LMFDB - Embedded newform 6015.2.a.b.1.7

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			1.7
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)

$f(q)$	$=$	$q-1.27466 q^{2} +1.00000 q^{3} -0.375250 q^{4} +1.00000 q^{5} -1.27466 q^{6} -0.831191 q^{7} +3.02763 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.27466 q^{2} +1.00000 q^{3} -0.375250 q^{4} +1.00000 q^{5} -1.27466 q^{6} -0.831191 q^{7} +3.02763 q^{8} +1.00000 q^{9} -1.27466 q^{10} +2.33541 q^{11} -0.375250 q^{12} +2.36868 q^{13} +1.05948 q^{14} +1.00000 q^{15} -3.10869 q^{16} +3.82186 q^{17} -1.27466 q^{18} -0.477321 q^{19} -0.375250 q^{20} -0.831191 q^{21} -2.97685 q^{22} -5.36053 q^{23} +3.02763 q^{24} +1.00000 q^{25} -3.01925 q^{26} +1.00000 q^{27} +0.311904 q^{28} -7.00290 q^{29} -1.27466 q^{30} -2.73114 q^{31} -2.09275 q^{32} +2.33541 q^{33} -4.87155 q^{34} -0.831191 q^{35} -0.375250 q^{36} -8.97949 q^{37} +0.608421 q^{38} +2.36868 q^{39} +3.02763 q^{40} -9.79865 q^{41} +1.05948 q^{42} -2.65346 q^{43} -0.876362 q^{44} +1.00000 q^{45} +6.83284 q^{46} -7.63974 q^{47} -3.10869 q^{48} -6.30912 q^{49} -1.27466 q^{50} +3.82186 q^{51} -0.888845 q^{52} -7.72465 q^{53} -1.27466 q^{54} +2.33541 q^{55} -2.51654 q^{56} -0.477321 q^{57} +8.92630 q^{58} -0.605475 q^{59} -0.375250 q^{60} +8.61468 q^{61} +3.48126 q^{62} -0.831191 q^{63} +8.88491 q^{64} +2.36868 q^{65} -2.97685 q^{66} +1.76522 q^{67} -1.43415 q^{68} -5.36053 q^{69} +1.05948 q^{70} -2.24886 q^{71} +3.02763 q^{72} -4.06305 q^{73} +11.4458 q^{74} +1.00000 q^{75} +0.179115 q^{76} -1.94117 q^{77} -3.01925 q^{78} +1.83211 q^{79} -3.10869 q^{80} +1.00000 q^{81} +12.4899 q^{82} -1.07725 q^{83} +0.311904 q^{84} +3.82186 q^{85} +3.38226 q^{86} -7.00290 q^{87} +7.07076 q^{88} -0.209689 q^{89} -1.27466 q^{90} -1.96882 q^{91} +2.01154 q^{92} -2.73114 q^{93} +9.73805 q^{94} -0.477321 q^{95} -2.09275 q^{96} -16.0934 q^{97} +8.04197 q^{98} +2.33541 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.27466	−0.901319	−0.450659	−	0.892696i	$-0.648811\pi$
$2$	−1.27466	−0.901319	−0.450659	+	0.892696i	$0.648811\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.375250	−0.187625
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.27466	−0.520377
$7$	−0.831191	−0.314161	−0.157080	−	0.987586i	$-0.550208\pi$
$7$	−0.831191	−0.314161	−0.157080	+	0.987586i	$0.550208\pi$
$8$	3.02763	1.07043
$9$	1.00000	0.333333
$10$	−1.27466	−0.403082
$11$	2.33541	0.704153	0.352077	−	0.935971i	$-0.385476\pi$
$11$	2.33541	0.704153	0.352077	+	0.935971i	$0.385476\pi$
$12$	−0.375250	−0.108325
$13$	2.36868	0.656953	0.328476	−	0.944512i	$-0.393465\pi$
$13$	2.36868	0.656953	0.328476	+	0.944512i	$0.393465\pi$
$14$	1.05948	0.283159
$15$	1.00000	0.258199
$16$	−3.10869	−0.777172
$17$	3.82186	0.926936	0.463468	−	0.886114i	$-0.346605\pi$
$17$	3.82186	0.926936	0.463468	+	0.886114i	$0.346605\pi$
$18$	−1.27466	−0.300440
$19$	−0.477321	−0.109505	−0.0547525	−	0.998500i	$-0.517437\pi$
$19$	−0.477321	−0.109505	−0.0547525	+	0.998500i	$0.517437\pi$
$20$	−0.375250	−0.0839084
$21$	−0.831191	−0.181381
$22$	−2.97685	−0.634666
$23$	−5.36053	−1.11775	−0.558874	−	0.829252i	$-0.688767\pi$
$23$	−5.36053	−1.11775	−0.558874	+	0.829252i	$0.688767\pi$
$24$	3.02763	0.618012
$25$	1.00000	0.200000
$26$	−3.01925	−0.592124
$27$	1.00000	0.192450
$28$	0.311904	0.0589443
$29$	−7.00290	−1.30041	−0.650203	−	0.759760i	$-0.725316\pi$
$29$	−7.00290	−1.30041	−0.650203	+	0.759760i	$0.725316\pi$
$30$	−1.27466	−0.232719
$31$	−2.73114	−0.490526	−0.245263	−	0.969457i	$-0.578874\pi$
$31$	−2.73114	−0.490526	−0.245263	+	0.969457i	$0.578874\pi$
$32$	−2.09275	−0.369949
$33$	2.33541	0.406543
$34$	−4.87155	−0.835465
$35$	−0.831191	−0.140497
$36$	−0.375250	−0.0625416
$37$	−8.97949	−1.47622	−0.738110	−	0.674680i	$-0.764281\pi$
$37$	−8.97949	−1.47622	−0.738110	+	0.674680i	$0.764281\pi$
$38$	0.608421	0.0986989
$39$	2.36868	0.379292
$40$	3.02763	0.478710
$41$	−9.79865	−1.53029	−0.765146	−	0.643857i	$-0.777333\pi$
$41$	−9.79865	−1.53029	−0.765146	+	0.643857i	$0.777333\pi$
$42$	1.05948	0.163482
$43$	−2.65346	−0.404649	−0.202325	−	0.979318i	$-0.564850\pi$
$43$	−2.65346	−0.404649	−0.202325	+	0.979318i	$0.564850\pi$
$44$	−0.876362	−0.132117
$45$	1.00000	0.149071
$46$	6.83284	1.00745
$47$	−7.63974	−1.11437	−0.557186	−	0.830388i	$-0.688119\pi$
$47$	−7.63974	−1.11437	−0.557186	+	0.830388i	$0.688119\pi$
$48$	−3.10869	−0.448701
$49$	−6.30912	−0.901303
$50$	−1.27466	−0.180264
$51$	3.82186	0.535167
$52$	−0.888845	−0.123261
$53$	−7.72465	−1.06106	−0.530531	−	0.847665i	$-0.678008\pi$
$53$	−7.72465	−1.06106	−0.530531	+	0.847665i	$0.678008\pi$
$54$	−1.27466	−0.173459
$55$	2.33541	0.314907
$56$	−2.51654	−0.336286
$57$	−0.477321	−0.0632227
$58$	8.92630	1.17208
$59$	−0.605475	−0.0788262	−0.0394131	−	0.999223i	$-0.512549\pi$
$59$	−0.605475	−0.0788262	−0.0394131	+	0.999223i	$0.512549\pi$
$60$	−0.375250	−0.0484445
$61$	8.61468	1.10300	0.551498	−	0.834176i	$-0.314056\pi$
$61$	8.61468	1.10300	0.551498	+	0.834176i	$0.314056\pi$
$62$	3.48126	0.442121
$63$	−0.831191	−0.104720
$64$	8.88491	1.11061
$65$	2.36868	0.293798
$66$	−2.97685	−0.366425
$67$	1.76522	0.215656	0.107828	−	0.994170i	$-0.465610\pi$
$67$	1.76522	0.215656	0.107828	+	0.994170i	$0.465610\pi$
$68$	−1.43415	−0.173916
$69$	−5.36053	−0.645332
$70$	1.05948	0.126632
$71$	−2.24886	−0.266891	−0.133445	−	0.991056i	$-0.542604\pi$
$71$	−2.24886	−0.266891	−0.133445	+	0.991056i	$0.542604\pi$
$72$	3.02763	0.356809
$73$	−4.06305	−0.475544	−0.237772	−	0.971321i	$-0.576417\pi$
$73$	−4.06305	−0.475544	−0.237772	+	0.971321i	$0.576417\pi$
$74$	11.4458	1.33054
$75$	1.00000	0.115470
$76$	0.179115	0.0205459
$77$	−1.94117	−0.221217
$78$	−3.01925	−0.341863
$79$	1.83211	0.206129	0.103064	−	0.994675i	$-0.467135\pi$
$79$	1.83211	0.206129	0.103064	+	0.994675i	$0.467135\pi$
$80$	−3.10869	−0.347562
$81$	1.00000	0.111111
$82$	12.4899	1.37928
$83$	−1.07725	−0.118243	−0.0591216	−	0.998251i	$-0.518830\pi$
$83$	−1.07725	−0.118243	−0.0591216	+	0.998251i	$0.518830\pi$
$84$	0.311904	0.0340315
$85$	3.82186	0.414538
$86$	3.38226	0.364718
$87$	−7.00290	−0.750790
$88$	7.07076	0.753746
$89$	−0.209689	−0.0222270	−0.0111135	−	0.999938i	$-0.503538\pi$
$89$	−0.209689	−0.0222270	−0.0111135	+	0.999938i	$0.503538\pi$
$90$	−1.27466	−0.134361
$91$	−1.96882	−0.206389
$92$	2.01154	0.209717
$93$	−2.73114	−0.283206
$94$	9.73805	1.00440
$95$	−0.477321	−0.0489721
$96$	−2.09275	−0.213590
$97$	−16.0934	−1.63404	−0.817020	−	0.576609i	$-0.804375\pi$
$97$	−16.0934	−1.63404	−0.817020	+	0.576609i	$0.804375\pi$
$98$	8.04197	0.812361
$99$	2.33541	0.234718
$100$	−0.375250	−0.0375250
$101$	14.8982	1.48243	0.741213	−	0.671270i	$-0.234251\pi$
$101$	14.8982	1.48243	0.741213	+	0.671270i	$0.234251\pi$
$102$	−4.87155	−0.482356
$103$	16.5721	1.63290	0.816450	−	0.577416i	$-0.195939\pi$
$103$	16.5721	1.63290	0.816450	+	0.577416i	$0.195939\pi$
$104$	7.17147	0.703221
$105$	−0.831191	−0.0811159
$106$	9.84628	0.956356
$107$	−14.1295	−1.36595	−0.682974	−	0.730443i	$-0.739314\pi$
$107$	−14.1295	−1.36595	−0.682974	+	0.730443i	$0.739314\pi$
$108$	−0.375250	−0.0361084
$109$	−3.07165	−0.294211	−0.147105	−	0.989121i	$-0.546996\pi$
$109$	−3.07165	−0.294211	−0.147105	+	0.989121i	$0.546996\pi$
$110$	−2.97685	−0.283831
$111$	−8.97949	−0.852296
$112$	2.58391	0.244157
$113$	9.15183	0.860932	0.430466	−	0.902607i	$-0.358349\pi$
$113$	9.15183	0.860932	0.430466	+	0.902607i	$0.358349\pi$
$114$	0.608421	0.0569838
$115$	−5.36053	−0.499872
$116$	2.62784	0.243989
$117$	2.36868	0.218984
$118$	0.771773	0.0710475
$119$	−3.17669	−0.291207
$120$	3.02763	0.276383
$121$	−5.54585	−0.504168
$122$	−10.9808	−0.994151
$123$	−9.79865	−0.883515
$124$	1.02486	0.0920349
$125$	1.00000	0.0894427
$126$	1.05948	0.0943862
$127$	−4.11508	−0.365154	−0.182577	−	0.983192i	$-0.558444\pi$
$127$	−4.11508	−0.365154	−0.182577	+	0.983192i	$0.558444\pi$
$128$	−7.13972	−0.631068
$129$	−2.65346	−0.233624
$130$	−3.01925	−0.264806
$131$	−8.79645	−0.768549	−0.384275	−	0.923219i	$-0.625548\pi$
$131$	−8.79645	−0.768549	−0.384275	+	0.923219i	$0.625548\pi$
$132$	−0.876362	−0.0762776
$133$	0.396745	0.0344021
$134$	−2.25005	−0.194375
$135$	1.00000	0.0860663
$136$	11.5712	0.992219
$137$	20.5536	1.75601	0.878007	−	0.478647i	$-0.158873\pi$
$137$	20.5536	1.75601	0.878007	+	0.478647i	$0.158873\pi$
$138$	6.83284	0.581650
$139$	5.33677	0.452659	0.226329	−	0.974051i	$-0.427327\pi$
$139$	5.33677	0.452659	0.226329	+	0.974051i	$0.427327\pi$
$140$	0.311904	0.0263607
$141$	−7.63974	−0.643382
$142$	2.86653	0.240554
$143$	5.53183	0.462595
$144$	−3.10869	−0.259057
$145$	−7.00290	−0.581560
$146$	5.17899	0.428616
$147$	−6.30912	−0.520368
$148$	3.36955	0.276975
$149$	14.4238	1.18165	0.590823	−	0.806801i	$-0.298803\pi$
$149$	14.4238	1.18165	0.590823	+	0.806801i	$0.298803\pi$
$150$	−1.27466	−0.104075
$151$	−15.4378	−1.25631	−0.628156	−	0.778087i	$-0.716190\pi$
$151$	−15.4378	−1.25631	−0.628156	+	0.778087i	$0.716190\pi$
$152$	−1.44515	−0.117217
$153$	3.82186	0.308979
$154$	2.47433	0.199387
$155$	−2.73114	−0.219370
$156$	−0.888845	−0.0711645
$157$	−7.64026	−0.609759	−0.304879	−	0.952391i	$-0.598616\pi$
$157$	−7.64026	−0.609759	−0.304879	+	0.952391i	$0.598616\pi$
$158$	−2.33532	−0.185788
$159$	−7.72465	−0.612605
$160$	−2.09275	−0.165446
$161$	4.45563	0.351152
$162$	−1.27466	−0.100147
$163$	8.79464	0.688849	0.344425	−	0.938814i	$-0.388074\pi$
$163$	8.79464	0.688849	0.344425	+	0.938814i	$0.388074\pi$
$164$	3.67694	0.287121
$165$	2.33541	0.181812
$166$	1.37312	0.106575
$167$	10.7320	0.830467	0.415234	−	0.909715i	$-0.363700\pi$
$167$	10.7320	0.830467	0.415234	+	0.909715i	$0.363700\pi$
$168$	−2.51654	−0.194155
$169$	−7.38937	−0.568413
$170$	−4.87155	−0.373631
$171$	−0.477321	−0.0365017
$172$	0.995711	0.0759223
$173$	1.65545	0.125862	0.0629308	−	0.998018i	$-0.479955\pi$
$173$	1.65545	0.125862	0.0629308	+	0.998018i	$0.479955\pi$
$174$	8.92630	0.676701
$175$	−0.831191	−0.0628321
$176$	−7.26007	−0.547248
$177$	−0.605475	−0.0455103
$178$	0.267281	0.0200336
$179$	−21.5180	−1.60833	−0.804164	−	0.594407i	$-0.797387\pi$
$179$	−21.5180	−1.60833	−0.804164	+	0.594407i	$0.797387\pi$
$180$	−0.375250	−0.0279695
$181$	−15.1110	−1.12319	−0.561595	−	0.827413i	$-0.689812\pi$
$181$	−15.1110	−1.12319	−0.561595	+	0.827413i	$0.689812\pi$
$182$	2.50957	0.186022
$183$	8.61468	0.636815
$184$	−16.2297	−1.19647
$185$	−8.97949	−0.660186
$186$	3.48126	0.255258
$187$	8.92561	0.652705
$188$	2.86681	0.209084
$189$	−0.831191	−0.0604602
$190$	0.608421	0.0441395
$191$	4.42090	0.319885	0.159942	−	0.987126i	$-0.448869\pi$
$191$	4.42090	0.319885	0.159942	+	0.987126i	$0.448869\pi$
$192$	8.88491	0.641213
$193$	8.05328	0.579688	0.289844	−	0.957074i	$-0.406397\pi$
$193$	8.05328	0.579688	0.289844	+	0.957074i	$0.406397\pi$
$194$	20.5136	1.47279
$195$	2.36868	0.169624
$196$	2.36750	0.169107
$197$	−17.1041	−1.21862	−0.609308	−	0.792934i	$-0.708553\pi$
$197$	−17.1041	−1.21862	−0.609308	+	0.792934i	$0.708553\pi$
$198$	−2.97685	−0.211555
$199$	−25.4831	−1.80645	−0.903226	−	0.429166i	$-0.858808\pi$
$199$	−25.4831	−1.80645	−0.903226	+	0.429166i	$0.858808\pi$
$200$	3.02763	0.214086
$201$	1.76522	0.124509
$202$	−18.9901	−1.33614
$203$	5.82075	0.408536
$204$	−1.43415	−0.100411
$205$	−9.79865	−0.684368
$206$	−21.1238	−1.47176
$207$	−5.36053	−0.372583
$208$	−7.36348	−0.510565
$209$	−1.11474	−0.0771083
$210$	1.05948	0.0731113
$211$	3.74908	0.258097	0.129049	−	0.991638i	$-0.458808\pi$
$211$	3.74908	0.258097	0.129049	+	0.991638i	$0.458808\pi$
$212$	2.89867	0.199082
$213$	−2.24886	−0.154090
$214$	18.0102	1.23115
$215$	−2.65346	−0.180965
$216$	3.02763	0.206004
$217$	2.27009	0.154104
$218$	3.91530	0.265178
$219$	−4.06305	−0.274555
$220$	−0.876362	−0.0590843
$221$	9.05274	0.608953
$222$	11.4458	0.768190
$223$	1.34596	0.0901320	0.0450660	−	0.998984i	$-0.485650\pi$
$223$	1.34596	0.0901320	0.0450660	+	0.998984i	$0.485650\pi$
$224$	1.73947	0.116223
$225$	1.00000	0.0666667
$226$	−11.6654	−0.775974
$227$	−3.09381	−0.205343	−0.102672	−	0.994715i	$-0.532739\pi$
$227$	−3.09381	−0.205343	−0.102672	+	0.994715i	$0.532739\pi$
$228$	0.179115	0.0118622
$229$	23.6433	1.56239	0.781196	−	0.624285i	$-0.214610\pi$
$229$	23.6433	1.56239	0.781196	+	0.624285i	$0.214610\pi$
$230$	6.83284	0.450544
$231$	−1.94117	−0.127720
$232$	−21.2022	−1.39199
$233$	10.3028	0.674957	0.337479	−	0.941333i	$-0.390426\pi$
$233$	10.3028	0.674957	0.337479	+	0.941333i	$0.390426\pi$
$234$	−3.01925	−0.197375
$235$	−7.63974	−0.498362
$236$	0.227204	0.0147897
$237$	1.83211	0.119009
$238$	4.04919	0.262470
$239$	17.0498	1.10286	0.551428	−	0.834222i	$-0.314083\pi$
$239$	17.0498	1.10286	0.551428	+	0.834222i	$0.314083\pi$
$240$	−3.10869	−0.200665
$241$	−21.2811	−1.37084	−0.685418	−	0.728150i	$-0.740381\pi$
$241$	−21.2811	−1.37084	−0.685418	+	0.728150i	$0.740381\pi$
$242$	7.06906	0.454416
$243$	1.00000	0.0641500
$244$	−3.23265	−0.206950
$245$	−6.30912	−0.403075
$246$	12.4899	0.796328
$247$	−1.13062	−0.0719396
$248$	−8.26886	−0.525073
$249$	−1.07725	−0.0682677
$250$	−1.27466	−0.0806164
$251$	4.15482	0.262250	0.131125	−	0.991366i	$-0.458141\pi$
$251$	4.15482	0.262250	0.131125	+	0.991366i	$0.458141\pi$
$252$	0.311904	0.0196481
$253$	−12.5191	−0.787066
$254$	5.24531	0.329120
$255$	3.82186	0.239334
$256$	−8.66912	−0.541820
$257$	−20.2915	−1.26575	−0.632876	−	0.774253i	$-0.718126\pi$
$257$	−20.2915	−1.26575	−0.632876	+	0.774253i	$0.718126\pi$
$258$	3.38226	0.210570
$259$	7.46367	0.463770
$260$	−0.888845	−0.0551238
$261$	−7.00290	−0.433469
$262$	11.2125	0.692708
$263$	−1.43224	−0.0883158	−0.0441579	−	0.999025i	$-0.514060\pi$
$263$	−1.43224	−0.0883158	−0.0441579	+	0.999025i	$0.514060\pi$
$264$	7.07076	0.435175
$265$	−7.72465	−0.474522
$266$	−0.505714	−0.0310073
$267$	−0.209689	−0.0128327
$268$	−0.662398	−0.0404624
$269$	−5.45845	−0.332808	−0.166404	−	0.986058i	$-0.553216\pi$
$269$	−5.45845	−0.332808	−0.166404	+	0.986058i	$0.553216\pi$
$270$	−1.27466	−0.0775732
$271$	23.4853	1.42663	0.713314	−	0.700844i	$-0.247193\pi$
$271$	23.4853	1.42663	0.713314	+	0.700844i	$0.247193\pi$
$272$	−11.8810	−0.720389
$273$	−1.96882	−0.119158
$274$	−26.1988	−1.58273
$275$	2.33541	0.140831
$276$	2.01154	0.121080
$277$	−6.19464	−0.372200	−0.186100	−	0.982531i	$-0.559585\pi$
$277$	−6.19464	−0.372200	−0.186100	+	0.982531i	$0.559585\pi$
$278$	−6.80255	−0.407990
$279$	−2.73114	−0.163509
$280$	−2.51654	−0.150392
$281$	−18.6504	−1.11259	−0.556296	−	0.830984i	$-0.687778\pi$
$281$	−18.6504	−1.11259	−0.556296	+	0.830984i	$0.687778\pi$
$282$	9.73805	0.579893
$283$	−18.8692	−1.12166	−0.560830	−	0.827931i	$-0.689518\pi$
$283$	−18.8692	−1.12166	−0.560830	+	0.827931i	$0.689518\pi$
$284$	0.843885	0.0500754
$285$	−0.477321	−0.0282741
$286$	−7.05119	−0.416946
$287$	8.14455	0.480757
$288$	−2.09275	−0.123316
$289$	−2.39342	−0.140789
$290$	8.92630	0.524170
$291$	−16.0934	−0.943413
$292$	1.52466	0.0892238
$293$	8.04845	0.470196	0.235098	−	0.971972i	$-0.424459\pi$
$293$	8.04845	0.470196	0.235098	+	0.971972i	$0.424459\pi$
$294$	8.04197	0.469017
$295$	−0.605475	−0.0352521
$296$	−27.1866	−1.58019
$297$	2.33541	0.135514
$298$	−18.3854	−1.06504
$299$	−12.6974	−0.734308
$300$	−0.375250	−0.0216650
$301$	2.20553	0.127125
$302$	19.6779	1.13234
$303$	14.8982	0.855879
$304$	1.48384	0.0851042
$305$	8.61468	0.493275
$306$	−4.87155	−0.278488
$307$	−13.7490	−0.784695	−0.392348	−	0.919817i	$-0.628337\pi$
$307$	−13.7490	−0.784695	−0.392348	+	0.919817i	$0.628337\pi$
$308$	0.728424	0.0415058
$309$	16.5721	0.942755
$310$	3.48126	0.197722
$311$	13.5367	0.767596	0.383798	−	0.923417i	$-0.374616\pi$
$311$	13.5367	0.767596	0.383798	+	0.923417i	$0.374616\pi$
$312$	7.17147	0.406005
$313$	−8.62817	−0.487693	−0.243847	−	0.969814i	$-0.578409\pi$
$313$	−8.62817	−0.487693	−0.243847	+	0.969814i	$0.578409\pi$
$314$	9.73871	0.549587
$315$	−0.831191	−0.0468323
$316$	−0.687500	−0.0386749
$317$	−26.8916	−1.51038	−0.755192	−	0.655503i	$-0.772457\pi$
$317$	−26.8916	−1.51038	−0.755192	+	0.655503i	$0.772457\pi$
$318$	9.84628	0.552152
$319$	−16.3547	−0.915686
$320$	8.88491	0.496682
$321$	−14.1295	−0.788630
$322$	−5.67939	−0.316500
$323$	−1.82425	−0.101504
$324$	−0.375250	−0.0208472
$325$	2.36868	0.131391
$326$	−11.2101	−0.620872
$327$	−3.07165	−0.169863
$328$	−29.6667	−1.63807
$329$	6.35008	0.350091
$330$	−2.97685	−0.163870
$331$	14.6783	0.806792	0.403396	−	0.915026i	$-0.367830\pi$
$331$	14.6783	0.806792	0.403396	+	0.915026i	$0.367830\pi$
$332$	0.404236	0.0221854
$333$	−8.97949	−0.492073
$334$	−13.6796	−0.748515
$335$	1.76522	0.0964442
$336$	2.58391	0.140964
$337$	16.0393	0.873717	0.436859	−	0.899530i	$-0.356091\pi$
$337$	16.0393	0.873717	0.436859	+	0.899530i	$0.356091\pi$
$338$	9.41892	0.512322
$339$	9.15183	0.497059
$340$	−1.43415	−0.0777777
$341$	−6.37833	−0.345406
$342$	0.608421	0.0328996
$343$	11.0624	0.597314
$344$	−8.03370	−0.433148
$345$	−5.36053	−0.288601
$346$	−2.11013	−0.113441
$347$	10.8678	0.583414	0.291707	−	0.956508i	$-0.405777\pi$
$347$	10.8678	0.583414	0.291707	+	0.956508i	$0.405777\pi$
$348$	2.62784	0.140867
$349$	5.09754	0.272865	0.136432	−	0.990649i	$-0.456436\pi$
$349$	5.09754	0.272865	0.136432	+	0.990649i	$0.456436\pi$
$350$	1.05948	0.0566317
$351$	2.36868	0.126431
$352$	−4.88742	−0.260501
$353$	0.743902	0.0395939	0.0197970	−	0.999804i	$-0.493698\pi$
$353$	0.743902	0.0395939	0.0197970	+	0.999804i	$0.493698\pi$
$354$	0.771773	0.0410193
$355$	−2.24886	−0.119357
$356$	0.0786856	0.00417033
$357$	−3.17669	−0.168128
$358$	27.4280	1.44962
$359$	29.2959	1.54618	0.773090	−	0.634297i	$-0.218710\pi$
$359$	29.2959	1.54618	0.773090	+	0.634297i	$0.218710\pi$
$360$	3.02763	0.159570
$361$	−18.7722	−0.988009
$362$	19.2613	1.01235
$363$	−5.54585	−0.291082
$364$	0.738799	0.0387236
$365$	−4.06305	−0.212670
$366$	−10.9808	−0.573974
$367$	−27.4439	−1.43256	−0.716279	−	0.697814i	$-0.754156\pi$
$367$	−27.4439	−1.43256	−0.716279	+	0.697814i	$0.754156\pi$
$368$	16.6642	0.868683
$369$	−9.79865	−0.510097
$370$	11.4458	0.595038
$371$	6.42066	0.333344
$372$	1.02486	0.0531364
$373$	26.9841	1.39718	0.698591	−	0.715522i	$-0.253811\pi$
$373$	26.9841	1.39718	0.698591	+	0.715522i	$0.253811\pi$
$374$	−11.3771	−0.588295
$375$	1.00000	0.0516398
$376$	−23.1303	−1.19285
$377$	−16.5876	−0.854306
$378$	1.05948	0.0544939
$379$	8.17253	0.419795	0.209897	−	0.977723i	$-0.432687\pi$
$379$	8.17253	0.419795	0.209897	+	0.977723i	$0.432687\pi$
$380$	0.179115	0.00918839
$381$	−4.11508	−0.210822
$382$	−5.63513	−0.288318
$383$	30.7677	1.57216	0.786078	−	0.618127i	$-0.212108\pi$
$383$	30.7677	1.57216	0.786078	+	0.618127i	$0.212108\pi$
$384$	−7.13972	−0.364347
$385$	−1.94117	−0.0989313
$386$	−10.2652	−0.522484
$387$	−2.65346	−0.134883
$388$	6.03905	0.306586
$389$	24.8162	1.25823	0.629116	−	0.777311i	$-0.283417\pi$
$389$	24.8162	1.25823	0.629116	+	0.777311i	$0.283417\pi$
$390$	−3.01925	−0.152886
$391$	−20.4872	−1.03608
$392$	−19.1017	−0.964780
$393$	−8.79645	−0.443722
$394$	21.8019	1.09836
$395$	1.83211	0.0921836
$396$	−0.876362	−0.0440389
$397$	9.34708	0.469117	0.234558	−	0.972102i	$-0.424636\pi$
$397$	9.34708	0.469117	0.234558	+	0.972102i	$0.424636\pi$
$398$	32.4823	1.62819
$399$	0.396745	0.0198621
$400$	−3.10869	−0.155434
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−2.25005	−0.112222
$403$	−6.46918	−0.322253
$404$	−5.59054	−0.278140
$405$	1.00000	0.0496904
$406$	−7.41946	−0.368222
$407$	−20.9708	−1.03948
$408$	11.5712	0.572858
$409$	9.48179	0.468845	0.234422	−	0.972135i	$-0.424680\pi$
$409$	9.48179	0.468845	0.234422	+	0.972135i	$0.424680\pi$
$410$	12.4899	0.616833
$411$	20.5536	1.01384
$412$	−6.21868	−0.306373
$413$	0.503265	0.0247641
$414$	6.83284	0.335816
$415$	−1.07725	−0.0528800
$416$	−4.95704	−0.243039
$417$	5.33677	0.261343
$418$	1.42091	0.0694991
$419$	1.21129	0.0591756	0.0295878	−	0.999562i	$-0.490581\pi$
$419$	1.21129	0.0591756	0.0295878	+	0.999562i	$0.490581\pi$
$420$	0.311904	0.0152194
$421$	−33.9270	−1.65350	−0.826750	−	0.562569i	$-0.809813\pi$
$421$	−33.9270	−1.65350	−0.826750	+	0.562569i	$0.809813\pi$
$422$	−4.77879	−0.232628
$423$	−7.63974	−0.371457
$424$	−23.3874	−1.13579
$425$	3.82186	0.185387
$426$	2.86653	0.138884
$427$	−7.16044	−0.346518
$428$	5.30208	0.256286
$429$	5.53183	0.267080
$430$	3.38226	0.163107
$431$	23.1663	1.11588	0.557942	−	0.829880i	$-0.311591\pi$
$431$	23.1663	1.11588	0.557942	+	0.829880i	$0.311591\pi$
$432$	−3.10869	−0.149567
$433$	−26.2270	−1.26039	−0.630195	−	0.776437i	$-0.717025\pi$
$433$	−26.2270	−1.26039	−0.630195	+	0.776437i	$0.717025\pi$
$434$	−2.89359	−0.138897
$435$	−7.00290	−0.335764
$436$	1.15264	0.0552013
$437$	2.55870	0.122399
$438$	5.17899	0.247462
$439$	6.88845	0.328768	0.164384	−	0.986396i	$-0.447436\pi$
$439$	6.88845	0.328768	0.164384	+	0.986396i	$0.447436\pi$
$440$	7.07076	0.337085
$441$	−6.30912	−0.300434
$442$	−11.5391	−0.548861
$443$	40.5624	1.92718	0.963590	−	0.267386i	$-0.0861599\pi$
$443$	40.5624	1.92718	0.963590	+	0.267386i	$0.0861599\pi$
$444$	3.36955	0.159912
$445$	−0.209689	−0.00994020
$446$	−1.71563	−0.0812376
$447$	14.4238	0.682224
$448$	−7.38505	−0.348911
$449$	−32.0045	−1.51039	−0.755194	−	0.655502i	$-0.772457\pi$
$449$	−32.0045	−1.51039	−0.755194	+	0.655502i	$0.772457\pi$
$450$	−1.27466	−0.0600879
$451$	−22.8839	−1.07756
$452$	−3.43422	−0.161532
$453$	−15.4378	−0.725332
$454$	3.94355	0.185080
$455$	−1.96882	−0.0922998
$456$	−1.44515	−0.0676754
$457$	−8.72885	−0.408318	−0.204159	−	0.978938i	$-0.565446\pi$
$457$	−8.72885	−0.408318	−0.204159	+	0.978938i	$0.565446\pi$
$458$	−30.1371	−1.40821
$459$	3.82186	0.178389
$460$	2.01154	0.0937884
$461$	−33.8123	−1.57480	−0.787398	−	0.616445i	$-0.788572\pi$
$461$	−33.8123	−1.57480	−0.787398	+	0.616445i	$0.788572\pi$
$462$	2.47433	0.115116
$463$	19.3570	0.899596	0.449798	−	0.893130i	$-0.351496\pi$
$463$	19.3570	0.899596	0.449798	+	0.893130i	$0.351496\pi$
$464$	21.7698	1.01064
$465$	−2.73114	−0.126653
$466$	−13.1325	−0.608352
$467$	2.64735	0.122505	0.0612523	−	0.998122i	$-0.480491\pi$
$467$	2.64735	0.122505	0.0612523	+	0.998122i	$0.480491\pi$
$468$	−0.888845	−0.0410869
$469$	−1.46723	−0.0677505
$470$	9.73805	0.449183
$471$	−7.64026	−0.352044
$472$	−1.83315	−0.0843777
$473$	−6.19693	−0.284935
$474$	−2.33532	−0.107265
$475$	−0.477321	−0.0219010
$476$	1.19205	0.0546376
$477$	−7.72465	−0.353688
$478$	−21.7326	−0.994025
$479$	16.0000	0.731061	0.365530	−	0.930799i	$-0.380888\pi$
$479$	16.0000	0.731061	0.365530	+	0.930799i	$0.380888\pi$
$480$	−2.09275	−0.0955203
$481$	−21.2695	−0.969806
$482$	27.1261	1.23556
$483$	4.45563	0.202738
$484$	2.08108	0.0945945
$485$	−16.0934	−0.730765
$486$	−1.27466	−0.0578196
$487$	−4.93910	−0.223812	−0.111906	−	0.993719i	$-0.535696\pi$
$487$	−4.93910	−0.223812	−0.111906	+	0.993719i	$0.535696\pi$
$488$	26.0820	1.18068
$489$	8.79464	0.397707
$490$	8.04197	0.363299
$491$	−14.4699	−0.653016	−0.326508	−	0.945194i	$-0.605872\pi$
$491$	−14.4699	−0.653016	−0.326508	+	0.945194i	$0.605872\pi$
$492$	3.67694	0.165769
$493$	−26.7641	−1.20539
$494$	1.44115	0.0648405
$495$	2.33541	0.104969
$496$	8.49025	0.381223
$497$	1.86923	0.0838466
$498$	1.37312	0.0615310
$499$	−33.7041	−1.50880	−0.754402	−	0.656412i	$-0.772073\pi$
$499$	−33.7041	−1.50880	−0.754402	+	0.656412i	$0.772073\pi$
$500$	−0.375250	−0.0167817
$501$	10.7320	0.479470
$502$	−5.29597	−0.236371
$503$	34.8165	1.55239	0.776195	−	0.630492i	$-0.217147\pi$
$503$	34.8165	1.55239	0.776195	+	0.630492i	$0.217147\pi$
$504$	−2.51654	−0.112095
$505$	14.8982	0.662961
$506$	15.9575	0.709397
$507$	−7.38937	−0.328174
$508$	1.54418	0.0685120
$509$	15.0300	0.666194	0.333097	−	0.942892i	$-0.391906\pi$
$509$	15.0300	0.666194	0.333097	+	0.942892i	$0.391906\pi$
$510$	−4.87155	−0.215716
$511$	3.37717	0.149397
$512$	25.3296	1.11942
$513$	−0.477321	−0.0210742
$514$	25.8647	1.14085
$515$	16.5721	0.730255
$516$	0.995711	0.0438337
$517$	−17.8419	−0.784688
$518$	−9.51362	−0.418005
$519$	1.65545	0.0726663
$520$	7.17147	0.314490
$521$	13.6992	0.600174	0.300087	−	0.953912i	$-0.402984\pi$
$521$	13.6992	0.600174	0.300087	+	0.953912i	$0.402984\pi$
$522$	8.92630	0.390694
$523$	4.49662	0.196623	0.0983117	−	0.995156i	$-0.468656\pi$
$523$	4.49662	0.196623	0.0983117	+	0.995156i	$0.468656\pi$
$524$	3.30086	0.144199
$525$	−0.831191	−0.0362761
$526$	1.82562	0.0796007
$527$	−10.4380	−0.454687
$528$	−7.26007	−0.315954
$529$	5.73532	0.249362
$530$	9.84628	0.427695
$531$	−0.605475	−0.0262754
$532$	−0.148878	−0.00645470
$533$	−23.2098	−1.00533
$534$	0.267281	0.0115664
$535$	−14.1295	−0.610871
$536$	5.34443	0.230844
$537$	−21.5180	−0.928569
$538$	6.95765	0.299966
$539$	−14.7344	−0.634656
$540$	−0.375250	−0.0161482
$541$	27.2518	1.17165	0.585823	−	0.810439i	$-0.300771\pi$
$541$	27.2518	1.17165	0.585823	+	0.810439i	$0.300771\pi$
$542$	−29.9357	−1.28585
$543$	−15.1110	−0.648474
$544$	−7.99817	−0.342919
$545$	−3.07165	−0.131575
$546$	2.50957	0.107400
$547$	−5.09423	−0.217814	−0.108907	−	0.994052i	$-0.534735\pi$
$547$	−5.09423	−0.217814	−0.108907	+	0.994052i	$0.534735\pi$
$548$	−7.71274	−0.329472
$549$	8.61468	0.367666
$550$	−2.97685	−0.126933
$551$	3.34263	0.142401
$552$	−16.2297	−0.690782
$553$	−1.52284	−0.0647576
$554$	7.89604	0.335471
$555$	−8.97949	−0.381158
$556$	−2.00262	−0.0849300
$557$	15.8991	0.673669	0.336834	−	0.941564i	$-0.390644\pi$
$557$	15.8991	0.673669	0.336834	+	0.941564i	$0.390644\pi$
$558$	3.48126	0.147374
$559$	−6.28520	−0.265835
$560$	2.58391	0.109190
$561$	8.92561	0.376839
$562$	23.7729	1.00280
$563$	3.51403	0.148099	0.0740493	−	0.997255i	$-0.476408\pi$
$563$	3.51403	0.148099	0.0740493	+	0.997255i	$0.476408\pi$
$564$	2.86681	0.120715
$565$	9.15183	0.385020
$566$	24.0518	1.01097
$567$	−0.831191	−0.0349067
$568$	−6.80872	−0.285688
$569$	−32.4195	−1.35910	−0.679548	−	0.733631i	$-0.737824\pi$
$569$	−32.4195	−1.35910	−0.679548	+	0.733631i	$0.737824\pi$
$570$	0.608421	0.0254839
$571$	−40.5592	−1.69735	−0.848675	−	0.528914i	$-0.822599\pi$
$571$	−40.5592	−1.69735	−0.848675	+	0.528914i	$0.822599\pi$
$572$	−2.07582	−0.0867943
$573$	4.42090	0.184686
$574$	−10.3815	−0.433316
$575$	−5.36053	−0.223550
$576$	8.88491	0.370205
$577$	21.2912	0.886363	0.443182	−	0.896432i	$-0.353850\pi$
$577$	21.2912	0.886363	0.443182	+	0.896432i	$0.353850\pi$
$578$	3.05079	0.126896
$579$	8.05328	0.334683
$580$	2.62784	0.109115
$581$	0.895397	0.0371473
$582$	20.5136	0.850316
$583$	−18.0403	−0.747151
$584$	−12.3014	−0.509035
$585$	2.36868	0.0979327
$586$	−10.2590	−0.423796
$587$	24.1206	0.995564	0.497782	−	0.867302i	$-0.334148\pi$
$587$	24.1206	0.995564	0.497782	+	0.867302i	$0.334148\pi$
$588$	2.36750	0.0976339
$589$	1.30363	0.0537151
$590$	0.771773	0.0317734
$591$	−17.1041	−0.703568
$592$	27.9145	1.14728
$593$	22.0541	0.905655	0.452827	−	0.891598i	$-0.350415\pi$
$593$	22.0541	0.905655	0.452827	+	0.891598i	$0.350415\pi$
$594$	−2.97685	−0.122142
$595$	−3.17669	−0.130232
$596$	−5.41254	−0.221706
$597$	−25.4831	−1.04296
$598$	16.1848	0.661845
$599$	−18.2088	−0.743993	−0.371996	−	0.928234i	$-0.621327\pi$
$599$	−18.2088	−0.743993	−0.371996	+	0.928234i	$0.621327\pi$
$600$	3.02763	0.123602
$601$	15.9810	0.651880	0.325940	−	0.945390i	$-0.394319\pi$
$601$	15.9810	0.651880	0.325940	+	0.945390i	$0.394319\pi$
$602$	−2.81130	−0.114580
$603$	1.76522	0.0718853
$604$	5.79304	0.235715
$605$	−5.54585	−0.225471
$606$	−18.9901	−0.771419
$607$	18.8135	0.763615	0.381807	−	0.924242i	$-0.375302\pi$
$607$	18.8135	0.763615	0.381807	+	0.924242i	$0.375302\pi$
$608$	0.998912	0.0405112
$609$	5.82075	0.235869
$610$	−10.9808	−0.444598
$611$	−18.0961	−0.732089
$612$	−1.43415	−0.0579721
$613$	−14.5901	−0.589289	−0.294645	−	0.955607i	$-0.595201\pi$
$613$	−14.5901	−0.589289	−0.294645	+	0.955607i	$0.595201\pi$
$614$	17.5252	0.707260
$615$	−9.79865	−0.395120
$616$	−5.87715	−0.236797
$617$	1.05014	0.0422772	0.0211386	−	0.999777i	$-0.493271\pi$
$617$	1.05014	0.0422772	0.0211386	+	0.999777i	$0.493271\pi$
$618$	−21.1238	−0.849723
$619$	−23.8139	−0.957163	−0.478581	−	0.878043i	$-0.658849\pi$
$619$	−23.8139	−0.957163	−0.478581	+	0.878043i	$0.658849\pi$
$620$	1.02486	0.0411593
$621$	−5.36053	−0.215111
$622$	−17.2547	−0.691849
$623$	0.174291	0.00698283
$624$	−7.36348	−0.294775
$625$	1.00000	0.0400000
$626$	10.9980	0.439567
$627$	−1.11474	−0.0445185
$628$	2.86700	0.114406
$629$	−34.3183	−1.36836
$630$	1.05948	0.0422108
$631$	−7.83455	−0.311888	−0.155944	−	0.987766i	$-0.549842\pi$
$631$	−7.83455	−0.311888	−0.155944	+	0.987766i	$0.549842\pi$
$632$	5.54696	0.220646
$633$	3.74908	0.149012
$634$	34.2776	1.36134
$635$	−4.11508	−0.163302
$636$	2.89867	0.114940
$637$	−14.9443	−0.592113
$638$	20.8466	0.825324
$639$	−2.24886	−0.0889637
$640$	−7.13972	−0.282222
$641$	−2.41302	−0.0953084	−0.0476542	−	0.998864i	$-0.515175\pi$
$641$	−2.41302	−0.0953084	−0.0476542	+	0.998864i	$0.515175\pi$
$642$	18.0102	0.710807
$643$	16.0930	0.634646	0.317323	−	0.948318i	$-0.397216\pi$
$643$	16.0930	0.634646	0.317323	+	0.948318i	$0.397216\pi$
$644$	−1.67197	−0.0658849
$645$	−2.65346	−0.104480
$646$	2.32530	0.0914876
$647$	28.9754	1.13914	0.569570	−	0.821943i	$-0.307110\pi$
$647$	28.9754	1.13914	0.569570	+	0.821943i	$0.307110\pi$
$648$	3.02763	0.118936
$649$	−1.41403	−0.0555057
$650$	−3.01925	−0.118425
$651$	2.27009	0.0889720
$652$	−3.30018	−0.129245
$653$	−0.120487	−0.00471501	−0.00235751	−	0.999997i	$-0.500750\pi$
$653$	−0.120487	−0.00471501	−0.00235751	+	0.999997i	$0.500750\pi$
$654$	3.91530	0.153100
$655$	−8.79645	−0.343706
$656$	30.4610	1.18930
$657$	−4.06305	−0.158515
$658$	−8.09418	−0.315544
$659$	−21.0646	−0.820559	−0.410280	−	0.911960i	$-0.634569\pi$
$659$	−21.0646	−0.820559	−0.410280	+	0.911960i	$0.634569\pi$
$660$	−0.876362	−0.0341124
$661$	15.7270	0.611709	0.305855	−	0.952078i	$-0.401058\pi$
$661$	15.7270	0.611709	0.305855	+	0.952078i	$0.401058\pi$
$662$	−18.7098	−0.727176
$663$	9.05274	0.351579
$664$	−3.26150	−0.126571
$665$	0.396745	0.0153851
$666$	11.4458	0.443515
$667$	37.5393	1.45353
$668$	−4.02718	−0.155816
$669$	1.34596	0.0520377
$670$	−2.25005	−0.0869270
$671$	20.1188	0.776679
$672$	1.73947	0.0671015
$673$	−33.0934	−1.27566	−0.637829	−	0.770178i	$-0.720167\pi$
$673$	−33.0934	−1.27566	−0.637829	+	0.770178i	$0.720167\pi$
$674$	−20.4446	−0.787498
$675$	1.00000	0.0384900
$676$	2.77286	0.106648
$677$	11.2867	0.433783	0.216892	−	0.976196i	$-0.430408\pi$
$677$	11.2867	0.433783	0.216892	+	0.976196i	$0.430408\pi$
$678$	−11.6654	−0.448009
$679$	13.3767	0.513351
$680$	11.5712	0.443734
$681$	−3.09381	−0.118555
$682$	8.13018	0.311321
$683$	−43.8340	−1.67726	−0.838631	−	0.544701i	$-0.816643\pi$
$683$	−43.8340	−1.67726	−0.838631	+	0.544701i	$0.816643\pi$
$684$	0.179115	0.00684862
$685$	20.5536	0.785314
$686$	−14.1008	−0.538371
$687$	23.6433	0.902048
$688$	8.24879	0.314482
$689$	−18.2972	−0.697068
$690$	6.83284	0.260122
$691$	4.57795	0.174153	0.0870766	−	0.996202i	$-0.472248\pi$
$691$	4.57795	0.174153	0.0870766	+	0.996202i	$0.472248\pi$
$692$	−0.621208	−0.0236148
$693$	−1.94117	−0.0737391
$694$	−13.8527	−0.525842
$695$	5.33677	0.202435
$696$	−21.2022	−0.803667
$697$	−37.4490	−1.41848
$698$	−6.49761	−0.245938
$699$	10.3028	0.389687
$700$	0.311904	0.0117889
$701$	40.0017	1.51085	0.755423	−	0.655238i	$-0.227432\pi$
$701$	40.0017	1.51085	0.755423	+	0.655238i	$0.227432\pi$
$702$	−3.01925	−0.113954
$703$	4.28610	0.161653
$704$	20.7499	0.782042
$705$	−7.63974	−0.287729
$706$	−0.948220	−0.0356867
$707$	−12.3832	−0.465720
$708$	0.227204	0.00853886
$709$	−40.4354	−1.51858	−0.759291	−	0.650751i	$-0.774454\pi$
$709$	−40.4354	−1.51858	−0.759291	+	0.650751i	$0.774454\pi$
$710$	2.86653	0.107579
$711$	1.83211	0.0687096
$712$	−0.634860	−0.0237924
$713$	14.6403	0.548285
$714$	4.04919	0.151537
$715$	5.53183	0.206879
$716$	8.07461	0.301762
$717$	17.0498	0.636735
$718$	−37.3423	−1.39360
$719$	−37.4209	−1.39556	−0.697781	−	0.716311i	$-0.745829\pi$
$719$	−37.4209	−1.39556	−0.697781	+	0.716311i	$0.745829\pi$
$720$	−3.10869	−0.115854
$721$	−13.7746	−0.512993
$722$	23.9281	0.890511
$723$	−21.2811	−0.791453
$724$	5.67038	0.210738
$725$	−7.00290	−0.260081
$726$	7.06906	0.262357
$727$	14.1863	0.526139	0.263070	−	0.964777i	$-0.415265\pi$
$727$	14.1863	0.526139	0.263070	+	0.964777i	$0.415265\pi$
$728$	−5.96086	−0.220924
$729$	1.00000	0.0370370
$730$	5.17899	0.191683
$731$	−10.1412	−0.375084
$732$	−3.23265	−0.119482
$733$	−13.2182	−0.488226	−0.244113	−	0.969747i	$-0.578497\pi$
$733$	−13.2182	−0.488226	−0.244113	+	0.969747i	$0.578497\pi$
$734$	34.9815	1.29119
$735$	−6.30912	−0.232715
$736$	11.2182	0.413510
$737$	4.12251	0.151855
$738$	12.4899	0.459760
$739$	−30.9659	−1.13910	−0.569549	−	0.821957i	$-0.692882\pi$
$739$	−30.9659	−1.13910	−0.569549	+	0.821957i	$0.692882\pi$
$740$	3.36955	0.123867
$741$	−1.13062	−0.0415343
$742$	−8.18414	−0.300449
$743$	13.4320	0.492773	0.246386	−	0.969172i	$-0.420757\pi$
$743$	13.4320	0.492773	0.246386	+	0.969172i	$0.420757\pi$
$744$	−8.26886	−0.303151
$745$	14.4238	0.528449
$746$	−34.3954	−1.25931
$747$	−1.07725	−0.0394144
$748$	−3.34933	−0.122464
$749$	11.7443	0.429127
$750$	−1.27466	−0.0465439
$751$	−47.9819	−1.75088	−0.875441	−	0.483324i	$-0.839429\pi$
$751$	−47.9819	−1.75088	−0.875441	+	0.483324i	$0.839429\pi$
$752$	23.7496	0.866058
$753$	4.15482	0.151410
$754$	21.1435	0.770001
$755$	−15.4378	−0.561840
$756$	0.311904	0.0113438
$757$	0.238311	0.00866155	0.00433077	−	0.999991i	$-0.498621\pi$
$757$	0.238311	0.00866155	0.00433077	+	0.999991i	$0.498621\pi$
$758$	−10.4172	−0.378369
$759$	−12.5191	−0.454413
$760$	−1.44515	−0.0524211
$761$	−33.3391	−1.20854	−0.604271	−	0.796779i	$-0.706536\pi$
$761$	−33.3391	−1.20854	−0.604271	+	0.796779i	$0.706536\pi$
$762$	5.24531	0.190018
$763$	2.55313	0.0924295
$764$	−1.65894	−0.0600183
$765$	3.82186	0.138179
$766$	−39.2183	−1.41701
$767$	−1.43417	−0.0517850
$768$	−8.66912	−0.312820
$769$	38.8066	1.39940	0.699701	−	0.714436i	$-0.253317\pi$
$769$	38.8066	1.39940	0.699701	+	0.714436i	$0.253317\pi$
$770$	2.47433	0.0891686
$771$	−20.2915	−0.730782
$772$	−3.02199	−0.108764
$773$	3.21611	0.115675	0.0578376	−	0.998326i	$-0.481579\pi$
$773$	3.21611	0.115675	0.0578376	+	0.998326i	$0.481579\pi$
$774$	3.38226	0.121573
$775$	−2.73114	−0.0981053
$776$	−48.7249	−1.74912
$777$	7.46367	0.267758
$778$	−31.6322	−1.13407
$779$	4.67710	0.167575
$780$	−0.888845	−0.0318257
$781$	−5.25202	−0.187932
$782$	26.1141	0.933839
$783$	−7.00290	−0.250263
$784$	19.6131	0.700468
$785$	−7.64026	−0.272692
$786$	11.2125	0.399935
$787$	−5.40138	−0.192539	−0.0962693	−	0.995355i	$-0.530691\pi$
$787$	−5.40138	−0.192539	−0.0962693	+	0.995355i	$0.530691\pi$
$788$	6.41830	0.228643
$789$	−1.43224	−0.0509892
$790$	−2.33532	−0.0830868
$791$	−7.60691	−0.270471
$792$	7.07076	0.251249
$793$	20.4054	0.724616
$794$	−11.9143	−0.422823
$795$	−7.72465	−0.273965
$796$	9.56254	0.338935
$797$	−8.71992	−0.308876	−0.154438	−	0.988003i	$-0.549357\pi$
$797$	−8.71992	−0.308876	−0.154438	+	0.988003i	$0.549357\pi$
$798$	−0.505714	−0.0179021
$799$	−29.1980	−1.03295
$800$	−2.09275	−0.0739897
$801$	−0.209689	−0.00740899
$802$	1.27466	0.0450097
$803$	−9.48889	−0.334856
$804$	−0.662398	−0.0233610
$805$	4.45563	0.157040
$806$	8.24598	0.290452
$807$	−5.45845	−0.192147
$808$	45.1062	1.58683
$809$	−46.3344	−1.62903	−0.814516	−	0.580142i	$-0.802997\pi$
$809$	−46.3344	−1.62903	−0.814516	+	0.580142i	$0.802997\pi$
$810$	−1.27466	−0.0447869
$811$	−26.6142	−0.934552	−0.467276	−	0.884112i	$-0.654765\pi$
$811$	−26.6142	−0.934552	−0.467276	+	0.884112i	$0.654765\pi$
$812$	−2.18423	−0.0766516
$813$	23.4853	0.823664
$814$	26.7306	0.936907
$815$	8.79464	0.308063
$816$	−11.8810	−0.415917
$817$	1.26655	0.0443111
$818$	−12.0860	−0.422578
$819$	−1.96882	−0.0687962
$820$	3.67694	0.128404
$821$	−2.49330	−0.0870168	−0.0435084	−	0.999053i	$-0.513854\pi$
$821$	−2.49330	−0.0870168	−0.0435084	+	0.999053i	$0.513854\pi$
$822$	−26.1988	−0.913789
$823$	53.4124	1.86184	0.930920	−	0.365222i	$-0.119007\pi$
$823$	53.4124	1.86184	0.930920	+	0.365222i	$0.119007\pi$
$824$	50.1742	1.74790
$825$	2.33541	0.0813086
$826$	−0.641491	−0.0223203
$827$	19.8115	0.688914	0.344457	−	0.938802i	$-0.388063\pi$
$827$	19.8115	0.688914	0.344457	+	0.938802i	$0.388063\pi$
$828$	2.01154	0.0699058
$829$	36.7715	1.27713	0.638563	−	0.769570i	$-0.279529\pi$
$829$	36.7715	1.27713	0.638563	+	0.769570i	$0.279529\pi$
$830$	1.37312	0.0476617
$831$	−6.19464	−0.214890
$832$	21.0455	0.729620
$833$	−24.1126	−0.835450
$834$	−6.80255	−0.235553
$835$	10.7320	0.371396
$836$	0.418306	0.0144674
$837$	−2.73114	−0.0944019
$838$	−1.54399	−0.0533361
$839$	15.1439	0.522825	0.261412	−	0.965227i	$-0.415812\pi$
$839$	15.1439	0.522825	0.261412	+	0.965227i	$0.415812\pi$
$840$	−2.51654	−0.0868288
$841$	20.0407	0.691058
$842$	43.2453	1.49033
$843$	−18.6504	−0.642355
$844$	−1.40684	−0.0484254
$845$	−7.38937	−0.254202
$846$	9.73805	0.334801
$847$	4.60966	0.158390
$848$	24.0135	0.824628
$849$	−18.8692	−0.647590
$850$	−4.87155	−0.167093
$851$	48.1349	1.65004
$852$	0.843885	0.0289110
$853$	17.9045	0.613037	0.306519	−	0.951865i	$-0.400836\pi$
$853$	17.9045	0.613037	0.306519	+	0.951865i	$0.400836\pi$
$854$	9.12710	0.312323
$855$	−0.477321	−0.0163240
$856$	−42.7788	−1.46215
$857$	−25.7915	−0.881021	−0.440510	−	0.897747i	$-0.645203\pi$
$857$	−25.7915	−0.881021	−0.440510	+	0.897747i	$0.645203\pi$
$858$	−7.05119	−0.240724
$859$	14.3549	0.489783	0.244892	−	0.969550i	$-0.421248\pi$
$859$	14.3549	0.489783	0.244892	+	0.969550i	$0.421248\pi$
$860$	0.995711	0.0339535
$861$	8.14455	0.277565
$862$	−29.5291	−1.00577
$863$	−9.31303	−0.317019	−0.158510	−	0.987357i	$-0.550669\pi$
$863$	−9.31303	−0.317019	−0.158510	+	0.987357i	$0.550669\pi$
$864$	−2.09275	−0.0711966
$865$	1.65545	0.0562871
$866$	33.4304	1.13601
$867$	−2.39342	−0.0812848
$868$	−0.851852	−0.0289137
$869$	4.27874	0.145146
$870$	8.92630	0.302630
$871$	4.18123	0.141676
$872$	−9.29982	−0.314932
$873$	−16.0934	−0.544680
$874$	−3.26146	−0.110321
$875$	−0.831191	−0.0280994
$876$	1.52466	0.0515134
$877$	−17.6556	−0.596188	−0.298094	−	0.954537i	$-0.596351\pi$
$877$	−17.6556	−0.596188	−0.298094	+	0.954537i	$0.596351\pi$
$878$	−8.78041	−0.296325
$879$	8.04845	0.271468
$880$	−7.26007	−0.244737
$881$	23.4733	0.790835	0.395417	−	0.918502i	$-0.370600\pi$
$881$	23.4733	0.790835	0.395417	+	0.918502i	$0.370600\pi$
$882$	8.04197	0.270787
$883$	39.8766	1.34195	0.670977	−	0.741478i	$-0.265875\pi$
$883$	39.8766	1.34195	0.670977	+	0.741478i	$0.265875\pi$
$884$	−3.39704	−0.114255
$885$	−0.605475	−0.0203528
$886$	−51.7032	−1.73700
$887$	42.7851	1.43658	0.718292	−	0.695742i	$-0.244924\pi$
$887$	42.7851	1.43658	0.718292	+	0.695742i	$0.244924\pi$
$888$	−27.1866	−0.912322
$889$	3.42042	0.114717
$890$	0.267281	0.00895929
$891$	2.33541	0.0782393
$892$	−0.505070	−0.0169110
$893$	3.64661	0.122029
$894$	−18.3854	−0.614901
$895$	−21.5180	−0.719266
$896$	5.93447	0.198257
$897$	−12.6974	−0.423953
$898$	40.7948	1.36134
$899$	19.1259	0.637884
$900$	−0.375250	−0.0125083
$901$	−29.5225	−0.983537
$902$	29.1691	0.971225
$903$	2.20553	0.0733956
$904$	27.7083	0.921566
$905$	−15.1110	−0.502305
$906$	19.6779	0.653755
$907$	−27.0993	−0.899817	−0.449909	−	0.893075i	$-0.648543\pi$
$907$	−27.0993	−0.899817	−0.449909	+	0.893075i	$0.648543\pi$
$908$	1.16095	0.0385275
$909$	14.8982	0.494142
$910$	2.50957	0.0831915
$911$	−11.4915	−0.380731	−0.190366	−	0.981713i	$-0.560967\pi$
$911$	−11.4915	−0.380731	−0.190366	+	0.981713i	$0.560967\pi$
$912$	1.48384	0.0491350
$913$	−2.51581	−0.0832613
$914$	11.1263	0.368025
$915$	8.61468	0.284792
$916$	−8.87214	−0.293144
$917$	7.31152	0.241448
$918$	−4.87155	−0.160785
$919$	−13.3123	−0.439131	−0.219565	−	0.975598i	$-0.570464\pi$
$919$	−13.3123	−0.439131	−0.219565	+	0.975598i	$0.570464\pi$
$920$	−16.2297	−0.535077
$921$	−13.7490	−0.453044
$922$	43.0991	1.41939
$923$	−5.32683	−0.175335
$924$	0.728424	0.0239634
$925$	−8.97949	−0.295244
$926$	−24.6735	−0.810823
$927$	16.5721	0.544300
$928$	14.6553	0.481084
$929$	−37.3513	−1.22546	−0.612729	−	0.790293i	$-0.709928\pi$
$929$	−37.3513	−1.22546	−0.612729	+	0.790293i	$0.709928\pi$
$930$	3.48126	0.114155
$931$	3.01148	0.0986972
$932$	−3.86611	−0.126639
$933$	13.5367	0.443172
$934$	−3.37446	−0.110416
$935$	8.92561	0.291899
$936$	7.17147	0.234407
$937$	−5.67341	−0.185342	−0.0926711	−	0.995697i	$-0.529541\pi$
$937$	−5.67341	−0.185342	−0.0926711	+	0.995697i	$0.529541\pi$
$938$	1.87022	0.0610648
$939$	−8.62817	−0.281570
$940$	2.86681	0.0935051
$941$	53.5555	1.74586	0.872930	−	0.487845i	$-0.162217\pi$
$941$	53.5555	1.74586	0.872930	+	0.487845i	$0.162217\pi$
$942$	9.73871	0.317304
$943$	52.5260	1.71048
$944$	1.88223	0.0612615
$945$	−0.831191	−0.0270386
$946$	7.89896	0.256817
$947$	26.4374	0.859100	0.429550	−	0.903043i	$-0.358672\pi$
$947$	26.4374	0.859100	0.429550	+	0.903043i	$0.358672\pi$
$948$	−0.687500	−0.0223290
$949$	−9.62404	−0.312410
$950$	0.608421	0.0197398
$951$	−26.8916	−0.872021
$952$	−9.61784	−0.311716
$953$	60.4795	1.95912	0.979562	−	0.201142i	$-0.0644653\pi$
$953$	60.4795	1.95912	0.979562	+	0.201142i	$0.0644653\pi$
$954$	9.84628	0.318785
$955$	4.42090	0.143057
$956$	−6.39791	−0.206923
$957$	−16.3547	−0.528671
$958$	−20.3946	−0.658918
$959$	−17.0840	−0.551671
$960$	8.88491	0.286759
$961$	−23.5409	−0.759384
$962$	27.1113	0.874105
$963$	−14.1295	−0.455316
$964$	7.98573	0.257203
$965$	8.05328	0.259244
$966$	−5.67939	−0.182731
$967$	52.6144	1.69197	0.845983	−	0.533210i	$-0.179014\pi$
$967$	52.6144	1.69197	0.845983	+	0.533210i	$0.179014\pi$
$968$	−16.7908	−0.539676
$969$	−1.82425	−0.0586034
$970$	20.5136	0.658652
$971$	−25.5936	−0.821337	−0.410668	−	0.911785i	$-0.634705\pi$
$971$	−25.5936	−0.821337	−0.410668	+	0.911785i	$0.634705\pi$
$972$	−0.375250	−0.0120361
$973$	−4.43587	−0.142207
$974$	6.29566	0.201726
$975$	2.36868	0.0758583
$976$	−26.7804	−0.857218
$977$	−26.5238	−0.848570	−0.424285	−	0.905529i	$-0.639475\pi$
$977$	−26.5238	−0.848570	−0.424285	+	0.905529i	$0.639475\pi$
$978$	−11.2101	−0.358461
$979$	−0.489710	−0.0156512
$980$	2.36750	0.0756269
$981$	−3.07165	−0.0980703
$982$	18.4441	0.588575
$983$	−45.4752	−1.45043	−0.725216	−	0.688521i	$-0.758260\pi$
$983$	−45.4752	−1.45043	−0.725216	+	0.688521i	$0.758260\pi$
$984$	−29.6667	−0.945739
$985$	−17.1041	−0.544982
$986$	34.1150	1.08644
$987$	6.35008	0.202125
$988$	0.424264	0.0134977
$989$	14.2240	0.452296
$990$	−2.97685	−0.0946105
$991$	−48.8321	−1.55120	−0.775602	−	0.631222i	$-0.782554\pi$
$991$	−48.8321	−1.55120	−0.775602	+	0.631222i	$0.782554\pi$
$992$	5.71557	0.181470
$993$	14.6783	0.465801
$994$	−2.38263	−0.0755725
$995$	−25.4831	−0.807870
$996$	0.404236	0.0128087
$997$	−20.1169	−0.637107	−0.318554	−	0.947905i	$-0.603197\pi$
$997$	−20.1169	−0.637107	−0.318554	+	0.947905i	$0.603197\pi$
$998$	42.9612	1.35991
$999$	−8.97949	−0.284099

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.b.1.7	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.b.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-1.27466 q^{2} +1.00000 q^{3} -0.375250 q^{4} +1.00000 q^{5} -1.27466 q^{6} -0.831191 q^{7} +3.02763 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.27466 q^{2} +1.00000 q^{3} -0.375250 q^{4} +1.00000 q^{5} -1.27466 q^{6} -0.831191 q^{7} +3.02763 q^{8} +1.00000 q^{9} -1.27466 q^{10} +2.33541 q^{11} -0.375250 q^{12} +2.36868 q^{13} +1.05948 q^{14} +1.00000 q^{15} -3.10869 q^{16} +3.82186 q^{17} -1.27466 q^{18} -0.477321 q^{19} -0.375250 q^{20} -0.831191 q^{21} -2.97685 q^{22} -5.36053 q^{23} +3.02763 q^{24} +1.00000 q^{25} -3.01925 q^{26} +1.00000 q^{27} +0.311904 q^{28} -7.00290 q^{29} -1.27466 q^{30} -2.73114 q^{31} -2.09275 q^{32} +2.33541 q^{33} -4.87155 q^{34} -0.831191 q^{35} -0.375250 q^{36} -8.97949 q^{37} +0.608421 q^{38} +2.36868 q^{39} +3.02763 q^{40} -9.79865 q^{41} +1.05948 q^{42} -2.65346 q^{43} -0.876362 q^{44} +1.00000 q^{45} +6.83284 q^{46} -7.63974 q^{47} -3.10869 q^{48} -6.30912 q^{49} -1.27466 q^{50} +3.82186 q^{51} -0.888845 q^{52} -7.72465 q^{53} -1.27466 q^{54} +2.33541 q^{55} -2.51654 q^{56} -0.477321 q^{57} +8.92630 q^{58} -0.605475 q^{59} -0.375250 q^{60} +8.61468 q^{61} +3.48126 q^{62} -0.831191 q^{63} +8.88491 q^{64} +2.36868 q^{65} -2.97685 q^{66} +1.76522 q^{67} -1.43415 q^{68} -5.36053 q^{69} +1.05948 q^{70} -2.24886 q^{71} +3.02763 q^{72} -4.06305 q^{73} +11.4458 q^{74} +1.00000 q^{75} +0.179115 q^{76} -1.94117 q^{77} -3.01925 q^{78} +1.83211 q^{79} -3.10869 q^{80} +1.00000 q^{81} +12.4899 q^{82} -1.07725 q^{83} +0.311904 q^{84} +3.82186 q^{85} +3.38226 q^{86} -7.00290 q^{87} +7.07076 q^{88} -0.209689 q^{89} -1.27466 q^{90} -1.96882 q^{91} +2.01154 q^{92} -2.73114 q^{93} +9.73805 q^{94} -0.477321 q^{95} -2.09275 q^{96} -16.0934 q^{97} +8.04197 q^{98} +2.33541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) \) 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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