LMFDB - Embedded newform 6023.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$138$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76304 q^{2} -0.570737 q^{3} +5.63440 q^{4} +2.36853 q^{5} +1.57697 q^{6} +1.21818 q^{7} -10.0420 q^{8} -2.67426 q^{9} +O(q^{10})$	\(q-2.76304 q^{2} -0.570737 q^{3} +5.63440 q^{4} +2.36853 q^{5} +1.57697 q^{6} +1.21818 q^{7} -10.0420 q^{8} -2.67426 q^{9} -6.54436 q^{10} -6.38132 q^{11} -3.21576 q^{12} -5.43341 q^{13} -3.36589 q^{14} -1.35181 q^{15} +16.4777 q^{16} -5.00782 q^{17} +7.38909 q^{18} +1.00000 q^{19} +13.3453 q^{20} -0.695262 q^{21} +17.6319 q^{22} -8.54435 q^{23} +5.73134 q^{24} +0.609955 q^{25} +15.0128 q^{26} +3.23851 q^{27} +6.86373 q^{28} -2.24969 q^{29} +3.73511 q^{30} +2.15138 q^{31} -25.4445 q^{32} +3.64206 q^{33} +13.8368 q^{34} +2.88531 q^{35} -15.0678 q^{36} +9.06341 q^{37} -2.76304 q^{38} +3.10105 q^{39} -23.7848 q^{40} -9.58889 q^{41} +1.92104 q^{42} -0.855833 q^{43} -35.9549 q^{44} -6.33408 q^{45} +23.6084 q^{46} +5.54538 q^{47} -9.40441 q^{48} -5.51603 q^{49} -1.68533 q^{50} +2.85815 q^{51} -30.6140 q^{52} +1.70553 q^{53} -8.94814 q^{54} -15.1144 q^{55} -12.2330 q^{56} -0.570737 q^{57} +6.21598 q^{58} +3.90467 q^{59} -7.61664 q^{60} -13.8150 q^{61} -5.94435 q^{62} -3.25774 q^{63} +37.3488 q^{64} -12.8692 q^{65} -10.0632 q^{66} +7.25386 q^{67} -28.2161 q^{68} +4.87658 q^{69} -7.97223 q^{70} -5.83924 q^{71} +26.8549 q^{72} -6.94870 q^{73} -25.0426 q^{74} -0.348124 q^{75} +5.63440 q^{76} -7.77361 q^{77} -8.56833 q^{78} -3.05433 q^{79} +39.0279 q^{80} +6.17444 q^{81} +26.4945 q^{82} +7.32433 q^{83} -3.91738 q^{84} -11.8612 q^{85} +2.36470 q^{86} +1.28398 q^{87} +64.0812 q^{88} -1.63139 q^{89} +17.5013 q^{90} -6.61889 q^{91} -48.1423 q^{92} -1.22787 q^{93} -15.3221 q^{94} +2.36853 q^{95} +14.5221 q^{96} +13.9641 q^{97} +15.2410 q^{98} +17.0653 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) $ 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.76304	−1.95377	−0.976883	−	0.213776i	$-0.931424\pi$
$2$	−2.76304	−1.95377	−0.976883	+	0.213776i	$0.931424\pi$
$3$	−0.570737	−0.329515	−0.164758	−	0.986334i	$-0.552684\pi$
$3$	−0.570737	−0.329515	−0.164758	+	0.986334i	$0.552684\pi$
$4$	5.63440	2.81720
$5$	2.36853	1.05924	0.529620	−	0.848235i	$-0.322334\pi$
$5$	2.36853	1.05924	0.529620	+	0.848235i	$0.322334\pi$
$6$	1.57697	0.643795
$7$	1.21818	0.460430	0.230215	−	0.973140i	$-0.426057\pi$
$7$	1.21818	0.460430	0.230215	+	0.973140i	$0.426057\pi$
$8$	−10.0420	−3.55038
$9$	−2.67426	−0.891420
$10$	−6.54436	−2.06951
$11$	−6.38132	−1.92404	−0.962020	−	0.272978i	$-0.911991\pi$
$11$	−6.38132	−1.92404	−0.962020	+	0.272978i	$0.911991\pi$
$12$	−3.21576	−0.928310
$13$	−5.43341	−1.50696	−0.753479	−	0.657472i	$-0.771626\pi$
$13$	−5.43341	−1.50696	−0.753479	+	0.657472i	$0.771626\pi$
$14$	−3.36589	−0.899572
$15$	−1.35181	−0.349036
$16$	16.4777	4.11942
$17$	−5.00782	−1.21457	−0.607287	−	0.794482i	$-0.707742\pi$
$17$	−5.00782	−1.21457	−0.607287	+	0.794482i	$0.707742\pi$
$18$	7.38909	1.74163
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	13.3453	2.98409
$21$	−0.695262	−0.151719
$22$	17.6319	3.75912
$23$	−8.54435	−1.78162	−0.890811	−	0.454375i	$-0.849863\pi$
$23$	−8.54435	−1.78162	−0.890811	+	0.454375i	$0.849863\pi$
$24$	5.73134	1.16990
$25$	0.609955	0.121991
$26$	15.0128	2.94424
$27$	3.23851	0.623251
$28$	6.86373	1.29712
$29$	−2.24969	−0.417757	−0.208878	−	0.977942i	$-0.566981\pi$
$29$	−2.24969	−0.417757	−0.208878	+	0.977942i	$0.566981\pi$
$30$	3.73511	0.681934
$31$	2.15138	0.386399	0.193200	−	0.981159i	$-0.438113\pi$
$31$	2.15138	0.386399	0.193200	+	0.981159i	$0.438113\pi$
$32$	−25.4445	−4.49799
$33$	3.64206	0.634000
$34$	13.8368	2.37299
$35$	2.88531	0.487706
$36$	−15.0678	−2.51131
$37$	9.06341	1.49002	0.745008	−	0.667056i	$-0.232446\pi$
$37$	9.06341	1.49002	0.745008	+	0.667056i	$0.232446\pi$
$38$	−2.76304	−0.448225
$39$	3.10105	0.496565
$40$	−23.7848	−3.76071
$41$	−9.58889	−1.49753	−0.748766	−	0.662834i	$-0.769353\pi$
$41$	−9.58889	−1.49753	−0.748766	+	0.662834i	$0.769353\pi$
$42$	1.92104	0.296423
$43$	−0.855833	−0.130513	−0.0652567	−	0.997869i	$-0.520787\pi$
$43$	−0.855833	−0.130513	−0.0652567	+	0.997869i	$0.520787\pi$
$44$	−35.9549	−5.42041
$45$	−6.33408	−0.944228
$46$	23.6084	3.48087
$47$	5.54538	0.808877	0.404438	−	0.914565i	$-0.367467\pi$
$47$	5.54538	0.808877	0.404438	+	0.914565i	$0.367467\pi$
$48$	−9.40441	−1.35741
$49$	−5.51603	−0.788004
$50$	−1.68533	−0.238342
$51$	2.85815	0.400221
$52$	−30.6140	−4.24540
$53$	1.70553	0.234273	0.117136	−	0.993116i	$-0.462629\pi$
$53$	1.70553	0.234273	0.117136	+	0.993116i	$0.462629\pi$
$54$	−8.94814	−1.21769
$55$	−15.1144	−2.03802
$56$	−12.2330	−1.63470
$57$	−0.570737	−0.0755959
$58$	6.21598	0.816198
$59$	3.90467	0.508344	0.254172	−	0.967159i	$-0.418197\pi$
$59$	3.90467	0.508344	0.254172	+	0.967159i	$0.418197\pi$
$60$	−7.61664	−0.983304
$61$	−13.8150	−1.76882	−0.884412	−	0.466707i	$-0.845440\pi$
$61$	−13.8150	−1.76882	−0.884412	+	0.466707i	$0.845440\pi$
$62$	−5.94435	−0.754934
$63$	−3.25774	−0.410436
$64$	37.3488	4.66860
$65$	−12.8692	−1.59623
$66$	−10.0632	−1.23869
$67$	7.25386	0.886200	0.443100	−	0.896472i	$-0.353879\pi$
$67$	7.25386	0.886200	0.443100	+	0.896472i	$0.353879\pi$
$68$	−28.2161	−3.42170
$69$	4.87658	0.587071
$70$	−7.97223	−0.952863
$71$	−5.83924	−0.692990	−0.346495	−	0.938052i	$-0.612628\pi$
$71$	−5.83924	−0.692990	−0.346495	+	0.938052i	$0.612628\pi$
$72$	26.8549	3.16488
$73$	−6.94870	−0.813284	−0.406642	−	0.913588i	$-0.633300\pi$
$73$	−6.94870	−0.813284	−0.406642	+	0.913588i	$0.633300\pi$
$74$	−25.0426	−2.91114
$75$	−0.348124	−0.0401979
$76$	5.63440	0.646310
$77$	−7.77361	−0.885886
$78$	−8.56833	−0.970172
$79$	−3.05433	−0.343638	−0.171819	−	0.985128i	$-0.554964\pi$
$79$	−3.05433	−0.343638	−0.171819	+	0.985128i	$0.554964\pi$
$80$	39.0279	4.36345
$81$	6.17444	0.686049
$82$	26.4945	2.92583
$83$	7.32433	0.803949	0.401975	−	0.915651i	$-0.368324\pi$
$83$	7.32433	0.803949	0.401975	+	0.915651i	$0.368324\pi$
$84$	−3.91738	−0.427422
$85$	−11.8612	−1.28653
$86$	2.36470	0.254992
$87$	1.28398	0.137657
$88$	64.0812	6.83108
$89$	−1.63139	−0.172927	−0.0864634	−	0.996255i	$-0.527557\pi$
$89$	−1.63139	−0.172927	−0.0864634	+	0.996255i	$0.527557\pi$
$90$	17.5013	1.84480
$91$	−6.61889	−0.693848
$92$	−48.1423	−5.01918
$93$	−1.22787	−0.127324
$94$	−15.3221	−1.58036
$95$	2.36853	0.243007
$96$	14.5221	1.48216
$97$	13.9641	1.41784	0.708918	−	0.705291i	$-0.249184\pi$
$97$	13.9641	1.41784	0.708918	+	0.705291i	$0.249184\pi$
$98$	15.2410	1.53958
$99$	17.0653	1.71513
$100$	3.43673	0.343673
$101$	−13.9444	−1.38752	−0.693762	−	0.720204i	$-0.744048\pi$
$101$	−13.9444	−1.38752	−0.693762	+	0.720204i	$0.744048\pi$
$102$	−7.89718	−0.781937
$103$	−11.9229	−1.17480	−0.587398	−	0.809298i	$-0.699848\pi$
$103$	−11.9229	−1.17480	−0.587398	+	0.809298i	$0.699848\pi$
$104$	54.5623	5.35028
$105$	−1.64675	−0.160706
$106$	−4.71246	−0.457714
$107$	−4.47000	−0.432132	−0.216066	−	0.976379i	$-0.569323\pi$
$107$	−4.47000	−0.432132	−0.216066	+	0.976379i	$0.569323\pi$
$108$	18.2471	1.75582
$109$	−7.19517	−0.689173	−0.344586	−	0.938755i	$-0.611981\pi$
$109$	−7.19517	−0.689173	−0.344586	+	0.938755i	$0.611981\pi$
$110$	41.7617	3.98182
$111$	−5.17282	−0.490983
$112$	20.0728	1.89670
$113$	16.1510	1.51936	0.759680	−	0.650297i	$-0.225356\pi$
$113$	16.1510	1.51936	0.759680	+	0.650297i	$0.225356\pi$
$114$	1.57697	0.147697
$115$	−20.2376	−1.88717
$116$	−12.6756	−1.17690
$117$	14.5304	1.34333
$118$	−10.7888	−0.993186
$119$	−6.10044	−0.559226
$120$	13.5749	1.23921
$121$	29.7213	2.70193
$122$	38.1713	3.45587
$123$	5.47273	0.493460
$124$	12.1217	1.08856
$125$	−10.3980	−0.930023
$126$	9.00126	0.801896
$127$	20.9250	1.85679	0.928397	−	0.371590i	$-0.121187\pi$
$127$	20.9250	1.85679	0.928397	+	0.371590i	$0.121187\pi$
$128$	−52.3074	−4.62336
$129$	0.488455	0.0430061
$130$	35.5582	3.11866
$131$	−13.7018	−1.19713	−0.598566	−	0.801073i	$-0.704263\pi$
$131$	−13.7018	−1.19713	−0.598566	+	0.801073i	$0.704263\pi$
$132$	20.5208	1.78611
$133$	1.21818	0.105630
$134$	−20.0427	−1.73143
$135$	7.67052	0.660173
$136$	50.2885	4.31221
$137$	10.2052	0.871886	0.435943	−	0.899974i	$-0.356415\pi$
$137$	10.2052	0.871886	0.435943	+	0.899974i	$0.356415\pi$
$138$	−13.4742	−1.14700
$139$	16.4960	1.39918	0.699588	−	0.714546i	$-0.253367\pi$
$139$	16.4960	1.39918	0.699588	+	0.714546i	$0.253367\pi$
$140$	16.2570	1.37397
$141$	−3.16495	−0.266537
$142$	16.1341	1.35394
$143$	34.6724	2.89945
$144$	−44.0655	−3.67213
$145$	−5.32846	−0.442505
$146$	19.1995	1.58897
$147$	3.14820	0.259659
$148$	51.0669	4.19767
$149$	16.7429	1.37163	0.685816	−	0.727775i	$-0.259445\pi$
$149$	16.7429	1.37163	0.685816	+	0.727775i	$0.259445\pi$
$150$	0.961881	0.0785372
$151$	−3.86767	−0.314747	−0.157373	−	0.987539i	$-0.550303\pi$
$151$	−3.86767	−0.314747	−0.157373	+	0.987539i	$0.550303\pi$
$152$	−10.0420	−0.814514
$153$	13.3922	1.08270
$154$	21.4788	1.73081
$155$	5.09562	0.409290
$156$	17.4726	1.39892
$157$	−18.3501	−1.46450	−0.732248	−	0.681039i	$-0.761529\pi$
$157$	−18.3501	−1.46450	−0.732248	+	0.681039i	$0.761529\pi$
$158$	8.43923	0.671389
$159$	−0.973410	−0.0771964
$160$	−60.2661	−4.76445
$161$	−10.4086	−0.820311
$162$	−17.0602	−1.34038
$163$	−11.3224	−0.886842	−0.443421	−	0.896313i	$-0.646235\pi$
$163$	−11.3224	−0.886842	−0.443421	+	0.896313i	$0.646235\pi$
$164$	−54.0276	−4.21885
$165$	8.62633	0.671559
$166$	−20.2374	−1.57073
$167$	−0.0300444	−0.00232490	−0.00116245	−	0.999999i	$-0.500370\pi$
$167$	−0.0300444	−0.00232490	−0.00116245	+	0.999999i	$0.500370\pi$
$168$	6.98182	0.538659
$169$	16.5220	1.27092
$170$	32.7730	2.51357
$171$	−2.67426	−0.204506
$172$	−4.82211	−0.367682
$173$	6.99905	0.532128	0.266064	−	0.963955i	$-0.414277\pi$
$173$	6.99905	0.532128	0.266064	+	0.963955i	$0.414277\pi$
$174$	−3.54769	−0.268950
$175$	0.743037	0.0561683
$176$	−105.149	−7.92592
$177$	−2.22854	−0.167507
$178$	4.50759	0.337858
$179$	22.7353	1.69932	0.849658	−	0.527334i	$-0.176808\pi$
$179$	22.7353	1.69932	0.849658	+	0.527334i	$0.176808\pi$
$180$	−35.6887	−2.66008
$181$	−9.16148	−0.680967	−0.340484	−	0.940250i	$-0.610591\pi$
$181$	−9.16148	−0.680967	−0.340484	+	0.940250i	$0.610591\pi$
$182$	18.2883	1.35562
$183$	7.88471	0.582854
$184$	85.8024	6.32544
$185$	21.4670	1.57829
$186$	3.39266	0.248762
$187$	31.9565	2.33689
$188$	31.2449	2.27877
$189$	3.94510	0.286964
$190$	−6.54436	−0.474778
$191$	7.07328	0.511804	0.255902	−	0.966703i	$-0.417628\pi$
$191$	7.07328	0.511804	0.255902	+	0.966703i	$0.417628\pi$
$192$	−21.3163	−1.53837
$193$	3.61015	0.259865	0.129932	−	0.991523i	$-0.458524\pi$
$193$	3.61015	0.259865	0.129932	+	0.991523i	$0.458524\pi$
$194$	−38.5833	−2.77012
$195$	7.34494	0.525982
$196$	−31.0795	−2.21997
$197$	−1.26871	−0.0903917	−0.0451958	−	0.998978i	$-0.514391\pi$
$197$	−1.26871	−0.0903917	−0.0451958	+	0.998978i	$0.514391\pi$
$198$	−47.1522	−3.35096
$199$	−24.5844	−1.74274	−0.871370	−	0.490626i	$-0.836768\pi$
$199$	−24.5844	−1.74274	−0.871370	+	0.490626i	$0.836768\pi$
$200$	−6.12517	−0.433115
$201$	−4.14005	−0.292016
$202$	38.5291	2.71090
$203$	−2.74053	−0.192348
$204$	16.1039	1.12750
$205$	−22.7116	−1.58625
$206$	32.9434	2.29528
$207$	22.8498	1.58817
$208$	−89.5300	−6.20779
$209$	−6.38132	−0.441405
$210$	4.55004	0.313983
$211$	−24.2934	−1.67243	−0.836213	−	0.548404i	$-0.815236\pi$
$211$	−24.2934	−1.67243	−0.836213	+	0.548404i	$0.815236\pi$
$212$	9.60965	0.659993
$213$	3.33267	0.228351
$214$	12.3508	0.844284
$215$	−2.02707	−0.138245
$216$	−32.5211	−2.21278
$217$	2.62077	0.177910
$218$	19.8806	1.34648
$219$	3.96588	0.267989
$220$	−85.1604	−5.74152
$221$	27.2096	1.83031
$222$	14.2927	0.959265
$223$	−4.40764	−0.295157	−0.147579	−	0.989050i	$-0.547148\pi$
$223$	−4.40764	−0.295157	−0.147579	+	0.989050i	$0.547148\pi$
$224$	−30.9960	−2.07101
$225$	−1.63118	−0.108745
$226$	−44.6259	−2.96847
$227$	14.5648	0.966697	0.483349	−	0.875428i	$-0.339420\pi$
$227$	14.5648	0.966697	0.483349	+	0.875428i	$0.339420\pi$
$228$	−3.21576	−0.212969
$229$	22.4162	1.48131	0.740653	−	0.671888i	$-0.234516\pi$
$229$	22.4162	1.48131	0.740653	+	0.671888i	$0.234516\pi$
$230$	55.9173	3.68708
$231$	4.43669	0.291913
$232$	22.5914	1.48320
$233$	−0.891527	−0.0584059	−0.0292029	−	0.999574i	$-0.509297\pi$
$233$	−0.891527	−0.0584059	−0.0292029	+	0.999574i	$0.509297\pi$
$234$	−40.1480	−2.62456
$235$	13.1344	0.856795
$236$	22.0005	1.43211
$237$	1.74322	0.113234
$238$	16.8558	1.09260
$239$	−8.96515	−0.579907	−0.289954	−	0.957041i	$-0.593640\pi$
$239$	−8.96515	−0.579907	−0.289954	+	0.957041i	$0.593640\pi$
$240$	−22.2747	−1.43782
$241$	6.27386	0.404135	0.202068	−	0.979372i	$-0.435234\pi$
$241$	6.27386	0.404135	0.202068	+	0.979372i	$0.435234\pi$
$242$	−82.1211	−5.27894
$243$	−13.2395	−0.849315
$244$	−77.8390	−4.98313
$245$	−13.0649	−0.834686
$246$	−15.1214	−0.964104
$247$	−5.43341	−0.345720
$248$	−21.6042	−1.37187
$249$	−4.18026	−0.264913
$250$	28.7300	1.81705
$251$	2.17583	0.137337	0.0686686	−	0.997640i	$-0.478125\pi$
$251$	2.17583	0.137337	0.0686686	+	0.997640i	$0.478125\pi$
$252$	−18.3554	−1.15628
$253$	54.5243	3.42791
$254$	−57.8167	−3.62774
$255$	6.76962	0.423930
$256$	69.8299	4.36437
$257$	−10.1716	−0.634488	−0.317244	−	0.948344i	$-0.602757\pi$
$257$	−10.1716	−0.634488	−0.317244	+	0.948344i	$0.602757\pi$
$258$	−1.34962	−0.0840238
$259$	11.0409	0.686048
$260$	−72.5104	−4.49690
$261$	6.01625	0.372396
$262$	37.8587	2.33892
$263$	−11.3321	−0.698768	−0.349384	−	0.936980i	$-0.613609\pi$
$263$	−11.3321	−0.698768	−0.349384	+	0.936980i	$0.613609\pi$
$264$	−36.5735	−2.25094
$265$	4.03961	0.248151
$266$	−3.36589	−0.206376
$267$	0.931094	0.0569820
$268$	40.8712	2.49660
$269$	2.97403	0.181330	0.0906649	−	0.995881i	$-0.471101\pi$
$269$	2.97403	0.181330	0.0906649	+	0.995881i	$0.471101\pi$
$270$	−21.1940	−1.28982
$271$	−4.69763	−0.285360	−0.142680	−	0.989769i	$-0.545572\pi$
$271$	−4.69763	−0.285360	−0.142680	+	0.989769i	$0.545572\pi$
$272$	−82.5172	−5.00334
$273$	3.77765	0.228634
$274$	−28.1973	−1.70346
$275$	−3.89232	−0.234716
$276$	27.4766	1.65390
$277$	14.9820	0.900182	0.450091	−	0.892983i	$-0.351392\pi$
$277$	14.9820	0.900182	0.450091	+	0.892983i	$0.351392\pi$
$278$	−45.5793	−2.73366
$279$	−5.75335	−0.344444
$280$	−28.9743	−1.73154
$281$	2.23524	0.133343	0.0666716	−	0.997775i	$-0.478762\pi$
$281$	2.23524	0.133343	0.0666716	+	0.997775i	$0.478762\pi$
$282$	8.74490	0.520751
$283$	−1.65588	−0.0984320	−0.0492160	−	0.998788i	$-0.515672\pi$
$283$	−1.65588	−0.0984320	−0.0492160	+	0.998788i	$0.515672\pi$
$284$	−32.9006	−1.95229
$285$	−1.35181	−0.0800743
$286$	−95.8012	−5.66484
$287$	−11.6810	−0.689509
$288$	68.0451	4.00960
$289$	8.07826	0.475192
$290$	14.7228	0.864551
$291$	−7.96980	−0.467198
$292$	−39.1517	−2.29118
$293$	−10.0699	−0.588289	−0.294145	−	0.955761i	$-0.595035\pi$
$293$	−10.0699	−0.588289	−0.294145	+	0.955761i	$0.595035\pi$
$294$	−8.69861	−0.507313
$295$	9.24834	0.538459
$296$	−91.0148	−5.29013
$297$	−20.6660	−1.19916
$298$	−46.2614	−2.67985
$299$	46.4250	2.68483
$300$	−1.96147	−0.113245
$301$	−1.04256	−0.0600922
$302$	10.6865	0.614942
$303$	7.95861	0.457210
$304$	16.4777	0.945059
$305$	−32.7212	−1.87361
$306$	−37.0032	−2.11533
$307$	4.45400	0.254203	0.127102	−	0.991890i	$-0.459433\pi$
$307$	4.45400	0.254203	0.127102	+	0.991890i	$0.459433\pi$
$308$	−43.7997	−2.49572
$309$	6.80482	0.387113
$310$	−14.0794	−0.799657
$311$	−14.9363	−0.846957	−0.423479	−	0.905906i	$-0.639191\pi$
$311$	−14.9363	−0.846957	−0.423479	+	0.905906i	$0.639191\pi$
$312$	−31.1407	−1.76300
$313$	4.58259	0.259023	0.129512	−	0.991578i	$-0.458659\pi$
$313$	4.58259	0.259023	0.129512	+	0.991578i	$0.458659\pi$
$314$	50.7020	2.86128
$315$	−7.71606	−0.434751
$316$	−17.2093	−0.968098
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	2.68957	0.150824
$319$	14.3560	0.803780
$320$	88.4620	4.94517
$321$	2.55120	0.142394
$322$	28.7594	1.60270
$323$	−5.00782	−0.278643
$324$	34.7893	1.93274
$325$	−3.31414	−0.183835
$326$	31.2844	1.73268
$327$	4.10655	0.227093
$328$	96.2916	5.31681
$329$	6.75529	0.372431
$330$	−23.8349	−1.31207
$331$	−20.2865	−1.11504	−0.557522	−	0.830162i	$-0.688248\pi$
$331$	−20.2865	−1.11504	−0.557522	+	0.830162i	$0.688248\pi$
$332$	41.2682	2.26489
$333$	−24.2379	−1.32823
$334$	0.0830138	0.00454231
$335$	17.1810	0.938700
$336$	−11.4563	−0.624992
$337$	14.3065	0.779324	0.389662	−	0.920958i	$-0.372592\pi$
$337$	14.3065	0.779324	0.389662	+	0.920958i	$0.372592\pi$
$338$	−45.6510	−2.48308
$339$	−9.21798	−0.500652
$340$	−66.8307	−3.62440
$341$	−13.7286	−0.743448
$342$	7.38909	0.399556
$343$	−15.2468	−0.823251
$344$	8.59427	0.463372
$345$	11.5503	0.621850
$346$	−19.3387	−1.03965
$347$	18.1257	0.973036	0.486518	−	0.873671i	$-0.338267\pi$
$347$	18.1257	0.973036	0.486518	+	0.873671i	$0.338267\pi$
$348$	7.23446	0.387808
$349$	13.1898	0.706032	0.353016	−	0.935617i	$-0.385156\pi$
$349$	13.1898	0.706032	0.353016	+	0.935617i	$0.385156\pi$
$350$	−2.05304	−0.109740
$351$	−17.5962	−0.939214
$352$	162.369	8.65432
$353$	1.70283	0.0906323	0.0453161	−	0.998973i	$-0.485570\pi$
$353$	1.70283	0.0906323	0.0453161	+	0.998973i	$0.485570\pi$
$354$	6.15754	0.327270
$355$	−13.8304	−0.734043
$356$	−9.19189	−0.487169
$357$	3.48175	0.184274
$358$	−62.8186	−3.32007
$359$	−8.17025	−0.431210	−0.215605	−	0.976481i	$-0.569172\pi$
$359$	−8.17025	−0.431210	−0.215605	+	0.976481i	$0.569172\pi$
$360$	63.6068	3.35237
$361$	1.00000	0.0526316
$362$	25.3135	1.33045
$363$	−16.9630	−0.890327
$364$	−37.2935	−1.95471
$365$	−16.4582	−0.861463
$366$	−21.7858	−1.13876
$367$	−30.2872	−1.58098	−0.790491	−	0.612474i	$-0.790174\pi$
$367$	−30.2872	−1.58098	−0.790491	+	0.612474i	$0.790174\pi$
$368$	−140.791	−7.33924
$369$	25.6432	1.33493
$370$	−59.3142	−3.08360
$371$	2.07765	0.107866
$372$	−6.91832	−0.358698
$373$	10.1627	0.526204	0.263102	−	0.964768i	$-0.415254\pi$
$373$	10.1627	0.526204	0.263102	+	0.964768i	$0.415254\pi$
$374$	−88.2972	−4.56574
$375$	5.93451	0.306457
$376$	−55.6867	−2.87182
$377$	12.2235	0.629542
$378$	−10.9005	−0.560659
$379$	1.39893	0.0718582	0.0359291	−	0.999354i	$-0.488561\pi$
$379$	1.39893	0.0718582	0.0359291	+	0.999354i	$0.488561\pi$
$380$	13.3453	0.684598
$381$	−11.9427	−0.611842
$382$	−19.5438	−0.999946
$383$	−11.7894	−0.602410	−0.301205	−	0.953559i	$-0.597389\pi$
$383$	−11.7894	−0.602410	−0.301205	+	0.953559i	$0.597389\pi$
$384$	29.8538	1.52347
$385$	−18.4121	−0.938366
$386$	−9.97501	−0.507714
$387$	2.28872	0.116342
$388$	78.6791	3.99433
$389$	38.7917	1.96682	0.983409	−	0.181403i	$-0.0580638\pi$
$389$	38.7917	1.96682	0.983409	+	0.181403i	$0.0580638\pi$
$390$	−20.2944	−1.02765
$391$	42.7886	2.16391
$392$	55.3920	2.79772
$393$	7.82013	0.394473
$394$	3.50549	0.176604
$395$	−7.23427	−0.363996
$396$	96.1528	4.83186
$397$	−11.0685	−0.555511	−0.277755	−	0.960652i	$-0.589590\pi$
$397$	−11.0685	−0.555511	−0.277755	+	0.960652i	$0.589590\pi$
$398$	67.9277	3.40491
$399$	−0.695262	−0.0348066
$400$	10.0506	0.502532
$401$	23.0502	1.15107	0.575536	−	0.817776i	$-0.304793\pi$
$401$	23.0502	1.15107	0.575536	+	0.817776i	$0.304793\pi$
$402$	11.4391	0.570532
$403$	−11.6893	−0.582288
$404$	−78.5686	−3.90893
$405$	14.6244	0.726691
$406$	7.57220	0.375802
$407$	−57.8365	−2.86685
$408$	−28.7015	−1.42094
$409$	36.1591	1.78795	0.893976	−	0.448115i	$-0.147904\pi$
$409$	36.1591	1.78795	0.893976	+	0.448115i	$0.147904\pi$
$410$	62.7531	3.09916
$411$	−5.82446	−0.287300
$412$	−67.1782	−3.30963
$413$	4.75660	0.234057
$414$	−63.1350	−3.10292
$415$	17.3479	0.851576
$416$	138.250	6.77828
$417$	−9.41490	−0.461050
$418$	17.6319	0.862402
$419$	7.02117	0.343006	0.171503	−	0.985184i	$-0.445138\pi$
$419$	7.02117	0.343006	0.171503	+	0.985184i	$0.445138\pi$
$420$	−9.27846	−0.452742
$421$	32.4861	1.58327	0.791637	−	0.610992i	$-0.209229\pi$
$421$	32.4861	1.58327	0.791637	+	0.610992i	$0.209229\pi$
$422$	67.1237	3.26753
$423$	−14.8298	−0.721049
$424$	−17.1270	−0.831758
$425$	−3.05455	−0.148167
$426$	−9.20830	−0.446144
$427$	−16.8291	−0.814419
$428$	−25.1858	−1.21740
$429$	−19.7888	−0.955412
$430$	5.60088	0.270098
$431$	21.2979	1.02588	0.512942	−	0.858423i	$-0.328556\pi$
$431$	21.2979	1.02588	0.512942	+	0.858423i	$0.328556\pi$
$432$	53.3631	2.56743
$433$	−14.7021	−0.706537	−0.353268	−	0.935522i	$-0.614930\pi$
$433$	−14.7021	−0.706537	−0.353268	+	0.935522i	$0.614930\pi$
$434$	−7.24131	−0.347594
$435$	3.04115	0.145812
$436$	−40.5405	−1.94154
$437$	−8.54435	−0.408732
$438$	−10.9579	−0.523588
$439$	−12.2986	−0.586980	−0.293490	−	0.955962i	$-0.594817\pi$
$439$	−12.2986	−0.586980	−0.293490	+	0.955962i	$0.594817\pi$
$440$	151.779	7.23576
$441$	14.7513	0.702443
$442$	−75.1812	−3.57600
$443$	0.161538	0.00767491	0.00383746	−	0.999993i	$-0.498778\pi$
$443$	0.161538	0.00767491	0.00383746	+	0.999993i	$0.498778\pi$
$444$	−29.1458	−1.38320
$445$	−3.86400	−0.183171
$446$	12.1785	0.576668
$447$	−9.55580	−0.451974
$448$	45.4977	2.14956
$449$	2.97574	0.140434	0.0702169	−	0.997532i	$-0.477631\pi$
$449$	2.97574	0.140434	0.0702169	+	0.997532i	$0.477631\pi$
$450$	4.50701	0.212463
$451$	61.1898	2.88131
$452$	91.0013	4.28034
$453$	2.20742	0.103714
$454$	−40.2431	−1.88870
$455$	−15.6771	−0.734953
$456$	5.73134	0.268395
$457$	33.1036	1.54852	0.774261	−	0.632866i	$-0.218122\pi$
$457$	33.1036	1.54852	0.774261	+	0.632866i	$0.218122\pi$
$458$	−61.9370	−2.89412
$459$	−16.2179	−0.756985
$460$	−114.027	−5.31652
$461$	−13.4368	−0.625816	−0.312908	−	0.949783i	$-0.601303\pi$
$461$	−13.4368	−0.625816	−0.312908	+	0.949783i	$0.601303\pi$
$462$	−12.2588	−0.570329
$463$	20.5193	0.953615	0.476807	−	0.879008i	$-0.341794\pi$
$463$	20.5193	0.953615	0.476807	+	0.879008i	$0.341794\pi$
$464$	−37.0696	−1.72091
$465$	−2.90826	−0.134867
$466$	2.46333	0.114111
$467$	31.1325	1.44064	0.720321	−	0.693641i	$-0.243995\pi$
$467$	31.1325	1.44064	0.720321	+	0.693641i	$0.243995\pi$
$468$	81.8699	3.78444
$469$	8.83653	0.408033
$470$	−36.2910	−1.67398
$471$	10.4731	0.482573
$472$	−39.2107	−1.80482
$473$	5.46134	0.251113
$474$	−4.81658	−0.221233
$475$	0.609955	0.0279867
$476$	−34.3723	−1.57545
$477$	−4.56104	−0.208835
$478$	24.7711	1.13300
$479$	−29.4209	−1.34428	−0.672138	−	0.740426i	$-0.734624\pi$
$479$	−29.4209	−1.34428	−0.672138	+	0.740426i	$0.734624\pi$
$480$	34.3961	1.56996
$481$	−49.2453	−2.24539
$482$	−17.3349	−0.789585
$483$	5.94056	0.270305
$484$	167.461	7.61188
$485$	33.0744	1.50183
$486$	36.5813	1.65936
$487$	41.4746	1.87939	0.939696	−	0.342011i	$-0.111108\pi$
$487$	41.4746	1.87939	0.939696	+	0.342011i	$0.111108\pi$
$488$	138.730	6.28000
$489$	6.46214	0.292228
$490$	36.0989	1.63078
$491$	−7.26171	−0.327716	−0.163858	−	0.986484i	$-0.552394\pi$
$491$	−7.26171	−0.327716	−0.163858	+	0.986484i	$0.552394\pi$
$492$	30.8356	1.39017
$493$	11.2660	0.507397
$494$	15.0128	0.675456
$495$	40.4198	1.81673
$496$	35.4497	1.59174
$497$	−7.11326	−0.319073
$498$	11.5502	0.517579
$499$	−20.7753	−0.930029	−0.465014	−	0.885303i	$-0.653951\pi$
$499$	−20.7753	−0.930029	−0.465014	+	0.885303i	$0.653951\pi$
$500$	−58.5863	−2.62006
$501$	0.0171474	0.000766090 0
$502$	−6.01191	−0.268325
$503$	−16.8347	−0.750622	−0.375311	−	0.926899i	$-0.622464\pi$
$503$	−16.8347	−0.750622	−0.375311	+	0.926899i	$0.622464\pi$
$504$	32.7142	1.45721
$505$	−33.0279	−1.46972
$506$	−150.653	−6.69733
$507$	−9.42971	−0.418788
$508$	117.900	5.23096
$509$	9.03115	0.400299	0.200149	−	0.979765i	$-0.435857\pi$
$509$	9.03115	0.400299	0.200149	+	0.979765i	$0.435857\pi$
$510$	−18.7047	−0.828260
$511$	−8.46478	−0.374460
$512$	−88.3281	−3.90359
$513$	3.23851	0.142984
$514$	28.1046	1.23964
$515$	−28.2397	−1.24439
$516$	2.75215	0.121157
$517$	−35.3868	−1.55631
$518$	−30.5064	−1.34038
$519$	−3.99462	−0.175344
$520$	129.233	5.66723
$521$	−34.3799	−1.50621	−0.753106	−	0.657900i	$-0.771445\pi$
$521$	−34.3799	−1.50621	−0.753106	+	0.657900i	$0.771445\pi$
$522$	−16.6231	−0.727575
$523$	−18.3774	−0.803589	−0.401794	−	0.915730i	$-0.631613\pi$
$523$	−18.3774	−0.803589	−0.401794	+	0.915730i	$0.631613\pi$
$524$	−77.2015	−3.37256
$525$	−0.424079	−0.0185083
$526$	31.3111	1.36523
$527$	−10.7737	−0.469311
$528$	60.0126	2.61171
$529$	50.0060	2.17417
$530$	−11.1616	−0.484830
$531$	−10.4421	−0.453148
$532$	6.86373	0.297580
$533$	52.1004	2.25672
$534$	−2.57265	−0.111329
$535$	−10.5874	−0.457731
$536$	−72.8433	−3.14635
$537$	−12.9759	−0.559950
$538$	−8.21737	−0.354276
$539$	35.1996	1.51615
$540$	43.2188	1.85984
$541$	−17.6373	−0.758285	−0.379143	−	0.925338i	$-0.623781\pi$
$541$	−17.6373	−0.758285	−0.379143	+	0.925338i	$0.623781\pi$
$542$	12.9797	0.557527
$543$	5.22879	0.224389
$544$	127.421	5.46315
$545$	−17.0420	−0.730000
$546$	−10.4378	−0.446696
$547$	−9.91582	−0.423970	−0.211985	−	0.977273i	$-0.567993\pi$
$547$	−9.91582	−0.423970	−0.211985	+	0.977273i	$0.567993\pi$
$548$	57.5000	2.45628
$549$	36.9448	1.57676
$550$	10.7546	0.458579
$551$	−2.24969	−0.0958399
$552$	−48.9706	−2.08433
$553$	−3.72073	−0.158221
$554$	−41.3959	−1.75874
$555$	−12.2520	−0.520069
$556$	92.9453	3.94176
$557$	14.1049	0.597644	0.298822	−	0.954309i	$-0.403406\pi$
$557$	14.1049	0.597644	0.298822	+	0.954309i	$0.403406\pi$
$558$	15.8967	0.672963
$559$	4.65010	0.196678
$560$	47.5431	2.00906
$561$	−18.2388	−0.770041
$562$	−6.17606	−0.260521
$563$	−19.2802	−0.812563	−0.406282	−	0.913748i	$-0.633175\pi$
$563$	−19.2802	−0.812563	−0.406282	+	0.913748i	$0.633175\pi$
$564$	−17.8326	−0.750888
$565$	38.2542	1.60937
$566$	4.57527	0.192313
$567$	7.52160	0.315877
$568$	58.6376	2.46038
$569$	−19.5144	−0.818085	−0.409043	−	0.912515i	$-0.634137\pi$
$569$	−19.5144	−0.818085	−0.409043	+	0.912515i	$0.634137\pi$
$570$	3.73511	0.156446
$571$	19.9202	0.833633	0.416816	−	0.908991i	$-0.363146\pi$
$571$	19.9202	0.833633	0.416816	+	0.908991i	$0.363146\pi$
$572$	195.358	8.16833
$573$	−4.03698	−0.168647
$574$	32.2751	1.34714
$575$	−5.21167	−0.217342
$576$	−99.8804	−4.16168
$577$	−13.2783	−0.552781	−0.276390	−	0.961045i	$-0.589138\pi$
$577$	−13.2783	−0.552781	−0.276390	+	0.961045i	$0.589138\pi$
$578$	−22.3206	−0.928413
$579$	−2.06045	−0.0856293
$580$	−30.0227	−1.24662
$581$	8.92237	0.370162
$582$	22.0209	0.912796
$583$	−10.8835	−0.450750
$584$	69.7788	2.88747
$585$	34.4157	1.42291
$586$	27.8235	1.14938
$587$	−4.97452	−0.205320	−0.102660	−	0.994716i	$-0.532735\pi$
$587$	−4.97452	−0.205320	−0.102660	+	0.994716i	$0.532735\pi$
$588$	17.7382	0.731512
$589$	2.15138	0.0886461
$590$	−25.5535	−1.05202
$591$	0.724098	0.0297854
$592$	149.344	6.13799
$593$	−8.46047	−0.347430	−0.173715	−	0.984796i	$-0.555577\pi$
$593$	−8.46047	−0.347430	−0.173715	+	0.984796i	$0.555577\pi$
$594$	57.1009	2.34288
$595$	−14.4491	−0.592355
$596$	94.3363	3.86416
$597$	14.0312	0.574259
$598$	−128.274	−5.24552
$599$	−47.3817	−1.93596	−0.967981	−	0.251023i	$-0.919233\pi$
$599$	−47.3817	−1.93596	−0.967981	+	0.251023i	$0.919233\pi$
$600$	3.49586	0.142718
$601$	−40.2393	−1.64139	−0.820697	−	0.571363i	$-0.806415\pi$
$601$	−40.2393	−1.64139	−0.820697	+	0.571363i	$0.806415\pi$
$602$	2.88064	0.117406
$603$	−19.3987	−0.789977
$604$	−21.7920	−0.886705
$605$	70.3958	2.86200
$606$	−21.9900	−0.893282
$607$	−16.9845	−0.689381	−0.344691	−	0.938716i	$-0.612016\pi$
$607$	−16.9845	−0.689381	−0.344691	+	0.938716i	$0.612016\pi$
$608$	−25.4445	−1.03191
$609$	1.56412	0.0633814
$610$	90.4101	3.66060
$611$	−30.1303	−1.21894
$612$	75.4571	3.05017
$613$	−1.50026	−0.0605950	−0.0302975	−	0.999541i	$-0.509645\pi$
$613$	−1.50026	−0.0605950	−0.0302975	+	0.999541i	$0.509645\pi$
$614$	−12.3066	−0.496653
$615$	12.9624	0.522693
$616$	78.0626	3.14523
$617$	14.7422	0.593498	0.296749	−	0.954956i	$-0.404098\pi$
$617$	14.7422	0.593498	0.296749	+	0.954956i	$0.404098\pi$
$618$	−18.8020	−0.756328
$619$	29.2850	1.17706	0.588532	−	0.808474i	$-0.299706\pi$
$619$	29.2850	1.17706	0.588532	+	0.808474i	$0.299706\pi$
$620$	28.7108	1.15305
$621$	−27.6710	−1.11040
$622$	41.2695	1.65476
$623$	−1.98733	−0.0796207
$624$	51.0981	2.04556
$625$	−27.6777	−1.10711
$626$	−12.6619	−0.506071
$627$	3.64206	0.145450
$628$	−103.392	−4.12578
$629$	−45.3879	−1.80974
$630$	21.3198	0.849401
$631$	−32.5773	−1.29688	−0.648441	−	0.761265i	$-0.724579\pi$
$631$	−32.5773	−1.29688	−0.648441	+	0.761265i	$0.724579\pi$
$632$	30.6715	1.22005
$633$	13.8651	0.551090
$634$	2.76304	0.109734
$635$	49.5616	1.96679
$636$	−5.48458	−0.217478
$637$	29.9709	1.18749
$638$	−39.6662	−1.57040
$639$	15.6156	0.617745
$640$	−123.892	−4.89726
$641$	0.701962	0.0277258	0.0138629	−	0.999904i	$-0.495587\pi$
$641$	0.701962	0.0277258	0.0138629	+	0.999904i	$0.495587\pi$
$642$	−7.04906	−0.278204
$643$	−27.6091	−1.08880	−0.544399	−	0.838827i	$-0.683242\pi$
$643$	−27.6091	−1.08880	−0.544399	+	0.838827i	$0.683242\pi$
$644$	−58.6461	−2.31098
$645$	1.15692	0.0455538
$646$	13.8368	0.544402
$647$	18.0325	0.708930	0.354465	−	0.935069i	$-0.384663\pi$
$647$	18.0325	0.708930	0.354465	+	0.935069i	$0.384663\pi$
$648$	−62.0037	−2.43574
$649$	−24.9169	−0.978075
$650$	9.15711	0.359171
$651$	−1.49577	−0.0586240
$652$	−63.7952	−2.49841
$653$	−14.4824	−0.566739	−0.283370	−	0.959011i	$-0.591452\pi$
$653$	−14.4824	−0.566739	−0.283370	+	0.959011i	$0.591452\pi$
$654$	−11.3466	−0.443686
$655$	−32.4532	−1.26805
$656$	−158.002	−6.16896
$657$	18.5826	0.724977
$658$	−18.6651	−0.727643
$659$	5.01808	0.195477	0.0977383	−	0.995212i	$-0.468839\pi$
$659$	5.01808	0.195477	0.0977383	+	0.995212i	$0.468839\pi$
$660$	48.6042	1.89192
$661$	−42.2753	−1.64432	−0.822160	−	0.569257i	$-0.807231\pi$
$661$	−42.2753	−1.64432	−0.822160	+	0.569257i	$0.807231\pi$
$662$	56.0523	2.17854
$663$	−15.5295	−0.603116
$664$	−73.5509	−2.85433
$665$	2.88531	0.111887
$666$	66.9704	2.59505
$667$	19.2221	0.744284
$668$	−0.169282	−0.00654972
$669$	2.51560	0.0972588
$670$	−47.4719	−1.83400
$671$	88.1577	3.40329
$672$	17.6906	0.682429
$673$	−6.71505	−0.258846	−0.129423	−	0.991589i	$-0.541313\pi$
$673$	−6.71505	−0.258846	−0.129423	+	0.991589i	$0.541313\pi$
$674$	−39.5294	−1.52262
$675$	1.97535	0.0760311
$676$	93.0915	3.58044
$677$	31.4260	1.20780	0.603900	−	0.797060i	$-0.293612\pi$
$677$	31.4260	1.20780	0.603900	+	0.797060i	$0.293612\pi$
$678$	25.4697	0.978156
$679$	17.0108	0.652814
$680$	119.110	4.56766
$681$	−8.31265	−0.318541
$682$	37.9328	1.45252
$683$	25.8726	0.989986	0.494993	−	0.868897i	$-0.335171\pi$
$683$	25.8726	0.989986	0.494993	+	0.868897i	$0.335171\pi$
$684$	−15.0678	−0.576134
$685$	24.1713	0.923537
$686$	42.1276	1.60844
$687$	−12.7938	−0.488113
$688$	−14.1021	−0.537639
$689$	−9.26686	−0.353039
$690$	−31.9141	−1.21495
$691$	−1.22961	−0.0467766	−0.0233883	−	0.999726i	$-0.507445\pi$
$691$	−1.22961	−0.0467766	−0.0233883	+	0.999726i	$0.507445\pi$
$692$	39.4354	1.49911
$693$	20.7887	0.789696
$694$	−50.0819	−1.90108
$695$	39.0714	1.48206
$696$	−12.8937	−0.488735
$697$	48.0194	1.81887
$698$	−36.4439	−1.37942
$699$	0.508827	0.0192456
$700$	4.18657	0.158237
$701$	−31.3023	−1.18227	−0.591135	−	0.806572i	$-0.701320\pi$
$701$	−31.3023	−1.18227	−0.591135	+	0.806572i	$0.701320\pi$
$702$	48.6189	1.83500
$703$	9.06341	0.341833
$704$	−238.335	−8.98258
$705$	−7.49630	−0.282327
$706$	−4.70498	−0.177074
$707$	−16.9869	−0.638858
$708$	−12.5565	−0.471901
$709$	15.7780	0.592554	0.296277	−	0.955102i	$-0.404255\pi$
$709$	15.7780	0.592554	0.296277	+	0.955102i	$0.404255\pi$
$710$	38.2141	1.43415
$711$	8.16806	0.306326
$712$	16.3824	0.613956
$713$	−18.3822	−0.688417
$714$	−9.62021	−0.360027
$715$	82.1227	3.07121
$716$	128.100	4.78731
$717$	5.11674	0.191088
$718$	22.5748	0.842482
$719$	−39.0090	−1.45479	−0.727394	−	0.686220i	$-0.759269\pi$
$719$	−39.0090	−1.45479	−0.727394	+	0.686220i	$0.759269\pi$
$720$	−104.371	−3.88967
$721$	−14.5242	−0.540911
$722$	−2.76304	−0.102830
$723$	−3.58073	−0.133169
$724$	−51.6194	−1.91842
$725$	−1.37221	−0.0509625
$726$	46.8695	1.73949
$727$	−6.15770	−0.228376	−0.114188	−	0.993459i	$-0.536427\pi$
$727$	−6.15770	−0.228376	−0.114188	+	0.993459i	$0.536427\pi$
$728$	66.4669	2.46343
$729$	−10.9670	−0.406187
$730$	45.4748	1.68310
$731$	4.28586	0.158518
$732$	44.4256	1.64202
$733$	−18.9646	−0.700473	−0.350237	−	0.936661i	$-0.613899\pi$
$733$	−18.9646	−0.700473	−0.350237	+	0.936661i	$0.613899\pi$
$734$	83.6849	3.08887
$735$	7.45663	0.275042
$736$	217.407	8.01371
$737$	−46.2892	−1.70509
$738$	−70.8532	−2.60814
$739$	−2.71781	−0.0999763	−0.0499882	−	0.998750i	$-0.515918\pi$
$739$	−2.71781	−0.0999763	−0.0499882	+	0.998750i	$0.515918\pi$
$740$	120.954	4.44635
$741$	3.10105	0.113920
$742$	−5.74063	−0.210745
$743$	9.64689	0.353910	0.176955	−	0.984219i	$-0.443375\pi$
$743$	9.64689	0.353910	0.176955	+	0.984219i	$0.443375\pi$
$744$	12.3303	0.452050
$745$	39.6562	1.45289
$746$	−28.0799	−1.02808
$747$	−19.5871	−0.716656
$748$	180.056	6.58349
$749$	−5.44528	−0.198966
$750$	−16.3973	−0.598744
$751$	−5.76144	−0.210238	−0.105119	−	0.994460i	$-0.533522\pi$
$751$	−5.76144	−0.210238	−0.105119	+	0.994460i	$0.533522\pi$
$752$	91.3749	3.33210
$753$	−1.24183	−0.0452547
$754$	−33.7740	−1.22998
$755$	−9.16072	−0.333393
$756$	22.2282	0.808434
$757$	−16.9098	−0.614598	−0.307299	−	0.951613i	$-0.599425\pi$
$757$	−16.9098	−0.614598	−0.307299	+	0.951613i	$0.599425\pi$
$758$	−3.86530	−0.140394
$759$	−31.1190	−1.12955
$760$	−23.7848	−0.862766
$761$	−14.5455	−0.527275	−0.263638	−	0.964622i	$-0.584922\pi$
$761$	−14.5455	−0.527275	−0.263638	+	0.964622i	$0.584922\pi$
$762$	32.9981	1.19539
$763$	−8.76504	−0.317316
$764$	39.8537	1.44185
$765$	31.7199	1.14684
$766$	32.5746	1.17697
$767$	−21.2157	−0.766053
$768$	−39.8545	−1.43813
$769$	20.8153	0.750620	0.375310	−	0.926899i	$-0.377536\pi$
$769$	20.8153	0.750620	0.375310	+	0.926899i	$0.377536\pi$
$770$	50.8733	1.83335
$771$	5.80532	0.209074
$772$	20.3411	0.732090
$773$	−27.7977	−0.999813	−0.499907	−	0.866079i	$-0.666632\pi$
$773$	−27.7977	−0.999813	−0.499907	+	0.866079i	$0.666632\pi$
$774$	−6.32383	−0.227305
$775$	1.31225	0.0471373
$776$	−140.227	−5.03386
$777$	−6.30144	−0.226063
$778$	−107.183	−3.84270
$779$	−9.58889	−0.343558
$780$	41.3844	1.48180
$781$	37.2620	1.33334
$782$	−118.227	−4.22778
$783$	−7.28563	−0.260367
$784$	−90.8913	−3.24612
$785$	−43.4628	−1.55125
$786$	−21.6073	−0.770708
$787$	30.4905	1.08687	0.543435	−	0.839451i	$-0.317124\pi$
$787$	30.4905	1.08687	0.543435	+	0.839451i	$0.317124\pi$
$788$	−7.14840	−0.254651
$789$	6.46765	0.230254
$790$	19.9886	0.711163
$791$	19.6749	0.699558
$792$	−171.370	−6.08936
$793$	75.0624	2.66554
$794$	30.5827	1.08534
$795$	−2.30556	−0.0817696
$796$	−138.518	−4.90965
$797$	5.26965	0.186661	0.0933303	−	0.995635i	$-0.470249\pi$
$797$	5.26965	0.186661	0.0933303	+	0.995635i	$0.470249\pi$
$798$	1.92104	0.0680040
$799$	−27.7703	−0.982441
$800$	−15.5200	−0.548714
$801$	4.36276	0.154150
$802$	−63.6887	−2.24893
$803$	44.3419	1.56479
$804$	−23.3267	−0.822669
$805$	−24.6531	−0.868907
$806$	32.2981	1.13765
$807$	−1.69739	−0.0597509
$808$	140.030	4.92624
$809$	−1.55081	−0.0545236	−0.0272618	−	0.999628i	$-0.508679\pi$
$809$	−1.55081	−0.0545236	−0.0272618	+	0.999628i	$0.508679\pi$
$810$	−40.4078	−1.41978
$811$	−24.6443	−0.865379	−0.432689	−	0.901543i	$-0.642435\pi$
$811$	−24.6443	−0.865379	−0.432689	+	0.901543i	$0.642435\pi$
$812$	−15.4412	−0.541882
$813$	2.68111	0.0940306
$814$	159.805	5.60115
$815$	−26.8176	−0.939380
$816$	47.0956	1.64868
$817$	−0.855833	−0.0299418
$818$	−99.9091	−3.49324
$819$	17.7006	0.618510
$820$	−127.966	−4.46878
$821$	−8.36831	−0.292056	−0.146028	−	0.989280i	$-0.546649\pi$
$821$	−8.36831	−0.292056	−0.146028	+	0.989280i	$0.546649\pi$
$822$	16.0932	0.561316
$823$	19.1585	0.667825	0.333912	−	0.942604i	$-0.391631\pi$
$823$	19.1585	0.667825	0.333912	+	0.942604i	$0.391631\pi$
$824$	119.730	4.17097
$825$	2.22149	0.0773424
$826$	−13.1427	−0.457292
$827$	40.1295	1.39544	0.697720	−	0.716371i	$-0.254198\pi$
$827$	40.1295	1.39544	0.697720	+	0.716371i	$0.254198\pi$
$828$	128.745	4.47420
$829$	−38.6004	−1.34065	−0.670324	−	0.742069i	$-0.733845\pi$
$829$	−38.6004	−1.34065	−0.670324	+	0.742069i	$0.733845\pi$
$830$	−47.9330	−1.66378
$831$	−8.55079	−0.296623
$832$	−202.932	−7.03539
$833$	27.6233	0.957090
$834$	26.0138	0.900783
$835$	−0.0711611	−0.00246263
$836$	−35.9549	−1.24353
$837$	6.96727	0.240824
$838$	−19.3998	−0.670154
$839$	−54.4750	−1.88069	−0.940343	−	0.340227i	$-0.889496\pi$
$839$	−54.4750	−1.88069	−0.940343	+	0.340227i	$0.889496\pi$
$840$	16.5367	0.570570
$841$	−23.9389	−0.825480
$842$	−89.7604	−3.09335
$843$	−1.27573	−0.0439386
$844$	−136.879	−4.71156
$845$	39.1329	1.34621
$846$	40.9753	1.40876
$847$	36.2059	1.24405
$848$	28.1032	0.965067
$849$	0.945073	0.0324348
$850$	8.43984	0.289484
$851$	−77.4410	−2.65464
$852$	18.7776	0.643309
$853$	58.2173	1.99332	0.996661	−	0.0816525i	$-0.0260198\pi$
$853$	58.2173	1.99332	0.996661	+	0.0816525i	$0.0260198\pi$
$854$	46.4996	1.59118
$855$	−6.33408	−0.216621
$856$	44.8878	1.53423
$857$	−0.835439	−0.0285381	−0.0142690	−	0.999898i	$-0.504542\pi$
$857$	−0.835439	−0.0285381	−0.0142690	+	0.999898i	$0.504542\pi$
$858$	54.6773	1.86665
$859$	4.24060	0.144687	0.0723437	−	0.997380i	$-0.476952\pi$
$859$	4.24060	0.144687	0.0723437	+	0.997380i	$0.476952\pi$
$860$	−11.4213	−0.389464
$861$	6.66679	0.227203
$862$	−58.8470	−2.00434
$863$	11.5175	0.392060	0.196030	−	0.980598i	$-0.437195\pi$
$863$	11.5175	0.392060	0.196030	+	0.980598i	$0.437195\pi$
$864$	−82.4022	−2.80338
$865$	16.5775	0.563652
$866$	40.6224	1.38041
$867$	−4.61056	−0.156583
$868$	14.7665	0.501207
$869$	19.4906	0.661174
$870$	−8.40282	−0.284882
$871$	−39.4132	−1.33547
$872$	72.2539	2.44683
$873$	−37.3435	−1.26389
$874$	23.6084	0.798566
$875$	−12.6666	−0.428210
$876$	22.3453	0.754979
$877$	−34.8236	−1.17591	−0.587955	−	0.808893i	$-0.700067\pi$
$877$	−34.8236	−1.17591	−0.587955	+	0.808893i	$0.700067\pi$
$878$	33.9815	1.14682
$879$	5.74726	0.193850
$880$	−249.050	−8.39546
$881$	13.2100	0.445055	0.222528	−	0.974926i	$-0.428569\pi$
$881$	13.2100	0.445055	0.222528	+	0.974926i	$0.428569\pi$
$882$	−40.7585	−1.37241
$883$	47.8414	1.60999	0.804996	−	0.593280i	$-0.202167\pi$
$883$	47.8414	1.60999	0.804996	+	0.593280i	$0.202167\pi$
$884$	153.310	5.15636
$885$	−5.27837	−0.177430
$886$	−0.446337	−0.0149950
$887$	−3.22044	−0.108132	−0.0540658	−	0.998537i	$-0.517218\pi$
$887$	−3.22044	−0.108132	−0.0540658	+	0.998537i	$0.517218\pi$
$888$	51.9455	1.74318
$889$	25.4905	0.854923
$890$	10.6764	0.357873
$891$	−39.4011	−1.31999
$892$	−24.8344	−0.831517
$893$	5.54538	0.185569
$894$	26.4031	0.883051
$895$	53.8493	1.79998
$896$	−63.7200	−2.12873
$897$	−26.4965	−0.884691
$898$	−8.22209	−0.274375
$899$	−4.83993	−0.161421
$900$	−9.19071	−0.306357
$901$	−8.54100	−0.284542
$902$	−169.070	−5.62941
$903$	0.595028	0.0198013
$904$	−162.188	−5.39431
$905$	−21.6993	−0.721308
$906$	−6.09921	−0.202633
$907$	34.9399	1.16016	0.580080	−	0.814560i	$-0.303021\pi$
$907$	34.9399	1.16016	0.580080	+	0.814560i	$0.303021\pi$
$908$	82.0637	2.72338
$909$	37.2911	1.23687
$910$	43.3164	1.43592
$911$	−0.310684	−0.0102934	−0.00514672	−	0.999987i	$-0.501638\pi$
$911$	−0.310684	−0.0102934	−0.00514672	+	0.999987i	$0.501638\pi$
$912$	−9.40441	−0.311411
$913$	−46.7389	−1.54683
$914$	−91.4667	−3.02545
$915$	18.6752	0.617383
$916$	126.302	4.17313
$917$	−16.6913	−0.551195
$918$	44.8107	1.47897
$919$	33.3143	1.09894	0.549468	−	0.835515i	$-0.314830\pi$
$919$	33.3143	1.09894	0.549468	+	0.835515i	$0.314830\pi$
$920$	203.226	6.70016
$921$	−2.54206	−0.0837637
$922$	37.1265	1.22270
$923$	31.7270	1.04431
$924$	24.9981	0.822376
$925$	5.52827	0.181769
$926$	−56.6958	−1.86314
$927$	31.8849	1.04724
$928$	57.2421	1.87906
$929$	−20.7604	−0.681128	−0.340564	−	0.940221i	$-0.610618\pi$
$929$	−20.7604	−0.681128	−0.340564	+	0.940221i	$0.610618\pi$
$930$	8.03564	0.263499
$931$	−5.51603	−0.180781
$932$	−5.02322	−0.164541
$933$	8.52467	0.279085
$934$	−86.0205	−2.81468
$935$	75.6901	2.47533
$936$	−145.914	−4.76934
$937$	2.09752	0.0685231	0.0342616	−	0.999413i	$-0.489092\pi$
$937$	2.09752	0.0685231	0.0342616	+	0.999413i	$0.489092\pi$
$938$	−24.4157	−0.797201
$939$	−2.61545	−0.0853521
$940$	74.0046	2.41376
$941$	18.2517	0.594990	0.297495	−	0.954723i	$-0.403849\pi$
$941$	18.2517	0.594990	0.297495	+	0.954723i	$0.403849\pi$
$942$	−28.9375	−0.942835
$943$	81.9308	2.66804
$944$	64.3398	2.09408
$945$	9.34410	0.303963
$946$	−15.0899	−0.490616
$947$	−26.0648	−0.846993	−0.423496	−	0.905898i	$-0.639197\pi$
$947$	−26.0648	−0.846993	−0.423496	+	0.905898i	$0.639197\pi$
$948$	9.82198	0.319003
$949$	37.7552	1.22558
$950$	−1.68533	−0.0546794
$951$	0.570737	0.0185074
$952$	61.2606	1.98547
$953$	−11.8612	−0.384222	−0.192111	−	0.981373i	$-0.561533\pi$
$953$	−11.8612	−0.384222	−0.192111	+	0.981373i	$0.561533\pi$
$954$	12.6023	0.408016
$955$	16.7533	0.542124
$956$	−50.5133	−1.63372
$957$	−8.19349	−0.264858
$958$	81.2913	2.62640
$959$	12.4318	0.401442
$960$	−50.4885	−1.62951
$961$	−26.3716	−0.850696
$962$	136.067	4.38697
$963$	11.9540	0.385211
$964$	35.3495	1.13853
$965$	8.55077	0.275259
$966$	−16.4140	−0.528113
$967$	−13.2801	−0.427058	−0.213529	−	0.976937i	$-0.568496\pi$
$967$	−13.2801	−0.427058	−0.213529	+	0.976937i	$0.568496\pi$
$968$	−298.461	−9.59289
$969$	2.85815	0.0918169
$970$	−91.3858	−2.93422
$971$	41.7810	1.34082	0.670408	−	0.741993i	$-0.266119\pi$
$971$	41.7810	1.34082	0.670408	+	0.741993i	$0.266119\pi$
$972$	−74.5967	−2.39269
$973$	20.0952	0.644222
$974$	−114.596	−3.67189
$975$	1.89150	0.0605765
$976$	−227.638	−7.28652
$977$	−29.7683	−0.952372	−0.476186	−	0.879345i	$-0.657981\pi$
$977$	−29.7683	−0.952372	−0.476186	+	0.879345i	$0.657981\pi$
$978$	−17.8552	−0.570945
$979$	10.4104	0.332718
$980$	−73.6129	−2.35148
$981$	19.2418	0.614342
$982$	20.0644	0.640281
$983$	−7.43553	−0.237157	−0.118578	−	0.992945i	$-0.537834\pi$
$983$	−7.43553	−0.237157	−0.118578	+	0.992945i	$0.537834\pi$
$984$	−54.9572	−1.75197
$985$	−3.00498	−0.0957465
$986$	−31.1285	−0.991334
$987$	−3.85549	−0.122722
$988$	−30.6140	−0.973962
$989$	7.31254	0.232525
$990$	−111.682	−3.54947
$991$	52.9471	1.68192	0.840961	−	0.541096i	$-0.181991\pi$
$991$	52.9471	1.68192	0.840961	+	0.541096i	$0.181991\pi$
$992$	−54.7407	−1.73802
$993$	11.5782	0.367424
$994$	19.6542	0.623394
$995$	−58.2290	−1.84598
$996$	−23.5533	−0.746314
$997$	57.0829	1.80783	0.903917	−	0.427708i	$-0.140679\pi$
$997$	57.0829	1.80783	0.903917	+	0.427708i	$0.140679\pi$
$998$	57.4029	1.81706
$999$	29.3519	0.928654

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.c.1.2	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.c.1.2	✓	138	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76304 q^{2} -0.570737 q^{3} +5.63440 q^{4} +2.36853 q^{5} +1.57697 q^{6} +1.21818 q^{7} -10.0420 q^{8} -2.67426 q^{9} +O(q^{10})\)	\(q-2.76304 q^{2} -0.570737 q^{3} +5.63440 q^{4} +2.36853 q^{5} +1.57697 q^{6} +1.21818 q^{7} -10.0420 q^{8} -2.67426 q^{9} -6.54436 q^{10} -6.38132 q^{11} -3.21576 q^{12} -5.43341 q^{13} -3.36589 q^{14} -1.35181 q^{15} +16.4777 q^{16} -5.00782 q^{17} +7.38909 q^{18} +1.00000 q^{19} +13.3453 q^{20} -0.695262 q^{21} +17.6319 q^{22} -8.54435 q^{23} +5.73134 q^{24} +0.609955 q^{25} +15.0128 q^{26} +3.23851 q^{27} +6.86373 q^{28} -2.24969 q^{29} +3.73511 q^{30} +2.15138 q^{31} -25.4445 q^{32} +3.64206 q^{33} +13.8368 q^{34} +2.88531 q^{35} -15.0678 q^{36} +9.06341 q^{37} -2.76304 q^{38} +3.10105 q^{39} -23.7848 q^{40} -9.58889 q^{41} +1.92104 q^{42} -0.855833 q^{43} -35.9549 q^{44} -6.33408 q^{45} +23.6084 q^{46} +5.54538 q^{47} -9.40441 q^{48} -5.51603 q^{49} -1.68533 q^{50} +2.85815 q^{51} -30.6140 q^{52} +1.70553 q^{53} -8.94814 q^{54} -15.1144 q^{55} -12.2330 q^{56} -0.570737 q^{57} +6.21598 q^{58} +3.90467 q^{59} -7.61664 q^{60} -13.8150 q^{61} -5.94435 q^{62} -3.25774 q^{63} +37.3488 q^{64} -12.8692 q^{65} -10.0632 q^{66} +7.25386 q^{67} -28.2161 q^{68} +4.87658 q^{69} -7.97223 q^{70} -5.83924 q^{71} +26.8549 q^{72} -6.94870 q^{73} -25.0426 q^{74} -0.348124 q^{75} +5.63440 q^{76} -7.77361 q^{77} -8.56833 q^{78} -3.05433 q^{79} +39.0279 q^{80} +6.17444 q^{81} +26.4945 q^{82} +7.32433 q^{83} -3.91738 q^{84} -11.8612 q^{85} +2.36470 q^{86} +1.28398 q^{87} +64.0812 q^{88} -1.63139 q^{89} +17.5013 q^{90} -6.61889 q^{91} -48.1423 q^{92} -1.22787 q^{93} -15.3221 q^{94} +2.36853 q^{95} +14.5221 q^{96} +13.9641 q^{97} +15.2410 q^{98} +17.0653 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

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