LMFDB - Embedded newform 6026.2.a.j.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.82570 q^{3} +1.00000 q^{4} -3.75704 q^{5} +1.82570 q^{6} +0.299528 q^{7} -1.00000 q^{8} +0.333191 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.82570 q^{3} +1.00000 q^{4} -3.75704 q^{5} +1.82570 q^{6} +0.299528 q^{7} -1.00000 q^{8} +0.333191 q^{9} +3.75704 q^{10} -5.56487 q^{11} -1.82570 q^{12} +5.41571 q^{13} -0.299528 q^{14} +6.85924 q^{15} +1.00000 q^{16} +0.273191 q^{17} -0.333191 q^{18} +3.10460 q^{19} -3.75704 q^{20} -0.546850 q^{21} +5.56487 q^{22} +1.00000 q^{23} +1.82570 q^{24} +9.11537 q^{25} -5.41571 q^{26} +4.86880 q^{27} +0.299528 q^{28} +2.79923 q^{29} -6.85924 q^{30} -9.18677 q^{31} -1.00000 q^{32} +10.1598 q^{33} -0.273191 q^{34} -1.12534 q^{35} +0.333191 q^{36} +8.29341 q^{37} -3.10460 q^{38} -9.88747 q^{39} +3.75704 q^{40} -9.40230 q^{41} +0.546850 q^{42} -5.89782 q^{43} -5.56487 q^{44} -1.25181 q^{45} -1.00000 q^{46} +5.57959 q^{47} -1.82570 q^{48} -6.91028 q^{49} -9.11537 q^{50} -0.498766 q^{51} +5.41571 q^{52} -12.1472 q^{53} -4.86880 q^{54} +20.9075 q^{55} -0.299528 q^{56} -5.66808 q^{57} -2.79923 q^{58} -13.8333 q^{59} +6.85924 q^{60} -14.9290 q^{61} +9.18677 q^{62} +0.0998002 q^{63} +1.00000 q^{64} -20.3470 q^{65} -10.1598 q^{66} +12.2726 q^{67} +0.273191 q^{68} -1.82570 q^{69} +1.12534 q^{70} +5.38928 q^{71} -0.333191 q^{72} -9.77168 q^{73} -8.29341 q^{74} -16.6420 q^{75} +3.10460 q^{76} -1.66684 q^{77} +9.88747 q^{78} -7.61916 q^{79} -3.75704 q^{80} -9.88856 q^{81} +9.40230 q^{82} +5.22664 q^{83} -0.546850 q^{84} -1.02639 q^{85} +5.89782 q^{86} -5.11056 q^{87} +5.56487 q^{88} +14.3890 q^{89} +1.25181 q^{90} +1.62216 q^{91} +1.00000 q^{92} +16.7723 q^{93} -5.57959 q^{94} -11.6641 q^{95} +1.82570 q^{96} -9.03763 q^{97} +6.91028 q^{98} -1.85417 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) $ 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9 + 4 * q^10 + 5 * q^11 + 3 * q^12 + 15 * q^13 - 11 * q^14 + 16 * q^15 + 33 * q^16 + 2 * q^17 - 44 * q^18 + 32 * q^19 - 4 * q^20 + 8 * q^21 - 5 * q^22 + 33 * q^23 - 3 * q^24 + 49 * q^25 - 15 * q^26 + 15 * q^27 + 11 * q^28 + 20 * q^29 - 16 * q^30 + 25 * q^31 - 33 * q^32 - 6 * q^33 - 2 * q^34 + 15 * q^35 + 44 * q^36 + 6 * q^37 - 32 * q^38 + 25 * q^39 + 4 * q^40 + 2 * q^41 - 8 * q^42 + 31 * q^43 + 5 * q^44 + 2 * q^45 - 33 * q^46 + 4 * q^47 + 3 * q^48 + 72 * q^49 - 49 * q^50 + 26 * q^51 + 15 * q^52 - 65 * q^53 - 15 * q^54 - 4 * q^55 - 11 * q^56 + 12 * q^57 - 20 * q^58 + 8 * q^59 + 16 * q^60 + 23 * q^61 - 25 * q^62 - 14 * q^63 + 33 * q^64 + 5 * q^65 + 6 * q^66 + 31 * q^67 + 2 * q^68 + 3 * q^69 - 15 * q^70 + 20 * q^71 - 44 * q^72 + 22 * q^73 - 6 * q^74 - 32 * q^75 + 32 * q^76 + 2 * q^77 - 25 * q^78 + 53 * q^79 - 4 * q^80 + 17 * q^81 - 2 * q^82 + 45 * q^83 + 8 * q^84 + 60 * q^85 - 31 * q^86 + 11 * q^87 - 5 * q^88 - 54 * q^89 - 2 * q^90 + 38 * q^91 + 33 * q^92 + 63 * q^93 - 4 * q^94 + 44 * q^95 - 3 * q^96 - 72 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.82570	−1.05407	−0.527035	−	0.849844i	$-0.676696\pi$
$3$	−1.82570	−1.05407	−0.527035	+	0.849844i	$0.676696\pi$
$4$	1.00000	0.500000
$5$	−3.75704	−1.68020	−0.840100	−	0.542431i	$-0.817504\pi$
$5$	−3.75704	−1.68020	−0.840100	+	0.542431i	$0.817504\pi$
$6$	1.82570	0.745340
$7$	0.299528	0.113211	0.0566056	−	0.998397i	$-0.481972\pi$
$7$	0.299528	0.113211	0.0566056	+	0.998397i	$0.481972\pi$
$8$	−1.00000	−0.353553
$9$	0.333191	0.111064
$10$	3.75704	1.18808
$11$	−5.56487	−1.67787	−0.838936	−	0.544230i	$-0.816822\pi$
$11$	−5.56487	−1.67787	−0.838936	+	0.544230i	$0.816822\pi$
$12$	−1.82570	−0.527035
$13$	5.41571	1.50205	0.751023	−	0.660276i	$-0.229560\pi$
$13$	5.41571	1.50205	0.751023	+	0.660276i	$0.229560\pi$
$14$	−0.299528	−0.0800524
$15$	6.85924	1.77105
$16$	1.00000	0.250000
$17$	0.273191	0.0662586	0.0331293	−	0.999451i	$-0.489453\pi$
$17$	0.273191	0.0662586	0.0331293	+	0.999451i	$0.489453\pi$
$18$	−0.333191	−0.0785339
$19$	3.10460	0.712245	0.356122	−	0.934439i	$-0.384099\pi$
$19$	3.10460	0.712245	0.356122	+	0.934439i	$0.384099\pi$
$20$	−3.75704	−0.840100
$21$	−0.546850	−0.119332
$22$	5.56487	1.18643
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.82570	0.372670
$25$	9.11537	1.82307
$26$	−5.41571	−1.06211
$27$	4.86880	0.937001
$28$	0.299528	0.0566056
$29$	2.79923	0.519804	0.259902	−	0.965635i	$-0.416310\pi$
$29$	2.79923	0.519804	0.259902	+	0.965635i	$0.416310\pi$
$30$	−6.85924	−1.25232
$31$	−9.18677	−1.64999	−0.824996	−	0.565139i	$-0.808823\pi$
$31$	−9.18677	−1.64999	−0.824996	+	0.565139i	$0.808823\pi$
$32$	−1.00000	−0.176777
$33$	10.1598	1.76859
$34$	−0.273191	−0.0468519
$35$	−1.12534	−0.190217
$36$	0.333191	0.0555318
$37$	8.29341	1.36343	0.681714	−	0.731619i	$-0.261235\pi$
$37$	8.29341	1.36343	0.681714	+	0.731619i	$0.261235\pi$
$38$	−3.10460	−0.503633
$39$	−9.88747	−1.58326
$40$	3.75704	0.594041
$41$	−9.40230	−1.46839	−0.734196	−	0.678937i	$-0.762441\pi$
$41$	−9.40230	−1.46839	−0.734196	+	0.678937i	$0.762441\pi$
$42$	0.546850	0.0843808
$43$	−5.89782	−0.899408	−0.449704	−	0.893178i	$-0.648471\pi$
$43$	−5.89782	−0.899408	−0.449704	+	0.893178i	$0.648471\pi$
$44$	−5.56487	−0.838936
$45$	−1.25181	−0.186609
$46$	−1.00000	−0.147442
$47$	5.57959	0.813866	0.406933	−	0.913458i	$-0.366598\pi$
$47$	5.57959	0.813866	0.406933	+	0.913458i	$0.366598\pi$
$48$	−1.82570	−0.263518
$49$	−6.91028	−0.987183
$50$	−9.11537	−1.28911
$51$	−0.498766	−0.0698412
$52$	5.41571	0.751023
$53$	−12.1472	−1.66855	−0.834274	−	0.551350i	$-0.814113\pi$
$53$	−12.1472	−1.66855	−0.834274	+	0.551350i	$0.814113\pi$
$54$	−4.86880	−0.662560
$55$	20.9075	2.81916
$56$	−0.299528	−0.0400262
$57$	−5.66808	−0.750756
$58$	−2.79923	−0.367557
$59$	−13.8333	−1.80094	−0.900472	−	0.434914i	$-0.856779\pi$
$59$	−13.8333	−1.80094	−0.900472	+	0.434914i	$0.856779\pi$
$60$	6.85924	0.885525
$61$	−14.9290	−1.91146	−0.955729	−	0.294247i	$-0.904931\pi$
$61$	−14.9290	−1.91146	−0.955729	+	0.294247i	$0.904931\pi$
$62$	9.18677	1.16672
$63$	0.0998002	0.0125736
$64$	1.00000	0.125000
$65$	−20.3470	−2.52374
$66$	−10.1598	−1.25058
$67$	12.2726	1.49934	0.749671	−	0.661811i	$-0.230212\pi$
$67$	12.2726	1.49934	0.749671	+	0.661811i	$0.230212\pi$
$68$	0.273191	0.0331293
$69$	−1.82570	−0.219789
$70$	1.12534	0.134504
$71$	5.38928	0.639590	0.319795	−	0.947487i	$-0.396386\pi$
$71$	5.38928	0.639590	0.319795	+	0.947487i	$0.396386\pi$
$72$	−0.333191	−0.0392669
$73$	−9.77168	−1.14369	−0.571844	−	0.820362i	$-0.693772\pi$
$73$	−9.77168	−1.14369	−0.571844	+	0.820362i	$0.693772\pi$
$74$	−8.29341	−0.964089
$75$	−16.6420	−1.92165
$76$	3.10460	0.356122
$77$	−1.66684	−0.189954
$78$	9.88747	1.11954
$79$	−7.61916	−0.857223	−0.428611	−	0.903489i	$-0.640997\pi$
$79$	−7.61916	−0.857223	−0.428611	+	0.903489i	$0.640997\pi$
$80$	−3.75704	−0.420050
$81$	−9.88856	−1.09873
$82$	9.40230	1.03831
$83$	5.22664	0.573699	0.286849	−	0.957976i	$-0.407392\pi$
$83$	5.22664	0.573699	0.286849	+	0.957976i	$0.407392\pi$
$84$	−0.546850	−0.0596662
$85$	−1.02639	−0.111328
$86$	5.89782	0.635978
$87$	−5.11056	−0.547910
$88$	5.56487	0.593217
$89$	14.3890	1.52523	0.762616	−	0.646852i	$-0.223915\pi$
$89$	14.3890	1.52523	0.762616	+	0.646852i	$0.223915\pi$
$90$	1.25181	0.131953
$91$	1.62216	0.170048
$92$	1.00000	0.104257
$93$	16.7723	1.73921
$94$	−5.57959	−0.575490
$95$	−11.6641	−1.19671
$96$	1.82570	0.186335
$97$	−9.03763	−0.917633	−0.458816	−	0.888531i	$-0.651726\pi$
$97$	−9.03763	−0.917633	−0.458816	+	0.888531i	$0.651726\pi$
$98$	6.91028	0.698044
$99$	−1.85417	−0.186351
$100$	9.11537	0.911537
$101$	−4.91929	−0.489487	−0.244744	−	0.969588i	$-0.578704\pi$
$101$	−4.91929	−0.489487	−0.244744	+	0.969588i	$0.578704\pi$
$102$	0.498766	0.0493852
$103$	18.5366	1.82647	0.913234	−	0.407436i	$-0.133577\pi$
$103$	18.5366	1.82647	0.913234	+	0.407436i	$0.133577\pi$
$104$	−5.41571	−0.531054
$105$	2.05454	0.200502
$106$	12.1472	1.17984
$107$	−3.37018	−0.325807	−0.162904	−	0.986642i	$-0.552086\pi$
$107$	−3.37018	−0.325807	−0.162904	+	0.986642i	$0.552086\pi$
$108$	4.86880	0.468501
$109$	−13.2847	−1.27244	−0.636221	−	0.771507i	$-0.719503\pi$
$109$	−13.2847	−1.27244	−0.636221	+	0.771507i	$0.719503\pi$
$110$	−20.9075	−1.99345
$111$	−15.1413	−1.43715
$112$	0.299528	0.0283028
$113$	−13.6667	−1.28566	−0.642828	−	0.766010i	$-0.722239\pi$
$113$	−13.6667	−1.28566	−0.642828	+	0.766010i	$0.722239\pi$
$114$	5.66808	0.530865
$115$	−3.75704	−0.350346
$116$	2.79923	0.259902
$117$	1.80447	0.166823
$118$	13.8333	1.27346
$119$	0.0818286	0.00750121
$120$	−6.85924	−0.626160
$121$	19.9678	1.81525
$122$	14.9290	1.35161
$123$	17.1658	1.54779
$124$	−9.18677	−0.824996
$125$	−15.4616	−1.38293
$126$	−0.0998002	−0.00889091
$127$	−0.210143	−0.0186472	−0.00932361	−	0.999957i	$-0.502968\pi$
$127$	−0.210143	−0.0186472	−0.00932361	+	0.999957i	$0.502968\pi$
$128$	−1.00000	−0.0883883
$129$	10.7677	0.948039
$130$	20.3470	1.78455
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	10.1598	0.884297
$133$	0.929917	0.0806340
$134$	−12.2726	−1.06019
$135$	−18.2923	−1.57435
$136$	−0.273191	−0.0234260
$137$	−5.66114	−0.483664	−0.241832	−	0.970318i	$-0.577748\pi$
$137$	−5.66114	−0.483664	−0.241832	+	0.970318i	$0.577748\pi$
$138$	1.82570	0.155414
$139$	5.31613	0.450908	0.225454	−	0.974254i	$-0.427613\pi$
$139$	5.31613	0.450908	0.225454	+	0.974254i	$0.427613\pi$
$140$	−1.12534	−0.0951087
$141$	−10.1867	−0.857872
$142$	−5.38928	−0.452258
$143$	−30.1377	−2.52024
$144$	0.333191	0.0277659
$145$	−10.5168	−0.873375
$146$	9.77168	0.808710
$147$	12.6161	1.04056
$148$	8.29341	0.681714
$149$	0.458207	0.0375378	0.0187689	−	0.999824i	$-0.494025\pi$
$149$	0.458207	0.0375378	0.0187689	+	0.999824i	$0.494025\pi$
$150$	16.6420	1.35881
$151$	11.6523	0.948254	0.474127	−	0.880456i	$-0.342764\pi$
$151$	11.6523	0.948254	0.474127	+	0.880456i	$0.342764\pi$
$152$	−3.10460	−0.251817
$153$	0.0910249	0.00735893
$154$	1.66684	0.134318
$155$	34.5151	2.77232
$156$	−9.88747	−0.791631
$157$	−1.72683	−0.137816	−0.0689080	−	0.997623i	$-0.521951\pi$
$157$	−1.72683	−0.137816	−0.0689080	+	0.997623i	$0.521951\pi$
$158$	7.61916	0.606148
$159$	22.1772	1.75877
$160$	3.75704	0.297020
$161$	0.299528	0.0236062
$162$	9.88856	0.776918
$163$	−19.1912	−1.50317	−0.751585	−	0.659637i	$-0.770710\pi$
$163$	−19.1912	−1.50317	−0.751585	+	0.659637i	$0.770710\pi$
$164$	−9.40230	−0.734196
$165$	−38.1708	−2.97159
$166$	−5.22664	−0.405666
$167$	−15.8437	−1.22602	−0.613012	−	0.790073i	$-0.710042\pi$
$167$	−15.8437	−1.22602	−0.613012	+	0.790073i	$0.710042\pi$
$168$	0.546850	0.0421904
$169$	16.3299	1.25614
$170$	1.02639	0.0787206
$171$	1.03443	0.0791045
$172$	−5.89782	−0.449704
$173$	3.83641	0.291677	0.145838	−	0.989308i	$-0.453412\pi$
$173$	3.83641	0.291677	0.145838	+	0.989308i	$0.453412\pi$
$174$	5.11056	0.387431
$175$	2.73031	0.206392
$176$	−5.56487	−0.419468
$177$	25.2555	1.89832
$178$	−14.3890	−1.07850
$179$	17.6108	1.31629	0.658145	−	0.752891i	$-0.271341\pi$
$179$	17.6108	1.31629	0.658145	+	0.752891i	$0.271341\pi$
$180$	−1.25181	−0.0933046
$181$	15.8496	1.17809	0.589044	−	0.808101i	$-0.299504\pi$
$181$	15.8496	1.17809	0.589044	+	0.808101i	$0.299504\pi$
$182$	−1.62216	−0.120242
$183$	27.2559	2.01481
$184$	−1.00000	−0.0737210
$185$	−31.1587	−2.29083
$186$	−16.7723	−1.22981
$187$	−1.52027	−0.111173
$188$	5.57959	0.406933
$189$	1.45834	0.106079
$190$	11.6641	0.846205
$191$	−16.0477	−1.16117	−0.580587	−	0.814198i	$-0.697177\pi$
$191$	−16.0477	−1.16117	−0.580587	+	0.814198i	$0.697177\pi$
$192$	−1.82570	−0.131759
$193$	3.17234	0.228350	0.114175	−	0.993461i	$-0.463577\pi$
$193$	3.17234	0.228350	0.114175	+	0.993461i	$0.463577\pi$
$194$	9.03763	0.648864
$195$	37.1477	2.66020
$196$	−6.91028	−0.493592
$197$	22.9023	1.63172	0.815861	−	0.578248i	$-0.196263\pi$
$197$	22.9023	1.63172	0.815861	+	0.578248i	$0.196263\pi$
$198$	1.85417	0.131770
$199$	−2.65675	−0.188332	−0.0941659	−	0.995557i	$-0.530018\pi$
$199$	−2.65675	−0.188332	−0.0941659	+	0.995557i	$0.530018\pi$
$200$	−9.11537	−0.644554
$201$	−22.4062	−1.58041
$202$	4.91929	0.346120
$203$	0.838449	0.0588476
$204$	−0.498766	−0.0349206
$205$	35.3249	2.46719
$206$	−18.5366	−1.29151
$207$	0.333191	0.0231584
$208$	5.41571	0.375512
$209$	−17.2767	−1.19506
$210$	−2.05454	−0.141777
$211$	−17.3531	−1.19463	−0.597317	−	0.802005i	$-0.703766\pi$
$211$	−17.3531	−1.19463	−0.597317	+	0.802005i	$0.703766\pi$
$212$	−12.1472	−0.834274
$213$	−9.83922	−0.674173
$214$	3.37018	0.230381
$215$	22.1583	1.51119
$216$	−4.86880	−0.331280
$217$	−2.75170	−0.186797
$218$	13.2847	0.899753
$219$	17.8402	1.20553
$220$	20.9075	1.40958
$221$	1.47952	0.0995236
$222$	15.1413	1.01622
$223$	−21.0369	−1.40874	−0.704368	−	0.709835i	$-0.748769\pi$
$223$	−21.0369	−1.40874	−0.704368	+	0.709835i	$0.748769\pi$
$224$	−0.299528	−0.0200131
$225$	3.03716	0.202477
$226$	13.6667	0.909097
$227$	24.4995	1.62609	0.813043	−	0.582204i	$-0.197809\pi$
$227$	24.4995	1.62609	0.813043	+	0.582204i	$0.197809\pi$
$228$	−5.66808	−0.375378
$229$	−4.90105	−0.323871	−0.161935	−	0.986801i	$-0.551774\pi$
$229$	−4.90105	−0.323871	−0.161935	+	0.986801i	$0.551774\pi$
$230$	3.75704	0.247732
$231$	3.04315	0.200225
$232$	−2.79923	−0.183778
$233$	−19.8284	−1.29900	−0.649500	−	0.760362i	$-0.725022\pi$
$233$	−19.8284	−1.29900	−0.649500	+	0.760362i	$0.725022\pi$
$234$	−1.80447	−0.117962
$235$	−20.9627	−1.36746
$236$	−13.8333	−0.900472
$237$	13.9103	0.903573
$238$	−0.0818286	−0.00530416
$239$	15.6868	1.01469	0.507346	−	0.861742i	$-0.330626\pi$
$239$	15.6868	1.01469	0.507346	+	0.861742i	$0.330626\pi$
$240$	6.85924	0.442762
$241$	−16.2315	−1.04556	−0.522781	−	0.852467i	$-0.675106\pi$
$241$	−16.2315	−1.04556	−0.522781	+	0.852467i	$0.675106\pi$
$242$	−19.9678	−1.28358
$243$	3.44716	0.221136
$244$	−14.9290	−0.955729
$245$	25.9622	1.65867
$246$	−17.1658	−1.09445
$247$	16.8136	1.06982
$248$	9.18677	0.583360
$249$	−9.54230	−0.604719
$250$	15.4616	0.977879
$251$	−7.60740	−0.480175	−0.240088	−	0.970751i	$-0.577176\pi$
$251$	−7.60740	−0.480175	−0.240088	+	0.970751i	$0.577176\pi$
$252$	0.0998002	0.00628682
$253$	−5.56487	−0.349860
$254$	0.210143	0.0131856
$255$	1.87389	0.117347
$256$	1.00000	0.0625000
$257$	−22.1385	−1.38096	−0.690481	−	0.723351i	$-0.742601\pi$
$257$	−22.1385	−1.38096	−0.690481	+	0.723351i	$0.742601\pi$
$258$	−10.7677	−0.670365
$259$	2.48411	0.154355
$260$	−20.3470	−1.26187
$261$	0.932678	0.0577313
$262$	1.00000	0.0617802
$263$	−11.0908	−0.683885	−0.341943	−	0.939721i	$-0.611085\pi$
$263$	−11.0908	−0.683885	−0.341943	+	0.939721i	$0.611085\pi$
$264$	−10.1598	−0.625292
$265$	45.6376	2.80349
$266$	−0.929917	−0.0570169
$267$	−26.2701	−1.60770
$268$	12.2726	0.749671
$269$	12.4167	0.757058	0.378529	−	0.925590i	$-0.376430\pi$
$269$	12.4167	0.757058	0.378529	+	0.925590i	$0.376430\pi$
$270$	18.2923	1.11323
$271$	19.0113	1.15485	0.577426	−	0.816443i	$-0.304057\pi$
$271$	19.0113	1.15485	0.577426	+	0.816443i	$0.304057\pi$
$272$	0.273191	0.0165647
$273$	−2.96158	−0.179243
$274$	5.66114	0.342002
$275$	−50.7259	−3.05888
$276$	−1.82570	−0.109894
$277$	28.5217	1.71371	0.856853	−	0.515561i	$-0.172416\pi$
$277$	28.5217	1.71371	0.856853	+	0.515561i	$0.172416\pi$
$278$	−5.31613	−0.318840
$279$	−3.06095	−0.183254
$280$	1.12534	0.0672520
$281$	−11.8238	−0.705346	−0.352673	−	0.935747i	$-0.614727\pi$
$281$	−11.8238	−0.705346	−0.352673	+	0.935747i	$0.614727\pi$
$282$	10.1867	0.606607
$283$	6.96095	0.413786	0.206893	−	0.978364i	$-0.433665\pi$
$283$	6.96095	0.413786	0.206893	+	0.978364i	$0.433665\pi$
$284$	5.38928	0.319795
$285$	21.2952	1.26142
$286$	30.1377	1.78208
$287$	−2.81626	−0.166238
$288$	−0.333191	−0.0196335
$289$	−16.9254	−0.995610
$290$	10.5168	0.617569
$291$	16.5000	0.967249
$292$	−9.77168	−0.571844
$293$	−4.63060	−0.270523	−0.135261	−	0.990810i	$-0.543187\pi$
$293$	−4.63060	−0.270523	−0.135261	+	0.990810i	$0.543187\pi$
$294$	−12.6161	−0.735787
$295$	51.9724	3.02595
$296$	−8.29341	−0.482044
$297$	−27.0942	−1.57217
$298$	−0.458207	−0.0265432
$299$	5.41571	0.313198
$300$	−16.6420	−0.960824
$301$	−1.76656	−0.101823
$302$	−11.6523	−0.670517
$303$	8.98116	0.515954
$304$	3.10460	0.178061
$305$	56.0888	3.21163
$306$	−0.0910249	−0.00520355
$307$	9.86792	0.563192	0.281596	−	0.959533i	$-0.409136\pi$
$307$	9.86792	0.563192	0.281596	+	0.959533i	$0.409136\pi$
$308$	−1.66684	−0.0949769
$309$	−33.8424	−1.92522
$310$	−34.5151	−1.96032
$311$	0.834950	0.0473457	0.0236728	−	0.999720i	$-0.492464\pi$
$311$	0.834950	0.0473457	0.0236728	+	0.999720i	$0.492464\pi$
$312$	9.88747	0.559768
$313$	2.61195	0.147636	0.0738182	−	0.997272i	$-0.476482\pi$
$313$	2.61195	0.147636	0.0738182	+	0.997272i	$0.476482\pi$
$314$	1.72683	0.0974506
$315$	−0.374954	−0.0211262
$316$	−7.61916	−0.428611
$317$	5.97828	0.335774	0.167887	−	0.985806i	$-0.446306\pi$
$317$	5.97828	0.335774	0.167887	+	0.985806i	$0.446306\pi$
$318$	−22.1772	−1.24364
$319$	−15.5773	−0.872164
$320$	−3.75704	−0.210025
$321$	6.15294	0.343424
$322$	−0.299528	−0.0166921
$323$	0.848150	0.0471923
$324$	−9.88856	−0.549364
$325$	49.3662	2.73834
$326$	19.1912	1.06290
$327$	24.2539	1.34124
$328$	9.40230	0.519155
$329$	1.67125	0.0921387
$330$	38.1708	2.10123
$331$	−4.28335	−0.235434	−0.117717	−	0.993047i	$-0.537558\pi$
$331$	−4.28335	−0.235434	−0.117717	+	0.993047i	$0.537558\pi$
$332$	5.22664	0.286849
$333$	2.76329	0.151427
$334$	15.8437	0.866930
$335$	−46.1088	−2.51919
$336$	−0.546850	−0.0298331
$337$	18.5667	1.01139	0.505696	−	0.862712i	$-0.331236\pi$
$337$	18.5667	1.01139	0.505696	+	0.862712i	$0.331236\pi$
$338$	−16.3299	−0.888229
$339$	24.9514	1.35517
$340$	−1.02639	−0.0556639
$341$	51.1232	2.76847
$342$	−1.03443	−0.0559353
$343$	−4.16653	−0.224971
$344$	5.89782	0.317989
$345$	6.85924	0.369289
$346$	−3.83641	−0.206247
$347$	6.21782	0.333790	0.166895	−	0.985975i	$-0.446626\pi$
$347$	6.21782	0.333790	0.166895	+	0.985975i	$0.446626\pi$
$348$	−5.11056	−0.273955
$349$	−14.7812	−0.791222	−0.395611	−	0.918418i	$-0.629467\pi$
$349$	−14.7812	−0.791222	−0.395611	+	0.918418i	$0.629467\pi$
$350$	−2.73031	−0.145941
$351$	26.3680	1.40742
$352$	5.56487	0.296609
$353$	−19.8284	−1.05536	−0.527679	−	0.849444i	$-0.676937\pi$
$353$	−19.8284	−1.05536	−0.527679	+	0.849444i	$0.676937\pi$
$354$	−25.2555	−1.34232
$355$	−20.2478	−1.07464
$356$	14.3890	0.762616
$357$	−0.149395	−0.00790680
$358$	−17.6108	−0.930758
$359$	7.13914	0.376789	0.188395	−	0.982093i	$-0.439672\pi$
$359$	7.13914	0.376789	0.188395	+	0.982093i	$0.439672\pi$
$360$	1.25181	0.0659763
$361$	−9.36144	−0.492708
$362$	−15.8496	−0.833034
$363$	−36.4552	−1.91340
$364$	1.62216	0.0850242
$365$	36.7126	1.92163
$366$	−27.2559	−1.42469
$367$	−11.1841	−0.583808	−0.291904	−	0.956448i	$-0.594289\pi$
$367$	−11.1841	−0.583808	−0.291904	+	0.956448i	$0.594289\pi$
$368$	1.00000	0.0521286
$369$	−3.13276	−0.163085
$370$	31.1587	1.61986
$371$	−3.63844	−0.188898
$372$	16.7723	0.869604
$373$	13.4973	0.698865	0.349433	−	0.936961i	$-0.386374\pi$
$373$	13.4973	0.698865	0.349433	+	0.936961i	$0.386374\pi$
$374$	1.52027	0.0786115
$375$	28.2283	1.45771
$376$	−5.57959	−0.287745
$377$	15.1598	0.780770
$378$	−1.45834	−0.0750091
$379$	2.49750	0.128288	0.0641439	−	0.997941i	$-0.479568\pi$
$379$	2.49750	0.128288	0.0641439	+	0.997941i	$0.479568\pi$
$380$	−11.6641	−0.598357
$381$	0.383660	0.0196555
$382$	16.0477	0.821074
$383$	−2.33445	−0.119285	−0.0596424	−	0.998220i	$-0.518996\pi$
$383$	−2.33445	−0.119285	−0.0596424	+	0.998220i	$0.518996\pi$
$384$	1.82570	0.0931675
$385$	6.26238	0.319160
$386$	−3.17234	−0.161468
$387$	−1.96510	−0.0998916
$388$	−9.03763	−0.458816
$389$	−14.1827	−0.719091	−0.359546	−	0.933127i	$-0.617068\pi$
$389$	−14.1827	−0.719091	−0.359546	+	0.933127i	$0.617068\pi$
$390$	−37.1477	−1.88104
$391$	0.273191	0.0138159
$392$	6.91028	0.349022
$393$	1.82570	0.0920945
$394$	−22.9023	−1.15380
$395$	28.6255	1.44031
$396$	−1.85417	−0.0931753
$397$	38.4821	1.93136	0.965680	−	0.259734i	$-0.0836349\pi$
$397$	38.4821	1.93136	0.965680	+	0.259734i	$0.0836349\pi$
$398$	2.65675	0.133171
$399$	−1.69775	−0.0849939
$400$	9.11537	0.455769
$401$	14.5965	0.728916	0.364458	−	0.931220i	$-0.381254\pi$
$401$	14.5965	0.728916	0.364458	+	0.931220i	$0.381254\pi$
$402$	22.4062	1.11752
$403$	−49.7528	−2.47837
$404$	−4.91929	−0.244744
$405$	37.1517	1.84608
$406$	−0.838449	−0.0416115
$407$	−46.1517	−2.28766
$408$	0.498766	0.0246926
$409$	29.7648	1.47177	0.735887	−	0.677105i	$-0.236766\pi$
$409$	29.7648	1.47177	0.735887	+	0.677105i	$0.236766\pi$
$410$	−35.3249	−1.74457
$411$	10.3356	0.509816
$412$	18.5366	0.913234
$413$	−4.14347	−0.203887
$414$	−0.333191	−0.0163754
$415$	−19.6367	−0.963929
$416$	−5.41571	−0.265527
$417$	−9.70567	−0.475289
$418$	17.2767	0.845032
$419$	−19.1729	−0.936658	−0.468329	−	0.883554i	$-0.655144\pi$
$419$	−19.1729	−0.936658	−0.468329	+	0.883554i	$0.655144\pi$
$420$	2.05454	0.100251
$421$	−37.8026	−1.84239	−0.921193	−	0.389105i	$-0.872784\pi$
$421$	−37.8026	−1.84239	−0.921193	+	0.389105i	$0.872784\pi$
$422$	17.3531	0.844733
$423$	1.85907	0.0903910
$424$	12.1472	0.589921
$425$	2.49024	0.120794
$426$	9.83922	0.476712
$427$	−4.47165	−0.216398
$428$	−3.37018	−0.162904
$429$	55.0225	2.65651
$430$	−22.1583	−1.06857
$431$	23.0393	1.10976	0.554881	−	0.831930i	$-0.312764\pi$
$431$	23.0393	1.10976	0.554881	+	0.831930i	$0.312764\pi$
$432$	4.86880	0.234250
$433$	−4.19441	−0.201570	−0.100785	−	0.994908i	$-0.532135\pi$
$433$	−4.19441	−0.201570	−0.100785	+	0.994908i	$0.532135\pi$
$434$	2.75170	0.132086
$435$	19.2006	0.920598
$436$	−13.2847	−0.636221
$437$	3.10460	0.148513
$438$	−17.8402	−0.852437
$439$	−15.5912	−0.744126	−0.372063	−	0.928208i	$-0.621349\pi$
$439$	−15.5912	−0.744126	−0.372063	+	0.928208i	$0.621349\pi$
$440$	−20.9075	−0.996724
$441$	−2.30244	−0.109640
$442$	−1.47952	−0.0703738
$443$	1.19813	0.0569248	0.0284624	−	0.999595i	$-0.490939\pi$
$443$	1.19813	0.0569248	0.0284624	+	0.999595i	$0.490939\pi$
$444$	−15.1413	−0.718574
$445$	−54.0601	−2.56270
$446$	21.0369	0.996126
$447$	−0.836550	−0.0395675
$448$	0.299528	0.0141514
$449$	−33.3653	−1.57461	−0.787303	−	0.616566i	$-0.788523\pi$
$449$	−33.3653	−1.57461	−0.787303	+	0.616566i	$0.788523\pi$
$450$	−3.03716	−0.143173
$451$	52.3226	2.46377
$452$	−13.6667	−0.642828
$453$	−21.2737	−0.999527
$454$	−24.4995	−1.14982
$455$	−6.09452	−0.285715
$456$	5.66808	0.265432
$457$	21.1733	0.990445	0.495223	−	0.868766i	$-0.335087\pi$
$457$	21.1733	0.990445	0.495223	+	0.868766i	$0.335087\pi$
$458$	4.90105	0.229011
$459$	1.33011	0.0620844
$460$	−3.75704	−0.175173
$461$	30.3950	1.41563	0.707817	−	0.706396i	$-0.249680\pi$
$461$	30.3950	1.41563	0.707817	+	0.706396i	$0.249680\pi$
$462$	−3.04315	−0.141580
$463$	−4.67251	−0.217150	−0.108575	−	0.994088i	$-0.534629\pi$
$463$	−4.67251	−0.217150	−0.108575	+	0.994088i	$0.534629\pi$
$464$	2.79923	0.129951
$465$	−63.0143	−2.92222
$466$	19.8284	0.918531
$467$	−0.395464	−0.0182999	−0.00914995	−	0.999958i	$-0.502913\pi$
$467$	−0.395464	−0.0182999	−0.00914995	+	0.999958i	$0.502913\pi$
$468$	1.80447	0.0834114
$469$	3.67600	0.169742
$470$	20.9627	0.966939
$471$	3.15268	0.145268
$472$	13.8333	0.636730
$473$	32.8206	1.50909
$474$	−13.9103	−0.638923
$475$	28.2996	1.29848
$476$	0.0818286	0.00375061
$477$	−4.04734	−0.185315
$478$	−15.6868	−0.717496
$479$	18.6516	0.852215	0.426107	−	0.904673i	$-0.359885\pi$
$479$	18.6516	0.852215	0.426107	+	0.904673i	$0.359885\pi$
$480$	−6.85924	−0.313080
$481$	44.9147	2.04793
$482$	16.2315	0.739325
$483$	−0.546850	−0.0248825
$484$	19.9678	0.907626
$485$	33.9548	1.54181
$486$	−3.44716	−0.156367
$487$	3.40051	0.154092	0.0770460	−	0.997028i	$-0.475451\pi$
$487$	3.40051	0.154092	0.0770460	+	0.997028i	$0.475451\pi$
$488$	14.9290	0.675803
$489$	35.0374	1.58445
$490$	−25.9622	−1.17285
$491$	−0.435564	−0.0196567	−0.00982836	−	0.999952i	$-0.503129\pi$
$491$	−0.435564	−0.0196567	−0.00982836	+	0.999952i	$0.503129\pi$
$492$	17.1658	0.773895
$493$	0.764725	0.0344415
$494$	−16.8136	−0.756480
$495$	6.96618	0.313106
$496$	−9.18677	−0.412498
$497$	1.61424	0.0724087
$498$	9.54230	0.427601
$499$	18.9085	0.846460	0.423230	−	0.906022i	$-0.360896\pi$
$499$	18.9085	0.846460	0.423230	+	0.906022i	$0.360896\pi$
$500$	−15.4616	−0.691465
$501$	28.9259	1.29232
$502$	7.60740	0.339535
$503$	12.0334	0.536543	0.268272	−	0.963343i	$-0.413548\pi$
$503$	12.0334	0.536543	0.268272	+	0.963343i	$0.413548\pi$
$504$	−0.0998002	−0.00444545
$505$	18.4820	0.822437
$506$	5.56487	0.247389
$507$	−29.8135	−1.32406
$508$	−0.210143	−0.00932361
$509$	33.3090	1.47640	0.738198	−	0.674584i	$-0.235677\pi$
$509$	33.3090	1.47640	0.738198	+	0.674584i	$0.235677\pi$
$510$	−1.87389	−0.0829771
$511$	−2.92690	−0.129478
$512$	−1.00000	−0.0441942
$513$	15.1157	0.667374
$514$	22.1385	0.976487
$515$	−69.6429	−3.06883
$516$	10.7677	0.474020
$517$	−31.0497	−1.36556
$518$	−2.48411	−0.109146
$519$	−7.00414	−0.307448
$520$	20.3470	0.892277
$521$	5.60719	0.245655	0.122828	−	0.992428i	$-0.460804\pi$
$521$	5.60719	0.245655	0.122828	+	0.992428i	$0.460804\pi$
$522$	−0.932678	−0.0408222
$523$	−2.01286	−0.0880161	−0.0440080	−	0.999031i	$-0.514013\pi$
$523$	−2.01286	−0.0880161	−0.0440080	+	0.999031i	$0.514013\pi$
$524$	−1.00000	−0.0436852
$525$	−4.98474	−0.217552
$526$	11.0908	0.483580
$527$	−2.50974	−0.109326
$528$	10.1598	0.442149
$529$	1.00000	0.0434783
$530$	−45.6376	−1.98237
$531$	−4.60914	−0.200019
$532$	0.929917	0.0403170
$533$	−50.9201	−2.20560
$534$	26.2701	1.13682
$535$	12.6619	0.547422
$536$	−12.2726	−0.530097
$537$	−32.1520	−1.38746
$538$	−12.4167	−0.535321
$539$	38.4548	1.65637
$540$	−18.2923	−0.787175
$541$	25.2174	1.08418	0.542091	−	0.840320i	$-0.317633\pi$
$541$	25.2174	1.08418	0.542091	+	0.840320i	$0.317633\pi$
$542$	−19.0113	−0.816603
$543$	−28.9366	−1.24179
$544$	−0.273191	−0.0117130
$545$	49.9111	2.13796
$546$	2.96158	0.126744
$547$	35.0809	1.49995	0.749975	−	0.661467i	$-0.230066\pi$
$547$	35.0809	1.49995	0.749975	+	0.661467i	$0.230066\pi$
$548$	−5.66114	−0.241832
$549$	−4.97420	−0.212294
$550$	50.7259	2.16296
$551$	8.69049	0.370228
$552$	1.82570	0.0777071
$553$	−2.28216	−0.0970472
$554$	−28.5217	−1.21177
$555$	56.8865	2.41470
$556$	5.31613	0.225454
$557$	−36.8266	−1.56039	−0.780196	−	0.625535i	$-0.784881\pi$
$557$	−36.8266	−1.56039	−0.780196	+	0.625535i	$0.784881\pi$
$558$	3.06095	0.129580
$559$	−31.9408	−1.35095
$560$	−1.12534	−0.0475544
$561$	2.77557	0.117185
$562$	11.8238	0.498755
$563$	−0.363934	−0.0153380	−0.00766899	−	0.999971i	$-0.502441\pi$
$563$	−0.363934	−0.0153380	−0.00766899	+	0.999971i	$0.502441\pi$
$564$	−10.1867	−0.428936
$565$	51.3464	2.16016
$566$	−6.96095	−0.292591
$567$	−2.96190	−0.124388
$568$	−5.38928	−0.226129
$569$	15.9559	0.668908	0.334454	−	0.942412i	$-0.391448\pi$
$569$	15.9559	0.668908	0.334454	+	0.942412i	$0.391448\pi$
$570$	−21.2952	−0.891959
$571$	−7.29710	−0.305374	−0.152687	−	0.988275i	$-0.548793\pi$
$571$	−7.29710	−0.305374	−0.152687	+	0.988275i	$0.548793\pi$
$572$	−30.1377	−1.26012
$573$	29.2984	1.22396
$574$	2.81626	0.117548
$575$	9.11537	0.380137
$576$	0.333191	0.0138830
$577$	−17.0009	−0.707759	−0.353879	−	0.935291i	$-0.615138\pi$
$577$	−17.0009	−0.707759	−0.353879	+	0.935291i	$0.615138\pi$
$578$	16.9254	0.704002
$579$	−5.79176	−0.240697
$580$	−10.5168	−0.436687
$581$	1.56553	0.0649491
$582$	−16.5000	−0.683948
$583$	67.5976	2.79961
$584$	9.77168	0.404355
$585$	−6.77945	−0.280296
$586$	4.63060	0.191288
$587$	45.6834	1.88556	0.942779	−	0.333419i	$-0.108202\pi$
$587$	45.6834	1.88556	0.942779	+	0.333419i	$0.108202\pi$
$588$	12.6161	0.520280
$589$	−28.5213	−1.17520
$590$	−51.9724	−2.13967
$591$	−41.8128	−1.71995
$592$	8.29341	0.340857
$593$	−13.0385	−0.535428	−0.267714	−	0.963498i	$-0.586268\pi$
$593$	−13.0385	−0.535428	−0.267714	+	0.963498i	$0.586268\pi$
$594$	27.0942	1.11169
$595$	−0.307433	−0.0126035
$596$	0.458207	0.0187689
$597$	4.85043	0.198515
$598$	−5.41571	−0.221465
$599$	6.60746	0.269973	0.134987	−	0.990847i	$-0.456901\pi$
$599$	6.60746	0.269973	0.134987	+	0.990847i	$0.456901\pi$
$600$	16.6420	0.679405
$601$	−17.7222	−0.722903	−0.361452	−	0.932391i	$-0.617719\pi$
$601$	−17.7222	−0.722903	−0.361452	+	0.932391i	$0.617719\pi$
$602$	1.76656	0.0719998
$603$	4.08913	0.166522
$604$	11.6523	0.474127
$605$	−75.0198	−3.04999
$606$	−8.98116	−0.364835
$607$	−0.533826	−0.0216673	−0.0108337	−	0.999941i	$-0.503449\pi$
$607$	−0.533826	−0.0216673	−0.0108337	+	0.999941i	$0.503449\pi$
$608$	−3.10460	−0.125908
$609$	−1.53076	−0.0620295
$610$	−56.0888	−2.27097
$611$	30.2174	1.22247
$612$	0.0910249	0.00367946
$613$	−34.8632	−1.40811	−0.704055	−	0.710145i	$-0.748629\pi$
$613$	−34.8632	−1.40811	−0.704055	+	0.710145i	$0.748629\pi$
$614$	−9.86792	−0.398237
$615$	−64.4927	−2.60060
$616$	1.66684	0.0671588
$617$	−15.5333	−0.625349	−0.312674	−	0.949860i	$-0.601225\pi$
$617$	−15.5333	−0.625349	−0.312674	+	0.949860i	$0.601225\pi$
$618$	33.8424	1.36134
$619$	−3.45239	−0.138763	−0.0693816	−	0.997590i	$-0.522103\pi$
$619$	−3.45239	−0.138763	−0.0693816	+	0.997590i	$0.522103\pi$
$620$	34.5151	1.38616
$621$	4.86880	0.195378
$622$	−0.834950	−0.0334785
$623$	4.30992	0.172673
$624$	−9.88747	−0.395816
$625$	12.5131	0.500526
$626$	−2.61195	−0.104395
$627$	31.5421	1.25967
$628$	−1.72683	−0.0689080
$629$	2.26569	0.0903388
$630$	0.374954	0.0149385
$631$	11.6456	0.463602	0.231801	−	0.972763i	$-0.425538\pi$
$631$	11.6456	0.463602	0.231801	+	0.972763i	$0.425538\pi$
$632$	7.61916	0.303074
$633$	31.6815	1.25923
$634$	−5.97828	−0.237428
$635$	0.789518	0.0313311
$636$	22.1772	0.879383
$637$	−37.4241	−1.48280
$638$	15.5773	0.616713
$639$	1.79566	0.0710352
$640$	3.75704	0.148510
$641$	−1.32691	−0.0524099	−0.0262049	−	0.999657i	$-0.508342\pi$
$641$	−1.32691	−0.0524099	−0.0262049	+	0.999657i	$0.508342\pi$
$642$	−6.15294	−0.242837
$643$	−10.1083	−0.398631	−0.199316	−	0.979935i	$-0.563872\pi$
$643$	−10.1083	−0.398631	−0.199316	+	0.979935i	$0.563872\pi$
$644$	0.299528	0.0118031
$645$	−40.4546	−1.59290
$646$	−0.848150	−0.0333700
$647$	21.8679	0.859714	0.429857	−	0.902897i	$-0.358564\pi$
$647$	21.8679	0.859714	0.429857	+	0.902897i	$0.358564\pi$
$648$	9.88856	0.388459
$649$	76.9806	3.02175
$650$	−49.3662	−1.93630
$651$	5.02378	0.196898
$652$	−19.1912	−0.751585
$653$	−26.5214	−1.03786	−0.518930	−	0.854817i	$-0.673670\pi$
$653$	−26.5214	−1.03786	−0.518930	+	0.854817i	$0.673670\pi$
$654$	−24.2539	−0.948402
$655$	3.75704	0.146800
$656$	−9.40230	−0.367098
$657$	−3.25584	−0.127022
$658$	−1.67125	−0.0651519
$659$	1.32641	0.0516694	0.0258347	−	0.999666i	$-0.491776\pi$
$659$	1.32641	0.0516694	0.0258347	+	0.999666i	$0.491776\pi$
$660$	−38.1708	−1.48580
$661$	28.6213	1.11324	0.556621	−	0.830767i	$-0.312098\pi$
$661$	28.6213	1.11324	0.556621	+	0.830767i	$0.312098\pi$
$662$	4.28335	0.166477
$663$	−2.70117	−0.104905
$664$	−5.22664	−0.202833
$665$	−3.49374	−0.135481
$666$	−2.76329	−0.107075
$667$	2.79923	0.108387
$668$	−15.8437	−0.613012
$669$	38.4071	1.48491
$670$	46.1088	1.78134
$671$	83.0778	3.20718
$672$	0.546850	0.0210952
$673$	−11.8040	−0.455010	−0.227505	−	0.973777i	$-0.573057\pi$
$673$	−11.8040	−0.455010	−0.227505	+	0.973777i	$0.573057\pi$
$674$	−18.5667	−0.715162
$675$	44.3809	1.70822
$676$	16.3299	0.628072
$677$	−35.9747	−1.38262	−0.691311	−	0.722557i	$-0.742966\pi$
$677$	−35.9747	−1.38262	−0.691311	+	0.722557i	$0.742966\pi$
$678$	−24.9514	−0.958251
$679$	−2.70703	−0.103886
$680$	1.02639	0.0393603
$681$	−44.7287	−1.71401
$682$	−51.1232	−1.95761
$683$	30.7899	1.17814	0.589071	−	0.808081i	$-0.299494\pi$
$683$	30.7899	1.17814	0.589071	+	0.808081i	$0.299494\pi$
$684$	1.03443	0.0395523
$685$	21.2692	0.812653
$686$	4.16653	0.159079
$687$	8.94786	0.341382
$688$	−5.89782	−0.224852
$689$	−65.7857	−2.50624
$690$	−6.85924	−0.261127
$691$	0.252449	0.00960360	0.00480180	−	0.999988i	$-0.498472\pi$
$691$	0.252449	0.00960360	0.00480180	+	0.999988i	$0.498472\pi$
$692$	3.83641	0.145838
$693$	−0.555375	−0.0210970
$694$	−6.21782	−0.236025
$695$	−19.9729	−0.757616
$696$	5.11056	0.193715
$697$	−2.56863	−0.0972937
$698$	14.7812	0.559478
$699$	36.2007	1.36924
$700$	2.73031	0.103196
$701$	34.7458	1.31233	0.656166	−	0.754617i	$-0.272177\pi$
$701$	34.7458	1.31233	0.656166	+	0.754617i	$0.272177\pi$
$702$	−26.3680	−0.995196
$703$	25.7477	0.971094
$704$	−5.56487	−0.209734
$705$	38.2717	1.44140
$706$	19.8284	0.746250
$707$	−1.47347	−0.0554154
$708$	25.2555	0.949161
$709$	−16.8748	−0.633747	−0.316873	−	0.948468i	$-0.602633\pi$
$709$	−16.8748	−0.633747	−0.316873	+	0.948468i	$0.602633\pi$
$710$	20.2478	0.759885
$711$	−2.53864	−0.0952063
$712$	−14.3890	−0.539251
$713$	−9.18677	−0.344047
$714$	0.149395	0.00559095
$715$	113.229	4.23451
$716$	17.6108	0.658145
$717$	−28.6394	−1.06956
$718$	−7.13914	−0.266430
$719$	40.5004	1.51041	0.755205	−	0.655488i	$-0.227537\pi$
$719$	40.5004	1.51041	0.755205	+	0.655488i	$0.227537\pi$
$720$	−1.25181	−0.0466523
$721$	5.55224	0.206776
$722$	9.36144	0.348397
$723$	29.6339	1.10210
$724$	15.8496	0.589044
$725$	25.5160	0.947641
$726$	36.4552	1.35298
$727$	−15.7963	−0.585852	−0.292926	−	0.956135i	$-0.594629\pi$
$727$	−15.7963	−0.585852	−0.292926	+	0.956135i	$0.594629\pi$
$728$	−1.62216	−0.0601212
$729$	23.3722	0.865636
$730$	−36.7126	−1.35879
$731$	−1.61123	−0.0595936
$732$	27.2559	1.00741
$733$	−41.4551	−1.53118	−0.765590	−	0.643329i	$-0.777553\pi$
$733$	−41.4551	−1.53118	−0.765590	+	0.643329i	$0.777553\pi$
$734$	11.1841	0.412814
$735$	−47.3993	−1.74835
$736$	−1.00000	−0.0368605
$737$	−68.2956	−2.51570
$738$	3.13276	0.115319
$739$	8.43532	0.310298	0.155149	−	0.987891i	$-0.450414\pi$
$739$	8.43532	0.310298	0.155149	+	0.987891i	$0.450414\pi$
$740$	−31.1587	−1.14542
$741$	−30.6967	−1.12767
$742$	3.63844	0.133571
$743$	−2.77388	−0.101764	−0.0508819	−	0.998705i	$-0.516203\pi$
$743$	−2.77388	−0.101764	−0.0508819	+	0.998705i	$0.516203\pi$
$744$	−16.7723	−0.614903
$745$	−1.72150	−0.0630710
$746$	−13.4973	−0.494172
$747$	1.74147	0.0637171
$748$	−1.52027	−0.0555867
$749$	−1.00946	−0.0368850
$750$	−28.2283	−1.03075
$751$	12.1700	0.444088	0.222044	−	0.975037i	$-0.428727\pi$
$751$	12.1700	0.444088	0.222044	+	0.975037i	$0.428727\pi$
$752$	5.57959	0.203467
$753$	13.8889	0.506138
$754$	−15.1598	−0.552088
$755$	−43.7784	−1.59326
$756$	1.45834	0.0530395
$757$	−5.85800	−0.212913	−0.106456	−	0.994317i	$-0.533950\pi$
$757$	−5.85800	−0.212913	−0.106456	+	0.994317i	$0.533950\pi$
$758$	−2.49750	−0.0907132
$759$	10.1598	0.368777
$760$	11.6641	0.423102
$761$	−5.58163	−0.202334	−0.101167	−	0.994869i	$-0.532258\pi$
$761$	−5.58163	−0.202334	−0.101167	+	0.994869i	$0.532258\pi$
$762$	−0.383660	−0.0138985
$763$	−3.97914	−0.144055
$764$	−16.0477	−0.580587
$765$	−0.341984	−0.0123645
$766$	2.33445	0.0843471
$767$	−74.9172	−2.70510
$768$	−1.82570	−0.0658794
$769$	−4.09751	−0.147760	−0.0738801	−	0.997267i	$-0.523538\pi$
$769$	−4.09751	−0.147760	−0.0738801	+	0.997267i	$0.523538\pi$
$770$	−6.26238	−0.225680
$771$	40.4183	1.45563
$772$	3.17234	0.114175
$773$	35.0397	1.26029	0.630145	−	0.776477i	$-0.282995\pi$
$773$	35.0397	1.26029	0.630145	+	0.776477i	$0.282995\pi$
$774$	1.96510	0.0706340
$775$	−83.7408	−3.00806
$776$	9.03763	0.324432
$777$	−4.53525	−0.162701
$778$	14.1827	0.508474
$779$	−29.1904	−1.04586
$780$	37.1477	1.33010
$781$	−29.9906	−1.07315
$782$	−0.273191	−0.00976930
$783$	13.6289	0.487057
$784$	−6.91028	−0.246796
$785$	6.48777	0.231558
$786$	−1.82570	−0.0651207
$787$	−42.9392	−1.53062	−0.765309	−	0.643663i	$-0.777414\pi$
$787$	−42.9392	−1.53062	−0.765309	+	0.643663i	$0.777414\pi$
$788$	22.9023	0.815861
$789$	20.2484	0.720863
$790$	−28.6255	−1.01845
$791$	−4.09357	−0.145551
$792$	1.85417	0.0658849
$793$	−80.8509	−2.87110
$794$	−38.4821	−1.36568
$795$	−83.3207	−2.95508
$796$	−2.65675	−0.0941659
$797$	25.9654	0.919741	0.459871	−	0.887986i	$-0.347896\pi$
$797$	25.9654	0.919741	0.459871	+	0.887986i	$0.347896\pi$
$798$	1.69775	0.0600998
$799$	1.52429	0.0539257
$800$	−9.11537	−0.322277
$801$	4.79429	0.169398
$802$	−14.5965	−0.515421
$803$	54.3781	1.91896
$804$	−22.4062	−0.790205
$805$	−1.12534	−0.0396631
$806$	49.7528	1.75247
$807$	−22.6691	−0.797992
$808$	4.91929	0.173060
$809$	−20.8376	−0.732611	−0.366306	−	0.930495i	$-0.619378\pi$
$809$	−20.8376	−0.732611	−0.366306	+	0.930495i	$0.619378\pi$
$810$	−37.1517	−1.30538
$811$	5.20889	0.182909	0.0914545	−	0.995809i	$-0.470848\pi$
$811$	5.20889	0.182909	0.0914545	+	0.995809i	$0.470848\pi$
$812$	0.838449	0.0294238
$813$	−34.7089	−1.21729
$814$	46.1517	1.61762
$815$	72.1021	2.52563
$816$	−0.498766	−0.0174603
$817$	−18.3104	−0.640599
$818$	−29.7648	−1.04070
$819$	0.540489	0.0188862
$820$	35.3249	1.23360
$821$	11.7575	0.410339	0.205170	−	0.978726i	$-0.434225\pi$
$821$	11.7575	0.410339	0.205170	+	0.978726i	$0.434225\pi$
$822$	−10.3356	−0.360494
$823$	30.9326	1.07824	0.539121	−	0.842229i	$-0.318757\pi$
$823$	30.9326	1.07824	0.539121	+	0.842229i	$0.318757\pi$
$824$	−18.5366	−0.645754
$825$	92.6104	3.22428
$826$	4.14347	0.144170
$827$	49.5521	1.72310	0.861548	−	0.507676i	$-0.169495\pi$
$827$	49.5521	1.72310	0.861548	+	0.507676i	$0.169495\pi$
$828$	0.333191	0.0115792
$829$	18.8899	0.656073	0.328037	−	0.944665i	$-0.393613\pi$
$829$	18.8899	0.656073	0.328037	+	0.944665i	$0.393613\pi$
$830$	19.6367	0.681601
$831$	−52.0722	−1.80637
$832$	5.41571	0.187756
$833$	−1.88783	−0.0654094
$834$	9.70567	0.336080
$835$	59.5256	2.05997
$836$	−17.2767	−0.597528
$837$	−44.7285	−1.54604
$838$	19.1729	0.662317
$839$	−18.3627	−0.633952	−0.316976	−	0.948434i	$-0.602667\pi$
$839$	−18.3627	−0.633952	−0.316976	+	0.948434i	$0.602667\pi$
$840$	−2.05454	−0.0708883
$841$	−21.1643	−0.729804
$842$	37.8026	1.30276
$843$	21.5867	0.743485
$844$	−17.3531	−0.597317
$845$	−61.3521	−2.11058
$846$	−1.85907	−0.0639161
$847$	5.98092	0.205507
$848$	−12.1472	−0.417137
$849$	−12.7086	−0.436159
$850$	−2.49024	−0.0854145
$851$	8.29341	0.284294
$852$	−9.83922	−0.337086
$853$	−44.9356	−1.53856	−0.769282	−	0.638909i	$-0.779386\pi$
$853$	−44.9356	−1.53856	−0.769282	+	0.638909i	$0.779386\pi$
$854$	4.47165	0.153017
$855$	−3.88638	−0.132911
$856$	3.37018	0.115190
$857$	26.8623	0.917597	0.458799	−	0.888540i	$-0.348280\pi$
$857$	26.8623	0.917597	0.458799	+	0.888540i	$0.348280\pi$
$858$	−55.0225	−1.87844
$859$	−40.2782	−1.37427	−0.687137	−	0.726528i	$-0.741133\pi$
$859$	−40.2782	−1.37427	−0.687137	+	0.726528i	$0.741133\pi$
$860$	22.1583	0.755593
$861$	5.14165	0.175227
$862$	−23.0393	−0.784720
$863$	50.1546	1.70728	0.853642	−	0.520860i	$-0.174389\pi$
$863$	50.1546	1.70728	0.853642	+	0.520860i	$0.174389\pi$
$864$	−4.86880	−0.165640
$865$	−14.4136	−0.490075
$866$	4.19441	0.142532
$867$	30.9007	1.04944
$868$	−2.75170	−0.0933987
$869$	42.3997	1.43831
$870$	−19.2006	−0.650961
$871$	66.4650	2.25208
$872$	13.2847	0.449876
$873$	−3.01126	−0.101916
$874$	−3.10460	−0.105015
$875$	−4.63120	−0.156563
$876$	17.8402	0.602764
$877$	6.66589	0.225091	0.112546	−	0.993647i	$-0.464100\pi$
$877$	6.66589	0.225091	0.112546	+	0.993647i	$0.464100\pi$
$878$	15.5912	0.526176
$879$	8.45410	0.285150
$880$	20.9075	0.704790
$881$	−38.3080	−1.29063	−0.645315	−	0.763917i	$-0.723274\pi$
$881$	−38.3080	−1.29063	−0.645315	+	0.763917i	$0.723274\pi$
$882$	2.30244	0.0775273
$883$	51.4443	1.73124	0.865620	−	0.500702i	$-0.166925\pi$
$883$	51.4443	1.73124	0.865620	+	0.500702i	$0.166925\pi$
$884$	1.47952	0.0497618
$885$	−94.8861	−3.18956
$886$	−1.19813	−0.0402519
$887$	−7.78946	−0.261544	−0.130772	−	0.991412i	$-0.541746\pi$
$887$	−7.78946	−0.261544	−0.130772	+	0.991412i	$0.541746\pi$
$888$	15.1413	0.508109
$889$	−0.0629440	−0.00211107
$890$	54.0601	1.81210
$891$	55.0285	1.84353
$892$	−21.0369	−0.704368
$893$	17.3224	0.579672
$894$	0.836550	0.0279784
$895$	−66.1644	−2.21163
$896$	−0.299528	−0.0100065
$897$	−9.88747	−0.330133
$898$	33.3653	1.11342
$899$	−25.7159	−0.857672
$900$	3.03716	0.101239
$901$	−3.31851	−0.110556
$902$	−52.3226	−1.74215
$903$	3.22522	0.107329
$904$	13.6667	0.454548
$905$	−59.5475	−1.97942
$906$	21.2737	0.706772
$907$	−21.4342	−0.711709	−0.355855	−	0.934541i	$-0.615810\pi$
$907$	−21.4342	−0.711709	−0.355855	+	0.934541i	$0.615810\pi$
$908$	24.4995	0.813043
$909$	−1.63906	−0.0543643
$910$	6.09452	0.202031
$911$	8.34991	0.276645	0.138322	−	0.990387i	$-0.455829\pi$
$911$	8.34991	0.276645	0.138322	+	0.990387i	$0.455829\pi$
$912$	−5.66808	−0.187689
$913$	−29.0856	−0.962593
$914$	−21.1733	−0.700350
$915$	−102.401	−3.38529
$916$	−4.90105	−0.161935
$917$	−0.299528	−0.00989130
$918$	−1.33011	−0.0439003
$919$	−1.37593	−0.0453877	−0.0226938	−	0.999742i	$-0.507224\pi$
$919$	−1.37593	−0.0453877	−0.0226938	+	0.999742i	$0.507224\pi$
$920$	3.75704	0.123866
$921$	−18.0159	−0.593644
$922$	−30.3950	−1.00100
$923$	29.1868	0.960694
$924$	3.04315	0.100112
$925$	75.5975	2.48563
$926$	4.67251	0.153548
$927$	6.17624	0.202854
$928$	−2.79923	−0.0918892
$929$	31.9927	1.04965	0.524823	−	0.851211i	$-0.324132\pi$
$929$	31.9927	1.04965	0.524823	+	0.851211i	$0.324132\pi$
$930$	63.0143	2.06632
$931$	−21.4537	−0.703116
$932$	−19.8284	−0.649500
$933$	−1.52437	−0.0499057
$934$	0.395464	0.0129400
$935$	5.71173	0.186794
$936$	−1.80447	−0.0589808
$937$	14.7353	0.481383	0.240691	−	0.970602i	$-0.422626\pi$
$937$	14.7353	0.481383	0.240691	+	0.970602i	$0.422626\pi$
$938$	−3.67600	−0.120026
$939$	−4.76865	−0.155619
$940$	−20.9627	−0.683729
$941$	−48.1466	−1.56954	−0.784768	−	0.619790i	$-0.787218\pi$
$941$	−48.1466	−1.56954	−0.784768	+	0.619790i	$0.787218\pi$
$942$	−3.15268	−0.102720
$943$	−9.40230	−0.306181
$944$	−13.8333	−0.450236
$945$	−5.47906	−0.178234
$946$	−32.8206	−1.06709
$947$	58.2212	1.89194	0.945968	−	0.324261i	$-0.105115\pi$
$947$	58.2212	1.89194	0.945968	+	0.324261i	$0.105115\pi$
$948$	13.9103	0.451786
$949$	−52.9205	−1.71787
$950$	−28.2996	−0.918161
$951$	−10.9146	−0.353929
$952$	−0.0818286	−0.00265208
$953$	−34.4615	−1.11632	−0.558158	−	0.829735i	$-0.688492\pi$
$953$	−34.4615	−1.11632	−0.558158	+	0.829735i	$0.688492\pi$
$954$	4.04734	0.131038
$955$	60.2920	1.95100
$956$	15.6868	0.507346
$957$	28.4396	0.919322
$958$	−18.6516	−0.602607
$959$	−1.69567	−0.0547561
$960$	6.85924	0.221381
$961$	53.3967	1.72247
$962$	−44.9147	−1.44811
$963$	−1.12291	−0.0361854
$964$	−16.2315	−0.522781
$965$	−11.9186	−0.383674
$966$	0.546850	0.0175946
$967$	−21.9628	−0.706277	−0.353138	−	0.935571i	$-0.614886\pi$
$967$	−21.9628	−0.706277	−0.353138	+	0.935571i	$0.614886\pi$
$968$	−19.9678	−0.641789
$969$	−1.54847	−0.0497440
$970$	−33.9548	−1.09022
$971$	2.69028	0.0863353	0.0431676	−	0.999068i	$-0.486255\pi$
$971$	2.69028	0.0863353	0.0431676	+	0.999068i	$0.486255\pi$
$972$	3.44716	0.110568
$973$	1.59233	0.0510478
$974$	−3.40051	−0.108959
$975$	−90.1280	−2.88641
$976$	−14.9290	−0.477865
$977$	−0.476949	−0.0152590	−0.00762948	−	0.999971i	$-0.502429\pi$
$977$	−0.476949	−0.0152590	−0.00762948	+	0.999971i	$0.502429\pi$
$978$	−35.0374	−1.12037
$979$	−80.0730	−2.55914
$980$	25.9622	0.829333
$981$	−4.42634	−0.141322
$982$	0.435564	0.0138994
$983$	23.9348	0.763401	0.381701	−	0.924286i	$-0.375339\pi$
$983$	23.9348	0.763401	0.381701	+	0.924286i	$0.375339\pi$
$984$	−17.1658	−0.547226
$985$	−86.0450	−2.74162
$986$	−0.764725	−0.0243538
$987$	−3.05120	−0.0971207
$988$	16.8136	0.534912
$989$	−5.89782	−0.187540
$990$	−6.96618	−0.221400
$991$	−36.4046	−1.15643	−0.578216	−	0.815884i	$-0.696251\pi$
$991$	−36.4046	−1.15643	−0.578216	+	0.815884i	$0.696251\pi$
$992$	9.18677	0.291680
$993$	7.82012	0.248164
$994$	−1.61424	−0.0512007
$995$	9.98151	0.316435
$996$	−9.54230	−0.302359
$997$	−11.6534	−0.369066	−0.184533	−	0.982826i	$-0.559077\pi$
$997$	−11.6534	−0.369066	−0.184533	+	0.982826i	$0.559077\pi$
$998$	−18.9085	−0.598538
$999$	40.3789	1.27753

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.j.1.8	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.j.1.8	✓	33	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.82570 q^{3} +1.00000 q^{4} -3.75704 q^{5} +1.82570 q^{6} +0.299528 q^{7} -1.00000 q^{8} +0.333191 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.82570 q^{3} +1.00000 q^{4} -3.75704 q^{5} +1.82570 q^{6} +0.299528 q^{7} -1.00000 q^{8} +0.333191 q^{9} +3.75704 q^{10} -5.56487 q^{11} -1.82570 q^{12} +5.41571 q^{13} -0.299528 q^{14} +6.85924 q^{15} +1.00000 q^{16} +0.273191 q^{17} -0.333191 q^{18} +3.10460 q^{19} -3.75704 q^{20} -0.546850 q^{21} +5.56487 q^{22} +1.00000 q^{23} +1.82570 q^{24} +9.11537 q^{25} -5.41571 q^{26} +4.86880 q^{27} +0.299528 q^{28} +2.79923 q^{29} -6.85924 q^{30} -9.18677 q^{31} -1.00000 q^{32} +10.1598 q^{33} -0.273191 q^{34} -1.12534 q^{35} +0.333191 q^{36} +8.29341 q^{37} -3.10460 q^{38} -9.88747 q^{39} +3.75704 q^{40} -9.40230 q^{41} +0.546850 q^{42} -5.89782 q^{43} -5.56487 q^{44} -1.25181 q^{45} -1.00000 q^{46} +5.57959 q^{47} -1.82570 q^{48} -6.91028 q^{49} -9.11537 q^{50} -0.498766 q^{51} +5.41571 q^{52} -12.1472 q^{53} -4.86880 q^{54} +20.9075 q^{55} -0.299528 q^{56} -5.66808 q^{57} -2.79923 q^{58} -13.8333 q^{59} +6.85924 q^{60} -14.9290 q^{61} +9.18677 q^{62} +0.0998002 q^{63} +1.00000 q^{64} -20.3470 q^{65} -10.1598 q^{66} +12.2726 q^{67} +0.273191 q^{68} -1.82570 q^{69} +1.12534 q^{70} +5.38928 q^{71} -0.333191 q^{72} -9.77168 q^{73} -8.29341 q^{74} -16.6420 q^{75} +3.10460 q^{76} -1.66684 q^{77} +9.88747 q^{78} -7.61916 q^{79} -3.75704 q^{80} -9.88856 q^{81} +9.40230 q^{82} +5.22664 q^{83} -0.546850 q^{84} -1.02639 q^{85} +5.89782 q^{86} -5.11056 q^{87} +5.56487 q^{88} +14.3890 q^{89} +1.25181 q^{90} +1.62216 q^{91} +1.00000 q^{92} +16.7723 q^{93} -5.57959 q^{94} -11.6641 q^{95} +1.82570 q^{96} -9.03763 q^{97} +6.91028 q^{98} -1.85417 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9 + 4 * q^10 + 5 * q^11 + 3 * q^12 + 15 * q^13 - 11 * q^14 + 16 * q^15 + 33 * q^16 + 2 * q^17 - 44 * q^18 + 32 * q^19 - 4 * q^20 + 8 * q^21 - 5 * q^22 + 33 * q^23 - 3 * q^24 + 49 * q^25 - 15 * q^26 + 15 * q^27 + 11 * q^28 + 20 * q^29 - 16 * q^30 + 25 * q^31 - 33 * q^32 - 6 * q^33 - 2 * q^34 + 15 * q^35 + 44 * q^36 + 6 * q^37 - 32 * q^38 + 25 * q^39 + 4 * q^40 + 2 * q^41 - 8 * q^42 + 31 * q^43 + 5 * q^44 + 2 * q^45 - 33 * q^46 + 4 * q^47 + 3 * q^48 + 72 * q^49 - 49 * q^50 + 26 * q^51 + 15 * q^52 - 65 * q^53 - 15 * q^54 - 4 * q^55 - 11 * q^56 + 12 * q^57 - 20 * q^58 + 8 * q^59 + 16 * q^60 + 23 * q^61 - 25 * q^62 - 14 * q^63 + 33 * q^64 + 5 * q^65 + 6 * q^66 + 31 * q^67 + 2 * q^68 + 3 * q^69 - 15 * q^70 + 20 * q^71 - 44 * q^72 + 22 * q^73 - 6 * q^74 - 32 * q^75 + 32 * q^76 + 2 * q^77 - 25 * q^78 + 53 * q^79 - 4 * q^80 + 17 * q^81 - 2 * q^82 + 45 * q^83 + 8 * q^84 + 60 * q^85 - 31 * q^86 + 11 * q^87 - 5 * q^88 - 54 * q^89 - 2 * q^90 + 38 * q^91 + 33 * q^92 + 63 * q^93 - 4 * q^94 + 44 * q^95 - 3 * q^96 - 72 * q^98 + 43 * q^99

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