LMFDB - Embedded newform 6026.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.33099 q^{3} +1.00000 q^{4} -3.73356 q^{5} -3.33099 q^{6} +2.28084 q^{7} +1.00000 q^{8} +8.09549 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.33099 q^{3} +1.00000 q^{4} -3.73356 q^{5} -3.33099 q^{6} +2.28084 q^{7} +1.00000 q^{8} +8.09549 q^{9} -3.73356 q^{10} -6.21504 q^{11} -3.33099 q^{12} -6.33964 q^{13} +2.28084 q^{14} +12.4365 q^{15} +1.00000 q^{16} -7.48655 q^{17} +8.09549 q^{18} +3.49466 q^{19} -3.73356 q^{20} -7.59746 q^{21} -6.21504 q^{22} +1.00000 q^{23} -3.33099 q^{24} +8.93950 q^{25} -6.33964 q^{26} -16.9730 q^{27} +2.28084 q^{28} -5.25887 q^{29} +12.4365 q^{30} +0.391307 q^{31} +1.00000 q^{32} +20.7022 q^{33} -7.48655 q^{34} -8.51567 q^{35} +8.09549 q^{36} -4.70049 q^{37} +3.49466 q^{38} +21.1173 q^{39} -3.73356 q^{40} -12.3276 q^{41} -7.59746 q^{42} -2.56744 q^{43} -6.21504 q^{44} -30.2250 q^{45} +1.00000 q^{46} -0.994962 q^{47} -3.33099 q^{48} -1.79776 q^{49} +8.93950 q^{50} +24.9376 q^{51} -6.33964 q^{52} +0.241660 q^{53} -16.9730 q^{54} +23.2042 q^{55} +2.28084 q^{56} -11.6407 q^{57} -5.25887 q^{58} +12.0074 q^{59} +12.4365 q^{60} -10.7362 q^{61} +0.391307 q^{62} +18.4645 q^{63} +1.00000 q^{64} +23.6695 q^{65} +20.7022 q^{66} -7.98157 q^{67} -7.48655 q^{68} -3.33099 q^{69} -8.51567 q^{70} -2.49281 q^{71} +8.09549 q^{72} +1.44499 q^{73} -4.70049 q^{74} -29.7774 q^{75} +3.49466 q^{76} -14.1755 q^{77} +21.1173 q^{78} -9.05545 q^{79} -3.73356 q^{80} +32.2505 q^{81} -12.3276 q^{82} -14.6828 q^{83} -7.59746 q^{84} +27.9515 q^{85} -2.56744 q^{86} +17.5172 q^{87} -6.21504 q^{88} -2.19752 q^{89} -30.2250 q^{90} -14.4597 q^{91} +1.00000 q^{92} -1.30344 q^{93} -0.994962 q^{94} -13.0475 q^{95} -3.33099 q^{96} -17.2097 q^{97} -1.79776 q^{98} -50.3138 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) $ 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.33099	−1.92315	−0.961574	−	0.274546i	$-0.911472\pi$
$3$	−3.33099	−1.92315	−0.961574	+	0.274546i	$0.911472\pi$
$4$	1.00000	0.500000
$5$	−3.73356	−1.66970	−0.834850	−	0.550477i	$-0.814446\pi$
$5$	−3.73356	−1.66970	−0.834850	+	0.550477i	$0.814446\pi$
$6$	−3.33099	−1.35987
$7$	2.28084	0.862077	0.431038	−	0.902334i	$-0.358147\pi$
$7$	2.28084	0.862077	0.431038	+	0.902334i	$0.358147\pi$
$8$	1.00000	0.353553
$9$	8.09549	2.69850
$10$	−3.73356	−1.18066
$11$	−6.21504	−1.87390	−0.936952	−	0.349458i	$-0.886366\pi$
$11$	−6.21504	−1.87390	−0.936952	+	0.349458i	$0.886366\pi$
$12$	−3.33099	−0.961574
$13$	−6.33964	−1.75830	−0.879150	−	0.476545i	$-0.841889\pi$
$13$	−6.33964	−1.75830	−0.879150	+	0.476545i	$0.841889\pi$
$14$	2.28084	0.609580
$15$	12.4365	3.21108
$16$	1.00000	0.250000
$17$	−7.48655	−1.81576	−0.907878	−	0.419235i	$-0.862298\pi$
$17$	−7.48655	−1.81576	−0.907878	+	0.419235i	$0.862298\pi$
$18$	8.09549	1.90813
$19$	3.49466	0.801729	0.400865	−	0.916137i	$-0.368710\pi$
$19$	3.49466	0.801729	0.400865	+	0.916137i	$0.368710\pi$
$20$	−3.73356	−0.834850
$21$	−7.59746	−1.65790
$22$	−6.21504	−1.32505
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−3.33099	−0.679935
$25$	8.93950	1.78790
$26$	−6.33964	−1.24331
$27$	−16.9730	−3.26646
$28$	2.28084	0.431038
$29$	−5.25887	−0.976547	−0.488273	−	0.872691i	$-0.662373\pi$
$29$	−5.25887	−0.976547	−0.488273	+	0.872691i	$0.662373\pi$
$30$	12.4365	2.27058
$31$	0.391307	0.0702808	0.0351404	−	0.999382i	$-0.488812\pi$
$31$	0.391307	0.0702808	0.0351404	+	0.999382i	$0.488812\pi$
$32$	1.00000	0.176777
$33$	20.7022	3.60379
$34$	−7.48655	−1.28393
$35$	−8.51567	−1.43941
$36$	8.09549	1.34925
$37$	−4.70049	−0.772756	−0.386378	−	0.922340i	$-0.626274\pi$
$37$	−4.70049	−0.772756	−0.386378	+	0.922340i	$0.626274\pi$
$38$	3.49466	0.566908
$39$	21.1173	3.38147
$40$	−3.73356	−0.590328
$41$	−12.3276	−1.92525	−0.962625	−	0.270838i	$-0.912699\pi$
$41$	−12.3276	−1.92525	−0.962625	+	0.270838i	$0.912699\pi$
$42$	−7.59746	−1.17231
$43$	−2.56744	−0.391531	−0.195765	−	0.980651i	$-0.562719\pi$
$43$	−2.56744	−0.391531	−0.195765	+	0.980651i	$0.562719\pi$
$44$	−6.21504	−0.936952
$45$	−30.2250	−4.50568
$46$	1.00000	0.147442
$47$	−0.994962	−0.145130	−0.0725650	−	0.997364i	$-0.523118\pi$
$47$	−0.994962	−0.145130	−0.0725650	+	0.997364i	$0.523118\pi$
$48$	−3.33099	−0.480787
$49$	−1.79776	−0.256823
$50$	8.93950	1.26424
$51$	24.9376	3.49197
$52$	−6.33964	−0.879150
$53$	0.241660	0.0331946	0.0165973	−	0.999862i	$-0.494717\pi$
$53$	0.241660	0.0331946	0.0165973	+	0.999862i	$0.494717\pi$
$54$	−16.9730	−2.30974
$55$	23.2042	3.12886
$56$	2.28084	0.304790
$57$	−11.6407	−1.54184
$58$	−5.25887	−0.690523
$59$	12.0074	1.56324	0.781618	−	0.623757i	$-0.214395\pi$
$59$	12.0074	1.56324	0.781618	+	0.623757i	$0.214395\pi$
$60$	12.4365	1.60554
$61$	−10.7362	−1.37463	−0.687313	−	0.726362i	$-0.741210\pi$
$61$	−10.7362	−1.37463	−0.687313	+	0.726362i	$0.741210\pi$
$62$	0.391307	0.0496960
$63$	18.4645	2.32631
$64$	1.00000	0.125000
$65$	23.6695	2.93583
$66$	20.7022	2.54827
$67$	−7.98157	−0.975104	−0.487552	−	0.873094i	$-0.662110\pi$
$67$	−7.98157	−0.975104	−0.487552	+	0.873094i	$0.662110\pi$
$68$	−7.48655	−0.907878
$69$	−3.33099	−0.401004
$70$	−8.51567	−1.01782
$71$	−2.49281	−0.295842	−0.147921	−	0.988999i	$-0.547258\pi$
$71$	−2.49281	−0.295842	−0.147921	+	0.988999i	$0.547258\pi$
$72$	8.09549	0.954063
$73$	1.44499	0.169123	0.0845614	−	0.996418i	$-0.473051\pi$
$73$	1.44499	0.169123	0.0845614	+	0.996418i	$0.473051\pi$
$74$	−4.70049	−0.546421
$75$	−29.7774	−3.43840
$76$	3.49466	0.400865
$77$	−14.1755	−1.61545
$78$	21.1173	2.39106
$79$	−9.05545	−1.01882	−0.509409	−	0.860524i	$-0.670136\pi$
$79$	−9.05545	−1.01882	−0.509409	+	0.860524i	$0.670136\pi$
$80$	−3.73356	−0.417425
$81$	32.2505	3.58339
$82$	−12.3276	−1.36136
$83$	−14.6828	−1.61165	−0.805826	−	0.592152i	$-0.798278\pi$
$83$	−14.6828	−1.61165	−0.805826	+	0.592152i	$0.798278\pi$
$84$	−7.59746	−0.828951
$85$	27.9515	3.03177
$86$	−2.56744	−0.276854
$87$	17.5172	1.87804
$88$	−6.21504	−0.662525
$89$	−2.19752	−0.232937	−0.116468	−	0.993194i	$-0.537157\pi$
$89$	−2.19752	−0.232937	−0.116468	+	0.993194i	$0.537157\pi$
$90$	−30.2250	−3.18600
$91$	−14.4597	−1.51579
$92$	1.00000	0.104257
$93$	−1.30344	−0.135160
$94$	−0.994962	−0.102622
$95$	−13.0475	−1.33865
$96$	−3.33099	−0.339968
$97$	−17.2097	−1.74738	−0.873692	−	0.486479i	$-0.838281\pi$
$97$	−17.2097	−1.74738	−0.873692	+	0.486479i	$0.838281\pi$
$98$	−1.79776	−0.181602
$99$	−50.3138	−5.05673
$100$	8.93950	0.893950
$101$	−1.47774	−0.147041	−0.0735204	−	0.997294i	$-0.523423\pi$
$101$	−1.47774	−0.147041	−0.0735204	+	0.997294i	$0.523423\pi$
$102$	24.9376	2.46919
$103$	−3.94763	−0.388971	−0.194486	−	0.980905i	$-0.562304\pi$
$103$	−3.94763	−0.388971	−0.194486	+	0.980905i	$0.562304\pi$
$104$	−6.33964	−0.621653
$105$	28.3656	2.76820
$106$	0.241660	0.0234721
$107$	−9.65781	−0.933656	−0.466828	−	0.884348i	$-0.654603\pi$
$107$	−9.65781	−0.933656	−0.466828	+	0.884348i	$0.654603\pi$
$108$	−16.9730	−1.63323
$109$	−7.54074	−0.722272	−0.361136	−	0.932513i	$-0.617611\pi$
$109$	−7.54074	−0.722272	−0.361136	+	0.932513i	$0.617611\pi$
$110$	23.2042	2.21244
$111$	15.6573	1.48612
$112$	2.28084	0.215519
$113$	−1.04564	−0.0983658	−0.0491829	−	0.998790i	$-0.515662\pi$
$113$	−1.04564	−0.0983658	−0.0491829	+	0.998790i	$0.515662\pi$
$114$	−11.6407	−1.09025
$115$	−3.73356	−0.348157
$116$	−5.25887	−0.488273
$117$	−51.3225	−4.74477
$118$	12.0074	1.10537
$119$	−17.0756	−1.56532
$120$	12.4365	1.13529
$121$	27.6267	2.51152
$122$	−10.7362	−0.972007
$123$	41.0632	3.70254
$124$	0.391307	0.0351404
$125$	−14.7084	−1.31556
$126$	18.4645	1.64495
$127$	−1.35822	−0.120523	−0.0602614	−	0.998183i	$-0.519193\pi$
$127$	−1.35822	−0.120523	−0.0602614	+	0.998183i	$0.519193\pi$
$128$	1.00000	0.0883883
$129$	8.55211	0.752972
$130$	23.6695	2.07595
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	20.7022	1.80190
$133$	7.97076	0.691152
$134$	−7.98157	−0.689503
$135$	63.3699	5.45401
$136$	−7.48655	−0.641967
$137$	10.0133	0.855498	0.427749	−	0.903898i	$-0.359307\pi$
$137$	10.0133	0.855498	0.427749	+	0.903898i	$0.359307\pi$
$138$	−3.33099	−0.283553
$139$	10.8507	0.920344	0.460172	−	0.887830i	$-0.347788\pi$
$139$	10.8507	0.920344	0.460172	+	0.887830i	$0.347788\pi$
$140$	−8.51567	−0.719705
$141$	3.31421	0.279107
$142$	−2.49281	−0.209192
$143$	39.4011	3.29489
$144$	8.09549	0.674624
$145$	19.6343	1.63054
$146$	1.44499	0.119588
$147$	5.98833	0.493909
$148$	−4.70049	−0.386378
$149$	10.1099	0.828233	0.414117	−	0.910224i	$-0.364091\pi$
$149$	10.1099	0.828233	0.414117	+	0.910224i	$0.364091\pi$
$150$	−29.7774	−2.43131
$151$	−15.1855	−1.23578	−0.617890	−	0.786265i	$-0.712012\pi$
$151$	−15.1855	−1.23578	−0.617890	+	0.786265i	$0.712012\pi$
$152$	3.49466	0.283454
$153$	−60.6073	−4.89981
$154$	−14.1755	−1.14230
$155$	−1.46097	−0.117348
$156$	21.1173	1.69074
$157$	9.62045	0.767795	0.383898	−	0.923376i	$-0.374582\pi$
$157$	9.62045	0.767795	0.383898	+	0.923376i	$0.374582\pi$
$158$	−9.05545	−0.720413
$159$	−0.804968	−0.0638381
$160$	−3.73356	−0.295164
$161$	2.28084	0.179755
$162$	32.2505	2.53384
$163$	−2.40856	−0.188653	−0.0943263	−	0.995541i	$-0.530070\pi$
$163$	−2.40856	−0.188653	−0.0943263	+	0.995541i	$0.530070\pi$
$164$	−12.3276	−0.962625
$165$	−77.2931	−6.01726
$166$	−14.6828	−1.13961
$167$	−10.3078	−0.797642	−0.398821	−	0.917029i	$-0.630581\pi$
$167$	−10.3078	−0.797642	−0.398821	+	0.917029i	$0.630581\pi$
$168$	−7.59746	−0.586157
$169$	27.1911	2.09162
$170$	27.9515	2.14378
$171$	28.2910	2.16347
$172$	−2.56744	−0.195765
$173$	0.619865	0.0471275	0.0235637	−	0.999722i	$-0.492499\pi$
$173$	0.619865	0.0471275	0.0235637	+	0.999722i	$0.492499\pi$
$174$	17.5172	1.32798
$175$	20.3896	1.54131
$176$	−6.21504	−0.468476
$177$	−39.9967	−3.00633
$178$	−2.19752	−0.164711
$179$	−14.3101	−1.06958	−0.534792	−	0.844984i	$-0.679610\pi$
$179$	−14.3101	−1.06958	−0.534792	+	0.844984i	$0.679610\pi$
$180$	−30.2250	−2.25284
$181$	23.5172	1.74802	0.874010	−	0.485908i	$-0.161511\pi$
$181$	23.5172	1.74802	0.874010	+	0.485908i	$0.161511\pi$
$182$	−14.4597	−1.07183
$183$	35.7621	2.64361
$184$	1.00000	0.0737210
$185$	17.5496	1.29027
$186$	−1.30344	−0.0955728
$187$	46.5292	3.40255
$188$	−0.994962	−0.0725650
$189$	−38.7128	−2.81594
$190$	−13.0475	−0.946567
$191$	−16.3898	−1.18593	−0.592963	−	0.805229i	$-0.702042\pi$
$191$	−16.3898	−1.18593	−0.592963	+	0.805229i	$0.702042\pi$
$192$	−3.33099	−0.240393
$193$	−1.55183	−0.111703	−0.0558517	−	0.998439i	$-0.517787\pi$
$193$	−1.55183	−0.111703	−0.0558517	+	0.998439i	$0.517787\pi$
$194$	−17.2097	−1.23559
$195$	−78.8427	−5.64604
$196$	−1.79776	−0.128412
$197$	15.0102	1.06943	0.534716	−	0.845032i	$-0.320418\pi$
$197$	15.0102	1.06943	0.534716	+	0.845032i	$0.320418\pi$
$198$	−50.3138	−3.57564
$199$	−4.91472	−0.348395	−0.174198	−	0.984711i	$-0.555733\pi$
$199$	−4.91472	−0.348395	−0.174198	+	0.984711i	$0.555733\pi$
$200$	8.93950	0.632118
$201$	26.5865	1.87527
$202$	−1.47774	−0.103974
$203$	−11.9946	−0.841859
$204$	24.9376	1.74598
$205$	46.0259	3.21459
$206$	−3.94763	−0.275044
$207$	8.09549	0.562676
$208$	−6.33964	−0.439575
$209$	−21.7194	−1.50236
$210$	28.3656	1.95741
$211$	9.69488	0.667423	0.333712	−	0.942675i	$-0.391699\pi$
$211$	9.69488	0.667423	0.333712	+	0.942675i	$0.391699\pi$
$212$	0.241660	0.0165973
$213$	8.30352	0.568948
$214$	−9.65781	−0.660195
$215$	9.58570	0.653739
$216$	−16.9730	−1.15487
$217$	0.892509	0.0605875
$218$	−7.54074	−0.510723
$219$	−4.81323	−0.325248
$220$	23.2042	1.56443
$221$	47.4621	3.19264
$222$	15.6573	1.05085
$223$	16.5195	1.10623	0.553113	−	0.833106i	$-0.313440\pi$
$223$	16.5195	1.10623	0.553113	+	0.833106i	$0.313440\pi$
$224$	2.28084	0.152395
$225$	72.3697	4.82464
$226$	−1.04564	−0.0695551
$227$	−7.61757	−0.505596	−0.252798	−	0.967519i	$-0.581351\pi$
$227$	−7.61757	−0.505596	−0.252798	+	0.967519i	$0.581351\pi$
$228$	−11.6407	−0.770922
$229$	−4.49469	−0.297018	−0.148509	−	0.988911i	$-0.547447\pi$
$229$	−4.49469	−0.297018	−0.148509	+	0.988911i	$0.547447\pi$
$230$	−3.73356	−0.246184
$231$	47.2185	3.10675
$232$	−5.25887	−0.345261
$233$	5.02000	0.328871	0.164436	−	0.986388i	$-0.447420\pi$
$233$	5.02000	0.328871	0.164436	+	0.986388i	$0.447420\pi$
$234$	−51.3225	−3.35506
$235$	3.71475	0.242324
$236$	12.0074	0.781618
$237$	30.1636	1.95934
$238$	−17.0756	−1.10685
$239$	7.32314	0.473694	0.236847	−	0.971547i	$-0.423886\pi$
$239$	7.32314	0.473694	0.236847	+	0.971547i	$0.423886\pi$
$240$	12.4365	0.802770
$241$	22.7651	1.46643	0.733213	−	0.679999i	$-0.238020\pi$
$241$	22.7651	1.46643	0.733213	+	0.679999i	$0.238020\pi$
$242$	27.6267	1.77591
$243$	−56.5071	−3.62493
$244$	−10.7362	−0.687313
$245$	6.71206	0.428818
$246$	41.0632	2.61809
$247$	−22.1549	−1.40968
$248$	0.391307	0.0248480
$249$	48.9084	3.09944
$250$	−14.7084	−0.930240
$251$	−5.53969	−0.349662	−0.174831	−	0.984598i	$-0.555938\pi$
$251$	−5.53969	−0.349662	−0.174831	+	0.984598i	$0.555938\pi$
$252$	18.4645	1.16316
$253$	−6.21504	−0.390736
$254$	−1.35822	−0.0852225
$255$	−93.1062	−5.83054
$256$	1.00000	0.0625000
$257$	−26.4030	−1.64698	−0.823488	−	0.567333i	$-0.807975\pi$
$257$	−26.4030	−1.64698	−0.823488	+	0.567333i	$0.807975\pi$
$258$	8.55211	0.532431
$259$	−10.7211	−0.666175
$260$	23.6695	1.46792
$261$	−42.5731	−2.63521
$262$	1.00000	0.0617802
$263$	6.38320	0.393605	0.196803	−	0.980443i	$-0.436944\pi$
$263$	6.38320	0.393605	0.196803	+	0.980443i	$0.436944\pi$
$264$	20.7022	1.27413
$265$	−0.902254	−0.0554250
$266$	7.97076	0.488719
$267$	7.31992	0.447972
$268$	−7.98157	−0.487552
$269$	−7.66932	−0.467607	−0.233803	−	0.972284i	$-0.575117\pi$
$269$	−7.66932	−0.467607	−0.233803	+	0.972284i	$0.575117\pi$
$270$	63.3699	3.85657
$271$	9.03410	0.548783	0.274391	−	0.961618i	$-0.411524\pi$
$271$	9.03410	0.548783	0.274391	+	0.961618i	$0.411524\pi$
$272$	−7.48655	−0.453939
$273$	48.1652	2.91509
$274$	10.0133	0.604928
$275$	−55.5593	−3.35035
$276$	−3.33099	−0.200502
$277$	10.5556	0.634227	0.317114	−	0.948388i	$-0.397286\pi$
$277$	10.5556	0.634227	0.317114	+	0.948388i	$0.397286\pi$
$278$	10.8507	0.650782
$279$	3.16782	0.189653
$280$	−8.51567	−0.508908
$281$	1.09868	0.0655416	0.0327708	−	0.999463i	$-0.489567\pi$
$281$	1.09868	0.0655416	0.0327708	+	0.999463i	$0.489567\pi$
$282$	3.31421	0.197358
$283$	25.8691	1.53776	0.768880	−	0.639393i	$-0.220814\pi$
$283$	25.8691	1.53776	0.768880	+	0.639393i	$0.220814\pi$
$284$	−2.49281	−0.147921
$285$	43.4612	2.57442
$286$	39.4011	2.32984
$287$	−28.1173	−1.65971
$288$	8.09549	0.477031
$289$	39.0485	2.29697
$290$	19.6343	1.15297
$291$	57.3255	3.36048
$292$	1.44499	0.0845614
$293$	−5.01414	−0.292929	−0.146465	−	0.989216i	$-0.546789\pi$
$293$	−5.01414	−0.292929	−0.146465	+	0.989216i	$0.546789\pi$
$294$	5.98833	0.349247
$295$	−44.8306	−2.61014
$296$	−4.70049	−0.273211
$297$	105.488	6.12104
$298$	10.1099	0.585649
$299$	−6.33964	−0.366631
$300$	−29.7774	−1.71920
$301$	−5.85592	−0.337530
$302$	−15.1855	−0.873828
$303$	4.92234	0.282781
$304$	3.49466	0.200432
$305$	40.0842	2.29521
$306$	−60.6073	−3.46469
$307$	−19.0396	−1.08665	−0.543323	−	0.839524i	$-0.682834\pi$
$307$	−19.0396	−1.08665	−0.543323	+	0.839524i	$0.682834\pi$
$308$	−14.1755	−0.807725
$309$	13.1495	0.748049
$310$	−1.46097	−0.0829775
$311$	−28.7826	−1.63211	−0.816055	−	0.577975i	$-0.803843\pi$
$311$	−28.7826	−1.63211	−0.816055	+	0.577975i	$0.803843\pi$
$312$	21.1173	1.19553
$313$	24.0608	1.36000	0.679999	−	0.733213i	$-0.261980\pi$
$313$	24.0608	1.36000	0.679999	+	0.733213i	$0.261980\pi$
$314$	9.62045	0.542913
$315$	−68.9385	−3.88425
$316$	−9.05545	−0.509409
$317$	−3.13277	−0.175954	−0.0879770	−	0.996123i	$-0.528040\pi$
$317$	−3.13277	−0.175954	−0.0879770	+	0.996123i	$0.528040\pi$
$318$	−0.804968	−0.0451403
$319$	32.6840	1.82995
$320$	−3.73356	−0.208713
$321$	32.1701	1.79556
$322$	2.28084	0.127106
$323$	−26.1629	−1.45574
$324$	32.2505	1.79170
$325$	−56.6732	−3.14367
$326$	−2.40856	−0.133398
$327$	25.1181	1.38904
$328$	−12.3276	−0.680679
$329$	−2.26935	−0.125113
$330$	−77.2931	−4.25484
$331$	21.1396	1.16194	0.580969	−	0.813926i	$-0.302674\pi$
$331$	21.1396	1.16194	0.580969	+	0.813926i	$0.302674\pi$
$332$	−14.6828	−0.805826
$333$	−38.0528	−2.08528
$334$	−10.3078	−0.564018
$335$	29.7997	1.62813
$336$	−7.59746	−0.414475
$337$	−23.0911	−1.25785	−0.628925	−	0.777466i	$-0.716505\pi$
$337$	−23.0911	−1.25785	−0.628925	+	0.777466i	$0.716505\pi$
$338$	27.1911	1.47900
$339$	3.48303	0.189172
$340$	27.9515	1.51588
$341$	−2.43199	−0.131699
$342$	28.2910	1.52980
$343$	−20.0663	−1.08348
$344$	−2.56744	−0.138427
$345$	12.4365	0.669557
$346$	0.619865	0.0333242
$347$	22.5658	1.21139	0.605697	−	0.795695i	$-0.292894\pi$
$347$	22.5658	1.21139	0.605697	+	0.795695i	$0.292894\pi$
$348$	17.5172	0.939022
$349$	6.61656	0.354176	0.177088	−	0.984195i	$-0.443332\pi$
$349$	6.61656	0.354176	0.177088	+	0.984195i	$0.443332\pi$
$350$	20.3896	1.08987
$351$	107.603	5.74342
$352$	−6.21504	−0.331263
$353$	−26.5216	−1.41160	−0.705800	−	0.708411i	$-0.749412\pi$
$353$	−26.5216	−1.41160	−0.705800	+	0.708411i	$0.749412\pi$
$354$	−39.9967	−2.12580
$355$	9.30706	0.493967
$356$	−2.19752	−0.116468
$357$	56.8788	3.01034
$358$	−14.3101	−0.756310
$359$	22.5246	1.18880	0.594402	−	0.804168i	$-0.297389\pi$
$359$	22.5246	1.18880	0.594402	+	0.804168i	$0.297389\pi$
$360$	−30.2250	−1.59300
$361$	−6.78737	−0.357230
$362$	23.5172	1.23604
$363$	−92.0242	−4.83002
$364$	−14.4597	−0.757895
$365$	−5.39494	−0.282384
$366$	35.7621	1.86931
$367$	11.6518	0.608219	0.304110	−	0.952637i	$-0.401641\pi$
$367$	11.6518	0.608219	0.304110	+	0.952637i	$0.401641\pi$
$368$	1.00000	0.0521286
$369$	−99.7981	−5.19528
$370$	17.5496	0.912360
$371$	0.551188	0.0286163
$372$	−1.30344	−0.0675802
$373$	16.0899	0.833101	0.416551	−	0.909113i	$-0.363239\pi$
$373$	16.0899	0.833101	0.416551	+	0.909113i	$0.363239\pi$
$374$	46.5292	2.40597
$375$	48.9935	2.53001
$376$	−0.994962	−0.0513112
$377$	33.3393	1.71706
$378$	−38.7128	−1.99117
$379$	4.84210	0.248722	0.124361	−	0.992237i	$-0.460312\pi$
$379$	4.84210	0.248722	0.124361	+	0.992237i	$0.460312\pi$
$380$	−13.0475	−0.669324
$381$	4.52423	0.231783
$382$	−16.3898	−0.838577
$383$	−30.2203	−1.54418	−0.772091	−	0.635511i	$-0.780789\pi$
$383$	−30.2203	−1.54418	−0.772091	+	0.635511i	$0.780789\pi$
$384$	−3.33099	−0.169984
$385$	52.9252	2.69732
$386$	−1.55183	−0.0789863
$387$	−20.7847	−1.05654
$388$	−17.2097	−0.873692
$389$	8.99461	0.456045	0.228022	−	0.973656i	$-0.426774\pi$
$389$	8.99461	0.456045	0.228022	+	0.973656i	$0.426774\pi$
$390$	−78.8427	−3.99236
$391$	−7.48655	−0.378611
$392$	−1.79776	−0.0908008
$393$	−3.33099	−0.168026
$394$	15.0102	0.756203
$395$	33.8091	1.70112
$396$	−50.3138	−2.52836
$397$	−7.66305	−0.384597	−0.192299	−	0.981336i	$-0.561594\pi$
$397$	−7.66305	−0.384597	−0.192299	+	0.981336i	$0.561594\pi$
$398$	−4.91472	−0.246353
$399$	−26.5505	−1.32919
$400$	8.93950	0.446975
$401$	−5.24384	−0.261865	−0.130932	−	0.991391i	$-0.541797\pi$
$401$	−5.24384	−0.261865	−0.130932	+	0.991391i	$0.541797\pi$
$402$	26.5865	1.32602
$403$	−2.48075	−0.123575
$404$	−1.47774	−0.0735204
$405$	−120.409	−5.98319
$406$	−11.9946	−0.595284
$407$	29.2137	1.44807
$408$	24.9376	1.23460
$409$	−19.6424	−0.971255	−0.485628	−	0.874166i	$-0.661409\pi$
$409$	−19.6424	−0.971255	−0.485628	+	0.874166i	$0.661409\pi$
$410$	46.0259	2.27306
$411$	−33.3543	−1.64525
$412$	−3.94763	−0.194486
$413$	27.3871	1.34763
$414$	8.09549	0.397872
$415$	54.8194	2.69098
$416$	−6.33964	−0.310826
$417$	−36.1436	−1.76996
$418$	−21.7194	−1.06233
$419$	−12.3354	−0.602624	−0.301312	−	0.953526i	$-0.597425\pi$
$419$	−12.3354	−0.602624	−0.301312	+	0.953526i	$0.597425\pi$
$420$	28.3656	1.38410
$421$	−7.25545	−0.353609	−0.176805	−	0.984246i	$-0.556576\pi$
$421$	−7.25545	−0.353609	−0.176805	+	0.984246i	$0.556576\pi$
$422$	9.69488	0.471939
$423$	−8.05470	−0.391633
$424$	0.241660	0.0117361
$425$	−66.9260	−3.24639
$426$	8.30352	0.402307
$427$	−24.4875	−1.18503
$428$	−9.65781	−0.466828
$429$	−131.245	−6.33655
$430$	9.58570	0.462263
$431$	16.8589	0.812063	0.406031	−	0.913859i	$-0.366912\pi$
$431$	16.8589	0.812063	0.406031	+	0.913859i	$0.366912\pi$
$432$	−16.9730	−0.816616
$433$	−18.3357	−0.881160	−0.440580	−	0.897713i	$-0.645227\pi$
$433$	−18.3357	−0.881160	−0.440580	+	0.897713i	$0.645227\pi$
$434$	0.892509	0.0428418
$435$	−65.4017	−3.13577
$436$	−7.54074	−0.361136
$437$	3.49466	0.167172
$438$	−4.81323	−0.229985
$439$	−8.00862	−0.382230	−0.191115	−	0.981568i	$-0.561210\pi$
$439$	−8.00862	−0.382230	−0.191115	+	0.981568i	$0.561210\pi$
$440$	23.2042	1.10622
$441$	−14.5538	−0.693037
$442$	47.4621	2.25754
$443$	15.2820	0.726068	0.363034	−	0.931776i	$-0.381741\pi$
$443$	15.2820	0.726068	0.363034	+	0.931776i	$0.381741\pi$
$444$	15.6573	0.743062
$445$	8.20458	0.388935
$446$	16.5195	0.782220
$447$	−33.6759	−1.59282
$448$	2.28084	0.107760
$449$	−8.15381	−0.384802	−0.192401	−	0.981316i	$-0.561627\pi$
$449$	−8.15381	−0.384802	−0.192401	+	0.981316i	$0.561627\pi$
$450$	72.3697	3.41154
$451$	76.6166	3.60773
$452$	−1.04564	−0.0491829
$453$	50.5828	2.37659
$454$	−7.61757	−0.357510
$455$	53.9863	2.53092
$456$	−11.6407	−0.545124
$457$	−7.69962	−0.360173	−0.180086	−	0.983651i	$-0.557638\pi$
$457$	−7.69962	−0.360173	−0.180086	+	0.983651i	$0.557638\pi$
$458$	−4.49469	−0.210023
$459$	127.070	5.93110
$460$	−3.73356	−0.174078
$461$	25.8213	1.20262	0.601309	−	0.799016i	$-0.294646\pi$
$461$	25.8213	1.20262	0.601309	+	0.799016i	$0.294646\pi$
$462$	47.2185	2.19680
$463$	−20.4905	−0.952276	−0.476138	−	0.879370i	$-0.657964\pi$
$463$	−20.4905	−0.952276	−0.476138	+	0.879370i	$0.657964\pi$
$464$	−5.25887	−0.244137
$465$	4.86648	0.225677
$466$	5.02000	0.232547
$467$	20.5717	0.951945	0.475973	−	0.879460i	$-0.342096\pi$
$467$	20.5717	0.951945	0.475973	+	0.879460i	$0.342096\pi$
$468$	−51.3225	−2.37238
$469$	−18.2047	−0.840615
$470$	3.71475	0.171349
$471$	−32.0456	−1.47658
$472$	12.0074	0.552687
$473$	15.9567	0.733691
$474$	30.1636	1.38546
$475$	31.2405	1.43341
$476$	−17.0756	−0.782660
$477$	1.95636	0.0895755
$478$	7.32314	0.334953
$479$	4.92693	0.225117	0.112559	−	0.993645i	$-0.464095\pi$
$479$	4.92693	0.225117	0.112559	+	0.993645i	$0.464095\pi$
$480$	12.4365	0.567644
$481$	29.7994	1.35874
$482$	22.7651	1.03692
$483$	−7.59746	−0.345696
$484$	27.6267	1.25576
$485$	64.2537	2.91761
$486$	−56.5071	−2.56321
$487$	−0.261472	−0.0118484	−0.00592421	−	0.999982i	$-0.501886\pi$
$487$	−0.261472	−0.0118484	−0.00592421	+	0.999982i	$0.501886\pi$
$488$	−10.7362	−0.486003
$489$	8.02287	0.362807
$490$	6.71206	0.303220
$491$	36.1193	1.63004	0.815020	−	0.579433i	$-0.196726\pi$
$491$	36.1193	1.63004	0.815020	+	0.579433i	$0.196726\pi$
$492$	41.0632	1.85127
$493$	39.3708	1.77317
$494$	−22.1549	−0.996795
$495$	187.850	8.44322
$496$	0.391307	0.0175702
$497$	−5.68570	−0.255039
$498$	48.9084	2.19164
$499$	23.3119	1.04358	0.521791	−	0.853073i	$-0.325264\pi$
$499$	23.3119	1.04358	0.521791	+	0.853073i	$0.325264\pi$
$500$	−14.7084	−0.657779
$501$	34.3352	1.53398
$502$	−5.53969	−0.247248
$503$	−31.2132	−1.39173	−0.695863	−	0.718174i	$-0.744978\pi$
$503$	−31.2132	−1.39173	−0.695863	+	0.718174i	$0.744978\pi$
$504$	18.4645	0.822476
$505$	5.51724	0.245514
$506$	−6.21504	−0.276292
$507$	−90.5731	−4.02249
$508$	−1.35822	−0.0602614
$509$	−30.2949	−1.34280	−0.671400	−	0.741095i	$-0.734307\pi$
$509$	−30.2949	−1.34280	−0.671400	+	0.741095i	$0.734307\pi$
$510$	−93.1062	−4.12281
$511$	3.29578	0.145797
$512$	1.00000	0.0441942
$513$	−59.3149	−2.61882
$514$	−26.4030	−1.16459
$515$	14.7387	0.649465
$516$	8.55211	0.376486
$517$	6.18372	0.271960
$518$	−10.7211	−0.471057
$519$	−2.06476	−0.0906331
$520$	23.6695	1.03797
$521$	−7.88491	−0.345444	−0.172722	−	0.984971i	$-0.555256\pi$
$521$	−7.88491	−0.345444	−0.172722	+	0.984971i	$0.555256\pi$
$522$	−42.5731	−1.86337
$523$	−27.9618	−1.22269	−0.611343	−	0.791366i	$-0.709370\pi$
$523$	−27.9618	−1.22269	−0.611343	+	0.791366i	$0.709370\pi$
$524$	1.00000	0.0436852
$525$	−67.9175	−2.96416
$526$	6.38320	0.278321
$527$	−2.92954	−0.127613
$528$	20.7022	0.900949
$529$	1.00000	0.0434783
$530$	−0.902254	−0.0391914
$531$	97.2062	4.21839
$532$	7.97076	0.345576
$533$	78.1527	3.38517
$534$	7.31992	0.316764
$535$	36.0581	1.55893
$536$	−7.98157	−0.344751
$537$	47.6667	2.05697
$538$	−7.66932	−0.330648
$539$	11.1732	0.481262
$540$	63.3699	2.72701
$541$	−11.6990	−0.502979	−0.251490	−	0.967860i	$-0.580920\pi$
$541$	−11.6990	−0.502979	−0.251490	+	0.967860i	$0.580920\pi$
$542$	9.03410	0.388048
$543$	−78.3356	−3.36170
$544$	−7.48655	−0.320983
$545$	28.1538	1.20598
$546$	48.1652	2.06128
$547$	−23.0751	−0.986620	−0.493310	−	0.869854i	$-0.664213\pi$
$547$	−23.0751	−0.986620	−0.493310	+	0.869854i	$0.664213\pi$
$548$	10.0133	0.427749
$549$	−86.9146	−3.70942
$550$	−55.5593	−2.36906
$551$	−18.3779	−0.782926
$552$	−3.33099	−0.141776
$553$	−20.6541	−0.878300
$554$	10.5556	0.448466
$555$	−58.4575	−2.48138
$556$	10.8507	0.460172
$557$	−14.5916	−0.618265	−0.309133	−	0.951019i	$-0.600039\pi$
$557$	−14.5916	−0.618265	−0.309133	+	0.951019i	$0.600039\pi$
$558$	3.16782	0.134105
$559$	16.2766	0.688429
$560$	−8.51567	−0.359853
$561$	−154.988	−6.54361
$562$	1.09868	0.0463449
$563$	−6.20450	−0.261488	−0.130744	−	0.991416i	$-0.541737\pi$
$563$	−6.20450	−0.261488	−0.130744	+	0.991416i	$0.541737\pi$
$564$	3.31421	0.139553
$565$	3.90398	0.164241
$566$	25.8691	1.08736
$567$	73.5583	3.08916
$568$	−2.49281	−0.104596
$569$	−7.29944	−0.306009	−0.153004	−	0.988226i	$-0.548895\pi$
$569$	−7.29944	−0.306009	−0.153004	+	0.988226i	$0.548895\pi$
$570$	43.4612	1.82039
$571$	−13.2645	−0.555103	−0.277551	−	0.960711i	$-0.589523\pi$
$571$	−13.2645	−0.555103	−0.277551	+	0.960711i	$0.589523\pi$
$572$	39.4011	1.64744
$573$	54.5944	2.28071
$574$	−28.1173	−1.17359
$575$	8.93950	0.372803
$576$	8.09549	0.337312
$577$	25.3519	1.05541	0.527706	−	0.849427i	$-0.323052\pi$
$577$	25.3519	1.05541	0.527706	+	0.849427i	$0.323052\pi$
$578$	39.0485	1.62420
$579$	5.16914	0.214822
$580$	19.6343	0.815270
$581$	−33.4892	−1.38937
$582$	57.3255	2.37622
$583$	−1.50193	−0.0622034
$584$	1.44499	0.0597939
$585$	191.616	7.92234
$586$	−5.01414	−0.207132
$587$	−11.1783	−0.461378	−0.230689	−	0.973028i	$-0.574098\pi$
$587$	−11.1783	−0.461378	−0.230689	+	0.973028i	$0.574098\pi$
$588$	5.98833	0.246955
$589$	1.36748	0.0563462
$590$	−44.8306	−1.84564
$591$	−49.9988	−2.05668
$592$	−4.70049	−0.193189
$593$	−36.1413	−1.48414	−0.742072	−	0.670321i	$-0.766157\pi$
$593$	−36.1413	−1.48414	−0.742072	+	0.670321i	$0.766157\pi$
$594$	105.488	4.32823
$595$	63.7530	2.61362
$596$	10.1099	0.414117
$597$	16.3709	0.670016
$598$	−6.33964	−0.259247
$599$	30.3382	1.23958	0.619792	−	0.784766i	$-0.287217\pi$
$599$	30.3382	1.23958	0.619792	+	0.784766i	$0.287217\pi$
$600$	−29.7774	−1.21566
$601$	6.11459	0.249419	0.124710	−	0.992193i	$-0.460200\pi$
$601$	6.11459	0.249419	0.124710	+	0.992193i	$0.460200\pi$
$602$	−5.85592	−0.238670
$603$	−64.6147	−2.63132
$604$	−15.1855	−0.617890
$605$	−103.146	−4.19348
$606$	4.92234	0.199957
$607$	8.46019	0.343389	0.171694	−	0.985150i	$-0.445076\pi$
$607$	8.46019	0.343389	0.171694	+	0.985150i	$0.445076\pi$
$608$	3.49466	0.141727
$609$	39.9540	1.61902
$610$	40.0842	1.62296
$611$	6.30770	0.255182
$612$	−60.6073	−2.44991
$613$	−10.3982	−0.419981	−0.209991	−	0.977703i	$-0.567343\pi$
$613$	−10.3982	−0.419981	−0.209991	+	0.977703i	$0.567343\pi$
$614$	−19.0396	−0.768374
$615$	−153.312	−6.18213
$616$	−14.1755	−0.571148
$617$	−0.474759	−0.0191131	−0.00955653	−	0.999954i	$-0.503042\pi$
$617$	−0.474759	−0.0191131	−0.00955653	+	0.999954i	$0.503042\pi$
$618$	13.1495	0.528951
$619$	−37.8760	−1.52236	−0.761182	−	0.648539i	$-0.775380\pi$
$619$	−37.8760	−1.52236	−0.761182	+	0.648539i	$0.775380\pi$
$620$	−1.46097	−0.0586740
$621$	−16.9730	−0.681104
$622$	−28.7826	−1.15408
$623$	−5.01219	−0.200809
$624$	21.1173	0.845368
$625$	10.2172	0.408687
$626$	24.0608	0.961664
$627$	72.3472	2.88927
$628$	9.62045	0.383898
$629$	35.1905	1.40314
$630$	−68.9385	−2.74658
$631$	0.0675185	0.00268787	0.00134393	−	0.999999i	$-0.499572\pi$
$631$	0.0675185	0.00268787	0.00134393	+	0.999999i	$0.499572\pi$
$632$	−9.05545	−0.360207
$633$	−32.2935	−1.28355
$634$	−3.13277	−0.124418
$635$	5.07101	0.201237
$636$	−0.804968	−0.0319190
$637$	11.3972	0.451572
$638$	32.6840	1.29397
$639$	−20.1805	−0.798329
$640$	−3.73356	−0.147582
$641$	−17.7688	−0.701825	−0.350913	−	0.936408i	$-0.614129\pi$
$641$	−17.7688	−0.701825	−0.350913	+	0.936408i	$0.614129\pi$
$642$	32.1701	1.26965
$643$	23.4696	0.925549	0.462775	−	0.886476i	$-0.346854\pi$
$643$	23.4696	0.925549	0.462775	+	0.886476i	$0.346854\pi$
$644$	2.28084	0.0898777
$645$	−31.9299	−1.25724
$646$	−26.1629	−1.02937
$647$	−41.7881	−1.64286	−0.821430	−	0.570309i	$-0.806823\pi$
$647$	−41.7881	−1.64286	−0.821430	+	0.570309i	$0.806823\pi$
$648$	32.2505	1.26692
$649$	−74.6267	−2.92935
$650$	−56.6732	−2.22291
$651$	−2.97294	−0.116519
$652$	−2.40856	−0.0943263
$653$	24.6073	0.962957	0.481478	−	0.876458i	$-0.340100\pi$
$653$	24.6073	0.962957	0.481478	+	0.876458i	$0.340100\pi$
$654$	25.1181	0.982197
$655$	−3.73356	−0.145882
$656$	−12.3276	−0.481312
$657$	11.6979	0.456377
$658$	−2.26935	−0.0884685
$659$	−16.4180	−0.639555	−0.319777	−	0.947493i	$-0.603608\pi$
$659$	−16.4180	−0.639555	−0.319777	+	0.947493i	$0.603608\pi$
$660$	−77.2931	−3.00863
$661$	27.2981	1.06177	0.530886	−	0.847443i	$-0.321859\pi$
$661$	27.2981	1.06177	0.530886	+	0.847443i	$0.321859\pi$
$662$	21.1396	0.821614
$663$	−158.096	−6.13992
$664$	−14.6828	−0.569805
$665$	−29.7593	−1.15402
$666$	−38.0528	−1.47452
$667$	−5.25887	−0.203624
$668$	−10.3078	−0.398821
$669$	−55.0262	−2.12744
$670$	29.7997	1.15126
$671$	66.7257	2.57592
$672$	−7.59746	−0.293078
$673$	−12.3038	−0.474277	−0.237139	−	0.971476i	$-0.576210\pi$
$673$	−12.3038	−0.474277	−0.237139	+	0.971476i	$0.576210\pi$
$674$	−23.0911	−0.889435
$675$	−151.730	−5.84011
$676$	27.1911	1.04581
$677$	−17.8012	−0.684155	−0.342078	−	0.939672i	$-0.611131\pi$
$677$	−17.8012	−0.684155	−0.342078	+	0.939672i	$0.611131\pi$
$678$	3.48303	0.133765
$679$	−39.2527	−1.50638
$680$	27.9515	1.07189
$681$	25.3740	0.972336
$682$	−2.43199	−0.0931256
$683$	19.5577	0.748355	0.374177	−	0.927357i	$-0.377925\pi$
$683$	19.5577	0.748355	0.374177	+	0.927357i	$0.377925\pi$
$684$	28.2910	1.08173
$685$	−37.3855	−1.42843
$686$	−20.0663	−0.766135
$687$	14.9718	0.571209
$688$	−2.56744	−0.0978827
$689$	−1.53204	−0.0583660
$690$	12.4365	0.473448
$691$	−8.39617	−0.319405	−0.159703	−	0.987165i	$-0.551054\pi$
$691$	−8.39617	−0.319405	−0.159703	+	0.987165i	$0.551054\pi$
$692$	0.619865	0.0235637
$693$	−114.758	−4.35929
$694$	22.5658	0.856585
$695$	−40.5118	−1.53670
$696$	17.5172	0.663989
$697$	92.2913	3.49578
$698$	6.61656	0.250440
$699$	−16.7216	−0.632468
$700$	20.3896	0.770654
$701$	−36.3059	−1.37126	−0.685628	−	0.727952i	$-0.740472\pi$
$701$	−36.3059	−1.37126	−0.685628	+	0.727952i	$0.740472\pi$
$702$	107.603	4.06121
$703$	−16.4266	−0.619541
$704$	−6.21504	−0.234238
$705$	−12.3738	−0.466024
$706$	−26.5216	−0.998152
$707$	−3.37049	−0.126761
$708$	−39.9967	−1.50317
$709$	39.2274	1.47322	0.736608	−	0.676320i	$-0.236426\pi$
$709$	39.2274	1.47322	0.736608	+	0.676320i	$0.236426\pi$
$710$	9.30706	0.349288
$711$	−73.3084	−2.74928
$712$	−2.19752	−0.0823556
$713$	0.391307	0.0146546
$714$	56.8788	2.12863
$715$	−147.107	−5.50147
$716$	−14.3101	−0.534792
$717$	−24.3933	−0.910984
$718$	22.5246	0.840612
$719$	−41.6556	−1.55349	−0.776746	−	0.629814i	$-0.783131\pi$
$719$	−41.6556	−1.55349	−0.776746	+	0.629814i	$0.783131\pi$
$720$	−30.2250	−1.12642
$721$	−9.00391	−0.335323
$722$	−6.78737	−0.252600
$723$	−75.8302	−2.82016
$724$	23.5172	0.874010
$725$	−47.0116	−1.74597
$726$	−92.0242	−3.41534
$727$	−12.0962	−0.448624	−0.224312	−	0.974517i	$-0.572013\pi$
$727$	−12.0962	−0.448624	−0.224312	+	0.974517i	$0.572013\pi$
$728$	−14.4597	−0.535913
$729$	91.4729	3.38789
$730$	−5.39494	−0.199676
$731$	19.2213	0.710924
$732$	35.7621	1.32180
$733$	−17.9338	−0.662399	−0.331200	−	0.943561i	$-0.607453\pi$
$733$	−17.9338	−0.662399	−0.331200	+	0.943561i	$0.607453\pi$
$734$	11.6518	0.430076
$735$	−22.3578	−0.824681
$736$	1.00000	0.0368605
$737$	49.6057	1.82725
$738$	−99.7981	−3.67362
$739$	−42.1384	−1.55009	−0.775043	−	0.631909i	$-0.782272\pi$
$739$	−42.1384	−1.55009	−0.775043	+	0.631909i	$0.782272\pi$
$740$	17.5496	0.645136
$741$	73.7977	2.71103
$742$	0.551188	0.0202348
$743$	−11.7431	−0.430812	−0.215406	−	0.976525i	$-0.569108\pi$
$743$	−11.7431	−0.430812	−0.215406	+	0.976525i	$0.569108\pi$
$744$	−1.30344	−0.0477864
$745$	−37.7459	−1.38290
$746$	16.0899	0.589091
$747$	−118.865	−4.34904
$748$	46.5292	1.70128
$749$	−22.0279	−0.804883
$750$	48.9935	1.78899
$751$	−44.3717	−1.61915	−0.809573	−	0.587020i	$-0.800301\pi$
$751$	−44.3717	−1.61915	−0.809573	+	0.587020i	$0.800301\pi$
$752$	−0.994962	−0.0362825
$753$	18.4526	0.672452
$754$	33.3393	1.21415
$755$	56.6961	2.06338
$756$	−38.7128	−1.40797
$757$	−32.8637	−1.19445	−0.597226	−	0.802073i	$-0.703731\pi$
$757$	−32.8637	−1.19445	−0.597226	+	0.802073i	$0.703731\pi$
$758$	4.84210	0.175873
$759$	20.7022	0.751443
$760$	−13.0475	−0.473284
$761$	11.5836	0.419906	0.209953	−	0.977711i	$-0.432669\pi$
$761$	11.5836	0.419906	0.209953	+	0.977711i	$0.432669\pi$
$762$	4.52423	0.163895
$763$	−17.1992	−0.622654
$764$	−16.3898	−0.592963
$765$	226.281	8.18122
$766$	−30.2203	−1.09190
$767$	−76.1229	−2.74864
$768$	−3.33099	−0.120197
$769$	48.2383	1.73952	0.869760	−	0.493476i	$-0.164274\pi$
$769$	48.2383	1.73952	0.869760	+	0.493476i	$0.164274\pi$
$770$	52.9252	1.90729
$771$	87.9483	3.16738
$772$	−1.55183	−0.0558517
$773$	−25.7989	−0.927922	−0.463961	−	0.885856i	$-0.653572\pi$
$773$	−25.7989	−0.927922	−0.463961	+	0.885856i	$0.653572\pi$
$774$	−20.7847	−0.747090
$775$	3.49809	0.125655
$776$	−17.2097	−0.617794
$777$	35.7118	1.28115
$778$	8.99461	0.322472
$779$	−43.0808	−1.54353
$780$	−78.8427	−2.82302
$781$	15.4929	0.554379
$782$	−7.48655	−0.267719
$783$	89.2589	3.18985
$784$	−1.79776	−0.0642058
$785$	−35.9186	−1.28199
$786$	−3.33099	−0.118812
$787$	27.5331	0.981448	0.490724	−	0.871315i	$-0.336732\pi$
$787$	27.5331	0.981448	0.490724	+	0.871315i	$0.336732\pi$
$788$	15.0102	0.534716
$789$	−21.2624	−0.756961
$790$	33.8091	1.20287
$791$	−2.38495	−0.0847989
$792$	−50.3138	−1.78782
$793$	68.0634	2.41700
$794$	−7.66305	−0.271951
$795$	3.00540	0.106590
$796$	−4.91472	−0.174198
$797$	49.4642	1.75211	0.876057	−	0.482208i	$-0.160165\pi$
$797$	49.4642	1.75211	0.876057	+	0.482208i	$0.160165\pi$
$798$	−26.5505	−0.939878
$799$	7.44883	0.263521
$800$	8.93950	0.316059
$801$	−17.7900	−0.628579
$802$	−5.24384	−0.185167
$803$	−8.98063	−0.316920
$804$	26.5865	0.937635
$805$	−8.51567	−0.300138
$806$	−2.48075	−0.0873806
$807$	25.5464	0.899277
$808$	−1.47774	−0.0519868
$809$	−15.0052	−0.527553	−0.263777	−	0.964584i	$-0.584968\pi$
$809$	−15.0052	−0.527553	−0.263777	+	0.964584i	$0.584968\pi$
$810$	−120.409	−4.23076
$811$	−30.0078	−1.05372	−0.526859	−	0.849953i	$-0.676630\pi$
$811$	−30.0078	−1.05372	−0.526859	+	0.849953i	$0.676630\pi$
$812$	−11.9946	−0.420929
$813$	−30.0925	−1.05539
$814$	29.2137	1.02394
$815$	8.99250	0.314993
$816$	24.9376	0.872992
$817$	−8.97232	−0.313902
$818$	−19.6424	−0.686781
$819$	−117.059	−4.09036
$820$	46.0259	1.60730
$821$	−48.3433	−1.68719	−0.843597	−	0.536977i	$-0.819566\pi$
$821$	−48.3433	−1.68719	−0.843597	+	0.536977i	$0.819566\pi$
$822$	−33.3543	−1.16337
$823$	7.46252	0.260127	0.130064	−	0.991506i	$-0.458482\pi$
$823$	7.46252	0.260127	0.130064	+	0.991506i	$0.458482\pi$
$824$	−3.94763	−0.137522
$825$	185.068	6.44322
$826$	27.3871	0.952918
$827$	−43.0029	−1.49536	−0.747679	−	0.664060i	$-0.768832\pi$
$827$	−43.0029	−1.49536	−0.747679	+	0.664060i	$0.768832\pi$
$828$	8.09549	0.281338
$829$	14.5370	0.504890	0.252445	−	0.967611i	$-0.418765\pi$
$829$	14.5370	0.504890	0.252445	+	0.967611i	$0.418765\pi$
$830$	54.8194	1.90281
$831$	−35.1607	−1.21971
$832$	−6.33964	−0.219788
$833$	13.4590	0.466328
$834$	−36.1436	−1.25155
$835$	38.4849	1.33182
$836$	−21.7194	−0.751182
$837$	−6.64167	−0.229570
$838$	−12.3354	−0.426119
$839$	−4.74327	−0.163756	−0.0818779	−	0.996642i	$-0.526092\pi$
$839$	−4.74327	−0.163756	−0.0818779	+	0.996642i	$0.526092\pi$
$840$	28.3656	0.978706
$841$	−1.34433	−0.0463563
$842$	−7.25545	−0.250039
$843$	−3.65968	−0.126046
$844$	9.69488	0.333712
$845$	−101.520	−3.49238
$846$	−8.05470	−0.276926
$847$	63.0121	2.16512
$848$	0.241660	0.00829864
$849$	−86.1698	−2.95734
$850$	−66.9260	−2.29554
$851$	−4.70049	−0.161131
$852$	8.30352	0.284474
$853$	40.2121	1.37683	0.688417	−	0.725315i	$-0.258306\pi$
$853$	40.2121	1.37683	0.688417	+	0.725315i	$0.258306\pi$
$854$	−24.4875	−0.837945
$855$	−105.626	−3.61234
$856$	−9.65781	−0.330097
$857$	2.30868	0.0788629	0.0394315	−	0.999222i	$-0.487445\pi$
$857$	2.30868	0.0788629	0.0394315	+	0.999222i	$0.487445\pi$
$858$	−131.245	−4.48062
$859$	7.72556	0.263593	0.131796	−	0.991277i	$-0.457926\pi$
$859$	7.72556	0.263593	0.131796	+	0.991277i	$0.457926\pi$
$860$	9.58570	0.326870
$861$	93.6585	3.19187
$862$	16.8589	0.574215
$863$	33.3891	1.13658	0.568289	−	0.822829i	$-0.307606\pi$
$863$	33.3891	1.13658	0.568289	+	0.822829i	$0.307606\pi$
$864$	−16.9730	−0.577434
$865$	−2.31431	−0.0786888
$866$	−18.3357	−0.623074
$867$	−130.070	−4.41741
$868$	0.892509	0.0302937
$869$	56.2800	1.90917
$870$	−65.4017	−2.21733
$871$	50.6003	1.71453
$872$	−7.54074	−0.255362
$873$	−139.321	−4.71531
$874$	3.49466	0.118209
$875$	−33.5475	−1.13411
$876$	−4.81323	−0.162624
$877$	−51.5964	−1.74229	−0.871143	−	0.491029i	$-0.836621\pi$
$877$	−51.5964	−1.74229	−0.871143	+	0.491029i	$0.836621\pi$
$878$	−8.00862	−0.270278
$879$	16.7021	0.563346
$880$	23.2042	0.782215
$881$	18.5231	0.624060	0.312030	−	0.950072i	$-0.398991\pi$
$881$	18.5231	0.624060	0.312030	+	0.950072i	$0.398991\pi$
$882$	−14.5538	−0.490051
$883$	13.5525	0.456076	0.228038	−	0.973652i	$-0.426769\pi$
$883$	13.5525	0.456076	0.228038	+	0.973652i	$0.426769\pi$
$884$	47.4621	1.59632
$885$	149.330	5.01968
$886$	15.2820	0.513408
$887$	−4.53426	−0.152245	−0.0761227	−	0.997098i	$-0.524254\pi$
$887$	−4.53426	−0.152245	−0.0761227	+	0.997098i	$0.524254\pi$
$888$	15.6573	0.525424
$889$	−3.09789	−0.103900
$890$	8.20458	0.275018
$891$	−200.438	−6.71493
$892$	16.5195	0.553113
$893$	−3.47705	−0.116355
$894$	−33.6759	−1.12629
$895$	53.4275	1.78589
$896$	2.28084	0.0761976
$897$	21.1173	0.705085
$898$	−8.15381	−0.272096
$899$	−2.05783	−0.0686325
$900$	72.3697	2.41232
$901$	−1.80920	−0.0602732
$902$	76.6166	2.55105
$903$	19.5060	0.649119
$904$	−1.04564	−0.0347776
$905$	−87.8030	−2.91867
$906$	50.5828	1.68050
$907$	−1.02076	−0.0338939	−0.0169470	−	0.999856i	$-0.505395\pi$
$907$	−1.02076	−0.0338939	−0.0169470	+	0.999856i	$0.505395\pi$
$908$	−7.61757	−0.252798
$909$	−11.9630	−0.396789
$910$	53.9863	1.78963
$911$	−0.0965462	−0.00319872	−0.00159936	−	0.999999i	$-0.500509\pi$
$911$	−0.0965462	−0.00319872	−0.00159936	+	0.999999i	$0.500509\pi$
$912$	−11.6407	−0.385461
$913$	91.2544	3.02008
$914$	−7.69962	−0.254681
$915$	−133.520	−4.41403
$916$	−4.49469	−0.148509
$917$	2.28084	0.0753200
$918$	127.070	4.19392
$919$	−3.86895	−0.127625	−0.0638125	−	0.997962i	$-0.520326\pi$
$919$	−3.86895	−0.127625	−0.0638125	+	0.997962i	$0.520326\pi$
$920$	−3.73356	−0.123092
$921$	63.4206	2.08978
$922$	25.8213	0.850380
$923$	15.8035	0.520179
$924$	47.2185	1.55337
$925$	−42.0201	−1.38161
$926$	−20.4905	−0.673361
$927$	−31.9580	−1.04964
$928$	−5.25887	−0.172631
$929$	21.5766	0.707907	0.353953	−	0.935263i	$-0.384837\pi$
$929$	21.5766	0.707907	0.353953	+	0.935263i	$0.384837\pi$
$930$	4.86648	0.159578
$931$	−6.28257	−0.205903
$932$	5.02000	0.164436
$933$	95.8744	3.13879
$934$	20.5717	0.673127
$935$	−173.720	−5.68124
$936$	−51.3225	−1.67753
$937$	−39.4404	−1.28846	−0.644232	−	0.764830i	$-0.722823\pi$
$937$	−39.4404	−1.28846	−0.644232	+	0.764830i	$0.722823\pi$
$938$	−18.2047	−0.594404
$939$	−80.1464	−2.61548
$940$	3.71475	0.121162
$941$	−1.40866	−0.0459211	−0.0229606	−	0.999736i	$-0.507309\pi$
$941$	−1.40866	−0.0459211	−0.0229606	+	0.999736i	$0.507309\pi$
$942$	−32.0456	−1.04410
$943$	−12.3276	−0.401442
$944$	12.0074	0.390809
$945$	144.537	4.70178
$946$	15.9567	0.518798
$947$	−36.1010	−1.17313	−0.586563	−	0.809903i	$-0.699519\pi$
$947$	−36.1010	−1.17313	−0.586563	+	0.809903i	$0.699519\pi$
$948$	30.1636	0.979669
$949$	−9.16069	−0.297368
$950$	31.2405	1.01358
$951$	10.4352	0.338386
$952$	−17.0756	−0.553425
$953$	−16.6945	−0.540788	−0.270394	−	0.962750i	$-0.587154\pi$
$953$	−16.6945	−0.540788	−0.270394	+	0.962750i	$0.587154\pi$
$954$	1.95636	0.0633394
$955$	61.1925	1.98014
$956$	7.32314	0.236847
$957$	−108.870	−3.51927
$958$	4.92693	0.159182
$959$	22.8388	0.737505
$960$	12.4365	0.401385
$961$	−30.8469	−0.995061
$962$	29.7994	0.960772
$963$	−78.1848	−2.51947
$964$	22.7651	0.733213
$965$	5.79387	0.186511
$966$	−7.59746	−0.244444
$967$	7.87390	0.253208	0.126604	−	0.991953i	$-0.459592\pi$
$967$	7.87390	0.253208	0.126604	+	0.991953i	$0.459592\pi$
$968$	27.6267	0.887955
$969$	87.1485	2.79961
$970$	64.2537	2.06306
$971$	−9.85289	−0.316194	−0.158097	−	0.987424i	$-0.550536\pi$
$971$	−9.85289	−0.316194	−0.158097	+	0.987424i	$0.550536\pi$
$972$	−56.5071	−1.81247
$973$	24.7487	0.793408
$974$	−0.261472	−0.00837810
$975$	188.778	6.04573
$976$	−10.7362	−0.343656
$977$	15.7931	0.505267	0.252634	−	0.967562i	$-0.418703\pi$
$977$	15.7931	0.505267	0.252634	+	0.967562i	$0.418703\pi$
$978$	8.02287	0.256543
$979$	13.6577	0.436501
$980$	6.71206	0.214409
$981$	−61.0460	−1.94905
$982$	36.1193	1.15261
$983$	19.9995	0.637885	0.318942	−	0.947774i	$-0.396672\pi$
$983$	19.9995	0.637885	0.318942	+	0.947774i	$0.396672\pi$
$984$	41.0632	1.30905
$985$	−56.0415	−1.78563
$986$	39.3708	1.25382
$987$	7.55918	0.240611
$988$	−22.1549	−0.704841
$989$	−2.56744	−0.0816398
$990$	187.850	5.97026
$991$	−53.5081	−1.69974	−0.849871	−	0.526991i	$-0.823320\pi$
$991$	−53.5081	−1.69974	−0.849871	+	0.526991i	$0.823320\pi$
$992$	0.391307	0.0124240
$993$	−70.4158	−2.23458
$994$	−5.68570	−0.180339
$995$	18.3494	0.581716
$996$	48.9084	1.54972
$997$	34.1467	1.08144	0.540719	−	0.841203i	$-0.318152\pi$
$997$	34.1467	1.08144	0.540719	+	0.841203i	$0.318152\pi$
$998$	23.3119	0.737924
$999$	79.7816	2.52418

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.m.1.1	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.m.1.1	✓	41	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.33099 q^{3} +1.00000 q^{4} -3.73356 q^{5} -3.33099 q^{6} +2.28084 q^{7} +1.00000 q^{8} +8.09549 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.33099 q^{3} +1.00000 q^{4} -3.73356 q^{5} -3.33099 q^{6} +2.28084 q^{7} +1.00000 q^{8} +8.09549 q^{9} -3.73356 q^{10} -6.21504 q^{11} -3.33099 q^{12} -6.33964 q^{13} +2.28084 q^{14} +12.4365 q^{15} +1.00000 q^{16} -7.48655 q^{17} +8.09549 q^{18} +3.49466 q^{19} -3.73356 q^{20} -7.59746 q^{21} -6.21504 q^{22} +1.00000 q^{23} -3.33099 q^{24} +8.93950 q^{25} -6.33964 q^{26} -16.9730 q^{27} +2.28084 q^{28} -5.25887 q^{29} +12.4365 q^{30} +0.391307 q^{31} +1.00000 q^{32} +20.7022 q^{33} -7.48655 q^{34} -8.51567 q^{35} +8.09549 q^{36} -4.70049 q^{37} +3.49466 q^{38} +21.1173 q^{39} -3.73356 q^{40} -12.3276 q^{41} -7.59746 q^{42} -2.56744 q^{43} -6.21504 q^{44} -30.2250 q^{45} +1.00000 q^{46} -0.994962 q^{47} -3.33099 q^{48} -1.79776 q^{49} +8.93950 q^{50} +24.9376 q^{51} -6.33964 q^{52} +0.241660 q^{53} -16.9730 q^{54} +23.2042 q^{55} +2.28084 q^{56} -11.6407 q^{57} -5.25887 q^{58} +12.0074 q^{59} +12.4365 q^{60} -10.7362 q^{61} +0.391307 q^{62} +18.4645 q^{63} +1.00000 q^{64} +23.6695 q^{65} +20.7022 q^{66} -7.98157 q^{67} -7.48655 q^{68} -3.33099 q^{69} -8.51567 q^{70} -2.49281 q^{71} +8.09549 q^{72} +1.44499 q^{73} -4.70049 q^{74} -29.7774 q^{75} +3.49466 q^{76} -14.1755 q^{77} +21.1173 q^{78} -9.05545 q^{79} -3.73356 q^{80} +32.2505 q^{81} -12.3276 q^{82} -14.6828 q^{83} -7.59746 q^{84} +27.9515 q^{85} -2.56744 q^{86} +17.5172 q^{87} -6.21504 q^{88} -2.19752 q^{89} -30.2250 q^{90} -14.4597 q^{91} +1.00000 q^{92} -1.30344 q^{93} -0.994962 q^{94} -13.0475 q^{95} -3.33099 q^{96} -17.2097 q^{97} -1.79776 q^{98} -50.3138 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * q^99

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