LMFDB - Embedded newform 6015.2.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.63766 q^{2} +1.00000 q^{3} +0.681937 q^{4} +1.00000 q^{5} -1.63766 q^{6} -0.197583 q^{7} +2.15854 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.63766 q^{2} +1.00000 q^{3} +0.681937 q^{4} +1.00000 q^{5} -1.63766 q^{6} -0.197583 q^{7} +2.15854 q^{8} +1.00000 q^{9} -1.63766 q^{10} -3.14058 q^{11} +0.681937 q^{12} +0.955857 q^{13} +0.323574 q^{14} +1.00000 q^{15} -4.89884 q^{16} +0.806949 q^{17} -1.63766 q^{18} -0.279169 q^{19} +0.681937 q^{20} -0.197583 q^{21} +5.14321 q^{22} -2.87927 q^{23} +2.15854 q^{24} +1.00000 q^{25} -1.56537 q^{26} +1.00000 q^{27} -0.134739 q^{28} -1.36722 q^{29} -1.63766 q^{30} +1.23074 q^{31} +3.70556 q^{32} -3.14058 q^{33} -1.32151 q^{34} -0.197583 q^{35} +0.681937 q^{36} -8.16406 q^{37} +0.457184 q^{38} +0.955857 q^{39} +2.15854 q^{40} +10.5304 q^{41} +0.323574 q^{42} +3.24785 q^{43} -2.14168 q^{44} +1.00000 q^{45} +4.71527 q^{46} +2.03289 q^{47} -4.89884 q^{48} -6.96096 q^{49} -1.63766 q^{50} +0.806949 q^{51} +0.651835 q^{52} -7.83302 q^{53} -1.63766 q^{54} -3.14058 q^{55} -0.426491 q^{56} -0.279169 q^{57} +2.23904 q^{58} -8.18075 q^{59} +0.681937 q^{60} +4.49022 q^{61} -2.01553 q^{62} -0.197583 q^{63} +3.72922 q^{64} +0.955857 q^{65} +5.14321 q^{66} -5.70624 q^{67} +0.550289 q^{68} -2.87927 q^{69} +0.323574 q^{70} +7.55169 q^{71} +2.15854 q^{72} -0.816975 q^{73} +13.3700 q^{74} +1.00000 q^{75} -0.190376 q^{76} +0.620525 q^{77} -1.56537 q^{78} -7.38258 q^{79} -4.89884 q^{80} +1.00000 q^{81} -17.2453 q^{82} -2.37094 q^{83} -0.134739 q^{84} +0.806949 q^{85} -5.31888 q^{86} -1.36722 q^{87} -6.77907 q^{88} +0.387236 q^{89} -1.63766 q^{90} -0.188861 q^{91} -1.96348 q^{92} +1.23074 q^{93} -3.32919 q^{94} -0.279169 q^{95} +3.70556 q^{96} -0.194040 q^{97} +11.3997 q^{98} -3.14058 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) $ 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.63766	−1.15800	−0.579001	−	0.815327i	$-0.696557\pi$
$2$	−1.63766	−1.15800	−0.579001	+	0.815327i	$0.696557\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.681937	0.340969
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.63766	−0.668573
$7$	−0.197583	−0.0746793	−0.0373397	−	0.999303i	$-0.511888\pi$
$7$	−0.197583	−0.0746793	−0.0373397	+	0.999303i	$0.511888\pi$
$8$	2.15854	0.763160
$9$	1.00000	0.333333
$10$	−1.63766	−0.517874
$11$	−3.14058	−0.946920	−0.473460	−	0.880815i	$-0.656995\pi$
$11$	−3.14058	−0.946920	−0.473460	+	0.880815i	$0.656995\pi$
$12$	0.681937	0.196858
$13$	0.955857	0.265107	0.132554	−	0.991176i	$-0.457682\pi$
$13$	0.955857	0.265107	0.132554	+	0.991176i	$0.457682\pi$
$14$	0.323574	0.0864788
$15$	1.00000	0.258199
$16$	−4.89884	−1.22471
$17$	0.806949	0.195714	0.0978570	−	0.995200i	$-0.468801\pi$
$17$	0.806949	0.195714	0.0978570	+	0.995200i	$0.468801\pi$
$18$	−1.63766	−0.386001
$19$	−0.279169	−0.0640457	−0.0320229	−	0.999487i	$-0.510195\pi$
$19$	−0.279169	−0.0640457	−0.0320229	+	0.999487i	$0.510195\pi$
$20$	0.681937	0.152486
$21$	−0.197583	−0.0431161
$22$	5.14321	1.09654
$23$	−2.87927	−0.600369	−0.300184	−	0.953881i	$-0.597048\pi$
$23$	−2.87927	−0.600369	−0.300184	+	0.953881i	$0.597048\pi$
$24$	2.15854	0.440610
$25$	1.00000	0.200000
$26$	−1.56537	−0.306995
$27$	1.00000	0.192450
$28$	−0.134739	−0.0254633
$29$	−1.36722	−0.253886	−0.126943	−	0.991910i	$-0.540517\pi$
$29$	−1.36722	−0.253886	−0.126943	+	0.991910i	$0.540517\pi$
$30$	−1.63766	−0.298995
$31$	1.23074	0.221047	0.110523	−	0.993874i	$-0.464747\pi$
$31$	1.23074	0.221047	0.110523	+	0.993874i	$0.464747\pi$
$32$	3.70556	0.655056
$33$	−3.14058	−0.546705
$34$	−1.32151	−0.226637
$35$	−0.197583	−0.0333976
$36$	0.681937	0.113656
$37$	−8.16406	−1.34216	−0.671081	−	0.741384i	$-0.734170\pi$
$37$	−8.16406	−1.34216	−0.671081	+	0.741384i	$0.734170\pi$
$38$	0.457184	0.0741651
$39$	0.955857	0.153060
$40$	2.15854	0.341295
$41$	10.5304	1.64458	0.822288	−	0.569071i	$-0.192697\pi$
$41$	10.5304	1.64458	0.822288	+	0.569071i	$0.192697\pi$
$42$	0.323574	0.0499286
$43$	3.24785	0.495292	0.247646	−	0.968851i	$-0.420343\pi$
$43$	3.24785	0.495292	0.247646	+	0.968851i	$0.420343\pi$
$44$	−2.14168	−0.322870
$45$	1.00000	0.149071
$46$	4.71527	0.695228
$47$	2.03289	0.296528	0.148264	−	0.988948i	$-0.452632\pi$
$47$	2.03289	0.296528	0.148264	+	0.988948i	$0.452632\pi$
$48$	−4.89884	−0.707086
$49$	−6.96096	−0.994423
$50$	−1.63766	−0.231600
$51$	0.806949	0.112995
$52$	0.651835	0.0903933
$53$	−7.83302	−1.07595	−0.537974	−	0.842961i	$-0.680810\pi$
$53$	−7.83302	−1.07595	−0.537974	+	0.842961i	$0.680810\pi$
$54$	−1.63766	−0.222858
$55$	−3.14058	−0.423476
$56$	−0.426491	−0.0569923
$57$	−0.279169	−0.0369768
$58$	2.23904	0.294000
$59$	−8.18075	−1.06504	−0.532521	−	0.846417i	$-0.678755\pi$
$59$	−8.18075	−1.06504	−0.532521	+	0.846417i	$0.678755\pi$
$60$	0.681937	0.0880378
$61$	4.49022	0.574914	0.287457	−	0.957794i	$-0.407190\pi$
$61$	4.49022	0.574914	0.287457	+	0.957794i	$0.407190\pi$
$62$	−2.01553	−0.255972
$63$	−0.197583	−0.0248931
$64$	3.72922	0.466153
$65$	0.955857	0.118560
$66$	5.14321	0.633085
$67$	−5.70624	−0.697129	−0.348564	−	0.937285i	$-0.613331\pi$
$67$	−5.70624	−0.697129	−0.348564	+	0.937285i	$0.613331\pi$
$68$	0.550289	0.0667323
$69$	−2.87927	−0.346623
$70$	0.323574	0.0386745
$71$	7.55169	0.896221	0.448111	−	0.893978i	$-0.352097\pi$
$71$	7.55169	0.896221	0.448111	+	0.893978i	$0.352097\pi$
$72$	2.15854	0.254387
$73$	−0.816975	−0.0956197	−0.0478099	−	0.998856i	$-0.515224\pi$
$73$	−0.816975	−0.0956197	−0.0478099	+	0.998856i	$0.515224\pi$
$74$	13.3700	1.55423
$75$	1.00000	0.115470
$76$	−0.190376	−0.0218376
$77$	0.620525	0.0707154
$78$	−1.56537	−0.177243
$79$	−7.38258	−0.830605	−0.415302	−	0.909683i	$-0.636324\pi$
$79$	−7.38258	−0.830605	−0.415302	+	0.909683i	$0.636324\pi$
$80$	−4.89884	−0.547707
$81$	1.00000	0.111111
$82$	−17.2453	−1.90442
$83$	−2.37094	−0.260245	−0.130122	−	0.991498i	$-0.541537\pi$
$83$	−2.37094	−0.260245	−0.130122	+	0.991498i	$0.541537\pi$
$84$	−0.134739	−0.0147013
$85$	0.806949	0.0875259
$86$	−5.31888	−0.573549
$87$	−1.36722	−0.146581
$88$	−6.77907	−0.722651
$89$	0.387236	0.0410469	0.0205235	−	0.999789i	$-0.493467\pi$
$89$	0.387236	0.0410469	0.0205235	+	0.999789i	$0.493467\pi$
$90$	−1.63766	−0.172625
$91$	−0.188861	−0.0197980
$92$	−1.96348	−0.204707
$93$	1.23074	0.127621
$94$	−3.32919	−0.343380
$95$	−0.279169	−0.0286421
$96$	3.70556	0.378197
$97$	−0.194040	−0.0197017	−0.00985087	−	0.999951i	$-0.503136\pi$
$97$	−0.194040	−0.0197017	−0.00985087	+	0.999951i	$0.503136\pi$
$98$	11.3997	1.15154
$99$	−3.14058	−0.315640
$100$	0.681937	0.0681937
$101$	−19.2532	−1.91577	−0.957884	−	0.287156i	$-0.907290\pi$
$101$	−19.2532	−1.91577	−0.957884	+	0.287156i	$0.907290\pi$
$102$	−1.32151	−0.130849
$103$	−3.21029	−0.316319	−0.158160	−	0.987414i	$-0.550556\pi$
$103$	−3.21029	−0.316319	−0.158160	+	0.987414i	$0.550556\pi$
$104$	2.06326	0.202319
$105$	−0.197583	−0.0192821
$106$	12.8278	1.24595
$107$	−0.792663	−0.0766296	−0.0383148	−	0.999266i	$-0.512199\pi$
$107$	−0.792663	−0.0766296	−0.0383148	+	0.999266i	$0.512199\pi$
$108$	0.681937	0.0656195
$109$	3.21016	0.307477	0.153739	−	0.988112i	$-0.450869\pi$
$109$	3.21016	0.307477	0.153739	+	0.988112i	$0.450869\pi$
$110$	5.14321	0.490386
$111$	−8.16406	−0.774898
$112$	0.967927	0.0914605
$113$	5.07385	0.477308	0.238654	−	0.971105i	$-0.423294\pi$
$113$	5.07385	0.477308	0.238654	+	0.971105i	$0.423294\pi$
$114$	0.457184	0.0428192
$115$	−2.87927	−0.268493
$116$	−0.932357	−0.0865671
$117$	0.955857	0.0883691
$118$	13.3973	1.23332
$119$	−0.159439	−0.0146158
$120$	2.15854	0.197047
$121$	−1.13676	−0.103342
$122$	−7.35346	−0.665751
$123$	10.5304	0.949497
$124$	0.839284	0.0753700
$125$	1.00000	0.0894427
$126$	0.323574	0.0288263
$127$	−1.60237	−0.142187	−0.0710935	−	0.997470i	$-0.522649\pi$
$127$	−1.60237	−0.142187	−0.0710935	+	0.997470i	$0.522649\pi$
$128$	−13.5183	−1.19486
$129$	3.24785	0.285957
$130$	−1.56537	−0.137292
$131$	19.0692	1.66608	0.833041	−	0.553212i	$-0.186598\pi$
$131$	19.0692	1.66608	0.833041	+	0.553212i	$0.186598\pi$
$132$	−2.14168	−0.186409
$133$	0.0551590	0.00478289
$134$	9.34490	0.807277
$135$	1.00000	0.0860663
$136$	1.74183	0.149361
$137$	−20.9734	−1.79188	−0.895941	−	0.444172i	$-0.853498\pi$
$137$	−20.9734	−1.79188	−0.895941	+	0.444172i	$0.853498\pi$
$138$	4.71527	0.401390
$139$	−10.4213	−0.883920	−0.441960	−	0.897035i	$-0.645717\pi$
$139$	−10.4213	−0.883920	−0.441960	+	0.897035i	$0.645717\pi$
$140$	−0.134739	−0.0113875
$141$	2.03289	0.171200
$142$	−12.3671	−1.03783
$143$	−3.00195	−0.251035
$144$	−4.89884	−0.408236
$145$	−1.36722	−0.113541
$146$	1.33793	0.110728
$147$	−6.96096	−0.574130
$148$	−5.56738	−0.457635
$149$	−15.1666	−1.24250	−0.621250	−	0.783613i	$-0.713375\pi$
$149$	−15.1666	−1.24250	−0.621250	+	0.783613i	$0.713375\pi$
$150$	−1.63766	−0.133715
$151$	5.86946	0.477650	0.238825	−	0.971063i	$-0.423238\pi$
$151$	5.86946	0.477650	0.238825	+	0.971063i	$0.423238\pi$
$152$	−0.602597	−0.0488771
$153$	0.806949	0.0652380
$154$	−1.01621	−0.0818886
$155$	1.23074	0.0988550
$156$	0.651835	0.0521886
$157$	−17.9745	−1.43452	−0.717262	−	0.696803i	$-0.754605\pi$
$157$	−17.9745	−1.43452	−0.717262	+	0.696803i	$0.754605\pi$
$158$	12.0902	0.961842
$159$	−7.83302	−0.621199
$160$	3.70556	0.292950
$161$	0.568894	0.0448351
$162$	−1.63766	−0.128667
$163$	20.6305	1.61591	0.807954	−	0.589245i	$-0.200575\pi$
$163$	20.6305	1.61591	0.807954	+	0.589245i	$0.200575\pi$
$164$	7.18109	0.560749
$165$	−3.14058	−0.244494
$166$	3.88280	0.301364
$167$	−13.3157	−1.03040	−0.515202	−	0.857069i	$-0.672283\pi$
$167$	−13.3157	−1.03040	−0.515202	+	0.857069i	$0.672283\pi$
$168$	−0.426491	−0.0329045
$169$	−12.0863	−0.929718
$170$	−1.32151	−0.101355
$171$	−0.279169	−0.0213486
$172$	2.21483	0.168879
$173$	20.2052	1.53617	0.768085	−	0.640348i	$-0.221210\pi$
$173$	20.2052	1.53617	0.768085	+	0.640348i	$0.221210\pi$
$174$	2.23904	0.169741
$175$	−0.197583	−0.0149359
$176$	15.3852	1.15970
$177$	−8.18075	−0.614903
$178$	−0.634162	−0.0475324
$179$	−2.17349	−0.162454	−0.0812271	−	0.996696i	$-0.525884\pi$
$179$	−2.17349	−0.162454	−0.0812271	+	0.996696i	$0.525884\pi$
$180$	0.681937	0.0508286
$181$	7.17151	0.533054	0.266527	−	0.963827i	$-0.414124\pi$
$181$	7.17151	0.533054	0.266527	+	0.963827i	$0.414124\pi$
$182$	0.309291	0.0229262
$183$	4.49022	0.331927
$184$	−6.21502	−0.458177
$185$	−8.16406	−0.600233
$186$	−2.01553	−0.147786
$187$	−2.53429	−0.185325
$188$	1.38630	0.101107
$189$	−0.197583	−0.0143720
$190$	0.457184	0.0331676
$191$	21.3729	1.54649	0.773243	−	0.634110i	$-0.218633\pi$
$191$	21.3729	1.54649	0.773243	+	0.634110i	$0.218633\pi$
$192$	3.72922	0.269133
$193$	−16.6694	−1.19989	−0.599943	−	0.800043i	$-0.704810\pi$
$193$	−16.6694	−1.19989	−0.599943	+	0.800043i	$0.704810\pi$
$194$	0.317771	0.0228146
$195$	0.955857	0.0684504
$196$	−4.74694	−0.339067
$197$	12.8071	0.912466	0.456233	−	0.889860i	$-0.349198\pi$
$197$	12.8071	0.912466	0.456233	+	0.889860i	$0.349198\pi$
$198$	5.14321	0.365512
$199$	16.5298	1.17177	0.585883	−	0.810396i	$-0.300748\pi$
$199$	16.5298	1.17177	0.585883	+	0.810396i	$0.300748\pi$
$200$	2.15854	0.152632
$201$	−5.70624	−0.402487
$202$	31.5303	2.21846
$203$	0.270139	0.0189600
$204$	0.550289	0.0385279
$205$	10.5304	0.735477
$206$	5.25737	0.366299
$207$	−2.87927	−0.200123
$208$	−4.68259	−0.324679
$209$	0.876752	0.0606462
$210$	0.323574	0.0223287
$211$	−26.6578	−1.83520	−0.917600	−	0.397505i	$-0.869876\pi$
$211$	−26.6578	−1.83520	−0.917600	+	0.397505i	$0.869876\pi$
$212$	−5.34163	−0.366865
$213$	7.55169	0.517433
$214$	1.29811	0.0887372
$215$	3.24785	0.221501
$216$	2.15854	0.146870
$217$	−0.243172	−0.0165076
$218$	−5.25715	−0.356059
$219$	−0.816975	−0.0552061
$220$	−2.14168	−0.144392
$221$	0.771328	0.0518852
$222$	13.3700	0.897333
$223$	−28.4122	−1.90262	−0.951310	−	0.308237i	$-0.900261\pi$
$223$	−28.4122	−1.90262	−0.951310	+	0.308237i	$0.900261\pi$
$224$	−0.732155	−0.0489192
$225$	1.00000	0.0666667
$226$	−8.30925	−0.552723
$227$	−4.19491	−0.278426	−0.139213	−	0.990262i	$-0.544457\pi$
$227$	−4.19491	−0.278426	−0.139213	+	0.990262i	$0.544457\pi$
$228$	−0.190376	−0.0126079
$229$	4.73978	0.313213	0.156607	−	0.987661i	$-0.449944\pi$
$229$	4.73978	0.313213	0.156607	+	0.987661i	$0.449944\pi$
$230$	4.71527	0.310915
$231$	0.620525	0.0408275
$232$	−2.95119	−0.193755
$233$	13.8192	0.905323	0.452662	−	0.891682i	$-0.350475\pi$
$233$	13.8192	0.905323	0.452662	+	0.891682i	$0.350475\pi$
$234$	−1.56537	−0.102332
$235$	2.03289	0.132611
$236$	−5.57876	−0.363146
$237$	−7.38258	−0.479550
$238$	0.261108	0.0169251
$239$	9.38427	0.607018	0.303509	−	0.952829i	$-0.401842\pi$
$239$	9.38427	0.607018	0.303509	+	0.952829i	$0.401842\pi$
$240$	−4.89884	−0.316219
$241$	−21.1958	−1.36534	−0.682671	−	0.730726i	$-0.739182\pi$
$241$	−21.1958	−1.36534	−0.682671	+	0.730726i	$0.739182\pi$
$242$	1.86163	0.119670
$243$	1.00000	0.0641500
$244$	3.06205	0.196028
$245$	−6.96096	−0.444719
$246$	−17.2453	−1.09952
$247$	−0.266846	−0.0169790
$248$	2.65659	0.168694
$249$	−2.37094	−0.150252
$250$	−1.63766	−0.103575
$251$	−22.7087	−1.43336	−0.716679	−	0.697403i	$-0.754339\pi$
$251$	−22.7087	−1.43336	−0.716679	+	0.697403i	$0.754339\pi$
$252$	−0.134739	−0.00848777
$253$	9.04256	0.568501
$254$	2.62413	0.164653
$255$	0.806949	0.0505331
$256$	14.6800	0.917500
$257$	12.7647	0.796240	0.398120	−	0.917333i	$-0.369663\pi$
$257$	12.7647	0.796240	0.398120	+	0.917333i	$0.369663\pi$
$258$	−5.31888	−0.331139
$259$	1.61308	0.100232
$260$	0.651835	0.0404251
$261$	−1.36722	−0.0846286
$262$	−31.2289	−1.92933
$263$	16.6458	1.02643	0.513213	−	0.858261i	$-0.328455\pi$
$263$	16.6458	1.02643	0.513213	+	0.858261i	$0.328455\pi$
$264$	−6.77907	−0.417223
$265$	−7.83302	−0.481179
$266$	−0.0903318	−0.00553860
$267$	0.387236	0.0236985
$268$	−3.89130	−0.237699
$269$	−13.9847	−0.852662	−0.426331	−	0.904567i	$-0.640194\pi$
$269$	−13.9847	−0.852662	−0.426331	+	0.904567i	$0.640194\pi$
$270$	−1.63766	−0.0996649
$271$	−15.5304	−0.943402	−0.471701	−	0.881758i	$-0.656360\pi$
$271$	−15.5304	−0.943402	−0.471701	+	0.881758i	$0.656360\pi$
$272$	−3.95311	−0.239693
$273$	−0.188861	−0.0114304
$274$	34.3474	2.07500
$275$	−3.14058	−0.189384
$276$	−1.96348	−0.118188
$277$	−1.52342	−0.0915335	−0.0457667	−	0.998952i	$-0.514573\pi$
$277$	−1.52342	−0.0915335	−0.0457667	+	0.998952i	$0.514573\pi$
$278$	17.0665	1.02358
$279$	1.23074	0.0736822
$280$	−0.426491	−0.0254877
$281$	−16.1096	−0.961019	−0.480509	−	0.876990i	$-0.659548\pi$
$281$	−16.1096	−0.961019	−0.480509	+	0.876990i	$0.659548\pi$
$282$	−3.32919	−0.198250
$283$	17.8606	1.06170	0.530850	−	0.847466i	$-0.321873\pi$
$283$	17.8606	1.06170	0.530850	+	0.847466i	$0.321873\pi$
$284$	5.14978	0.305583
$285$	−0.279169	−0.0165365
$286$	4.91617	0.290699
$287$	−2.08063	−0.122816
$288$	3.70556	0.218352
$289$	−16.3488	−0.961696
$290$	2.23904	0.131481
$291$	−0.194040	−0.0113748
$292$	−0.557126	−0.0326033
$293$	29.8156	1.74184	0.870922	−	0.491421i	$-0.163522\pi$
$293$	29.8156	1.74184	0.870922	+	0.491421i	$0.163522\pi$
$294$	11.3997	0.664844
$295$	−8.18075	−0.476302
$296$	−17.6224	−1.02428
$297$	−3.14058	−0.182235
$298$	24.8378	1.43882
$299$	−2.75217	−0.159162
$300$	0.681937	0.0393717
$301$	−0.641719	−0.0369881
$302$	−9.61219	−0.553119
$303$	−19.2532	−1.10607
$304$	1.36760	0.0784374
$305$	4.49022	0.257109
$306$	−1.32151	−0.0755457
$307$	20.6998	1.18140	0.590699	−	0.806892i	$-0.298852\pi$
$307$	20.6998	1.18140	0.590699	+	0.806892i	$0.298852\pi$
$308$	0.423159	0.0241117
$309$	−3.21029	−0.182627
$310$	−2.01553	−0.114474
$311$	10.1788	0.577184	0.288592	−	0.957452i	$-0.406813\pi$
$311$	10.1788	0.577184	0.288592	+	0.957452i	$0.406813\pi$
$312$	2.06326	0.116809
$313$	−34.5577	−1.95332	−0.976659	−	0.214795i	$-0.931092\pi$
$313$	−34.5577	−1.95332	−0.976659	+	0.214795i	$0.931092\pi$
$314$	29.4362	1.66118
$315$	−0.197583	−0.0111325
$316$	−5.03446	−0.283210
$317$	24.5879	1.38100	0.690498	−	0.723334i	$-0.257391\pi$
$317$	24.5879	1.38100	0.690498	+	0.723334i	$0.257391\pi$
$318$	12.8278	0.719350
$319$	4.29385	0.240410
$320$	3.72922	0.208470
$321$	−0.792663	−0.0442421
$322$	−0.931656	−0.0519192
$323$	−0.225275	−0.0125346
$324$	0.681937	0.0378854
$325$	0.955857	0.0530214
$326$	−33.7859	−1.87123
$327$	3.21016	0.177522
$328$	22.7304	1.25507
$329$	−0.401665	−0.0221445
$330$	5.14321	0.283124
$331$	−21.1381	−1.16185	−0.580926	−	0.813956i	$-0.697310\pi$
$331$	−21.1381	−1.16185	−0.580926	+	0.813956i	$0.697310\pi$
$332$	−1.61683	−0.0887353
$333$	−8.16406	−0.447387
$334$	21.8067	1.19321
$335$	−5.70624	−0.311765
$336$	0.967927	0.0528047
$337$	18.1527	0.988841	0.494421	−	0.869223i	$-0.335380\pi$
$337$	18.1527	0.988841	0.494421	+	0.869223i	$0.335380\pi$
$338$	19.7933	1.07662
$339$	5.07385	0.275574
$340$	0.550289	0.0298436
$341$	−3.86522	−0.209313
$342$	0.457184	0.0247217
$343$	2.75845	0.148942
$344$	7.01061	0.377987
$345$	−2.87927	−0.155014
$346$	−33.0892	−1.77889
$347$	−2.98635	−0.160316	−0.0801578	−	0.996782i	$-0.525542\pi$
$347$	−2.98635	−0.160316	−0.0801578	+	0.996782i	$0.525542\pi$
$348$	−0.932357	−0.0499796
$349$	−3.62255	−0.193911	−0.0969554	−	0.995289i	$-0.530910\pi$
$349$	−3.62255	−0.193911	−0.0969554	+	0.995289i	$0.530910\pi$
$350$	0.323574	0.0172958
$351$	0.955857	0.0510199
$352$	−11.6376	−0.620286
$353$	7.00760	0.372977	0.186489	−	0.982457i	$-0.440289\pi$
$353$	7.00760	0.372977	0.186489	+	0.982457i	$0.440289\pi$
$354$	13.3973	0.712059
$355$	7.55169	0.400802
$356$	0.264071	0.0139957
$357$	−0.159439	−0.00843843
$358$	3.55944	0.188122
$359$	7.93357	0.418718	0.209359	−	0.977839i	$-0.432862\pi$
$359$	7.93357	0.418718	0.209359	+	0.977839i	$0.432862\pi$
$360$	2.15854	0.113765
$361$	−18.9221	−0.995898
$362$	−11.7445	−0.617278
$363$	−1.13676	−0.0596645
$364$	−0.128792	−0.00675051
$365$	−0.816975	−0.0427624
$366$	−7.35346	−0.384372
$367$	−19.5155	−1.01870	−0.509351	−	0.860559i	$-0.670115\pi$
$367$	−19.5155	−1.01870	−0.509351	+	0.860559i	$0.670115\pi$
$368$	14.1051	0.735277
$369$	10.5304	0.548192
$370$	13.3700	0.695071
$371$	1.54767	0.0803511
$372$	0.839284	0.0435149
$373$	−24.7764	−1.28287	−0.641437	−	0.767176i	$-0.721661\pi$
$373$	−24.7764	−1.28287	−0.641437	+	0.767176i	$0.721661\pi$
$374$	4.15031	0.214607
$375$	1.00000	0.0516398
$376$	4.38808	0.226298
$377$	−1.30686	−0.0673070
$378$	0.323574	0.0166429
$379$	10.3457	0.531425	0.265712	−	0.964052i	$-0.414393\pi$
$379$	10.3457	0.531425	0.265712	+	0.964052i	$0.414393\pi$
$380$	−0.190376	−0.00976607
$381$	−1.60237	−0.0820917
$382$	−35.0015	−1.79083
$383$	−29.2288	−1.49352	−0.746762	−	0.665091i	$-0.768393\pi$
$383$	−29.2288	−1.49352	−0.746762	+	0.665091i	$0.768393\pi$
$384$	−13.5183	−0.689854
$385$	0.620525	0.0316249
$386$	27.2988	1.38947
$387$	3.24785	0.165097
$388$	−0.132323	−0.00671768
$389$	−17.9449	−0.909840	−0.454920	−	0.890532i	$-0.650332\pi$
$389$	−17.9449	−0.909840	−0.454920	+	0.890532i	$0.650332\pi$
$390$	−1.56537	−0.0792657
$391$	−2.32342	−0.117500
$392$	−15.0255	−0.758903
$393$	19.0692	0.961912
$394$	−20.9737	−1.05664
$395$	−7.38258	−0.371458
$396$	−2.14168	−0.107623
$397$	17.5440	0.880508	0.440254	−	0.897873i	$-0.354888\pi$
$397$	17.5440	0.880508	0.440254	+	0.897873i	$0.354888\pi$
$398$	−27.0702	−1.35691
$399$	0.0551590	0.00276140
$400$	−4.89884	−0.244942
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	9.34490	0.466081
$403$	1.17641	0.0586010
$404$	−13.1295	−0.653217
$405$	1.00000	0.0496904
$406$	−0.442396	−0.0219558
$407$	25.6399	1.27092
$408$	1.74183	0.0862336
$409$	−35.4113	−1.75097	−0.875487	−	0.483241i	$-0.839459\pi$
$409$	−35.4113	−1.75097	−0.875487	+	0.483241i	$0.839459\pi$
$410$	−17.2453	−0.851684
$411$	−20.9734	−1.03454
$412$	−2.18922	−0.107855
$413$	1.61638	0.0795367
$414$	4.71527	0.231743
$415$	−2.37094	−0.116385
$416$	3.54198	0.173660
$417$	−10.4213	−0.510331
$418$	−1.43582	−0.0702284
$419$	−11.1196	−0.543228	−0.271614	−	0.962406i	$-0.587557\pi$
$419$	−11.1196	−0.543228	−0.271614	+	0.962406i	$0.587557\pi$
$420$	−0.134739	−0.00657460
$421$	−35.5465	−1.73243	−0.866214	−	0.499673i	$-0.833454\pi$
$421$	−35.5465	−1.73243	−0.866214	+	0.499673i	$0.833454\pi$
$422$	43.6565	2.12517
$423$	2.03289	0.0988426
$424$	−16.9079	−0.821120
$425$	0.806949	0.0391428
$426$	−12.3671	−0.599189
$427$	−0.887191	−0.0429342
$428$	−0.540546	−0.0261283
$429$	−3.00195	−0.144935
$430$	−5.31888	−0.256499
$431$	25.7959	1.24254	0.621272	−	0.783595i	$-0.286616\pi$
$431$	25.7959	1.24254	0.621272	+	0.783595i	$0.286616\pi$
$432$	−4.89884	−0.235695
$433$	19.2738	0.926240	0.463120	−	0.886296i	$-0.346730\pi$
$433$	19.2738	0.926240	0.463120	+	0.886296i	$0.346730\pi$
$434$	0.398234	0.0191158
$435$	−1.36722	−0.0655530
$436$	2.18913	0.104840
$437$	0.803801	0.0384510
$438$	1.33793	0.0639287
$439$	−0.244968	−0.0116917	−0.00584585	−	0.999983i	$-0.501861\pi$
$439$	−0.244968	−0.0116917	−0.00584585	+	0.999983i	$0.501861\pi$
$440$	−6.77907	−0.323179
$441$	−6.96096	−0.331474
$442$	−1.26318	−0.0600831
$443$	8.33907	0.396201	0.198100	−	0.980182i	$-0.436523\pi$
$443$	8.33907	0.396201	0.198100	+	0.980182i	$0.436523\pi$
$444$	−5.56738	−0.264216
$445$	0.387236	0.0183567
$446$	46.5295	2.20324
$447$	−15.1666	−0.717358
$448$	−0.736831	−0.0348120
$449$	−33.1126	−1.56268	−0.781340	−	0.624105i	$-0.785464\pi$
$449$	−33.1126	−1.56268	−0.781340	+	0.624105i	$0.785464\pi$
$450$	−1.63766	−0.0772001
$451$	−33.0716	−1.55728
$452$	3.46005	0.162747
$453$	5.86946	0.275771
$454$	6.86984	0.322418
$455$	−0.188861	−0.00885395
$456$	−0.602597	−0.0282192
$457$	−29.6016	−1.38470	−0.692352	−	0.721560i	$-0.743425\pi$
$457$	−29.6016	−1.38470	−0.692352	+	0.721560i	$0.743425\pi$
$458$	−7.76216	−0.362702
$459$	0.806949	0.0376652
$460$	−1.96348	−0.0915477
$461$	30.2846	1.41049	0.705247	−	0.708962i	$-0.250836\pi$
$461$	30.2846	1.41049	0.705247	+	0.708962i	$0.250836\pi$
$462$	−1.01621	−0.0472784
$463$	−13.5280	−0.628701	−0.314350	−	0.949307i	$-0.601787\pi$
$463$	−13.5280	−0.628701	−0.314350	+	0.949307i	$0.601787\pi$
$464$	6.69777	0.310936
$465$	1.23074	0.0570740
$466$	−22.6311	−1.04837
$467$	1.22179	0.0565376	0.0282688	−	0.999600i	$-0.491001\pi$
$467$	1.22179	0.0565376	0.0282688	+	0.999600i	$0.491001\pi$
$468$	0.651835	0.0301311
$469$	1.12746	0.0520611
$470$	−3.32919	−0.153564
$471$	−17.9745	−0.828223
$472$	−17.6585	−0.812798
$473$	−10.2001	−0.469002
$474$	12.0902	0.555320
$475$	−0.279169	−0.0128091
$476$	−0.108728	−0.00498353
$477$	−7.83302	−0.358649
$478$	−15.3683	−0.702928
$479$	−12.2338	−0.558976	−0.279488	−	0.960149i	$-0.590165\pi$
$479$	−12.2338	−0.558976	−0.279488	+	0.960149i	$0.590165\pi$
$480$	3.70556	0.169135
$481$	−7.80367	−0.355817
$482$	34.7116	1.58107
$483$	0.568894	0.0258856
$484$	−0.775200	−0.0352364
$485$	−0.194040	−0.00881088
$486$	−1.63766	−0.0742859
$487$	−14.5829	−0.660813	−0.330407	−	0.943839i	$-0.607186\pi$
$487$	−14.5829	−0.660813	−0.330407	+	0.943839i	$0.607186\pi$
$488$	9.69232	0.438751
$489$	20.6305	0.932945
$490$	11.3997	0.514986
$491$	26.3744	1.19026	0.595131	−	0.803629i	$-0.297100\pi$
$491$	26.3744	1.19026	0.595131	+	0.803629i	$0.297100\pi$
$492$	7.18109	0.323749
$493$	−1.10327	−0.0496890
$494$	0.437003	0.0196617
$495$	−3.14058	−0.141159
$496$	−6.02917	−0.270718
$497$	−1.49209	−0.0669292
$498$	3.88280	0.173993
$499$	30.3749	1.35977	0.679884	−	0.733319i	$-0.262030\pi$
$499$	30.3749	1.35977	0.679884	+	0.733319i	$0.262030\pi$
$500$	0.681937	0.0304972
$501$	−13.3157	−0.594904
$502$	37.1891	1.65983
$503$	10.9275	0.487232	0.243616	−	0.969872i	$-0.421666\pi$
$503$	10.9275	0.487232	0.243616	+	0.969872i	$0.421666\pi$
$504$	−0.426491	−0.0189974
$505$	−19.2532	−0.856757
$506$	−14.8087	−0.658326
$507$	−12.0863	−0.536773
$508$	−1.09271	−0.0484813
$509$	35.5805	1.57708	0.788539	−	0.614985i	$-0.210838\pi$
$509$	35.5805	1.57708	0.788539	+	0.614985i	$0.210838\pi$
$510$	−1.32151	−0.0585174
$511$	0.161420	0.00714082
$512$	2.99576	0.132395
$513$	−0.279169	−0.0123256
$514$	−20.9043	−0.922048
$515$	−3.21029	−0.141462
$516$	2.21483	0.0975024
$517$	−6.38446	−0.280788
$518$	−2.64168	−0.116069
$519$	20.2052	0.886908
$520$	2.06326	0.0904798
$521$	−12.2887	−0.538378	−0.269189	−	0.963087i	$-0.586756\pi$
$521$	−12.2887	−0.538378	−0.269189	+	0.963087i	$0.586756\pi$
$522$	2.23904	0.0980001
$523$	0.433500	0.0189556	0.00947782	−	0.999955i	$-0.496983\pi$
$523$	0.433500	0.0189556	0.00947782	+	0.999955i	$0.496983\pi$
$524$	13.0040	0.568082
$525$	−0.197583	−0.00862323
$526$	−27.2603	−1.18860
$527$	0.993141	0.0432619
$528$	15.3852	0.669554
$529$	−14.7098	−0.639558
$530$	12.8278	0.557206
$531$	−8.18075	−0.355014
$532$	0.0376150	0.00163082
$533$	10.0656	0.435989
$534$	−0.634162	−0.0274429
$535$	−0.792663	−0.0342698
$536$	−12.3172	−0.532020
$537$	−2.17349	−0.0937930
$538$	22.9022	0.987384
$539$	21.8615	0.941639
$540$	0.681937	0.0293459
$541$	−38.6646	−1.66232	−0.831161	−	0.556032i	$-0.812323\pi$
$541$	−38.6646	−1.66232	−0.831161	+	0.556032i	$0.812323\pi$
$542$	25.4335	1.09246
$543$	7.17151	0.307759
$544$	2.99020	0.128204
$545$	3.21016	0.137508
$546$	0.309291	0.0132364
$547$	10.1920	0.435780	0.217890	−	0.975973i	$-0.430083\pi$
$547$	10.1920	0.435780	0.217890	+	0.975973i	$0.430083\pi$
$548$	−14.3026	−0.610976
$549$	4.49022	0.191638
$550$	5.14321	0.219307
$551$	0.381684	0.0162603
$552$	−6.21502	−0.264529
$553$	1.45867	0.0620290
$554$	2.49485	0.105996
$555$	−8.16406	−0.346545
$556$	−7.10665	−0.301389
$557$	−34.7606	−1.47285	−0.736427	−	0.676517i	$-0.763488\pi$
$557$	−34.7606	−1.47285	−0.736427	+	0.676517i	$0.763488\pi$
$558$	−2.01553	−0.0853241
$559$	3.10448	0.131305
$560$	0.967927	0.0409024
$561$	−2.53429	−0.106998
$562$	26.3821	1.11286
$563$	25.4543	1.07277	0.536386	−	0.843973i	$-0.319789\pi$
$563$	25.4543	1.07277	0.536386	+	0.843973i	$0.319789\pi$
$564$	1.38630	0.0583740
$565$	5.07385	0.213459
$566$	−29.2496	−1.22945
$567$	−0.197583	−0.00829770
$568$	16.3006	0.683960
$569$	19.2383	0.806513	0.403257	−	0.915087i	$-0.367878\pi$
$569$	19.2383	0.806513	0.403257	+	0.915087i	$0.367878\pi$
$570$	0.457184	0.0191493
$571$	42.4677	1.77722	0.888609	−	0.458666i	$-0.151673\pi$
$571$	42.4677	1.77722	0.888609	+	0.458666i	$0.151673\pi$
$572$	−2.04714	−0.0855952
$573$	21.3729	0.892864
$574$	3.40737	0.142221
$575$	−2.87927	−0.120074
$576$	3.72922	0.155384
$577$	−10.2219	−0.425542	−0.212771	−	0.977102i	$-0.568249\pi$
$577$	−10.2219	−0.425542	−0.212771	+	0.977102i	$0.568249\pi$
$578$	26.7739	1.11365
$579$	−16.6694	−0.692755
$580$	−0.932357	−0.0387140
$581$	0.468458	0.0194349
$582$	0.317771	0.0131720
$583$	24.6002	1.01884
$584$	−1.76347	−0.0729731
$585$	0.955857	0.0395198
$586$	−48.8278	−2.01706
$587$	−24.3665	−1.00571	−0.502857	−	0.864370i	$-0.667718\pi$
$587$	−24.3665	−1.00571	−0.502857	+	0.864370i	$0.667718\pi$
$588$	−4.74694	−0.195761
$589$	−0.343583	−0.0141571
$590$	13.3973	0.551558
$591$	12.8071	0.526813
$592$	39.9944	1.64376
$593$	−1.37917	−0.0566358	−0.0283179	−	0.999599i	$-0.509015\pi$
$593$	−1.37917	−0.0566358	−0.0283179	+	0.999599i	$0.509015\pi$
$594$	5.14321	0.211028
$595$	−0.159439	−0.00653638
$596$	−10.3427	−0.423654
$597$	16.5298	0.676519
$598$	4.50712	0.184310
$599$	−5.22599	−0.213528	−0.106764	−	0.994284i	$-0.534049\pi$
$599$	−5.22599	−0.213528	−0.106764	+	0.994284i	$0.534049\pi$
$600$	2.15854	0.0881221
$601$	−29.3594	−1.19760	−0.598798	−	0.800900i	$-0.704355\pi$
$601$	−29.3594	−1.19760	−0.598798	+	0.800900i	$0.704355\pi$
$602$	1.05092	0.0428323
$603$	−5.70624	−0.232376
$604$	4.00260	0.162864
$605$	−1.13676	−0.0462159
$606$	31.5303	1.28083
$607$	6.57828	0.267004	0.133502	−	0.991049i	$-0.457378\pi$
$607$	6.57828	0.267004	0.133502	+	0.991049i	$0.457378\pi$
$608$	−1.03448	−0.0419535
$609$	0.270139	0.0109466
$610$	−7.35346	−0.297733
$611$	1.94315	0.0786116
$612$	0.550289	0.0222441
$613$	−32.2314	−1.30181	−0.650907	−	0.759157i	$-0.725611\pi$
$613$	−32.2314	−1.30181	−0.650907	+	0.759157i	$0.725611\pi$
$614$	−33.8992	−1.36806
$615$	10.5304	0.424628
$616$	1.33943	0.0539671
$617$	−1.91708	−0.0771786	−0.0385893	−	0.999255i	$-0.512286\pi$
$617$	−1.91708	−0.0771786	−0.0385893	+	0.999255i	$0.512286\pi$
$618$	5.25737	0.211483
$619$	−33.7485	−1.35647	−0.678234	−	0.734846i	$-0.737254\pi$
$619$	−33.7485	−1.35647	−0.678234	+	0.734846i	$0.737254\pi$
$620$	0.839284	0.0337065
$621$	−2.87927	−0.115541
$622$	−16.6694	−0.668381
$623$	−0.0765112	−0.00306536
$624$	−4.68259	−0.187454
$625$	1.00000	0.0400000
$626$	56.5939	2.26195
$627$	0.876752	0.0350141
$628$	−12.2575	−0.489128
$629$	−6.58798	−0.262680
$630$	0.323574	0.0128915
$631$	−12.2536	−0.487808	−0.243904	−	0.969799i	$-0.578428\pi$
$631$	−12.2536	−0.487808	−0.243904	+	0.969799i	$0.578428\pi$
$632$	−15.9356	−0.633884
$633$	−26.6578	−1.05955
$634$	−40.2668	−1.59920
$635$	−1.60237	−0.0635879
$636$	−5.34163	−0.211809
$637$	−6.65369	−0.263629
$638$	−7.03188	−0.278395
$639$	7.55169	0.298740
$640$	−13.5183	−0.534359
$641$	−43.6646	−1.72465	−0.862324	−	0.506357i	$-0.830992\pi$
$641$	−43.6646	−1.72465	−0.862324	+	0.506357i	$0.830992\pi$
$642$	1.29811	0.0512325
$643$	46.6925	1.84137	0.920686	−	0.390305i	$-0.127630\pi$
$643$	46.6925	1.84137	0.920686	+	0.390305i	$0.127630\pi$
$644$	0.387950	0.0152874
$645$	3.24785	0.127884
$646$	0.368924	0.0145151
$647$	−29.9235	−1.17641	−0.588206	−	0.808711i	$-0.700166\pi$
$647$	−29.9235	−1.17641	−0.588206	+	0.808711i	$0.700166\pi$
$648$	2.15854	0.0847955
$649$	25.6923	1.00851
$650$	−1.56537	−0.0613989
$651$	−0.243172	−0.00953067
$652$	14.0687	0.550974
$653$	12.7439	0.498709	0.249354	−	0.968412i	$-0.419782\pi$
$653$	12.7439	0.498709	0.249354	+	0.968412i	$0.419782\pi$
$654$	−5.25715	−0.205571
$655$	19.0692	0.745094
$656$	−51.5868	−2.01413
$657$	−0.816975	−0.0318732
$658$	0.657791	0.0256434
$659$	−35.4513	−1.38099	−0.690493	−	0.723339i	$-0.742606\pi$
$659$	−35.4513	−1.38099	−0.690493	+	0.723339i	$0.742606\pi$
$660$	−2.14168	−0.0833647
$661$	−10.4625	−0.406945	−0.203473	−	0.979081i	$-0.565223\pi$
$661$	−10.4625	−0.406945	−0.203473	+	0.979081i	$0.565223\pi$
$662$	34.6170	1.34543
$663$	0.771328	0.0299559
$664$	−5.11778	−0.198608
$665$	0.0551590	0.00213897
$666$	13.3700	0.518076
$667$	3.93658	0.152425
$668$	−9.08051	−0.351335
$669$	−28.4122	−1.09848
$670$	9.34490	0.361025
$671$	−14.1019	−0.544398
$672$	−0.732155	−0.0282435
$673$	−31.6209	−1.21890	−0.609449	−	0.792825i	$-0.708609\pi$
$673$	−31.6209	−1.21890	−0.609449	+	0.792825i	$0.708609\pi$
$674$	−29.7280	−1.14508
$675$	1.00000	0.0384900
$676$	−8.24213	−0.317005
$677$	10.6779	0.410384	0.205192	−	0.978722i	$-0.434218\pi$
$677$	10.6779	0.410384	0.205192	+	0.978722i	$0.434218\pi$
$678$	−8.30925	−0.319115
$679$	0.0383389	0.00147131
$680$	1.74183	0.0667962
$681$	−4.19491	−0.160749
$682$	6.32993	0.242385
$683$	−2.23655	−0.0855793	−0.0427896	−	0.999084i	$-0.513625\pi$
$683$	−2.23655	−0.0855793	−0.0427896	+	0.999084i	$0.513625\pi$
$684$	−0.190376	−0.00727920
$685$	−20.9734	−0.801354
$686$	−4.51741	−0.172475
$687$	4.73978	0.180834
$688$	−15.9107	−0.606589
$689$	−7.48725	−0.285242
$690$	4.71527	0.179507
$691$	37.3581	1.42117	0.710584	−	0.703613i	$-0.248431\pi$
$691$	37.3581	1.42117	0.710584	+	0.703613i	$0.248431\pi$
$692$	13.7787	0.523786
$693$	0.620525	0.0235718
$694$	4.89063	0.185646
$695$	−10.4213	−0.395301
$696$	−2.95119	−0.111865
$697$	8.49752	0.321866
$698$	5.93252	0.224549
$699$	13.8192	0.522689
$700$	−0.134739	−0.00509266
$701$	−39.8006	−1.50325	−0.751624	−	0.659592i	$-0.770729\pi$
$701$	−39.8006	−1.50325	−0.751624	+	0.659592i	$0.770729\pi$
$702$	−1.56537	−0.0590811
$703$	2.27915	0.0859598
$704$	−11.7119	−0.441410
$705$	2.03289	0.0765631
$706$	−11.4761	−0.431908
$707$	3.80411	0.143068
$708$	−5.57876	−0.209663
$709$	−1.45300	−0.0545686	−0.0272843	−	0.999628i	$-0.508686\pi$
$709$	−1.45300	−0.0545686	−0.0272843	+	0.999628i	$0.508686\pi$
$710$	−12.3671	−0.464130
$711$	−7.38258	−0.276868
$712$	0.835865	0.0313254
$713$	−3.54361	−0.132709
$714$	0.261108	0.00977172
$715$	−3.00195	−0.112266
$716$	−1.48218	−0.0553918
$717$	9.38427	0.350462
$718$	−12.9925	−0.484876
$719$	−3.56199	−0.132840	−0.0664200	−	0.997792i	$-0.521158\pi$
$719$	−3.56199	−0.132840	−0.0664200	+	0.997792i	$0.521158\pi$
$720$	−4.89884	−0.182569
$721$	0.634299	0.0236225
$722$	30.9880	1.15325
$723$	−21.1958	−0.788281
$724$	4.89052	0.181755
$725$	−1.36722	−0.0507772
$726$	1.86163	0.0690916
$727$	1.86927	0.0693274	0.0346637	−	0.999399i	$-0.488964\pi$
$727$	1.86927	0.0693274	0.0346637	+	0.999399i	$0.488964\pi$
$728$	−0.407665	−0.0151091
$729$	1.00000	0.0370370
$730$	1.33793	0.0495190
$731$	2.62085	0.0969355
$732$	3.06205	0.113177
$733$	19.8881	0.734584	0.367292	−	0.930106i	$-0.380285\pi$
$733$	19.8881	0.734584	0.367292	+	0.930106i	$0.380285\pi$
$734$	31.9599	1.17966
$735$	−6.96096	−0.256759
$736$	−10.6693	−0.393275
$737$	17.9209	0.660125
$738$	−17.2453	−0.634808
$739$	5.63606	0.207326	0.103663	−	0.994612i	$-0.466944\pi$
$739$	5.63606	0.207326	0.103663	+	0.994612i	$0.466944\pi$
$740$	−5.56738	−0.204661
$741$	−0.266846	−0.00980282
$742$	−2.53456	−0.0930467
$743$	−22.1494	−0.812584	−0.406292	−	0.913743i	$-0.633178\pi$
$743$	−22.1494	−0.812584	−0.406292	+	0.913743i	$0.633178\pi$
$744$	2.65659	0.0973954
$745$	−15.1666	−0.555663
$746$	40.5754	1.48557
$747$	−2.37094	−0.0867483
$748$	−1.72823	−0.0631902
$749$	0.156617	0.00572265
$750$	−1.63766	−0.0597990
$751$	−3.88568	−0.141791	−0.0708953	−	0.997484i	$-0.522586\pi$
$751$	−3.88568	−0.141791	−0.0708953	+	0.997484i	$0.522586\pi$
$752$	−9.95880	−0.363160
$753$	−22.7087	−0.827550
$754$	2.14020	0.0779416
$755$	5.86946	0.213611
$756$	−0.134739	−0.00490042
$757$	−5.69585	−0.207019	−0.103510	−	0.994628i	$-0.533007\pi$
$757$	−5.69585	−0.207019	−0.103510	+	0.994628i	$0.533007\pi$
$758$	−16.9428	−0.615391
$759$	9.04256	0.328224
$760$	−0.602597	−0.0218585
$761$	46.8684	1.69898	0.849488	−	0.527607i	$-0.176911\pi$
$761$	46.8684	1.69898	0.849488	+	0.527607i	$0.176911\pi$
$762$	2.62413	0.0950623
$763$	−0.634272	−0.0229622
$764$	14.5750	0.527303
$765$	0.806949	0.0291753
$766$	47.8670	1.72950
$767$	−7.81963	−0.282350
$768$	14.6800	0.529719
$769$	8.57764	0.309318	0.154659	−	0.987968i	$-0.450572\pi$
$769$	8.57764	0.309318	0.154659	+	0.987968i	$0.450572\pi$
$770$	−1.01621	−0.0366217
$771$	12.7647	0.459709
$772$	−11.3675	−0.409124
$773$	−12.8145	−0.460905	−0.230452	−	0.973084i	$-0.574021\pi$
$773$	−12.8145	−0.460905	−0.230452	+	0.973084i	$0.574021\pi$
$774$	−5.31888	−0.191183
$775$	1.23074	0.0442093
$776$	−0.418842	−0.0150356
$777$	1.61308	0.0578689
$778$	29.3876	1.05360
$779$	−2.93977	−0.105328
$780$	0.651835	0.0233394
$781$	−23.7167	−0.848650
$782$	3.80498	0.136066
$783$	−1.36722	−0.0488604
$784$	34.1006	1.21788
$785$	−17.9745	−0.641539
$786$	−31.2289	−1.11390
$787$	39.8120	1.41915	0.709573	−	0.704632i	$-0.248888\pi$
$787$	39.8120	1.41915	0.709573	+	0.704632i	$0.248888\pi$
$788$	8.73362	0.311122
$789$	16.6458	0.592608
$790$	12.0902	0.430149
$791$	−1.00251	−0.0356450
$792$	−6.77907	−0.240884
$793$	4.29201	0.152414
$794$	−28.7311	−1.01963
$795$	−7.83302	−0.277809
$796$	11.2723	0.399536
$797$	−23.2946	−0.825137	−0.412568	−	0.910927i	$-0.635368\pi$
$797$	−23.2946	−0.825137	−0.412568	+	0.910927i	$0.635368\pi$
$798$	−0.0903318	−0.00319771
$799$	1.64044	0.0580346
$800$	3.70556	0.131011
$801$	0.387236	0.0136823
$802$	1.63766	0.0578279
$803$	2.56578	0.0905442
$804$	−3.89130	−0.137236
$805$	0.568894	0.0200509
$806$	−1.92656	−0.0678601
$807$	−13.9847	−0.492284
$808$	−41.5589	−1.46204
$809$	−6.94815	−0.244284	−0.122142	−	0.992513i	$-0.538976\pi$
$809$	−6.94815	−0.244284	−0.122142	+	0.992513i	$0.538976\pi$
$810$	−1.63766	−0.0575416
$811$	−53.7588	−1.88773	−0.943863	−	0.330337i	$-0.892837\pi$
$811$	−53.7588	−1.88773	−0.943863	+	0.330337i	$0.892837\pi$
$812$	0.184218	0.00646478
$813$	−15.5304	−0.544674
$814$	−41.9894	−1.47173
$815$	20.6305	0.722656
$816$	−3.95311	−0.138387
$817$	−0.906697	−0.0317213
$818$	57.9917	2.02763
$819$	−0.188861	−0.00659934
$820$	7.18109	0.250775
$821$	−6.47851	−0.226101	−0.113051	−	0.993589i	$-0.536062\pi$
$821$	−6.47851	−0.226101	−0.113051	+	0.993589i	$0.536062\pi$
$822$	34.3474	1.19800
$823$	−55.8461	−1.94667	−0.973336	−	0.229383i	$-0.926329\pi$
$823$	−55.8461	−1.94667	−0.973336	+	0.229383i	$0.926329\pi$
$824$	−6.92955	−0.241402
$825$	−3.14058	−0.109341
$826$	−2.64708	−0.0921037
$827$	−51.2952	−1.78371	−0.891855	−	0.452322i	$-0.850596\pi$
$827$	−51.2952	−1.78371	−0.891855	+	0.452322i	$0.850596\pi$
$828$	−1.96348	−0.0682356
$829$	48.9417	1.69982	0.849908	−	0.526931i	$-0.176657\pi$
$829$	48.9417	1.69982	0.849908	+	0.526931i	$0.176657\pi$
$830$	3.88280	0.134774
$831$	−1.52342	−0.0528469
$832$	3.56461	0.123580
$833$	−5.61714	−0.194622
$834$	17.0665	0.590965
$835$	−13.3157	−0.460810
$836$	0.597890	0.0206785
$837$	1.23074	0.0425404
$838$	18.2101	0.629059
$839$	−16.4813	−0.568998	−0.284499	−	0.958676i	$-0.591827\pi$
$839$	−16.4813	−0.568998	−0.284499	+	0.958676i	$0.591827\pi$
$840$	−0.426491	−0.0147153
$841$	−27.1307	−0.935542
$842$	58.2131	2.00616
$843$	−16.1096	−0.554844
$844$	−18.1790	−0.625746
$845$	−12.0863	−0.415783
$846$	−3.32919	−0.114460
$847$	0.224605	0.00771751
$848$	38.3727	1.31772
$849$	17.8606	0.612973
$850$	−1.32151	−0.0453274
$851$	23.5065	0.805792
$852$	5.14978	0.176429
$853$	−20.1230	−0.688998	−0.344499	−	0.938787i	$-0.611951\pi$
$853$	−20.1230	−0.688998	−0.344499	+	0.938787i	$0.611951\pi$
$854$	1.45292	0.0497179
$855$	−0.279169	−0.00954737
$856$	−1.71100	−0.0584806
$857$	−5.30617	−0.181255	−0.0906277	−	0.995885i	$-0.528887\pi$
$857$	−5.30617	−0.181255	−0.0906277	+	0.995885i	$0.528887\pi$
$858$	4.91617	0.167835
$859$	−4.61063	−0.157313	−0.0786563	−	0.996902i	$-0.525063\pi$
$859$	−4.61063	−0.157313	−0.0786563	+	0.996902i	$0.525063\pi$
$860$	2.21483	0.0755250
$861$	−2.08063	−0.0709078
$862$	−42.2450	−1.43887
$863$	15.8471	0.539440	0.269720	−	0.962939i	$-0.413069\pi$
$863$	15.8471	0.539440	0.269720	+	0.962939i	$0.413069\pi$
$864$	3.70556	0.126066
$865$	20.2052	0.686996
$866$	−31.5640	−1.07259
$867$	−16.3488	−0.555235
$868$	−0.165828	−0.00562858
$869$	23.1856	0.786516
$870$	2.23904	0.0759106
$871$	−5.45436	−0.184814
$872$	6.92926	0.234654
$873$	−0.194040	−0.00656724
$874$	−1.31636	−0.0445264
$875$	−0.197583	−0.00667952
$876$	−0.557126	−0.0188235
$877$	−20.8873	−0.705314	−0.352657	−	0.935753i	$-0.614722\pi$
$877$	−20.8873	−0.705314	−0.352657	+	0.935753i	$0.614722\pi$
$878$	0.401175	0.0135390
$879$	29.8156	1.00565
$880$	15.3852	0.518634
$881$	−7.39528	−0.249153	−0.124577	−	0.992210i	$-0.539757\pi$
$881$	−7.39528	−0.249153	−0.124577	+	0.992210i	$0.539757\pi$
$882$	11.3997	0.383848
$883$	38.2039	1.28566	0.642832	−	0.766008i	$-0.277760\pi$
$883$	38.2039	1.28566	0.642832	+	0.766008i	$0.277760\pi$
$884$	0.525998	0.0176912
$885$	−8.18075	−0.274993
$886$	−13.6566	−0.458802
$887$	12.5739	0.422190	0.211095	−	0.977465i	$-0.432297\pi$
$887$	12.5739	0.422190	0.211095	+	0.977465i	$0.432297\pi$
$888$	−17.6224	−0.591371
$889$	0.316600	0.0106184
$890$	−0.634162	−0.0212571
$891$	−3.14058	−0.105213
$892$	−19.3753	−0.648734
$893$	−0.567520	−0.0189913
$894$	24.8378	0.830702
$895$	−2.17349	−0.0726517
$896$	2.67099	0.0892315
$897$	−2.75217	−0.0918922
$898$	54.2273	1.80959
$899$	−1.68268	−0.0561206
$900$	0.681937	0.0227312
$901$	−6.32085	−0.210578
$902$	54.1602	1.80334
$903$	−0.641719	−0.0213551
$904$	10.9521	0.364262
$905$	7.17151	0.238389
$906$	−9.61219	−0.319343
$907$	−8.50503	−0.282405	−0.141202	−	0.989981i	$-0.545097\pi$
$907$	−8.50503	−0.282405	−0.141202	+	0.989981i	$0.545097\pi$
$908$	−2.86067	−0.0949345
$909$	−19.2532	−0.638589
$910$	0.309291	0.0102529
$911$	−15.5304	−0.514544	−0.257272	−	0.966339i	$-0.582824\pi$
$911$	−15.5304	−0.514544	−0.257272	+	0.966339i	$0.582824\pi$
$912$	1.36760	0.0452858
$913$	7.44613	0.246431
$914$	48.4774	1.60349
$915$	4.49022	0.148442
$916$	3.23223	0.106796
$917$	−3.76774	−0.124422
$918$	−1.32151	−0.0436163
$919$	−52.9394	−1.74631	−0.873156	−	0.487442i	$-0.837930\pi$
$919$	−52.9394	−1.74631	−0.873156	+	0.487442i	$0.837930\pi$
$920$	−6.21502	−0.204903
$921$	20.6998	0.682080
$922$	−49.5959	−1.63336
$923$	7.21834	0.237595
$924$	0.423159	0.0139209
$925$	−8.16406	−0.268432
$926$	22.1543	0.728037
$927$	−3.21029	−0.105440
$928$	−5.06630	−0.166309
$929$	−10.7372	−0.352277	−0.176139	−	0.984365i	$-0.556361\pi$
$929$	−10.7372	−0.352277	−0.176139	+	0.984365i	$0.556361\pi$
$930$	−2.01553	−0.0660918
$931$	1.94328	0.0636885
$932$	9.42380	0.308687
$933$	10.1788	0.333238
$934$	−2.00088	−0.0654707
$935$	−2.53429	−0.0828801
$936$	2.06326	0.0674397
$937$	35.6352	1.16415	0.582075	−	0.813135i	$-0.302241\pi$
$937$	35.6352	1.16415	0.582075	+	0.813135i	$0.302241\pi$
$938$	−1.84639	−0.0602869
$939$	−34.5577	−1.12775
$940$	1.38630	0.0452163
$941$	−21.3131	−0.694786	−0.347393	−	0.937720i	$-0.612933\pi$
$941$	−21.3131	−0.694786	−0.347393	+	0.937720i	$0.612933\pi$
$942$	29.4362	0.959084
$943$	−30.3199	−0.987352
$944$	40.0761	1.30437
$945$	−0.197583	−0.00642737
$946$	16.7044	0.543105
$947$	−42.0933	−1.36785	−0.683925	−	0.729553i	$-0.739728\pi$
$947$	−42.0933	−1.36785	−0.683925	+	0.729553i	$0.739728\pi$
$948$	−5.03446	−0.163512
$949$	−0.780912	−0.0253495
$950$	0.457184	0.0148330
$951$	24.5879	0.797319
$952$	−0.344157	−0.0111542
$953$	−1.43609	−0.0465194	−0.0232597	−	0.999729i	$-0.507404\pi$
$953$	−1.43609	−0.0465194	−0.0232597	+	0.999729i	$0.507404\pi$
$954$	12.8278	0.415317
$955$	21.3729	0.691609
$956$	6.39948	0.206974
$957$	4.29385	0.138801
$958$	20.0348	0.647296
$959$	4.14400	0.133817
$960$	3.72922	0.120360
$961$	−29.4853	−0.951138
$962$	12.7798	0.412037
$963$	−0.792663	−0.0255432
$964$	−14.4542	−0.465539
$965$	−16.6694	−0.536605
$966$	−0.931656	−0.0299755
$967$	−16.5626	−0.532617	−0.266309	−	0.963888i	$-0.585804\pi$
$967$	−16.5626	−0.532617	−0.266309	+	0.963888i	$0.585804\pi$
$968$	−2.45375	−0.0788664
$969$	−0.225275	−0.00723688
$970$	0.317771	0.0102030
$971$	16.9577	0.544198	0.272099	−	0.962269i	$-0.412282\pi$
$971$	16.9577	0.544198	0.272099	+	0.962269i	$0.412282\pi$
$972$	0.681937	0.0218732
$973$	2.05906	0.0660105
$974$	23.8818	0.765223
$975$	0.955857	0.0306119
$976$	−21.9969	−0.704102
$977$	−19.9734	−0.639007	−0.319504	−	0.947585i	$-0.603516\pi$
$977$	−19.9734	−0.639007	−0.319504	+	0.947585i	$0.603516\pi$
$978$	−33.7859	−1.08035
$979$	−1.21615	−0.0388682
$980$	−4.74694	−0.151635
$981$	3.21016	0.102492
$982$	−43.1924	−1.37833
$983$	8.38327	0.267385	0.133692	−	0.991023i	$-0.457317\pi$
$983$	8.38327	0.267385	0.133692	+	0.991023i	$0.457317\pi$
$984$	22.7304	0.724617
$985$	12.8071	0.408067
$986$	1.80679	0.0575400
$987$	−0.401665	−0.0127851
$988$	−0.181972	−0.00578930
$989$	−9.35142	−0.297358
$990$	5.14321	0.163462
$991$	31.0581	0.986593	0.493296	−	0.869861i	$-0.335792\pi$
$991$	31.0581	0.986593	0.493296	+	0.869861i	$0.335792\pi$
$992$	4.56056	0.144798
$993$	−21.1381	−0.670796
$994$	2.44353	0.0775042
$995$	16.5298	0.524030
$996$	−1.61683	−0.0512314
$997$	31.8097	1.00742	0.503711	−	0.863872i	$-0.331968\pi$
$997$	31.8097	1.00742	0.503711	+	0.863872i	$0.331968\pi$
$998$	−49.7439	−1.57461
$999$	−8.16406	−0.258299

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.b.1.6	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.b.1.6	✓	23	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.63766 q^{2} +1.00000 q^{3} +0.681937 q^{4} +1.00000 q^{5} -1.63766 q^{6} -0.197583 q^{7} +2.15854 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.63766 q^{2} +1.00000 q^{3} +0.681937 q^{4} +1.00000 q^{5} -1.63766 q^{6} -0.197583 q^{7} +2.15854 q^{8} +1.00000 q^{9} -1.63766 q^{10} -3.14058 q^{11} +0.681937 q^{12} +0.955857 q^{13} +0.323574 q^{14} +1.00000 q^{15} -4.89884 q^{16} +0.806949 q^{17} -1.63766 q^{18} -0.279169 q^{19} +0.681937 q^{20} -0.197583 q^{21} +5.14321 q^{22} -2.87927 q^{23} +2.15854 q^{24} +1.00000 q^{25} -1.56537 q^{26} +1.00000 q^{27} -0.134739 q^{28} -1.36722 q^{29} -1.63766 q^{30} +1.23074 q^{31} +3.70556 q^{32} -3.14058 q^{33} -1.32151 q^{34} -0.197583 q^{35} +0.681937 q^{36} -8.16406 q^{37} +0.457184 q^{38} +0.955857 q^{39} +2.15854 q^{40} +10.5304 q^{41} +0.323574 q^{42} +3.24785 q^{43} -2.14168 q^{44} +1.00000 q^{45} +4.71527 q^{46} +2.03289 q^{47} -4.89884 q^{48} -6.96096 q^{49} -1.63766 q^{50} +0.806949 q^{51} +0.651835 q^{52} -7.83302 q^{53} -1.63766 q^{54} -3.14058 q^{55} -0.426491 q^{56} -0.279169 q^{57} +2.23904 q^{58} -8.18075 q^{59} +0.681937 q^{60} +4.49022 q^{61} -2.01553 q^{62} -0.197583 q^{63} +3.72922 q^{64} +0.955857 q^{65} +5.14321 q^{66} -5.70624 q^{67} +0.550289 q^{68} -2.87927 q^{69} +0.323574 q^{70} +7.55169 q^{71} +2.15854 q^{72} -0.816975 q^{73} +13.3700 q^{74} +1.00000 q^{75} -0.190376 q^{76} +0.620525 q^{77} -1.56537 q^{78} -7.38258 q^{79} -4.89884 q^{80} +1.00000 q^{81} -17.2453 q^{82} -2.37094 q^{83} -0.134739 q^{84} +0.806949 q^{85} -5.31888 q^{86} -1.36722 q^{87} -6.77907 q^{88} +0.387236 q^{89} -1.63766 q^{90} -0.188861 q^{91} -1.96348 q^{92} +1.23074 q^{93} -3.32919 q^{94} -0.279169 q^{95} +3.70556 q^{96} -0.194040 q^{97} +11.3997 q^{98} -3.14058 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * q^99

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