LMFDB - Embedded newform 4029.2.a.l.1.26

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			1.26
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)

$f(q)$	$=$	$q+1.90365 q^{2} -1.00000 q^{3} +1.62390 q^{4} -1.74973 q^{5} -1.90365 q^{6} -2.76075 q^{7} -0.715966 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.90365 q^{2} -1.00000 q^{3} +1.62390 q^{4} -1.74973 q^{5} -1.90365 q^{6} -2.76075 q^{7} -0.715966 q^{8} +1.00000 q^{9} -3.33088 q^{10} -4.86082 q^{11} -1.62390 q^{12} +4.21653 q^{13} -5.25551 q^{14} +1.74973 q^{15} -4.61075 q^{16} -1.00000 q^{17} +1.90365 q^{18} -2.06533 q^{19} -2.84139 q^{20} +2.76075 q^{21} -9.25332 q^{22} +6.78605 q^{23} +0.715966 q^{24} -1.93844 q^{25} +8.02682 q^{26} -1.00000 q^{27} -4.48317 q^{28} +1.05862 q^{29} +3.33088 q^{30} -1.35472 q^{31} -7.34534 q^{32} +4.86082 q^{33} -1.90365 q^{34} +4.83056 q^{35} +1.62390 q^{36} +1.37098 q^{37} -3.93167 q^{38} -4.21653 q^{39} +1.25275 q^{40} +2.38690 q^{41} +5.25551 q^{42} +2.48028 q^{43} -7.89348 q^{44} -1.74973 q^{45} +12.9183 q^{46} +12.3542 q^{47} +4.61075 q^{48} +0.621718 q^{49} -3.69012 q^{50} +1.00000 q^{51} +6.84723 q^{52} +9.48673 q^{53} -1.90365 q^{54} +8.50513 q^{55} +1.97660 q^{56} +2.06533 q^{57} +2.01525 q^{58} +3.60782 q^{59} +2.84139 q^{60} +0.816668 q^{61} -2.57891 q^{62} -2.76075 q^{63} -4.76149 q^{64} -7.37780 q^{65} +9.25332 q^{66} +13.5176 q^{67} -1.62390 q^{68} -6.78605 q^{69} +9.19572 q^{70} -5.74864 q^{71} -0.715966 q^{72} -11.8620 q^{73} +2.60987 q^{74} +1.93844 q^{75} -3.35389 q^{76} +13.4195 q^{77} -8.02682 q^{78} +1.00000 q^{79} +8.06757 q^{80} +1.00000 q^{81} +4.54383 q^{82} -8.93411 q^{83} +4.48317 q^{84} +1.74973 q^{85} +4.72159 q^{86} -1.05862 q^{87} +3.48018 q^{88} -10.7218 q^{89} -3.33088 q^{90} -11.6408 q^{91} +11.0199 q^{92} +1.35472 q^{93} +23.5181 q^{94} +3.61377 q^{95} +7.34534 q^{96} +12.3864 q^{97} +1.18354 q^{98} -4.86082 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.90365	1.34609	0.673043	−	0.739603i	$-0.264987\pi$
$2$	1.90365	1.34609	0.673043	+	0.739603i	$0.264987\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.62390	0.811950
$5$	−1.74973	−0.782504	−0.391252	−	0.920284i	$-0.627958\pi$
$5$	−1.74973	−0.782504	−0.391252	+	0.920284i	$0.627958\pi$
$6$	−1.90365	−0.777164
$7$	−2.76075	−1.04346	−0.521732	−	0.853109i	$-0.674714\pi$
$7$	−2.76075	−1.04346	−0.521732	+	0.853109i	$0.674714\pi$
$8$	−0.715966	−0.253132
$9$	1.00000	0.333333
$10$	−3.33088	−1.05332
$11$	−4.86082	−1.46559	−0.732796	−	0.680448i	$-0.761785\pi$
$11$	−4.86082	−1.46559	−0.732796	+	0.680448i	$0.761785\pi$
$12$	−1.62390	−0.468779
$13$	4.21653	1.16946	0.584728	−	0.811229i	$-0.301201\pi$
$13$	4.21653	1.16946	0.584728	+	0.811229i	$0.301201\pi$
$14$	−5.25551	−1.40459
$15$	1.74973	0.451779
$16$	−4.61075	−1.15269
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.90365	0.448696
$19$	−2.06533	−0.473819	−0.236909	−	0.971532i	$-0.576134\pi$
$19$	−2.06533	−0.473819	−0.236909	+	0.971532i	$0.576134\pi$
$20$	−2.84139	−0.635354
$21$	2.76075	0.602444
$22$	−9.25332	−1.97281
$23$	6.78605	1.41499	0.707495	−	0.706719i	$-0.249825\pi$
$23$	6.78605	1.41499	0.707495	+	0.706719i	$0.249825\pi$
$24$	0.715966	0.146146
$25$	−1.93844	−0.387688
$26$	8.02682	1.57419
$27$	−1.00000	−0.192450
$28$	−4.48317	−0.847240
$29$	1.05862	0.196581	0.0982907	−	0.995158i	$-0.468663\pi$
$29$	1.05862	0.196581	0.0982907	+	0.995158i	$0.468663\pi$
$30$	3.33088	0.608133
$31$	−1.35472	−0.243315	−0.121657	−	0.992572i	$-0.538821\pi$
$31$	−1.35472	−0.243315	−0.121657	+	0.992572i	$0.538821\pi$
$32$	−7.34534	−1.29849
$33$	4.86082	0.846160
$34$	−1.90365	−0.326474
$35$	4.83056	0.816514
$36$	1.62390	0.270650
$37$	1.37098	0.225387	0.112694	−	0.993630i	$-0.464052\pi$
$37$	1.37098	0.225387	0.112694	+	0.993630i	$0.464052\pi$
$38$	−3.93167	−0.637801
$39$	−4.21653	−0.675186
$40$	1.25275	0.198077
$41$	2.38690	0.372771	0.186386	−	0.982477i	$-0.440323\pi$
$41$	2.38690	0.372771	0.186386	+	0.982477i	$0.440323\pi$
$42$	5.25551	0.810942
$43$	2.48028	0.378239	0.189119	−	0.981954i	$-0.439437\pi$
$43$	2.48028	0.378239	0.189119	+	0.981954i	$0.439437\pi$
$44$	−7.89348	−1.18999
$45$	−1.74973	−0.260835
$46$	12.9183	1.90470
$47$	12.3542	1.80205	0.901023	−	0.433771i	$-0.142817\pi$
$47$	12.3542	1.80205	0.901023	+	0.433771i	$0.142817\pi$
$48$	4.61075	0.665504
$49$	0.621718	0.0888169
$50$	−3.69012	−0.521862
$51$	1.00000	0.140028
$52$	6.84723	0.949540
$53$	9.48673	1.30310	0.651551	−	0.758605i	$-0.274119\pi$
$53$	9.48673	1.30310	0.651551	+	0.758605i	$0.274119\pi$
$54$	−1.90365	−0.259055
$55$	8.50513	1.14683
$56$	1.97660	0.264134
$57$	2.06533	0.273560
$58$	2.01525	0.264616
$59$	3.60782	0.469698	0.234849	−	0.972032i	$-0.424540\pi$
$59$	3.60782	0.469698	0.234849	+	0.972032i	$0.424540\pi$
$60$	2.84139	0.366822
$61$	0.816668	0.104564	0.0522818	−	0.998632i	$-0.483351\pi$
$61$	0.816668	0.104564	0.0522818	+	0.998632i	$0.483351\pi$
$62$	−2.57891	−0.327522
$63$	−2.76075	−0.347821
$64$	−4.76149	−0.595186
$65$	−7.37780	−0.915104
$66$	9.25332	1.13900
$67$	13.5176	1.65143	0.825716	−	0.564086i	$-0.190771\pi$
$67$	13.5176	1.65143	0.825716	+	0.564086i	$0.190771\pi$
$68$	−1.62390	−0.196927
$69$	−6.78605	−0.816944
$70$	9.19572	1.09910
$71$	−5.74864	−0.682238	−0.341119	−	0.940020i	$-0.610806\pi$
$71$	−5.74864	−0.682238	−0.341119	+	0.940020i	$0.610806\pi$
$72$	−0.715966	−0.0843773
$73$	−11.8620	−1.38835	−0.694173	−	0.719808i	$-0.744230\pi$
$73$	−11.8620	−1.38835	−0.694173	+	0.719808i	$0.744230\pi$
$74$	2.60987	0.303391
$75$	1.93844	0.223832
$76$	−3.35389	−0.384717
$77$	13.4195	1.52929
$78$	−8.02682	−0.908859
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	8.06757	0.901982
$81$	1.00000	0.111111
$82$	4.54383	0.501782
$83$	−8.93411	−0.980646	−0.490323	−	0.871541i	$-0.663121\pi$
$83$	−8.93411	−0.980646	−0.490323	+	0.871541i	$0.663121\pi$
$84$	4.48317	0.489154
$85$	1.74973	0.189785
$86$	4.72159	0.509142
$87$	−1.05862	−0.113496
$88$	3.48018	0.370988
$89$	−10.7218	−1.13650	−0.568252	−	0.822855i	$-0.692380\pi$
$89$	−10.7218	−1.13650	−0.568252	+	0.822855i	$0.692380\pi$
$90$	−3.33088	−0.351106
$91$	−11.6408	−1.22029
$92$	11.0199	1.14890
$93$	1.35472	0.140478
$94$	23.5181	2.42571
$95$	3.61377	0.370765
$96$	7.34534	0.749681
$97$	12.3864	1.25765	0.628825	−	0.777547i	$-0.283536\pi$
$97$	12.3864	1.25765	0.628825	+	0.777547i	$0.283536\pi$
$98$	1.18354	0.119555
$99$	−4.86082	−0.488531
$100$	−3.14783	−0.314783
$101$	−16.2224	−1.61419	−0.807094	−	0.590422i	$-0.798961\pi$
$101$	−16.2224	−1.61419	−0.807094	+	0.590422i	$0.798961\pi$
$102$	1.90365	0.188490
$103$	18.2616	1.79937	0.899685	−	0.436539i	$-0.143796\pi$
$103$	18.2616	1.79937	0.899685	+	0.436539i	$0.143796\pi$
$104$	−3.01889	−0.296027
$105$	−4.83056	−0.471415
$106$	18.0594	1.75409
$107$	11.7346	1.13442	0.567212	−	0.823572i	$-0.308022\pi$
$107$	11.7346	1.13442	0.567212	+	0.823572i	$0.308022\pi$
$108$	−1.62390	−0.156260
$109$	3.42998	0.328532	0.164266	−	0.986416i	$-0.447474\pi$
$109$	3.42998	0.328532	0.164266	+	0.986416i	$0.447474\pi$
$110$	16.1908	1.54373
$111$	−1.37098	−0.130128
$112$	12.7291	1.20279
$113$	−12.9247	−1.21585	−0.607926	−	0.793994i	$-0.707998\pi$
$113$	−12.9247	−1.21585	−0.607926	+	0.793994i	$0.707998\pi$
$114$	3.93167	0.368235
$115$	−11.8738	−1.10723
$116$	1.71910	0.159614
$117$	4.21653	0.389819
$118$	6.86804	0.632254
$119$	2.76075	0.253077
$120$	−1.25275	−0.114360
$121$	12.6276	1.14796
$122$	1.55465	0.140752
$123$	−2.38690	−0.215220
$124$	−2.19993	−0.197559
$125$	12.1404	1.08587
$126$	−5.25551	−0.468198
$127$	20.8078	1.84639	0.923197	−	0.384328i	$-0.125567\pi$
$127$	20.8078	1.84639	0.923197	+	0.384328i	$0.125567\pi$
$128$	5.62645	0.497313
$129$	−2.48028	−0.218376
$130$	−14.0448	−1.23181
$131$	17.9429	1.56768	0.783841	−	0.620962i	$-0.213258\pi$
$131$	17.9429	1.56768	0.783841	+	0.620962i	$0.213258\pi$
$132$	7.89348	0.687039
$133$	5.70185	0.494413
$134$	25.7328	2.22297
$135$	1.74973	0.150593
$136$	0.715966	0.0613935
$137$	−10.8322	−0.925455	−0.462728	−	0.886500i	$-0.653129\pi$
$137$	−10.8322	−0.925455	−0.462728	+	0.886500i	$0.653129\pi$
$138$	−12.9183	−1.09968
$139$	−16.2906	−1.38175	−0.690875	−	0.722975i	$-0.742774\pi$
$139$	−16.2906	−1.38175	−0.690875	+	0.722975i	$0.742774\pi$
$140$	7.84435	0.662969
$141$	−12.3542	−1.04041
$142$	−10.9434	−0.918352
$143$	−20.4958	−1.71395
$144$	−4.61075	−0.384229
$145$	−1.85231	−0.153826
$146$	−22.5812	−1.86883
$147$	−0.621718	−0.0512784
$148$	2.22633	0.183003
$149$	−10.6512	−0.872577	−0.436288	−	0.899807i	$-0.643707\pi$
$149$	−10.6512	−0.872577	−0.436288	+	0.899807i	$0.643707\pi$
$150$	3.69012	0.301297
$151$	19.4390	1.58192	0.790962	−	0.611865i	$-0.209580\pi$
$151$	19.4390	1.58192	0.790962	+	0.611865i	$0.209580\pi$
$152$	1.47870	0.119939
$153$	−1.00000	−0.0808452
$154$	25.5461	2.05856
$155$	2.37039	0.190394
$156$	−6.84723	−0.548217
$157$	17.4912	1.39595	0.697975	−	0.716122i	$-0.254085\pi$
$157$	17.4912	1.39595	0.697975	+	0.716122i	$0.254085\pi$
$158$	1.90365	0.151447
$159$	−9.48673	−0.752346
$160$	12.8524	1.01607
$161$	−18.7346	−1.47649
$162$	1.90365	0.149565
$163$	2.58878	0.202769	0.101385	−	0.994847i	$-0.467673\pi$
$163$	2.58878	0.202769	0.101385	+	0.994847i	$0.467673\pi$
$164$	3.87609	0.302671
$165$	−8.50513	−0.662123
$166$	−17.0074	−1.32003
$167$	11.1980	0.866530	0.433265	−	0.901267i	$-0.357361\pi$
$167$	11.1980	0.866530	0.433265	+	0.901267i	$0.357361\pi$
$168$	−1.97660	−0.152498
$169$	4.77916	0.367628
$170$	3.33088	0.255467
$171$	−2.06533	−0.157940
$172$	4.02772	0.307111
$173$	23.8164	1.81072	0.905362	−	0.424640i	$-0.139599\pi$
$173$	23.8164	1.81072	0.905362	+	0.424640i	$0.139599\pi$
$174$	−2.01525	−0.152776
$175$	5.35154	0.404539
$176$	22.4120	1.68937
$177$	−3.60782	−0.271180
$178$	−20.4105	−1.52983
$179$	1.49768	0.111942	0.0559711	−	0.998432i	$-0.482175\pi$
$179$	1.49768	0.111942	0.0559711	+	0.998432i	$0.482175\pi$
$180$	−2.84139	−0.211785
$181$	−22.8296	−1.69691	−0.848456	−	0.529266i	$-0.822467\pi$
$181$	−22.8296	−1.69691	−0.848456	+	0.529266i	$0.822467\pi$
$182$	−22.1600	−1.64261
$183$	−0.816668	−0.0603698
$184$	−4.85858	−0.358179
$185$	−2.39884	−0.176367
$186$	2.57891	0.189095
$187$	4.86082	0.355458
$188$	20.0620	1.46317
$189$	2.76075	0.200815
$190$	6.87937	0.499082
$191$	−2.70156	−0.195478	−0.0977390	−	0.995212i	$-0.531161\pi$
$191$	−2.70156	−0.195478	−0.0977390	+	0.995212i	$0.531161\pi$
$192$	4.76149	0.343631
$193$	−6.47511	−0.466088	−0.233044	−	0.972466i	$-0.574869\pi$
$193$	−6.47511	−0.466088	−0.233044	+	0.972466i	$0.574869\pi$
$194$	23.5794	1.69290
$195$	7.37780	0.528335
$196$	1.00961	0.0721148
$197$	−25.9582	−1.84945	−0.924723	−	0.380642i	$-0.875703\pi$
$197$	−25.9582	−1.84945	−0.924723	+	0.380642i	$0.875703\pi$
$198$	−9.25332	−0.657605
$199$	4.29175	0.304234	0.152117	−	0.988363i	$-0.451391\pi$
$199$	4.29175	0.304234	0.152117	+	0.988363i	$0.451391\pi$
$200$	1.38786	0.0981363
$201$	−13.5176	−0.953455
$202$	−30.8818	−2.17284
$203$	−2.92259	−0.205126
$204$	1.62390	0.113696
$205$	−4.17643	−0.291695
$206$	34.7638	2.42211
$207$	6.78605	0.471663
$208$	−19.4414	−1.34802
$209$	10.0392	0.694425
$210$	−9.19572	−0.634565
$211$	−7.02208	−0.483420	−0.241710	−	0.970349i	$-0.577708\pi$
$211$	−7.02208	−0.483420	−0.241710	+	0.970349i	$0.577708\pi$
$212$	15.4055	1.05805
$213$	5.74864	0.393891
$214$	22.3386	1.52703
$215$	−4.33982	−0.295973
$216$	0.715966	0.0487153
$217$	3.74003	0.253890
$218$	6.52949	0.442233
$219$	11.8620	0.801562
$220$	13.8115	0.931169
$221$	−4.21653	−0.283635
$222$	−2.60987	−0.175163
$223$	21.4316	1.43517	0.717583	−	0.696473i	$-0.245248\pi$
$223$	21.4316	1.43517	0.717583	+	0.696473i	$0.245248\pi$
$224$	20.2786	1.35492
$225$	−1.93844	−0.129229
$226$	−24.6041	−1.63664
$227$	−17.8303	−1.18344	−0.591720	−	0.806144i	$-0.701551\pi$
$227$	−17.8303	−1.18344	−0.591720	+	0.806144i	$0.701551\pi$
$228$	3.35389	0.222117
$229$	26.1200	1.72606	0.863029	−	0.505154i	$-0.168564\pi$
$229$	26.1200	1.72606	0.863029	+	0.505154i	$0.168564\pi$
$230$	−22.6035	−1.49043
$231$	−13.4195	−0.882937
$232$	−0.757937	−0.0497610
$233$	−11.0396	−0.723229	−0.361615	−	0.932328i	$-0.617774\pi$
$233$	−11.0396	−0.723229	−0.361615	+	0.932328i	$0.617774\pi$
$234$	8.02682	0.524730
$235$	−21.6165	−1.41011
$236$	5.85874	0.381371
$237$	−1.00000	−0.0649570
$238$	5.25551	0.340664
$239$	4.35381	0.281625	0.140812	−	0.990036i	$-0.455029\pi$
$239$	4.35381	0.281625	0.140812	+	0.990036i	$0.455029\pi$
$240$	−8.06757	−0.520760
$241$	−15.8415	−1.02044	−0.510221	−	0.860043i	$-0.670436\pi$
$241$	−15.8415	−1.02044	−0.510221	+	0.860043i	$0.670436\pi$
$242$	24.0385	1.54525
$243$	−1.00000	−0.0641500
$244$	1.32619	0.0849004
$245$	−1.08784	−0.0694995
$246$	−4.54383	−0.289704
$247$	−8.70853	−0.554110
$248$	0.969931	0.0615907
$249$	8.93411	0.566176
$250$	23.1111	1.46168
$251$	5.02061	0.316898	0.158449	−	0.987367i	$-0.449351\pi$
$251$	5.02061	0.316898	0.158449	+	0.987367i	$0.449351\pi$
$252$	−4.48317	−0.282413
$253$	−32.9858	−2.07380
$254$	39.6108	2.48541
$255$	−1.74973	−0.109572
$256$	20.2338	1.26461
$257$	6.15958	0.384224	0.192112	−	0.981373i	$-0.438466\pi$
$257$	6.15958	0.384224	0.192112	+	0.981373i	$0.438466\pi$
$258$	−4.72159	−0.293954
$259$	−3.78492	−0.235184
$260$	−11.9808	−0.743018
$261$	1.05862	0.0655271
$262$	34.1571	2.11024
$263$	10.8580	0.669534	0.334767	−	0.942301i	$-0.391342\pi$
$263$	10.8580	0.669534	0.334767	+	0.942301i	$0.391342\pi$
$264$	−3.48018	−0.214190
$265$	−16.5992	−1.01968
$266$	10.8543	0.665523
$267$	10.7218	0.656161
$268$	21.9512	1.34088
$269$	−6.49851	−0.396221	−0.198111	−	0.980180i	$-0.563481\pi$
$269$	−6.49851	−0.396221	−0.198111	+	0.980180i	$0.563481\pi$
$270$	3.33088	0.202711
$271$	−13.6937	−0.831833	−0.415916	−	0.909403i	$-0.636539\pi$
$271$	−13.6937	−0.831833	−0.415916	+	0.909403i	$0.636539\pi$
$272$	4.61075	0.279568
$273$	11.6408	0.704532
$274$	−20.6207	−1.24574
$275$	9.42241	0.568193
$276$	−11.0199	−0.663318
$277$	−4.23247	−0.254304	−0.127152	−	0.991883i	$-0.540584\pi$
$277$	−4.23247	−0.254304	−0.127152	+	0.991883i	$0.540584\pi$
$278$	−31.0116	−1.85995
$279$	−1.35472	−0.0811048
$280$	−3.45852	−0.206686
$281$	−2.41832	−0.144265	−0.0721325	−	0.997395i	$-0.522980\pi$
$281$	−2.41832	−0.144265	−0.0721325	+	0.997395i	$0.522980\pi$
$282$	−23.5181	−1.40048
$283$	16.3333	0.970917	0.485458	−	0.874260i	$-0.338653\pi$
$283$	16.3333	0.970917	0.485458	+	0.874260i	$0.338653\pi$
$284$	−9.33522	−0.553943
$285$	−3.61377	−0.214061
$286$	−39.0169	−2.30712
$287$	−6.58963	−0.388973
$288$	−7.34534	−0.432828
$289$	1.00000	0.0588235
$290$	−3.52615	−0.207063
$291$	−12.3864	−0.726104
$292$	−19.2627	−1.12727
$293$	−13.8865	−0.811259	−0.405629	−	0.914038i	$-0.632948\pi$
$293$	−13.8865	−0.811259	−0.405629	+	0.914038i	$0.632948\pi$
$294$	−1.18354	−0.0690252
$295$	−6.31271	−0.367540
$296$	−0.981573	−0.0570528
$297$	4.86082	0.282053
$298$	−20.2761	−1.17456
$299$	28.6136	1.65477
$300$	3.14783	0.181740
$301$	−6.84742	−0.394679
$302$	37.0052	2.12941
$303$	16.2224	0.931952
$304$	9.52272	0.546165
$305$	−1.42895	−0.0818214
$306$	−1.90365	−0.108825
$307$	−18.1444	−1.03556	−0.517779	−	0.855515i	$-0.673241\pi$
$307$	−18.1444	−1.03556	−0.517779	+	0.855515i	$0.673241\pi$
$308$	21.7919	1.24171
$309$	−18.2616	−1.03887
$310$	4.51241	0.256288
$311$	−10.6185	−0.602118	−0.301059	−	0.953606i	$-0.597340\pi$
$311$	−10.6185	−0.602118	−0.301059	+	0.953606i	$0.597340\pi$
$312$	3.01889	0.170911
$313$	−18.7857	−1.06183	−0.530914	−	0.847425i	$-0.678151\pi$
$313$	−18.7857	−1.06183	−0.530914	+	0.847425i	$0.678151\pi$
$314$	33.2972	1.87907
$315$	4.83056	0.272171
$316$	1.62390	0.0913515
$317$	−14.9787	−0.841287	−0.420644	−	0.907226i	$-0.638196\pi$
$317$	−14.9787	−0.841287	−0.420644	+	0.907226i	$0.638196\pi$
$318$	−18.0594	−1.01272
$319$	−5.14577	−0.288108
$320$	8.33133	0.465736
$321$	−11.7346	−0.654959
$322$	−35.6641	−1.98748
$323$	2.06533	0.114918
$324$	1.62390	0.0902166
$325$	−8.17350	−0.453384
$326$	4.92815	0.272945
$327$	−3.42998	−0.189678
$328$	−1.70894	−0.0943603
$329$	−34.1068	−1.88037
$330$	−16.1908	−0.891275
$331$	18.1031	0.995039	0.497519	−	0.867453i	$-0.334244\pi$
$331$	18.1031	0.995039	0.497519	+	0.867453i	$0.334244\pi$
$332$	−14.5081	−0.796235
$333$	1.37098	0.0751292
$334$	21.3172	1.16642
$335$	−23.6521	−1.29225
$336$	−12.7291	−0.694430
$337$	23.6326	1.28735	0.643676	−	0.765298i	$-0.277409\pi$
$337$	23.6326	1.28735	0.643676	+	0.765298i	$0.277409\pi$
$338$	9.09786	0.494859
$339$	12.9247	0.701972
$340$	2.84139	0.154096
$341$	6.58504	0.356600
$342$	−3.93167	−0.212600
$343$	17.6088	0.950787
$344$	−1.77579	−0.0957444
$345$	11.8738	0.639262
$346$	45.3381	2.43739
$347$	−10.6255	−0.570408	−0.285204	−	0.958467i	$-0.592061\pi$
$347$	−10.6255	−0.570408	−0.285204	+	0.958467i	$0.592061\pi$
$348$	−1.71910	−0.0921533
$349$	15.2658	0.817157	0.408578	−	0.912723i	$-0.366025\pi$
$349$	15.2658	0.817157	0.408578	+	0.912723i	$0.366025\pi$
$350$	10.1875	0.544544
$351$	−4.21653	−0.225062
$352$	35.7044	1.90305
$353$	−18.4056	−0.979634	−0.489817	−	0.871825i	$-0.662936\pi$
$353$	−18.4056	−0.979634	−0.489817	+	0.871825i	$0.662936\pi$
$354$	−6.86804	−0.365032
$355$	10.0586	0.533854
$356$	−17.4110	−0.922784
$357$	−2.76075	−0.146114
$358$	2.85107	0.150684
$359$	−0.328322	−0.0173282	−0.00866410	−	0.999962i	$-0.502758\pi$
$359$	−0.328322	−0.0173282	−0.00866410	+	0.999962i	$0.502758\pi$
$360$	1.25275	0.0660256
$361$	−14.7344	−0.775496
$362$	−43.4597	−2.28419
$363$	−12.6276	−0.662775
$364$	−18.9035	−0.990810
$365$	20.7554	1.08639
$366$	−1.55465	−0.0812630
$367$	30.1448	1.57355	0.786774	−	0.617241i	$-0.211750\pi$
$367$	30.1448	1.57355	0.786774	+	0.617241i	$0.211750\pi$
$368$	−31.2888	−1.63104
$369$	2.38690	0.124257
$370$	−4.56657	−0.237405
$371$	−26.1904	−1.35974
$372$	2.19993	0.114061
$373$	29.9784	1.55222	0.776111	−	0.630597i	$-0.217190\pi$
$373$	29.9784	1.55222	0.776111	+	0.630597i	$0.217190\pi$
$374$	9.25332	0.478478
$375$	−12.1404	−0.626928
$376$	−8.84519	−0.456156
$377$	4.46372	0.229893
$378$	5.25551	0.270314
$379$	2.29938	0.118111	0.0590556	−	0.998255i	$-0.481191\pi$
$379$	2.29938	0.118111	0.0590556	+	0.998255i	$0.481191\pi$
$380$	5.86840	0.301043
$381$	−20.8078	−1.06602
$382$	−5.14284	−0.263130
$383$	10.9291	0.558452	0.279226	−	0.960225i	$-0.409922\pi$
$383$	10.9291	0.558452	0.279226	+	0.960225i	$0.409922\pi$
$384$	−5.62645	−0.287124
$385$	−23.4805	−1.19668
$386$	−12.3264	−0.627395
$387$	2.48028	0.126080
$388$	20.1143	1.02115
$389$	7.19303	0.364701	0.182351	−	0.983234i	$-0.441629\pi$
$389$	7.19303	0.364701	0.182351	+	0.983234i	$0.441629\pi$
$390$	14.0448	0.711185
$391$	−6.78605	−0.343185
$392$	−0.445129	−0.0224824
$393$	−17.9429	−0.905101
$394$	−49.4154	−2.48951
$395$	−1.74973	−0.0880385
$396$	−7.89348	−0.396662
$397$	11.2377	0.564003	0.282001	−	0.959414i	$-0.409002\pi$
$397$	11.2377	0.564003	0.282001	+	0.959414i	$0.409002\pi$
$398$	8.17000	0.409525
$399$	−5.70185	−0.285449
$400$	8.93766	0.446883
$401$	7.39783	0.369430	0.184715	−	0.982792i	$-0.440864\pi$
$401$	7.39783	0.369430	0.184715	+	0.982792i	$0.440864\pi$
$402$	−25.7328	−1.28343
$403$	−5.71221	−0.284546
$404$	−26.3435	−1.31064
$405$	−1.74973	−0.0869448
$406$	−5.56360	−0.276117
$407$	−6.66408	−0.330326
$408$	−0.715966	−0.0354456
$409$	9.44590	0.467070	0.233535	−	0.972348i	$-0.424971\pi$
$409$	9.44590	0.467070	0.233535	+	0.972348i	$0.424971\pi$
$410$	−7.95049	−0.392647
$411$	10.8322	0.534312
$412$	29.6550	1.46100
$413$	−9.96027	−0.490113
$414$	12.9183	0.634900
$415$	15.6323	0.767359
$416$	−30.9719	−1.51852
$417$	16.2906	0.797753
$418$	19.1111	0.934757
$419$	25.7269	1.25684	0.628419	−	0.777875i	$-0.283702\pi$
$419$	25.7269	1.25684	0.628419	+	0.777875i	$0.283702\pi$
$420$	−7.84435	−0.382765
$421$	22.5054	1.09684	0.548422	−	0.836202i	$-0.315229\pi$
$421$	22.5054	1.09684	0.548422	+	0.836202i	$0.315229\pi$
$422$	−13.3676	−0.650725
$423$	12.3542	0.600682
$424$	−6.79217	−0.329857
$425$	1.93844	0.0940282
$426$	10.9434	0.530211
$427$	−2.25461	−0.109108
$428$	19.0558	0.921094
$429$	20.4958	0.989547
$430$	−8.26152	−0.398406
$431$	7.98096	0.384429	0.192215	−	0.981353i	$-0.438433\pi$
$431$	7.98096	0.384429	0.192215	+	0.981353i	$0.438433\pi$
$432$	4.61075	0.221835
$433$	3.70080	0.177849	0.0889245	−	0.996038i	$-0.471657\pi$
$433$	3.70080	0.177849	0.0889245	+	0.996038i	$0.471657\pi$
$434$	7.11973	0.341758
$435$	1.85231	0.0888113
$436$	5.56994	0.266752
$437$	−14.0154	−0.670449
$438$	22.5812	1.07897
$439$	19.7471	0.942479	0.471240	−	0.882005i	$-0.343807\pi$
$439$	19.7471	0.942479	0.471240	+	0.882005i	$0.343807\pi$
$440$	−6.08938	−0.290300
$441$	0.621718	0.0296056
$442$	−8.02682	−0.381797
$443$	−15.5548	−0.739032	−0.369516	−	0.929224i	$-0.620476\pi$
$443$	−15.5548	−0.739032	−0.369516	+	0.929224i	$0.620476\pi$
$444$	−2.22633	−0.105657
$445$	18.7602	0.889318
$446$	40.7984	1.93186
$447$	10.6512	0.503782
$448$	13.1453	0.621056
$449$	−30.7115	−1.44936	−0.724682	−	0.689084i	$-0.758013\pi$
$449$	−30.7115	−1.44936	−0.724682	+	0.689084i	$0.758013\pi$
$450$	−3.69012	−0.173954
$451$	−11.6023	−0.546331
$452$	−20.9884	−0.987211
$453$	−19.4390	−0.913325
$454$	−33.9428	−1.59301
$455$	20.3682	0.954878
$456$	−1.47870	−0.0692467
$457$	−2.94642	−0.137828	−0.0689138	−	0.997623i	$-0.521953\pi$
$457$	−2.94642	−0.137828	−0.0689138	+	0.997623i	$0.521953\pi$
$458$	49.7234	2.32342
$459$	1.00000	0.0466760
$460$	−19.2818	−0.899019
$461$	9.05252	0.421618	0.210809	−	0.977527i	$-0.432390\pi$
$461$	9.05252	0.421618	0.210809	+	0.977527i	$0.432390\pi$
$462$	−25.5461	−1.18851
$463$	−31.5962	−1.46840	−0.734199	−	0.678934i	$-0.762442\pi$
$463$	−31.5962	−1.46840	−0.734199	+	0.678934i	$0.762442\pi$
$464$	−4.88104	−0.226597
$465$	−2.37039	−0.109924
$466$	−21.0156	−0.973529
$467$	12.2531	0.567007	0.283504	−	0.958971i	$-0.408503\pi$
$467$	12.2531	0.567007	0.283504	+	0.958971i	$0.408503\pi$
$468$	6.84723	0.316513
$469$	−37.3185	−1.72321
$470$	−41.1504	−1.89813
$471$	−17.4912	−0.805952
$472$	−2.58307	−0.118896
$473$	−12.0562	−0.554344
$474$	−1.90365	−0.0874377
$475$	4.00352	0.183694
$476$	4.48317	0.205486
$477$	9.48673	0.434367
$478$	8.28816	0.379091
$479$	11.5197	0.526348	0.263174	−	0.964748i	$-0.415231\pi$
$479$	11.5197	0.526348	0.263174	+	0.964748i	$0.415231\pi$
$480$	−12.8524	−0.586628
$481$	5.78078	0.263581
$482$	−30.1568	−1.37360
$483$	18.7346	0.852452
$484$	20.5059	0.932086
$485$	−21.6729	−0.984115
$486$	−1.90365	−0.0863515
$487$	−19.3649	−0.877508	−0.438754	−	0.898607i	$-0.644580\pi$
$487$	−19.3649	−0.877508	−0.438754	+	0.898607i	$0.644580\pi$
$488$	−0.584706	−0.0264684
$489$	−2.58878	−0.117069
$490$	−2.07087	−0.0935524
$491$	4.35863	0.196702	0.0983510	−	0.995152i	$-0.468643\pi$
$491$	4.35863	0.196702	0.0983510	+	0.995152i	$0.468643\pi$
$492$	−3.87609	−0.174747
$493$	−1.05862	−0.0476780
$494$	−16.5780	−0.745881
$495$	8.50513	0.382277
$496$	6.24627	0.280466
$497$	15.8705	0.711891
$498$	17.0074	0.762122
$499$	5.32720	0.238478	0.119239	−	0.992866i	$-0.461954\pi$
$499$	5.32720	0.238478	0.119239	+	0.992866i	$0.461954\pi$
$500$	19.7148	0.881673
$501$	−11.1980	−0.500291
$502$	9.55750	0.426572
$503$	23.8446	1.06318	0.531590	−	0.847002i	$-0.321595\pi$
$503$	23.8446	1.06318	0.531590	+	0.847002i	$0.321595\pi$
$504$	1.97660	0.0880447
$505$	28.3848	1.26311
$506$	−62.7935	−2.79151
$507$	−4.77916	−0.212250
$508$	33.7898	1.49918
$509$	−24.4634	−1.08432	−0.542161	−	0.840275i	$-0.682394\pi$
$509$	−24.4634	−1.08432	−0.542161	+	0.840275i	$0.682394\pi$
$510$	−3.33088	−0.147494
$511$	32.7481	1.44869
$512$	27.2653	1.20497
$513$	2.06533	0.0911865
$514$	11.7257	0.517199
$515$	−31.9529	−1.40801
$516$	−4.02772	−0.177311
$517$	−60.0516	−2.64106
$518$	−7.20518	−0.316578
$519$	−23.8164	−1.04542
$520$	5.28225	0.231642
$521$	10.1659	0.445376	0.222688	−	0.974890i	$-0.428517\pi$
$521$	10.1659	0.445376	0.222688	+	0.974890i	$0.428517\pi$
$522$	2.01525	0.0882052
$523$	−32.6836	−1.42915	−0.714576	−	0.699558i	$-0.753380\pi$
$523$	−32.6836	−1.42915	−0.714576	+	0.699558i	$0.753380\pi$
$524$	29.1375	1.27288
$525$	−5.35154	−0.233560
$526$	20.6699	0.901250
$527$	1.35472	0.0590124
$528$	−22.4120	−0.975358
$529$	23.0505	1.00219
$530$	−31.5992	−1.37258
$531$	3.60782	0.156566
$532$	9.25923	0.401438
$533$	10.0644	0.435940
$534$	20.4105	0.883249
$535$	−20.5323	−0.887690
$536$	−9.67811	−0.418031
$537$	−1.49768	−0.0646298
$538$	−12.3709	−0.533348
$539$	−3.02206	−0.130169
$540$	2.84139	0.122274
$541$	−7.46706	−0.321034	−0.160517	−	0.987033i	$-0.551316\pi$
$541$	−7.46706	−0.321034	−0.160517	+	0.987033i	$0.551316\pi$
$542$	−26.0681	−1.11972
$543$	22.8296	0.979713
$544$	7.34534	0.314929
$545$	−6.00154	−0.257078
$546$	22.1600	0.948361
$547$	12.3096	0.526322	0.263161	−	0.964752i	$-0.415235\pi$
$547$	12.3096	0.526322	0.263161	+	0.964752i	$0.415235\pi$
$548$	−17.5904	−0.751423
$549$	0.816668	0.0348545
$550$	17.9370	0.764837
$551$	−2.18640	−0.0931440
$552$	4.85858	0.206795
$553$	−2.76075	−0.117399
$554$	−8.05716	−0.342316
$555$	2.39884	0.101825
$556$	−26.4543	−1.12191
$557$	40.2407	1.70505	0.852526	−	0.522684i	$-0.175069\pi$
$557$	40.2407	1.70505	0.852526	+	0.522684i	$0.175069\pi$
$558$	−2.57891	−0.109174
$559$	10.4582	0.442334
$560$	−22.2725	−0.941186
$561$	−4.86082	−0.205224
$562$	−4.60365	−0.194193
$563$	34.7564	1.46481	0.732405	−	0.680870i	$-0.238398\pi$
$563$	34.7564	1.46481	0.732405	+	0.680870i	$0.238398\pi$
$564$	−20.0620	−0.844762
$565$	22.6147	0.951408
$566$	31.0930	1.30694
$567$	−2.76075	−0.115940
$568$	4.11583	0.172696
$569$	−40.3442	−1.69132	−0.845658	−	0.533724i	$-0.820792\pi$
$569$	−40.3442	−1.69132	−0.845658	+	0.533724i	$0.820792\pi$
$570$	−6.87937	−0.288145
$571$	37.2922	1.56063	0.780314	−	0.625388i	$-0.215059\pi$
$571$	37.2922	1.56063	0.780314	+	0.625388i	$0.215059\pi$
$572$	−33.2831	−1.39164
$573$	2.70156	0.112859
$574$	−12.5444	−0.523592
$575$	−13.1544	−0.548575
$576$	−4.76149	−0.198395
$577$	32.4591	1.35129	0.675644	−	0.737228i	$-0.263865\pi$
$577$	32.4591	1.35129	0.675644	+	0.737228i	$0.263865\pi$
$578$	1.90365	0.0791816
$579$	6.47511	0.269096
$580$	−3.00796	−0.124899
$581$	24.6648	1.02327
$582$	−23.5794	−0.977399
$583$	−46.1133	−1.90982
$584$	8.49280	0.351435
$585$	−7.37780	−0.305035
$586$	−26.4351	−1.09202
$587$	−42.7068	−1.76270	−0.881349	−	0.472466i	$-0.843364\pi$
$587$	−42.7068	−1.76270	−0.881349	+	0.472466i	$0.843364\pi$
$588$	−1.00961	−0.0416355
$589$	2.79794	0.115287
$590$	−12.0172	−0.494741
$591$	25.9582	1.06778
$592$	−6.32124	−0.259801
$593$	28.4864	1.16980	0.584898	−	0.811107i	$-0.301135\pi$
$593$	28.4864	1.16980	0.584898	+	0.811107i	$0.301135\pi$
$594$	9.25332	0.379668
$595$	−4.83056	−0.198034
$596$	−17.2964	−0.708488
$597$	−4.29175	−0.175649
$598$	54.4704	2.22746
$599$	−13.1001	−0.535254	−0.267627	−	0.963523i	$-0.586240\pi$
$599$	−13.1001	−0.535254	−0.267627	+	0.963523i	$0.586240\pi$
$600$	−1.38786	−0.0566590
$601$	31.8151	1.29777	0.648883	−	0.760889i	$-0.275237\pi$
$601$	31.8151	1.29777	0.648883	+	0.760889i	$0.275237\pi$
$602$	−13.0351	−0.531272
$603$	13.5176	0.550478
$604$	31.5670	1.28444
$605$	−22.0948	−0.898283
$606$	30.8818	1.25449
$607$	−20.5854	−0.835534	−0.417767	−	0.908554i	$-0.637187\pi$
$607$	−20.5854	−0.835534	−0.417767	+	0.908554i	$0.637187\pi$
$608$	15.1705	0.615247
$609$	2.92259	0.118429
$610$	−2.72023	−0.110139
$611$	52.0919	2.10741
$612$	−1.62390	−0.0656422
$613$	30.8583	1.24636	0.623178	−	0.782080i	$-0.285841\pi$
$613$	30.8583	1.24636	0.623178	+	0.782080i	$0.285841\pi$
$614$	−34.5407	−1.39395
$615$	4.17643	0.168410
$616$	−9.60789	−0.387113
$617$	−32.7679	−1.31919	−0.659593	−	0.751623i	$-0.729272\pi$
$617$	−32.7679	−1.31919	−0.659593	+	0.751623i	$0.729272\pi$
$618$	−34.7638	−1.39841
$619$	30.9550	1.24419	0.622093	−	0.782944i	$-0.286283\pi$
$619$	30.9550	1.24419	0.622093	+	0.782944i	$0.286283\pi$
$620$	3.84928	0.154591
$621$	−6.78605	−0.272315
$622$	−20.2139	−0.810503
$623$	29.6000	1.18590
$624$	19.4414	0.778278
$625$	−11.5502	−0.462010
$626$	−35.7614	−1.42931
$627$	−10.0392	−0.400927
$628$	28.4040	1.13344
$629$	−1.37098	−0.0546645
$630$	9.19572	0.366366
$631$	−34.2754	−1.36448	−0.682241	−	0.731128i	$-0.738994\pi$
$631$	−34.2754	−1.36448	−0.682241	+	0.731128i	$0.738994\pi$
$632$	−0.715966	−0.0284796
$633$	7.02208	0.279103
$634$	−28.5143	−1.13245
$635$	−36.4080	−1.44481
$636$	−15.4055	−0.610867
$637$	2.62150	0.103867
$638$	−9.79577	−0.387818
$639$	−5.74864	−0.227413
$640$	−9.84478	−0.389149
$641$	10.1838	0.402238	0.201119	−	0.979567i	$-0.435542\pi$
$641$	10.1838	0.402238	0.201119	+	0.979567i	$0.435542\pi$
$642$	−22.3386	−0.881632
$643$	−9.31012	−0.367155	−0.183578	−	0.983005i	$-0.558768\pi$
$643$	−9.31012	−0.367155	−0.183578	+	0.983005i	$0.558768\pi$
$644$	−30.4230	−1.19884
$645$	4.33982	0.170880
$646$	3.93167	0.154690
$647$	15.6131	0.613815	0.306908	−	0.951739i	$-0.400706\pi$
$647$	15.6131	0.613815	0.306908	+	0.951739i	$0.400706\pi$
$648$	−0.715966	−0.0281258
$649$	−17.5370	−0.688386
$650$	−15.5595	−0.610294
$651$	−3.74003	−0.146583
$652$	4.20392	0.164638
$653$	−12.4062	−0.485492	−0.242746	−	0.970090i	$-0.578048\pi$
$653$	−12.4062	−0.485492	−0.242746	+	0.970090i	$0.578048\pi$
$654$	−6.52949	−0.255323
$655$	−31.3953	−1.22672
$656$	−11.0054	−0.429689
$657$	−11.8620	−0.462782
$658$	−64.9276	−2.53114
$659$	−22.7247	−0.885228	−0.442614	−	0.896712i	$-0.645949\pi$
$659$	−22.7247	−0.885228	−0.442614	+	0.896712i	$0.645949\pi$
$660$	−13.8115	−0.537611
$661$	−7.12341	−0.277068	−0.138534	−	0.990358i	$-0.544239\pi$
$661$	−7.12341	−0.277068	−0.138534	+	0.990358i	$0.544239\pi$
$662$	34.4621	1.33941
$663$	4.21653	0.163757
$664$	6.39651	0.248233
$665$	−9.97670	−0.386880
$666$	2.60987	0.101130
$667$	7.18387	0.278160
$668$	18.1845	0.703579
$669$	−21.4316	−0.828594
$670$	−45.0254	−1.73948
$671$	−3.96968	−0.153248
$672$	−20.2786	−0.782265
$673$	29.8336	1.15000	0.575001	−	0.818153i	$-0.305002\pi$
$673$	29.8336	1.15000	0.575001	+	0.818153i	$0.305002\pi$
$674$	44.9883	1.73289
$675$	1.93844	0.0746106
$676$	7.76087	0.298495
$677$	36.3115	1.39556	0.697782	−	0.716311i	$-0.254171\pi$
$677$	36.3115	1.39556	0.697782	+	0.716311i	$0.254171\pi$
$678$	24.6041	0.944916
$679$	−34.1957	−1.31231
$680$	−1.25275	−0.0480407
$681$	17.8303	0.683259
$682$	12.5356	0.480014
$683$	36.9375	1.41338	0.706688	−	0.707526i	$-0.250189\pi$
$683$	36.9375	1.41338	0.706688	+	0.707526i	$0.250189\pi$
$684$	−3.35389	−0.128239
$685$	18.9534	0.724172
$686$	33.5211	1.27984
$687$	−26.1200	−0.996540
$688$	−11.4359	−0.435991
$689$	40.0011	1.52392
$690$	22.6035	0.860502
$691$	−40.7253	−1.54926	−0.774631	−	0.632414i	$-0.782064\pi$
$691$	−40.7253	−1.54926	−0.774631	+	0.632414i	$0.782064\pi$
$692$	38.6754	1.47022
$693$	13.4195	0.509764
$694$	−20.2273	−0.767818
$695$	28.5041	1.08122
$696$	0.757937	0.0287295
$697$	−2.38690	−0.0904103
$698$	29.0607	1.09996
$699$	11.0396	0.417557
$700$	8.69037	0.328465
$701$	27.4401	1.03640	0.518200	−	0.855260i	$-0.326602\pi$
$701$	27.4401	1.03640	0.518200	+	0.855260i	$0.326602\pi$
$702$	−8.02682	−0.302953
$703$	−2.83152	−0.106793
$704$	23.1447	0.872301
$705$	21.6165	0.814126
$706$	−35.0380	−1.31867
$707$	44.7859	1.68435
$708$	−5.85874	−0.220185
$709$	−16.1447	−0.606326	−0.303163	−	0.952939i	$-0.598043\pi$
$709$	−16.1447	−0.606326	−0.303163	+	0.952939i	$0.598043\pi$
$710$	19.1481	0.718614
$711$	1.00000	0.0375029
$712$	7.67641	0.287685
$713$	−9.19318	−0.344287
$714$	−5.25551	−0.196682
$715$	35.8622	1.34117
$716$	2.43209	0.0908914
$717$	−4.35381	−0.162596
$718$	−0.625012	−0.0233252
$719$	20.7803	0.774974	0.387487	−	0.921875i	$-0.373343\pi$
$719$	20.7803	0.774974	0.387487	+	0.921875i	$0.373343\pi$
$720$	8.06757	0.300661
$721$	−50.4157	−1.87758
$722$	−28.0492	−1.04388
$723$	15.8415	0.589152
$724$	−37.0730	−1.37781
$725$	−2.05208	−0.0762122
$726$	−24.0385	−0.892153
$727$	−9.85061	−0.365339	−0.182669	−	0.983174i	$-0.558474\pi$
$727$	−9.85061	−0.365339	−0.182669	+	0.983174i	$0.558474\pi$
$728$	8.33440	0.308893
$729$	1.00000	0.0370370
$730$	39.5110	1.46237
$731$	−2.48028	−0.0917364
$732$	−1.32619	−0.0490173
$733$	−16.0574	−0.593094	−0.296547	−	0.955018i	$-0.595835\pi$
$733$	−16.0574	−0.593094	−0.296547	+	0.955018i	$0.595835\pi$
$734$	57.3854	2.11813
$735$	1.08784	0.0401256
$736$	−49.8459	−1.83734
$737$	−65.7064	−2.42033
$738$	4.54383	0.167261
$739$	13.4971	0.496498	0.248249	−	0.968696i	$-0.420145\pi$
$739$	13.4971	0.496498	0.248249	+	0.968696i	$0.420145\pi$
$740$	−3.89548	−0.143201
$741$	8.70853	0.319916
$742$	−49.8575	−1.83033
$743$	−34.5189	−1.26638	−0.633188	−	0.773998i	$-0.718254\pi$
$743$	−34.5189	−1.26638	−0.633188	+	0.773998i	$0.718254\pi$
$744$	−0.969931	−0.0355594
$745$	18.6367	0.682794
$746$	57.0685	2.08942
$747$	−8.93411	−0.326882
$748$	7.89348	0.288614
$749$	−32.3961	−1.18373
$750$	−23.1111	−0.843899
$751$	4.92688	0.179784	0.0898922	−	0.995951i	$-0.471348\pi$
$751$	4.92688	0.179784	0.0898922	+	0.995951i	$0.471348\pi$
$752$	−56.9621	−2.07720
$753$	−5.02061	−0.182961
$754$	8.49738	0.309456
$755$	−34.0131	−1.23786
$756$	4.48317	0.163051
$757$	8.81237	0.320291	0.160145	−	0.987093i	$-0.448804\pi$
$757$	8.81237	0.320291	0.160145	+	0.987093i	$0.448804\pi$
$758$	4.37723	0.158988
$759$	32.9858	1.19731
$760$	−2.58734	−0.0938525
$761$	3.72359	0.134980	0.0674900	−	0.997720i	$-0.478501\pi$
$761$	3.72359	0.134980	0.0674900	+	0.997720i	$0.478501\pi$
$762$	−39.6108	−1.43495
$763$	−9.46930	−0.342812
$764$	−4.38706	−0.158718
$765$	1.74973	0.0632617
$766$	20.8053	0.751725
$767$	15.2125	0.549291
$768$	−20.2338	−0.730124
$769$	−9.27668	−0.334526	−0.167263	−	0.985912i	$-0.553493\pi$
$769$	−9.27668	−0.334526	−0.167263	+	0.985912i	$0.553493\pi$
$770$	−44.6987	−1.61083
$771$	−6.15958	−0.221832
$772$	−10.5149	−0.378440
$773$	35.8580	1.28972	0.644861	−	0.764300i	$-0.276915\pi$
$773$	35.8580	1.28972	0.644861	+	0.764300i	$0.276915\pi$
$774$	4.72159	0.169714
$775$	2.62604	0.0943301
$776$	−8.86824	−0.318351
$777$	3.78492	0.135783
$778$	13.6930	0.490919
$779$	−4.92973	−0.176626
$780$	11.9808	0.428982
$781$	27.9431	0.999883
$782$	−12.9183	−0.461957
$783$	−1.05862	−0.0378321
$784$	−2.86659	−0.102378
$785$	−30.6049	−1.09234
$786$	−34.1571	−1.21834
$787$	50.5472	1.80181	0.900907	−	0.434013i	$-0.142903\pi$
$787$	50.5472	1.80181	0.900907	+	0.434013i	$0.142903\pi$
$788$	−42.1535	−1.50166
$789$	−10.8580	−0.386555
$790$	−3.33088	−0.118508
$791$	35.6818	1.26870
$792$	3.48018	0.123663
$793$	3.44351	0.122283
$794$	21.3926	0.759197
$795$	16.5992	0.588714
$796$	6.96936	0.247023
$797$	−8.39823	−0.297480	−0.148740	−	0.988876i	$-0.547522\pi$
$797$	−8.39823	−0.297480	−0.148740	+	0.988876i	$0.547522\pi$
$798$	−10.8543	−0.384240
$799$	−12.3542	−0.437060
$800$	14.2385	0.503407
$801$	−10.7218	−0.378835
$802$	14.0829	0.497285
$803$	57.6592	2.03475
$804$	−21.9512	−0.774158
$805$	32.7804	1.15536
$806$	−10.8741	−0.383023
$807$	6.49851	0.228758
$808$	11.6147	0.408603
$809$	−37.7464	−1.32709	−0.663547	−	0.748134i	$-0.730950\pi$
$809$	−37.7464	−1.32709	−0.663547	+	0.748134i	$0.730950\pi$
$810$	−3.33088	−0.117035
$811$	50.1912	1.76245	0.881226	−	0.472695i	$-0.156719\pi$
$811$	50.1912	1.76245	0.881226	+	0.472695i	$0.156719\pi$
$812$	−4.74599	−0.166552
$813$	13.6937	0.480259
$814$	−12.6861	−0.444648
$815$	−4.52967	−0.158667
$816$	−4.61075	−0.161409
$817$	−5.12259	−0.179217
$818$	17.9817	0.628716
$819$	−11.6408	−0.406762
$820$	−6.78211	−0.236842
$821$	15.3100	0.534321	0.267161	−	0.963652i	$-0.413915\pi$
$821$	15.3100	0.534321	0.267161	+	0.963652i	$0.413915\pi$
$822$	20.6207	0.719230
$823$	−27.3041	−0.951761	−0.475880	−	0.879510i	$-0.657870\pi$
$823$	−27.3041	−0.951761	−0.475880	+	0.879510i	$0.657870\pi$
$824$	−13.0747	−0.455478
$825$	−9.42241	−0.328046
$826$	−18.9609	−0.659735
$827$	−7.68790	−0.267334	−0.133667	−	0.991026i	$-0.542675\pi$
$827$	−7.68790	−0.267334	−0.133667	+	0.991026i	$0.542675\pi$
$828$	11.0199	0.382967
$829$	50.8222	1.76513	0.882563	−	0.470194i	$-0.155816\pi$
$829$	50.8222	1.76513	0.882563	+	0.470194i	$0.155816\pi$
$830$	29.7585	1.03293
$831$	4.23247	0.146823
$832$	−20.0770	−0.696044
$833$	−0.621718	−0.0215413
$834$	31.0116	1.07385
$835$	−19.5936	−0.678063
$836$	16.3026	0.563838
$837$	1.35472	0.0468259
$838$	48.9750	1.69181
$839$	−16.4500	−0.567916	−0.283958	−	0.958837i	$-0.591648\pi$
$839$	−16.4500	−0.567916	−0.283958	+	0.958837i	$0.591648\pi$
$840$	3.45852	0.119330
$841$	−27.8793	−0.961356
$842$	42.8424	1.47645
$843$	2.41832	0.0832914
$844$	−11.4032	−0.392513
$845$	−8.36224	−0.287670
$846$	23.5181	0.808570
$847$	−34.8615	−1.19785
$848$	−43.7409	−1.50207
$849$	−16.3333	−0.560559
$850$	3.69012	0.126570
$851$	9.30353	0.318921
$852$	9.33522	0.319819
$853$	7.38413	0.252828	0.126414	−	0.991978i	$-0.459653\pi$
$853$	7.38413	0.252828	0.126414	+	0.991978i	$0.459653\pi$
$854$	−4.29200	−0.146869
$855$	3.61377	0.123588
$856$	−8.40154	−0.287159
$857$	−21.4449	−0.732543	−0.366271	−	0.930508i	$-0.619366\pi$
$857$	−21.4449	−0.732543	−0.366271	+	0.930508i	$0.619366\pi$
$858$	39.0169	1.33202
$859$	−37.6384	−1.28421	−0.642103	−	0.766619i	$-0.721938\pi$
$859$	−37.6384	−1.28421	−0.642103	+	0.766619i	$0.721938\pi$
$860$	−7.04743	−0.240315
$861$	6.58963	0.224574
$862$	15.1930	0.517475
$863$	−23.0879	−0.785922	−0.392961	−	0.919555i	$-0.628549\pi$
$863$	−23.0879	−0.785922	−0.392961	+	0.919555i	$0.628549\pi$
$864$	7.34534	0.249894
$865$	−41.6722	−1.41690
$866$	7.04504	0.239400
$867$	−1.00000	−0.0339618
$868$	6.07344	0.206146
$869$	−4.86082	−0.164892
$870$	3.52615	0.119548
$871$	56.9972	1.93128
$872$	−2.45575	−0.0831621
$873$	12.3864	0.419216
$874$	−26.6805	−0.902482
$875$	−33.5166	−1.13307
$876$	19.2627	0.650828
$877$	53.3526	1.80159	0.900795	−	0.434245i	$-0.142985\pi$
$877$	53.3526	1.80159	0.900795	+	0.434245i	$0.142985\pi$
$878$	37.5917	1.26866
$879$	13.8865	0.468381
$880$	−39.2150	−1.32194
$881$	50.4140	1.69849	0.849245	−	0.528000i	$-0.177058\pi$
$881$	50.4140	1.69849	0.849245	+	0.528000i	$0.177058\pi$
$882$	1.18354	0.0398517
$883$	−32.6109	−1.09744	−0.548722	−	0.836005i	$-0.684885\pi$
$883$	−32.6109	−1.09744	−0.548722	+	0.836005i	$0.684885\pi$
$884$	−6.84723	−0.230297
$885$	6.31271	0.212200
$886$	−29.6110	−0.994801
$887$	50.2880	1.68851	0.844254	−	0.535944i	$-0.180044\pi$
$887$	50.2880	1.68851	0.844254	+	0.535944i	$0.180044\pi$
$888$	0.981573	0.0329394
$889$	−57.4450	−1.92664
$890$	35.7129	1.19710
$891$	−4.86082	−0.162844
$892$	34.8028	1.16528
$893$	−25.5155	−0.853844
$894$	20.2761	0.678135
$895$	−2.62054	−0.0875951
$896$	−15.5332	−0.518928
$897$	−28.6136	−0.955381
$898$	−58.4640	−1.95097
$899$	−1.43414	−0.0478311
$900$	−3.14783	−0.104928
$901$	−9.48673	−0.316049
$902$	−22.0867	−0.735408
$903$	6.84742	0.227868
$904$	9.25363	0.307771
$905$	39.9457	1.32784
$906$	−37.0052	−1.22941
$907$	−2.25225	−0.0747848	−0.0373924	−	0.999301i	$-0.511905\pi$
$907$	−2.25225	−0.0747848	−0.0373924	+	0.999301i	$0.511905\pi$
$908$	−28.9546	−0.960894
$909$	−16.2224	−0.538063
$910$	38.7741	1.28535
$911$	38.8401	1.28683	0.643415	−	0.765518i	$-0.277517\pi$
$911$	38.8401	1.28683	0.643415	+	0.765518i	$0.277517\pi$
$912$	−9.52272	−0.315329
$913$	43.4271	1.43723
$914$	−5.60896	−0.185528
$915$	1.42895	0.0472396
$916$	42.4162	1.40147
$917$	−49.5359	−1.63582
$918$	1.90365	0.0628300
$919$	−24.2943	−0.801395	−0.400697	−	0.916210i	$-0.631232\pi$
$919$	−24.2943	−0.801395	−0.400697	+	0.916210i	$0.631232\pi$
$920$	8.50121	0.280276
$921$	18.1444	0.597879
$922$	17.2329	0.567534
$923$	−24.2393	−0.797848
$924$	−21.7919	−0.716901
$925$	−2.65756	−0.0873800
$926$	−60.1482	−1.97659
$927$	18.2616	0.599790
$928$	−7.77595	−0.255258
$929$	−26.4355	−0.867320	−0.433660	−	0.901077i	$-0.642778\pi$
$929$	−26.4355	−0.867320	−0.433660	+	0.901077i	$0.642778\pi$
$930$	−4.51241	−0.147968
$931$	−1.28405	−0.0420831
$932$	−17.9272	−0.587226
$933$	10.6185	0.347633
$934$	23.3257	0.763241
$935$	−8.50513	−0.278147
$936$	−3.01889	−0.0986756
$937$	31.0347	1.01386	0.506930	−	0.861987i	$-0.330780\pi$
$937$	31.0347	1.01386	0.506930	+	0.861987i	$0.330780\pi$
$938$	−71.0416	−2.31959
$939$	18.7857	0.613047
$940$	−35.1031	−1.14494
$941$	11.6244	0.378945	0.189472	−	0.981886i	$-0.439322\pi$
$941$	11.6244	0.378945	0.189472	+	0.981886i	$0.439322\pi$
$942$	−33.2972	−1.08488
$943$	16.1976	0.527467
$944$	−16.6347	−0.541415
$945$	−4.83056	−0.157138
$946$	−22.9508	−0.746195
$947$	−17.5297	−0.569640	−0.284820	−	0.958581i	$-0.591934\pi$
$947$	−17.5297	−0.569640	−0.284820	+	0.958581i	$0.591934\pi$
$948$	−1.62390	−0.0527418
$949$	−50.0167	−1.62361
$950$	7.62131	0.247268
$951$	14.9787	0.485717
$952$	−1.97660	−0.0640619
$953$	−43.1342	−1.39725	−0.698627	−	0.715486i	$-0.746205\pi$
$953$	−43.1342	−1.39725	−0.698627	+	0.715486i	$0.746205\pi$
$954$	18.0594	0.584696
$955$	4.72700	0.152962
$956$	7.07016	0.228665
$957$	5.14577	0.166339
$958$	21.9295	0.708510
$959$	29.9049	0.965679
$960$	−8.33133	−0.268893
$961$	−29.1647	−0.940798
$962$	11.0046	0.354803
$963$	11.7346	0.378141
$964$	−25.7250	−0.828547
$965$	11.3297	0.364716
$966$	35.6641	1.14747
$967$	−40.2424	−1.29411	−0.647054	−	0.762444i	$-0.723999\pi$
$967$	−40.2424	−1.29411	−0.647054	+	0.762444i	$0.723999\pi$
$968$	−9.04090	−0.290585
$969$	−2.06533	−0.0663479
$970$	−41.2577	−1.32470
$971$	−52.5535	−1.68652	−0.843261	−	0.537505i	$-0.819367\pi$
$971$	−52.5535	−1.68652	−0.843261	+	0.537505i	$0.819367\pi$
$972$	−1.62390	−0.0520866
$973$	44.9742	1.44181
$974$	−36.8641	−1.18120
$975$	8.17350	0.261761
$976$	−3.76545	−0.120529
$977$	−42.4666	−1.35863	−0.679313	−	0.733849i	$-0.737722\pi$
$977$	−42.4666	−1.35863	−0.679313	+	0.733849i	$0.737722\pi$
$978$	−4.92815	−0.157585
$979$	52.1165	1.66565
$980$	−1.76654	−0.0564301
$981$	3.42998	0.109511
$982$	8.29732	0.264778
$983$	14.1439	0.451121	0.225560	−	0.974229i	$-0.427579\pi$
$983$	14.1439	0.451121	0.225560	+	0.974229i	$0.427579\pi$
$984$	1.70894	0.0544790
$985$	45.4199	1.44720
$986$	−2.01525	−0.0641787
$987$	34.1068	1.08563
$988$	−14.1418	−0.449910
$989$	16.8313	0.535204
$990$	16.1908	0.514578
$991$	−39.6470	−1.25943	−0.629715	−	0.776826i	$-0.716828\pi$
$991$	−39.6470	−1.25943	−0.629715	+	0.776826i	$0.716828\pi$
$992$	9.95087	0.315940
$993$	−18.1031	−0.574486
$994$	30.2120	0.958267
$995$	−7.50940	−0.238064
$996$	14.5081	0.459706
$997$	40.9202	1.29596	0.647978	−	0.761659i	$-0.275615\pi$
$997$	40.9202	1.29596	0.647978	+	0.761659i	$0.275615\pi$
$998$	10.1411	0.321012
$999$	−1.37098	−0.0433758

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.l.1.26	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.l.1.26	✓	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)

\(f(q)\)	\(=\)	\(q+1.90365 q^{2} -1.00000 q^{3} +1.62390 q^{4} -1.74973 q^{5} -1.90365 q^{6} -2.76075 q^{7} -0.715966 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.90365 q^{2} -1.00000 q^{3} +1.62390 q^{4} -1.74973 q^{5} -1.90365 q^{6} -2.76075 q^{7} -0.715966 q^{8} +1.00000 q^{9} -3.33088 q^{10} -4.86082 q^{11} -1.62390 q^{12} +4.21653 q^{13} -5.25551 q^{14} +1.74973 q^{15} -4.61075 q^{16} -1.00000 q^{17} +1.90365 q^{18} -2.06533 q^{19} -2.84139 q^{20} +2.76075 q^{21} -9.25332 q^{22} +6.78605 q^{23} +0.715966 q^{24} -1.93844 q^{25} +8.02682 q^{26} -1.00000 q^{27} -4.48317 q^{28} +1.05862 q^{29} +3.33088 q^{30} -1.35472 q^{31} -7.34534 q^{32} +4.86082 q^{33} -1.90365 q^{34} +4.83056 q^{35} +1.62390 q^{36} +1.37098 q^{37} -3.93167 q^{38} -4.21653 q^{39} +1.25275 q^{40} +2.38690 q^{41} +5.25551 q^{42} +2.48028 q^{43} -7.89348 q^{44} -1.74973 q^{45} +12.9183 q^{46} +12.3542 q^{47} +4.61075 q^{48} +0.621718 q^{49} -3.69012 q^{50} +1.00000 q^{51} +6.84723 q^{52} +9.48673 q^{53} -1.90365 q^{54} +8.50513 q^{55} +1.97660 q^{56} +2.06533 q^{57} +2.01525 q^{58} +3.60782 q^{59} +2.84139 q^{60} +0.816668 q^{61} -2.57891 q^{62} -2.76075 q^{63} -4.76149 q^{64} -7.37780 q^{65} +9.25332 q^{66} +13.5176 q^{67} -1.62390 q^{68} -6.78605 q^{69} +9.19572 q^{70} -5.74864 q^{71} -0.715966 q^{72} -11.8620 q^{73} +2.60987 q^{74} +1.93844 q^{75} -3.35389 q^{76} +13.4195 q^{77} -8.02682 q^{78} +1.00000 q^{79} +8.06757 q^{80} +1.00000 q^{81} +4.54383 q^{82} -8.93411 q^{83} +4.48317 q^{84} +1.74973 q^{85} +4.72159 q^{86} -1.05862 q^{87} +3.48018 q^{88} -10.7218 q^{89} -3.33088 q^{90} -11.6408 q^{91} +11.0199 q^{92} +1.35472 q^{93} +23.5181 q^{94} +3.61377 q^{95} +7.34534 q^{96} +12.3864 q^{97} +1.18354 q^{98} -4.86082 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) \) 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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