LMFDB - Embedded newform 4029.2.a.l.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.27866 q^{2} -1.00000 q^{3} +3.19228 q^{4} -3.13196 q^{5} +2.27866 q^{6} -0.0802156 q^{7} -2.71679 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.27866 q^{2} -1.00000 q^{3} +3.19228 q^{4} -3.13196 q^{5} +2.27866 q^{6} -0.0802156 q^{7} -2.71679 q^{8} +1.00000 q^{9} +7.13667 q^{10} -5.00047 q^{11} -3.19228 q^{12} +3.99267 q^{13} +0.182784 q^{14} +3.13196 q^{15} -0.193918 q^{16} -1.00000 q^{17} -2.27866 q^{18} +2.46147 q^{19} -9.99809 q^{20} +0.0802156 q^{21} +11.3944 q^{22} +2.52357 q^{23} +2.71679 q^{24} +4.80919 q^{25} -9.09792 q^{26} -1.00000 q^{27} -0.256070 q^{28} -8.32033 q^{29} -7.13667 q^{30} -0.805575 q^{31} +5.87546 q^{32} +5.00047 q^{33} +2.27866 q^{34} +0.251232 q^{35} +3.19228 q^{36} +10.3580 q^{37} -5.60884 q^{38} -3.99267 q^{39} +8.50889 q^{40} -0.183280 q^{41} -0.182784 q^{42} -7.55934 q^{43} -15.9629 q^{44} -3.13196 q^{45} -5.75036 q^{46} -4.65435 q^{47} +0.193918 q^{48} -6.99357 q^{49} -10.9585 q^{50} +1.00000 q^{51} +12.7457 q^{52} +5.82371 q^{53} +2.27866 q^{54} +15.6613 q^{55} +0.217929 q^{56} -2.46147 q^{57} +18.9592 q^{58} +4.80944 q^{59} +9.99809 q^{60} -10.0824 q^{61} +1.83563 q^{62} -0.0802156 q^{63} -13.0003 q^{64} -12.5049 q^{65} -11.3944 q^{66} -8.96523 q^{67} -3.19228 q^{68} -2.52357 q^{69} -0.572472 q^{70} +7.92651 q^{71} -2.71679 q^{72} -4.57642 q^{73} -23.6024 q^{74} -4.80919 q^{75} +7.85768 q^{76} +0.401116 q^{77} +9.09792 q^{78} +1.00000 q^{79} +0.607343 q^{80} +1.00000 q^{81} +0.417632 q^{82} +9.12814 q^{83} +0.256070 q^{84} +3.13196 q^{85} +17.2251 q^{86} +8.32033 q^{87} +13.5852 q^{88} -0.860630 q^{89} +7.13667 q^{90} -0.320274 q^{91} +8.05594 q^{92} +0.805575 q^{93} +10.6057 q^{94} -7.70922 q^{95} -5.87546 q^{96} -15.2883 q^{97} +15.9359 q^{98} -5.00047 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * 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 $

$2$	−2.27866	−1.61125	−0.805627	−	0.592423i	$-0.798171\pi$
$2$	−2.27866	−1.61125	−0.805627	+	0.592423i	$0.798171\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.19228	1.59614
$5$	−3.13196	−1.40066	−0.700328	−	0.713821i	$-0.746963\pi$
$5$	−3.13196	−1.40066	−0.700328	+	0.713821i	$0.746963\pi$
$6$	2.27866	0.930258
$7$	−0.0802156	−0.0303186	−0.0151593	−	0.999885i	$-0.504826\pi$
$7$	−0.0802156	−0.0303186	−0.0151593	+	0.999885i	$0.504826\pi$
$8$	−2.71679	−0.960531
$9$	1.00000	0.333333
$10$	7.13667	2.25681
$11$	−5.00047	−1.50770	−0.753849	−	0.657047i	$-0.771805\pi$
$11$	−5.00047	−1.50770	−0.753849	+	0.657047i	$0.771805\pi$
$12$	−3.19228	−0.921531
$13$	3.99267	1.10737	0.553683	−	0.832727i	$-0.313222\pi$
$13$	3.99267	1.10737	0.553683	+	0.832727i	$0.313222\pi$
$14$	0.182784	0.0488510
$15$	3.13196	0.808669
$16$	−0.193918	−0.0484794
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.27866	−0.537085
$19$	2.46147	0.564699	0.282350	−	0.959312i	$-0.408886\pi$
$19$	2.46147	0.564699	0.282350	+	0.959312i	$0.408886\pi$
$20$	−9.99809	−2.23564
$21$	0.0802156	0.0175045
$22$	11.3944	2.42929
$23$	2.52357	0.526201	0.263101	−	0.964768i	$-0.415255\pi$
$23$	2.52357	0.526201	0.263101	+	0.964768i	$0.415255\pi$
$24$	2.71679	0.554563
$25$	4.80919	0.961838
$26$	−9.09792	−1.78425
$27$	−1.00000	−0.192450
$28$	−0.256070	−0.0483927
$29$	−8.32033	−1.54505	−0.772523	−	0.634987i	$-0.781006\pi$
$29$	−8.32033	−1.54505	−0.772523	+	0.634987i	$0.781006\pi$
$30$	−7.13667	−1.30297
$31$	−0.805575	−0.144686	−0.0723428	−	0.997380i	$-0.523048\pi$
$31$	−0.805575	−0.144686	−0.0723428	+	0.997380i	$0.523048\pi$
$32$	5.87546	1.03864
$33$	5.00047	0.870470
$34$	2.27866	0.390786
$35$	0.251232	0.0424660
$36$	3.19228	0.532046
$37$	10.3580	1.70285	0.851426	−	0.524475i	$-0.175738\pi$
$37$	10.3580	1.70285	0.851426	+	0.524475i	$0.175738\pi$
$38$	−5.60884	−0.909874
$39$	−3.99267	−0.639338
$40$	8.50889	1.34537
$41$	−0.183280	−0.0286235	−0.0143118	−	0.999898i	$-0.504556\pi$
$41$	−0.183280	−0.0286235	−0.0143118	+	0.999898i	$0.504556\pi$
$42$	−0.182784	−0.0282041
$43$	−7.55934	−1.15279	−0.576394	−	0.817172i	$-0.695541\pi$
$43$	−7.55934	−1.15279	−0.576394	+	0.817172i	$0.695541\pi$
$44$	−15.9629	−2.40650
$45$	−3.13196	−0.466885
$46$	−5.75036	−0.847844
$47$	−4.65435	−0.678907	−0.339453	−	0.940623i	$-0.610242\pi$
$47$	−4.65435	−0.678907	−0.339453	+	0.940623i	$0.610242\pi$
$48$	0.193918	0.0279896
$49$	−6.99357	−0.999081
$50$	−10.9585	−1.54976
$51$	1.00000	0.140028
$52$	12.7457	1.76751
$53$	5.82371	0.799948	0.399974	−	0.916527i	$-0.369019\pi$
$53$	5.82371	0.799948	0.399974	+	0.916527i	$0.369019\pi$
$54$	2.27866	0.310086
$55$	15.6613	2.11177
$56$	0.217929	0.0291220
$57$	−2.46147	−0.326029
$58$	18.9592	2.48946
$59$	4.80944	0.626135	0.313068	−	0.949731i	$-0.398643\pi$
$59$	4.80944	0.626135	0.313068	+	0.949731i	$0.398643\pi$
$60$	9.99809	1.29075
$61$	−10.0824	−1.29092	−0.645461	−	0.763793i	$-0.723335\pi$
$61$	−10.0824	−1.29092	−0.645461	+	0.763793i	$0.723335\pi$
$62$	1.83563	0.233125
$63$	−0.0802156	−0.0101062
$64$	−13.0003	−1.62504
$65$	−12.5049	−1.55104
$66$	−11.3944	−1.40255
$67$	−8.96523	−1.09528	−0.547639	−	0.836715i	$-0.684473\pi$
$67$	−8.96523	−1.09528	−0.547639	+	0.836715i	$0.684473\pi$
$68$	−3.19228	−0.387121
$69$	−2.52357	−0.303802
$70$	−0.572472	−0.0684235
$71$	7.92651	0.940704	0.470352	−	0.882479i	$-0.344127\pi$
$71$	7.92651	0.940704	0.470352	+	0.882479i	$0.344127\pi$
$72$	−2.71679	−0.320177
$73$	−4.57642	−0.535630	−0.267815	−	0.963470i	$-0.586302\pi$
$73$	−4.57642	−0.535630	−0.267815	+	0.963470i	$0.586302\pi$
$74$	−23.6024	−2.74373
$75$	−4.80919	−0.555317
$76$	7.85768	0.901338
$77$	0.401116	0.0457114
$78$	9.09792	1.03014
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	0.607343	0.0679030
$81$	1.00000	0.111111
$82$	0.417632	0.0461198
$83$	9.12814	1.00194	0.500972	−	0.865464i	$-0.332976\pi$
$83$	9.12814	1.00194	0.500972	+	0.865464i	$0.332976\pi$
$84$	0.256070	0.0279396
$85$	3.13196	0.339709
$86$	17.2251	1.85743
$87$	8.32033	0.892033
$88$	13.5852	1.44819
$89$	−0.860630	−0.0912265	−0.0456133	−	0.998959i	$-0.514524\pi$
$89$	−0.860630	−0.0912265	−0.0456133	+	0.998959i	$0.514524\pi$
$90$	7.13667	0.752271
$91$	−0.320274	−0.0335738
$92$	8.05594	0.839890
$93$	0.805575	0.0835342
$94$	10.6057	1.09389
$95$	−7.70922	−0.790949
$96$	−5.87546	−0.599661
$97$	−15.2883	−1.55229	−0.776144	−	0.630556i	$-0.782827\pi$
$97$	−15.2883	−1.55229	−0.776144	+	0.630556i	$0.782827\pi$
$98$	15.9359	1.60977
$99$	−5.00047	−0.502566
$100$	15.3523	1.53523
$101$	5.41552	0.538864	0.269432	−	0.963019i	$-0.413164\pi$
$101$	5.41552	0.538864	0.269432	+	0.963019i	$0.413164\pi$
$102$	−2.27866	−0.225621
$103$	−18.1777	−1.79110	−0.895551	−	0.444959i	$-0.853218\pi$
$103$	−18.1777	−1.79110	−0.895551	+	0.444959i	$0.853218\pi$
$104$	−10.8472	−1.06366
$105$	−0.251232	−0.0245177
$106$	−13.2702	−1.28892
$107$	−6.64674	−0.642565	−0.321283	−	0.946983i	$-0.604114\pi$
$107$	−6.64674	−0.642565	−0.321283	+	0.946983i	$0.604114\pi$
$108$	−3.19228	−0.307177
$109$	−0.892414	−0.0854778	−0.0427389	−	0.999086i	$-0.513608\pi$
$109$	−0.892414	−0.0854778	−0.0427389	+	0.999086i	$0.513608\pi$
$110$	−35.6867	−3.40259
$111$	−10.3580	−0.983142
$112$	0.0155552	0.00146983
$113$	−17.6218	−1.65772	−0.828860	−	0.559457i	$-0.811010\pi$
$113$	−17.6218	−1.65772	−0.828860	+	0.559457i	$0.811010\pi$
$114$	5.60884	0.525316
$115$	−7.90373	−0.737027
$116$	−26.5608	−2.46611
$117$	3.99267	0.369122
$118$	−10.9591	−1.00886
$119$	0.0802156	0.00735335
$120$	−8.50889	−0.776752
$121$	14.0047	1.27316
$122$	22.9744	2.08000
$123$	0.183280	0.0165258
$124$	−2.57162	−0.230938
$125$	0.597617	0.0534525
$126$	0.182784	0.0162837
$127$	16.4533	1.45999	0.729996	−	0.683451i	$-0.239522\pi$
$127$	16.4533	1.45999	0.729996	+	0.683451i	$0.239522\pi$
$128$	17.8723	1.57971
$129$	7.55934	0.665562
$130$	28.4943	2.49912
$131$	−9.58929	−0.837820	−0.418910	−	0.908028i	$-0.637588\pi$
$131$	−9.58929	−0.837820	−0.418910	+	0.908028i	$0.637588\pi$
$132$	15.9629	1.38939
$133$	−0.197448	−0.0171209
$134$	20.4287	1.76477
$135$	3.13196	0.269556
$136$	2.71679	0.232963
$137$	−14.7192	−1.25754	−0.628771	−	0.777590i	$-0.716442\pi$
$137$	−14.7192	−1.25754	−0.628771	+	0.777590i	$0.716442\pi$
$138$	5.75036	0.489503
$139$	21.6385	1.83535	0.917675	−	0.397332i	$-0.130064\pi$
$139$	21.6385	1.83535	0.917675	+	0.397332i	$0.130064\pi$
$140$	0.802003	0.0677816
$141$	4.65435	0.391967
$142$	−18.0618	−1.51571
$143$	−19.9652	−1.66957
$144$	−0.193918	−0.0161598
$145$	26.0589	2.16408
$146$	10.4281	0.863036
$147$	6.99357	0.576820
$148$	33.0658	2.71799
$149$	−10.8910	−0.892228	−0.446114	−	0.894976i	$-0.647192\pi$
$149$	−10.8910	−0.892228	−0.446114	+	0.894976i	$0.647192\pi$
$150$	10.9585	0.894757
$151$	−4.99158	−0.406209	−0.203104	−	0.979157i	$-0.565103\pi$
$151$	−4.99158	−0.406209	−0.203104	+	0.979157i	$0.565103\pi$
$152$	−6.68729	−0.542411
$153$	−1.00000	−0.0808452
$154$	−0.914005	−0.0736526
$155$	2.52303	0.202655
$156$	−12.7457	−1.02047
$157$	−6.57973	−0.525119	−0.262560	−	0.964916i	$-0.584567\pi$
$157$	−6.57973	−0.525119	−0.262560	+	0.964916i	$0.584567\pi$
$158$	−2.27866	−0.181280
$159$	−5.82371	−0.461850
$160$	−18.4017	−1.45478
$161$	−0.202430	−0.0159537
$162$	−2.27866	−0.179028
$163$	−0.857319	−0.0671504	−0.0335752	−	0.999436i	$-0.510689\pi$
$163$	−0.857319	−0.0671504	−0.0335752	+	0.999436i	$0.510689\pi$
$164$	−0.585081	−0.0456871
$165$	−15.6613	−1.21923
$166$	−20.7999	−1.61438
$167$	−9.20838	−0.712566	−0.356283	−	0.934378i	$-0.615956\pi$
$167$	−9.20838	−0.712566	−0.356283	+	0.934378i	$0.615956\pi$
$168$	−0.217929	−0.0168136
$169$	2.94138	0.226260
$170$	−7.13667	−0.547357
$171$	2.46147	0.188233
$172$	−24.1315	−1.84001
$173$	11.7701	0.894867	0.447433	−	0.894317i	$-0.352338\pi$
$173$	11.7701	0.894867	0.447433	+	0.894317i	$0.352338\pi$
$174$	−18.9592	−1.43729
$175$	−0.385772	−0.0291616
$176$	0.969680	0.0730923
$177$	−4.80944	−0.361499
$178$	1.96108	0.146989
$179$	1.68419	0.125882	0.0629412	−	0.998017i	$-0.479952\pi$
$179$	1.68419	0.125882	0.0629412	+	0.998017i	$0.479952\pi$
$180$	−9.99809	−0.745214
$181$	24.5296	1.82327	0.911636	−	0.410998i	$-0.134820\pi$
$181$	24.5296	1.82327	0.911636	+	0.410998i	$0.134820\pi$
$182$	0.729794	0.0540960
$183$	10.0824	0.745315
$184$	−6.85602	−0.505433
$185$	−32.4410	−2.38511
$186$	−1.83563	−0.134595
$187$	5.00047	0.365671
$188$	−14.8580	−1.08363
$189$	0.0802156	0.00583482
$190$	17.5667	1.27442
$191$	13.2575	0.959276	0.479638	−	0.877466i	$-0.340768\pi$
$191$	13.2575	0.959276	0.479638	+	0.877466i	$0.340768\pi$
$192$	13.0003	0.938217
$193$	−5.21102	−0.375097	−0.187549	−	0.982255i	$-0.560054\pi$
$193$	−5.21102	−0.375097	−0.187549	+	0.982255i	$0.560054\pi$
$194$	34.8367	2.50113
$195$	12.5049	0.895493
$196$	−22.3254	−1.59467
$197$	−19.6192	−1.39781	−0.698905	−	0.715214i	$-0.746329\pi$
$197$	−19.6192	−1.39781	−0.698905	+	0.715214i	$0.746329\pi$
$198$	11.3944	0.809762
$199$	−20.5492	−1.45669	−0.728347	−	0.685209i	$-0.759711\pi$
$199$	−20.5492	−1.45669	−0.728347	+	0.685209i	$0.759711\pi$
$200$	−13.0656	−0.923875
$201$	8.96523	0.632359
$202$	−12.3401	−0.868247
$203$	0.667420	0.0468437
$204$	3.19228	0.223504
$205$	0.574026	0.0400917
$206$	41.4207	2.88592
$207$	2.52357	0.175400
$208$	−0.774248	−0.0536845
$209$	−12.3085	−0.851396
$210$	0.572472	0.0395043
$211$	3.60397	0.248108	0.124054	−	0.992275i	$-0.460410\pi$
$211$	3.60397	0.248108	0.124054	+	0.992275i	$0.460410\pi$
$212$	18.5909	1.27683
$213$	−7.92651	−0.543116
$214$	15.1457	1.03534
$215$	23.6756	1.61466
$216$	2.71679	0.184854
$217$	0.0646196	0.00438667
$218$	2.03351	0.137726
$219$	4.57642	0.309246
$220$	49.9952	3.37067
$221$	−3.99267	−0.268576
$222$	23.6024	1.58409
$223$	11.5968	0.776578	0.388289	−	0.921538i	$-0.373066\pi$
$223$	11.5968	0.776578	0.388289	+	0.921538i	$0.373066\pi$
$224$	−0.471303	−0.0314903
$225$	4.80919	0.320613
$226$	40.1540	2.67101
$227$	−17.2034	−1.14183	−0.570914	−	0.821010i	$-0.693411\pi$
$227$	−17.2034	−1.14183	−0.570914	+	0.821010i	$0.693411\pi$
$228$	−7.85768	−0.520388
$229$	4.97398	0.328690	0.164345	−	0.986403i	$-0.447449\pi$
$229$	4.97398	0.328690	0.164345	+	0.986403i	$0.447449\pi$
$230$	18.0099	1.18754
$231$	−0.401116	−0.0263915
$232$	22.6046	1.48406
$233$	21.9040	1.43498	0.717488	−	0.696571i	$-0.245292\pi$
$233$	21.9040	1.43498	0.717488	+	0.696571i	$0.245292\pi$
$234$	−9.09792	−0.594749
$235$	14.5772	0.950915
$236$	15.3531	0.999399
$237$	−1.00000	−0.0649570
$238$	−0.182784	−0.0118481
$239$	−0.639024	−0.0413350	−0.0206675	−	0.999786i	$-0.506579\pi$
$239$	−0.639024	−0.0413350	−0.0206675	+	0.999786i	$0.506579\pi$
$240$	−0.607343	−0.0392038
$241$	−12.4379	−0.801197	−0.400599	−	0.916254i	$-0.631198\pi$
$241$	−12.4379	−0.801197	−0.400599	+	0.916254i	$0.631198\pi$
$242$	−31.9119	−2.05138
$243$	−1.00000	−0.0641500
$244$	−32.1859	−2.06049
$245$	21.9036	1.39937
$246$	−0.417632	−0.0266273
$247$	9.82781	0.625329
$248$	2.18858	0.138975
$249$	−9.12814	−0.578472
$250$	−1.36176	−0.0861255
$251$	16.4360	1.03743	0.518715	−	0.854947i	$-0.326411\pi$
$251$	16.4360	1.03743	0.518715	+	0.854947i	$0.326411\pi$
$252$	−0.256070	−0.0161309
$253$	−12.6191	−0.793353
$254$	−37.4914	−2.35242
$255$	−3.13196	−0.196131
$256$	−14.7243	−0.920270
$257$	−21.6122	−1.34813	−0.674067	−	0.738670i	$-0.735454\pi$
$257$	−21.6122	−1.34813	−0.674067	+	0.738670i	$0.735454\pi$
$258$	−17.2251	−1.07239
$259$	−0.830876	−0.0516281
$260$	−39.9190	−2.47567
$261$	−8.32033	−0.515015
$262$	21.8507	1.34994
$263$	29.9488	1.84672	0.923361	−	0.383932i	$-0.125430\pi$
$263$	29.9488	1.84672	0.923361	+	0.383932i	$0.125430\pi$
$264$	−13.5852	−0.836114
$265$	−18.2396	−1.12045
$266$	0.449916	0.0275861
$267$	0.860630	0.0526697
$268$	−28.6195	−1.74822
$269$	14.5218	0.885408	0.442704	−	0.896668i	$-0.354019\pi$
$269$	14.5218	0.885408	0.442704	+	0.896668i	$0.354019\pi$
$270$	−7.13667	−0.434324
$271$	−8.49164	−0.515831	−0.257915	−	0.966168i	$-0.583036\pi$
$271$	−8.49164	−0.515831	−0.257915	+	0.966168i	$0.583036\pi$
$272$	0.193918	0.0117580
$273$	0.320274	0.0193839
$274$	33.5399	2.02622
$275$	−24.0482	−1.45016
$276$	−8.05594	−0.484911
$277$	−29.6576	−1.78195	−0.890976	−	0.454051i	$-0.849978\pi$
$277$	−29.6576	−1.78195	−0.890976	+	0.454051i	$0.849978\pi$
$278$	−49.3066	−2.95722
$279$	−0.805575	−0.0482285
$280$	−0.682545	−0.0407899
$281$	−6.07216	−0.362234	−0.181117	−	0.983462i	$-0.557971\pi$
$281$	−6.07216	−0.362234	−0.181117	+	0.983462i	$0.557971\pi$
$282$	−10.6057	−0.631558
$283$	−7.51003	−0.446425	−0.223213	−	0.974770i	$-0.571654\pi$
$283$	−7.51003	−0.446425	−0.223213	+	0.974770i	$0.571654\pi$
$284$	25.3036	1.50149
$285$	7.70922	0.456655
$286$	45.4939	2.69011
$287$	0.0147019	0.000867826 0
$288$	5.87546	0.346215
$289$	1.00000	0.0588235
$290$	−59.3794	−3.48688
$291$	15.2883	0.896214
$292$	−14.6092	−0.854940
$293$	5.79465	0.338527	0.169264	−	0.985571i	$-0.445861\pi$
$293$	5.79465	0.338527	0.169264	+	0.985571i	$0.445861\pi$
$294$	−15.9359	−0.929403
$295$	−15.0630	−0.877000
$296$	−28.1407	−1.63564
$297$	5.00047	0.290157
$298$	24.8169	1.43761
$299$	10.0758	0.582698
$300$	−15.3523	−0.886363
$301$	0.606376	0.0349509
$302$	11.3741	0.654506
$303$	−5.41552	−0.311113
$304$	−0.477322	−0.0273763
$305$	31.5778	1.80814
$306$	2.27866	0.130262
$307$	5.18300	0.295810	0.147905	−	0.989002i	$-0.452747\pi$
$307$	5.18300	0.295810	0.147905	+	0.989002i	$0.452747\pi$
$308$	1.28047	0.0729617
$309$	18.1777	1.03409
$310$	−5.74912	−0.326528
$311$	2.73651	0.155173	0.0775866	−	0.996986i	$-0.475279\pi$
$311$	2.73651	0.155173	0.0775866	+	0.996986i	$0.475279\pi$
$312$	10.8472	0.614104
$313$	25.8591	1.46165	0.730823	−	0.682568i	$-0.239137\pi$
$313$	25.8591	1.46165	0.730823	+	0.682568i	$0.239137\pi$
$314$	14.9929	0.846101
$315$	0.251232	0.0141553
$316$	3.19228	0.179580
$317$	−8.90858	−0.500356	−0.250178	−	0.968200i	$-0.580489\pi$
$317$	−8.90858	−0.500356	−0.250178	+	0.968200i	$0.580489\pi$
$318$	13.2702	0.744158
$319$	41.6056	2.32946
$320$	40.7165	2.27612
$321$	6.64674	0.370985
$322$	0.461268	0.0257055
$323$	−2.46147	−0.136960
$324$	3.19228	0.177349
$325$	19.2015	1.06511
$326$	1.95354	0.108196
$327$	0.892414	0.0493506
$328$	0.497934	0.0274938
$329$	0.373351	0.0205835
$330$	35.6867	1.96449
$331$	−3.14995	−0.173137	−0.0865684	−	0.996246i	$-0.527590\pi$
$331$	−3.14995	−0.173137	−0.0865684	+	0.996246i	$0.527590\pi$
$332$	29.1395	1.59924
$333$	10.3580	0.567617
$334$	20.9827	1.14812
$335$	28.0788	1.53411
$336$	−0.0155552	−0.000848606 0
$337$	4.15782	0.226491	0.113245	−	0.993567i	$-0.463875\pi$
$337$	4.15782	0.226491	0.113245	+	0.993567i	$0.463875\pi$
$338$	−6.70240	−0.364562
$339$	17.6218	0.957085
$340$	9.99809	0.542223
$341$	4.02825	0.218142
$342$	−5.60884	−0.303291
$343$	1.12250	0.0606094
$344$	20.5371	1.10729
$345$	7.90373	0.425523
$346$	−26.8201	−1.44186
$347$	29.4796	1.58255	0.791274	−	0.611462i	$-0.209418\pi$
$347$	29.4796	1.58255	0.791274	+	0.611462i	$0.209418\pi$
$348$	26.5608	1.42381
$349$	16.6926	0.893536	0.446768	−	0.894650i	$-0.352575\pi$
$349$	16.6926	0.893536	0.446768	+	0.894650i	$0.352575\pi$
$350$	0.879041	0.0469867
$351$	−3.99267	−0.213113
$352$	−29.3801	−1.56596
$353$	−30.1349	−1.60392	−0.801961	−	0.597377i	$-0.796210\pi$
$353$	−30.1349	−1.60392	−0.801961	+	0.597377i	$0.796210\pi$
$354$	10.9591	0.582467
$355$	−24.8255	−1.31760
$356$	−2.74737	−0.145610
$357$	−0.0802156	−0.00424546
$358$	−3.83769	−0.202828
$359$	23.1741	1.22308	0.611541	−	0.791213i	$-0.290550\pi$
$359$	23.1741	1.22308	0.611541	+	0.791213i	$0.290550\pi$
$360$	8.50889	0.448458
$361$	−12.9412	−0.681115
$362$	−55.8946	−2.93775
$363$	−14.0047	−0.735057
$364$	−1.02240	−0.0535885
$365$	14.3332	0.750233
$366$	−22.9744	−1.20089
$367$	20.9380	1.09295	0.546476	−	0.837474i	$-0.315969\pi$
$367$	20.9380	1.09295	0.546476	+	0.837474i	$0.315969\pi$
$368$	−0.489365	−0.0255099
$369$	−0.183280	−0.00954118
$370$	73.9219	3.84302
$371$	−0.467152	−0.0242533
$372$	2.57162	0.133332
$373$	36.5130	1.89057	0.945285	−	0.326246i	$-0.105784\pi$
$373$	36.5130	1.89057	0.945285	+	0.326246i	$0.105784\pi$
$374$	−11.3944	−0.589188
$375$	−0.597617	−0.0308608
$376$	12.6449	0.652111
$377$	−33.2203	−1.71093
$378$	−0.182784	−0.00940138
$379$	35.5181	1.82444	0.912221	−	0.409699i	$-0.134366\pi$
$379$	35.5181	1.82444	0.912221	+	0.409699i	$0.134366\pi$
$380$	−24.6100	−1.26246
$381$	−16.4533	−0.842927
$382$	−30.2092	−1.54564
$383$	6.70074	0.342392	0.171196	−	0.985237i	$-0.445237\pi$
$383$	6.70074	0.342392	0.171196	+	0.985237i	$0.445237\pi$
$384$	−17.8723	−0.912044
$385$	−1.25628	−0.0640259
$386$	11.8741	0.604377
$387$	−7.55934	−0.384263
$388$	−48.8044	−2.47767
$389$	20.8753	1.05842	0.529211	−	0.848491i	$-0.322488\pi$
$389$	20.8753	1.05842	0.529211	+	0.848491i	$0.322488\pi$
$390$	−28.4943	−1.44287
$391$	−2.52357	−0.127623
$392$	19.0001	0.959648
$393$	9.58929	0.483715
$394$	44.7054	2.25223
$395$	−3.13196	−0.157586
$396$	−15.9629	−0.802166
$397$	−17.4239	−0.874482	−0.437241	−	0.899344i	$-0.644044\pi$
$397$	−17.4239	−0.874482	−0.437241	+	0.899344i	$0.644044\pi$
$398$	46.8245	2.34710
$399$	0.197448	0.00988476
$400$	−0.932586	−0.0466293
$401$	20.2799	1.01273	0.506366	−	0.862319i	$-0.330988\pi$
$401$	20.2799	1.01273	0.506366	+	0.862319i	$0.330988\pi$
$402$	−20.4287	−1.01889
$403$	−3.21639	−0.160220
$404$	17.2878	0.860102
$405$	−3.13196	−0.155628
$406$	−1.52082	−0.0754770
$407$	−51.7951	−2.56739
$408$	−2.71679	−0.134501
$409$	−6.31609	−0.312310	−0.156155	−	0.987733i	$-0.549910\pi$
$409$	−6.31609	−0.312310	−0.156155	+	0.987733i	$0.549910\pi$
$410$	−1.30801	−0.0645980
$411$	14.7192	0.726043
$412$	−58.0283	−2.85885
$413$	−0.385792	−0.0189836
$414$	−5.75036	−0.282615
$415$	−28.5890	−1.40338
$416$	23.4587	1.15016
$417$	−21.6385	−1.05964
$418$	28.0468	1.37182
$419$	−6.94256	−0.339166	−0.169583	−	0.985516i	$-0.554242\pi$
$419$	−6.94256	−0.339166	−0.169583	+	0.985516i	$0.554242\pi$
$420$	−0.802003	−0.0391337
$421$	32.6805	1.59275	0.796375	−	0.604803i	$-0.206748\pi$
$421$	32.6805	1.59275	0.796375	+	0.604803i	$0.206748\pi$
$422$	−8.21222	−0.399765
$423$	−4.65435	−0.226302
$424$	−15.8218	−0.768375
$425$	−4.80919	−0.233280
$426$	18.0618	0.875097
$427$	0.808768	0.0391390
$428$	−21.2183	−1.02562
$429$	19.9652	0.963930
$430$	−53.9485	−2.60163
$431$	−5.96004	−0.287085	−0.143543	−	0.989644i	$-0.545849\pi$
$431$	−5.96004	−0.287085	−0.143543	+	0.989644i	$0.545849\pi$
$432$	0.193918	0.00932987
$433$	19.3247	0.928686	0.464343	−	0.885655i	$-0.346290\pi$
$433$	19.3247	0.928686	0.464343	+	0.885655i	$0.346290\pi$
$434$	−0.147246	−0.00706803
$435$	−26.0589	−1.24943
$436$	−2.84883	−0.136434
$437$	6.21169	0.297145
$438$	−10.4281	−0.498274
$439$	17.7190	0.845681	0.422841	−	0.906204i	$-0.361033\pi$
$439$	17.7190	0.845681	0.422841	+	0.906204i	$0.361033\pi$
$440$	−42.5485	−2.02842
$441$	−6.99357	−0.333027
$442$	9.09792	0.432744
$443$	−9.58390	−0.455345	−0.227672	−	0.973738i	$-0.573112\pi$
$443$	−9.58390	−0.455345	−0.227672	+	0.973738i	$0.573112\pi$
$444$	−33.0658	−1.56923
$445$	2.69546	0.127777
$446$	−26.4251	−1.25126
$447$	10.8910	0.515128
$448$	1.04283	0.0492690
$449$	5.77131	0.272365	0.136182	−	0.990684i	$-0.456517\pi$
$449$	5.77131	0.272365	0.136182	+	0.990684i	$0.456517\pi$
$450$	−10.9585	−0.516588
$451$	0.916487	0.0431557
$452$	−56.2537	−2.64595
$453$	4.99158	0.234525
$454$	39.2006	1.83977
$455$	1.00309	0.0470254
$456$	6.68729	0.313161
$457$	11.4674	0.536422	0.268211	−	0.963360i	$-0.413568\pi$
$457$	11.4674	0.536422	0.268211	+	0.963360i	$0.413568\pi$
$458$	−11.3340	−0.529602
$459$	1.00000	0.0466760
$460$	−25.2309	−1.17640
$461$	20.0962	0.935976	0.467988	−	0.883735i	$-0.344979\pi$
$461$	20.0962	0.935976	0.467988	+	0.883735i	$0.344979\pi$
$462$	0.914005	0.0425234
$463$	19.8957	0.924631	0.462315	−	0.886716i	$-0.347019\pi$
$463$	19.8957	0.924631	0.462315	+	0.886716i	$0.347019\pi$
$464$	1.61346	0.0749029
$465$	−2.52303	−0.117003
$466$	−49.9116	−2.31211
$467$	38.1231	1.76413	0.882063	−	0.471132i	$-0.156154\pi$
$467$	38.1231	1.76413	0.882063	+	0.471132i	$0.156154\pi$
$468$	12.7457	0.589170
$469$	0.719151	0.0332073
$470$	−33.2165	−1.53216
$471$	6.57973	0.303178
$472$	−13.0662	−0.601422
$473$	37.8002	1.73806
$474$	2.27866	0.104662
$475$	11.8377	0.543149
$476$	0.256070	0.0117370
$477$	5.82371	0.266649
$478$	1.45612	0.0666012
$479$	−5.17431	−0.236420	−0.118210	−	0.992989i	$-0.537716\pi$
$479$	−5.17431	−0.236420	−0.118210	+	0.992989i	$0.537716\pi$
$480$	18.4017	0.839919
$481$	41.3562	1.88568
$482$	28.3418	1.29093
$483$	0.202430	0.00921087
$484$	44.7069	2.03213
$485$	47.8823	2.17422
$486$	2.27866	0.103362
$487$	−31.1587	−1.41193	−0.705967	−	0.708244i	$-0.749487\pi$
$487$	−31.1587	−1.41193	−0.705967	+	0.708244i	$0.749487\pi$
$488$	27.3919	1.23997
$489$	0.857319	0.0387693
$490$	−49.9108	−2.25474
$491$	33.7654	1.52381	0.761906	−	0.647688i	$-0.224264\pi$
$491$	33.7654	1.52381	0.761906	+	0.647688i	$0.224264\pi$
$492$	0.585081	0.0263775
$493$	8.32033	0.374729
$494$	−22.3942	−1.00756
$495$	15.6613	0.703923
$496$	0.156215	0.00701427
$497$	−0.635830	−0.0285209
$498$	20.7999	0.932065
$499$	5.17688	0.231749	0.115874	−	0.993264i	$-0.463033\pi$
$499$	5.17688	0.231749	0.115874	+	0.993264i	$0.463033\pi$
$500$	1.90776	0.0853176
$501$	9.20838	0.411400
$502$	−37.4519	−1.67156
$503$	−30.2454	−1.34858	−0.674289	−	0.738468i	$-0.735550\pi$
$503$	−30.2454	−1.34858	−0.674289	+	0.738468i	$0.735550\pi$
$504$	0.217929	0.00970733
$505$	−16.9612	−0.754764
$506$	28.7545	1.27829
$507$	−2.94138	−0.130631
$508$	52.5235	2.33035
$509$	1.03524	0.0458861	0.0229431	−	0.999737i	$-0.492696\pi$
$509$	1.03524	0.0458861	0.0229431	+	0.999737i	$0.492696\pi$
$510$	7.13667	0.316017
$511$	0.367100	0.0162396
$512$	−2.19302	−0.0969188
$513$	−2.46147	−0.108676
$514$	49.2469	2.17219
$515$	56.9319	2.50872
$516$	24.1315	1.06233
$517$	23.2739	1.02359
$518$	1.89328	0.0831860
$519$	−11.7701	−0.516652
$520$	33.9732	1.48982
$521$	−35.6551	−1.56208	−0.781039	−	0.624482i	$-0.785310\pi$
$521$	−35.6551	−1.56208	−0.781039	+	0.624482i	$0.785310\pi$
$522$	18.9592	0.829820
$523$	−26.2397	−1.14738	−0.573691	−	0.819072i	$-0.694489\pi$
$523$	−26.2397	−1.14738	−0.573691	+	0.819072i	$0.694489\pi$
$524$	−30.6117	−1.33728
$525$	0.385772	0.0168365
$526$	−68.2431	−2.97554
$527$	0.805575	0.0350914
$528$	−0.969680	−0.0421999
$529$	−16.6316	−0.723112
$530$	41.5619	1.80533
$531$	4.80944	0.208712
$532$	−0.630309	−0.0273273
$533$	−0.731776	−0.0316967
$534$	−1.96108	−0.0848642
$535$	20.8174	0.900013
$536$	24.3567	1.05205
$537$	−1.68419	−0.0726782
$538$	−33.0901	−1.42662
$539$	34.9711	1.50631
$540$	9.99809	0.430249
$541$	38.4426	1.65277	0.826387	−	0.563102i	$-0.190392\pi$
$541$	38.4426	1.65277	0.826387	+	0.563102i	$0.190392\pi$
$542$	19.3495	0.831134
$543$	−24.5296	−1.05267
$544$	−5.87546	−0.251908
$545$	2.79501	0.119725
$546$	−0.729794	−0.0312323
$547$	2.92026	0.124861	0.0624307	−	0.998049i	$-0.480115\pi$
$547$	2.92026	0.124861	0.0624307	+	0.998049i	$0.480115\pi$
$548$	−46.9877	−2.00721
$549$	−10.0824	−0.430308
$550$	54.7976	2.33658
$551$	−20.4802	−0.872486
$552$	6.85602	0.291812
$553$	−0.0802156	−0.00341111
$554$	67.5795	2.87118
$555$	32.4410	1.37704
$556$	69.0760	2.92947
$557$	5.31643	0.225264	0.112632	−	0.993637i	$-0.464072\pi$
$557$	5.31643	0.225264	0.112632	+	0.993637i	$0.464072\pi$
$558$	1.83563	0.0777084
$559$	−30.1819	−1.27656
$560$	−0.0487183	−0.00205873
$561$	−5.00047	−0.211120
$562$	13.8364	0.583652
$563$	28.2136	1.18906	0.594530	−	0.804073i	$-0.297338\pi$
$563$	28.2136	1.18906	0.594530	+	0.804073i	$0.297338\pi$
$564$	14.8580	0.625634
$565$	55.1908	2.32189
$566$	17.1128	0.719304
$567$	−0.0802156	−0.00336874
$568$	−21.5347	−0.903576
$569$	31.7669	1.33174	0.665868	−	0.746070i	$-0.268061\pi$
$569$	31.7669	1.33174	0.665868	+	0.746070i	$0.268061\pi$
$570$	−17.5667	−0.735787
$571$	−24.7303	−1.03493	−0.517465	−	0.855705i	$-0.673124\pi$
$571$	−24.7303	−1.03493	−0.517465	+	0.855705i	$0.673124\pi$
$572$	−63.7345	−2.66487
$573$	−13.2575	−0.553838
$574$	−0.0335006	−0.00139829
$575$	12.1363	0.506120
$576$	−13.0003	−0.541680
$577$	24.8099	1.03285	0.516424	−	0.856333i	$-0.327263\pi$
$577$	24.8099	1.03285	0.516424	+	0.856333i	$0.327263\pi$
$578$	−2.27866	−0.0947796
$579$	5.21102	0.216563
$580$	83.1874	3.45417
$581$	−0.732218	−0.0303775
$582$	−34.8367	−1.44403
$583$	−29.1213	−1.20608
$584$	12.4332	0.514489
$585$	−12.5049	−0.517013
$586$	−13.2040	−0.545453
$587$	18.5163	0.764248	0.382124	−	0.924111i	$-0.375193\pi$
$587$	18.5163	0.764248	0.382124	+	0.924111i	$0.375193\pi$
$588$	22.3254	0.920684
$589$	−1.98290	−0.0817038
$590$	34.3234	1.41307
$591$	19.6192	0.807026
$592$	−2.00861	−0.0825533
$593$	1.94295	0.0797872	0.0398936	−	0.999204i	$-0.487298\pi$
$593$	1.94295	0.0797872	0.0398936	+	0.999204i	$0.487298\pi$
$594$	−11.3944	−0.467516
$595$	−0.251232	−0.0102995
$596$	−34.7672	−1.42412
$597$	20.5492	0.841022
$598$	−22.9593	−0.938874
$599$	−18.1498	−0.741579	−0.370790	−	0.928717i	$-0.620913\pi$
$599$	−18.1498	−0.741579	−0.370790	+	0.928717i	$0.620913\pi$
$600$	13.0656	0.533399
$601$	14.5527	0.593615	0.296808	−	0.954937i	$-0.404078\pi$
$601$	14.5527	0.593615	0.296808	+	0.954937i	$0.404078\pi$
$602$	−1.38172	−0.0563149
$603$	−8.96523	−0.365093
$604$	−15.9345	−0.648366
$605$	−43.8622	−1.78325
$606$	12.3401	0.501283
$607$	−10.9062	−0.442670	−0.221335	−	0.975198i	$-0.571041\pi$
$607$	−10.9062	−0.442670	−0.221335	+	0.975198i	$0.571041\pi$
$608$	14.4622	0.586521
$609$	−0.667420	−0.0270452
$610$	−71.9550	−2.91337
$611$	−18.5833	−0.751798
$612$	−3.19228	−0.129040
$613$	25.5889	1.03353	0.516763	−	0.856129i	$-0.327137\pi$
$613$	25.5889	1.03353	0.516763	+	0.856129i	$0.327137\pi$
$614$	−11.8103	−0.476624
$615$	−0.574026	−0.0231470
$616$	−1.08975	−0.0439072
$617$	4.58156	0.184447	0.0922234	−	0.995738i	$-0.470603\pi$
$617$	4.58156	0.184447	0.0922234	+	0.995738i	$0.470603\pi$
$618$	−41.4207	−1.66619
$619$	29.1831	1.17297	0.586483	−	0.809961i	$-0.300512\pi$
$619$	29.1831	1.17297	0.586483	+	0.809961i	$0.300512\pi$
$620$	8.05421	0.323465
$621$	−2.52357	−0.101267
$622$	−6.23557	−0.250023
$623$	0.0690359	0.00276586
$624$	0.774248	0.0309947
$625$	−25.9177	−1.03671
$626$	−58.9241	−2.35508
$627$	12.3085	0.491554
$628$	−21.0043	−0.838163
$629$	−10.3580	−0.413002
$630$	−0.572472	−0.0228078
$631$	−3.87039	−0.154078	−0.0770388	−	0.997028i	$-0.524547\pi$
$631$	−3.87039	−0.154078	−0.0770388	+	0.997028i	$0.524547\pi$
$632$	−2.71679	−0.108068
$633$	−3.60397	−0.143245
$634$	20.2996	0.806200
$635$	−51.5311	−2.04495
$636$	−18.5909	−0.737177
$637$	−27.9230	−1.10635
$638$	−94.8048	−3.75336
$639$	7.92651	0.313568
$640$	−55.9755	−2.21263
$641$	37.1247	1.46634	0.733169	−	0.680047i	$-0.238040\pi$
$641$	37.1247	1.46634	0.733169	+	0.680047i	$0.238040\pi$
$642$	−15.1457	−0.597751
$643$	−5.02996	−0.198362	−0.0991811	−	0.995069i	$-0.531622\pi$
$643$	−5.02996	−0.198362	−0.0991811	+	0.995069i	$0.531622\pi$
$644$	−0.646212	−0.0254643
$645$	−23.6756	−0.932224
$646$	5.60884	0.220677
$647$	44.5467	1.75131	0.875656	−	0.482935i	$-0.160429\pi$
$647$	44.5467	1.75131	0.875656	+	0.482935i	$0.160429\pi$
$648$	−2.71679	−0.106726
$649$	−24.0494	−0.944023
$650$	−43.7536	−1.71616
$651$	−0.0646196	−0.00253264
$652$	−2.73680	−0.107181
$653$	−2.15396	−0.0842908	−0.0421454	−	0.999111i	$-0.513419\pi$
$653$	−2.15396	−0.0842908	−0.0421454	+	0.999111i	$0.513419\pi$
$654$	−2.03351	−0.0795164
$655$	30.0333	1.17350
$656$	0.0355412	0.00138765
$657$	−4.57642	−0.178543
$658$	−0.850739	−0.0331653
$659$	39.7479	1.54836	0.774178	−	0.632967i	$-0.218163\pi$
$659$	39.7479	1.54836	0.774178	+	0.632967i	$0.218163\pi$
$660$	−49.9952	−1.94606
$661$	−10.7167	−0.416832	−0.208416	−	0.978040i	$-0.566831\pi$
$661$	−10.7167	−0.416832	−0.208416	+	0.978040i	$0.566831\pi$
$662$	7.17765	0.278967
$663$	3.99267	0.155062
$664$	−24.7993	−0.962398
$665$	0.618399	0.0239805
$666$	−23.6024	−0.914576
$667$	−20.9969	−0.813005
$668$	−29.3957	−1.13735
$669$	−11.5968	−0.448357
$670$	−63.9819	−2.47184
$671$	50.4169	1.94632
$672$	0.471303	0.0181809
$673$	−34.0914	−1.31413	−0.657063	−	0.753836i	$-0.728201\pi$
$673$	−34.0914	−1.31413	−0.657063	+	0.753836i	$0.728201\pi$
$674$	−9.47424	−0.364934
$675$	−4.80919	−0.185106
$676$	9.38970	0.361142
$677$	−13.5518	−0.520839	−0.260419	−	0.965496i	$-0.583861\pi$
$677$	−13.5518	−0.520839	−0.260419	+	0.965496i	$0.583861\pi$
$678$	−40.1540	−1.54211
$679$	1.22636	0.0470632
$680$	−8.50889	−0.326301
$681$	17.2034	0.659234
$682$	−9.17901	−0.351482
$683$	−1.09317	−0.0418291	−0.0209146	−	0.999781i	$-0.506658\pi$
$683$	−1.09317	−0.0418291	−0.0209146	+	0.999781i	$0.506658\pi$
$684$	7.85768	0.300446
$685$	46.0999	1.76139
$686$	−2.55780	−0.0976571
$687$	−4.97398	−0.189769
$688$	1.46589	0.0558865
$689$	23.2521	0.885835
$690$	−18.0099	−0.685625
$691$	29.8337	1.13493	0.567463	−	0.823399i	$-0.307925\pi$
$691$	29.8337	1.13493	0.567463	+	0.823399i	$0.307925\pi$
$692$	37.5735	1.42833
$693$	0.401116	0.0152371
$694$	−67.1739	−2.54989
$695$	−67.7708	−2.57069
$696$	−22.6046	−0.856825
$697$	0.183280	0.00694223
$698$	−38.0368	−1.43971
$699$	−21.9040	−0.828484
$700$	−1.23149	−0.0465460
$701$	−36.2508	−1.36917	−0.684587	−	0.728931i	$-0.740018\pi$
$701$	−36.2508	−1.36917	−0.684587	+	0.728931i	$0.740018\pi$
$702$	9.09792	0.343379
$703$	25.4960	0.961599
$704$	65.0077	2.45007
$705$	−14.5772	−0.549011
$706$	68.6672	2.58432
$707$	−0.434409	−0.0163376
$708$	−15.3531	−0.577003
$709$	12.9505	0.486368	0.243184	−	0.969980i	$-0.421808\pi$
$709$	12.9505	0.486368	0.243184	+	0.969980i	$0.421808\pi$
$710$	56.5689	2.12299
$711$	1.00000	0.0375029
$712$	2.33815	0.0876259
$713$	−2.03293	−0.0761337
$714$	0.182784	0.00684051
$715$	62.5303	2.33850
$716$	5.37640	0.200926
$717$	0.639024	0.0238648
$718$	−52.8058	−1.97069
$719$	−22.8899	−0.853648	−0.426824	−	0.904335i	$-0.640368\pi$
$719$	−22.8899	−0.853648	−0.426824	+	0.904335i	$0.640368\pi$
$720$	0.607343	0.0226343
$721$	1.45813	0.0543037
$722$	29.4885	1.09745
$723$	12.4379	0.462571
$724$	78.3054	2.91020
$725$	−40.0140	−1.48608
$726$	31.9119	1.18436
$727$	41.8150	1.55083	0.775416	−	0.631451i	$-0.217540\pi$
$727$	41.8150	1.55083	0.775416	+	0.631451i	$0.217540\pi$
$728$	0.870118	0.0322487
$729$	1.00000	0.0370370
$730$	−32.6604	−1.20882
$731$	7.55934	0.279592
$732$	32.1859	1.18963
$733$	20.3543	0.751805	0.375902	−	0.926659i	$-0.377333\pi$
$733$	20.3543	0.751805	0.375902	+	0.926659i	$0.377333\pi$
$734$	−47.7104	−1.76102
$735$	−21.9036	−0.807926
$736$	14.8271	0.546536
$737$	44.8304	1.65135
$738$	0.417632	0.0153733
$739$	−41.4339	−1.52417	−0.762085	−	0.647478i	$-0.775824\pi$
$739$	−41.4339	−1.52417	−0.762085	+	0.647478i	$0.775824\pi$
$740$	−103.561	−3.80697
$741$	−9.82781	−0.361034
$742$	1.06448	0.0390783
$743$	9.15548	0.335882	0.167941	−	0.985797i	$-0.446288\pi$
$743$	9.15548	0.335882	0.167941	+	0.985797i	$0.446288\pi$
$744$	−2.18858	−0.0802372
$745$	34.1103	1.24971
$746$	−83.2005	−3.04619
$747$	9.12814	0.333981
$748$	15.9629	0.583661
$749$	0.533172	0.0194817
$750$	1.36176	0.0497246
$751$	−11.8805	−0.433526	−0.216763	−	0.976224i	$-0.569550\pi$
$751$	−11.8805	−0.433526	−0.216763	+	0.976224i	$0.569550\pi$
$752$	0.902560	0.0329130
$753$	−16.4360	−0.598960
$754$	75.6976	2.75675
$755$	15.6334	0.568959
$756$	0.256070	0.00931319
$757$	10.4120	0.378431	0.189216	−	0.981936i	$-0.439405\pi$
$757$	10.4120	0.378431	0.189216	+	0.981936i	$0.439405\pi$
$758$	−80.9335	−2.93964
$759$	12.6191	0.458043
$760$	20.9444	0.759731
$761$	−15.2424	−0.552538	−0.276269	−	0.961080i	$-0.589098\pi$
$761$	−15.2424	−0.552538	−0.276269	+	0.961080i	$0.589098\pi$
$762$	37.4914	1.35817
$763$	0.0715855	0.00259157
$764$	42.3215	1.53114
$765$	3.13196	0.113236
$766$	−15.2687	−0.551680
$767$	19.2025	0.693361
$768$	14.7243	0.531318
$769$	9.11189	0.328583	0.164292	−	0.986412i	$-0.447466\pi$
$769$	9.11189	0.328583	0.164292	+	0.986412i	$0.447466\pi$
$770$	2.86263	0.103162
$771$	21.6122	0.778345
$772$	−16.6350	−0.598708
$773$	−30.8868	−1.11092	−0.555460	−	0.831543i	$-0.687458\pi$
$773$	−30.8868	−1.11092	−0.555460	+	0.831543i	$0.687458\pi$
$774$	17.2251	0.619145
$775$	−3.87416	−0.139164
$776$	41.5350	1.49102
$777$	0.830876	0.0298075
$778$	−47.5677	−1.70539
$779$	−0.451138	−0.0161637
$780$	39.9190	1.42933
$781$	−39.6363	−1.41830
$782$	5.75036	0.205632
$783$	8.32033	0.297344
$784$	1.35618	0.0484348
$785$	20.6075	0.735512
$786$	−21.8507	−0.779388
$787$	−38.2764	−1.36441	−0.682203	−	0.731163i	$-0.738978\pi$
$787$	−38.2764	−1.36441	−0.682203	+	0.731163i	$0.738978\pi$
$788$	−62.6299	−2.23110
$789$	−29.9488	−1.06621
$790$	7.13667	0.253911
$791$	1.41354	0.0502598
$792$	13.5852	0.482731
$793$	−40.2558	−1.42952
$794$	39.7032	1.40901
$795$	18.2396	0.646893
$796$	−65.5987	−2.32508
$797$	2.92436	0.103586	0.0517930	−	0.998658i	$-0.483506\pi$
$797$	2.92436	0.103586	0.0517930	+	0.998658i	$0.483506\pi$
$798$	−0.449916	−0.0159269
$799$	4.65435	0.164659
$800$	28.2562	0.999007
$801$	−0.860630	−0.0304088
$802$	−46.2110	−1.63177
$803$	22.8843	0.807569
$804$	28.6195	1.00933
$805$	0.634002	0.0223456
$806$	7.32905	0.258155
$807$	−14.5218	−0.511191
$808$	−14.7128	−0.517596
$809$	−38.8161	−1.36470	−0.682351	−	0.731024i	$-0.739043\pi$
$809$	−38.8161	−1.36470	−0.682351	+	0.731024i	$0.739043\pi$
$810$	7.13667	0.250757
$811$	−21.2527	−0.746284	−0.373142	−	0.927774i	$-0.621719\pi$
$811$	−21.2527	−0.746284	−0.373142	+	0.927774i	$0.621719\pi$
$812$	2.13059	0.0747690
$813$	8.49164	0.297815
$814$	118.023	4.13671
$815$	2.68509	0.0940547
$816$	−0.193918	−0.00678847
$817$	−18.6071	−0.650978
$818$	14.3922	0.503211
$819$	−0.320274	−0.0111913
$820$	1.83245	0.0639920
$821$	−23.0227	−0.803498	−0.401749	−	0.915750i	$-0.631598\pi$
$821$	−23.0227	−0.803498	−0.401749	+	0.915750i	$0.631598\pi$
$822$	−33.5399	−1.16984
$823$	−18.9477	−0.660476	−0.330238	−	0.943898i	$-0.607129\pi$
$823$	−18.9477	−0.660476	−0.330238	+	0.943898i	$0.607129\pi$
$824$	49.3850	1.72041
$825$	24.0482	0.837251
$826$	0.879087	0.0305873
$827$	−40.6847	−1.41475	−0.707373	−	0.706840i	$-0.750120\pi$
$827$	−40.6847	−1.41475	−0.707373	+	0.706840i	$0.750120\pi$
$828$	8.05594	0.279963
$829$	−37.3942	−1.29875	−0.649377	−	0.760466i	$-0.724970\pi$
$829$	−37.3942	−1.29875	−0.649377	+	0.760466i	$0.724970\pi$
$830$	65.1445	2.26120
$831$	29.6576	1.02881
$832$	−51.9059	−1.79951
$833$	6.99357	0.242313
$834$	49.3066	1.70735
$835$	28.8403	0.998060
$836$	−39.2921	−1.35895
$837$	0.805575	0.0278447
$838$	15.8197	0.546483
$839$	−55.9603	−1.93196	−0.965982	−	0.258610i	$-0.916736\pi$
$839$	−55.9603	−1.93196	−0.965982	+	0.258610i	$0.916736\pi$
$840$	0.682545	0.0235501
$841$	40.2278	1.38717
$842$	−74.4677	−2.56632
$843$	6.07216	0.209136
$844$	11.5049	0.396014
$845$	−9.21229	−0.316912
$846$	10.6057	0.364630
$847$	−1.12340	−0.0386003
$848$	−1.12932	−0.0387810
$849$	7.51003	0.257744
$850$	10.9585	0.375873
$851$	26.1393	0.896043
$852$	−25.3036	−0.866888
$853$	−14.5050	−0.496641	−0.248321	−	0.968678i	$-0.579879\pi$
$853$	−14.5050	−0.496641	−0.248321	+	0.968678i	$0.579879\pi$
$854$	−1.84290	−0.0630629
$855$	−7.70922	−0.263650
$856$	18.0578	0.617204
$857$	22.2635	0.760508	0.380254	−	0.924882i	$-0.375837\pi$
$857$	22.2635	0.760508	0.380254	+	0.924882i	$0.375837\pi$
$858$	−45.4939	−1.55314
$859$	−13.0018	−0.443614	−0.221807	−	0.975091i	$-0.571196\pi$
$859$	−13.0018	−0.443614	−0.221807	+	0.975091i	$0.571196\pi$
$860$	75.5789	2.57722
$861$	−0.0147019	−0.000501040 0
$862$	13.5809	0.462567
$863$	15.7527	0.536228	0.268114	−	0.963387i	$-0.413600\pi$
$863$	15.7527	0.536228	0.268114	+	0.963387i	$0.413600\pi$
$864$	−5.87546	−0.199887
$865$	−36.8636	−1.25340
$866$	−44.0344	−1.49635
$867$	−1.00000	−0.0339618
$868$	0.206284	0.00700173
$869$	−5.00047	−0.169629
$870$	59.3794	2.01315
$871$	−35.7952	−1.21287
$872$	2.42450	0.0821041
$873$	−15.2883	−0.517429
$874$	−14.1543	−0.478777
$875$	−0.0479382	−0.00162061
$876$	14.6092	0.493600
$877$	−47.5301	−1.60498	−0.802488	−	0.596668i	$-0.796491\pi$
$877$	−47.5301	−1.60498	−0.802488	+	0.596668i	$0.796491\pi$
$878$	−40.3755	−1.36261
$879$	−5.79465	−0.195449
$880$	−3.03700	−0.102377
$881$	2.84828	0.0959611	0.0479805	−	0.998848i	$-0.484721\pi$
$881$	2.84828	0.0959611	0.0479805	+	0.998848i	$0.484721\pi$
$882$	15.9359	0.536591
$883$	31.8623	1.07225	0.536126	−	0.844138i	$-0.319887\pi$
$883$	31.8623	1.07225	0.536126	+	0.844138i	$0.319887\pi$
$884$	−12.7457	−0.428684
$885$	15.0630	0.506336
$886$	21.8384	0.733676
$887$	−10.3429	−0.347280	−0.173640	−	0.984809i	$-0.555553\pi$
$887$	−10.3429	−0.347280	−0.173640	+	0.984809i	$0.555553\pi$
$888$	28.1407	0.944339
$889$	−1.31981	−0.0442650
$890$	−6.14203	−0.205881
$891$	−5.00047	−0.167522
$892$	37.0201	1.23953
$893$	−11.4565	−0.383378
$894$	−24.8169	−0.830002
$895$	−5.27482	−0.176318
$896$	−1.43364	−0.0478946
$897$	−10.0758	−0.336421
$898$	−13.1508	−0.438849
$899$	6.70265	0.223546
$900$	15.3523	0.511742
$901$	−5.82371	−0.194016
$902$	−2.08836	−0.0695347
$903$	−0.606376	−0.0201789
$904$	47.8748	1.59229
$905$	−76.8259	−2.55378
$906$	−11.3741	−0.377879
$907$	53.5268	1.77733	0.888664	−	0.458559i	$-0.151634\pi$
$907$	53.5268	1.77733	0.888664	+	0.458559i	$0.151634\pi$
$908$	−54.9179	−1.82252
$909$	5.41552	0.179621
$910$	−2.28569	−0.0757698
$911$	−18.3563	−0.608170	−0.304085	−	0.952645i	$-0.598351\pi$
$911$	−18.3563	−0.608170	−0.304085	+	0.952645i	$0.598351\pi$
$912$	0.477322	0.0158057
$913$	−45.6450	−1.51063
$914$	−26.1302	−0.864311
$915$	−31.5778	−1.04393
$916$	15.8783	0.524634
$917$	0.769210	0.0254015
$918$	−2.27866	−0.0752069
$919$	17.8225	0.587909	0.293955	−	0.955819i	$-0.405029\pi$
$919$	17.8225	0.587909	0.293955	+	0.955819i	$0.405029\pi$
$920$	21.4728	0.707937
$921$	−5.18300	−0.170786
$922$	−45.7925	−1.50809
$923$	31.6479	1.04170
$924$	−1.28047	−0.0421245
$925$	49.8138	1.63787
$926$	−45.3354	−1.48981
$927$	−18.1777	−0.597034
$928$	−48.8857	−1.60475
$929$	50.1602	1.64570	0.822851	−	0.568257i	$-0.192382\pi$
$929$	50.1602	1.64570	0.822851	+	0.568257i	$0.192382\pi$
$930$	5.74912	0.188521
$931$	−17.2144	−0.564180
$932$	69.9235	2.29042
$933$	−2.73651	−0.0895893
$934$	−86.8694	−2.84245
$935$	−15.6613	−0.512179
$936$	−10.8472	−0.354553
$937$	37.3705	1.22084	0.610421	−	0.792077i	$-0.291000\pi$
$937$	37.3705	1.22084	0.610421	+	0.792077i	$0.291000\pi$
$938$	−1.63870	−0.0535054
$939$	−25.8591	−0.843881
$940$	46.5346	1.51779
$941$	22.7989	0.743222	0.371611	−	0.928389i	$-0.378806\pi$
$941$	22.7989	0.743222	0.371611	+	0.928389i	$0.378806\pi$
$942$	−14.9929	−0.488496
$943$	−0.462521	−0.0150617
$944$	−0.932634	−0.0303547
$945$	−0.251232	−0.00817258
$946$	−86.1338	−2.80045
$947$	−4.19066	−0.136178	−0.0680890	−	0.997679i	$-0.521690\pi$
$947$	−4.19066	−0.136178	−0.0680890	+	0.997679i	$0.521690\pi$
$948$	−3.19228	−0.103680
$949$	−18.2721	−0.593138
$950$	−26.9740	−0.875151
$951$	8.90858	0.288881
$952$	−0.217929	−0.00706312
$953$	37.9263	1.22855	0.614277	−	0.789091i	$-0.289448\pi$
$953$	37.9263	1.22855	0.614277	+	0.789091i	$0.289448\pi$
$954$	−13.2702	−0.429640
$955$	−41.5219	−1.34362
$956$	−2.03994	−0.0659764
$957$	−41.6056	−1.34492
$958$	11.7905	0.380933
$959$	1.18071	0.0381270
$960$	−40.7165	−1.31412
$961$	−30.3510	−0.979066
$962$	−94.2366	−3.03831
$963$	−6.64674	−0.214188
$964$	−39.7053	−1.27882
$965$	16.3207	0.525382
$966$	−0.461268	−0.0148411
$967$	−12.9773	−0.417322	−0.208661	−	0.977988i	$-0.566911\pi$
$967$	−12.9773	−0.417322	−0.208661	+	0.977988i	$0.566911\pi$
$968$	−38.0479	−1.22291
$969$	2.46147	0.0790737
$970$	−109.107	−3.50322
$971$	47.8786	1.53650	0.768248	−	0.640152i	$-0.221129\pi$
$971$	47.8786	1.53650	0.768248	+	0.640152i	$0.221129\pi$
$972$	−3.19228	−0.102392
$973$	−1.73574	−0.0556453
$974$	70.9999	2.27498
$975$	−19.2015	−0.614939
$976$	1.95516	0.0625832
$977$	−61.6649	−1.97283	−0.986417	−	0.164260i	$-0.947476\pi$
$977$	−61.6649	−1.97283	−0.986417	+	0.164260i	$0.947476\pi$
$978$	−1.95354	−0.0624672
$979$	4.30355	0.137542
$980$	69.9223	2.23359
$981$	−0.892414	−0.0284926
$982$	−76.9398	−2.45525
$983$	43.1638	1.37671	0.688355	−	0.725374i	$-0.258333\pi$
$983$	43.1638	1.37671	0.688355	+	0.725374i	$0.258333\pi$
$984$	−0.497934	−0.0158736
$985$	61.4466	1.95785
$986$	−18.9592	−0.603783
$987$	−0.373351	−0.0118839
$988$	31.3731	0.998112
$989$	−19.0765	−0.606598
$990$	−35.6867	−1.13420
$991$	39.2846	1.24792	0.623958	−	0.781458i	$-0.285524\pi$
$991$	39.2846	1.24792	0.623958	+	0.781458i	$0.285524\pi$
$992$	−4.73312	−0.150277
$993$	3.14995	0.0999606
$994$	1.44884	0.0459543
$995$	64.3593	2.04033
$996$	−29.1395	−0.923322
$997$	6.66094	0.210954	0.105477	−	0.994422i	$-0.466363\pi$
$997$	6.66094	0.210954	0.105477	+	0.994422i	$0.466363\pi$
$998$	−11.7963	−0.373406
$999$	−10.3580	−0.327714

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.l.1.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.l.1.5	✓	32	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.27866 q^{2} -1.00000 q^{3} +3.19228 q^{4} -3.13196 q^{5} +2.27866 q^{6} -0.0802156 q^{7} -2.71679 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.27866 q^{2} -1.00000 q^{3} +3.19228 q^{4} -3.13196 q^{5} +2.27866 q^{6} -0.0802156 q^{7} -2.71679 q^{8} +1.00000 q^{9} +7.13667 q^{10} -5.00047 q^{11} -3.19228 q^{12} +3.99267 q^{13} +0.182784 q^{14} +3.13196 q^{15} -0.193918 q^{16} -1.00000 q^{17} -2.27866 q^{18} +2.46147 q^{19} -9.99809 q^{20} +0.0802156 q^{21} +11.3944 q^{22} +2.52357 q^{23} +2.71679 q^{24} +4.80919 q^{25} -9.09792 q^{26} -1.00000 q^{27} -0.256070 q^{28} -8.32033 q^{29} -7.13667 q^{30} -0.805575 q^{31} +5.87546 q^{32} +5.00047 q^{33} +2.27866 q^{34} +0.251232 q^{35} +3.19228 q^{36} +10.3580 q^{37} -5.60884 q^{38} -3.99267 q^{39} +8.50889 q^{40} -0.183280 q^{41} -0.182784 q^{42} -7.55934 q^{43} -15.9629 q^{44} -3.13196 q^{45} -5.75036 q^{46} -4.65435 q^{47} +0.193918 q^{48} -6.99357 q^{49} -10.9585 q^{50} +1.00000 q^{51} +12.7457 q^{52} +5.82371 q^{53} +2.27866 q^{54} +15.6613 q^{55} +0.217929 q^{56} -2.46147 q^{57} +18.9592 q^{58} +4.80944 q^{59} +9.99809 q^{60} -10.0824 q^{61} +1.83563 q^{62} -0.0802156 q^{63} -13.0003 q^{64} -12.5049 q^{65} -11.3944 q^{66} -8.96523 q^{67} -3.19228 q^{68} -2.52357 q^{69} -0.572472 q^{70} +7.92651 q^{71} -2.71679 q^{72} -4.57642 q^{73} -23.6024 q^{74} -4.80919 q^{75} +7.85768 q^{76} +0.401116 q^{77} +9.09792 q^{78} +1.00000 q^{79} +0.607343 q^{80} +1.00000 q^{81} +0.417632 q^{82} +9.12814 q^{83} +0.256070 q^{84} +3.13196 q^{85} +17.2251 q^{86} +8.32033 q^{87} +13.5852 q^{88} -0.860630 q^{89} +7.13667 q^{90} -0.320274 q^{91} +8.05594 q^{92} +0.805575 q^{93} +10.6057 q^{94} -7.70922 q^{95} -5.87546 q^{96} -15.2883 q^{97} +15.9359 q^{98} -5.00047 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * q^99

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