	0.865985i	$0.333308\pi$
$332$	3.27157	0.179551
$333$	21.5934	1.18331
$334$	21.0716	1.15299
$335$	7.84386	0.428556
$336$	7.90861	0.431450
$337$	−15.9942	−0.871261	−0.435631	−	0.900126i	$-0.643475\pi$
$337$	−15.9942	−0.871261	−0.435631	+	0.900126i	$0.643475\pi$
$338$	25.4493	1.38426
$339$	−10.3965	−0.564659
$340$	−8.67747	−0.470602
$341$	0.706381	0.0382527
$342$	8.47591	0.458324
$343$	11.5980	0.626232
$344$	0.308971	0.0166586
$345$	−21.4109	−1.15272
$346$	−13.7897	−0.741337
$347$	−4.62680	−0.248380	−0.124190	−	0.992258i	$-0.539633\pi$
$347$	−4.62680	−0.248380	−0.124190	+	0.992258i	$0.539633\pi$
$348$	4.61490	0.247385
$349$	−9.51176	−0.509153	−0.254576	−	0.967053i	$-0.581936\pi$
$349$	−9.51176	−0.509153	−0.254576	+	0.967053i	$0.581936\pi$
$350$	20.0277	1.07052
$351$	1.01030	0.0539260
$352$	3.01830	0.160876
$353$	4.63035	0.246449	0.123224	−	0.992379i	$-0.460677\pi$
$353$	4.63035	0.246449	0.123224	+	0.992379i	$0.460677\pi$
$354$	28.3863	1.50871
$355$	−31.5021	−1.67196
$356$	27.6553	1.46573
$357$	−2.11931	−0.112166
$358$	13.3617	0.706188
$359$	−30.7262	−1.62167	−0.810834	−	0.585276i	$-0.800986\pi$
$359$	−30.7262	−1.62167	−0.810834	+	0.585276i	$0.800986\pi$
$360$	0.404373	0.0213124
$361$	−15.3306	−0.806871
$362$	2.46660	0.129642
$363$	−24.7756	−1.30038
$364$	0.988835	0.0518290
$365$	63.9548	3.34755
$366$	28.1816	1.47308
$367$	9.95885	0.519848	0.259924	−	0.965629i	$-0.416303\pi$
$367$	9.95885	0.519848	0.259924	+	0.965629i	$0.416303\pi$
$368$	−9.16497	−0.477757
$369$	21.1512	1.10109
$370$	79.4803	4.13199
$371$	−1.70263	−0.0883960
$372$	8.66353	0.449183
$373$	−15.7559	−0.815812	−0.407906	−	0.913024i	$-0.633741\pi$
$373$	−15.7559	−0.815812	−0.407906	+	0.913024i	$0.633741\pi$
$374$	−0.799701	−0.0413516
$375$	−59.0520	−3.04943
$376$	−0.0880948	−0.00454314
$377$	−0.557767	−0.0287264
$378$	−3.18433	−0.163784
$379$	4.24937	0.218275	0.109138	−	0.994027i	$-0.465191\pi$
$379$	4.24937	0.218275	0.109138	+	0.994027i	$0.465191\pi$
$380$	15.6864	0.804697
$381$	−10.2306	−0.524129
$382$	−22.5789	−1.15524
$383$	20.3043	1.03750	0.518750	−	0.854926i	$-0.326397\pi$
$383$	20.3043	1.03750	0.518750	+	0.854926i	$0.326397\pi$
$384$	0.826322	0.0421681
$385$	1.33535	0.0680555
$386$	6.92753	0.352602
$387$	−15.0565	−0.765363
$388$	−4.33341	−0.219996
$389$	24.0872	1.22127	0.610634	−	0.791913i	$-0.290914\pi$
$389$	24.0872	1.22127	0.610634	+	0.791913i	$0.290914\pi$
$390$	−10.3343	−0.523299
$391$	2.45598	0.124204
$392$	0.282121	0.0142492
$393$	10.7112	0.540306
$394$	35.4303	1.78495
$395$	5.21124	0.262206
$396$	1.67898	0.0843718
$397$	18.1930	0.913079	0.456539	−	0.889703i	$-0.349089\pi$
$397$	18.1930	0.913079	0.456539	+	0.889703i	$0.349089\pi$
$398$	41.6187	2.08616
$399$	3.83112	0.191796
$400$	−45.0491	−2.25245
$401$	−12.7846	−0.638434	−0.319217	−	0.947682i	$-0.603420\pi$
$401$	−12.7846	−0.638434	−0.319217	+	0.947682i	$0.603420\pi$
$402$	8.86584	0.442188
$403$	−1.04709	−0.0521594
$404$	−19.5646	−0.973374
$405$	43.5295	2.16300
$406$	1.75800	0.0872481
$407$	3.68294	0.182556
$408$	−0.109460	−0.00541909
$409$	7.83467	0.387400	0.193700	−	0.981061i	$-0.437951\pi$
$409$	7.83467	0.387400	0.193700	+	0.981061i	$0.437951\pi$
$410$	77.8526	3.84487
$411$	−47.2367	−2.33001
$412$	2.74538	0.135255
$413$	5.43708	0.267541
$414$	−10.2552	−0.504013
$415$	−6.54895	−0.321475
$416$	−4.47414	−0.219363
$417$	2.28170	0.111735
$418$	1.44563	0.0707083
$419$	−5.62286	−0.274695	−0.137347	−	0.990523i	$-0.543858\pi$
$419$	−5.62286	−0.274695	−0.137347	+	0.990523i	$0.543858\pi$
$420$	16.3776	0.799143
$421$	−0.635736	−0.0309839	−0.0154919	−	0.999880i	$-0.504931\pi$
$421$	−0.635736	−0.0309839	−0.0154919	+	0.999880i	$0.504931\pi$
$422$	−16.8868	−0.822036
$423$	4.29295	0.208730
$424$	−0.0879389	−0.00427069
$425$	12.0720	0.585580
$426$	−35.6066	−1.72514
$427$	5.39788	0.261222
$428$	9.53022	0.460660
$429$	−0.478870	−0.0231200
$430$	−55.4193	−2.67255
$431$	−39.0272	−1.87988	−0.939938	−	0.341346i	$-0.889117\pi$
$431$	−39.0272	−1.87988	−0.939938	+	0.341346i	$0.889117\pi$
$432$	7.16265	0.344613
$433$	−21.7415	−1.04483	−0.522414	−	0.852692i	$-0.674969\pi$
$433$	−21.7415	−1.04483	−0.522414	+	0.852692i	$0.674969\pi$
$434$	3.30029	0.158419
$435$	−9.23800	−0.442928
$436$	4.74375	0.227185
$437$	−4.43973	−0.212381
$438$	72.2875	3.45403
$439$	−10.6178	−0.506760	−0.253380	−	0.967367i	$-0.581542\pi$
$439$	−10.6178	−0.506760	−0.253380	+	0.967367i	$0.581542\pi$
$440$	0.0689692	0.00328798
$441$	−13.7480	−0.654668
$442$	1.18542	0.0563849
$443$	−4.73316	−0.224879	−0.112440	−	0.993659i	$-0.535866\pi$
$443$	−4.73316	−0.224879	−0.112440	+	0.993659i	$0.535866\pi$
$444$	45.1700	2.14367
$445$	−55.3597	−2.62430
$446$	−12.5017	−0.591971
$447$	16.6749	0.788696
$448$	7.16963	0.338733
$449$	22.4033	1.05728	0.528639	−	0.848847i	$-0.322703\pi$
$449$	22.4033	1.05728	0.528639	+	0.848847i	$0.322703\pi$
$450$	−50.4077	−2.37624
$451$	3.60751	0.169871
$452$	−9.21577	−0.433474
$453$	−8.92476	−0.419322
$454$	28.2955	1.32798
$455$	−1.97943	−0.0927970
$456$	0.197873	0.00926626
$457$	−33.3201	−1.55865	−0.779325	−	0.626620i	$-0.784438\pi$
$457$	−33.3201	−1.55865	−0.779325	+	0.626620i	$0.784438\pi$
$458$	−25.4015	−1.18694
$459$	−1.91941	−0.0895906
$460$	−18.9793	−0.884914
$461$	13.2002	0.614797	0.307398	−	0.951581i	$-0.400542\pi$
$461$	13.2002	0.614797	0.307398	+	0.951581i	$0.400542\pi$
$462$	1.50933	0.0702203
$463$	−0.832633	−0.0386957	−0.0193479	−	0.999813i	$-0.506159\pi$
$463$	−0.832633	−0.0386957	−0.0193479	+	0.999813i	$0.506159\pi$
$464$	−3.95435	−0.183576
$465$	−17.3425	−0.804237
$466$	−49.1774	−2.27810
$467$	34.9893	1.61911	0.809556	−	0.587043i	$-0.199708\pi$
$467$	34.9893	1.61911	0.809556	+	0.587043i	$0.199708\pi$
$468$	−2.48880	−0.115045
$469$	1.69815	0.0784135
$470$	15.8013	0.728861
$471$	−2.06473	−0.0951376
$472$	0.280819	0.0129258
$473$	−2.56800	−0.118077
$474$	5.89022	0.270547
$475$	−21.8228	−1.00130
$476$	−1.87863	−0.0861068
$477$	4.28535	0.196213
$478$	0.625472	0.0286084
$479$	32.0686	1.46525	0.732627	−	0.680631i	$-0.238294\pi$
$479$	32.0686	1.46525	0.732627	+	0.680631i	$0.238294\pi$
$480$	−74.1028	−3.38231
$481$	−5.45934	−0.248925
$482$	27.9803	1.27447
$483$	−4.63534	−0.210915
$484$	−21.9619	−0.998270
$485$	8.67452	0.393890
$486$	38.3023	1.73743
$487$	−18.6729	−0.846151	−0.423076	−	0.906094i	$-0.639050\pi$
$487$	−18.6729	−0.846151	−0.423076	+	0.906094i	$0.639050\pi$
$488$	0.278795	0.0126205
$489$	−14.7657	−0.667727
$490$	−50.6032	−2.28602
$491$	−2.92788	−0.132133	−0.0660666	−	0.997815i	$-0.521045\pi$
$491$	−2.92788	−0.132133	−0.0660666	+	0.997815i	$0.521045\pi$
$492$	44.2449	1.99472
$493$	1.05967	0.0477250
$494$	−2.14291	−0.0964142
$495$	−3.36094	−0.151063
$496$	−7.42347	−0.333324
$497$	−6.82005	−0.305921
$498$	−7.40222	−0.331701
$499$	−8.53759	−0.382195	−0.191098	−	0.981571i	$-0.561205\pi$
$499$	−8.53759	−0.382195	−0.191098	+	0.981571i	$0.561205\pi$
$500$	−52.3457	−2.34097
$501$	−23.9719	−1.07099
$502$	43.7064	1.95071
$503$	2.72561	0.121529	0.0607645	−	0.998152i	$-0.480646\pi$
$503$	2.72561	0.121529	0.0607645	+	0.998152i	$0.480646\pi$
$504$	0.0875447	0.00389955
$505$	39.1639	1.74277
$506$	−1.74910	−0.0777570
$507$	−28.9522	−1.28581
$508$	−9.06872	−0.402360
$509$	10.7190	0.475112	0.237556	−	0.971374i	$-0.423654\pi$
$509$	10.7190	0.475112	0.237556	+	0.971374i	$0.423654\pi$
$510$	19.6336	0.869389
$511$	13.8459	0.612505
$512$	−32.0779	−1.41766
$513$	3.46976	0.153194
$514$	14.5696	0.642638
$515$	−5.49563	−0.242166
$516$	−31.4957	−1.38652
$517$	0.732197	0.0322020
$518$	17.2071	0.756035
$519$	15.6877	0.688615
$520$	−0.102235	−0.00448332
$521$	−39.5819	−1.73412	−0.867058	−	0.498208i	$-0.833992\pi$
$521$	−39.5819	−1.73412	−0.867058	+	0.498208i	$0.833992\pi$
$522$	−4.42472	−0.193665
$523$	−18.3216	−0.801146	−0.400573	−	0.916265i	$-0.631189\pi$
$523$	−18.3216	−0.801146	−0.400573	+	0.916265i	$0.631189\pi$
$524$	9.49472	0.414779
$525$	−22.7843	−0.994390
$526$	44.3461	1.93358
$527$	1.98931	0.0866556
$528$	−3.39500	−0.147748
$529$	−17.6283	−0.766447
$530$	15.7734	0.685151
$531$	−13.6846	−0.593862
$532$	3.39603	0.147237
$533$	−5.34754	−0.231628
$534$	−62.5725	−2.70778
$535$	−19.0774	−0.824787
$536$	0.0877079	0.00378840
$537$	−15.2008	−0.655965
$538$	−17.9455	−0.773684
$539$	−2.34484	−0.100999
$540$	14.8328	0.638302
$541$	−28.6109	−1.23008	−0.615040	−	0.788496i	$-0.710860\pi$
$541$	−28.6109	−1.23008	−0.615040	+	0.788496i	$0.710860\pi$
$542$	−12.1731	−0.522878
$543$	−2.80612	−0.120422
$544$	8.50014	0.364440
$545$	−9.49594	−0.406761
$546$	−2.23733	−0.0957489
$547$	−42.1334	−1.80150	−0.900748	−	0.434343i	$-0.856981\pi$
$547$	−42.1334	−1.80150	−0.900748	+	0.434343i	$0.856981\pi$
$548$	−41.8721	−1.78869
$549$	−13.5860	−0.579835
$550$	−8.59745	−0.366596
$551$	−1.91558	−0.0816064
$552$	−0.239410	−0.0101900
$553$	1.12821	0.0479762
$554$	12.0974	0.513971
$555$	−90.4203	−3.83813
$556$	2.02257	0.0857762
$557$	3.25222	0.137801	0.0689006	−	0.997624i	$-0.478051\pi$
$557$	3.25222	0.137801	0.0689006	+	0.997624i	$0.478051\pi$
$558$	−8.30651	−0.351643
$559$	3.80664	0.161004
$560$	−14.0334	−0.593018
$561$	0.909775	0.0384107
$562$	33.6071	1.41763
$563$	14.4762	0.610101	0.305050	−	0.952336i	$-0.401327\pi$
$563$	14.4762	0.610101	0.305050	+	0.952336i	$0.401327\pi$
$564$	8.98016	0.378133
$565$	18.4479	0.776110
$566$	−15.5197	−0.652341
$567$	9.42390	0.395767
$568$	−0.352248	−0.0147800
$569$	11.1866	0.468969	0.234484	−	0.972120i	$-0.424660\pi$
$569$	11.1866	0.468969	0.234484	+	0.972120i	$0.424660\pi$
$570$	−35.4920	−1.48659
$571$	15.8397	0.662870	0.331435	−	0.943478i	$-0.392467\pi$
$571$	15.8397	0.662870	0.331435	+	0.943478i	$0.392467\pi$
$572$	−0.424486	−0.0177486
$573$	25.6867	1.07308
$574$	16.8547	0.703501
$575$	26.4039	1.10112
$576$	−18.0453	−0.751886
$577$	1.19655	0.0498131	0.0249066	−	0.999690i	$-0.492071\pi$
$577$	1.19655	0.0498131	0.0249066	+	0.999690i	$0.492071\pi$
$578$	31.8437	1.32452
$579$	−7.88106	−0.327526
$580$	−8.18887	−0.340024
$581$	−1.41781	−0.0588208
$582$	9.80473	0.406419
$583$	0.730901	0.0302708
$584$	0.715125	0.0295921
$585$	4.98203	0.205982
$586$	−33.9075	−1.40070
$587$	−41.6504	−1.71909	−0.859547	−	0.511056i	$-0.829254\pi$
$587$	−41.6504	−1.71909	−0.859547	+	0.511056i	$0.829254\pi$
$588$	−28.7586	−1.18599
$589$	−3.59611	−0.148175
$590$	−50.3698	−2.07369
$591$	−40.3070	−1.65801
$592$	−38.7046	−1.59075
$593$	41.9877	1.72423	0.862114	−	0.506714i	$-0.169140\pi$
$593$	41.9877	1.72423	0.862114	+	0.506714i	$0.169140\pi$
$594$	1.36697	0.0560873
$595$	3.76059	0.154169
$596$	14.7812	0.605461
$597$	−47.3473	−1.93780
$598$	2.59275	0.106025
$599$	−8.94929	−0.365658	−0.182829	−	0.983145i	$-0.558525\pi$
$599$	−8.94929	−0.365658	−0.182829	+	0.983145i	$0.558525\pi$
$600$	−1.17679	−0.0480421
$601$	5.33677	0.217691	0.108846	−	0.994059i	$-0.465285\pi$
$601$	5.33677	0.217691	0.108846	+	0.994059i	$0.465285\pi$
$602$	−11.9980	−0.489001
$603$	−4.27409	−0.174055
$604$	−7.91120	−0.321902
$605$	43.9629	1.78735
$606$	44.2666	1.79821
$607$	0.0843386	0.00342320	0.00171160	−	0.999999i	$-0.499455\pi$
$607$	0.0843386	0.00342320	0.00171160	+	0.999999i	$0.499455\pi$
$608$	−15.3659	−0.623168
$609$	−1.99998	−0.0810432
$610$	−50.0067	−2.02471
$611$	−1.08536	−0.0439090
$612$	4.72833	0.191131
$613$	−23.2114	−0.937501	−0.468751	−	0.883331i	$-0.655296\pi$
$613$	−23.2114	−0.937501	−0.468751	+	0.883331i	$0.655296\pi$
$614$	−21.7474	−0.877654
$615$	−88.5685	−3.57143
$616$	0.0149315	0.000601606 0
$617$	−4.75714	−0.191515	−0.0957575	−	0.995405i	$-0.530527\pi$
$617$	−4.75714	−0.191515	−0.0957575	+	0.995405i	$0.530527\pi$
$618$	−6.21166	−0.249870
$619$	17.7130	0.711944	0.355972	−	0.934497i	$-0.384150\pi$
$619$	17.7130	0.711944	0.355972	+	0.934497i	$0.384150\pi$
$620$	−15.3729	−0.617391
$621$	−4.19812	−0.168465
$622$	35.9566	1.44173
$623$	−11.9851	−0.480172
$624$	5.03252	0.201462
$625$	47.8229	1.91292
$626$	37.0251	1.47982
$627$	−1.64462	−0.0656797
$628$	−1.83024	−0.0730346
$629$	10.3719	0.413554
$630$	−15.7027	−0.625609
$631$	38.2721	1.52359	0.761793	−	0.647820i	$-0.224319\pi$
$631$	38.2721	1.52359	0.761793	+	0.647820i	$0.224319\pi$
$632$	0.0582707	0.00231788
$633$	19.2112	0.763575
$634$	25.1230	0.997760
$635$	18.1536	0.720402
$636$	8.96426	0.355456
$637$	3.47583	0.137717
$638$	−0.754672	−0.0298778
$639$	17.1654	0.679053
$640$	−1.46626	−0.0579590
$641$	−40.2850	−1.59116	−0.795580	−	0.605848i	$-0.792834\pi$
$641$	−40.2850	−1.59116	−0.795580	+	0.605848i	$0.792834\pi$
$642$	−21.5630	−0.851023
$643$	−1.67043	−0.0658753	−0.0329376	−	0.999457i	$-0.510486\pi$
$643$	−1.67043	−0.0658753	−0.0329376	+	0.999457i	$0.510486\pi$
$644$	−4.10892	−0.161914
$645$	63.0474	2.48249
$646$	4.07119	0.160179
$647$	−42.7683	−1.68140	−0.840698	−	0.541505i	$-0.817855\pi$
$647$	−42.7683	−1.68140	−0.840698	+	0.541505i	$0.817855\pi$
$648$	0.486734	0.0191207
$649$	−2.33402	−0.0916184
$650$	12.7443	0.499872
$651$	−3.75455	−0.147152
$652$	−13.0888	−0.512597
$653$	26.4246	1.03407	0.517037	−	0.855963i	$-0.327035\pi$
$653$	26.4246	1.03407	0.517037	+	0.855963i	$0.327035\pi$
$654$	−10.7332	−0.419700
$655$	−19.0063	−0.742638
$656$	−37.9119	−1.48021
$657$	−34.8487	−1.35958
$658$	3.42090	0.133361
$659$	29.9662	1.16732	0.583660	−	0.811998i	$-0.301620\pi$
$659$	29.9662	1.16732	0.583660	+	0.811998i	$0.301620\pi$
$660$	−7.03054	−0.273663
$661$	13.2274	0.514486	0.257243	−	0.966347i	$-0.417186\pi$
$661$	13.2274	0.514486	0.257243	+	0.966347i	$0.417186\pi$
$662$	−36.4944	−1.41840
$663$	−1.34859	−0.0523749
$664$	−0.0732286	−0.00284182
$665$	−6.79809	−0.263619
$666$	−43.3086	−1.67817
$667$	2.31769	0.0897415
$668$	−21.2495	−0.822169
$669$	14.2224	0.549871
$670$	−15.7319	−0.607777
$671$	−2.31720	−0.0894544
$672$	−16.0429	−0.618867
$673$	−20.5948	−0.793872	−0.396936	−	0.917846i	$-0.629926\pi$
$673$	−20.5948	−0.793872	−0.396936	+	0.917846i	$0.629926\pi$
$674$	32.0786	1.23562
$675$	−20.6353	−0.794252
$676$	−25.6642	−0.987085
$677$	34.4592	1.32437	0.662187	−	0.749338i	$-0.269628\pi$
$677$	34.4592	1.32437	0.662187	+	0.749338i	$0.269628\pi$
$678$	20.8515	0.800798
$679$	1.87799	0.0720706
$680$	0.194231	0.00744841
$681$	−32.1902	−1.23353
$682$	−1.41674	−0.0542499
$683$	27.7881	1.06328	0.531640	−	0.846970i	$-0.321576\pi$
$683$	27.7881	1.06328	0.531640	+	0.846970i	$0.321576\pi$
$684$	−8.54748	−0.326821
$685$	83.8187	3.20255
$686$	−23.2613	−0.888122
$687$	28.8979	1.10252
$688$	26.9876	1.02889
$689$	−1.08344	−0.0412758
$690$	42.9424	1.63479
$691$	−2.97657	−0.113234	−0.0566171	−	0.998396i	$-0.518031\pi$
$691$	−2.97657	−0.113234	−0.0566171	+	0.998396i	$0.518031\pi$
$692$	13.9061	0.528631
$693$	−0.727625	−0.0276402
$694$	9.27968	0.352252
$695$	−4.04874	−0.153577
$696$	−0.103297	−0.00391545
$697$	10.1595	0.384817
$698$	19.0771	0.722080
$699$	55.9464	2.11609
$700$	−20.1968	−0.763367
$701$	−16.5652	−0.625660	−0.312830	−	0.949809i	$-0.601277\pi$
$701$	−16.5652	−0.625660	−0.312830	+	0.949809i	$0.601277\pi$
$702$	−2.02630	−0.0764778
$703$	−18.7494	−0.707148
$704$	−3.07777	−0.115998
$705$	−17.9763	−0.677026
$706$	−9.28679	−0.349513
$707$	8.47879	0.318878
$708$	−28.6260	−1.07583
$709$	−2.98052	−0.111936	−0.0559679	−	0.998433i	$-0.517824\pi$
$709$	−2.98052	−0.111936	−0.0559679	+	0.998433i	$0.517824\pi$
$710$	63.1818	2.37117
$711$	−2.83959	−0.106493
$712$	−0.619017	−0.0231986
$713$	4.35100	0.162946
$714$	4.25057	0.159073
$715$	0.849726	0.0317780
$716$	−13.4745	−0.503567
$717$	−0.711564	−0.0265738
$718$	61.6256	2.29985
$719$	−0.902671	−0.0336640	−0.0168320	−	0.999858i	$-0.505358\pi$
$719$	−0.902671	−0.0336640	−0.0168320	+	0.999858i	$0.505358\pi$
$720$	35.3206	1.31632
$721$	−1.18978	−0.0443096
$722$	30.7475	1.14430
$723$	−31.8316	−1.18383
$724$	−2.48743	−0.0924448
$725$	11.3923	0.423099
$726$	49.6909	1.84420
$727$	−31.2314	−1.15831	−0.579155	−	0.815218i	$-0.696617\pi$
$727$	−31.2314	−1.15831	−0.579155	+	0.815218i	$0.696617\pi$
$728$	−0.0221334	−0.000820319 0
$729$	−11.3203	−0.419270
$730$	−128.270	−4.74748
$731$	−7.23200	−0.267485
$732$	−28.4196	−1.05042
$733$	22.2476	0.821735	0.410868	−	0.911695i	$-0.365226\pi$
$733$	22.2476	0.821735	0.410868	+	0.911695i	$0.365226\pi$
$734$	−19.9738	−0.737247
$735$	57.5684	2.12344
$736$	18.5914	0.685289
$737$	−0.728981	−0.0268524
$738$	−42.4216	−1.56156
$739$	−13.4639	−0.495278	−0.247639	−	0.968852i	$-0.579655\pi$
$739$	−13.4639	−0.495278	−0.247639	+	0.968852i	$0.579655\pi$
$740$	−80.1515	−2.94643
$741$	2.43787	0.0895575
$742$	3.41485	0.125363
$743$	−39.5459	−1.45080	−0.725400	−	0.688328i	$-0.758345\pi$
$743$	−39.5459	−1.45080	−0.725400	+	0.688328i	$0.758345\pi$
$744$	−0.193919	−0.00710940
$745$	−29.5887	−1.08404
$746$	31.6007	1.15698
$747$	3.56850	0.130565
$748$	0.806455	0.0294869
$749$	−4.13015	−0.150912
$750$	118.437	4.32470
$751$	−34.3025	−1.25172	−0.625858	−	0.779937i	$-0.715251\pi$
$751$	−34.3025	−1.25172	−0.625858	+	0.779937i	$0.715251\pi$
$752$	−7.69478	−0.280600
$753$	−49.7223	−1.81198
$754$	1.11868	0.0407398
$755$	15.8365	0.576348
$756$	3.21122	0.116791
$757$	−15.2070	−0.552706	−0.276353	−	0.961056i	$-0.589126\pi$
$757$	−15.2070	−0.552706	−0.276353	+	0.961056i	$0.589126\pi$
$758$	−8.52268	−0.309558
$759$	1.98985	0.0722271
$760$	−0.351114	−0.0127363
$761$	−10.0425	−0.364040	−0.182020	−	0.983295i	$-0.558264\pi$
$761$	−10.0425	−0.364040	−0.182020	+	0.983295i	$0.558264\pi$
$762$	20.5188	0.743318
$763$	−2.05582	−0.0744257
$764$	22.7696	0.823775
$765$	−9.46506	−0.342210
$766$	−40.7230	−1.47138
$767$	3.45980	0.124926
$768$	35.6692	1.28710
$769$	43.0024	1.55071	0.775354	−	0.631527i	$-0.217571\pi$
$769$	43.0024	1.55071	0.775354	+	0.631527i	$0.217571\pi$
$770$	−2.67822	−0.0965162
$771$	−16.5750	−0.596935
$772$	−6.98603	−0.251433
$773$	44.9414	1.61643	0.808214	−	0.588889i	$-0.200434\pi$
$773$	44.9414	1.61643	0.808214	+	0.588889i	$0.200434\pi$
$774$	30.1978	1.08544
$775$	21.3867	0.768233
$776$	0.0969961	0.00348196
$777$	−19.5755	−0.702268
$778$	−48.3101	−1.73200
$779$	−18.3654	−0.658010
$780$	10.4216	0.373153
$781$	2.92770	0.104761
$782$	−4.92581	−0.176147
$783$	−1.81134	−0.0647319
$784$	24.6423	0.880081
$785$	3.66374	0.130764
$786$	−21.4827	−0.766261
$787$	18.0171	0.642239	0.321120	−	0.947039i	$-0.395941\pi$
$787$	18.0171	0.642239	0.321120	+	0.947039i	$0.395941\pi$
$788$	−35.7295	−1.27281
$789$	−50.4501	−1.79607
$790$	−10.4518	−0.371860
$791$	3.99388	0.142006
$792$	−0.0375811	−0.00133539
$793$	3.43486	0.121975
$794$	−36.4885	−1.29493
$795$	−17.9445	−0.636424
$796$	−41.9702	−1.48759
$797$	−46.1839	−1.63592	−0.817960	−	0.575276i	$-0.804895\pi$
$797$	−46.1839	−1.63592	−0.817960	+	0.575276i	$0.804895\pi$
$798$	−7.68382	−0.272004
$799$	2.06201	0.0729487
$800$	91.3835	3.23089
$801$	30.1653	1.06584
$802$	25.6413	0.905426
$803$	−5.94374	−0.209750
$804$	−8.94071	−0.315315
$805$	8.22514	0.289898
$806$	2.10009	0.0739724
$807$	20.4156	0.718661
$808$	0.437920	0.0154060
$809$	−6.71005	−0.235913	−0.117956	−	0.993019i	$-0.537634\pi$
$809$	−6.71005	−0.235913	−0.117956	+	0.993019i	$0.537634\pi$
$810$	−87.3042	−3.06756
$811$	24.5558	0.862270	0.431135	−	0.902288i	$-0.358113\pi$
$811$	24.5558	0.862270	0.431135	+	0.902288i	$0.358113\pi$
$812$	−1.77285	−0.0622147
$813$	13.8486	0.485692
$814$	−7.38663	−0.258901
$815$	26.2008	0.917776
$816$	−9.56098	−0.334701
$817$	13.0734	0.457381
$818$	−15.7135	−0.549409
$819$	1.07858	0.0376888
$820$	−78.5101	−2.74169
$821$	22.4784	0.784500	0.392250	−	0.919859i	$-0.371697\pi$
$821$	22.4784	0.784500	0.392250	+	0.919859i	$0.371697\pi$
$822$	94.7395	3.30442
$823$	44.0183	1.53438	0.767191	−	0.641418i	$-0.221654\pi$
$823$	44.0183	1.53438	0.767191	+	0.641418i	$0.221654\pi$
$824$	−0.0614506	−0.00214073
$825$	9.78083	0.340525
$826$	−10.9048	−0.379427
$827$	28.8314	1.00257	0.501283	−	0.865283i	$-0.332861\pi$
$827$	28.8314	1.00257	0.501283	+	0.865283i	$0.332861\pi$
$828$	10.3418	0.359401
$829$	20.8682	0.724783	0.362392	−	0.932026i	$-0.381960\pi$
$829$	20.8682	0.724783	0.362392	+	0.932026i	$0.381960\pi$
$830$	13.1348	0.455916
$831$	−13.7626	−0.477418
$832$	4.56228	0.158169
$833$	−6.60352	−0.228798
$834$	−4.57625	−0.158463
$835$	42.5368	1.47205
$836$	−1.45784	−0.0504205
$837$	−3.40041	−0.117535
$838$	11.2774	0.389571
$839$	31.8996	1.10130	0.550648	−	0.834737i	$-0.314381\pi$
$839$	31.8996	1.10130	0.550648	+	0.834737i	$0.314381\pi$
$840$	−0.366584	−0.0126484
$841$	1.00000	0.0344828
$842$	1.27506	0.0439413
$843$	−38.2329	−1.31681
$844$	17.0294	0.586176
$845$	51.3740	1.76732
$846$	−8.61009	−0.296021
$847$	9.51774	0.327033
$848$	−7.68116	−0.263772
$849$	17.6559	0.605948
$850$	−24.2121	−0.830468
$851$	22.6853	0.777641
$852$	35.9073	1.23016
$853$	52.0336	1.78160	0.890798	−	0.454399i	$-0.150146\pi$
$853$	52.0336	1.78160	0.890798	+	0.454399i	$0.150146\pi$
$854$	−10.8262	−0.370464
$855$	17.1102	0.585155
$856$	−0.213318	−0.00729106
$857$	19.9668	0.682054	0.341027	−	0.940054i	$-0.389225\pi$
$857$	19.9668	0.682054	0.341027	+	0.940054i	$0.389225\pi$
$858$	0.960438	0.0327888
$859$	−9.49691	−0.324030	−0.162015	−	0.986788i	$-0.551799\pi$
$859$	−9.49691	−0.324030	−0.162015	+	0.986788i	$0.551799\pi$
$860$	55.8873	1.90574
$861$	−19.1746	−0.653469
$862$	78.2744	2.66604
$863$	40.5412	1.38004	0.690020	−	0.723790i	$-0.257602\pi$
$863$	40.5412	1.38004	0.690020	+	0.723790i	$0.257602\pi$
$864$	−14.5297	−0.494309
$865$	−27.8369	−0.946485
$866$	43.6055	1.48177
$867$	−36.2268	−1.23033
$868$	−3.32816	−0.112965
$869$	−0.484315	−0.0164293
$870$	18.5281	0.628160
$871$	1.08059	0.0366145
$872$	−0.106181	−0.00359574
$873$	−4.72672	−0.159975
$874$	8.90447	0.301198
$875$	22.6853	0.766902
$876$	−72.8979	−2.46299
$877$	−12.7961	−0.432093	−0.216047	−	0.976383i	$-0.569316\pi$
$877$	−12.7961	−0.432093	−0.216047	+	0.976383i	$0.569316\pi$
$878$	21.2954	0.718686
$879$	38.5746	1.30109
$880$	6.02422	0.203077
$881$	−25.3415	−0.853776	−0.426888	−	0.904305i	$-0.640390\pi$
$881$	−25.3415	−0.853776	−0.426888	+	0.904305i	$0.640390\pi$
$882$	27.5735	0.928449
$883$	58.2952	1.96179	0.980895	−	0.194536i	$-0.0623202\pi$
$883$	58.2952	1.96179	0.980895	+	0.194536i	$0.0623202\pi$
$884$	−1.19544	−0.0402068
$885$	57.3029	1.92622
$886$	9.49298	0.318923
$887$	36.6171	1.22948	0.614741	−	0.788729i	$-0.289260\pi$
$887$	36.6171	1.22948	0.614741	+	0.788729i	$0.289260\pi$
$888$	−1.01105	−0.0339288
$889$	3.93015	0.131813
$890$	111.031	3.72178
$891$	−4.04548	−0.135529
$892$	12.6072	0.422122
$893$	−3.72754	−0.124737
$894$	−33.4438	−1.11853
$895$	26.9730	0.901609
$896$	−0.317437	−0.0106048
$897$	−2.94963	−0.0984851
$898$	−44.9329	−1.49943
$899$	1.87729	0.0626113
$900$	50.8334	1.69445
$901$	2.05836	0.0685740
$902$	−7.23536	−0.240911
$903$	13.6494	0.454224
$904$	0.206280	0.00686076
$905$	4.97929	0.165517
$906$	17.8998	0.594682
$907$	−58.8957	−1.95560	−0.977800	−	0.209541i	$-0.932803\pi$
$907$	−58.8957	−1.95560	−0.977800	+	0.209541i	$0.932803\pi$
$908$	−28.5345	−0.946950
$909$	−21.3403	−0.707813
$910$	3.97001	0.131605
$911$	−41.8294	−1.38587	−0.692935	−	0.721000i	$-0.743683\pi$
$911$	−41.8294	−1.38587	−0.692935	+	0.721000i	$0.743683\pi$
$912$	17.2835	0.572315
$913$	0.608637	0.0201429
$914$	66.8280	2.21047
$915$	56.8898	1.88072
$916$	25.6161	0.846378
$917$	−4.11477	−0.135882
$918$	3.84964	0.127057
$919$	−39.2096	−1.29341	−0.646703	−	0.762742i	$-0.723853\pi$
$919$	−39.2096	−1.29341	−0.646703	+	0.762742i	$0.723853\pi$
$920$	0.424820	0.0140059
$921$	24.7408	0.815237
$922$	−26.4749	−0.871904
$923$	−4.33983	−0.142847
$924$	−1.52207	−0.0500726
$925$	111.506	3.66630
$926$	1.66996	0.0548782
$927$	2.99455	0.0983540
$928$	8.02152	0.263319
$929$	−8.47624	−0.278096	−0.139048	−	0.990286i	$-0.544404\pi$
$929$	−8.47624	−0.278096	−0.139048	+	0.990286i	$0.544404\pi$
$930$	34.7826	1.14057
$931$	11.9373	0.391229
$932$	49.5927	1.62446
$933$	−40.9058	−1.33920
$934$	−70.1758	−2.29622
$935$	−1.61434	−0.0527947
$936$	0.0557077	0.00182086
$937$	43.7166	1.42816	0.714079	−	0.700065i	$-0.246846\pi$
$937$	43.7166	1.42816	0.714079	+	0.700065i	$0.246846\pi$
$938$	−3.40588	−0.111206
$939$	−42.1214	−1.37458
$940$	−15.9348	−0.519735
$941$	13.4517	0.438511	0.219256	−	0.975667i	$-0.429637\pi$
$941$	13.4517	0.438511	0.219256	+	0.975667i	$0.429637\pi$
$942$	4.14109	0.134924
$943$	22.2207	0.723605
$944$	24.5286	0.798339
$945$	−6.42815	−0.209108
$946$	5.15048	0.167456
$947$	−29.2734	−0.951257	−0.475629	−	0.879646i	$-0.657779\pi$
$947$	−29.2734	−0.951257	−0.475629	+	0.879646i	$0.657779\pi$
$948$	−5.93996	−0.192921
$949$	8.81060	0.286004
$950$	43.7687	1.42004
$951$	−28.5810	−0.926802
$952$	0.0420499	0.00136285
$953$	37.1162	1.20231	0.601155	−	0.799132i	$-0.294707\pi$
$953$	37.1162	1.20231	0.601155	+	0.799132i	$0.294707\pi$
$954$	−8.59485	−0.278269
$955$	−45.5796	−1.47492
$956$	−0.630754	−0.0204000
$957$	0.858548	0.0277529
$958$	−64.3180	−2.07802
$959$	18.1463	0.585975
$960$	75.5627	2.43877
$961$	−27.4758	−0.886315
$962$	10.9495	0.353025
$963$	10.3952	0.334981
$964$	−28.2166	−0.908795
$965$	13.9845	0.450176
$966$	9.29680	0.299120
$967$	−32.5562	−1.04694	−0.523468	−	0.852045i	$-0.675362\pi$
$967$	−32.5562	−1.04694	−0.523468	+	0.852045i	$0.675362\pi$
$968$	0.491581	0.0158000
$969$	−4.63156	−0.148787
$970$	−17.3979	−0.558614
$971$	9.70039	0.311300	0.155650	−	0.987812i	$-0.450253\pi$
$971$	9.70039	0.311300	0.155650	+	0.987812i	$0.450253\pi$
$972$	−38.6258	−1.23892
$973$	−0.876531	−0.0281003
$974$	37.4511	1.20001
$975$	−14.4985	−0.464322
$976$	24.3518	0.779482
$977$	−15.2245	−0.487075	−0.243538	−	0.969891i	$-0.578308\pi$
$977$	−15.2245	−0.487075	−0.243538	+	0.969891i	$0.578308\pi$
$978$	29.6146	0.946970
$979$	5.14494	0.164433
$980$	51.0305	1.63011
$981$	5.17431	0.165203
$982$	5.87225	0.187391
$983$	−17.8340	−0.568817	−0.284408	−	0.958703i	$-0.591797\pi$
$983$	−17.8340	−0.568817	−0.284408	+	0.958703i	$0.591797\pi$
$984$	−0.990349	−0.0315712
$985$	71.5224	2.27889
$986$	−2.12531	−0.0676835
$987$	−3.89177	−0.123876
$988$	2.16101	0.0687509
$989$	−15.8178	−0.502976
$990$	6.74082	0.214237
$991$	6.70256	0.212914	0.106457	−	0.994317i	$-0.466049\pi$
$991$	6.70256	0.212914	0.106457	+	0.994317i	$0.466049\pi$
$992$	15.0588	0.478116
$993$	41.5177	1.31752
$994$	13.6785	0.433857
$995$	84.0150	2.66345
$996$	7.46473	0.236529
$997$	−37.5246	−1.18842	−0.594209	−	0.804311i	$-0.702535\pi$
$997$	−37.5246	−1.18842	−0.594209	+	0.804311i	$0.702535\pi$
$998$	17.1233	0.542028
$999$	−17.7291	−0.560924

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.b.1.10	✓	59

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.b.1.10	✓	59	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)

\(f(q)\)	\(=\)	\(q-2.00564 q^{2} +2.28170 q^{3} +2.02257 q^{4} -4.04874 q^{5} -4.57625 q^{6} -0.876531 q^{7} -0.0452719 q^{8} +2.20615 q^{9} +O(q^{10})\)	\(q-2.00564 q^{2} +2.28170 q^{3} +2.02257 q^{4} -4.04874 q^{5} -4.57625 q^{6} -0.876531 q^{7} -0.0452719 q^{8} +2.20615 q^{9} +8.12030 q^{10} +0.376276 q^{11} +4.61490 q^{12} -0.557767 q^{13} +1.75800 q^{14} -9.23800 q^{15} -3.95435 q^{16} +1.05967 q^{17} -4.42472 q^{18} -1.91558 q^{19} -8.18887 q^{20} -1.99998 q^{21} -0.754672 q^{22} +2.31769 q^{23} -0.103297 q^{24} +11.3923 q^{25} +1.11868 q^{26} -1.81134 q^{27} -1.77285 q^{28} +1.00000 q^{29} +18.5281 q^{30} +1.87729 q^{31} +8.02152 q^{32} +0.858548 q^{33} -2.12531 q^{34} +3.54885 q^{35} +4.46209 q^{36} +9.78786 q^{37} +3.84195 q^{38} -1.27266 q^{39} +0.183294 q^{40} +9.58741 q^{41} +4.01123 q^{42} -6.82479 q^{43} +0.761045 q^{44} -8.93211 q^{45} -4.64845 q^{46} +1.94591 q^{47} -9.02262 q^{48} -6.23169 q^{49} -22.8488 q^{50} +2.41784 q^{51} -1.12812 q^{52} +1.94246 q^{53} +3.63288 q^{54} -1.52344 q^{55} +0.0396822 q^{56} -4.37077 q^{57} -2.00564 q^{58} -6.20295 q^{59} -18.6845 q^{60} -6.15824 q^{61} -3.76517 q^{62} -1.93375 q^{63} -8.17955 q^{64} +2.25825 q^{65} -1.72193 q^{66} -1.93736 q^{67} +2.14325 q^{68} +5.28828 q^{69} -7.11769 q^{70} +7.78073 q^{71} -0.0998764 q^{72} -15.7962 q^{73} -19.6309 q^{74} +25.9938 q^{75} -3.87440 q^{76} -0.329818 q^{77} +2.55248 q^{78} -1.28713 q^{79} +16.0101 q^{80} -10.7514 q^{81} -19.2289 q^{82} +1.61753 q^{83} -4.04510 q^{84} -4.29032 q^{85} +13.6880 q^{86} +2.28170 q^{87} -0.0170347 q^{88} +13.6733 q^{89} +17.9146 q^{90} +0.488900 q^{91} +4.68770 q^{92} +4.28342 q^{93} -3.90278 q^{94} +7.75568 q^{95} +18.3027 q^{96} -2.14252 q^{97} +12.4985 q^{98} +0.830119 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) \) 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9	\( 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9} - 18 q^{10} - 27 q^{11} - 8 q^{12} - 22 q^{13} - 24 q^{14} - 18 q^{15} + 5 q^{16} - 23 q^{17} + q^{18} - 32 q^{19} - 14 q^{20} - 36 q^{21} - 6 q^{22} - 3 q^{23} - 18 q^{24} - 8 q^{25} - q^{26} - 12 q^{27} - 9 q^{28} + 59 q^{29} - 18 q^{30} - 32 q^{31} - 39 q^{32} - 12 q^{33} - 18 q^{34} - 9 q^{35} + 10 q^{36} - 44 q^{37} + 5 q^{38} - 27 q^{39} - 68 q^{40} - 44 q^{41} - 25 q^{42} - 40 q^{43} - 56 q^{44} - 39 q^{45} - 40 q^{46} - 20 q^{47} - 9 q^{48} - 39 q^{49} - 21 q^{50} - 28 q^{51} - 49 q^{52} - 31 q^{53} - 32 q^{54} - 32 q^{55} - 48 q^{56} - 58 q^{57} - 5 q^{58} + 6 q^{59} - 44 q^{60} - 88 q^{61} + 35 q^{62} - 22 q^{63} - 10 q^{64} - 43 q^{65} - 31 q^{66} - 45 q^{67} - 29 q^{68} - 60 q^{69} - 14 q^{70} - 20 q^{71} - 4 q^{72} - 90 q^{73} - 25 q^{74} + 15 q^{75} - 64 q^{76} - 39 q^{77} - 28 q^{78} - 120 q^{79} + 24 q^{80} - 77 q^{81} - 71 q^{82} - 33 q^{83} - 14 q^{84} - 71 q^{85} - 61 q^{86} - 6 q^{87} - 34 q^{88} - 78 q^{89} - 88 q^{90} - 28 q^{91} - 31 q^{92} - 36 q^{93} - 4 q^{94} - 12 q^{95} - 29 q^{96} - 48 q^{97} - 4 q^{98} - 43 q^{99}+O(q^{100}) \) 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9 - 18 * q^10 - 27 * q^11 - 8 * q^12 - 22 * q^13 - 24 * q^14 - 18 * q^15 + 5 * q^16 - 23 * q^17 + q^18 - 32 * q^19 - 14 * q^20 - 36 * q^21 - 6 * q^22 - 3 * q^23 - 18 * q^24 - 8 * q^25 - q^26 - 12 * q^27 - 9 * q^28 + 59 * q^29 - 18 * q^30 - 32 * q^31 - 39 * q^32 - 12 * q^33 - 18 * q^34 - 9 * q^35 + 10 * q^36 - 44 * q^37 + 5 * q^38 - 27 * q^39 - 68 * q^40 - 44 * q^41 - 25 * q^42 - 40 * q^43 - 56 * q^44 - 39 * q^45 - 40 * q^46 - 20 * q^47 - 9 * q^48 - 39 * q^49 - 21 * q^50 - 28 * q^51 - 49 * q^52 - 31 * q^53 - 32 * q^54 - 32 * q^55 - 48 * q^56 - 58 * q^57 - 5 * q^58 + 6 * q^59 - 44 * q^60 - 88 * q^61 + 35 * q^62 - 22 * q^63 - 10 * q^64 - 43 * q^65 - 31 * q^66 - 45 * q^67 - 29 * q^68 - 60 * q^69 - 14 * q^70 - 20 * q^71 - 4 * q^72 - 90 * q^73 - 25 * q^74 + 15 * q^75 - 64 * q^76 - 39 * q^77 - 28 * q^78 - 120 * q^79 + 24 * q^80 - 77 * q^81 - 71 * q^82 - 33 * q^83 - 14 * q^84 - 71 * q^85 - 61 * q^86 - 6 * q^87 - 34 * q^88 - 78 * q^89 - 88 * q^90 - 28 * q^91 - 31 * q^92 - 36 * q^93 - 4 * q^94 - 12 * q^95 - 29 * q^96 - 48 * q^97 - 4 * q^98 - 43 * q^99

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