LMFDB - Embedded newform 6023.2.a.a.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:	$1$
Dimension:	$98$
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)

$f(q)$	$=$	$q-2.72324 q^{2} -3.03839 q^{3} +5.41603 q^{4} -0.824121 q^{5} +8.27426 q^{6} -3.50609 q^{7} -9.30267 q^{8} +6.23182 q^{9} +O(q^{10})$	\(q-2.72324 q^{2} -3.03839 q^{3} +5.41603 q^{4} -0.824121 q^{5} +8.27426 q^{6} -3.50609 q^{7} -9.30267 q^{8} +6.23182 q^{9} +2.24428 q^{10} +0.569007 q^{11} -16.4560 q^{12} -3.25194 q^{13} +9.54792 q^{14} +2.50400 q^{15} +14.5013 q^{16} +2.62489 q^{17} -16.9707 q^{18} +1.00000 q^{19} -4.46347 q^{20} +10.6529 q^{21} -1.54954 q^{22} -0.600244 q^{23} +28.2651 q^{24} -4.32082 q^{25} +8.85581 q^{26} -9.81952 q^{27} -18.9891 q^{28} -4.10994 q^{29} -6.81900 q^{30} -0.0410899 q^{31} -20.8852 q^{32} -1.72887 q^{33} -7.14821 q^{34} +2.88944 q^{35} +33.7517 q^{36} +1.08062 q^{37} -2.72324 q^{38} +9.88067 q^{39} +7.66652 q^{40} -2.93193 q^{41} -29.0103 q^{42} +1.40497 q^{43} +3.08176 q^{44} -5.13577 q^{45} +1.63461 q^{46} +5.49746 q^{47} -44.0607 q^{48} +5.29267 q^{49} +11.7666 q^{50} -7.97545 q^{51} -17.6126 q^{52} -8.72679 q^{53} +26.7409 q^{54} -0.468931 q^{55} +32.6160 q^{56} -3.03839 q^{57} +11.1923 q^{58} -2.26602 q^{59} +13.5617 q^{60} +7.16612 q^{61} +0.111898 q^{62} -21.8493 q^{63} +27.8728 q^{64} +2.67999 q^{65} +4.70812 q^{66} +4.37513 q^{67} +14.2165 q^{68} +1.82378 q^{69} -7.86864 q^{70} +10.2853 q^{71} -57.9725 q^{72} -4.33950 q^{73} -2.94278 q^{74} +13.1284 q^{75} +5.41603 q^{76} -1.99499 q^{77} -26.9074 q^{78} -17.2864 q^{79} -11.9508 q^{80} +11.1401 q^{81} +7.98435 q^{82} +3.92035 q^{83} +57.6963 q^{84} -2.16323 q^{85} -3.82608 q^{86} +12.4876 q^{87} -5.29329 q^{88} -6.68955 q^{89} +13.9859 q^{90} +11.4016 q^{91} -3.25094 q^{92} +0.124847 q^{93} -14.9709 q^{94} -0.824121 q^{95} +63.4575 q^{96} -6.86728 q^{97} -14.4132 q^{98} +3.54595 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) $ 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9 - 24 * q^10 - 12 * q^11 - 51 * q^12 - 58 * q^13 - 15 * q^14 - 18 * q^15 + 58 * q^16 - 25 * q^17 - 40 * q^18 + 98 * q^19 - 12 * q^20 - 24 * q^21 - 59 * q^22 - 38 * q^23 - 9 * q^24 - 12 * q^25 - 3 * q^26 - 85 * q^27 - 33 * q^28 - 24 * q^29 - 22 * q^30 - 56 * q^31 - 29 * q^32 - 51 * q^33 - 38 * q^34 - 10 * q^35 + 50 * q^36 - 124 * q^37 - 8 * q^38 - 4 * q^39 - 80 * q^40 - 28 * q^41 - 37 * q^42 - 63 * q^43 - 7 * q^44 - 32 * q^45 - 47 * q^46 - 10 * q^47 - 88 * q^48 + 6 * q^49 - 17 * q^50 - 22 * q^51 - 119 * q^52 - 65 * q^53 + 24 * q^54 - 30 * q^55 - 39 * q^56 - 25 * q^57 - 91 * q^58 - 26 * q^59 - 60 * q^60 - 60 * q^61 + 6 * q^62 - 26 * q^63 + 50 * q^64 - 40 * q^65 + 57 * q^66 - 108 * q^67 - 41 * q^68 - 15 * q^69 - 36 * q^70 - 19 * q^71 - 47 * q^72 - 136 * q^73 + 22 * q^74 - 48 * q^75 + 82 * q^76 - 35 * q^77 - 56 * q^78 - 98 * q^79 - 42 * q^80 + 6 * q^81 - 37 * q^82 - 31 * q^83 - 24 * q^84 - 71 * q^85 - 24 * q^86 + 7 * q^87 - 166 * q^88 - 38 * q^89 + 26 * q^90 - 100 * q^91 - 59 * q^92 - 21 * q^93 - 48 * q^94 - 10 * q^95 - 16 * q^96 - 190 * q^97 - 80 * q^98 - 17 * 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 $

$2$	−2.72324	−1.92562	−0.962810	−	0.270178i	$-0.912917\pi$
$2$	−2.72324	−1.92562	−0.962810	+	0.270178i	$0.912917\pi$
$3$	−3.03839	−1.75422	−0.877108	−	0.480294i	$-0.840530\pi$
$3$	−3.03839	−1.75422	−0.877108	+	0.480294i	$0.840530\pi$
$4$	5.41603	2.70802
$5$	−0.824121	−0.368558	−0.184279	−	0.982874i	$-0.558995\pi$
$5$	−0.824121	−0.368558	−0.184279	+	0.982874i	$0.558995\pi$
$6$	8.27426	3.37795
$7$	−3.50609	−1.32518	−0.662589	−	0.748983i	$-0.730542\pi$
$7$	−3.50609	−1.32518	−0.662589	+	0.748983i	$0.730542\pi$
$8$	−9.30267	−3.28899
$9$	6.23182	2.07727
$10$	2.24428	0.709703
$11$	0.569007	0.171562	0.0857811	−	0.996314i	$-0.472661\pi$
$11$	0.569007	0.171562	0.0857811	+	0.996314i	$0.472661\pi$
$12$	−16.4560	−4.75044
$13$	−3.25194	−0.901926	−0.450963	−	0.892543i	$-0.648919\pi$
$13$	−3.25194	−0.901926	−0.450963	+	0.892543i	$0.648919\pi$
$14$	9.54792	2.55179
$15$	2.50400	0.646530
$16$	14.5013	3.62533
$17$	2.62489	0.636630	0.318315	−	0.947985i	$-0.396883\pi$
$17$	2.62489	0.636630	0.318315	+	0.947985i	$0.396883\pi$
$18$	−16.9707	−4.00004
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−4.46347	−0.998061
$21$	10.6529	2.32465
$22$	−1.54954	−0.330364
$23$	−0.600244	−0.125160	−0.0625798	−	0.998040i	$-0.519933\pi$
$23$	−0.600244	−0.125160	−0.0625798	+	0.998040i	$0.519933\pi$
$24$	28.2651	5.76960
$25$	−4.32082	−0.864165
$26$	8.85581	1.73677
$27$	−9.81952	−1.88977
$28$	−18.9891	−3.58860
$29$	−4.10994	−0.763197	−0.381598	−	0.924328i	$-0.624626\pi$
$29$	−4.10994	−0.763197	−0.381598	+	0.924328i	$0.624626\pi$
$30$	−6.81900	−1.24497
$31$	−0.0410899	−0.00737997	−0.00368998	−	0.999993i	$-0.501175\pi$
$31$	−0.0410899	−0.00737997	−0.00368998	+	0.999993i	$0.501175\pi$
$32$	−20.8852	−3.69202
$33$	−1.72887	−0.300957
$34$	−7.14821	−1.22591
$35$	2.88944	0.488405
$36$	33.7517	5.62528
$37$	1.08062	0.177653	0.0888263	−	0.996047i	$-0.471688\pi$
$37$	1.08062	0.177653	0.0888263	+	0.996047i	$0.471688\pi$
$38$	−2.72324	−0.441768
$39$	9.88067	1.58217
$40$	7.66652	1.21218
$41$	−2.93193	−0.457891	−0.228945	−	0.973439i	$-0.573528\pi$
$41$	−2.93193	−0.457891	−0.228945	+	0.973439i	$0.573528\pi$
$42$	−29.0103	−4.47639
$43$	1.40497	0.214256	0.107128	−	0.994245i	$-0.465834\pi$
$43$	1.40497	0.214256	0.107128	+	0.994245i	$0.465834\pi$
$44$	3.08176	0.464593
$45$	−5.13577	−0.765596
$46$	1.63461	0.241010
$47$	5.49746	0.801887	0.400943	−	0.916103i	$-0.368682\pi$
$47$	5.49746	0.801887	0.400943	+	0.916103i	$0.368682\pi$
$48$	−44.0607	−6.35961
$49$	5.29267	0.756095
$50$	11.7666	1.66405
$51$	−7.97545	−1.11679
$52$	−17.6126	−2.44243
$53$	−8.72679	−1.19872	−0.599359	−	0.800481i	$-0.704578\pi$
$53$	−8.72679	−1.19872	−0.599359	+	0.800481i	$0.704578\pi$
$54$	26.7409	3.63897
$55$	−0.468931	−0.0632306
$56$	32.6160	4.35849
$57$	−3.03839	−0.402445
$58$	11.1923	1.46963
$59$	−2.26602	−0.295011	−0.147506	−	0.989061i	$-0.547124\pi$
$59$	−2.26602	−0.295011	−0.147506	+	0.989061i	$0.547124\pi$
$60$	13.5617	1.75081
$61$	7.16612	0.917527	0.458764	−	0.888558i	$-0.348292\pi$
$61$	7.16612	0.917527	0.458764	+	0.888558i	$0.348292\pi$
$62$	0.111898	0.0142110
$63$	−21.8493	−2.75275
$64$	27.8728	3.48410
$65$	2.67999	0.332412
$66$	4.70812	0.579529
$67$	4.37513	0.534507	0.267254	−	0.963626i	$-0.413884\pi$
$67$	4.37513	0.534507	0.267254	+	0.963626i	$0.413884\pi$
$68$	14.2165	1.72400
$69$	1.82378	0.219557
$70$	−7.86864	−0.940483
$71$	10.2853	1.22065	0.610323	−	0.792153i	$-0.291040\pi$
$71$	10.2853	1.22065	0.610323	+	0.792153i	$0.291040\pi$
$72$	−57.9725	−6.83212
$73$	−4.33950	−0.507901	−0.253950	−	0.967217i	$-0.581730\pi$
$73$	−4.33950	−0.507901	−0.253950	+	0.967217i	$0.581730\pi$
$74$	−2.94278	−0.342091
$75$	13.1284	1.51593
$76$	5.41603	0.621261
$77$	−1.99499	−0.227350
$78$	−26.9074	−3.04666
$79$	−17.2864	−1.94488	−0.972438	−	0.233161i	$-0.925093\pi$
$79$	−17.2864	−1.94488	−0.972438	+	0.233161i	$0.925093\pi$
$80$	−11.9508	−1.33615
$81$	11.1401	1.23779
$82$	7.98435	0.881724
$83$	3.92035	0.430315	0.215157	−	0.976579i	$-0.430974\pi$
$83$	3.92035	0.430315	0.215157	+	0.976579i	$0.430974\pi$
$84$	57.6963	6.29518
$85$	−2.16323	−0.234635
$86$	−3.82608	−0.412577
$87$	12.4876	1.33881
$88$	−5.29329	−0.564266
$89$	−6.68955	−0.709091	−0.354545	−	0.935039i	$-0.615364\pi$
$89$	−6.68955	−0.709091	−0.354545	+	0.935039i	$0.615364\pi$
$90$	13.9859	1.47425
$91$	11.4016	1.19521
$92$	−3.25094	−0.338934
$93$	0.124847	0.0129461
$94$	−14.9709	−1.54413
$95$	−0.824121	−0.0845531
$96$	63.4575	6.47660
$97$	−6.86728	−0.697266	−0.348633	−	0.937259i	$-0.613354\pi$
$97$	−6.86728	−0.697266	−0.348633	+	0.937259i	$0.613354\pi$
$98$	−14.4132	−1.45595
$99$	3.54595	0.356381
$100$	−23.4017	−2.34017
$101$	2.07135	0.206107	0.103054	−	0.994676i	$-0.467139\pi$
$101$	2.07135	0.206107	0.103054	+	0.994676i	$0.467139\pi$
$102$	21.7191	2.15051
$103$	−2.60443	−0.256622	−0.128311	−	0.991734i	$-0.540956\pi$
$103$	−2.60443	−0.256622	−0.128311	+	0.991734i	$0.540956\pi$
$104$	30.2517	2.96643
$105$	−8.77926	−0.856768
$106$	23.7651	2.30828
$107$	10.5383	1.01878	0.509390	−	0.860536i	$-0.329871\pi$
$107$	10.5383	1.01878	0.509390	+	0.860536i	$0.329871\pi$
$108$	−53.1828	−5.11752
$109$	−1.49268	−0.142973	−0.0714864	−	0.997442i	$-0.522774\pi$
$109$	−1.49268	−0.142973	−0.0714864	+	0.997442i	$0.522774\pi$
$110$	1.27701	0.121758
$111$	−3.28334	−0.311641
$112$	−50.8429	−4.80421
$113$	16.7042	1.57139	0.785697	−	0.618611i	$-0.212304\pi$
$113$	16.7042	1.57139	0.785697	+	0.618611i	$0.212304\pi$
$114$	8.27426	0.774956
$115$	0.494674	0.0461286
$116$	−22.2596	−2.06675
$117$	−20.2655	−1.87355
$118$	6.17092	0.568080
$119$	−9.20311	−0.843648
$120$	−23.2939	−2.12643
$121$	−10.6762	−0.970566
$122$	−19.5151	−1.76681
$123$	8.90835	0.803239
$124$	−0.222544	−0.0199851
$125$	7.68149	0.687053
$126$	59.5009	5.30076
$127$	2.62336	0.232785	0.116393	−	0.993203i	$-0.462867\pi$
$127$	2.62336	0.232785	0.116393	+	0.993203i	$0.462867\pi$
$128$	−34.1339	−3.01704
$129$	−4.26886	−0.375852
$130$	−7.29826	−0.640100
$131$	1.67299	0.146170	0.0730850	−	0.997326i	$-0.476716\pi$
$131$	1.67299	0.146170	0.0730850	+	0.997326i	$0.476716\pi$
$132$	−9.36359	−0.814996
$133$	−3.50609	−0.304017
$134$	−11.9145	−1.02926
$135$	8.09247	0.696489
$136$	−24.4185	−2.09387
$137$	1.78897	0.152842	0.0764210	−	0.997076i	$-0.475651\pi$
$137$	1.78897	0.152842	0.0764210	+	0.997076i	$0.475651\pi$
$138$	−4.96658	−0.422783
$139$	2.42669	0.205830	0.102915	−	0.994690i	$-0.467183\pi$
$139$	2.42669	0.205830	0.102915	+	0.994690i	$0.467183\pi$
$140$	15.6493	1.32261
$141$	−16.7034	−1.40668
$142$	−28.0094	−2.35050
$143$	−1.85038	−0.154736
$144$	90.3696	7.53080
$145$	3.38709	0.281282
$146$	11.8175	0.978024
$147$	−16.0812	−1.32635
$148$	5.85266	0.481086
$149$	9.88098	0.809482	0.404741	−	0.914431i	$-0.367362\pi$
$149$	9.88098	0.809482	0.404741	+	0.914431i	$0.367362\pi$
$150$	−35.7516	−2.91911
$151$	16.5184	1.34425	0.672123	−	0.740440i	$-0.265383\pi$
$151$	16.5184	1.34425	0.672123	+	0.740440i	$0.265383\pi$
$152$	−9.30267	−0.754546
$153$	16.3578	1.32245
$154$	5.43284	0.437790
$155$	0.0338631	0.00271995
$156$	53.5140	4.28455
$157$	−13.1071	−1.04606	−0.523031	−	0.852313i	$-0.675199\pi$
$157$	−13.1071	−1.04606	−0.523031	+	0.852313i	$0.675199\pi$
$158$	47.0751	3.74509
$159$	26.5154	2.10281
$160$	17.2120	1.36073
$161$	2.10451	0.165859
$162$	−30.3371	−2.38351
$163$	−10.8935	−0.853249	−0.426624	−	0.904429i	$-0.640297\pi$
$163$	−10.8935	−0.853249	−0.426624	+	0.904429i	$0.640297\pi$
$164$	−15.8794	−1.23998
$165$	1.42480	0.110920
$166$	−10.6761	−0.828623
$167$	−3.11449	−0.241007	−0.120503	−	0.992713i	$-0.538451\pi$
$167$	−3.11449	−0.241007	−0.120503	+	0.992713i	$0.538451\pi$
$168$	−99.1001	−7.64574
$169$	−2.42488	−0.186529
$170$	5.89099	0.451818
$171$	6.23182	0.476559
$172$	7.60938	0.580210
$173$	7.63281	0.580312	0.290156	−	0.956979i	$-0.406293\pi$
$173$	7.63281	0.580312	0.290156	+	0.956979i	$0.406293\pi$
$174$	−34.0067	−2.57804
$175$	15.1492	1.14517
$176$	8.25136	0.621970
$177$	6.88506	0.517513
$178$	18.2172	1.36544
$179$	−12.5214	−0.935891	−0.467946	−	0.883757i	$-0.655006\pi$
$179$	−12.5214	−0.935891	−0.467946	+	0.883757i	$0.655006\pi$
$180$	−27.8155	−2.07324
$181$	−2.56933	−0.190977	−0.0954883	−	0.995431i	$-0.530441\pi$
$181$	−2.56933	−0.190977	−0.0954883	+	0.995431i	$0.530441\pi$
$182$	−31.0493	−2.30153
$183$	−21.7735	−1.60954
$184$	5.58387	0.411648
$185$	−0.890560	−0.0654753
$186$	−0.339989	−0.0249292
$187$	1.49358	0.109222
$188$	29.7744	2.17152
$189$	34.4281	2.50428
$190$	2.24428	0.162817
$191$	12.2526	0.886566	0.443283	−	0.896382i	$-0.353814\pi$
$191$	12.2526	0.886566	0.443283	+	0.896382i	$0.353814\pi$
$192$	−84.6886	−6.11187
$193$	−23.9525	−1.72414	−0.862070	−	0.506789i	$-0.830832\pi$
$193$	−23.9525	−1.72414	−0.862070	+	0.506789i	$0.830832\pi$
$194$	18.7012	1.34267
$195$	−8.14287	−0.583123
$196$	28.6652	2.04752
$197$	2.06555	0.147164	0.0735820	−	0.997289i	$-0.476557\pi$
$197$	2.06555	0.147164	0.0735820	+	0.997289i	$0.476557\pi$
$198$	−9.65647	−0.686255
$199$	0.422407	0.0299436	0.0149718	−	0.999888i	$-0.495234\pi$
$199$	0.422407	0.0299436	0.0149718	+	0.999888i	$0.495234\pi$
$200$	40.1952	2.84223
$201$	−13.2934	−0.937641
$202$	−5.64079	−0.396884
$203$	14.4098	1.01137
$204$	−43.1953	−3.02427
$205$	2.41627	0.168759
$206$	7.09248	0.494157
$207$	−3.74061	−0.259990
$208$	−47.1575	−3.26978
$209$	0.569007	0.0393591
$210$	23.9080	1.64981
$211$	27.2219	1.87403	0.937017	−	0.349284i	$-0.113575\pi$
$211$	27.2219	1.87403	0.937017	+	0.349284i	$0.113575\pi$
$212$	−47.2646	−3.24614
$213$	−31.2509	−2.14127
$214$	−28.6984	−1.96178
$215$	−1.15787	−0.0789660
$216$	91.3477	6.21542
$217$	0.144065	0.00977977
$218$	4.06492	0.275311
$219$	13.1851	0.890967
$220$	−2.53974	−0.171230
$221$	−8.53600	−0.574193
$222$	8.94132	0.600102
$223$	21.8748	1.46484	0.732422	−	0.680851i	$-0.238390\pi$
$223$	21.8748	1.46484	0.732422	+	0.680851i	$0.238390\pi$
$224$	73.2255	4.89258
$225$	−26.9266	−1.79511
$226$	−45.4894	−3.02591
$227$	18.5046	1.22819	0.614095	−	0.789232i	$-0.289521\pi$
$227$	18.5046	1.22819	0.614095	+	0.789232i	$0.289521\pi$
$228$	−16.4560	−1.08983
$229$	14.9026	0.984792	0.492396	−	0.870371i	$-0.336121\pi$
$229$	14.9026	0.984792	0.492396	+	0.870371i	$0.336121\pi$
$230$	−1.34712	−0.0888261
$231$	6.06156	0.398821
$232$	38.2334	2.51015
$233$	25.8247	1.69183	0.845917	−	0.533315i	$-0.179054\pi$
$233$	25.8247	1.69183	0.845917	+	0.533315i	$0.179054\pi$
$234$	55.1878	3.60774
$235$	−4.53057	−0.295542
$236$	−12.2729	−0.798895
$237$	52.5229	3.41173
$238$	25.0623	1.62455
$239$	8.87457	0.574048	0.287024	−	0.957923i	$-0.407334\pi$
$239$	8.87457	0.574048	0.287024	+	0.957923i	$0.407334\pi$
$240$	36.3113	2.34389
$241$	27.3794	1.76366	0.881831	−	0.471566i	$-0.156311\pi$
$241$	27.3794	1.76366	0.881831	+	0.471566i	$0.156311\pi$
$242$	29.0739	1.86894
$243$	−4.38935	−0.281577
$244$	38.8119	2.48468
$245$	−4.36180	−0.278665
$246$	−24.2596	−1.54673
$247$	−3.25194	−0.206916
$248$	0.382246	0.0242726
$249$	−11.9116	−0.754865
$250$	−20.9185	−1.32300
$251$	−4.10313	−0.258987	−0.129493	−	0.991580i	$-0.541335\pi$
$251$	−4.10313	−0.258987	−0.129493	+	0.991580i	$0.541335\pi$
$252$	−118.336	−7.45450
$253$	−0.341543	−0.0214726
$254$	−7.14403	−0.448256
$255$	6.57274	0.411601
$256$	37.2092	2.32557
$257$	−0.656772	−0.0409683	−0.0204842	−	0.999790i	$-0.506521\pi$
$257$	−0.656772	−0.0409683	−0.0204842	+	0.999790i	$0.506521\pi$
$258$	11.6251	0.723748
$259$	−3.78874	−0.235421
$260$	14.5149	0.900178
$261$	−25.6124	−1.58537
$262$	−4.55596	−0.281468
$263$	30.4806	1.87951	0.939756	−	0.341846i	$-0.111052\pi$
$263$	30.4806	1.87951	0.939756	+	0.341846i	$0.111052\pi$
$264$	16.0831	0.989844
$265$	7.19194	0.441797
$266$	9.54792	0.585421
$267$	20.3255	1.24390
$268$	23.6958	1.44745
$269$	26.7064	1.62832	0.814159	−	0.580641i	$-0.197198\pi$
$269$	26.7064	1.62832	0.814159	+	0.580641i	$0.197198\pi$
$270$	−22.0377	−1.34117
$271$	14.7530	0.896183	0.448092	−	0.893988i	$-0.352104\pi$
$271$	14.7530	0.896183	0.448092	+	0.893988i	$0.352104\pi$
$272$	38.0644	2.30799
$273$	−34.6425	−2.09666
$274$	−4.87179	−0.294316
$275$	−2.45858	−0.148258
$276$	9.87763	0.594563
$277$	16.4418	0.987891	0.493946	−	0.869493i	$-0.335554\pi$
$277$	16.4418	0.987891	0.493946	+	0.869493i	$0.335554\pi$
$278$	−6.60847	−0.396350
$279$	−0.256065	−0.0153302
$280$	−26.8795	−1.60636
$281$	−1.51621	−0.0904496	−0.0452248	−	0.998977i	$-0.514400\pi$
$281$	−1.51621	−0.0904496	−0.0452248	+	0.998977i	$0.514400\pi$
$282$	45.4874	2.70874
$283$	−23.4261	−1.39254	−0.696268	−	0.717782i	$-0.745157\pi$
$283$	−23.4261	−1.39254	−0.696268	+	0.717782i	$0.745157\pi$
$284$	55.7057	3.30553
$285$	2.50400	0.148324
$286$	5.03902	0.297964
$287$	10.2796	0.606786
$288$	−130.153	−7.66933
$289$	−10.1099	−0.594702
$290$	−9.22385	−0.541643
$291$	20.8655	1.22316
$292$	−23.5029	−1.37540
$293$	−6.93755	−0.405296	−0.202648	−	0.979252i	$-0.564955\pi$
$293$	−6.93755	−0.405296	−0.202648	+	0.979252i	$0.564955\pi$
$294$	43.7929	2.55405
$295$	1.86748	0.108729
$296$	−10.0526	−0.584297
$297$	−5.58738	−0.324213
$298$	−26.9083	−1.55875
$299$	1.95196	0.112885
$300$	71.1035	4.10516
$301$	−4.92596	−0.283928
$302$	−44.9834	−2.58851
$303$	−6.29358	−0.361556
$304$	14.5013	0.831708
$305$	−5.90575	−0.338162
$306$	−44.5463	−2.54654
$307$	11.3000	0.644926	0.322463	−	0.946582i	$-0.395489\pi$
$307$	11.3000	0.644926	0.322463	+	0.946582i	$0.395489\pi$
$308$	−10.8049	−0.615668
$309$	7.91327	0.450170
$310$	−0.0922172	−0.00523759
$311$	10.5769	0.599760	0.299880	−	0.953977i	$-0.403053\pi$
$311$	10.5769	0.599760	0.299880	+	0.953977i	$0.403053\pi$
$312$	−91.9165	−5.20375
$313$	5.31095	0.300193	0.150096	−	0.988671i	$-0.452042\pi$
$313$	5.31095	0.300193	0.150096	+	0.988671i	$0.452042\pi$
$314$	35.6939	2.01432
$315$	18.0065	1.01455
$316$	−93.6239	−5.26675
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	−72.2078	−4.04921
$319$	−2.33859	−0.130936
$320$	−22.9706	−1.28410
$321$	−32.0196	−1.78716
$322$	−5.73108	−0.319381
$323$	2.62489	0.146053
$324$	60.3350	3.35194
$325$	14.0511	0.779413
$326$	29.6657	1.64303
$327$	4.53534	0.250805
$328$	27.2748	1.50600
$329$	−19.2746	−1.06264
$330$	−3.88006	−0.213590
$331$	9.46961	0.520497	0.260248	−	0.965542i	$-0.416196\pi$
$331$	9.46961	0.520497	0.260248	+	0.965542i	$0.416196\pi$
$332$	21.2327	1.16530
$333$	6.73421	0.369033
$334$	8.48150	0.464087
$335$	−3.60564	−0.196997
$336$	154.481	8.42761
$337$	−17.6465	−0.961267	−0.480634	−	0.876921i	$-0.659593\pi$
$337$	−17.6465	−0.961267	−0.480634	+	0.876921i	$0.659593\pi$
$338$	6.60352	0.359184
$339$	−50.7537	−2.75656
$340$	−11.7161	−0.635396
$341$	−0.0233805	−0.00126612
$342$	−16.9707	−0.917672
$343$	5.98607	0.323217
$344$	−13.0700	−0.704687
$345$	−1.50301	−0.0809195
$346$	−20.7860	−1.11746
$347$	13.5300	0.726330	0.363165	−	0.931725i	$-0.381696\pi$
$347$	13.5300	0.726330	0.363165	+	0.931725i	$0.381696\pi$
$348$	67.6332	3.62552
$349$	−11.6195	−0.621977	−0.310988	−	0.950414i	$-0.600660\pi$
$349$	−11.6195	−0.621977	−0.310988	+	0.950414i	$0.600660\pi$
$350$	−41.2549	−2.20517
$351$	31.9325	1.70443
$352$	−11.8839	−0.633411
$353$	27.5495	1.46631	0.733157	−	0.680059i	$-0.238046\pi$
$353$	27.5495	1.46631	0.733157	+	0.680059i	$0.238046\pi$
$354$	−18.7497	−0.996534
$355$	−8.47637	−0.449879
$356$	−36.2308	−1.92023
$357$	27.9626	1.47994
$358$	34.0987	1.80217
$359$	15.2119	0.802854	0.401427	−	0.915891i	$-0.368514\pi$
$359$	15.2119	0.802854	0.401427	+	0.915891i	$0.368514\pi$
$360$	47.7764	2.51804
$361$	1.00000	0.0526316
$362$	6.99690	0.367749
$363$	32.4386	1.70258
$364$	61.7514	3.23665
$365$	3.57628	0.187191
$366$	59.2943	3.09937
$367$	−9.23393	−0.482007	−0.241004	−	0.970524i	$-0.577477\pi$
$367$	−9.23393	−0.482007	−0.241004	+	0.970524i	$0.577477\pi$
$368$	−8.70433	−0.453745
$369$	−18.2713	−0.951164
$370$	2.42521	0.126081
$371$	30.5969	1.58851
$372$	0.676176	0.0350581
$373$	21.5810	1.11742	0.558710	−	0.829363i	$-0.311296\pi$
$373$	21.5810	1.11742	0.558710	+	0.829363i	$0.311296\pi$
$374$	−4.06738	−0.210319
$375$	−23.3394	−1.20524
$376$	−51.1410	−2.63740
$377$	13.3653	0.688347
$378$	−93.7560	−4.82229
$379$	−23.9328	−1.22934	−0.614671	−	0.788783i	$-0.710711\pi$
$379$	−23.9328	−1.22934	−0.614671	+	0.788783i	$0.710711\pi$
$380$	−4.46347	−0.228971
$381$	−7.97079	−0.408356
$382$	−33.3667	−1.70719
$383$	−20.4466	−1.04477	−0.522385	−	0.852710i	$-0.674958\pi$
$383$	−20.4466	−1.04477	−0.522385	+	0.852710i	$0.674958\pi$
$384$	103.712	5.29254
$385$	1.64411	0.0837918
$386$	65.2284	3.32004
$387$	8.75554	0.445069
$388$	−37.1934	−1.88821
$389$	−29.9600	−1.51903	−0.759516	−	0.650488i	$-0.774564\pi$
$389$	−29.9600	−1.51903	−0.759516	+	0.650488i	$0.774564\pi$
$390$	22.1750	1.12287
$391$	−1.57558	−0.0796803
$392$	−49.2359	−2.48679
$393$	−5.08320	−0.256414
$394$	−5.62497	−0.283382
$395$	14.2461	0.716800
$396$	19.2050	0.965086
$397$	−4.61728	−0.231735	−0.115867	−	0.993265i	$-0.536965\pi$
$397$	−4.61728	−0.231735	−0.115867	+	0.993265i	$0.536965\pi$
$398$	−1.15031	−0.0576601
$399$	10.6529	0.533311
$400$	−62.6577	−3.13288
$401$	−29.9514	−1.49570	−0.747852	−	0.663866i	$-0.768915\pi$
$401$	−29.9514	−1.49570	−0.747852	+	0.663866i	$0.768915\pi$
$402$	36.2010	1.80554
$403$	0.133622	0.00665619
$404$	11.2185	0.558141
$405$	−9.18077	−0.456196
$406$	−39.2414	−1.94752
$407$	0.614880	0.0304784
$408$	74.1929	3.67310
$409$	−2.29070	−0.113268	−0.0566338	−	0.998395i	$-0.518037\pi$
$409$	−2.29070	−0.113268	−0.0566338	+	0.998395i	$0.518037\pi$
$410$	−6.58007	−0.324967
$411$	−5.43559	−0.268118
$412$	−14.1057	−0.694936
$413$	7.94488	0.390942
$414$	10.1866	0.500643
$415$	−3.23085	−0.158596
$416$	67.9176	3.32993
$417$	−7.37324	−0.361069
$418$	−1.54954	−0.0757906
$419$	34.9113	1.70553	0.852765	−	0.522295i	$-0.174924\pi$
$419$	34.9113	1.70553	0.852765	+	0.522295i	$0.174924\pi$
$420$	−47.5487	−2.32014
$421$	−12.5159	−0.609987	−0.304994	−	0.952354i	$-0.598654\pi$
$421$	−12.5159	−0.609987	−0.304994	+	0.952354i	$0.598654\pi$
$422$	−74.1318	−3.60868
$423$	34.2591	1.66574
$424$	81.1825	3.94257
$425$	−11.3417	−0.550153
$426$	85.1036	4.12328
$427$	−25.1251	−1.21589
$428$	57.0760	2.75887
$429$	5.62217	0.271441
$430$	3.15315	0.152059
$431$	4.66658	0.224781	0.112391	−	0.993664i	$-0.464149\pi$
$431$	4.66658	0.224781	0.112391	+	0.993664i	$0.464149\pi$
$432$	−142.396	−6.85103
$433$	−35.3557	−1.69909	−0.849544	−	0.527518i	$-0.823123\pi$
$433$	−35.3557	−1.69909	−0.849544	+	0.527518i	$0.823123\pi$
$434$	−0.392323	−0.0188321
$435$	−10.2913	−0.493430
$436$	−8.08440	−0.387173
$437$	−0.600244	−0.0287136
$438$	−35.9062	−1.71566
$439$	−32.7073	−1.56104	−0.780518	−	0.625133i	$-0.785045\pi$
$439$	−32.7073	−1.56104	−0.780518	+	0.625133i	$0.785045\pi$
$440$	4.36231	0.207965
$441$	32.9829	1.57062
$442$	23.2456	1.10568
$443$	−14.4577	−0.686906	−0.343453	−	0.939170i	$-0.611597\pi$
$443$	−14.4577	−0.686906	−0.343453	+	0.939170i	$0.611597\pi$
$444$	−17.7827	−0.843928
$445$	5.51300	0.261341
$446$	−59.5703	−2.82073
$447$	−30.0223	−1.42001
$448$	−97.7247	−4.61706
$449$	−20.1772	−0.952221	−0.476111	−	0.879385i	$-0.657954\pi$
$449$	−20.1772	−0.952221	−0.476111	+	0.879385i	$0.657954\pi$
$450$	73.3275	3.45669
$451$	−1.66829	−0.0785567
$452$	90.4702	4.25536
$453$	−50.1892	−2.35810
$454$	−50.3923	−2.36503
$455$	−9.39630	−0.440505
$456$	28.2651	1.32364
$457$	17.7371	0.829709	0.414854	−	0.909888i	$-0.363833\pi$
$457$	17.7371	0.829709	0.414854	+	0.909888i	$0.363833\pi$
$458$	−40.5834	−1.89634
$459$	−25.7752	−1.20308
$460$	2.67917	0.124917
$461$	30.4889	1.42001	0.710005	−	0.704197i	$-0.248693\pi$
$461$	30.4889	1.42001	0.710005	+	0.704197i	$0.248693\pi$
$462$	−16.5071	−0.767979
$463$	17.2627	0.802266	0.401133	−	0.916020i	$-0.368617\pi$
$463$	17.2627	0.802266	0.401133	+	0.916020i	$0.368617\pi$
$464$	−59.5996	−2.76684
$465$	−0.102889	−0.00477137
$466$	−70.3269	−3.25783
$467$	−29.3658	−1.35889	−0.679443	−	0.733728i	$-0.737779\pi$
$467$	−29.3658	−1.35889	−0.679443	+	0.733728i	$0.737779\pi$
$468$	−109.759	−5.07359
$469$	−15.3396	−0.708317
$470$	12.3378	0.569102
$471$	39.8246	1.83502
$472$	21.0801	0.970288
$473$	0.799440	0.0367583
$474$	−143.033	−6.56970
$475$	−4.32082	−0.198253
$476$	−49.8443	−2.28461
$477$	−54.3838	−2.49006
$478$	−24.1676	−1.10540
$479$	−12.6694	−0.578879	−0.289439	−	0.957196i	$-0.593469\pi$
$479$	−12.6694	−0.578879	−0.289439	+	0.957196i	$0.593469\pi$
$480$	−52.2967	−2.38701
$481$	−3.51411	−0.160229
$482$	−74.5606	−3.39614
$483$	−6.39432	−0.290952
$484$	−57.8228	−2.62831
$485$	5.65947	0.256983
$486$	11.9533	0.542211
$487$	−40.2776	−1.82515	−0.912575	−	0.408908i	$-0.865910\pi$
$487$	−40.2776	−1.82515	−0.912575	+	0.408908i	$0.865910\pi$
$488$	−66.6640	−3.01774
$489$	33.0989	1.49678
$490$	11.8782	0.536603
$491$	13.5378	0.610951	0.305475	−	0.952200i	$-0.401185\pi$
$491$	13.5378	0.610951	0.305475	+	0.952200i	$0.401185\pi$
$492$	48.2479	2.17518
$493$	−10.7882	−0.485874
$494$	8.85581	0.398442
$495$	−2.92229	−0.131347
$496$	−0.595858	−0.0267548
$497$	−36.0613	−1.61757
$498$	32.4380	1.45358
$499$	0.314687	0.0140873	0.00704366	−	0.999975i	$-0.497758\pi$
$499$	0.314687	0.0140873	0.00704366	+	0.999975i	$0.497758\pi$
$500$	41.6032	1.86055
$501$	9.46304	0.422778
$502$	11.1738	0.498711
$503$	3.57123	0.159233	0.0796167	−	0.996826i	$-0.474630\pi$
$503$	3.57123	0.159233	0.0796167	+	0.996826i	$0.474630\pi$
$504$	203.257	9.05378
$505$	−1.70705	−0.0759625
$506$	0.930104	0.0413482
$507$	7.36773	0.327212
$508$	14.2082	0.630387
$509$	15.7601	0.698555	0.349278	−	0.937019i	$-0.386427\pi$
$509$	15.7601	0.698555	0.349278	+	0.937019i	$0.386427\pi$
$510$	−17.8991	−0.792587
$511$	15.2147	0.673058
$512$	−33.0616	−1.46113
$513$	−9.81952	−0.433542
$514$	1.78855	0.0788895
$515$	2.14637	0.0945802
$516$	−23.1203	−1.01781
$517$	3.12809	0.137573
$518$	10.3177	0.453332
$519$	−23.1915	−1.01799
$520$	−24.9311	−1.09330
$521$	−37.2574	−1.63228	−0.816138	−	0.577858i	$-0.803889\pi$
$521$	−37.2574	−1.63228	−0.816138	+	0.577858i	$0.803889\pi$
$522$	69.7486	3.05281
$523$	−17.9455	−0.784700	−0.392350	−	0.919816i	$-0.628338\pi$
$523$	−17.9455	−0.784700	−0.392350	+	0.919816i	$0.628338\pi$
$524$	9.06097	0.395831
$525$	−46.0292	−2.00888
$526$	−83.0059	−3.61923
$527$	−0.107857	−0.00469831
$528$	−25.0708	−1.09107
$529$	−22.6397	−0.984335
$530$	−19.5854	−0.850734
$531$	−14.1214	−0.612818
$532$	−18.9891	−0.823281
$533$	9.53447	0.412984
$534$	−55.3511	−2.39528
$535$	−8.68487	−0.375480
$536$	−40.7004	−1.75799
$537$	38.0448	1.64175
$538$	−72.7280	−3.13552
$539$	3.01157	0.129717
$540$	43.8291	1.88610
$541$	−42.3574	−1.82109	−0.910543	−	0.413414i	$-0.864336\pi$
$541$	−42.3574	−1.82109	−0.910543	+	0.413414i	$0.864336\pi$
$542$	−40.1760	−1.72571
$543$	7.80662	0.335014
$544$	−54.8215	−2.35045
$545$	1.23015	0.0526938
$546$	94.3398	4.03737
$547$	5.05728	0.216234	0.108117	−	0.994138i	$-0.465518\pi$
$547$	5.05728	0.216234	0.108117	+	0.994138i	$0.465518\pi$
$548$	9.68911	0.413898
$549$	44.6579	1.90595
$550$	6.69530	0.285489
$551$	−4.10994	−0.175089
$552$	−16.9660	−0.722120
$553$	60.6078	2.57731
$554$	−44.7749	−1.90230
$555$	2.70587	0.114858
$556$	13.1430	0.557389
$557$	2.32729	0.0986104	0.0493052	−	0.998784i	$-0.484299\pi$
$557$	2.32729	0.0986104	0.0493052	+	0.998784i	$0.484299\pi$
$558$	0.697326	0.0295201
$559$	−4.56889	−0.193244
$560$	41.9007	1.77063
$561$	−4.53809	−0.191598
$562$	4.12901	0.174172
$563$	41.7572	1.75986	0.879928	−	0.475107i	$-0.157591\pi$
$563$	41.7572	1.75986	0.879928	+	0.475107i	$0.157591\pi$
$564$	−90.4663	−3.80932
$565$	−13.7662	−0.579150
$566$	63.7948	2.68149
$567$	−39.0581	−1.64029
$568$	−95.6811	−4.01469
$569$	28.2746	1.18533	0.592666	−	0.805448i	$-0.298075\pi$
$569$	28.2746	1.18533	0.592666	+	0.805448i	$0.298075\pi$
$570$	−6.81900	−0.285616
$571$	4.10532	0.171802	0.0859011	−	0.996304i	$-0.472623\pi$
$571$	4.10532	0.171802	0.0859011	+	0.996304i	$0.472623\pi$
$572$	−10.0217	−0.419029
$573$	−37.2281	−1.55523
$574$	−27.9938	−1.16844
$575$	2.59355	0.108158
$576$	173.698	7.23743
$577$	−26.4627	−1.10166	−0.550828	−	0.834619i	$-0.685688\pi$
$577$	−26.4627	−1.10166	−0.550828	+	0.834619i	$0.685688\pi$
$578$	27.5318	1.14517
$579$	72.7771	3.02451
$580$	18.3446	0.761717
$581$	−13.7451	−0.570243
$582$	−56.8217	−2.35533
$583$	−4.96561	−0.205655
$584$	40.3690	1.67048
$585$	16.7012	0.690511
$586$	18.8926	0.780447
$587$	−6.84937	−0.282704	−0.141352	−	0.989959i	$-0.545145\pi$
$587$	−6.84937	−0.282704	−0.141352	+	0.989959i	$0.545145\pi$
$588$	−87.0962	−3.59179
$589$	−0.0410899	−0.00169308
$590$	−5.08559	−0.209370
$591$	−6.27593	−0.258157
$592$	15.6704	0.644049
$593$	5.18103	0.212759	0.106380	−	0.994326i	$-0.466074\pi$
$593$	5.18103	0.212759	0.106380	+	0.994326i	$0.466074\pi$
$594$	15.2158	0.624310
$595$	7.58448	0.310933
$596$	53.5157	2.19209
$597$	−1.28344	−0.0525276
$598$	−5.31565	−0.217373
$599$	−14.0254	−0.573062	−0.286531	−	0.958071i	$-0.592502\pi$
$599$	−14.0254	−0.573062	−0.286531	+	0.958071i	$0.592502\pi$
$600$	−122.129	−4.98588
$601$	−0.206028	−0.00840407	−0.00420204	−	0.999991i	$-0.501338\pi$
$601$	−0.206028	−0.00840407	−0.00420204	+	0.999991i	$0.501338\pi$
$602$	13.4146	0.546737
$603$	27.2650	1.11032
$604$	89.4639	3.64024
$605$	8.79851	0.357710
$606$	17.1389	0.696221
$607$	25.9685	1.05403	0.527014	−	0.849857i	$-0.323312\pi$
$607$	25.9685	1.05403	0.527014	+	0.849857i	$0.323312\pi$
$608$	−20.8852	−0.847008
$609$	−43.7826	−1.77416
$610$	16.0828	0.651172
$611$	−17.8774	−0.723243
$612$	88.5946	3.58122
$613$	1.55071	0.0626326	0.0313163	−	0.999510i	$-0.490030\pi$
$613$	1.55071	0.0626326	0.0313163	+	0.999510i	$0.490030\pi$
$614$	−30.7726	−1.24188
$615$	−7.34156	−0.296040
$616$	18.5587	0.747753
$617$	38.1067	1.53412	0.767058	−	0.641578i	$-0.221720\pi$
$617$	38.1067	1.53412	0.767058	+	0.641578i	$0.221720\pi$
$618$	−21.5497	−0.866857
$619$	41.7703	1.67889	0.839445	−	0.543445i	$-0.182880\pi$
$619$	41.7703	1.67889	0.839445	+	0.543445i	$0.182880\pi$
$620$	0.183403	0.00736566
$621$	5.89411	0.236522
$622$	−28.8034	−1.15491
$623$	23.4542	0.939671
$624$	143.283	5.73590
$625$	15.2736	0.610946
$626$	−14.4630	−0.578058
$627$	−1.72887	−0.0690443
$628$	−70.9886	−2.83275
$629$	2.83651	0.113099
$630$	−49.0359	−1.95364
$631$	−29.1613	−1.16089	−0.580446	−	0.814299i	$-0.697122\pi$
$631$	−29.1613	−1.16089	−0.580446	+	0.814299i	$0.697122\pi$
$632$	160.810	6.39668
$633$	−82.7108	−3.28746
$634$	−2.72324	−0.108154
$635$	−2.16197	−0.0857950
$636$	143.608	5.69444
$637$	−17.2114	−0.681942
$638$	6.36853	0.252132
$639$	64.0963	2.53561
$640$	28.1305	1.11196
$641$	−25.2930	−0.999014	−0.499507	−	0.866310i	$-0.666485\pi$
$641$	−25.2930	−0.999014	−0.499507	+	0.866310i	$0.666485\pi$
$642$	87.1970	3.44139
$643$	29.2917	1.15515	0.577577	−	0.816336i	$-0.303998\pi$
$643$	29.2917	1.15515	0.577577	+	0.816336i	$0.303998\pi$
$644$	11.3981	0.449148
$645$	3.51806	0.138523
$646$	−7.14821	−0.281243
$647$	29.9561	1.17770	0.588848	−	0.808244i	$-0.299582\pi$
$647$	29.9561	1.17770	0.588848	+	0.808244i	$0.299582\pi$
$648$	−103.632	−4.07107
$649$	−1.28938	−0.0506127
$650$	−38.2644	−1.50085
$651$	−0.437726	−0.0171558
$652$	−58.9998	−2.31061
$653$	2.46383	0.0964171	0.0482085	−	0.998837i	$-0.484649\pi$
$653$	2.46383	0.0964171	0.0482085	+	0.998837i	$0.484649\pi$
$654$	−12.3508	−0.482956
$655$	−1.37875	−0.0538721
$656$	−42.5169	−1.66001
$657$	−27.0430	−1.05505
$658$	52.4893	2.04625
$659$	0.412838	0.0160819	0.00804095	−	0.999968i	$-0.497440\pi$
$659$	0.412838	0.0160819	0.00804095	+	0.999968i	$0.497440\pi$
$660$	7.71674	0.300374
$661$	48.5867	1.88980	0.944901	−	0.327356i	$-0.106158\pi$
$661$	48.5867	1.88980	0.944901	+	0.327356i	$0.106158\pi$
$662$	−25.7880	−1.00228
$663$	25.9357	1.00726
$664$	−36.4697	−1.41530
$665$	2.88944	0.112048
$666$	−18.3389	−0.710617
$667$	2.46697	0.0955213
$668$	−16.8682	−0.652650
$669$	−66.4641	−2.56965
$670$	9.81901	0.379342
$671$	4.07757	0.157413
$672$	−222.488	−8.58265
$673$	20.8948	0.805434	0.402717	−	0.915325i	$-0.368066\pi$
$673$	20.8948	0.805434	0.402717	+	0.915325i	$0.368066\pi$
$674$	48.0557	1.85104
$675$	42.4284	1.63307
$676$	−13.1332	−0.505124
$677$	−32.4160	−1.24585	−0.622924	−	0.782282i	$-0.714055\pi$
$677$	−32.4160	−1.24585	−0.622924	+	0.782282i	$0.714055\pi$
$678$	138.215	5.30810
$679$	24.0773	0.924002
$680$	20.1238	0.771713
$681$	−56.2241	−2.15451
$682$	0.0636706	0.00243807
$683$	−29.7343	−1.13775	−0.568877	−	0.822423i	$-0.692622\pi$
$683$	−29.7343	−1.13775	−0.568877	+	0.822423i	$0.692622\pi$
$684$	33.7517	1.29053
$685$	−1.47433	−0.0563312
$686$	−16.3015	−0.622394
$687$	−45.2799	−1.72754
$688$	20.3740	0.776751
$689$	28.3790	1.08115
$690$	4.09306	0.155820
$691$	20.3367	0.773644	0.386822	−	0.922154i	$-0.373573\pi$
$691$	20.3367	0.773644	0.386822	+	0.922154i	$0.373573\pi$
$692$	41.3395	1.57149
$693$	−12.4324	−0.472268
$694$	−36.8455	−1.39864
$695$	−1.99989	−0.0758602
$696$	−116.168	−4.40334
$697$	−7.69601	−0.291507
$698$	31.6426	1.19769
$699$	−78.4656	−2.96784
$700$	82.0485	3.10114
$701$	−34.3189	−1.29621	−0.648104	−	0.761552i	$-0.724438\pi$
$701$	−34.3189	−1.29621	−0.648104	+	0.761552i	$0.724438\pi$
$702$	−86.9598	−3.28209
$703$	1.08062	0.0407563
$704$	15.8598	0.597741
$705$	13.7656	0.518444
$706$	−75.0240	−2.82356
$707$	−7.26235	−0.273129
$708$	37.2897	1.40143
$709$	−21.5975	−0.811113	−0.405556	−	0.914070i	$-0.632922\pi$
$709$	−21.5975	−0.811113	−0.405556	+	0.914070i	$0.632922\pi$
$710$	23.0832	0.866296
$711$	−107.726	−4.04004
$712$	62.2306	2.33219
$713$	0.0246640	0.000923673 0
$714$	−76.1490	−2.84980
$715$	1.52494	0.0570294
$716$	−67.8161	−2.53441
$717$	−26.9644	−1.00700
$718$	−41.4257	−1.54599
$719$	−43.9813	−1.64023	−0.820113	−	0.572201i	$-0.806090\pi$
$719$	−43.9813	−1.64023	−0.820113	+	0.572201i	$0.806090\pi$
$720$	−74.4755	−2.77554
$721$	9.13136	0.340070
$722$	−2.72324	−0.101348
$723$	−83.1893	−3.09384
$724$	−13.9156	−0.517168
$725$	17.7583	0.659528
$726$	−88.3379	−3.27853
$727$	−33.8269	−1.25457	−0.627285	−	0.778790i	$-0.715834\pi$
$727$	−33.8269	−1.25457	−0.627285	+	0.778790i	$0.715834\pi$
$728$	−106.065	−3.93104
$729$	−20.0837	−0.743839
$730$	−9.73906	−0.360459
$731$	3.68791	0.136402
$732$	−117.926	−4.35866
$733$	9.25488	0.341837	0.170918	−	0.985285i	$-0.445327\pi$
$733$	9.25488	0.341837	0.170918	+	0.985285i	$0.445327\pi$
$734$	25.1462	0.928164
$735$	13.2528	0.488839
$736$	12.5362	0.462092
$737$	2.48948	0.0917012
$738$	49.7570	1.83158
$739$	−10.4256	−0.383513	−0.191756	−	0.981443i	$-0.561418\pi$
$739$	−10.4256	−0.383513	−0.191756	+	0.981443i	$0.561418\pi$
$740$	−4.82330	−0.177308
$741$	9.88067	0.362975
$742$	−83.3227	−3.05887
$743$	−0.744819	−0.0273248	−0.0136624	−	0.999907i	$-0.504349\pi$
$743$	−0.744819	−0.0273248	−0.0136624	+	0.999907i	$0.504349\pi$
$744$	−1.16141	−0.0425794
$745$	−8.14313	−0.298341
$746$	−58.7701	−2.15173
$747$	24.4309	0.893880
$748$	8.08929	0.295774
$749$	−36.9484	−1.35006
$750$	63.5587	2.32083
$751$	36.6797	1.33846	0.669231	−	0.743055i	$-0.266624\pi$
$751$	36.6797	1.33846	0.669231	+	0.743055i	$0.266624\pi$
$752$	79.7204	2.90710
$753$	12.4669	0.454319
$754$	−36.3969	−1.32550
$755$	−13.6131	−0.495433
$756$	186.464	6.78162
$757$	−37.4593	−1.36148	−0.680741	−	0.732524i	$-0.738342\pi$
$757$	−37.4593	−1.36148	−0.680741	+	0.732524i	$0.738342\pi$
$758$	65.1746	2.36725
$759$	1.03774	0.0376676
$760$	7.66652	0.278094
$761$	−45.0040	−1.63140	−0.815698	−	0.578479i	$-0.803647\pi$
$761$	−45.0040	−1.63140	−0.815698	+	0.578479i	$0.803647\pi$
$762$	21.7064	0.786338
$763$	5.23347	0.189464
$764$	66.3604	2.40083
$765$	−13.4808	−0.487401
$766$	55.6809	2.01183
$767$	7.36898	0.266078
$768$	−113.056	−4.07955
$769$	−35.2197	−1.27005	−0.635027	−	0.772490i	$-0.719011\pi$
$769$	−35.2197	−1.27005	−0.635027	+	0.772490i	$0.719011\pi$
$770$	−4.47732	−0.161351
$771$	1.99553	0.0718673
$772$	−129.728	−4.66900
$773$	22.7114	0.816871	0.408436	−	0.912787i	$-0.366074\pi$
$773$	22.7114	0.816871	0.408436	+	0.912787i	$0.366074\pi$
$774$	−23.8434	−0.857034
$775$	0.177542	0.00637751
$776$	63.8840	2.29330
$777$	11.5117	0.412979
$778$	81.5883	2.92508
$779$	−2.93193	−0.105047
$780$	−44.1020	−1.57911
$781$	5.85243	0.209417
$782$	4.29067	0.153434
$783$	40.3576	1.44226
$784$	76.7507	2.74109
$785$	10.8019	0.385535
$786$	13.8428	0.493755
$787$	2.37817	0.0847727	0.0423864	−	0.999101i	$-0.486504\pi$
$787$	2.37817	0.0847727	0.0423864	+	0.999101i	$0.486504\pi$
$788$	11.1871	0.398522
$789$	−92.6118	−3.29707
$790$	−38.7956	−1.38029
$791$	−58.5663	−2.08238
$792$	−32.9868	−1.17213
$793$	−23.3038	−0.827542
$794$	12.5740	0.446233
$795$	−21.8519	−0.775007
$796$	2.28777	0.0810878
$797$	10.3496	0.366602	0.183301	−	0.983057i	$-0.441322\pi$
$797$	10.3496	0.366602	0.183301	+	0.983057i	$0.441322\pi$
$798$	−29.0103	−1.02695
$799$	14.4302	0.510505
$800$	90.2414	3.19052
$801$	−41.6880	−1.47297
$802$	81.5649	2.88016
$803$	−2.46921	−0.0871365
$804$	−71.9972	−2.53915
$805$	−1.73437	−0.0611285
$806$	−0.363885	−0.0128173
$807$	−81.1445	−2.85642
$808$	−19.2691	−0.677884
$809$	−17.1391	−0.602580	−0.301290	−	0.953532i	$-0.597417\pi$
$809$	−17.1391	−0.602580	−0.301290	+	0.953532i	$0.597417\pi$
$810$	25.0014	0.878461
$811$	−7.86075	−0.276028	−0.138014	−	0.990430i	$-0.544072\pi$
$811$	−7.86075	−0.276028	−0.138014	+	0.990430i	$0.544072\pi$
$812$	78.0440	2.73881
$813$	−44.8255	−1.57210
$814$	−1.67446	−0.0586899
$815$	8.97760	0.314472
$816$	−115.655	−4.04872
$817$	1.40497	0.0491538
$818$	6.23811	0.218111
$819$	71.0527	2.48278
$820$	13.0866	0.457003
$821$	30.4590	1.06303	0.531514	−	0.847049i	$-0.321623\pi$
$821$	30.4590	1.06303	0.531514	+	0.847049i	$0.321623\pi$
$822$	14.8024	0.516293
$823$	−45.4070	−1.58279	−0.791394	−	0.611307i	$-0.790644\pi$
$823$	−45.4070	−1.58279	−0.791394	+	0.611307i	$0.790644\pi$
$824$	24.2281	0.844027
$825$	7.47013	0.260076
$826$	−21.6358	−0.752806
$827$	−18.3116	−0.636758	−0.318379	−	0.947963i	$-0.603139\pi$
$827$	−18.3116	−0.636758	−0.318379	+	0.947963i	$0.603139\pi$
$828$	−20.2593	−0.704058
$829$	41.2350	1.43215	0.716076	−	0.698022i	$-0.245936\pi$
$829$	41.2350	1.43215	0.716076	+	0.698022i	$0.245936\pi$
$830$	8.79837	0.305396
$831$	−49.9566	−1.73297
$832$	−90.6408	−3.14241
$833$	13.8927	0.481353
$834$	20.0791	0.695283
$835$	2.56672	0.0888250
$836$	3.08176	0.106585
$837$	0.403483	0.0139464
$838$	−95.0719	−3.28420
$839$	−18.0629	−0.623602	−0.311801	−	0.950147i	$-0.600932\pi$
$839$	−18.0629	−0.623602	−0.311801	+	0.950147i	$0.600932\pi$
$840$	81.6705	2.81790
$841$	−12.1084	−0.417531
$842$	34.0838	1.17460
$843$	4.60684	0.158668
$844$	147.435	5.07491
$845$	1.99839	0.0687468
$846$	−93.2958	−3.20758
$847$	37.4318	1.28617
$848$	−126.550	−4.34575
$849$	71.1775	2.44281
$850$	30.8862	1.05939
$851$	−0.648635	−0.0222349
$852$	−169.256	−5.79860
$853$	−42.6317	−1.45968	−0.729841	−	0.683617i	$-0.760406\pi$
$853$	−42.6317	−1.45968	−0.729841	+	0.683617i	$0.760406\pi$
$854$	68.4215	2.34134
$855$	−5.13577	−0.175640
$856$	−98.0347	−3.35076
$857$	−41.8499	−1.42957	−0.714783	−	0.699347i	$-0.753474\pi$
$857$	−41.8499	−1.42957	−0.714783	+	0.699347i	$0.753474\pi$
$858$	−15.3105	−0.522692
$859$	31.0379	1.05900	0.529500	−	0.848310i	$-0.322380\pi$
$859$	31.0379	1.05900	0.529500	+	0.848310i	$0.322380\pi$
$860$	−6.27105	−0.213841
$861$	−31.2335	−1.06443
$862$	−12.7082	−0.432843
$863$	5.99710	0.204144	0.102072	−	0.994777i	$-0.467453\pi$
$863$	5.99710	0.204144	0.102072	+	0.994777i	$0.467453\pi$
$864$	205.083	6.97706
$865$	−6.29036	−0.213879
$866$	96.2821	3.27180
$867$	30.7179	1.04324
$868$	0.780260	0.0264838
$869$	−9.83611	−0.333667
$870$	28.0257	0.950159
$871$	−14.2277	−0.482086
$872$	13.8859	0.470236
$873$	−42.7956	−1.44841
$874$	1.63461	0.0552914
$875$	−26.9320	−0.910467
$876$	71.4109	2.41275
$877$	3.07924	0.103978	0.0519892	−	0.998648i	$-0.483444\pi$
$877$	3.07924	0.103978	0.0519892	+	0.998648i	$0.483444\pi$
$878$	89.0699	3.00596
$879$	21.0790	0.710977
$880$	−6.80012	−0.229232
$881$	−42.1362	−1.41961	−0.709803	−	0.704400i	$-0.751216\pi$
$881$	−42.1362	−1.41961	−0.709803	+	0.704400i	$0.751216\pi$
$882$	−89.8204	−3.02441
$883$	50.2050	1.68953	0.844766	−	0.535136i	$-0.179740\pi$
$883$	50.2050	1.68953	0.844766	+	0.535136i	$0.179740\pi$
$884$	−46.2312	−1.55492
$885$	−5.67413	−0.190734
$886$	39.3718	1.32272
$887$	32.3988	1.08784	0.543922	−	0.839136i	$-0.316939\pi$
$887$	32.3988	1.08784	0.543922	+	0.839136i	$0.316939\pi$
$888$	30.5438	1.02498
$889$	−9.19773	−0.308482
$890$	−15.0132	−0.503244
$891$	6.33879	0.212357
$892$	118.474	3.96682
$893$	5.49746	0.183965
$894$	81.7578	2.73439
$895$	10.3191	0.344930
$896$	119.677	3.99811
$897$	−5.93081	−0.198024
$898$	54.9474	1.83362
$899$	0.168877	0.00563237
$900$	−145.835	−4.86117
$901$	−22.9069	−0.763140
$902$	4.54315	0.151270
$903$	14.9670	0.498071
$904$	−155.393	−5.16830
$905$	2.11744	0.0703860
$906$	136.677	4.54080
$907$	−20.3661	−0.676245	−0.338123	−	0.941102i	$-0.609792\pi$
$907$	−20.3661	−0.676245	−0.338123	+	0.941102i	$0.609792\pi$
$908$	100.221	3.32596
$909$	12.9083	0.428141
$910$	25.5884	0.848246
$911$	−44.8030	−1.48439	−0.742195	−	0.670184i	$-0.766215\pi$
$911$	−44.8030	−1.48439	−0.742195	+	0.670184i	$0.766215\pi$
$912$	−44.0607	−1.45899
$913$	2.23071	0.0738257
$914$	−48.3025	−1.59770
$915$	17.9440	0.593209
$916$	80.7130	2.66683
$917$	−5.86566	−0.193701
$918$	70.1920	2.31668
$919$	−26.5803	−0.876804	−0.438402	−	0.898779i	$-0.644455\pi$
$919$	−26.5803	−0.876804	−0.438402	+	0.898779i	$0.644455\pi$
$920$	−4.60179	−0.151716
$921$	−34.3338	−1.13134
$922$	−83.0285	−2.73440
$923$	−33.4473	−1.10093
$924$	32.8296	1.08001
$925$	−4.66916	−0.153521
$926$	−47.0105	−1.54486
$927$	−16.2303	−0.533074
$928$	85.8370	2.81774
$929$	−32.7641	−1.07495	−0.537477	−	0.843278i	$-0.680622\pi$
$929$	−32.7641	−1.07495	−0.537477	+	0.843278i	$0.680622\pi$
$930$	0.280192	0.00918786
$931$	5.29267	0.173460
$932$	139.867	4.58151
$933$	−32.1367	−1.05211
$934$	79.9700	2.61670
$935$	−1.23089	−0.0402545
$936$	188.523	6.16207
$937$	45.4529	1.48488	0.742440	−	0.669913i	$-0.233668\pi$
$937$	45.4529	1.48488	0.742440	+	0.669913i	$0.233668\pi$
$938$	41.7734	1.36395
$939$	−16.1368	−0.526603
$940$	−24.5377	−0.800332
$941$	5.47086	0.178345	0.0891724	−	0.996016i	$-0.471578\pi$
$941$	5.47086	0.178345	0.0891724	+	0.996016i	$0.471578\pi$
$942$	−108.452	−3.53355
$943$	1.75987	0.0573094
$944$	−32.8603	−1.06951
$945$	−28.3729	−0.922972
$946$	−2.17707	−0.0707826
$947$	15.0461	0.488932	0.244466	−	0.969658i	$-0.421387\pi$
$947$	15.0461	0.488932	0.244466	+	0.969658i	$0.421387\pi$
$948$	284.466	9.23902
$949$	14.1118	0.458089
$950$	11.7666	0.381760
$951$	−3.03839	−0.0985266
$952$	85.6135	2.77475
$953$	−53.7281	−1.74042	−0.870212	−	0.492678i	$-0.836018\pi$
$953$	−53.7281	−1.74042	−0.870212	+	0.492678i	$0.836018\pi$
$954$	148.100	4.79491
$955$	−10.0976	−0.326751
$956$	48.0649	1.55453
$957$	7.10554	0.229689
$958$	34.5017	1.11470
$959$	−6.27229	−0.202543
$960$	69.7936	2.25258
$961$	−30.9983	−0.999946
$962$	9.56975	0.308541
$963$	65.6730	2.11628
$964$	148.288	4.77602
$965$	19.7398	0.635446
$966$	17.4133	0.560263
$967$	6.57376	0.211398	0.105699	−	0.994398i	$-0.466292\pi$
$967$	6.57376	0.211398	0.105699	+	0.994398i	$0.466292\pi$
$968$	99.3174	3.19218
$969$	−7.97545	−0.256208
$970$	−15.4121	−0.494852
$971$	11.7586	0.377353	0.188676	−	0.982039i	$-0.439580\pi$
$971$	11.7586	0.377353	0.188676	+	0.982039i	$0.439580\pi$
$972$	−23.7729	−0.762515
$973$	−8.50821	−0.272761
$974$	109.685	3.51455
$975$	−42.6926	−1.36726
$976$	103.918	3.32634
$977$	30.8041	0.985511	0.492756	−	0.870168i	$-0.335990\pi$
$977$	30.8041	0.985511	0.492756	+	0.870168i	$0.335990\pi$
$978$	−90.1361	−2.88223
$979$	−3.80640	−0.121653
$980$	−23.6236	−0.754629
$981$	−9.30211	−0.296993
$982$	−36.8666	−1.17646
$983$	48.6918	1.55303	0.776514	−	0.630100i	$-0.216986\pi$
$983$	48.6918	1.55303	0.776514	+	0.630100i	$0.216986\pi$
$984$	−82.8714	−2.64184
$985$	−1.70226	−0.0542385
$986$	29.3787	0.935609
$987$	58.5637	1.86410
$988$	−17.6126	−0.560332
$989$	−0.843327	−0.0268162
$990$	7.95810	0.252925
$991$	24.0180	0.762956	0.381478	−	0.924378i	$-0.375415\pi$
$991$	24.0180	0.762956	0.381478	+	0.924378i	$0.375415\pi$
$992$	0.858173	0.0272470
$993$	−28.7724	−0.913063
$994$	98.2036	3.11483
$995$	−0.348114	−0.0110360
$996$	−64.5134	−2.04418
$997$	−4.80404	−0.152146	−0.0760728	−	0.997102i	$-0.524238\pi$
$997$	−4.80404	−0.152146	−0.0760728	+	0.997102i	$0.524238\pi$
$998$	−0.856967	−0.0271268
$999$	−10.6111	−0.335722

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.a.1.2	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.a.1.2	✓	98	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)

\(f(q)\)	\(=\)	\(q-2.72324 q^{2} -3.03839 q^{3} +5.41603 q^{4} -0.824121 q^{5} +8.27426 q^{6} -3.50609 q^{7} -9.30267 q^{8} +6.23182 q^{9} +O(q^{10})\)	\(q-2.72324 q^{2} -3.03839 q^{3} +5.41603 q^{4} -0.824121 q^{5} +8.27426 q^{6} -3.50609 q^{7} -9.30267 q^{8} +6.23182 q^{9} +2.24428 q^{10} +0.569007 q^{11} -16.4560 q^{12} -3.25194 q^{13} +9.54792 q^{14} +2.50400 q^{15} +14.5013 q^{16} +2.62489 q^{17} -16.9707 q^{18} +1.00000 q^{19} -4.46347 q^{20} +10.6529 q^{21} -1.54954 q^{22} -0.600244 q^{23} +28.2651 q^{24} -4.32082 q^{25} +8.85581 q^{26} -9.81952 q^{27} -18.9891 q^{28} -4.10994 q^{29} -6.81900 q^{30} -0.0410899 q^{31} -20.8852 q^{32} -1.72887 q^{33} -7.14821 q^{34} +2.88944 q^{35} +33.7517 q^{36} +1.08062 q^{37} -2.72324 q^{38} +9.88067 q^{39} +7.66652 q^{40} -2.93193 q^{41} -29.0103 q^{42} +1.40497 q^{43} +3.08176 q^{44} -5.13577 q^{45} +1.63461 q^{46} +5.49746 q^{47} -44.0607 q^{48} +5.29267 q^{49} +11.7666 q^{50} -7.97545 q^{51} -17.6126 q^{52} -8.72679 q^{53} +26.7409 q^{54} -0.468931 q^{55} +32.6160 q^{56} -3.03839 q^{57} +11.1923 q^{58} -2.26602 q^{59} +13.5617 q^{60} +7.16612 q^{61} +0.111898 q^{62} -21.8493 q^{63} +27.8728 q^{64} +2.67999 q^{65} +4.70812 q^{66} +4.37513 q^{67} +14.2165 q^{68} +1.82378 q^{69} -7.86864 q^{70} +10.2853 q^{71} -57.9725 q^{72} -4.33950 q^{73} -2.94278 q^{74} +13.1284 q^{75} +5.41603 q^{76} -1.99499 q^{77} -26.9074 q^{78} -17.2864 q^{79} -11.9508 q^{80} +11.1401 q^{81} +7.98435 q^{82} +3.92035 q^{83} +57.6963 q^{84} -2.16323 q^{85} -3.82608 q^{86} +12.4876 q^{87} -5.29329 q^{88} -6.68955 q^{89} +13.9859 q^{90} +11.4016 q^{91} -3.25094 q^{92} +0.124847 q^{93} -14.9709 q^{94} -0.824121 q^{95} +63.4575 q^{96} -6.86728 q^{97} -14.4132 q^{98} +3.54595 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9 - 24 * q^10 - 12 * q^11 - 51 * q^12 - 58 * q^13 - 15 * q^14 - 18 * q^15 + 58 * q^16 - 25 * q^17 - 40 * q^18 + 98 * q^19 - 12 * q^20 - 24 * q^21 - 59 * q^22 - 38 * q^23 - 9 * q^24 - 12 * q^25 - 3 * q^26 - 85 * q^27 - 33 * q^28 - 24 * q^29 - 22 * q^30 - 56 * q^31 - 29 * q^32 - 51 * q^33 - 38 * q^34 - 10 * q^35 + 50 * q^36 - 124 * q^37 - 8 * q^38 - 4 * q^39 - 80 * q^40 - 28 * q^41 - 37 * q^42 - 63 * q^43 - 7 * q^44 - 32 * q^45 - 47 * q^46 - 10 * q^47 - 88 * q^48 + 6 * q^49 - 17 * q^50 - 22 * q^51 - 119 * q^52 - 65 * q^53 + 24 * q^54 - 30 * q^55 - 39 * q^56 - 25 * q^57 - 91 * q^58 - 26 * q^59 - 60 * q^60 - 60 * q^61 + 6 * q^62 - 26 * q^63 + 50 * q^64 - 40 * q^65 + 57 * q^66 - 108 * q^67 - 41 * q^68 - 15 * q^69 - 36 * q^70 - 19 * q^71 - 47 * q^72 - 136 * q^73 + 22 * q^74 - 48 * q^75 + 82 * q^76 - 35 * q^77 - 56 * q^78 - 98 * q^79 - 42 * q^80 + 6 * q^81 - 37 * q^82 - 31 * q^83 - 24 * q^84 - 71 * q^85 - 24 * q^86 + 7 * q^87 - 166 * q^88 - 38 * q^89 + 26 * q^90 - 100 * q^91 - 59 * q^92 - 21 * q^93 - 48 * q^94 - 10 * q^95 - 16 * q^96 - 190 * q^97 - 80 * q^98 - 17 * q^99

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