LMFDB - Embedded newform 4031.2.a.e.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.34575 q^{2} -2.20403 q^{3} +3.50256 q^{4} -4.15589 q^{5} +5.17012 q^{6} +5.11824 q^{7} -3.52465 q^{8} +1.85776 q^{9} +O(q^{10})$	\(q-2.34575 q^{2} -2.20403 q^{3} +3.50256 q^{4} -4.15589 q^{5} +5.17012 q^{6} +5.11824 q^{7} -3.52465 q^{8} +1.85776 q^{9} +9.74869 q^{10} -1.89858 q^{11} -7.71977 q^{12} -0.600152 q^{13} -12.0061 q^{14} +9.15972 q^{15} +1.26283 q^{16} +4.53543 q^{17} -4.35786 q^{18} -2.68180 q^{19} -14.5563 q^{20} -11.2808 q^{21} +4.45360 q^{22} +5.04396 q^{23} +7.76844 q^{24} +12.2714 q^{25} +1.40781 q^{26} +2.51753 q^{27} +17.9270 q^{28} -1.00000 q^{29} -21.4864 q^{30} +8.81858 q^{31} +4.08701 q^{32} +4.18453 q^{33} -10.6390 q^{34} -21.2708 q^{35} +6.50693 q^{36} -4.88426 q^{37} +6.29084 q^{38} +1.32276 q^{39} +14.6480 q^{40} -8.72655 q^{41} +26.4619 q^{42} +5.15224 q^{43} -6.64990 q^{44} -7.72065 q^{45} -11.8319 q^{46} +1.21846 q^{47} -2.78331 q^{48} +19.1964 q^{49} -28.7857 q^{50} -9.99623 q^{51} -2.10207 q^{52} +13.4283 q^{53} -5.90550 q^{54} +7.89028 q^{55} -18.0400 q^{56} +5.91077 q^{57} +2.34575 q^{58} -8.32625 q^{59} +32.0825 q^{60} +12.8661 q^{61} -20.6862 q^{62} +9.50848 q^{63} -12.1128 q^{64} +2.49417 q^{65} -9.81588 q^{66} +8.46028 q^{67} +15.8856 q^{68} -11.1171 q^{69} +49.8962 q^{70} +14.3147 q^{71} -6.54796 q^{72} -6.60893 q^{73} +11.4573 q^{74} -27.0466 q^{75} -9.39317 q^{76} -9.71738 q^{77} -3.10286 q^{78} +9.25080 q^{79} -5.24816 q^{80} -11.1220 q^{81} +20.4703 q^{82} -12.9990 q^{83} -39.5116 q^{84} -18.8487 q^{85} -12.0859 q^{86} +2.20403 q^{87} +6.69182 q^{88} -5.14775 q^{89} +18.1108 q^{90} -3.07172 q^{91} +17.6668 q^{92} -19.4364 q^{93} -2.85820 q^{94} +11.1453 q^{95} -9.00791 q^{96} -6.38800 q^{97} -45.0300 q^{98} -3.52711 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.34575	−1.65870	−0.829349	−	0.558730i	$-0.811289\pi$
$2$	−2.34575	−1.65870	−0.829349	+	0.558730i	$0.811289\pi$
$3$	−2.20403	−1.27250	−0.636250	−	0.771483i	$-0.719515\pi$
$3$	−2.20403	−1.27250	−0.636250	+	0.771483i	$0.719515\pi$
$4$	3.50256	1.75128
$5$	−4.15589	−1.85857	−0.929285	−	0.369364i	$-0.879576\pi$
$5$	−4.15589	−1.85857	−0.929285	+	0.369364i	$0.879576\pi$
$6$	5.17012	2.11069
$7$	5.11824	1.93451	0.967256	−	0.253801i	$-0.0816808\pi$
$7$	5.11824	1.93451	0.967256	+	0.253801i	$0.0816808\pi$
$8$	−3.52465	−1.24615
$9$	1.85776	0.619254
$10$	9.74869	3.08281
$11$	−1.89858	−0.572443	−0.286222	−	0.958163i	$-0.592399\pi$
$11$	−1.89858	−0.572443	−0.286222	+	0.958163i	$0.592399\pi$
$12$	−7.71977	−2.22850
$13$	−0.600152	−0.166452	−0.0832261	−	0.996531i	$-0.526522\pi$
$13$	−0.600152	−0.166452	−0.0832261	+	0.996531i	$0.526522\pi$
$14$	−12.0061	−3.20877
$15$	9.15972	2.36503
$16$	1.26283	0.315707
$17$	4.53543	1.10000	0.550001	−	0.835164i	$-0.314627\pi$
$17$	4.53543	1.10000	0.550001	+	0.835164i	$0.314627\pi$
$18$	−4.35786	−1.02716
$19$	−2.68180	−0.615247	−0.307623	−	0.951508i	$-0.599534\pi$
$19$	−2.68180	−0.615247	−0.307623	+	0.951508i	$0.599534\pi$
$20$	−14.5563	−3.25488
$21$	−11.2808	−2.46167
$22$	4.45360	0.949511
$23$	5.04396	1.05174	0.525869	−	0.850566i	$-0.323740\pi$
$23$	5.04396	1.05174	0.525869	+	0.850566i	$0.323740\pi$
$24$	7.76844	1.58573
$25$	12.2714	2.45428
$26$	1.40781	0.276094
$27$	2.51753	0.484499
$28$	17.9270	3.38788
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−21.4864	−3.92287
$31$	8.81858	1.58386	0.791931	−	0.610610i	$-0.209076\pi$
$31$	8.81858	1.58386	0.791931	+	0.610610i	$0.209076\pi$
$32$	4.08701	0.722488
$33$	4.18453	0.728434
$34$	−10.6390	−1.82457
$35$	−21.2708	−3.59543
$36$	6.50693	1.08449
$37$	−4.88426	−0.802967	−0.401483	−	0.915866i	$-0.631505\pi$
$37$	−4.88426	−0.802967	−0.401483	+	0.915866i	$0.631505\pi$
$38$	6.29084	1.02051
$39$	1.32276	0.211810
$40$	14.6480	2.31606
$41$	−8.72655	−1.36286	−0.681429	−	0.731884i	$-0.738641\pi$
$41$	−8.72655	−1.36286	−0.681429	+	0.731884i	$0.738641\pi$
$42$	26.4619	4.08316
$43$	5.15224	0.785709	0.392855	−	0.919601i	$-0.371488\pi$
$43$	5.15224	0.785709	0.392855	+	0.919601i	$0.371488\pi$
$44$	−6.64990	−1.00251
$45$	−7.72065	−1.15093
$46$	−11.8319	−1.74452
$47$	1.21846	0.177730	0.0888652	−	0.996044i	$-0.471676\pi$
$47$	1.21846	0.177730	0.0888652	+	0.996044i	$0.471676\pi$
$48$	−2.78331	−0.401736
$49$	19.1964	2.74234
$50$	−28.7857	−4.07091
$51$	−9.99623	−1.39975
$52$	−2.10207	−0.291505
$53$	13.4283	1.84452	0.922259	−	0.386573i	$-0.126341\pi$
$53$	13.4283	1.84452	0.922259	+	0.386573i	$0.126341\pi$
$54$	−5.90550	−0.803637
$55$	7.89028	1.06393
$56$	−18.0400	−2.41069
$57$	5.91077	0.782901
$58$	2.34575	0.308013
$59$	−8.32625	−1.08399	−0.541993	−	0.840383i	$-0.682330\pi$
$59$	−8.32625	−1.08399	−0.541993	+	0.840383i	$0.682330\pi$
$60$	32.0825	4.14183
$61$	12.8661	1.64733	0.823667	−	0.567074i	$-0.191925\pi$
$61$	12.8661	1.64733	0.823667	+	0.567074i	$0.191925\pi$
$62$	−20.6862	−2.62715
$63$	9.50848	1.19796
$64$	−12.1128	−1.51410
$65$	2.49417	0.309363
$66$	−9.81588	−1.20825
$67$	8.46028	1.03359	0.516794	−	0.856110i	$-0.327125\pi$
$67$	8.46028	1.03359	0.516794	+	0.856110i	$0.327125\pi$
$68$	15.8856	1.92641
$69$	−11.1171	−1.33834
$70$	49.8962	5.96373
$71$	14.3147	1.69885	0.849423	−	0.527713i	$-0.176950\pi$
$71$	14.3147	1.69885	0.849423	+	0.527713i	$0.176950\pi$
$72$	−6.54796	−0.771684
$73$	−6.60893	−0.773517	−0.386758	−	0.922181i	$-0.626405\pi$
$73$	−6.60893	−0.773517	−0.386758	+	0.922181i	$0.626405\pi$
$74$	11.4573	1.33188
$75$	−27.0466	−3.12307
$76$	−9.39317	−1.07747
$77$	−9.71738	−1.10740
$78$	−3.10286	−0.351330
$79$	9.25080	1.04080	0.520398	−	0.853924i	$-0.325783\pi$
$79$	9.25080	1.04080	0.520398	+	0.853924i	$0.325783\pi$
$80$	−5.24816	−0.586763
$81$	−11.1220	−1.23578
$82$	20.4703	2.26057
$83$	−12.9990	−1.42683	−0.713414	−	0.700743i	$-0.752852\pi$
$83$	−12.9990	−1.42683	−0.713414	+	0.700743i	$0.752852\pi$
$84$	−39.5116	−4.31107
$85$	−18.8487	−2.04443
$86$	−12.0859	−1.30325
$87$	2.20403	0.236297
$88$	6.69182	0.713350
$89$	−5.14775	−0.545660	−0.272830	−	0.962062i	$-0.587960\pi$
$89$	−5.14775	−0.545660	−0.272830	+	0.962062i	$0.587960\pi$
$90$	18.1108	1.90904
$91$	−3.07172	−0.322004
$92$	17.6668	1.84189
$93$	−19.4364	−2.01546
$94$	−2.85820	−0.294801
$95$	11.1453	1.14348
$96$	−9.00791	−0.919366
$97$	−6.38800	−0.648603	−0.324301	−	0.945954i	$-0.605129\pi$
$97$	−6.38800	−0.648603	−0.324301	+	0.945954i	$0.605129\pi$
$98$	−45.0300	−4.54872
$99$	−3.52711	−0.354488
$100$	42.9814	4.29814
$101$	3.12527	0.310976	0.155488	−	0.987838i	$-0.450305\pi$
$101$	3.12527	0.310976	0.155488	+	0.987838i	$0.450305\pi$
$102$	23.4487	2.32177
$103$	−8.28967	−0.816806	−0.408403	−	0.912802i	$-0.633914\pi$
$103$	−8.28967	−0.816806	−0.408403	+	0.912802i	$0.633914\pi$
$104$	2.11532	0.207425
$105$	46.8816	4.57518
$106$	−31.4995	−3.05950
$107$	18.6289	1.80092	0.900460	−	0.434938i	$-0.143230\pi$
$107$	18.6289	1.80092	0.900460	+	0.434938i	$0.143230\pi$
$108$	8.81780	0.848494
$109$	0.709485	0.0679564	0.0339782	−	0.999423i	$-0.489182\pi$
$109$	0.709485	0.0679564	0.0339782	+	0.999423i	$0.489182\pi$
$110$	−18.5087	−1.76473
$111$	10.7651	1.02177
$112$	6.46345	0.610738
$113$	−9.90952	−0.932210	−0.466105	−	0.884730i	$-0.654343\pi$
$113$	−9.90952	−0.932210	−0.466105	+	0.884730i	$0.654343\pi$
$114$	−13.8652	−1.29860
$115$	−20.9621	−1.95473
$116$	−3.50256	−0.325205
$117$	−1.11494	−0.103076
$118$	19.5313	1.79801
$119$	23.2134	2.12797
$120$	−32.2848	−2.94718
$121$	−7.39540	−0.672309
$122$	−30.1807	−2.73243
$123$	19.2336	1.73424
$124$	30.8876	2.77379
$125$	−30.2191	−2.70288
$126$	−22.3046	−1.98705
$127$	−12.3088	−1.09223	−0.546115	−	0.837710i	$-0.683894\pi$
$127$	−12.3088	−1.09223	−0.546115	+	0.837710i	$0.683894\pi$
$128$	20.2396	1.78894
$129$	−11.3557	−0.999814
$130$	−5.85070	−0.513140
$131$	−1.46056	−0.127610	−0.0638048	−	0.997962i	$-0.520324\pi$
$131$	−1.46056	−0.127610	−0.0638048	+	0.997962i	$0.520324\pi$
$132$	14.6566	1.27569
$133$	−13.7261	−1.19020
$134$	−19.8457	−1.71441
$135$	−10.4626	−0.900474
$136$	−15.9858	−1.37077
$137$	−12.1890	−1.04137	−0.520687	−	0.853748i	$-0.674324\pi$
$137$	−12.1890	−1.04137	−0.520687	+	0.853748i	$0.674324\pi$
$138$	26.0779	2.21990
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	−74.5025	−6.29661
$141$	−2.68552	−0.226162
$142$	−33.5788	−2.81787
$143$	1.13944	0.0952845
$144$	2.34603	0.195503
$145$	4.15589	0.345128
$146$	15.5029	1.28303
$147$	−42.3095	−3.48963
$148$	−17.1074	−1.40622
$149$	−4.78744	−0.392203	−0.196101	−	0.980584i	$-0.562828\pi$
$149$	−4.78744	−0.392203	−0.196101	+	0.980584i	$0.562828\pi$
$150$	63.4446	5.18023
$151$	−9.16671	−0.745976	−0.372988	−	0.927836i	$-0.621667\pi$
$151$	−9.16671	−0.745976	−0.372988	+	0.927836i	$0.621667\pi$
$152$	9.45239	0.766690
$153$	8.42575	0.681181
$154$	22.7946	1.83684
$155$	−36.6490	−2.94372
$156$	4.63304	0.370940
$157$	−22.2798	−1.77812	−0.889062	−	0.457788i	$-0.848642\pi$
$157$	−22.2798	−1.77812	−0.889062	+	0.457788i	$0.848642\pi$
$158$	−21.7001	−1.72637
$159$	−29.5964	−2.34715
$160$	−16.9852	−1.34280
$161$	25.8162	2.03460
$162$	26.0895	2.04978
$163$	−4.90120	−0.383891	−0.191946	−	0.981406i	$-0.561480\pi$
$163$	−4.90120	−0.383891	−0.191946	+	0.981406i	$0.561480\pi$
$164$	−30.5653	−2.38675
$165$	−17.3904	−1.35384
$166$	30.4925	2.36668
$167$	−11.9009	−0.920921	−0.460460	−	0.887680i	$-0.652316\pi$
$167$	−11.9009	−0.920921	−0.460460	+	0.887680i	$0.652316\pi$
$168$	39.7607	3.06761
$169$	−12.6398	−0.972294
$170$	44.2145	3.39110
$171$	−4.98214	−0.380994
$172$	18.0460	1.37600
$173$	20.6126	1.56715	0.783575	−	0.621298i	$-0.213394\pi$
$173$	20.6126	1.56715	0.783575	+	0.621298i	$0.213394\pi$
$174$	−5.17012	−0.391946
$175$	62.8080	4.74784
$176$	−2.39758	−0.180724
$177$	18.3513	1.37937
$178$	12.0754	0.905086
$179$	14.7448	1.10208	0.551038	−	0.834480i	$-0.314232\pi$
$179$	14.7448	1.10208	0.551038	+	0.834480i	$0.314232\pi$
$180$	−27.0421	−2.01560
$181$	17.8070	1.32358	0.661792	−	0.749688i	$-0.269796\pi$
$181$	17.8070	1.32358	0.661792	+	0.749688i	$0.269796\pi$
$182$	7.20551	0.534108
$183$	−28.3573	−2.09623
$184$	−17.7782	−1.31062
$185$	20.2984	1.49237
$186$	45.5931	3.34305
$187$	−8.61087	−0.629689
$188$	4.26773	0.311256
$189$	12.8853	0.937269
$190$	−26.1440	−1.89669
$191$	−0.698136	−0.0505154	−0.0252577	−	0.999681i	$-0.508041\pi$
$191$	−0.698136	−0.0505154	−0.0252577	+	0.999681i	$0.508041\pi$
$192$	26.6970	1.92669
$193$	−5.71136	−0.411112	−0.205556	−	0.978645i	$-0.565900\pi$
$193$	−5.71136	−0.411112	−0.205556	+	0.978645i	$0.565900\pi$
$194$	14.9847	1.07584
$195$	−5.49722	−0.393664
$196$	67.2366	4.80261
$197$	−16.1239	−1.14878	−0.574390	−	0.818582i	$-0.694761\pi$
$197$	−16.1239	−1.14878	−0.574390	+	0.818582i	$0.694761\pi$
$198$	8.27373	0.587989
$199$	21.3967	1.51677	0.758385	−	0.651807i	$-0.225989\pi$
$199$	21.3967	1.51677	0.758385	+	0.651807i	$0.225989\pi$
$200$	−43.2524	−3.05840
$201$	−18.6467	−1.31524
$202$	−7.33112	−0.515816
$203$	−5.11824	−0.359230
$204$	−35.0124	−2.45136
$205$	36.2666	2.53297
$206$	19.4455	1.35483
$207$	9.37048	0.651293
$208$	−0.757888	−0.0525501
$209$	5.09161	0.352194
$210$	−109.973	−7.58884
$211$	11.3147	0.778935	0.389467	−	0.921040i	$-0.372659\pi$
$211$	11.3147	0.778935	0.389467	+	0.921040i	$0.372659\pi$
$212$	47.0335	3.23027
$213$	−31.5501	−2.16178
$214$	−43.6987	−2.98718
$215$	−21.4121	−1.46030
$216$	−8.87340	−0.603758
$217$	45.1356	3.06400
$218$	−1.66428	−0.112719
$219$	14.5663	0.984300
$220$	27.6362	1.86323
$221$	−2.72195	−0.183098
$222$	−25.2522	−1.69482
$223$	20.8480	1.39608	0.698041	−	0.716058i	$-0.254055\pi$
$223$	20.8480	1.39608	0.698041	+	0.716058i	$0.254055\pi$
$224$	20.9183	1.39766
$225$	22.7974	1.51982
$226$	23.2453	1.54625
$227$	−20.3334	−1.34958	−0.674789	−	0.738011i	$-0.735765\pi$
$227$	−20.3334	−1.34958	−0.674789	+	0.738011i	$0.735765\pi$
$228$	20.7029	1.37108
$229$	6.60164	0.436248	0.218124	−	0.975921i	$-0.430006\pi$
$229$	6.60164	0.436248	0.218124	+	0.975921i	$0.430006\pi$
$230$	49.1720	3.24231
$231$	21.4174	1.40916
$232$	3.52465	0.231404
$233$	14.1028	0.923904	0.461952	−	0.886905i	$-0.347149\pi$
$233$	14.1028	0.923904	0.461952	+	0.886905i	$0.347149\pi$
$234$	2.61538	0.170973
$235$	−5.06378	−0.330324
$236$	−29.1632	−1.89837
$237$	−20.3891	−1.32441
$238$	−54.4529	−3.52966
$239$	22.1850	1.43503	0.717514	−	0.696544i	$-0.245280\pi$
$239$	22.1850	1.43503	0.717514	+	0.696544i	$0.245280\pi$
$240$	11.5671	0.746655
$241$	−22.0901	−1.42295	−0.711474	−	0.702713i	$-0.751972\pi$
$241$	−22.0901	−1.42295	−0.711474	+	0.702713i	$0.751972\pi$
$242$	17.3478	1.11516
$243$	16.9607	1.08803
$244$	45.0643	2.88495
$245$	−79.7780	−5.09683
$246$	−45.1173	−2.87658
$247$	1.60949	0.102409
$248$	−31.0824	−1.97373
$249$	28.6503	1.81564
$250$	70.8867	4.48327
$251$	−14.3268	−0.904301	−0.452150	−	0.891942i	$-0.649343\pi$
$251$	−14.3268	−0.904301	−0.452150	+	0.891942i	$0.649343\pi$
$252$	33.3040	2.09796
$253$	−9.57635	−0.602060
$254$	28.8735	1.81168
$255$	41.5432	2.60154
$256$	−23.2515	−1.45322
$257$	2.99432	0.186781	0.0933903	−	0.995630i	$-0.470230\pi$
$257$	2.99432	0.186781	0.0933903	+	0.995630i	$0.470230\pi$
$258$	26.6377	1.65839
$259$	−24.9988	−1.55335
$260$	8.73597	0.541782
$261$	−1.85776	−0.114993
$262$	3.42611	0.211666
$263$	10.6164	0.654635	0.327318	−	0.944914i	$-0.393855\pi$
$263$	10.6164	0.654635	0.327318	+	0.944914i	$0.393855\pi$
$264$	−14.7490	−0.907738
$265$	−55.8065	−3.42816
$266$	32.1980	1.97419
$267$	11.3458	0.694352
$268$	29.6327	1.81010
$269$	−11.0733	−0.675149	−0.337575	−	0.941299i	$-0.609607\pi$
$269$	−11.0733	−0.675149	−0.337575	+	0.941299i	$0.609607\pi$
$270$	24.5426	1.49362
$271$	3.29642	0.200244	0.100122	−	0.994975i	$-0.468077\pi$
$271$	3.29642	0.200244	0.100122	+	0.994975i	$0.468077\pi$
$272$	5.72745	0.347278
$273$	6.77018	0.409750
$274$	28.5923	1.72733
$275$	−23.2982	−1.40494
$276$	−38.9382	−2.34380
$277$	11.5673	0.695009	0.347505	−	0.937678i	$-0.387029\pi$
$277$	11.5673	0.695009	0.347505	+	0.937678i	$0.387029\pi$
$278$	−2.34575	−0.140689
$279$	16.3828	0.980814
$280$	74.9722	4.48044
$281$	−6.47319	−0.386158	−0.193079	−	0.981183i	$-0.561847\pi$
$281$	−6.47319	−0.386158	−0.193079	+	0.981183i	$0.561847\pi$
$282$	6.29958	0.375134
$283$	21.7443	1.29256	0.646281	−	0.763100i	$-0.276323\pi$
$283$	21.7443	1.29256	0.646281	+	0.763100i	$0.276323\pi$
$284$	50.1383	2.97516
$285$	−24.5645	−1.45508
$286$	−2.67284	−0.158048
$287$	−44.6646	−2.63647
$288$	7.59270	0.447404
$289$	3.57009	0.210005
$290$	−9.74869	−0.572463
$291$	14.0794	0.825347
$292$	−23.1482	−1.35465
$293$	−1.54916	−0.0905031	−0.0452515	−	0.998976i	$-0.514409\pi$
$293$	−1.54916	−0.0905031	−0.0452515	+	0.998976i	$0.514409\pi$
$294$	99.2476	5.78824
$295$	34.6030	2.01466
$296$	17.2153	1.00062
$297$	−4.77973	−0.277348
$298$	11.2302	0.650546
$299$	−3.02714	−0.175064
$300$	−94.7324	−5.46938
$301$	26.3704	1.51996
$302$	21.5028	1.23735
$303$	−6.88820	−0.395717
$304$	−3.38664	−0.194237
$305$	−53.4700	−3.06168
$306$	−19.7647	−1.12987
$307$	−11.8214	−0.674683	−0.337341	−	0.941382i	$-0.609528\pi$
$307$	−11.8214	−0.674683	−0.337341	+	0.941382i	$0.609528\pi$
$308$	−34.0358	−1.93937
$309$	18.2707	1.03938
$310$	85.9696	4.88274
$311$	16.6757	0.945595	0.472797	−	0.881171i	$-0.343244\pi$
$311$	16.6757	0.945595	0.472797	+	0.881171i	$0.343244\pi$
$312$	−4.66224	−0.263948
$313$	18.8504	1.06549	0.532743	−	0.846277i	$-0.321161\pi$
$313$	18.8504	1.06549	0.532743	+	0.846277i	$0.321161\pi$
$314$	52.2630	2.94937
$315$	−39.5162	−2.22648
$316$	32.4015	1.82273
$317$	23.9354	1.34434	0.672172	−	0.740395i	$-0.265362\pi$
$317$	23.9354	1.34434	0.672172	+	0.740395i	$0.265362\pi$
$318$	69.4259	3.89321
$319$	1.89858	0.106300
$320$	50.3394	2.81406
$321$	−41.0586	−2.29167
$322$	−60.5584	−3.37479
$323$	−12.1631	−0.676773
$324$	−38.9555	−2.16420
$325$	−7.36471	−0.408521
$326$	11.4970	0.636760
$327$	−1.56373	−0.0864744
$328$	30.7580	1.69833
$329$	6.23636	0.343822
$330$	40.7937	2.24562
$331$	−9.65837	−0.530872	−0.265436	−	0.964128i	$-0.585516\pi$
$331$	−9.65837	−0.530872	−0.265436	+	0.964128i	$0.585516\pi$
$332$	−45.5299	−2.49878
$333$	−9.07379	−0.497241
$334$	27.9166	1.52753
$335$	−35.1600	−1.92099
$336$	−14.2457	−0.777164
$337$	−13.6693	−0.744616	−0.372308	−	0.928109i	$-0.621433\pi$
$337$	−13.6693	−0.744616	−0.372308	+	0.928109i	$0.621433\pi$
$338$	29.6499	1.61274
$339$	21.8409	1.18624
$340$	−66.0189	−3.58037
$341$	−16.7428	−0.906672
$342$	11.6869	0.631955
$343$	62.4240	3.37058
$344$	−18.1598	−0.979112
$345$	46.2012	2.48739
$346$	−48.3522	−2.59943
$347$	7.19429	0.386210	0.193105	−	0.981178i	$-0.438144\pi$
$347$	7.19429	0.386210	0.193105	+	0.981178i	$0.438144\pi$
$348$	7.71977	0.413823
$349$	25.1605	1.34681	0.673407	−	0.739272i	$-0.264830\pi$
$349$	25.1605	1.34681	0.673407	+	0.739272i	$0.264830\pi$
$350$	−147.332	−7.87523
$351$	−1.51090	−0.0806459
$352$	−7.75952	−0.413584
$353$	6.64785	0.353829	0.176915	−	0.984226i	$-0.443388\pi$
$353$	6.64785	0.353829	0.176915	+	0.984226i	$0.443388\pi$
$354$	−43.0477	−2.28796
$355$	−59.4904	−3.15742
$356$	−18.0303	−0.955605
$357$	−51.1631	−2.70784
$358$	−34.5876	−1.82801
$359$	25.6501	1.35376	0.676880	−	0.736093i	$-0.263331\pi$
$359$	25.6501	1.35376	0.676880	+	0.736093i	$0.263331\pi$
$360$	27.2126	1.43423
$361$	−11.8080	−0.621472
$362$	−41.7708	−2.19543
$363$	16.2997	0.855512
$364$	−10.7589	−0.563920
$365$	27.4660	1.43764
$366$	66.5192	3.47702
$367$	−4.20766	−0.219638	−0.109819	−	0.993952i	$-0.535027\pi$
$367$	−4.20766	−0.219638	−0.109819	+	0.993952i	$0.535027\pi$
$368$	6.36964	0.332041
$369$	−16.2119	−0.843956
$370$	−47.6151	−2.47539
$371$	68.7292	3.56824
$372$	−68.0774	−3.52965
$373$	−21.7554	−1.12645	−0.563226	−	0.826303i	$-0.690440\pi$
$373$	−21.7554	−1.12645	−0.563226	+	0.826303i	$0.690440\pi$
$374$	20.1990	1.04446
$375$	66.6040	3.43942
$376$	−4.29464	−0.221479
$377$	0.600152	0.0309094
$378$	−30.2258	−1.55465
$379$	12.4272	0.638341	0.319170	−	0.947697i	$-0.396596\pi$
$379$	12.4272	0.638341	0.319170	+	0.947697i	$0.396596\pi$
$380$	39.0370	2.00255
$381$	27.1290	1.38986
$382$	1.63766	0.0837898
$383$	−22.4964	−1.14951	−0.574755	−	0.818325i	$-0.694903\pi$
$383$	−22.4964	−1.14951	−0.574755	+	0.818325i	$0.694903\pi$
$384$	−44.6087	−2.27643
$385$	40.3844	2.05818
$386$	13.3974	0.681912
$387$	9.57164	0.486554
$388$	−22.3744	−1.13589
$389$	−14.2437	−0.722185	−0.361092	−	0.932530i	$-0.617596\pi$
$389$	−14.2437	−0.722185	−0.361092	+	0.932530i	$0.617596\pi$
$390$	12.8951	0.652971
$391$	22.8765	1.15691
$392$	−67.6605	−3.41737
$393$	3.21912	0.162383
$394$	37.8227	1.90548
$395$	−38.4453	−1.93439
$396$	−12.3539	−0.620808
$397$	5.31786	0.266896	0.133448	−	0.991056i	$-0.457395\pi$
$397$	5.31786	0.266896	0.133448	+	0.991056i	$0.457395\pi$
$398$	−50.1914	−2.51587
$399$	30.2528	1.51453
$400$	15.4967	0.774833
$401$	−9.99294	−0.499024	−0.249512	−	0.968372i	$-0.580270\pi$
$401$	−9.99294	−0.499024	−0.249512	+	0.968372i	$0.580270\pi$
$402$	43.7407	2.18159
$403$	−5.29249	−0.263638
$404$	10.9465	0.544607
$405$	46.2218	2.29678
$406$	12.0061	0.595854
$407$	9.27315	0.459653
$408$	35.2332	1.74430
$409$	−19.1510	−0.946954	−0.473477	−	0.880806i	$-0.657001\pi$
$409$	−19.1510	−0.946954	−0.473477	+	0.880806i	$0.657001\pi$
$410$	−85.0725	−4.20143
$411$	26.8649	1.32515
$412$	−29.0351	−1.43046
$413$	−42.6158	−2.09698
$414$	−21.9808	−1.08030
$415$	54.0225	2.65186
$416$	−2.45283	−0.120260
$417$	−2.20403	−0.107932
$418$	−11.9437	−0.584183
$419$	21.6218	1.05629	0.528146	−	0.849154i	$-0.322887\pi$
$419$	21.6218	1.05629	0.528146	+	0.849154i	$0.322887\pi$
$420$	164.206	8.01243
$421$	−9.84494	−0.479813	−0.239906	−	0.970796i	$-0.577117\pi$
$421$	−9.84494	−0.479813	−0.239906	+	0.970796i	$0.577117\pi$
$422$	−26.5415	−1.29202
$423$	2.26361	0.110060
$424$	−47.3300	−2.29855
$425$	55.6560	2.69971
$426$	74.0089	3.58574
$427$	65.8517	3.18679
$428$	65.2488	3.15392
$429$	−2.51136	−0.121249
$430$	50.2276	2.42219
$431$	22.9241	1.10422	0.552108	−	0.833773i	$-0.313824\pi$
$431$	22.9241	1.10422	0.552108	+	0.833773i	$0.313824\pi$
$432$	3.17920	0.152959
$433$	−5.70317	−0.274077	−0.137038	−	0.990566i	$-0.543758\pi$
$433$	−5.70317	−0.274077	−0.137038	+	0.990566i	$0.543758\pi$
$434$	−105.877	−5.08226
$435$	−9.15972	−0.439175
$436$	2.48502	0.119011
$437$	−13.5269	−0.647078
$438$	−34.1690	−1.63266
$439$	16.7472	0.799301	0.399650	−	0.916668i	$-0.369132\pi$
$439$	16.7472	0.799301	0.399650	+	0.916668i	$0.369132\pi$
$440$	−27.8105	−1.32581
$441$	35.6623	1.69821
$442$	6.38502	0.303704
$443$	19.5199	0.927420	0.463710	−	0.885987i	$-0.346518\pi$
$443$	19.5199	0.927420	0.463710	+	0.885987i	$0.346518\pi$
$444$	37.7053	1.78942
$445$	21.3935	1.01415
$446$	−48.9042	−2.31568
$447$	10.5517	0.499077
$448$	−61.9961	−2.92904
$449$	−16.8123	−0.793422	−0.396711	−	0.917944i	$-0.629848\pi$
$449$	−16.8123	−0.793422	−0.396711	+	0.917944i	$0.629848\pi$
$450$	−53.4770	−2.52093
$451$	16.5680	0.780159
$452$	−34.7087	−1.63256
$453$	20.2037	0.949254
$454$	47.6973	2.23854
$455$	12.7657	0.598467
$456$	−20.8334	−0.975612
$457$	−11.1342	−0.520838	−0.260419	−	0.965496i	$-0.583861\pi$
$457$	−11.1342	−0.520838	−0.260419	+	0.965496i	$0.583861\pi$
$458$	−15.4858	−0.723605
$459$	11.4181	0.532950
$460$	−73.4212	−3.42328
$461$	14.9506	0.696321	0.348160	−	0.937435i	$-0.386806\pi$
$461$	14.9506	0.696321	0.348160	+	0.937435i	$0.386806\pi$
$462$	−50.2401	−2.33738
$463$	23.5492	1.09442	0.547211	−	0.836995i	$-0.315690\pi$
$463$	23.5492	1.09442	0.547211	+	0.836995i	$0.315690\pi$
$464$	−1.26283	−0.0586252
$465$	80.7756	3.74588
$466$	−33.0817	−1.53248
$467$	−27.9683	−1.29422	−0.647109	−	0.762398i	$-0.724022\pi$
$467$	−27.9683	−1.29422	−0.647109	+	0.762398i	$0.724022\pi$
$468$	−3.90515	−0.180516
$469$	43.3017	1.99949
$470$	11.8784	0.547909
$471$	49.1055	2.26266
$472$	29.3471	1.35081
$473$	−9.78194	−0.449774
$474$	47.8278	2.19680
$475$	−32.9094	−1.50999
$476$	81.3064	3.72667
$477$	24.9466	1.14223
$478$	−52.0405	−2.38028
$479$	38.3460	1.75207	0.876036	−	0.482245i	$-0.160178\pi$
$479$	38.3460	1.75207	0.876036	+	0.482245i	$0.160178\pi$
$480$	37.4359	1.70871
$481$	2.93130	0.133656
$482$	51.8179	2.36024
$483$	−56.8997	−2.58903
$484$	−25.9028	−1.17740
$485$	26.5478	1.20547
$486$	−39.7856	−1.80471
$487$	−30.8760	−1.39912	−0.699562	−	0.714572i	$-0.746622\pi$
$487$	−30.8760	−1.39912	−0.699562	+	0.714572i	$0.746622\pi$
$488$	−45.3484	−2.05283
$489$	10.8024	0.488501
$490$	187.140	8.45411
$491$	−22.3150	−1.00706	−0.503531	−	0.863977i	$-0.667966\pi$
$491$	−22.3150	−1.00706	−0.503531	+	0.863977i	$0.667966\pi$
$492$	67.3669	3.03714
$493$	−4.53543	−0.204265
$494$	−3.77546	−0.169866
$495$	14.6583	0.658840
$496$	11.1363	0.500036
$497$	73.2662	3.28644
$498$	−67.2065	−3.01160
$499$	−1.50579	−0.0674082	−0.0337041	−	0.999432i	$-0.510730\pi$
$499$	−1.50579	−0.0674082	−0.0337041	+	0.999432i	$0.510730\pi$
$500$	−105.844	−4.73351
$501$	26.2300	1.17187
$502$	33.6072	1.49996
$503$	19.4009	0.865044	0.432522	−	0.901623i	$-0.357624\pi$
$503$	19.4009	0.865044	0.432522	+	0.901623i	$0.357624\pi$
$504$	−33.5140	−1.49283
$505$	−12.9883	−0.577971
$506$	22.4638	0.998637
$507$	27.8586	1.23724
$508$	−43.1124	−1.91280
$509$	13.7402	0.609026	0.304513	−	0.952508i	$-0.401506\pi$
$509$	13.7402	0.609026	0.304513	+	0.952508i	$0.401506\pi$
$510$	−97.4502	−4.31517
$511$	−33.8261	−1.49638
$512$	14.0632	0.621512
$513$	−6.75150	−0.298086
$514$	−7.02394	−0.309813
$515$	34.4509	1.51809
$516$	−39.7741	−1.75096
$517$	−2.31334	−0.101741
$518$	58.6410	2.57654
$519$	−45.4309	−1.99420
$520$	−8.79105	−0.385513
$521$	−0.127435	−0.00558302	−0.00279151	−	0.999996i	$-0.500889\pi$
$521$	−0.127435	−0.00558302	−0.00279151	+	0.999996i	$0.500889\pi$
$522$	4.35786	0.190738
$523$	12.0231	0.525734	0.262867	−	0.964832i	$-0.415332\pi$
$523$	12.0231	0.525734	0.262867	+	0.964832i	$0.415332\pi$
$524$	−5.11570	−0.223480
$525$	−138.431	−6.04162
$526$	−24.9035	−1.08584
$527$	39.9960	1.74225
$528$	5.28434	0.229971
$529$	2.44151	0.106153
$530$	130.908	5.68629
$531$	−15.4682	−0.671263
$532$	−48.0765	−2.08438
$533$	5.23726	0.226851
$534$	−26.6145	−1.15172
$535$	−77.4195	−3.34714
$536$	−29.8195	−1.28801
$537$	−32.4979	−1.40239
$538$	25.9752	1.11987
$539$	−36.4459	−1.56983
$540$	−36.6458	−1.57698
$541$	−20.7759	−0.893225	−0.446613	−	0.894727i	$-0.647370\pi$
$541$	−20.7759	−0.893225	−0.446613	+	0.894727i	$0.647370\pi$
$542$	−7.73260	−0.332144
$543$	−39.2472	−1.68426
$544$	18.5363	0.794739
$545$	−2.94854	−0.126302
$546$	−15.8812	−0.679652
$547$	−0.609301	−0.0260518	−0.0130259	−	0.999915i	$-0.504146\pi$
$547$	−0.609301	−0.0260518	−0.0130259	+	0.999915i	$0.504146\pi$
$548$	−42.6926	−1.82374
$549$	23.9021	1.02012
$550$	54.6519	2.33037
$551$	2.68180	0.114248
$552$	39.1837	1.66777
$553$	47.3478	2.01343
$554$	−27.1340	−1.15281
$555$	−44.7384	−1.89904
$556$	3.50256	0.148542
$557$	44.8880	1.90196	0.950982	−	0.309246i	$-0.100077\pi$
$557$	44.8880	1.90196	0.950982	+	0.309246i	$0.100077\pi$
$558$	−38.4301	−1.62687
$559$	−3.09213	−0.130783
$560$	−26.8614	−1.13510
$561$	18.9786	0.801279
$562$	15.1845	0.640520
$563$	29.3316	1.23618	0.618090	−	0.786107i	$-0.287907\pi$
$563$	29.3316	1.23618	0.618090	+	0.786107i	$0.287907\pi$
$564$	−9.40622	−0.396073
$565$	41.1829	1.73258
$566$	−51.0067	−2.14397
$567$	−56.9251	−2.39063
$568$	−50.4544	−2.11702
$569$	26.2936	1.10228	0.551142	−	0.834412i	$-0.314192\pi$
$569$	26.2936	1.10228	0.551142	+	0.834412i	$0.314192\pi$
$570$	57.6223	2.41353
$571$	−13.6170	−0.569853	−0.284927	−	0.958549i	$-0.591969\pi$
$571$	−13.6170	−0.569853	−0.284927	+	0.958549i	$0.591969\pi$
$572$	3.99095	0.166870
$573$	1.53872	0.0642807
$574$	104.772	4.37310
$575$	61.8964	2.58126
$576$	−22.5027	−0.937611
$577$	23.7965	0.990663	0.495332	−	0.868704i	$-0.335047\pi$
$577$	23.7965	0.990663	0.495332	+	0.868704i	$0.335047\pi$
$578$	−8.37455	−0.348335
$579$	12.5880	0.523140
$580$	14.5563	0.604416
$581$	−66.5321	−2.76022
$582$	−33.0267	−1.36900
$583$	−25.4947	−1.05588
$584$	23.2941	0.963919
$585$	4.63357	0.191574
$586$	3.63396	0.150117
$587$	−26.4987	−1.09372	−0.546859	−	0.837225i	$-0.684177\pi$
$587$	−26.4987	−1.09372	−0.546859	+	0.837225i	$0.684177\pi$
$588$	−148.192	−6.11132
$589$	−23.6496	−0.974466
$590$	−81.1701	−3.34172
$591$	35.5376	1.46182
$592$	−6.16797	−0.253502
$593$	−8.05340	−0.330713	−0.165357	−	0.986234i	$-0.552878\pi$
$593$	−8.05340	−0.330713	−0.165357	+	0.986234i	$0.552878\pi$
$594$	11.2121	0.460037
$595$	−96.4723	−3.95498
$596$	−16.7683	−0.686857
$597$	−47.1590	−1.93009
$598$	7.10093	0.290379
$599$	−1.46434	−0.0598312	−0.0299156	−	0.999552i	$-0.509524\pi$
$599$	−1.46434	−0.0598312	−0.0299156	+	0.999552i	$0.509524\pi$
$600$	95.3296	3.89182
$601$	−4.92786	−0.201011	−0.100506	−	0.994936i	$-0.532046\pi$
$601$	−4.92786	−0.201011	−0.100506	+	0.994936i	$0.532046\pi$
$602$	−61.8585	−2.52116
$603$	15.7172	0.640053
$604$	−32.1070	−1.30641
$605$	30.7344	1.24953
$606$	16.1580	0.656375
$607$	−18.9563	−0.769411	−0.384706	−	0.923039i	$-0.625697\pi$
$607$	−18.9563	−0.769411	−0.384706	+	0.923039i	$0.625697\pi$
$608$	−10.9605	−0.444509
$609$	11.2808	0.457120
$610$	125.428	5.07841
$611$	−0.731261	−0.0295836
$612$	29.5117	1.19294
$613$	−33.9617	−1.37170	−0.685851	−	0.727742i	$-0.740570\pi$
$613$	−33.9617	−1.37170	−0.685851	+	0.727742i	$0.740570\pi$
$614$	27.7301	1.11910
$615$	−79.9327	−3.22320
$616$	34.2503	1.37999
$617$	−10.0249	−0.403587	−0.201794	−	0.979428i	$-0.564677\pi$
$617$	−10.0249	−0.403587	−0.201794	+	0.979428i	$0.564677\pi$
$618$	−42.8586	−1.72403
$619$	18.1231	0.728427	0.364214	−	0.931315i	$-0.381338\pi$
$619$	18.1231	0.728427	0.364214	+	0.931315i	$0.381338\pi$
$620$	−128.366	−5.15528
$621$	12.6983	0.509566
$622$	−39.1172	−1.56846
$623$	−26.3474	−1.05559
$624$	1.67041	0.0668699
$625$	64.2304	2.56921
$626$	−44.2183	−1.76732
$627$	−11.2221	−0.448166
$628$	−78.0365	−3.11399
$629$	−22.1522	−0.883265
$630$	92.6952	3.69307
$631$	13.4659	0.536067	0.268034	−	0.963410i	$-0.413626\pi$
$631$	13.4659	0.536067	0.268034	+	0.963410i	$0.413626\pi$
$632$	−32.6058	−1.29699
$633$	−24.9379	−0.991194
$634$	−56.1465	−2.22986
$635$	51.1541	2.02999
$636$	−103.663	−4.11052
$637$	−11.5208	−0.456469
$638$	−4.45360	−0.176320
$639$	26.5934	1.05202
$640$	−84.1134	−3.32488
$641$	33.6310	1.32834	0.664172	−	0.747580i	$-0.268784\pi$
$641$	33.6310	1.32834	0.664172	+	0.747580i	$0.268784\pi$
$642$	96.3135	3.80119
$643$	−16.2127	−0.639365	−0.319683	−	0.947525i	$-0.603576\pi$
$643$	−16.2127	−0.639365	−0.319683	+	0.947525i	$0.603576\pi$
$644$	90.4228	3.56316
$645$	47.1930	1.85822
$646$	28.5316	1.12256
$647$	35.1219	1.38078	0.690392	−	0.723436i	$-0.257438\pi$
$647$	35.1219	1.38078	0.690392	+	0.723436i	$0.257438\pi$
$648$	39.2011	1.53997
$649$	15.8081	0.620520
$650$	17.2758	0.677613
$651$	−99.4803	−3.89894
$652$	−17.1668	−0.672302
$653$	15.1009	0.590943	0.295471	−	0.955352i	$-0.404523\pi$
$653$	15.1009	0.590943	0.295471	+	0.955352i	$0.404523\pi$
$654$	3.66813	0.143435
$655$	6.06992	0.237171
$656$	−11.0201	−0.430263
$657$	−12.2778	−0.479004
$658$	−14.6290	−0.570297
$659$	−37.3635	−1.45548	−0.727738	−	0.685855i	$-0.759428\pi$
$659$	−37.3635	−1.45548	−0.727738	+	0.685855i	$0.759428\pi$
$660$	−60.9112	−2.37096
$661$	−24.2761	−0.944232	−0.472116	−	0.881536i	$-0.656510\pi$
$661$	−24.2761	−0.944232	−0.472116	+	0.881536i	$0.656510\pi$
$662$	22.6562	0.880557
$663$	5.99926	0.232992
$664$	45.8170	1.77804
$665$	57.0441	2.21207
$666$	21.2849	0.824772
$667$	−5.04396	−0.195303
$668$	−41.6837	−1.61279
$669$	−45.9496	−1.77651
$670$	82.4767	3.18635
$671$	−24.4273	−0.943005
$672$	−46.1046	−1.77853
$673$	42.0096	1.61935	0.809675	−	0.586878i	$-0.199643\pi$
$673$	42.0096	1.61935	0.809675	+	0.586878i	$0.199643\pi$
$674$	32.0649	1.23509
$675$	30.8936	1.18910
$676$	−44.2718	−1.70276
$677$	−32.8480	−1.26245	−0.631226	−	0.775599i	$-0.717448\pi$
$677$	−32.8480	−1.26245	−0.631226	+	0.775599i	$0.717448\pi$
$678$	−51.2334	−1.96761
$679$	−32.6953	−1.25473
$680$	66.4351	2.54767
$681$	44.8156	1.71734
$682$	39.2744	1.50390
$683$	1.98811	0.0760727	0.0380364	−	0.999276i	$-0.487890\pi$
$683$	1.98811	0.0760727	0.0380364	+	0.999276i	$0.487890\pi$
$684$	−17.4503	−0.667228
$685$	50.6560	1.93547
$686$	−146.431	−5.59078
$687$	−14.5502	−0.555126
$688$	6.50638	0.248054
$689$	−8.05902	−0.307024
$690$	−108.377	−4.12583
$691$	−16.0568	−0.610829	−0.305415	−	0.952219i	$-0.598795\pi$
$691$	−16.0568	−0.610829	−0.305415	+	0.952219i	$0.598795\pi$
$692$	72.1970	2.74452
$693$	−18.0526	−0.685761
$694$	−16.8760	−0.640606
$695$	−4.15589	−0.157642
$696$	−7.76844	−0.294462
$697$	−39.5786	−1.49915
$698$	−59.0205	−2.23396
$699$	−31.0830	−1.17567
$700$	219.989	8.31480
$701$	10.6789	0.403337	0.201669	−	0.979454i	$-0.435364\pi$
$701$	10.6789	0.403337	0.201669	+	0.979454i	$0.435364\pi$
$702$	3.54420	0.133767
$703$	13.0986	0.494023
$704$	22.9971	0.866735
$705$	11.1607	0.420338
$706$	−15.5942	−0.586896
$707$	15.9959	0.601587
$708$	64.2767	2.41567
$709$	31.6235	1.18764	0.593822	−	0.804596i	$-0.297618\pi$
$709$	31.6235	1.18764	0.593822	+	0.804596i	$0.297618\pi$
$710$	139.550	5.23721
$711$	17.1858	0.644518
$712$	18.1440	0.679975
$713$	44.4805	1.66581
$714$	120.016	4.49149
$715$	−4.73537	−0.177093
$716$	51.6445	1.93004
$717$	−48.8965	−1.82607
$718$	−60.1689	−2.24548
$719$	−13.6365	−0.508557	−0.254279	−	0.967131i	$-0.581838\pi$
$719$	−13.6365	−0.508557	−0.254279	+	0.967131i	$0.581838\pi$
$720$	−9.74984	−0.363355
$721$	−42.4285	−1.58012
$722$	27.6986	1.03083
$723$	48.6873	1.81070
$724$	62.3701	2.31797
$725$	−12.2714	−0.455749
$726$	−38.2351	−1.41904
$727$	−20.6932	−0.767469	−0.383735	−	0.923443i	$-0.625362\pi$
$727$	−20.6932	−0.767469	−0.383735	+	0.923443i	$0.625362\pi$
$728$	10.8267	0.401266
$729$	−4.01590	−0.148737
$730$	−64.4284	−2.38460
$731$	23.3676	0.864282
$732$	−99.3232	−3.67109
$733$	18.0433	0.666444	0.333222	−	0.942848i	$-0.391864\pi$
$733$	18.0433	0.666444	0.333222	+	0.942848i	$0.391864\pi$
$734$	9.87014	0.364313
$735$	175.833	6.48571
$736$	20.6147	0.759868
$737$	−16.0625	−0.591670
$738$	38.0291	1.39987
$739$	32.6291	1.20028	0.600141	−	0.799894i	$-0.295111\pi$
$739$	32.6291	1.20028	0.600141	+	0.799894i	$0.295111\pi$
$740$	71.0965	2.61356
$741$	−3.54736	−0.130316
$742$	−161.222	−5.91864
$743$	9.85026	0.361371	0.180686	−	0.983541i	$-0.442168\pi$
$743$	9.85026	0.361371	0.180686	+	0.983541i	$0.442168\pi$
$744$	68.5065	2.51157
$745$	19.8961	0.728936
$746$	51.0328	1.86845
$747$	−24.1491	−0.883569
$748$	−30.1601	−1.10276
$749$	95.3470	3.48390
$750$	−156.237	−5.70496
$751$	−52.0527	−1.89943	−0.949715	−	0.313115i	$-0.898627\pi$
$751$	−52.0527	−1.89943	−0.949715	+	0.313115i	$0.898627\pi$
$752$	1.53870	0.0561107
$753$	31.5768	1.15072
$754$	−1.40781	−0.0512694
$755$	38.0958	1.38645
$756$	45.1316	1.64142
$757$	12.0261	0.437095	0.218547	−	0.975826i	$-0.429868\pi$
$757$	12.0261	0.437095	0.218547	+	0.975826i	$0.429868\pi$
$758$	−29.1511	−1.05881
$759$	21.1066	0.766121
$760$	−39.2831	−1.42495
$761$	−15.7908	−0.572415	−0.286207	−	0.958168i	$-0.592395\pi$
$761$	−15.7908	−0.572415	−0.286207	+	0.958168i	$0.592395\pi$
$762$	−63.6381	−2.30536
$763$	3.63132	0.131462
$764$	−2.44527	−0.0884666
$765$	−35.0165	−1.26602
$766$	52.7709	1.90669
$767$	4.99702	0.180432
$768$	51.2471	1.84922
$769$	39.3844	1.42024	0.710118	−	0.704082i	$-0.248641\pi$
$769$	39.3844	1.42024	0.710118	+	0.704082i	$0.248641\pi$
$770$	−94.7318	−3.41390
$771$	−6.59958	−0.237678
$772$	−20.0044	−0.719974
$773$	−19.2931	−0.693926	−0.346963	−	0.937879i	$-0.612787\pi$
$773$	−19.2931	−0.693926	−0.346963	+	0.937879i	$0.612787\pi$
$774$	−22.4527	−0.807046
$775$	108.216	3.88724
$776$	22.5154	0.808257
$777$	55.0982	1.97664
$778$	33.4123	1.19789
$779$	23.4028	0.838494
$780$	−19.2544	−0.689417
$781$	−27.1777	−0.972493
$782$	−53.6626	−1.91897
$783$	−2.51753	−0.0899691
$784$	24.2417	0.865775
$785$	92.5924	3.30477
$786$	−7.55127	−0.269345
$787$	−38.9920	−1.38991	−0.694957	−	0.719051i	$-0.744577\pi$
$787$	−38.9920	−1.38991	−0.694957	+	0.719051i	$0.744577\pi$
$788$	−56.4749	−2.01184
$789$	−23.3989	−0.833023
$790$	90.1832	3.20858
$791$	−50.7193	−1.80337
$792$	12.4318	0.441745
$793$	−7.72161	−0.274202
$794$	−12.4744	−0.442700
$795$	122.999	4.36234
$796$	74.9432	2.65629
$797$	28.1720	0.997904	0.498952	−	0.866630i	$-0.333718\pi$
$797$	28.1720	0.997904	0.498952	+	0.866630i	$0.333718\pi$
$798$	−70.9655	−2.51215
$799$	5.52623	0.195504
$800$	50.1534	1.77319
$801$	−9.56330	−0.337902
$802$	23.4410	0.827730
$803$	12.5476	0.442795
$804$	−65.3114	−2.30335
$805$	−107.289	−3.78145
$806$	12.4149	0.437295
$807$	24.4059	0.859127
$808$	−11.0155	−0.387523
$809$	−6.44028	−0.226428	−0.113214	−	0.993571i	$-0.536115\pi$
$809$	−6.44028	−0.226428	−0.113214	+	0.993571i	$0.536115\pi$
$810$	−108.425	−3.80967
$811$	−22.7243	−0.797958	−0.398979	−	0.916960i	$-0.630635\pi$
$811$	−22.7243	−0.797958	−0.398979	+	0.916960i	$0.630635\pi$
$812$	−17.9270	−0.629113
$813$	−7.26543	−0.254810
$814$	−21.7525	−0.762426
$815$	20.3688	0.713489
$816$	−12.6235	−0.441911
$817$	−13.8173	−0.483405
$818$	44.9234	1.57071
$819$	−5.70653	−0.199402
$820$	127.026	4.43594
$821$	6.55199	0.228666	0.114333	−	0.993442i	$-0.463527\pi$
$821$	6.55199	0.228666	0.114333	+	0.993442i	$0.463527\pi$
$822$	−63.0184	−2.19802
$823$	−2.12070	−0.0739231	−0.0369616	−	0.999317i	$-0.511768\pi$
$823$	−2.12070	−0.0739231	−0.0369616	+	0.999317i	$0.511768\pi$
$824$	29.2182	1.01786
$825$	51.3501	1.78778
$826$	99.9661	3.47827
$827$	3.44505	0.119796	0.0598981	−	0.998204i	$-0.480922\pi$
$827$	3.44505	0.119796	0.0598981	+	0.998204i	$0.480922\pi$
$828$	32.8207	1.14060
$829$	−11.9121	−0.413725	−0.206862	−	0.978370i	$-0.566325\pi$
$829$	−11.9121	−0.413725	−0.206862	+	0.978370i	$0.566325\pi$
$830$	−126.723	−4.39864
$831$	−25.4946	−0.884399
$832$	7.26951	0.252025
$833$	87.0638	3.01658
$834$	5.17012	0.179027
$835$	49.4589	1.71160
$836$	17.8337	0.616791
$837$	22.2010	0.767379
$838$	−50.7193	−1.75207
$839$	24.4357	0.843614	0.421807	−	0.906686i	$-0.361396\pi$
$839$	24.4357	0.843614	0.421807	+	0.906686i	$0.361396\pi$
$840$	−165.241	−5.70136
$841$	1.00000	0.0344828
$842$	23.0938	0.795865
$843$	14.2671	0.491386
$844$	39.6304	1.36413
$845$	52.5297	1.80708
$846$	−5.30987	−0.182557
$847$	−37.8514	−1.30059
$848$	16.9576	0.582326
$849$	−47.9251	−1.64478
$850$	−130.555	−4.47801
$851$	−24.6360	−0.844511
$852$	−110.506	−3.78589
$853$	−1.09284	−0.0374181	−0.0187090	−	0.999825i	$-0.505956\pi$
$853$	−1.09284	−0.0374181	−0.0187090	+	0.999825i	$0.505956\pi$
$854$	−154.472	−5.28592
$855$	20.7052	0.708104
$856$	−65.6602	−2.24422
$857$	−37.7887	−1.29084	−0.645418	−	0.763830i	$-0.723317\pi$
$857$	−37.7887	−1.29084	−0.645418	+	0.763830i	$0.723317\pi$
$858$	5.89103	0.201116
$859$	13.6572	0.465977	0.232989	−	0.972479i	$-0.425149\pi$
$859$	13.6572	0.465977	0.232989	+	0.972479i	$0.425149\pi$
$860$	−74.9974	−2.55739
$861$	98.4422	3.35490
$862$	−53.7743	−1.83156
$863$	35.7435	1.21672	0.608362	−	0.793660i	$-0.291827\pi$
$863$	35.7435	1.21672	0.608362	+	0.793660i	$0.291827\pi$
$864$	10.2892	0.350045
$865$	−85.6638	−2.91266
$866$	13.3782	0.454611
$867$	−7.86859	−0.267231
$868$	158.090	5.36593
$869$	−17.5634	−0.595797
$870$	21.4864	0.728459
$871$	−5.07745	−0.172043
$872$	−2.50068	−0.0846839
$873$	−11.8674	−0.401650
$874$	31.7307	1.07331
$875$	−154.669	−5.22876
$876$	51.0194	1.72379
$877$	−28.2430	−0.953700	−0.476850	−	0.878985i	$-0.658221\pi$
$877$	−28.2430	−0.953700	−0.476850	+	0.878985i	$0.658221\pi$
$878$	−39.2848	−1.32580
$879$	3.41441	0.115165
$880$	9.96406	0.335888
$881$	−34.3857	−1.15848	−0.579241	−	0.815156i	$-0.696651\pi$
$881$	−34.3857	−1.15848	−0.579241	+	0.815156i	$0.696651\pi$
$882$	−83.6551	−2.81681
$883$	19.1846	0.645612	0.322806	−	0.946465i	$-0.395374\pi$
$883$	19.1846	0.645612	0.322806	+	0.946465i	$0.395374\pi$
$884$	−9.53379	−0.320656
$885$	−76.2661	−2.56366
$886$	−45.7890	−1.53831
$887$	−25.7691	−0.865241	−0.432620	−	0.901576i	$-0.642411\pi$
$887$	−25.7691	−0.865241	−0.432620	+	0.901576i	$0.642411\pi$
$888$	−37.9430	−1.27328
$889$	−62.9995	−2.11293
$890$	−50.1838	−1.68217
$891$	21.1160	0.707413
$892$	73.0213	2.44493
$893$	−3.26766	−0.109348
$894$	−24.7517	−0.827819
$895$	−61.2776	−2.04828
$896$	103.591	3.46073
$897$	6.67192	0.222769
$898$	39.4375	1.31605
$899$	−8.81858	−0.294116
$900$	79.8492	2.66164
$901$	60.9030	2.02897
$902$	−38.8646	−1.29405
$903$	−58.1212	−1.93415
$904$	34.9276	1.16167
$905$	−74.0039	−2.45997
$906$	−47.3930	−1.57453
$907$	11.0002	0.365256	0.182628	−	0.983182i	$-0.441540\pi$
$907$	11.0002	0.365256	0.182628	+	0.983182i	$0.441540\pi$
$908$	−71.2192	−2.36349
$909$	5.80601	0.192573
$910$	−29.9453	−0.992677
$911$	−31.6904	−1.04995	−0.524974	−	0.851118i	$-0.675925\pi$
$911$	−31.6904	−1.04995	−0.524974	+	0.851118i	$0.675925\pi$
$912$	7.46428	0.247167
$913$	24.6797	0.816778
$914$	26.1182	0.863913
$915$	117.850	3.89599
$916$	23.1227	0.763994
$917$	−7.47549	−0.246863
$918$	−26.7840	−0.884003
$919$	11.7259	0.386801	0.193401	−	0.981120i	$-0.438048\pi$
$919$	11.7259	0.386801	0.193401	+	0.981120i	$0.438048\pi$
$920$	73.8841	2.43589
$921$	26.0548	0.858534
$922$	−35.0705	−1.15499
$923$	−8.59102	−0.282777
$924$	75.0160	2.46784
$925$	−59.9367	−1.97071
$926$	−55.2405	−1.81532
$927$	−15.4002	−0.505810
$928$	−4.08701	−0.134163
$929$	17.5156	0.574669	0.287334	−	0.957830i	$-0.407231\pi$
$929$	17.5156	0.574669	0.287334	+	0.957830i	$0.407231\pi$
$930$	−189.480	−6.21329
$931$	−51.4808	−1.68722
$932$	49.3959	1.61802
$933$	−36.7539	−1.20327
$934$	65.6067	2.14672
$935$	35.7858	1.17032
$936$	3.92977	0.128449
$937$	−3.56991	−0.116624	−0.0583119	−	0.998298i	$-0.518572\pi$
$937$	−3.56991	−0.116624	−0.0583119	+	0.998298i	$0.518572\pi$
$938$	−101.575	−3.31655
$939$	−41.5468	−1.35583
$940$	−17.7362	−0.578491
$941$	11.5206	0.375561	0.187781	−	0.982211i	$-0.439871\pi$
$941$	11.5206	0.375561	0.187781	+	0.982211i	$0.439871\pi$
$942$	−115.189	−3.75307
$943$	−44.0164	−1.43337
$944$	−10.5146	−0.342221
$945$	−53.5499	−1.74198
$946$	22.9460	0.746039
$947$	−3.90317	−0.126836	−0.0634181	−	0.997987i	$-0.520200\pi$
$947$	−3.90317	−0.126836	−0.0634181	+	0.997987i	$0.520200\pi$
$948$	−71.4141	−2.31942
$949$	3.96637	0.128754
$950$	77.1974	2.50462
$951$	−52.7543	−1.71068
$952$	−81.8190	−2.65177
$953$	30.0662	0.973939	0.486969	−	0.873419i	$-0.338102\pi$
$953$	30.0662	0.973939	0.486969	+	0.873419i	$0.338102\pi$
$954$	−58.5186	−1.89461
$955$	2.90138	0.0938863
$956$	77.7043	2.51314
$957$	−4.18453	−0.135267
$958$	−89.9503	−2.90616
$959$	−62.3861	−2.01455
$960$	−110.950	−3.58088
$961$	46.7673	1.50862
$962$	−6.87610	−0.221694
$963$	34.6080	1.11523
$964$	−77.3719	−2.49198
$965$	23.7358	0.764081
$966$	133.473	4.29442
$967$	26.7370	0.859805	0.429903	−	0.902875i	$-0.358548\pi$
$967$	26.7370	0.859805	0.429903	+	0.902875i	$0.358548\pi$
$968$	26.0662	0.837798
$969$	26.8079	0.861193
$970$	−62.2746	−1.99952
$971$	−57.5195	−1.84589	−0.922944	−	0.384934i	$-0.874224\pi$
$971$	−57.5195	−1.84589	−0.922944	+	0.384934i	$0.874224\pi$
$972$	59.4059	1.90544
$973$	5.11824	0.164083
$974$	72.4275	2.32073
$975$	16.2321	0.519842
$976$	16.2476	0.520074
$977$	49.6808	1.58943	0.794715	−	0.606983i	$-0.207620\pi$
$977$	49.6808	1.58943	0.794715	+	0.606983i	$0.207620\pi$
$978$	−25.3398	−0.810277
$979$	9.77341	0.312359
$980$	−279.428	−8.92599
$981$	1.31806	0.0420823
$982$	52.3455	1.67041
$983$	10.8560	0.346253	0.173126	−	0.984900i	$-0.444613\pi$
$983$	10.8560	0.346253	0.173126	+	0.984900i	$0.444613\pi$
$984$	−67.7917	−2.16112
$985$	67.0091	2.13509
$986$	10.6390	0.338815
$987$	−13.7452	−0.437513
$988$	5.63733	0.179347
$989$	25.9877	0.826360
$990$	−34.3847	−1.09282
$991$	2.72212	0.0864711	0.0432356	−	0.999065i	$-0.486233\pi$
$991$	2.72212	0.0864711	0.0432356	+	0.999065i	$0.486233\pi$
$992$	36.0416	1.14432
$993$	21.2874	0.675534
$994$	−171.865	−5.45121
$995$	−88.9222	−2.81902
$996$	100.349	3.17969
$997$	−8.49146	−0.268927	−0.134464	−	0.990919i	$-0.542931\pi$
$997$	−8.49146	−0.268927	−0.134464	+	0.990919i	$0.542931\pi$
$998$	3.53220	0.111810
$999$	−12.2963	−0.389036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.e.1.15	✓	103

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.e.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.34575 q^{2} -2.20403 q^{3} +3.50256 q^{4} -4.15589 q^{5} +5.17012 q^{6} +5.11824 q^{7} -3.52465 q^{8} +1.85776 q^{9} +O(q^{10})\)	\(q-2.34575 q^{2} -2.20403 q^{3} +3.50256 q^{4} -4.15589 q^{5} +5.17012 q^{6} +5.11824 q^{7} -3.52465 q^{8} +1.85776 q^{9} +9.74869 q^{10} -1.89858 q^{11} -7.71977 q^{12} -0.600152 q^{13} -12.0061 q^{14} +9.15972 q^{15} +1.26283 q^{16} +4.53543 q^{17} -4.35786 q^{18} -2.68180 q^{19} -14.5563 q^{20} -11.2808 q^{21} +4.45360 q^{22} +5.04396 q^{23} +7.76844 q^{24} +12.2714 q^{25} +1.40781 q^{26} +2.51753 q^{27} +17.9270 q^{28} -1.00000 q^{29} -21.4864 q^{30} +8.81858 q^{31} +4.08701 q^{32} +4.18453 q^{33} -10.6390 q^{34} -21.2708 q^{35} +6.50693 q^{36} -4.88426 q^{37} +6.29084 q^{38} +1.32276 q^{39} +14.6480 q^{40} -8.72655 q^{41} +26.4619 q^{42} +5.15224 q^{43} -6.64990 q^{44} -7.72065 q^{45} -11.8319 q^{46} +1.21846 q^{47} -2.78331 q^{48} +19.1964 q^{49} -28.7857 q^{50} -9.99623 q^{51} -2.10207 q^{52} +13.4283 q^{53} -5.90550 q^{54} +7.89028 q^{55} -18.0400 q^{56} +5.91077 q^{57} +2.34575 q^{58} -8.32625 q^{59} +32.0825 q^{60} +12.8661 q^{61} -20.6862 q^{62} +9.50848 q^{63} -12.1128 q^{64} +2.49417 q^{65} -9.81588 q^{66} +8.46028 q^{67} +15.8856 q^{68} -11.1171 q^{69} +49.8962 q^{70} +14.3147 q^{71} -6.54796 q^{72} -6.60893 q^{73} +11.4573 q^{74} -27.0466 q^{75} -9.39317 q^{76} -9.71738 q^{77} -3.10286 q^{78} +9.25080 q^{79} -5.24816 q^{80} -11.1220 q^{81} +20.4703 q^{82} -12.9990 q^{83} -39.5116 q^{84} -18.8487 q^{85} -12.0859 q^{86} +2.20403 q^{87} +6.69182 q^{88} -5.14775 q^{89} +18.1108 q^{90} -3.07172 q^{91} +17.6668 q^{92} -19.4364 q^{93} -2.85820 q^{94} +11.1453 q^{95} -9.00791 q^{96} -6.38800 q^{97} -45.0300 q^{98} -3.52711 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) \) 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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