LMFDB - Embedded newform 6026.2.a.j.1.14

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			1.14
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.909549 q^{3} +1.00000 q^{4} +0.734986 q^{5} +0.909549 q^{6} +5.27401 q^{7} -1.00000 q^{8} -2.17272 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.909549 q^{3} +1.00000 q^{4} +0.734986 q^{5} +0.909549 q^{6} +5.27401 q^{7} -1.00000 q^{8} -2.17272 q^{9} -0.734986 q^{10} +2.39968 q^{11} -0.909549 q^{12} +3.37941 q^{13} -5.27401 q^{14} -0.668506 q^{15} +1.00000 q^{16} -0.0921942 q^{17} +2.17272 q^{18} -0.769922 q^{19} +0.734986 q^{20} -4.79697 q^{21} -2.39968 q^{22} +1.00000 q^{23} +0.909549 q^{24} -4.45980 q^{25} -3.37941 q^{26} +4.70484 q^{27} +5.27401 q^{28} -1.18871 q^{29} +0.668506 q^{30} +6.49005 q^{31} -1.00000 q^{32} -2.18262 q^{33} +0.0921942 q^{34} +3.87632 q^{35} -2.17272 q^{36} +7.95985 q^{37} +0.769922 q^{38} -3.07374 q^{39} -0.734986 q^{40} -1.03871 q^{41} +4.79697 q^{42} -1.18581 q^{43} +2.39968 q^{44} -1.59692 q^{45} -1.00000 q^{46} -10.6159 q^{47} -0.909549 q^{48} +20.8152 q^{49} +4.45980 q^{50} +0.0838552 q^{51} +3.37941 q^{52} +6.70761 q^{53} -4.70484 q^{54} +1.76373 q^{55} -5.27401 q^{56} +0.700282 q^{57} +1.18871 q^{58} -6.08440 q^{59} -0.668506 q^{60} -10.6020 q^{61} -6.49005 q^{62} -11.4590 q^{63} +1.00000 q^{64} +2.48382 q^{65} +2.18262 q^{66} +7.09957 q^{67} -0.0921942 q^{68} -0.909549 q^{69} -3.87632 q^{70} -5.87499 q^{71} +2.17272 q^{72} +14.8382 q^{73} -7.95985 q^{74} +4.05640 q^{75} -0.769922 q^{76} +12.6559 q^{77} +3.07374 q^{78} +11.7498 q^{79} +0.734986 q^{80} +2.23888 q^{81} +1.03871 q^{82} +4.09777 q^{83} -4.79697 q^{84} -0.0677615 q^{85} +1.18581 q^{86} +1.08119 q^{87} -2.39968 q^{88} +13.2737 q^{89} +1.59692 q^{90} +17.8231 q^{91} +1.00000 q^{92} -5.90302 q^{93} +10.6159 q^{94} -0.565882 q^{95} +0.909549 q^{96} +2.83124 q^{97} -20.8152 q^{98} -5.21383 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.909549	−0.525128	−0.262564	−	0.964915i	$-0.584568\pi$
$3$	−0.909549	−0.525128	−0.262564	+	0.964915i	$0.584568\pi$
$4$	1.00000	0.500000
$5$	0.734986	0.328696	0.164348	−	0.986402i	$-0.447448\pi$
$5$	0.734986	0.328696	0.164348	+	0.986402i	$0.447448\pi$
$6$	0.909549	0.371322
$7$	5.27401	1.99339	0.996694	−	0.0812419i	$-0.0258886\pi$
$7$	5.27401	1.99339	0.996694	+	0.0812419i	$0.0258886\pi$
$8$	−1.00000	−0.353553
$9$	−2.17272	−0.724240
$10$	−0.734986	−0.232423
$11$	2.39968	0.723530	0.361765	−	0.932269i	$-0.382174\pi$
$11$	2.39968	0.723530	0.361765	+	0.932269i	$0.382174\pi$
$12$	−0.909549	−0.262564
$13$	3.37941	0.937281	0.468640	−	0.883389i	$-0.344744\pi$
$13$	3.37941	0.937281	0.468640	+	0.883389i	$0.344744\pi$
$14$	−5.27401	−1.40954
$15$	−0.668506	−0.172607
$16$	1.00000	0.250000
$17$	−0.0921942	−0.0223604	−0.0111802	−	0.999937i	$-0.503559\pi$
$17$	−0.0921942	−0.0223604	−0.0111802	+	0.999937i	$0.503559\pi$
$18$	2.17272	0.512115
$19$	−0.769922	−0.176632	−0.0883161	−	0.996092i	$-0.528149\pi$
$19$	−0.769922	−0.176632	−0.0883161	+	0.996092i	$0.528149\pi$
$20$	0.734986	0.164348
$21$	−4.79697	−1.04679
$22$	−2.39968	−0.511613
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0.909549	0.185661
$25$	−4.45980	−0.891959
$26$	−3.37941	−0.662757
$27$	4.70484	0.905447
$28$	5.27401	0.996694
$29$	−1.18871	−0.220738	−0.110369	−	0.993891i	$-0.535203\pi$
$29$	−1.18871	−0.220738	−0.110369	+	0.993891i	$0.535203\pi$
$30$	0.668506	0.122052
$31$	6.49005	1.16565	0.582824	−	0.812599i	$-0.301948\pi$
$31$	6.49005	1.16565	0.582824	+	0.812599i	$0.301948\pi$
$32$	−1.00000	−0.176777
$33$	−2.18262	−0.379946
$34$	0.0921942	0.0158112
$35$	3.87632	0.655218
$36$	−2.17272	−0.362120
$37$	7.95985	1.30859	0.654295	−	0.756239i	$-0.272965\pi$
$37$	7.95985	1.30859	0.654295	+	0.756239i	$0.272965\pi$
$38$	0.769922	0.124898
$39$	−3.07374	−0.492193
$40$	−0.734986	−0.116211
$41$	−1.03871	−0.162220	−0.0811098	−	0.996705i	$-0.525846\pi$
$41$	−1.03871	−0.162220	−0.0811098	+	0.996705i	$0.525846\pi$
$42$	4.79697	0.740189
$43$	−1.18581	−0.180834	−0.0904170	−	0.995904i	$-0.528820\pi$
$43$	−1.18581	−0.180834	−0.0904170	+	0.995904i	$0.528820\pi$
$44$	2.39968	0.361765
$45$	−1.59692	−0.238055
$46$	−1.00000	−0.147442
$47$	−10.6159	−1.54848	−0.774240	−	0.632891i	$-0.781868\pi$
$47$	−10.6159	−1.54848	−0.774240	+	0.632891i	$0.781868\pi$
$48$	−0.909549	−0.131282
$49$	20.8152	2.97360
$50$	4.45980	0.630710
$51$	0.0838552	0.0117421
$52$	3.37941	0.468640
$53$	6.70761	0.921362	0.460681	−	0.887566i	$-0.347605\pi$
$53$	6.70761	0.921362	0.460681	+	0.887566i	$0.347605\pi$
$54$	−4.70484	−0.640248
$55$	1.76373	0.237821
$56$	−5.27401	−0.704769
$57$	0.700282	0.0927546
$58$	1.18871	0.156086
$59$	−6.08440	−0.792122	−0.396061	−	0.918224i	$-0.629623\pi$
$59$	−6.08440	−0.792122	−0.396061	+	0.918224i	$0.629623\pi$
$60$	−0.668506	−0.0863037
$61$	−10.6020	−1.35745	−0.678725	−	0.734393i	$-0.737467\pi$
$61$	−10.6020	−1.35745	−0.678725	+	0.734393i	$0.737467\pi$
$62$	−6.49005	−0.824237
$63$	−11.4590	−1.44369
$64$	1.00000	0.125000
$65$	2.48382	0.308080
$66$	2.18262	0.268662
$67$	7.09957	0.867351	0.433675	−	0.901069i	$-0.357216\pi$
$67$	7.09957	0.867351	0.433675	+	0.901069i	$0.357216\pi$
$68$	−0.0921942	−0.0111802
$69$	−0.909549	−0.109497
$70$	−3.87632	−0.463309
$71$	−5.87499	−0.697233	−0.348616	−	0.937266i	$-0.613348\pi$
$71$	−5.87499	−0.697233	−0.348616	+	0.937266i	$0.613348\pi$
$72$	2.17272	0.256058
$73$	14.8382	1.73668	0.868339	−	0.495971i	$-0.165188\pi$
$73$	14.8382	1.73668	0.868339	+	0.495971i	$0.165188\pi$
$74$	−7.95985	−0.925314
$75$	4.05640	0.468393
$76$	−0.769922	−0.0883161
$77$	12.6559	1.44228
$78$	3.07374	0.348033
$79$	11.7498	1.32196	0.660979	−	0.750404i	$-0.270141\pi$
$79$	11.7498	1.32196	0.660979	+	0.750404i	$0.270141\pi$
$80$	0.734986	0.0821739
$81$	2.23888	0.248764
$82$	1.03871	0.114707
$83$	4.09777	0.449788	0.224894	−	0.974383i	$-0.427796\pi$
$83$	4.09777	0.449788	0.224894	+	0.974383i	$0.427796\pi$
$84$	−4.79697	−0.523393
$85$	−0.0677615	−0.00734976
$86$	1.18581	0.127869
$87$	1.08119	0.115916
$88$	−2.39968	−0.255806
$89$	13.2737	1.40701	0.703504	−	0.710692i	$-0.251618\pi$
$89$	13.2737	1.40701	0.703504	+	0.710692i	$0.251618\pi$
$90$	1.59692	0.168330
$91$	17.8231	1.86836
$92$	1.00000	0.104257
$93$	−5.90302	−0.612114
$94$	10.6159	1.09494
$95$	−0.565882	−0.0580583
$96$	0.909549	0.0928305
$97$	2.83124	0.287469	0.143734	−	0.989616i	$-0.454089\pi$
$97$	2.83124	0.287469	0.143734	+	0.989616i	$0.454089\pi$
$98$	−20.8152	−2.10265
$99$	−5.21383	−0.524009
$100$	−4.45980	−0.445980
$101$	1.23052	0.122441	0.0612207	−	0.998124i	$-0.480501\pi$
$101$	1.23052	0.122441	0.0612207	+	0.998124i	$0.480501\pi$
$102$	−0.0838552	−0.00830290
$103$	−1.35453	−0.133465	−0.0667327	−	0.997771i	$-0.521257\pi$
$103$	−1.35453	−0.133465	−0.0667327	+	0.997771i	$0.521257\pi$
$104$	−3.37941	−0.331379
$105$	−3.52571	−0.344074
$106$	−6.70761	−0.651501
$107$	6.28074	0.607182	0.303591	−	0.952802i	$-0.401814\pi$
$107$	6.28074	0.607182	0.303591	+	0.952802i	$0.401814\pi$
$108$	4.70484	0.452724
$109$	−0.499922	−0.0478838	−0.0239419	−	0.999713i	$-0.507622\pi$
$109$	−0.499922	−0.0478838	−0.0239419	+	0.999713i	$0.507622\pi$
$110$	−1.76373	−0.168165
$111$	−7.23987	−0.687178
$112$	5.27401	0.498347
$113$	0.140966	0.0132610	0.00663051	−	0.999978i	$-0.497889\pi$
$113$	0.140966	0.0132610	0.00663051	+	0.999978i	$0.497889\pi$
$114$	−0.700282	−0.0655874
$115$	0.734986	0.0685378
$116$	−1.18871	−0.110369
$117$	−7.34252	−0.678816
$118$	6.08440	0.560115
$119$	−0.486233	−0.0445729
$120$	0.668506	0.0610259
$121$	−5.24155	−0.476505
$122$	10.6020	0.959862
$123$	0.944759	0.0851861
$124$	6.49005	0.582824
$125$	−6.95282	−0.621879
$126$	11.4590	1.02084
$127$	−2.07972	−0.184546	−0.0922729	−	0.995734i	$-0.529413\pi$
$127$	−2.07972	−0.184546	−0.0922729	+	0.995734i	$0.529413\pi$
$128$	−1.00000	−0.0883883
$129$	1.07855	0.0949610
$130$	−2.48382	−0.217846
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−2.18262	−0.189973
$133$	−4.06058	−0.352097
$134$	−7.09957	−0.613309
$135$	3.45799	0.297617
$136$	0.0921942	0.00790559
$137$	−5.66428	−0.483932	−0.241966	−	0.970285i	$-0.577792\pi$
$137$	−5.66428	−0.483932	−0.241966	+	0.970285i	$0.577792\pi$
$138$	0.909549	0.0774260
$139$	−21.2326	−1.80092	−0.900461	−	0.434937i	$-0.856771\pi$
$139$	−21.2326	−1.80092	−0.900461	+	0.434937i	$0.856771\pi$
$140$	3.87632	0.327609
$141$	9.65564	0.813151
$142$	5.87499	0.493018
$143$	8.10950	0.678150
$144$	−2.17272	−0.181060
$145$	−0.873687	−0.0725558
$146$	−14.8382	−1.22802
$147$	−18.9324	−1.56152
$148$	7.95985	0.654295
$149$	−5.70702	−0.467537	−0.233769	−	0.972292i	$-0.575106\pi$
$149$	−5.70702	−0.467537	−0.233769	+	0.972292i	$0.575106\pi$
$150$	−4.05640	−0.331204
$151$	7.06173	0.574675	0.287338	−	0.957829i	$-0.407230\pi$
$151$	7.06173	0.574675	0.287338	+	0.957829i	$0.407230\pi$
$152$	0.769922	0.0624489
$153$	0.200312	0.0161943
$154$	−12.6559	−1.01984
$155$	4.77010	0.383143
$156$	−3.07374	−0.246096
$157$	1.12675	0.0899241	0.0449620	−	0.998989i	$-0.485683\pi$
$157$	1.12675	0.0899241	0.0449620	+	0.998989i	$0.485683\pi$
$158$	−11.7498	−0.934765
$159$	−6.10090	−0.483833
$160$	−0.734986	−0.0581057
$161$	5.27401	0.415650
$162$	−2.23888	−0.175903
$163$	−7.45161	−0.583655	−0.291828	−	0.956471i	$-0.594263\pi$
$163$	−7.45161	−0.583655	−0.291828	+	0.956471i	$0.594263\pi$
$164$	−1.03871	−0.0811098
$165$	−1.60420	−0.124887
$166$	−4.09777	−0.318048
$167$	−18.2902	−1.41534	−0.707668	−	0.706545i	$-0.750253\pi$
$167$	−18.2902	−1.41534	−0.707668	+	0.706545i	$0.750253\pi$
$168$	4.79697	0.370094
$169$	−1.57957	−0.121505
$170$	0.0677615	0.00519707
$171$	1.67283	0.127924
$172$	−1.18581	−0.0904170
$173$	22.4982	1.71050	0.855252	−	0.518212i	$-0.173402\pi$
$173$	22.4982	1.71050	0.855252	+	0.518212i	$0.173402\pi$
$174$	−1.08119	−0.0819650
$175$	−23.5210	−1.77802
$176$	2.39968	0.180882
$177$	5.53406	0.415966
$178$	−13.2737	−0.994905
$179$	6.70109	0.500863	0.250432	−	0.968134i	$-0.419427\pi$
$179$	6.70109	0.500863	0.250432	+	0.968134i	$0.419427\pi$
$180$	−1.59692	−0.119027
$181$	−24.3084	−1.80683	−0.903415	−	0.428767i	$-0.858948\pi$
$181$	−24.3084	−1.80683	−0.903415	+	0.428767i	$0.858948\pi$
$182$	−17.8231	−1.32113
$183$	9.64306	0.712835
$184$	−1.00000	−0.0737210
$185$	5.85038	0.430128
$186$	5.90302	0.432830
$187$	−0.221236	−0.0161784
$188$	−10.6159	−0.774240
$189$	24.8134	1.80491
$190$	0.565882	0.0410534
$191$	−11.4573	−0.829021	−0.414510	−	0.910045i	$-0.636047\pi$
$191$	−11.4573	−0.829021	−0.414510	+	0.910045i	$0.636047\pi$
$192$	−0.909549	−0.0656410
$193$	−7.88746	−0.567752	−0.283876	−	0.958861i	$-0.591620\pi$
$193$	−7.88746	−0.567752	−0.283876	+	0.958861i	$0.591620\pi$
$194$	−2.83124	−0.203271
$195$	−2.25916	−0.161782
$196$	20.8152	1.48680
$197$	18.1333	1.29194	0.645972	−	0.763361i	$-0.276452\pi$
$197$	18.1333	1.29194	0.645972	+	0.763361i	$0.276452\pi$
$198$	5.21383	0.370531
$199$	9.95726	0.705852	0.352926	−	0.935651i	$-0.385187\pi$
$199$	9.95726	0.705852	0.352926	+	0.935651i	$0.385187\pi$
$200$	4.45980	0.315355
$201$	−6.45741	−0.455470
$202$	−1.23052	−0.0865792
$203$	−6.26928	−0.440018
$204$	0.0838552	0.00587104
$205$	−0.763439	−0.0533209
$206$	1.35453	0.0943743
$207$	−2.17272	−0.151015
$208$	3.37941	0.234320
$209$	−1.84756	−0.127799
$210$	3.52571	0.243297
$211$	−3.94509	−0.271591	−0.135796	−	0.990737i	$-0.543359\pi$
$211$	−3.94509	−0.271591	−0.135796	+	0.990737i	$0.543359\pi$
$212$	6.70761	0.460681
$213$	5.34359	0.366137
$214$	−6.28074	−0.429343
$215$	−0.871552	−0.0594393
$216$	−4.70484	−0.320124
$217$	34.2286	2.32359
$218$	0.499922	0.0338590
$219$	−13.4961	−0.911979
$220$	1.76373	0.118911
$221$	−0.311562	−0.0209580
$222$	7.23987	0.485908
$223$	8.32478	0.557469	0.278734	−	0.960368i	$-0.410085\pi$
$223$	8.32478	0.557469	0.278734	+	0.960368i	$0.410085\pi$
$224$	−5.27401	−0.352385
$225$	9.68989	0.645993
$226$	−0.140966	−0.00937695
$227$	3.47534	0.230666	0.115333	−	0.993327i	$-0.463206\pi$
$227$	3.47534	0.230666	0.115333	+	0.993327i	$0.463206\pi$
$228$	0.700282	0.0463773
$229$	11.4478	0.756495	0.378247	−	0.925705i	$-0.376527\pi$
$229$	11.4478	0.756495	0.378247	+	0.925705i	$0.376527\pi$
$230$	−0.734986	−0.0484635
$231$	−11.5112	−0.757380
$232$	1.18871	0.0780428
$233$	27.1588	1.77923	0.889616	−	0.456709i	$-0.150972\pi$
$233$	27.1588	1.77923	0.889616	+	0.456709i	$0.150972\pi$
$234$	7.34252	0.479996
$235$	−7.80250	−0.508979
$236$	−6.08440	−0.396061
$237$	−10.6870	−0.694198
$238$	0.486233	0.0315178
$239$	3.02649	0.195767	0.0978837	−	0.995198i	$-0.468793\pi$
$239$	3.02649	0.195767	0.0978837	+	0.995198i	$0.468793\pi$
$240$	−0.668506	−0.0431519
$241$	−5.13542	−0.330801	−0.165401	−	0.986226i	$-0.552892\pi$
$241$	−5.13542	−0.330801	−0.165401	+	0.986226i	$0.552892\pi$
$242$	5.24155	0.336940
$243$	−16.1509	−1.03608
$244$	−10.6020	−0.678725
$245$	15.2989	0.977409
$246$	−0.944759	−0.0602357
$247$	−2.60188	−0.165554
$248$	−6.49005	−0.412119
$249$	−3.72712	−0.236197
$250$	6.95282	0.439735
$251$	−0.783930	−0.0494812	−0.0247406	−	0.999694i	$-0.507876\pi$
$251$	−0.783930	−0.0494812	−0.0247406	+	0.999694i	$0.507876\pi$
$252$	−11.4590	−0.721846
$253$	2.39968	0.150866
$254$	2.07972	0.130494
$255$	0.0616324	0.00385957
$256$	1.00000	0.0625000
$257$	0.358210	0.0223445	0.0111723	−	0.999938i	$-0.496444\pi$
$257$	0.358210	0.0223445	0.0111723	+	0.999938i	$0.496444\pi$
$258$	−1.07855	−0.0671476
$259$	41.9803	2.60853
$260$	2.48382	0.154040
$261$	2.58274	0.159868
$262$	1.00000	0.0617802
$263$	−16.6762	−1.02830	−0.514149	−	0.857701i	$-0.671892\pi$
$263$	−16.6762	−1.02830	−0.514149	+	0.857701i	$0.671892\pi$
$264$	2.18262	0.134331
$265$	4.93000	0.302848
$266$	4.06058	0.248970
$267$	−12.0731	−0.738860
$268$	7.09957	0.433675
$269$	−30.5365	−1.86184	−0.930921	−	0.365221i	$-0.880993\pi$
$269$	−30.5365	−1.86184	−0.930921	+	0.365221i	$0.880993\pi$
$270$	−3.45799	−0.210447
$271$	22.7263	1.38052	0.690262	−	0.723560i	$-0.257495\pi$
$271$	22.7263	1.38052	0.690262	+	0.723560i	$0.257495\pi$
$272$	−0.0921942	−0.00559010
$273$	−16.2109	−0.981131
$274$	5.66428	0.342191
$275$	−10.7021	−0.645359
$276$	−0.909549	−0.0547484
$277$	−8.55547	−0.514048	−0.257024	−	0.966405i	$-0.582742\pi$
$277$	−8.55547	−0.514048	−0.257024	+	0.966405i	$0.582742\pi$
$278$	21.2326	1.27344
$279$	−14.1011	−0.844209
$280$	−3.87632	−0.231655
$281$	−24.0429	−1.43428	−0.717140	−	0.696929i	$-0.754549\pi$
$281$	−24.0429	−1.43428	−0.717140	+	0.696929i	$0.754549\pi$
$282$	−9.65564	−0.574985
$283$	−12.0489	−0.716232	−0.358116	−	0.933677i	$-0.616581\pi$
$283$	−12.0489	−0.716232	−0.358116	+	0.933677i	$0.616581\pi$
$284$	−5.87499	−0.348616
$285$	0.514697	0.0304880
$286$	−8.10950	−0.479525
$287$	−5.47818	−0.323367
$288$	2.17272	0.128029
$289$	−16.9915	−0.999500
$290$	0.873687	0.0513047
$291$	−2.57515	−0.150958
$292$	14.8382	0.868339
$293$	−1.56649	−0.0915156	−0.0457578	−	0.998953i	$-0.514570\pi$
$293$	−1.56649	−0.0915156	−0.0457578	+	0.998953i	$0.514570\pi$
$294$	18.9324	1.10416
$295$	−4.47195	−0.260367
$296$	−7.95985	−0.462657
$297$	11.2901	0.655118
$298$	5.70702	0.330599
$299$	3.37941	0.195437
$300$	4.05640	0.234197
$301$	−6.25396	−0.360472
$302$	−7.06173	−0.406357
$303$	−1.11922	−0.0642975
$304$	−0.769922	−0.0441581
$305$	−7.79234	−0.446188
$306$	−0.200312	−0.0114511
$307$	21.8839	1.24898	0.624489	−	0.781034i	$-0.285307\pi$
$307$	21.8839	1.24898	0.624489	+	0.781034i	$0.285307\pi$
$308$	12.6559	0.721138
$309$	1.23201	0.0700865
$310$	−4.77010	−0.270923
$311$	−20.2829	−1.15014	−0.575069	−	0.818105i	$-0.695025\pi$
$311$	−20.2829	−1.15014	−0.575069	+	0.818105i	$0.695025\pi$
$312$	3.07374	0.174016
$313$	32.7559	1.85147	0.925736	−	0.378169i	$-0.123446\pi$
$313$	32.7559	1.85147	0.925736	+	0.378169i	$0.123446\pi$
$314$	−1.12675	−0.0635859
$315$	−8.42217	−0.474535
$316$	11.7498	0.660979
$317$	22.4101	1.25868	0.629339	−	0.777131i	$-0.283326\pi$
$317$	22.4101	1.25868	0.629339	+	0.777131i	$0.283326\pi$
$318$	6.10090	0.342122
$319$	−2.85253	−0.159711
$320$	0.734986	0.0410870
$321$	−5.71264	−0.318849
$322$	−5.27401	−0.293909
$323$	0.0709824	0.00394957
$324$	2.23888	0.124382
$325$	−15.0715	−0.836016
$326$	7.45161	0.412707
$327$	0.454703	0.0251452
$328$	1.03871	0.0573533
$329$	−55.9881	−3.08672
$330$	1.60420	0.0883082
$331$	17.4954	0.961636	0.480818	−	0.876821i	$-0.340340\pi$
$331$	17.4954	0.961636	0.480818	+	0.876821i	$0.340340\pi$
$332$	4.09777	0.224894
$333$	−17.2945	−0.947734
$334$	18.2902	1.00079
$335$	5.21808	0.285094
$336$	−4.79697	−0.261696
$337$	14.2293	0.775122	0.387561	−	0.921844i	$-0.373318\pi$
$337$	14.2293	0.775122	0.387561	+	0.921844i	$0.373318\pi$
$338$	1.57957	0.0859171
$339$	−0.128216	−0.00696373
$340$	−0.0677615	−0.00367488
$341$	15.5740	0.843380
$342$	−1.67283	−0.0904560
$343$	72.8615	3.93415
$344$	1.18581	0.0639344
$345$	−0.668506	−0.0359911
$346$	−22.4982	−1.20951
$347$	−10.2551	−0.550523	−0.275261	−	0.961369i	$-0.588764\pi$
$347$	−10.2551	−0.550523	−0.275261	+	0.961369i	$0.588764\pi$
$348$	1.08119	0.0579580
$349$	−13.1773	−0.705367	−0.352683	−	0.935743i	$-0.614731\pi$
$349$	−13.1773	−0.705367	−0.352683	+	0.935743i	$0.614731\pi$
$350$	23.5210	1.25725
$351$	15.8996	0.848658
$352$	−2.39968	−0.127903
$353$	6.86772	0.365532	0.182766	−	0.983156i	$-0.441495\pi$
$353$	6.86772	0.365532	0.182766	+	0.983156i	$0.441495\pi$
$354$	−5.53406	−0.294132
$355$	−4.31803	−0.229177
$356$	13.2737	0.703504
$357$	0.442253	0.0234065
$358$	−6.70109	−0.354164
$359$	14.2120	0.750081	0.375041	−	0.927008i	$-0.377629\pi$
$359$	14.2120	0.750081	0.375041	+	0.927008i	$0.377629\pi$
$360$	1.59692	0.0841650
$361$	−18.4072	−0.968801
$362$	24.3084	1.27762
$363$	4.76745	0.250226
$364$	17.8231	0.934182
$365$	10.9059	0.570839
$366$	−9.64306	−0.504051
$367$	−4.15571	−0.216926	−0.108463	−	0.994100i	$-0.534593\pi$
$367$	−4.15571	−0.216926	−0.108463	+	0.994100i	$0.534593\pi$
$368$	1.00000	0.0521286
$369$	2.25683	0.117486
$370$	−5.85038	−0.304147
$371$	35.3760	1.83663
$372$	−5.90302	−0.306057
$373$	25.8762	1.33982	0.669911	−	0.742442i	$-0.266332\pi$
$373$	25.8762	1.33982	0.669911	+	0.742442i	$0.266332\pi$
$374$	0.221236	0.0114399
$375$	6.32393	0.326566
$376$	10.6159	0.547471
$377$	−4.01715	−0.206894
$378$	−24.8134	−1.27626
$379$	6.99865	0.359497	0.179748	−	0.983713i	$-0.442472\pi$
$379$	6.99865	0.359497	0.179748	+	0.983713i	$0.442472\pi$
$380$	−0.565882	−0.0290291
$381$	1.89161	0.0969102
$382$	11.4573	0.586206
$383$	−7.39907	−0.378075	−0.189037	−	0.981970i	$-0.560537\pi$
$383$	−7.39907	−0.378075	−0.189037	+	0.981970i	$0.560537\pi$
$384$	0.909549	0.0464152
$385$	9.30192	0.474070
$386$	7.88746	0.401461
$387$	2.57643	0.130967
$388$	2.83124	0.143734
$389$	−5.13411	−0.260310	−0.130155	−	0.991494i	$-0.541547\pi$
$389$	−5.13411	−0.260310	−0.130155	+	0.991494i	$0.541547\pi$
$390$	2.25916	0.114397
$391$	−0.0921942	−0.00466246
$392$	−20.8152	−1.05133
$393$	0.909549	0.0458807
$394$	−18.1333	−0.913542
$395$	8.63595	0.434522
$396$	−5.21383	−0.262005
$397$	−14.7764	−0.741609	−0.370804	−	0.928711i	$-0.620918\pi$
$397$	−14.7764	−0.741609	−0.370804	+	0.928711i	$0.620918\pi$
$398$	−9.95726	−0.499112
$399$	3.69329	0.184896
$400$	−4.45980	−0.222990
$401$	−28.1495	−1.40572	−0.702859	−	0.711330i	$-0.748093\pi$
$401$	−28.1495	−1.40572	−0.702859	+	0.711330i	$0.748093\pi$
$402$	6.45741	0.322066
$403$	21.9326	1.09254
$404$	1.23052	0.0612207
$405$	1.64554	0.0817677
$406$	6.26928	0.311139
$407$	19.1011	0.946804
$408$	−0.0838552	−0.00415145
$409$	26.2831	1.29961	0.649807	−	0.760099i	$-0.274850\pi$
$409$	26.2831	1.29961	0.649807	+	0.760099i	$0.274850\pi$
$410$	0.763439	0.0377035
$411$	5.15194	0.254126
$412$	−1.35453	−0.0667327
$413$	−32.0892	−1.57901
$414$	2.17272	0.106783
$415$	3.01180	0.147844
$416$	−3.37941	−0.165689
$417$	19.3121	0.945715
$418$	1.84756	0.0903673
$419$	19.6102	0.958022	0.479011	−	0.877809i	$-0.340995\pi$
$419$	19.6102	0.958022	0.479011	+	0.877809i	$0.340995\pi$
$420$	−3.52571	−0.172037
$421$	24.4239	1.19035	0.595175	−	0.803596i	$-0.297083\pi$
$421$	24.4239	1.19035	0.595175	+	0.803596i	$0.297083\pi$
$422$	3.94509	0.192044
$423$	23.0653	1.12147
$424$	−6.70761	−0.325750
$425$	0.411167	0.0199446
$426$	−5.34359	−0.258898
$427$	−55.9152	−2.70592
$428$	6.28074	0.303591
$429$	−7.37599	−0.356116
$430$	0.871552	0.0420300
$431$	21.8803	1.05394	0.526969	−	0.849884i	$-0.323328\pi$
$431$	21.8803	1.05394	0.526969	+	0.849884i	$0.323328\pi$
$432$	4.70484	0.226362
$433$	13.0149	0.625457	0.312729	−	0.949843i	$-0.398757\pi$
$433$	13.0149	0.625457	0.312729	+	0.949843i	$0.398757\pi$
$434$	−34.2286	−1.64303
$435$	0.794661	0.0381011
$436$	−0.499922	−0.0239419
$437$	−0.769922	−0.0368304
$438$	13.4961	0.644867
$439$	6.90581	0.329596	0.164798	−	0.986327i	$-0.447303\pi$
$439$	6.90581	0.329596	0.164798	+	0.986327i	$0.447303\pi$
$440$	−1.76373	−0.0840825
$441$	−45.2256	−2.15360
$442$	0.311562	0.0148195
$443$	−13.2565	−0.629833	−0.314917	−	0.949119i	$-0.601977\pi$
$443$	−13.2565	−0.629833	−0.314917	+	0.949119i	$0.601977\pi$
$444$	−7.23987	−0.343589
$445$	9.75597	0.462477
$446$	−8.32478	−0.394190
$447$	5.19082	0.245517
$448$	5.27401	0.249174
$449$	24.3778	1.15046	0.575229	−	0.817993i	$-0.304913\pi$
$449$	24.3778	1.15046	0.575229	+	0.817993i	$0.304913\pi$
$450$	−9.68989	−0.456786
$451$	−2.49257	−0.117371
$452$	0.140966	0.00663051
$453$	−6.42299	−0.301778
$454$	−3.47534	−0.163106
$455$	13.0997	0.614123
$456$	−0.700282	−0.0327937
$457$	−33.3649	−1.56075	−0.780373	−	0.625315i	$-0.784971\pi$
$457$	−33.3649	−1.56075	−0.780373	+	0.625315i	$0.784971\pi$
$458$	−11.4478	−0.534923
$459$	−0.433759	−0.0202462
$460$	0.734986	0.0342689
$461$	−29.2897	−1.36416	−0.682078	−	0.731280i	$-0.738923\pi$
$461$	−29.2897	−1.36416	−0.682078	+	0.731280i	$0.738923\pi$
$462$	11.5112	0.535549
$463$	12.4436	0.578304	0.289152	−	0.957283i	$-0.406627\pi$
$463$	12.4436	0.578304	0.289152	+	0.957283i	$0.406627\pi$
$464$	−1.18871	−0.0551846
$465$	−4.33864	−0.201199
$466$	−27.1588	−1.25811
$467$	−17.9771	−0.831881	−0.415940	−	0.909392i	$-0.636547\pi$
$467$	−17.9771	−0.831881	−0.415940	+	0.909392i	$0.636547\pi$
$468$	−7.34252	−0.339408
$469$	37.4432	1.72897
$470$	7.80250	0.359903
$471$	−1.02483	−0.0472217
$472$	6.08440	0.280057
$473$	−2.84555	−0.130839
$474$	10.6870	0.490872
$475$	3.43369	0.157549
$476$	−0.486233	−0.0222865
$477$	−14.5738	−0.667287
$478$	−3.02649	−0.138428
$479$	19.5428	0.892933	0.446467	−	0.894800i	$-0.352682\pi$
$479$	19.5428	0.892933	0.446467	+	0.894800i	$0.352682\pi$
$480$	0.668506	0.0305130
$481$	26.8996	1.22652
$482$	5.13542	0.233912
$483$	−4.79697	−0.218270
$484$	−5.24155	−0.238252
$485$	2.08092	0.0944897
$486$	16.1509	0.732620
$487$	1.93393	0.0876349	0.0438175	−	0.999040i	$-0.486048\pi$
$487$	1.93393	0.0876349	0.0438175	+	0.999040i	$0.486048\pi$
$488$	10.6020	0.479931
$489$	6.77761	0.306494
$490$	−15.2989	−0.691133
$491$	17.7887	0.802791	0.401396	−	0.915905i	$-0.368525\pi$
$491$	17.7887	0.802791	0.401396	+	0.915905i	$0.368525\pi$
$492$	0.944759	0.0425930
$493$	0.109592	0.00493580
$494$	2.60188	0.117064
$495$	−3.83209	−0.172240
$496$	6.49005	0.291412
$497$	−30.9847	−1.38986
$498$	3.72712	0.167016
$499$	−5.64124	−0.252536	−0.126268	−	0.991996i	$-0.540300\pi$
$499$	−5.64124	−0.252536	−0.126268	+	0.991996i	$0.540300\pi$
$500$	−6.95282	−0.310939
$501$	16.6358	0.743233
$502$	0.783930	0.0349885
$503$	24.4144	1.08858	0.544292	−	0.838896i	$-0.316798\pi$
$503$	24.4144	1.08858	0.544292	+	0.838896i	$0.316798\pi$
$504$	11.4590	0.510422
$505$	0.904416	0.0402460
$506$	−2.39968	−0.106679
$507$	1.43669	0.0638058
$508$	−2.07972	−0.0922729
$509$	27.0070	1.19706	0.598532	−	0.801099i	$-0.295751\pi$
$509$	27.0070	1.19706	0.598532	+	0.801099i	$0.295751\pi$
$510$	−0.0616324	−0.00272913
$511$	78.2568	3.46188
$512$	−1.00000	−0.0441942
$513$	−3.62236	−0.159931
$514$	−0.358210	−0.0158000
$515$	−0.995558	−0.0438695
$516$	1.07855	0.0474805
$517$	−25.4746	−1.12037
$518$	−41.9803	−1.84451
$519$	−20.4632	−0.898234
$520$	−2.48382	−0.108923
$521$	−15.1432	−0.663434	−0.331717	−	0.943379i	$-0.607628\pi$
$521$	−15.1432	−0.663434	−0.331717	+	0.943379i	$0.607628\pi$
$522$	−2.58274	−0.113043
$523$	−7.32852	−0.320454	−0.160227	−	0.987080i	$-0.551223\pi$
$523$	−7.32852	−0.320454	−0.160227	+	0.987080i	$0.551223\pi$
$524$	−1.00000	−0.0436852
$525$	21.3935	0.933689
$526$	16.6762	0.727117
$527$	−0.598345	−0.0260643
$528$	−2.18262	−0.0949865
$529$	1.00000	0.0434783
$530$	−4.93000	−0.214146
$531$	13.2197	0.573687
$532$	−4.06058	−0.176048
$533$	−3.51024	−0.152045
$534$	12.0731	0.522453
$535$	4.61626	0.199578
$536$	−7.09957	−0.306655
$537$	−6.09497	−0.263017
$538$	30.5365	1.31652
$539$	49.9497	2.15149
$540$	3.45799	0.148808
$541$	−0.651772	−0.0280219	−0.0140109	−	0.999902i	$-0.504460\pi$
$541$	−0.651772	−0.0280219	−0.0140109	+	0.999902i	$0.504460\pi$
$542$	−22.7263	−0.976177
$543$	22.1097	0.948818
$544$	0.0921942	0.00395280
$545$	−0.367435	−0.0157392
$546$	16.2109	0.693765
$547$	2.40619	0.102881	0.0514407	−	0.998676i	$-0.483619\pi$
$547$	2.40619	0.102881	0.0514407	+	0.998676i	$0.483619\pi$
$548$	−5.66428	−0.241966
$549$	23.0352	0.983120
$550$	10.7021	0.456338
$551$	0.915216	0.0389895
$552$	0.909549	0.0387130
$553$	61.9687	2.63518
$554$	8.55547	0.363487
$555$	−5.32120	−0.225873
$556$	−21.2326	−0.900461
$557$	24.2238	1.02640	0.513198	−	0.858270i	$-0.328461\pi$
$557$	24.2238	1.02640	0.513198	+	0.858270i	$0.328461\pi$
$558$	14.1011	0.596946
$559$	−4.00733	−0.169492
$560$	3.87632	0.163805
$561$	0.201225	0.00849574
$562$	24.0429	1.01419
$563$	14.2703	0.601420	0.300710	−	0.953716i	$-0.402776\pi$
$563$	14.2703	0.601420	0.300710	+	0.953716i	$0.402776\pi$
$564$	9.65564	0.406576
$565$	0.103608	0.00435884
$566$	12.0489	0.506452
$567$	11.8079	0.495884
$568$	5.87499	0.246509
$569$	5.24234	0.219770	0.109885	−	0.993944i	$-0.464952\pi$
$569$	5.24234	0.219770	0.109885	+	0.993944i	$0.464952\pi$
$570$	−0.514697	−0.0215583
$571$	0.294542	0.0123262	0.00616310	−	0.999981i	$-0.498038\pi$
$571$	0.294542	0.0123262	0.00616310	+	0.999981i	$0.498038\pi$
$572$	8.10950	0.339075
$573$	10.4210	0.435342
$574$	5.47818	0.228655
$575$	−4.45980	−0.185986
$576$	−2.17272	−0.0905300
$577$	−46.1363	−1.92068	−0.960340	−	0.278831i	$-0.910053\pi$
$577$	−46.1363	−1.92068	−0.960340	+	0.278831i	$0.910053\pi$
$578$	16.9915	0.706753
$579$	7.17403	0.298143
$580$	−0.873687	−0.0362779
$581$	21.6117	0.896603
$582$	2.57515	0.106743
$583$	16.0961	0.666632
$584$	−14.8382	−0.614008
$585$	−5.39665	−0.223124
$586$	1.56649	0.0647113
$587$	23.6586	0.976497	0.488248	−	0.872705i	$-0.337636\pi$
$587$	23.6586	0.976497	0.488248	+	0.872705i	$0.337636\pi$
$588$	−18.9324	−0.780761
$589$	−4.99683	−0.205891
$590$	4.47195	0.184107
$591$	−16.4931	−0.678436
$592$	7.95985	0.327148
$593$	9.28349	0.381227	0.190614	−	0.981665i	$-0.438952\pi$
$593$	9.28349	0.381227	0.190614	+	0.981665i	$0.438952\pi$
$594$	−11.2901	−0.463238
$595$	−0.357375	−0.0146509
$596$	−5.70702	−0.233769
$597$	−9.05662	−0.370663
$598$	−3.37941	−0.138194
$599$	−45.1507	−1.84481	−0.922403	−	0.386228i	$-0.873778\pi$
$599$	−45.1507	−1.84481	−0.922403	+	0.386228i	$0.873778\pi$
$600$	−4.05640	−0.165602
$601$	−23.1374	−0.943795	−0.471897	−	0.881653i	$-0.656431\pi$
$601$	−23.1374	−0.943795	−0.471897	+	0.881653i	$0.656431\pi$
$602$	6.25396	0.254892
$603$	−15.4254	−0.628170
$604$	7.06173	0.287338
$605$	−3.85247	−0.156625
$606$	1.11922	0.0454652
$607$	−20.1406	−0.817483	−0.408741	−	0.912650i	$-0.634032\pi$
$607$	−20.1406	−0.817483	−0.408741	+	0.912650i	$0.634032\pi$
$608$	0.769922	0.0312245
$609$	5.70222	0.231066
$610$	7.79234	0.315502
$611$	−35.8753	−1.45136
$612$	0.200312	0.00809715
$613$	22.3730	0.903637	0.451819	−	0.892110i	$-0.350775\pi$
$613$	22.3730	0.903637	0.451819	+	0.892110i	$0.350775\pi$
$614$	−21.8839	−0.883161
$615$	0.694385	0.0280003
$616$	−12.6559	−0.509922
$617$	−14.4780	−0.582861	−0.291430	−	0.956592i	$-0.594131\pi$
$617$	−14.4780	−0.582861	−0.291430	+	0.956592i	$0.594131\pi$
$618$	−1.23201	−0.0495586
$619$	41.3875	1.66351	0.831753	−	0.555146i	$-0.187338\pi$
$619$	41.3875	1.66351	0.831753	+	0.555146i	$0.187338\pi$
$620$	4.77010	0.191572
$621$	4.70484	0.188799
$622$	20.2829	0.813271
$623$	70.0055	2.80471
$624$	−3.07374	−0.123048
$625$	17.1888	0.687550
$626$	−32.7559	−1.30919
$627$	1.68045	0.0671107
$628$	1.12675	0.0449620
$629$	−0.733852	−0.0292606
$630$	8.42217	0.335547
$631$	48.4993	1.93073	0.965364	−	0.260908i	$-0.0840221\pi$
$631$	48.4993	1.93073	0.965364	+	0.260908i	$0.0840221\pi$
$632$	−11.7498	−0.467383
$633$	3.58825	0.142620
$634$	−22.4101	−0.890019
$635$	−1.52857	−0.0606594
$636$	−6.10090	−0.241917
$637$	70.3431	2.78710
$638$	2.85253	0.112933
$639$	12.7647	0.504964
$640$	−0.734986	−0.0290529
$641$	−5.97200	−0.235880	−0.117940	−	0.993021i	$-0.537629\pi$
$641$	−5.97200	−0.235880	−0.117940	+	0.993021i	$0.537629\pi$
$642$	5.71264	0.225460
$643$	48.6419	1.91825	0.959124	−	0.282985i	$-0.0913246\pi$
$643$	48.6419	1.91825	0.959124	+	0.282985i	$0.0913246\pi$
$644$	5.27401	0.207825
$645$	0.792719	0.0312133
$646$	−0.0709824	−0.00279276
$647$	5.91929	0.232711	0.116356	−	0.993208i	$-0.462879\pi$
$647$	5.91929	0.232711	0.116356	+	0.993208i	$0.462879\pi$
$648$	−2.23888	−0.0879514
$649$	−14.6006	−0.573124
$650$	15.0715	0.591153
$651$	−31.1326	−1.22018
$652$	−7.45161	−0.291828
$653$	−0.680104	−0.0266145	−0.0133073	−	0.999911i	$-0.504236\pi$
$653$	−0.680104	−0.0266145	−0.0133073	+	0.999911i	$0.504236\pi$
$654$	−0.454703	−0.0177803
$655$	−0.734986	−0.0287183
$656$	−1.03871	−0.0405549
$657$	−32.2392	−1.25777
$658$	55.9881	2.18264
$659$	20.8766	0.813238	0.406619	−	0.913598i	$-0.366708\pi$
$659$	20.8766	0.813238	0.406619	+	0.913598i	$0.366708\pi$
$660$	−1.60420	−0.0624433
$661$	26.4130	1.02735	0.513674	−	0.857985i	$-0.328284\pi$
$661$	26.4130	1.02735	0.513674	+	0.857985i	$0.328284\pi$
$662$	−17.4954	−0.679979
$663$	0.283381	0.0110056
$664$	−4.09777	−0.159024
$665$	−2.98447	−0.115733
$666$	17.2945	0.670149
$667$	−1.18871	−0.0460271
$668$	−18.2902	−0.707668
$669$	−7.57180	−0.292743
$670$	−5.21808	−0.201592
$671$	−25.4414	−0.982155
$672$	4.79697	0.185047
$673$	−35.0180	−1.34985	−0.674923	−	0.737888i	$-0.735823\pi$
$673$	−35.0180	−1.34985	−0.674923	+	0.737888i	$0.735823\pi$
$674$	−14.2293	−0.548094
$675$	−20.9826	−0.807622
$676$	−1.57957	−0.0607525
$677$	13.7888	0.529947	0.264974	−	0.964256i	$-0.414637\pi$
$677$	13.7888	0.529947	0.264974	+	0.964256i	$0.414637\pi$
$678$	0.128216	0.00492410
$679$	14.9320	0.573037
$680$	0.0677615	0.00259853
$681$	−3.16099	−0.121129
$682$	−15.5740	−0.596360
$683$	−14.0962	−0.539376	−0.269688	−	0.962948i	$-0.586921\pi$
$683$	−14.0962	−0.539376	−0.269688	+	0.962948i	$0.586921\pi$
$684$	1.67283	0.0639621
$685$	−4.16316	−0.159066
$686$	−72.8615	−2.78186
$687$	−10.4124	−0.397257
$688$	−1.18581	−0.0452085
$689$	22.6678	0.863574
$690$	0.668506	0.0254496
$691$	−21.7675	−0.828075	−0.414038	−	0.910260i	$-0.635882\pi$
$691$	−21.7675	−0.828075	−0.414038	+	0.910260i	$0.635882\pi$
$692$	22.4982	0.855252
$693$	−27.4978	−1.04455
$694$	10.2551	0.389278
$695$	−15.6056	−0.591955
$696$	−1.08119	−0.0409825
$697$	0.0957632	0.00362729
$698$	13.1773	0.498770
$699$	−24.7023	−0.934325
$700$	−23.5210	−0.889011
$701$	12.7922	0.483156	0.241578	−	0.970381i	$-0.422335\pi$
$701$	12.7922	0.483156	0.241578	+	0.970381i	$0.422335\pi$
$702$	−15.8996	−0.600092
$703$	−6.12846	−0.231139
$704$	2.39968	0.0904412
$705$	7.09676	0.267279
$706$	−6.86772	−0.258470
$707$	6.48978	0.244073
$708$	5.53406	0.207983
$709$	−2.44722	−0.0919071	−0.0459536	−	0.998944i	$-0.514633\pi$
$709$	−2.44722	−0.0919071	−0.0459536	+	0.998944i	$0.514633\pi$
$710$	4.31803	0.162053
$711$	−25.5291	−0.957415
$712$	−13.2737	−0.497452
$713$	6.49005	0.243054
$714$	−0.442253	−0.0165509
$715$	5.96037	0.222905
$716$	6.70109	0.250432
$717$	−2.75274	−0.102803
$718$	−14.2120	−0.530388
$719$	49.7415	1.85505	0.927523	−	0.373765i	$-0.121933\pi$
$719$	49.7415	1.85505	0.927523	+	0.373765i	$0.121933\pi$
$720$	−1.59692	−0.0595137
$721$	−7.14379	−0.266049
$722$	18.4072	0.685046
$723$	4.67092	0.173713
$724$	−24.3084	−0.903415
$725$	5.30142	0.196890
$726$	−4.76745	−0.176937
$727$	19.4111	0.719918	0.359959	−	0.932968i	$-0.382791\pi$
$727$	19.4111	0.719918	0.359959	+	0.932968i	$0.382791\pi$
$728$	−17.8231	−0.660567
$729$	7.97340	0.295311
$730$	−10.9059	−0.403644
$731$	0.109325	0.00404352
$732$	9.64306	0.356418
$733$	18.7936	0.694157	0.347078	−	0.937836i	$-0.387174\pi$
$733$	18.7936	0.694157	0.347078	+	0.937836i	$0.387174\pi$
$734$	4.15571	0.153390
$735$	−13.9151	−0.513265
$736$	−1.00000	−0.0368605
$737$	17.0367	0.627554
$738$	−2.25683	−0.0830751
$739$	−37.3753	−1.37487	−0.687437	−	0.726244i	$-0.741264\pi$
$739$	−37.3753	−1.37487	−0.687437	+	0.726244i	$0.741264\pi$
$740$	5.85038	0.215064
$741$	2.36654	0.0869371
$742$	−35.3760	−1.29869
$743$	−10.5212	−0.385984	−0.192992	−	0.981200i	$-0.561819\pi$
$743$	−10.5212	−0.385984	−0.192992	+	0.981200i	$0.561819\pi$
$744$	5.90302	0.216415
$745$	−4.19458	−0.153678
$746$	−25.8762	−0.947397
$747$	−8.90331	−0.325755
$748$	−0.221236	−0.00808920
$749$	33.1247	1.21035
$750$	−6.32393	−0.230917
$751$	37.1049	1.35398	0.676989	−	0.735993i	$-0.263285\pi$
$751$	37.1049	1.35398	0.676989	+	0.735993i	$0.263285\pi$
$752$	−10.6159	−0.387120
$753$	0.713023	0.0259840
$754$	4.01715	0.146296
$755$	5.19027	0.188893
$756$	24.8134	0.902454
$757$	−3.05572	−0.111062	−0.0555309	−	0.998457i	$-0.517685\pi$
$757$	−3.05572	−0.111062	−0.0555309	+	0.998457i	$0.517685\pi$
$758$	−6.99865	−0.254203
$759$	−2.18262	−0.0792242
$760$	0.565882	0.0205267
$761$	−40.1924	−1.45697	−0.728486	−	0.685061i	$-0.759776\pi$
$761$	−40.1924	−1.45697	−0.728486	+	0.685061i	$0.759776\pi$
$762$	−1.89161	−0.0685258
$763$	−2.63659	−0.0954511
$764$	−11.4573	−0.414510
$765$	0.147227	0.00532299
$766$	7.39907	0.267339
$767$	−20.5617	−0.742441
$768$	−0.909549	−0.0328205
$769$	34.0970	1.22957	0.614784	−	0.788696i	$-0.289243\pi$
$769$	34.0970	1.22957	0.614784	+	0.788696i	$0.289243\pi$
$770$	−9.30192	−0.335218
$771$	−0.325809	−0.0117337
$772$	−7.88746	−0.283876
$773$	−34.4838	−1.24030	−0.620148	−	0.784485i	$-0.712927\pi$
$773$	−34.4838	−1.24030	−0.620148	+	0.784485i	$0.712927\pi$
$774$	−2.57643	−0.0926078
$775$	−28.9443	−1.03971
$776$	−2.83124	−0.101635
$777$	−38.1832	−1.36981
$778$	5.13411	0.184067
$779$	0.799727	0.0286532
$780$	−2.25916	−0.0808908
$781$	−14.0981	−0.504469
$782$	0.0921942	0.00329686
$783$	−5.59271	−0.199867
$784$	20.8152	0.743400
$785$	0.828142	0.0295577
$786$	−0.909549	−0.0324425
$787$	−20.6315	−0.735433	−0.367717	−	0.929938i	$-0.619860\pi$
$787$	−20.6315	−0.735433	−0.367717	+	0.929938i	$0.619860\pi$
$788$	18.1333	0.645972
$789$	15.1678	0.539989
$790$	−8.63595	−0.307253
$791$	0.743459	0.0264343
$792$	5.21383	0.185265
$793$	−35.8286	−1.27231
$794$	14.7764	0.524397
$795$	−4.48408	−0.159034
$796$	9.95726	0.352926
$797$	−29.7310	−1.05312	−0.526562	−	0.850137i	$-0.676519\pi$
$797$	−29.7310	−1.05312	−0.526562	+	0.850137i	$0.676519\pi$
$798$	−3.69329	−0.130741
$799$	0.978720	0.0346246
$800$	4.45980	0.157678
$801$	−28.8400	−1.01901
$802$	28.1495	0.993992
$803$	35.6068	1.25654
$804$	−6.45741	−0.227735
$805$	3.87632	0.136622
$806$	−21.9326	−0.772541
$807$	27.7744	0.977706
$808$	−1.23052	−0.0432896
$809$	16.0003	0.562542	0.281271	−	0.959628i	$-0.409244\pi$
$809$	16.0003	0.562542	0.281271	+	0.959628i	$0.409244\pi$
$810$	−1.64554	−0.0578185
$811$	−19.7611	−0.693907	−0.346954	−	0.937882i	$-0.612784\pi$
$811$	−19.7611	−0.693907	−0.346954	+	0.937882i	$0.612784\pi$
$812$	−6.26928	−0.220009
$813$	−20.6707	−0.724952
$814$	−19.1011	−0.669492
$815$	−5.47683	−0.191845
$816$	0.0838552	0.00293552
$817$	0.912979	0.0319411
$818$	−26.2831	−0.918966
$819$	−38.7245	−1.35314
$820$	−0.763439	−0.0266604
$821$	21.1529	0.738240	0.369120	−	0.929382i	$-0.379659\pi$
$821$	21.1529	0.738240	0.369120	+	0.929382i	$0.379659\pi$
$822$	−5.15194	−0.179694
$823$	34.7313	1.21066	0.605328	−	0.795976i	$-0.293042\pi$
$823$	34.7313	1.21066	0.605328	+	0.795976i	$0.293042\pi$
$824$	1.35453	0.0471872
$825$	9.73405	0.338896
$826$	32.0892	1.11653
$827$	−21.5320	−0.748741	−0.374371	−	0.927279i	$-0.622141\pi$
$827$	−21.5320	−0.748741	−0.374371	+	0.927279i	$0.622141\pi$
$828$	−2.17272	−0.0755073
$829$	20.5728	0.714522	0.357261	−	0.934005i	$-0.383711\pi$
$829$	20.5728	0.714522	0.357261	+	0.934005i	$0.383711\pi$
$830$	−3.01180	−0.104541
$831$	7.78162	0.269941
$832$	3.37941	0.117160
$833$	−1.91904	−0.0664908
$834$	−19.3121	−0.668722
$835$	−13.4430	−0.465215
$836$	−1.84756	−0.0638993
$837$	30.5347	1.05543
$838$	−19.6102	−0.677424
$839$	−49.7553	−1.71774	−0.858871	−	0.512191i	$-0.828834\pi$
$839$	−49.7553	−1.71774	−0.858871	+	0.512191i	$0.828834\pi$
$840$	3.52571	0.121648
$841$	−27.5870	−0.951275
$842$	−24.4239	−0.841704
$843$	21.8682	0.753181
$844$	−3.94509	−0.135796
$845$	−1.16096	−0.0399382
$846$	−23.0653	−0.793001
$847$	−27.6440	−0.949859
$848$	6.70761	0.230340
$849$	10.9591	0.376114
$850$	−0.411167	−0.0141029
$851$	7.95985	0.272860
$852$	5.34359	0.183068
$853$	−4.35466	−0.149101	−0.0745503	−	0.997217i	$-0.523752\pi$
$853$	−4.35466	−0.149101	−0.0745503	+	0.997217i	$0.523752\pi$
$854$	55.9152	1.91338
$855$	1.22950	0.0420481
$856$	−6.28074	−0.214671
$857$	−24.4142	−0.833972	−0.416986	−	0.908913i	$-0.636914\pi$
$857$	−24.4142	−0.833972	−0.416986	+	0.908913i	$0.636914\pi$
$858$	7.37599	0.251812
$859$	17.0049	0.580199	0.290099	−	0.956997i	$-0.406312\pi$
$859$	17.0049	0.580199	0.290099	+	0.956997i	$0.406312\pi$
$860$	−0.871552	−0.0297197
$861$	4.98267	0.169809
$862$	−21.8803	−0.745247
$863$	19.7791	0.673289	0.336645	−	0.941632i	$-0.390708\pi$
$863$	19.7791	0.673289	0.336645	+	0.941632i	$0.390708\pi$
$864$	−4.70484	−0.160062
$865$	16.5358	0.562235
$866$	−13.0149	−0.442265
$867$	15.4546	0.524866
$868$	34.2286	1.16179
$869$	28.1958	0.956476
$870$	−0.794661	−0.0269415
$871$	23.9924	0.812951
$872$	0.499922	0.0169295
$873$	−6.15149	−0.208196
$874$	0.769922	0.0260430
$875$	−36.6692	−1.23965
$876$	−13.4961	−0.455990
$877$	7.66594	0.258860	0.129430	−	0.991589i	$-0.458685\pi$
$877$	7.66594	0.258860	0.129430	+	0.991589i	$0.458685\pi$
$878$	−6.90581	−0.233060
$879$	1.42480	0.0480574
$880$	1.76373	0.0594553
$881$	50.1252	1.68876	0.844380	−	0.535745i	$-0.179969\pi$
$881$	50.1252	1.68876	0.844380	+	0.535745i	$0.179969\pi$
$882$	45.2256	1.52283
$883$	25.9682	0.873899	0.436950	−	0.899486i	$-0.356059\pi$
$883$	25.9682	0.873899	0.436950	+	0.899486i	$0.356059\pi$
$884$	−0.311562	−0.0104790
$885$	4.06746	0.136726
$886$	13.2565	0.445359
$887$	−41.7788	−1.40279	−0.701397	−	0.712770i	$-0.747440\pi$
$887$	−41.7788	−1.40279	−0.701397	+	0.712770i	$0.747440\pi$
$888$	7.23987	0.242954
$889$	−10.9685	−0.367871
$890$	−9.75597	−0.327021
$891$	5.37258	0.179988
$892$	8.32478	0.278734
$893$	8.17338	0.273512
$894$	−5.19082	−0.173607
$895$	4.92521	0.164632
$896$	−5.27401	−0.176192
$897$	−3.07374	−0.102629
$898$	−24.3778	−0.813496
$899$	−7.71480	−0.257303
$900$	9.68989	0.322996
$901$	−0.618403	−0.0206020
$902$	2.49257	0.0829936
$903$	5.68828	0.189294
$904$	−0.140966	−0.00468848
$905$	−17.8663	−0.593897
$906$	6.42299	0.213390
$907$	−46.7546	−1.55246	−0.776230	−	0.630449i	$-0.782871\pi$
$907$	−46.7546	−1.55246	−0.776230	+	0.630449i	$0.782871\pi$
$908$	3.47534	0.115333
$909$	−2.67358	−0.0886770
$910$	−13.0997	−0.434251
$911$	21.6067	0.715861	0.357931	−	0.933748i	$-0.383482\pi$
$911$	21.6067	0.715861	0.357931	+	0.933748i	$0.383482\pi$
$912$	0.700282	0.0231886
$913$	9.83332	0.325435
$914$	33.3649	1.10361
$915$	7.08751	0.234306
$916$	11.4478	0.378247
$917$	−5.27401	−0.174163
$918$	0.433759	0.0143162
$919$	29.1031	0.960024	0.480012	−	0.877262i	$-0.340632\pi$
$919$	29.1031	0.960024	0.480012	+	0.877262i	$0.340632\pi$
$920$	−0.734986	−0.0242318
$921$	−19.9044	−0.655874
$922$	29.2897	0.964604
$923$	−19.8540	−0.653503
$924$	−11.5112	−0.378690
$925$	−35.4993	−1.16721
$926$	−12.4436	−0.408923
$927$	2.94301	0.0966611
$928$	1.18871	0.0390214
$929$	−30.8361	−1.01170	−0.505850	−	0.862622i	$-0.668821\pi$
$929$	−30.8361	−1.01170	−0.505850	+	0.862622i	$0.668821\pi$
$930$	4.33864	0.142269
$931$	−16.0261	−0.525233
$932$	27.1588	0.889616
$933$	18.4483	0.603970
$934$	17.9771	0.588228
$935$	−0.162606	−0.00531777
$936$	7.34252	0.239998
$937$	4.41783	0.144324	0.0721620	−	0.997393i	$-0.477010\pi$
$937$	4.41783	0.144324	0.0721620	+	0.997393i	$0.477010\pi$
$938$	−37.4432	−1.22256
$939$	−29.7931	−0.972261
$940$	−7.80250	−0.254490
$941$	−23.5591	−0.768006	−0.384003	−	0.923332i	$-0.625455\pi$
$941$	−23.5591	−0.768006	−0.384003	+	0.923332i	$0.625455\pi$
$942$	1.02483	0.0333908
$943$	−1.03871	−0.0338251
$944$	−6.08440	−0.198030
$945$	18.2375	0.593266
$946$	2.84555	0.0925169
$947$	42.8796	1.39340	0.696699	−	0.717364i	$-0.254651\pi$
$947$	42.8796	1.39340	0.696699	+	0.717364i	$0.254651\pi$
$948$	−10.6870	−0.347099
$949$	50.1444	1.62775
$950$	−3.43369	−0.111404
$951$	−20.3831	−0.660967
$952$	0.486233	0.0157589
$953$	−38.7475	−1.25516	−0.627578	−	0.778554i	$-0.715954\pi$
$953$	−38.7475	−1.25516	−0.627578	+	0.778554i	$0.715954\pi$
$954$	14.5738	0.471843
$955$	−8.42095	−0.272496
$956$	3.02649	0.0978837
$957$	2.59451	0.0838687
$958$	−19.5428	−0.631399
$959$	−29.8735	−0.964664
$960$	−0.668506	−0.0215759
$961$	11.1207	0.358734
$962$	−26.8996	−0.867278
$963$	−13.6463	−0.439746
$964$	−5.13542	−0.165401
$965$	−5.79717	−0.186618
$966$	4.79697	0.154340
$967$	−34.4940	−1.10925	−0.554627	−	0.832099i	$-0.687139\pi$
$967$	−34.4940	−1.10925	−0.554627	+	0.832099i	$0.687139\pi$
$968$	5.24155	0.168470
$969$	−0.0645619	−0.00207403
$970$	−2.08092	−0.0668143
$971$	−15.6443	−0.502048	−0.251024	−	0.967981i	$-0.580767\pi$
$971$	−15.6443	−0.502048	−0.251024	+	0.967981i	$0.580767\pi$
$972$	−16.1509	−0.518040
$973$	−111.981	−3.58994
$974$	−1.93393	−0.0619672
$975$	13.7083	0.439016
$976$	−10.6020	−0.339362
$977$	27.0292	0.864741	0.432371	−	0.901696i	$-0.357677\pi$
$977$	27.0292	0.864741	0.432371	+	0.901696i	$0.357677\pi$
$978$	−6.77761	−0.216724
$979$	31.8525	1.01801
$980$	15.2989	0.488705
$981$	1.08619	0.0346794
$982$	−17.7887	−0.567659
$983$	−40.6804	−1.29750	−0.648752	−	0.761000i	$-0.724709\pi$
$983$	−40.6804	−1.29750	−0.648752	+	0.761000i	$0.724709\pi$
$984$	−0.944759	−0.0301178
$985$	13.3277	0.424656
$986$	−0.109592	−0.00349014
$987$	50.9239	1.62093
$988$	−2.60188	−0.0827770
$989$	−1.18581	−0.0377065
$990$	3.83209	0.121792
$991$	−26.1878	−0.831882	−0.415941	−	0.909392i	$-0.636548\pi$
$991$	−26.1878	−0.831882	−0.415941	+	0.909392i	$0.636548\pi$
$992$	−6.49005	−0.206059
$993$	−15.9129	−0.504982
$994$	30.9847	0.982776
$995$	7.31845	0.232010
$996$	−3.72712	−0.118098
$997$	−35.9986	−1.14009	−0.570043	−	0.821615i	$-0.693074\pi$
$997$	−35.9986	−1.14009	−0.570043	+	0.821615i	$0.693074\pi$
$998$	5.64124	0.178570
$999$	37.4498	1.18486

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.j.1.14	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.j.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.909549 q^{3} +1.00000 q^{4} +0.734986 q^{5} +0.909549 q^{6} +5.27401 q^{7} -1.00000 q^{8} -2.17272 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.909549 q^{3} +1.00000 q^{4} +0.734986 q^{5} +0.909549 q^{6} +5.27401 q^{7} -1.00000 q^{8} -2.17272 q^{9} -0.734986 q^{10} +2.39968 q^{11} -0.909549 q^{12} +3.37941 q^{13} -5.27401 q^{14} -0.668506 q^{15} +1.00000 q^{16} -0.0921942 q^{17} +2.17272 q^{18} -0.769922 q^{19} +0.734986 q^{20} -4.79697 q^{21} -2.39968 q^{22} +1.00000 q^{23} +0.909549 q^{24} -4.45980 q^{25} -3.37941 q^{26} +4.70484 q^{27} +5.27401 q^{28} -1.18871 q^{29} +0.668506 q^{30} +6.49005 q^{31} -1.00000 q^{32} -2.18262 q^{33} +0.0921942 q^{34} +3.87632 q^{35} -2.17272 q^{36} +7.95985 q^{37} +0.769922 q^{38} -3.07374 q^{39} -0.734986 q^{40} -1.03871 q^{41} +4.79697 q^{42} -1.18581 q^{43} +2.39968 q^{44} -1.59692 q^{45} -1.00000 q^{46} -10.6159 q^{47} -0.909549 q^{48} +20.8152 q^{49} +4.45980 q^{50} +0.0838552 q^{51} +3.37941 q^{52} +6.70761 q^{53} -4.70484 q^{54} +1.76373 q^{55} -5.27401 q^{56} +0.700282 q^{57} +1.18871 q^{58} -6.08440 q^{59} -0.668506 q^{60} -10.6020 q^{61} -6.49005 q^{62} -11.4590 q^{63} +1.00000 q^{64} +2.48382 q^{65} +2.18262 q^{66} +7.09957 q^{67} -0.0921942 q^{68} -0.909549 q^{69} -3.87632 q^{70} -5.87499 q^{71} +2.17272 q^{72} +14.8382 q^{73} -7.95985 q^{74} +4.05640 q^{75} -0.769922 q^{76} +12.6559 q^{77} +3.07374 q^{78} +11.7498 q^{79} +0.734986 q^{80} +2.23888 q^{81} +1.03871 q^{82} +4.09777 q^{83} -4.79697 q^{84} -0.0677615 q^{85} +1.18581 q^{86} +1.08119 q^{87} -2.39968 q^{88} +13.2737 q^{89} +1.59692 q^{90} +17.8231 q^{91} +1.00000 q^{92} -5.90302 q^{93} +10.6159 q^{94} -0.565882 q^{95} +0.909549 q^{96} +2.83124 q^{97} -20.8152 q^{98} -5.21383 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) \) 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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